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LOGIC 
 
 BERNARD BOSANQV,ET 
 
LOGIC 
 
 OR THE MORPHOLOGY OF ,g 
 KNOWLEDGE [\ [ 
 
 BY 
 
 BERNARD BOSANQUET 
 
 M.A., LL.D., D.C.L.; FELLOW OF THE BRITISH ACADEMY 
 
 IN TWO VOLUMES: VOL. I 
 
 SECOND EDITION 
 
 OXFORD UNIVERSITY PRESS 
 LONDON: HUMPHREY MILFORD 
 
 ■\) 
 
Impression of igjr 
 Second edition, igii 
 
 Printed photographically from sheets of the Second edition 
 
 in Great Britain for the Muston Company 
 
 4 Bell Yard, Temple Bar, W.C. 2 
 
 by Lowe & Brydone, London 
 
PREFACE TO 
 THE FIRST EDITION 
 
 The conception of Logical Science, which has been my guide 
 in the present work, is that of an unprejudiced study of the 
 forms of knowledge in their development, their inter-con- 
 nection, and their comparative value as embodiments of truth. 
 If an attempt founded on such a conception appears to err 
 by over-ambitiousness, I can only plead that an honest effort 
 in the right direction does not depend for its value solely on 
 its intrinsic success. It is at any rate a heavy wager laid by 
 the author on his judgment of the true aim and future of his 
 science, and may attain results as a suggestion which it misses 
 as an achievement. 
 
 In the present centrifugal state of logical research, no under- 
 taking, perhaps, can be entirely valueless which aims at rein- 
 troducing some sort of unity into the enquiry. Such an aim is 
 necessarily involved in the idea of a single connected science of 
 logical processes and products. It has therefore been my object 
 to maintain the central identity of judgment and reasoning 
 throughout, and in no case to permit the variety of applications 
 due to diversity of matter to interrupt the comiedtiion and sub- 
 ordination demanded by unity of principle: Although in 
 periods of transition logical science has been most effectually 
 advanced by detached discussion, in separate chapters, 
 ' books,' or volumes, of Inductive. or experimental method, 
 of equational reasoning, and of the Logic of Chance, yet it 
 seems plain that a time must come when the various cases 
 and species of inference shall fall into their respective places 
 
vd Preface to the First Edition 
 
 as organic members within the intellectual whole. But when 
 this transformation is effected it is necessary that they should 
 lose something of their interesting peculiarity and novelty ; 
 and it is natural, from the difficulty of the task, that they 
 should lose more of these qualities than is necessary. For this 
 reason, as well as from incompetence in the field of exact 
 science, I claim no discoveries in scientific method or in mathe- 
 matical reasoning, but shall be content if my attempts to 
 represent them have not many more errors 'than are either 
 necessary or natural. 
 
 There is in England a healthy objection to system-making, 
 and a preference for free criticism, against which I should be 
 sorry to offend. I think however that systematic form is 
 essential to clear exposition and to really effective criticism, 
 and I have not supposed that my work will be considered as 
 a system in any other sense than that thus implied. In par- 
 ticular, I do not hope or even desire that the specific names 
 which I have invented for some kinds of Judgment and argu- 
 ment should come into general use. I have endeavoured 
 in every case to retain the accepted usage of the generic 
 names, which are all that are recognised in ordinary logical 
 discussion, and have only used strange titles for sub- 
 divisions which have no accepted place in existing logic, and 
 which merely serve to insist upon certain views of logical 
 evolution. 
 
 It is almost superfluous to acknowledge here what I owe to 
 other writers, as the Index bears copious testimony to the 
 amount of my borrowings. In bringing together ' Inductive ' 
 and ' Deductive ' Logic I have followed mOre particularly 
 Sigwart and Jevons ; in the arrangement and analysis of 
 Judgment-forms and forms of Inference I have gone to a great 
 extent in the track of Lotze, and also of Hegel, to whom, so 
 far as I know, the idea of this organic treatment of Logic is 
 primarily due ; and in fundamental theory of judgment as 
 
Preface to the First Edition vii 
 
 in many details I owe even more, probably, than I have 
 acknowledged, to Mr. Bradley, whose work, ' Principles of 
 Logic,' appears to me no less valuable now than it did three 
 years ago.^ On one particular point, relating to the simplest 
 process of equation (colour-equation, for example), I am 
 especially indebted to Mr. Spencer's Psychology. 
 
 Every student will understand that my obligation to former 
 writers is frequently as great when I diverge from them as when 
 I assent to their opinion. As I have often been led to express 
 disagreement with Lotze, portions of whose views certainly 
 appear to me strange in so eminent a philosopher, I ought to 
 say that but for his great work on Logic the larger part of 
 what I have written would never have come into my head. 
 I may also express my strong conviction that the reform of 
 Logic in this country dates from the work of Stuart Mill, whose 
 genius placed him, in spite of all philosophical short-comings, 
 on the right side as against the degenerate representatives of 
 Aristotle. A glance at the Index will suffice to show how 
 constantly I have referred to his treatise. 
 
 I may venture, finally, to discharge an obligation of older 
 standing, and at the same time to emphasise the guiding idea 
 of my work, by observing that the first germ of unprejudiced 
 interest in the forms of knowledge was implanted in my mind, 
 when wholly innocent of Hegel or Lotze, by some remarks 
 made in a course of Logic lectures which I had the good fortune 
 to hear about twenty years ago, the lecturer being Mr. Alfred 
 Robinson, of New College, Oxford. A comparison, which he 
 threw out, between the study and analysis of judgment-forms 
 and the study and analysis of the forms of flowers or plants 
 has never left me since, and I have never seemed to myself able 
 to exhaust its suggestiveness. If I have at all reproduced for 
 others the spectacle of continuity and unity in the intellectual 
 
 ^ See the author's ' Knowledge and Reality, a Criticism of Mr. Brad- 
 ley's " Principles of Logic " '. Kegan Paul, Trench & Co. 1885. 
 
viii Preface to tke First Edition 
 
 life, combined with the most varied and precise adaptation 
 of its fundamentally identical function to manifold conditions 
 and purposes, which this comparison never fails to present to 
 my own mind, I shall so far have succeeded in the object of 
 my work. 
 
 BERNARD BOSANQUET. 
 
 London, April, li 
 
PREFACE TO 
 THE SECOND EDITION 
 
 In preparing the second edition of this work, I have en- 
 deavoured to put myself in the position of a reader of the 
 first edition, aware of recent logical discussions, and interested 
 to know how the book he is reading would respond to them. 
 I have therefore offered explanations which I hoped might be 
 of service to such a reader, by enabling him to judge of the 
 attitude which my theory would naturally assume towards 
 a number of problems which have recently been emphasised. 
 
 I have made few alterations in the text,* but have added 
 a good many footnotes, referred to by letters of the alphabet, 
 while the old ones are as before referred to by numbers. I sub- 
 join at the end of the Preface a list of substantive additions 
 other than footnotes. 
 
 I am gratified by Mr. Keynes's appreciative reference to 
 some of my views, in the fourth edition of his Formal Logic. 
 I note that while favourable on the whole to my treatment 
 of the concept as in close union with the judgment, he remains 
 cold to my interest in the reciprocity of propositions and in 
 the exclusiveness of members under a disjunction. I only 
 mention these points, because they seem to me to be involved 
 in the ideal of complete expression by adequate conditioning 
 of connections, which I take as defining the essential cognitive 
 interest, on which, as the central idea of my work, I especially 
 desire to insist. 
 
 It is, in my view, from the operation of this ideal, that there 
 
 * The addition on i. 57, concerning Mr. Keynes's view of Extension, 
 has involved some alteration of the text. 
 
X Preface to the Second Edition 
 
 arises the development of substantial knowledge within forms 
 of sentence framed for all sorts of varied emergencies, and 
 diversely one-sided in their emphasis. This is why the dispute 
 as to the meaning of propositional forms, on the field of mere 
 usage, is really unending, but also why it is worth while to take 
 pains in eliciting, from the full spirit and purpose implied in 
 sentences, an import in the way of judgment relative to the 
 ultimate interest which is continuously operative within them. 
 The true meaning of propositions lies always ahead of fully 
 conscious usage, as the real reality lies ahead of actual ex- 
 perience (ii. 303-4 below). To maintain the reality of a central 
 cognitive interest as such, and the doctrine that it expresses 
 its nature, though roughly, through forms of sentence * which 
 cover phases of judgment progressive towards its satisfaction, 
 is the double motive which inspires my logical theory. 
 
 Additions in Edition 2 
 
 Note on Miss E. C. Jones's ' New Law of Thought ' 
 Vol. I. On a point in Mr. Keynes's view of Extension 
 On Infinity . . . . . 
 
 On recent discussions of Disjunction (views of Mr 
 
 Keynes and Mr. G. R. T. Ross) . 
 On Error (Professor Stout's view) 
 Vol. II. Appendix to chapter i ' On Symbolic Logic ' 
 
 On a Defective Formulation of the Inductive Principl 
 
 On the Limits of a Genetic Theory of Logic 
 
 The above Theory of Judgment in relation to 
 
 Absolutism ...... 
 
 Truth and Coherence .... 
 
 The relation of mental states to judgment and to 
 reality ....... 
 
 57 
 163 
 
 355 
 
 383 
 
 40 
 
 174 
 238 
 
 ch. viii 
 ch. ix 
 
 ch. X 
 
 * I may venture to cite from Knowledge and Reality, p. 57, a few 
 words which express the problem as I stated it to myself ab initio, and 
 still envisage it. ' Affirmation about the unanalysed present perception 
 may be considered as one extreme ; supposal, having its subject 
 indicated by a mere idea, definite but fictitious, as the opposite extreme. 
 The forms of proposition from which the kinds of judgment have 
 respectively drawn their names, are most precisely adapted for the 
 expression of these two contrasted activities. For the true region of 
 human knowledge, which for the most lies between the two, neither 
 form of sentence, neither class of proposition, or even of judgment, 
 
Preface to the Second Edition xi 
 
 The addition ' On a Defective Formulation of the Inductive 
 Principle ' is based on a paper published in the Proceedings 
 of the Aristotelian Society of London ; that ' On the Limits of 
 a Genetic Theory of Logic ' on a paper published in the 
 Psychological Review. I have to thank the proprietors of 
 both these journals for their permission to use the papers in 
 question. 
 
 BERNARD BOSANQUET. 
 
 OXSHOTT, 191 1. 
 
 is, if pressed home, absolutely and unrestrictedly appropriate,' and the 
 passage proceeds to describe the transition between the two extremes. 
 
 I may here refer very briefly to Miss Jones's interesting treatise on 
 ' A New Law. of Thought ', with Professor Stout's Preface, both of 
 which contain much that would repay a fuller discussion. 
 
 The substitution of 5 is P, as the general formula of thinking, for 
 ^ is ^, which, taken as such a formula, is meaningless, will I hope be 
 adopted by logical theory and practice. By dealing with a difficulty 
 which so great a logician as Lotze could not overcome, the suggestion 
 shows itself to possess a considerable value. 
 
 The form 5 is P is certainly appropriate to the expression of the 
 judgment. But the precise analysis by which Miss Jones interprets 
 it raises, I think, a very fundamental difficulty, to which I propose 
 merely to call attention. (The same analysis has been repeatedly 
 urged totidem verbis by Mr. Bradley and others, but with restrictions 
 which point to the difficulty in question. See Bradley's Logic, pp. 29, 
 167, and the author's Knowledge and Reality, 273, and Essentials, 140, 
 where the story from Thackeray has the same moral as Professor Stout 
 arrived at in his Preface, though the point is less clearly stated). 
 
 That a judgment asserts difference of Intension along with Identity 
 of Extension is an interpretation which holds good prima facie over the 
 area of what commonly passes as the Categorical Judgment. But 
 ( I ) beyond this area it is not applicable, at least in any natural sense. 
 And (2) we are thus forced to see that within this area it is not perfectly 
 applicable. 
 
 (i) When what the judgment affirms is explicitly a law of connection 
 or implication between intensions — when, say, you have before you 
 a true hypothetical judgment, the analysis in question does not really 
 apply. You cannot reduce the meaning of such a judgment to the 
 identification of cases. Systematic continuity of any kind, causality 
 relation of antecedent to consequent, of condition to conditioned — 
 these seem quite irreducible to an identity of subjects plus difference 
 of attributes. But that one intension can ' be ' — involve or imply — 
 another is a possibility which, as I understand, Miss Jones absolutely 
 and in principle denies (cp., however, p, 46 of her work). I should have 
 thought that this denial brings her view into sharp collision with usage, 
 
xii Preface to the Second Edition 
 
 e. g. on p. 41, where, if I understand right, it is contended that admitting 
 the judgment ' All politicians are statesmen ' . we are yet entitled to 
 deny that the quality of statesmanship can be inferred from that of 
 being a politician. And so elsewhere, pp. 45-6, and 73. 
 
 Here is the root of the difference between us referred to on p. 7 of 
 ' A New Law of Thought '. Between the letters A and B I recognise 
 no such continuity as I look for, say, between a cause and its effect. 
 And therefore I call them unfit to symbolise the continuous identity 
 expressed in a judgment which states a law. 'A is J5 ' would not, in 
 fact, be self-explaining as a formula for the new law of thought. ' S is 
 P ' is rightly chosen, because it obviously refers to the structure of the 
 judgment. But what this is, still needs explanation. 
 
 (2) ' Un giudizio e sempre la formulazione d'una legge,' Varisco, 
 * I massimi Problemi,' p. 89. The point here is in the word ' sempre '. 
 At bottom, according to the view which I have adopted, all judgment, 
 and even association, contains in it the principle of universal con- 
 nection, of a law, however imperfectly formulated. From the very 
 beginning, conjunction covers connection. The doctrine is well known, 
 and it would be idle to re-argue it here. I need only point out that for 
 good or evil, what stands between us is the conception that identity 
 must be reduced to numerical identity. The judgment is split up into 
 numerical identity plus intensional difference. This answers prima 
 facie for apparent categoricals, but I doubt whether it is sound in 
 principle even for them. 
 
 It occurred to me, indeed, that the author might intend to restrict 
 the explanation to these judgments, which play so large a part in the 
 operations of Formal Logic. But I believe that any such restriction 
 would be disowned. (See analysis of a geometrical truth on p. 46, and 
 note the treatment of the inseparability of the 5 and P intensions as 
 merely compatible with the meaning). 
 
 I may add that I welcome the criticism of Jevons's ' Simple and 
 Obvious Law of Thought ', p. 36, for which, so far as I know, the 
 author is right in claiming priority. And I do not deny that in so 
 far as a universal connection presupposes a world or system within 
 which it falls, a further analysis of identity in difference might bring 
 out features bearing a superficial likeness to those of Miss Jones's 
 conception. But I cannot think that any analysis can finally acquiesce 
 in a view which restricts itself to irrelevant conjunctions. 
 
TABLE OF CONTENTS 
 
 VOL. I 
 
 INTRODUCTION 
 
 1. Title of the work explained 
 
 2. Knowledge and its content 
 
 i. Truth ..... 
 
 ii. Meaning ..... 
 
 3. What is the knowledge which we investigati 
 
 4. The act of Naming 
 
 5. What that act implies 
 
 i. Logical significance . 
 
 ii. Meaning of ' implies ' 
 iii. Objectification 
 iv. A positive content . 
 
 V. Meaning of Verb- and Case-endings 
 vi. Naming and distinction 
 vii. Naming and Comparison 
 
 6. Concept and Judgment 
 
 7. Logical meaning and the individual mind 
 
 8. Intension and Extension . 
 
 i. Intension and Extension complementary and inseparable 
 
 a. Their nature 
 
 /8, Fictitious Ideas . 
 
 7, Nonsensical expressions 
 
 5, Names of Attributes . 
 
 f. Proper names ... 
 
 f. Names with number attached 
 ii. Alleged inverse ratio of Extension to Intension 
 
 a. Mathematical phrase wrong 
 
 0. Assumptions involved regarding Intension and Ex 
 tension .... 
 (i) Co-ordinate adjectives not considered 
 
 (2) Qualities taken as additions not variations 
 
 (3) All Intension held reducible to class-predicates 
 
 (4) Subsumption main principle of reasoning 
 
 iii. Truth of the inverse ratio ..... 
 
 a. Alternative Classification . . . . 
 
 P. Inverse ratio partially justified .... 
 
 I 
 2 
 2 
 
 4 
 6 
 
 7 
 
 12 
 12 
 
 IS 
 17 
 17 
 19 
 21 
 
 25 
 
 29 
 39 
 44 
 44 
 44 
 45 
 46 
 46 
 47 
 51 
 55 
 56 
 
 57 
 57 
 57 
 59 
 60 
 61 
 61 
 62 
 
XIV 
 
 Table of Contents 
 
 Book I. The Judgment 
 
 CHAPTER I 
 Of Judgment and Judgment- forms in general 
 
 I, Nature of Judgment as such 
 
 11. 
 
 i. Symbolic Ideas 
 ii. Reference to Reality 
 iii. Judgment and Proposition 
 
 a. The parts of the Judgment 
 0. Judgment in relation to Time 
 
 1. Arriving at Judgment 
 
 2. The complete Judgment 
 Arrangement of Judgments 
 
 i. Purpose of Scheme 
 
 ii. Explanations .... 
 
 a. Use of the terms Categorical and Hypothetical 
 
 i8. Divergent species of Judgment . 
 
 .7. Use of the terms ' Analytic ' and ' Synthetic ' 
 
 PAGE 
 
 67 
 
 CHAPTER n 
 
 Quality and Comparison 
 
 Quality and Comparison 
 
 The Judgment of Quality . 
 i. Meaning of Quality 
 ii. Judgment of Quality proper 
 iii. Demonstrative Judgment 
 The Judgment of Comparison 
 i. Quantitative . . 
 
 ii. In space and Time as such 
 iii. So-called Qualitative . 
 
 CHAPTER HI 
 
 Quantity and Proportion 
 
 The Judgment of Measurement ..... 
 
 I. Measurement and Individuality .... 
 
 i. Simple measurement. Pure Quantity . 
 ii. Complex, mediate or ideal measurement. Propor 
 tion ....... 
 
 iii. Qualitative unity of Individual 
 
 iv. Change and Motion as revealing Individuality 
 
 V. Abstraction and Necessity . . . . 
 
 vi. Absolute and Conditional affirmation . 
 vii. Knowledge as union of absolute and relative 
 
Table of Contents 
 
 XV 
 
 CHAPTER IV 
 
 Measurement [continued) — Abstract Quantity 
 
 PAGE 
 
 !. One-sided forms of measurement . . . .144 
 
 i. Enumeration and Simple Counting . . .144 
 
 Corollaries : a. Simple Counting . . . 146 
 
 B. Discrete and Continuous . .149 
 
 ii. Judgments Afifiliated to the Enumerative Judgment 150 
 
 a. Plural or Particular Judgment . . ,150 
 
 P. Collective Judgment . . . . .152 
 
 7. Enumerative Judgment reverting towards Generic, 
 
 Exhaustive Judgment . . . . .157 
 
 8. Judgment of Complex or Mediate Counting, Addi- 
 
 tion and Multiplication. The Equation . .159 
 
 t. Abstract Enumeration and the Infinite Series . 161 
 f. New Theory of Infinity . . . .163 
 
 (i) Problem Actual ..... 163 
 
 (2) Split in Whole . , . . . .164 
 
 (3) Demand of Logic ..... 164 
 T]. Infinite number in general . . . .165 
 
 0. Abstract and Infinite Time . . . .169 
 
 1. Abstract and Infinite Space . . . .174 
 
 a. Measurement of actual distances . . 175 
 
 b. Theoretical relations of spatial attributes . 177 
 
 (i) Individuality of figures in Space . 177 
 
 (2) Existence of figures in Space . . 181 
 
 (3) The quasi-generic Judgment . . 185 
 
 c. Infinite Space . . . . . .187 
 
 iii. Mechanical view of Universe and general relation of 
 
 Equation to Judgment . . . . .189 
 
 CHAPTER V 
 
 Singular and Universal Judgment 
 
 Singular Judgment . 
 i. Individual Judgment . 
 a. with Proper Name 
 ^. with Name and ideas 
 ii. Corporate Judgement 
 iii. Existential and Temporal element in the Singular 
 ment .... 
 Universal Judgment . 
 i. Generic Judgment 
 
 a. Quasi-collective Judgment 
 ;3. True Generic Judgment 
 
 a. Analogical Judgment 
 
 b. Its existential meaning 
 
 c. Individual (Generic) Judgment 
 
 Judg 
 
 196 
 196 
 196 
 198 
 199 
 
 202 
 207 
 209 
 211 
 212 
 212 
 223 
 227 
 
XVI 
 
 Table of Contents 
 
 CHAPTER VI 
 
 Universal Judgment {contmued) 
 
 ii. Pure Hypothetical Judgment 
 
 a. Its relation to previous forms 
 
 )3. Its external form 
 
 7. The assertion which it makes 
 
 a. The idea of Ground 
 
 b. The idea of Cause . 
 
 ( 1 ) Cause as corresponding to Complete Ground 
 
 (2) Cause as an event ; i. e. distinguished from 
 
 Ground Complete or Incomplete 
 
 c. The element of supposition in universal Judgment 
 
 ( 1 ) Historical relations of simple and hypothetical 
 
 judgment ...... 
 
 (2) The basis of hypothetical judgment . 
 
 CHAPTER VII 
 Negation, Opposition, and Conversion 
 
 Negation how related to Affirmation 
 Bare Denial and the Infinite Judgment 
 Significant Denial .... 
 
 Opposition and Conversion 
 
 i. The opposition of Judgments . 
 
 a. In the case of Singular Judgments 
 /3. In the case of Particular Judgments 
 7. In the case of Generic Judgments 
 5. In the case of Hypothetical Judgments 
 ii. Double negation ..... 
 
 iii. Conversion ...... 
 
 a. Simple Conversion of Singular . 
 
 /3. Conversion by limitation . 
 
 7. Modal Conversion .... 
 
 5. Simple Conversion of Universal Negative 
 
 6. Contraposition .... 
 Privation as warrant of Affirmation and of Exclusion 
 
 a. Privation and real possibility 
 ;3. Privation and impossibility 
 
 PAGE 
 
 234 
 234 
 236 
 2^8 
 238 
 250 
 250 
 
 252 
 263 
 
 268 
 271 
 
 277 
 281 
 283 
 
 294 
 294 
 
 294 
 294 
 296 
 299 
 302 
 
 307 
 308 
 
 309 
 
 312 
 
 313 
 314 
 315 
 
 318 
 
 CHAPTER VIII 
 
 Disjunction and the Statement of Chances 
 
 I. The disjunctive judgment 
 
 i. Genesis of the disjunctive judgment 
 ii. Imperfect disjunctions 
 a. Not exclusive . 
 3. Disjunctions of Ignorance 
 7. Disjunctions referred to point of Time 
 
 322 
 
 322 
 324 
 324 
 324 
 326 
 
Table of Contents 
 
 XVI 1 
 
 1. The disjunctive judgment {continued) 
 
 iii. Logical affiliation of true disjunction 
 
 a. The Generic judgment 
 
 j3. The hypothetical judgment 
 iv. When are parts disjunctively related ? 
 V, Is Disjunction reducible to Hypotheticals ? 
 
 2. The statement of chances 
 
 i. Limits of the problem in present work . 
 ii. Affiliation of the abstract disjunction 
 iii. Essence of the statement of chances 
 iv. Applications of the statement as calculus 
 
 a. Alternatives and Results . 
 
 /3. Physical Alternatives 
 
 7. Interesting Results . 
 V. What does statement of chances represent 
 vi. Chance and series .... 
 
 a. Fallacies relating to series . 
 
 ^. Causal inference from series 
 
 7. Coincidence of observed and calculated series 
 
 5. Series a reality for some purposes 
 vii. Probability of Judgments in the absence of Knowledge 
 
 Appendix to Chapter VIII 
 On some recent Discussions of Disjunction .... 
 a. Usage guided by feeling that alternatives are meant 
 to be incompatible ..... 
 
 ^. Exhaustive must be exclusive. Relations of con- 
 joined to single cases ..... 
 7. Alternatives ex hyp. incompatible because offered 
 as adequate ....... 
 
 6. Other criticisms ...... 
 
 page 
 
 327 
 328 
 330 
 332 
 2,iZ 
 iii 
 334 
 336 
 
 in 
 
 337 
 11^ 
 339 
 342 
 342 
 349 
 350 
 350 
 351 
 
 355 
 
 356 
 
 356 
 
 360 
 361 
 
 CHAPTER IX 
 Modality 
 
 Kant's view of Modality fundamentally just . . . 2,61 
 
 The Problematic Judgment ...... 365 
 
 i. Nature of mere suggestion or question . . . 366 
 ii. Is the Problematic Judgment a form of the Apodeictic 
 
 Judgment ?....... 367 
 
 a. The Particular Judgment — the exception and the 
 
 instance . . . . . . . 369 
 
 ^. The modal Particular — negative and positive possi- 
 bility 371 
 
 7. Essence of the Problematic Judgment . . ■^ti 
 
 The Assertory Judgment ....... 374 
 
 The Apodeictic Judgment ...... 376 
 
 i. The hypothetical judgment ..... 376 
 
 ii. The disjunctive judgment . . . . .381 
 
 Note on Error ......... 383 
 
 103- b 
 
xviii Table of Contents 
 
 VOL. II. 
 
 Book II. Inference 
 
 CHAPTER I 
 The Nature of Inferenc6 
 
 PAGE 
 
 1. The Essence of Inference ...... i 
 
 2. Some Accidents of Inference . . . . . .4 
 
 i. Mental transition in Time ..... 4 
 
 ii. Discovery or novelty . , . ... . 8 
 
 iii. Omission of relevant matter ..... 8 
 
 iv. Selection, and omission- of irrelevant matter ? . . 12 
 
 V. Three terms ? . . . . . . .12 
 
 3. The lower limit of Inference . . . . . .14 
 
 i. The reproduction of Ideas . . . . .14 
 
 ii. General necessity of Judgment . . . .15 
 
 iii. Specific necessity of Judgment . . . .17 
 
 iv. The true immediate Inferences . . . ,19 
 
 a. Comparison ....... 19 
 
 /3. Abstraction ....... 20 
 
 7. Recognition . . . . . . .22 
 
 7i. Discrimination, etc. ...... 24 
 
 6. Inferential character of above processes . . 25 
 (,'. Comparative Science . . . . .25 
 
 4. Species of Inference which have been erroneously identified with 
 
 its principle ......... 27 
 
 i. Inference from particulars to particulars ... 27 
 ii. Subsumption . . . . . . . .28 
 
 iii. Calculation and equation . . . . . 29 
 
 o. Calculation proper . , . . . .30 
 
 /3. The Equational Logic . . . . .31 
 
 iv. Construction . . . . , . . -33 
 
 r. Physical ........ 34 
 
 B. Imaginative . . . . . . -35 
 
 7. Intellectual, in geometry and mechanics . . 36 
 5. Intellectual, without limitation to geometry and 
 
 mechanics ....... 37 
 
 Scheme of types of Inference ...... 39 
 
 Appendix on Symbolic Logic 
 The contrast of Formal or Mathematical Logic (Russell) witli 
 
 Philosophical Logic ....... 40 
 
 I. The point of divergence between the two ... 40 
 a. As indicated above in this work (taking Quantity 
 
 as characteristic of Mathematics) ... 40 
 r. Taking pure Mathematics as= Formal Logic (as 
 
 study of implications) . . . . .42 
 
Table of Contents xix 
 
 The contrast of Formal or Mathematical Logic etc. {continued) 
 
 2. Pi ecise nature of the divergence ..... 45 
 
 Contrast of Modes of Formal Deduction with ideal of 
 
 Logical Stability. . . . . . .45 
 
 a. Meaning of Logical Stability ... 45 
 i8. Formal Logic cares more for forms of Deduction 46 
 
 CHAPTER II 
 
 Enumerative Induction and Mathematical Reasoning 
 
 1. Enumerative Induction . . . . . . .50 
 
 a. Syllogism in fig. 3 . . . ... .50 
 
 /3. Divergent tendencies . . . . .52 
 
 7. The Individual Judgment in Induction Lotze . 53 
 
 2. Mathematical Reasoning . . . . . . -55 
 
 i. Number and Analogy — Divergence . . . -55 
 
 a. Complete Enumeration as false Ideal. Syllogism 
 
 and Induction . . . . . -55 
 
 6. Enumeration as Arithmetical computation . 58 
 
 7. Calculation compared with argument . . 60 
 ii. Applications of Calculation^ ..... 62 
 
 a. Substitutive Inference . . . . .62 
 
 (;3. Apprehension of Connections in Space and Time) 64 
 7. Calculation applied to Geonietrical Reasoning. The 
 
 Constitutive Equation . . . . .68 
 
 5. Calculation applied to disparates. Proportion . j^ 
 (i) Homogeneous Terhis . . . -72) 
 
 (2) ' a and a ' series ..... 74 
 
 f. Proportion, Analogy, and the Hypothetical Judg- 
 ment ........ 77 
 
 (,'. Consciousness and Conservation of energy . . 79 
 
 iii. The ttiechanical aspect of Knowledge . . .81 
 
 CHAPTER III 
 
 Analogy 
 
 1. Analogy and Enumerative Induction. Examples . . 86 
 
 2. Logical criticism of the Analogical argument . . .90 
 
 i. Fig. 2. Undistributed middle. Import of this defect 90 
 
 ii. Real value of Analogical argument .... 92 
 
 iii. No ratio of Identities to Differences . . . 100 
 
 iv. Concurrent Analogies. Negative confirmation . .104 
 
 v. Divergent tendencies in Analogy . . . .107 
 
XX 
 
 Table of Contents 
 
 CHAPTER IV 
 
 Scientific Induction by Perceptive Analysis 
 
 1. Negative Inference .... 
 
 i. Its nature and conditions 
 
 ii. No conclusion from two negatives 
 
 iii. The negative instance 
 
 2. Scientific Induction .... 
 
 i. Induction and other Inference 
 ii. Induction as Perceptive Analysis 
 
 a. Symbolic expression of the problem 
 ^. Establishment of ordinary Hypothetical Judgment 
 7. Establishment of reciprocal Hypothetical Judgment 
 5. Conversion or Generalisation 
 iii. Logical character of Perceptive Induction 
 a. Its essence as Inference 
 /S. Theoretical purpose of representation by symbol 
 7. Part played by number of instances 
 (i) In Perceptive Analysis proper 
 (2) In assigning known effects to classes of un 
 known conditions 
 iv. Observation and Experiment 
 a. Natural Experiment 
 j8. Observation with accurate instruments 
 7. Experiment expressed in logical symbols 
 S. Experiment with the Siren analysed 
 
 PAGE 
 
 I eg 
 109 
 112 
 
 "5 
 117 
 117 
 122 
 122 
 124 
 127 
 129 
 
 131 
 132 
 
 134 
 134 
 135 
 
 135 
 141 
 141 
 142 
 143 
 147 
 
 CHAPTER V 
 Scientific Induction by Hypothesis. Generalis.^tion 
 
 1. Hypothesis and Postulate .... 
 
 i. Hypothesis falls outside Postulate 
 ii. But not if Hypothesis alleges Vera causa 
 
 2. Phases of Hypothesis ..... 
 
 i. Rudimentary Hypothesis 
 
 ii. Mediate Hypothesis .... 
 
 a. Hypothetical nature of Induction 
 
 i3. Example of fusion between Hypothesis and data 
 
 3. Generalisation . . 
 
 i. ' From many to all ' exploded 
 ii. By mere determination . . . 
 
 iii. Material or Analogical Generalisation 
 
 4. General view of Induction _. . . . 
 
 i. Difference from Jevpns . . . . 
 
 ii. Ultimate nature of Induction . 
 iii. On a Defective Formulation of the Inductive Principle 
 
 151 
 151 
 154 
 155 
 155 
 156 
 
 156 
 157 
 163 
 163 
 163 
 165 
 169 
 169 
 170 
 174 
 
Table of Contents 
 
 General view of Induction {continued) 
 iii. On a Defective Formulation etc. {continued) 
 Inference and Repetition. 
 
 a. ' Same Cause Same Effect ' 
 /3. A Tautology 
 7. The true Principle 
 Developing the Nexus 
 
 XXI 
 
 PAGE 
 
 176 
 181 
 1S2 
 
 4- 
 
 CHAPTER VI 
 
 Concrete systematic Inference 
 
 Philosopliical Subsumption .... 
 
 i. Logical content of these Inferences 
 o. Real system 
 j8. Apodeictic sequence 
 ii. Their form, Syllogism in fig. i 
 Disjunctive reasoning 
 The judgment of value 
 i. Real Teleology 
 
 ii. Mediation .... 
 
 Recapitulation of the main characteristics of Inference 
 i. No antecedent scheme of Inference 
 ii. Conditions of Inference ..... 
 iii. Relation of Syllogism to these conditions 
 a. The traditional syllogism 
 j3. The syllogism as reasoned judgment 
 
 185 
 190 
 190 
 191 
 192 
 194 
 199 
 199 
 199 
 200 
 201 
 203 
 204 
 204 
 206 
 
 CHAPTER VII 
 
 The Relation of Knowledge to its Postulates 
 
 The formal postulates of Knowledge .... 208 
 
 1. The Law of Identity . . . . . .210 
 
 ii. The Law of Contradiction ... . . .211 
 
 iii. The Law of Excluded Middle . . . . .213 
 
 iv. The Law of Sufficient Reason and Law of Causation 215 
 The material postulates of Knowledge . . . .216 
 
 i. The maintenance of life . . . . . .218 
 
 ii. The reality of values . . . . . .221 
 
 The ultimate nature of Necessity . . . . . .223 
 
 i. A pnon necessity and mediation .... 223 
 
 a. Mediate nature of necessity forgotten in controversy 224 
 P. Organised and unorganised experience, with am- 
 biguity of test by Conception . . .226 
 I ii. Rehabilitation of formal distinctions in Logic . .230 
 iii. Criticism of ' Aesthetic ' necessity . . . .233 
 
 a. Aesthetic necessity as a contradiction in terms . 233 
 /3. Aesthetic necessity as a mere case of logical necessity 234 
 
xxu 
 
 Table of Contents 
 
 Genetic Theory and Imitation . 
 i. Reason as an Adaptation 
 ii. Imitation plus Selection ? 
 iii. Meaning of Imitation 
 
 a. Imitation dist. Response 
 0. Imitation why held a Vera causa ? . 
 7. False separation of Imitator and Inventor 
 iv. Truth or Belief due to Evolution ? . 
 a. Limits of Genetic account 
 /3, The ' making of Truth ' . 
 
 PAGE 
 
 238 
 
 239 
 240 
 241 
 241 
 241 
 242 
 243 
 243 
 246 
 
 CHAPTER VIII 
 
 The Above Theory of Judgment in Relation to 
 Absolutism 
 
 Our theory treated as prejudiced. Answers to objections . 251 
 
 i. No finite real self-existent . . . . .252 
 
 ii. Degrees of Individuality . . . , .253 
 
 iii. Experience of self fatal to doc crine of substances . -255 
 
 iv. DifiSiculty arising from conception of class-inclusion. 
 
 This conception foreign to S P judgment as such . 255 
 
 v. Imperfect Individual can be conditional Predicate . 257 
 
 vi. Absolutism rests on its own substantial grounds . 259 
 
 Freedom of expression in Judgment on this theory . . 259 
 
 i. Traditional S P analysis rejected by it . . .259 
 
 ii. Individuality said to demand Designation as opposed 
 
 to Definition — the reverse of the truth . . 260 
 
 iii. Doctrine of ultimate ' subject ' leaves philosophical theory 
 
 free, taking shape from the latter ... 262 
 
 CHAPTER IX 
 
 Truth and Coherence 
 
 Disclaimer of Correspondence Theory 
 
 i. An expression which might be misleading 
 ii. The Criterion immanent . ' . 
 
 iii. Truth its own test .... 
 
 iv. Not all correspondence means copying 
 The Logical world to-day .... 
 
 i. ' Life,' ' Practice,' ' Feeling,' forms of Immediacy 
 ii. The misconception which governs the movement 
 iii. Fallacies of Genetic Logic according to a recent exposition 
 
 Dualism, Occasionalism, Adaptationism 
 iv. How Psychology passes into Logic . 
 V. Summary — defects of the new attitude 
 
 263 
 264 
 265 
 266 
 267 
 268 
 268 
 268 
 
 270 
 274 
 
 275 
 
Table of Contents xxiii 
 
 PAGE 
 
 3. Realism — a complementary form of Immediacy . . 276 
 
 a. The world of related simple things .... 277 
 
 Rejection of ' internal ' (relevant) relations . ; 277 
 
 (i) Relations relevant to kinds .... 277 
 
 (2) The meaning of terms relevant to their grouping 278 
 
 (3) Relations express behaviour of terms in groups. 
 
 ' Sense ' of relations ..... 278 
 
 h. Relations not asserted to be adjectives . . . 279 
 
 c. Truth and Error not absolute, because things not simple . 280 
 
 d. The illusion of simple fact . . . . .281 
 
 (i) Stating what is 'a fact ' may be telling a lie . 282 
 
 (2) or may be an error (' true ' conclusion from false 
 
 premisses) ....... 283 
 
 (3) How we come by ' simple ' facts ... . 284 
 
 (4) The facts are more not less than simple realities . 285 
 
 (5) In the 'reality' the 'simple facts' are lost . 285 
 
 (6) The ' full facts ' or ' reality ' are comprehensive 
 
 systems . . . . . . . . 287 
 
 4. Coherence is defective, like all theory, but not in a way that 
 
 implies correspondence as its standard .... 288 
 
 i. Coherence does not fall back on Correspondence . 289 
 
 ii. No ' approximation ' to an original . . . 290 
 
 5. Our quasi-solid world ....... 292 
 
 6. Does Truth copy this world ? No, it is plastic . . 294 
 
 CHAPTER X 
 
 The Relation of Mental States to Judgment and to 
 
 Reality 
 
 The Mental States in question ...... 295 
 
 1. Doctrine of the present work ..... 295 
 
 a. All sense-content significant, and any of it may become 
 
 a ' state of mind '...... 295 
 
 ^. The ' use ' of contents as ideas .... 298 
 
 2. The Real not arrived at by subtraction . . . 301 
 
 a. Knowledge involves mental states. . . . 302 
 
 (i) Reality lies ahead, not behind . . . 302 
 
 (2) Truth in ' Mind can only apprehend itself ' . 303 
 
 ( 3 ) What explanation means, viz. complete thinking 305 
 
 (4) Fallacy that ' independent of ' = ' apart from ' 305 
 
 (5) A simple real must duplicate mental being . 307 
 
 (6) If ' independent ' = 'apart from', different phy- 
 
 sical objects are the same for apprehension . 307 
 
 (7) The object of perception is conditionally, i. e. 
 
 forme . . . . . . . . 310 
 
xxiv Table of Contents 
 
 The Real not arrived at by subtraction {continued) — • 
 li. Subjective Idealism insists on vital continuity of universe 3 1 1 
 7. ' Sustaining ' and ' constructing ' the world. Answer to 
 
 criticisms . . . . . . . -313 
 
 (i) Judgment involves a world, and one world . 314 
 
 (2) Both realists and pragmatists put mind outside 
 
 reality . . . . . . . -317 
 
 (3) Nature of object of cognition — strictly we neither 
 
 ' apprehend ' nor ' create ' it. We are organs 
 within the universe for ' eliciting ' its reality in the 
 form of truth. The true driving force of Idealism 318 
 
 ABBREVIATIONS 
 
 Bradley's Appearance = Bradley's Appearance and Reality, ed. 2. 
 Sonnenschein, 1897. 
 
 Bradley's Logic = Bradley's Principles of Logic. Kegan Paul, 
 Trench & Co., 1883. 
 
 Keynes = Keynes's Formal Logic, ed. 4. Macmillan, 1906. 
 
 Prichard = H. A. Prichard's Kant's Theory of Knowledge. Clarendon 
 Press, 1909. 
 
 Essentials = Bosanquet's Essentials of Logic. Macmillan, 1895. 
 
 Sigwart = Logik, von Dr. Christoph Sigwart. 2nd edition. Freiburg, 
 
INTRODUCTION 
 
 ' If it is held a valuable achievement to have discovered sixty and odd 
 species of parrot, a hundred and thirty-seven species of veronica, and so 
 forth, it should surely be held a far more valuable achievement to dis- 
 cover the forms of reason ; is not a figure of the syllogism something 
 infinitely higher than a species of parrot or of veronica ? ' — Hegel, 
 WissenSchaft dev Logik, p. 1 39. 
 
 ' We have seen that the members of the same class, independently of 
 their habits of life, resemble each other in the general plan of their 
 organisation. This resemblance is often expressed by the term " unity 
 of type " ; or by saying that the several parts and organs in the different 
 species of the class are homologous. The whole subject is included 
 under the general term of morphology. This is one of the most interest- 
 ing departments of natural history, and may almost be said to be its 
 very soul.' — Darwin, Origin of Species, p. 382. 
 
 I. In giving to the present work the title of ' Morphology Title 
 
 of the 
 Work. 
 
 of Knowledge ' 1 intended to indicate as its purpose the °* *^^ 
 
 unprejudiced study of judgment and inference, throughout 
 the varied forms in which their evolution may be traced and 
 their relationships determined. Mere classification, therefore, 
 or mere enumeration of the species of judgment or of inference, 
 would not achieve the aim which I have set before myself, 
 although I am wholly of Hegel's mind when he says that the 
 species of syllogisms are at least as well worth discovering as 
 those of parrots or of veronicas. The two quotations which 
 stand at the head of this Introduction may together exhibit 
 my conception of a logical system, if interpreted to mean that 
 I would treat the forms of judgment and of inference as science 
 treats the forms of animals or of plants, not in the spirit of 
 enumerative classification, but in the spirit of morphological 
 analysis. In the conception so determined, however, one 
 further correction must be made. Morphology, as the science 
 of external shape, involves, I understand, an antithesis to 
 physiology as the science of vital function. This contrast 
 belongs to the distinction of outer and inner, of persistent 
 bodily form and living productive process, which appears at 
 
 1337 B 
 
2 Introduction [Introd. 
 
 first sight to prevail in the world of visible and tangible matter. 
 Were we to transfer any such contrast to the scientific treat- 
 ment of intelligence, we should obviously be forced to identify 
 the morphology of knowledge with the science of language or 
 of grammar, and reserve for the analysis of the vital thinkmg 
 function some such appellation as that of Mental Physiology. 
 I do not say that such an antithesis would be false, but it 
 would fail to illustrate the point of view on which I am now 
 desirous to insist. In the systematic activity of thought the 
 contrast between bodily shape and vital process is non- 
 existent. Even the evolution of the animal organism might 
 be considered as the development of a function which is 
 a system of functions, and the science of life if thus regarded 
 would unite, as it appears to me, what is valuable in mor- 
 phology with the essence and spirit of physiology. Of the 
 system of knowledge, at any rate, this is the true account. The 
 form of thought is a living function, and the phases and 
 moments of this function are varieties and elements of the form. 
 Therefore the ' Morphology of Knowledge ' must be construed 
 as not excluding the Physiology of Thought. The science of 
 intellectual form includes the science of intellectual life. 
 Know- 2. Knowledge involves the ideas (i) of Truth and (ii) of 
 
 its Con^*^ Meaning, i. How does the analysis of knowledge as a sys- 
 tent. tematic function, or system of functions, explain that relation 
 in which truth appears to consist, between the human intelli- 
 gence on the one hand and fact or reality on the other ? At 
 first sight, even the genetic a analysis of a systematic develop- 
 ment which v/e propose to undertake, though a more genuine 
 explanation of that development than any mere summary of 
 types, is powerless to grasp the relation between the system 
 so developed, and an object-matter that lies outside it. To 
 this difficulty there is only one reply. If the object-matter of 
 reality lay genuinely outside the system of thought, not only 
 our analysis, but thought itself, would be unable to lay hold 
 of reality. For logic, at all events, it is a postulate that ' the 
 truth is the whole '.*> The forms of thought have the relation 
 
 ' For a discussion of the Genetic Theory of Logic, in relation to the 
 standpoint of the present work, see ii, pp. 238, 269. 
 
 '' See further, on the coherence theory of truth, ii, ch. ix. 
 
iNTROTj.] Truth 3 
 
 which is their truth in their power to constitute a totality ; 
 which power, as referred to the individual mind, is its power 
 to understand a totality. The work of intellectually consti- 
 tuting that totality which we call the real world is the work 
 of knowledge. The work of analysing the process of this con- 
 stitution or determination is the work of logic, which might 
 be described as the self-consciousness of knowledge, or the 
 reflection of knowledge upon itself. Logic has no criterion of 
 truth nor test of reasoning. Truth is individual, and no 
 general principle, no abstract reflection, can be adequate to 
 the content of what is individual. It is indeed impossible to 
 study the growth of knowledge without lighting upon con- 
 fusions of thought that evoke a warning word. But even 
 a confusion of thought may have a material significance, and 
 therefore contain a material truth, which escapes the logical 
 critic who perforce ignores its individual content . The relation 
 of logic to truth consists in examining the characteristics by 
 which the various phases of the one intellectual function are 
 fitted for their place in the intellectual totality which consti- 
 tutes knowledge. The truth, the fact, the reality, may be 
 considered, in relation to the human intelligence, as the 
 content of a single persistent and all-embracing judgment, by 
 which every individual intelligence affirms the ideas that form 
 its knowledge to be true of the world which is brought home 
 to it as real by sense-perception. 
 
 The real world for every individual is thus emphatically 
 his world ; an extension and determination of his present 
 perception, which perception is to him not indeed reality as 
 such, but his point of contact with reality as such. Thus in 
 the enquiry which will have to be undertaken as to the logical 
 subject of the judgment, we shall find that the subject, how- 
 ever it may shift, contract, and expand, is always in the last 
 resort some greater or smaller element of this determinate 
 reality, which the individual has constructed by identifying 
 significant ideas with that world of which he has assurance 
 through his own perceptive experience. In analysing common 
 judgment it is ultimately one to say that I judge, and that the 
 real world for me, my real world, extends itself, or maintains its 
 organised extension. This is the ultimate connexion by which 
 
 B2 
 
4 Introduction [Introd. 
 
 the distinction of subject and predication is involved in the 
 act of affirmation or enunciation which is the differentia of 
 judgment. 
 Meaning. ii. To speak of consciousness as a single persistent judgment 
 is at first sight a paradox, in view of the distinction between 
 an idea and the affirmation of an idea. It is not easy to deny 
 that there is a world of ideas or of meanings, which simply 
 consists in that identical reference of symbols by which mutual 
 understanding between rational beings is made possible. 
 A mere suggestion, a mere question, a mere negation, seem all 
 of them to imply that we sometimes entertain ideas without 
 affirming them of reality, and therefore without affirming their 
 reference to be a reference to something real or their meaning 
 to be fact. We may be puzzled indeed to say what an idea 
 can mean, or to what it can refer, if it does not mean or refer 
 to something real — to some element in the fabric continuously 
 sustained by the judgment which is our consciousness. On 
 the other hand, it would be shirking a difficulty to neglect the 
 consideration that an idea, while denied of reality, may never- 
 theless, or even must, possess an identical and so intelligible 
 reference — a symbolic value — for the rational beings who deny 
 it. A reference, it may be argued, must be a reference to 
 something. But it seems as if in this case the something were 
 the fact of reference itself, the rational convention between 
 intelligent beings, or rather the world which has existence, 
 whether for one rational being or for many, merely as contained 
 in and sustained by such intellectual reference. 
 
 I only adduce these considerations in order to explain that 
 transitional conception of an objective world or world of 
 meanings, distinct from the real world or world of facts, with 
 which it is impossible wholly to dispense in an account of 
 thought starting from the individual subject. The paradox 
 is that the real world or world of fact thus seems for us to 
 fall within and be included in the objective world or world of 
 meanings, as if all that is fact were meaning, but not every 
 meaning were fact. This results in the contradiction that 
 something is objective, which is not real. 
 
 We do not meet this paradox adequately by reminding our- 
 selves that e.g. a negation or a question is a fact in some one's 
 
iNTROD.] Meaning 5 
 
 mind, and therefore as a psychical occurrence is a real event, 
 and in that sense falls within reality. In considering an idea 
 as a psychical occurrence we abstract from its meaning, which 
 apparently consists in some identity or persistent unity that 
 extends beyond the isolated occurrence of the idea in time. 
 
 The solution of the difficulty appears however to be sug- 
 gested by the distinction which we have just taken. As the 
 psychical occurrence and objective reference are distinguish- 
 able by abstraction only, so objective reference and reference 
 to reality (affirmation) are distinguishable by abstraction only. 
 The world of objective reference and the world of reality are the 
 same world, regarded in the former case as composed of isolated 
 though determined contents, and in the latter case as composed 
 of contents determined by systematic combination in a single 
 coherent structure. The former point of view is an abstraction 
 that goes near to be a fiction, for isolated contents qua isolated 
 are not determined. But it is possible and usual to consider 
 ideas, by help of abstraction, in respect of those relations which 
 especially determine them, as detached islands or spheres of 
 knowledge, without actually referring them in a thoroughly 
 determinate judgment to a place in the one individual system 
 which for each of us is the reality. Ideas thus isolated are 
 what we ' entertain ' as significant or symbolic ideas which 
 have meaning or objective reference, and yet are not affirmed 
 of Reality. Objective reference is the substance of the conven- 
 tion by which rational beings communicate with each other 
 and with themselves, and which, though a consequence of the 
 unity of Reality, can be regarded without being directly 
 identified with that unity. To show that every idea which is 
 entertained, as for example suggested or supposed, must be 
 taken to be ultimately affirmed of reality, is the task of those 
 portions of logic which deal with question, suggestion, suppo- 
 sition, and denial. Thus in the discussion of mere or bare 
 denial we shall be forced to the conclusion that where, in an 
 attempted judgment of denial, no positive basis nor positive 
 consequence of the denial is to be discovered, — where, that is, 
 the idea which is verbally denied forms no element in any 
 affirmation of any kind about Reality, there no judgment can 
 really take place, nor can the idea in question be enunciated 
 
6 Introduction [Introd. 
 
 as an intelligible idea. The meaning which an idea seems to 
 retain when named in a spurious judgment or unintelligible 
 proposition of this kind depends on its initiation of other acts 
 of thought than the denial in which, ex hypothesi, we were to 
 look for its unaffirmed signification. Our treatment of suppo- 
 sition will lead us to the same result. All significant, i.e. all 
 logical, ideas are ultimately elements in a single judgment, the 
 judgment which sustains the ideal structure of the real world. 
 Thus the world of truth and the world of meaning are not 
 really distinct, and the process which logic investigates is the 
 single process and individual self-determination of the whole 
 which is the truth or reality. 
 What 3. It is natural to ask, ' Where and what is this self-deter- 
 
 ledge^ are miration ? Where does it begin ? Where does it end ? Is 
 we inves- it in the individual mind or in the history of the race, or in an 
 iga ing . ^j.]3J^j.^j.y combination of the two ? ' 
 
 I cannot attach much importance to this question, which 
 might be asked with no less justice, as it appears to me, of 
 any other science. But no other science would admit that it 
 has a meaning. A science deals with its object-matter where- 
 ever it finds it. The self-dqtermination of the knowing intelli- 
 gence as the real world takes place wherever there is know- 
 ledge and in as far as there is knowledge. If the question is 
 whether the process as described is necessarily involved in 
 knowledge or is a mere fact like any isolated fact, there can be 
 no answer except that the question is either superfluous or 
 meaningless. Of any particular logical theory, such as that 
 contained in the present work, it is superfluous to ask whether 
 it is in all respects necessary and absolute. Of course it will 
 contain many erroneous and many accidental elements. But 
 to ask whether a true account of the logical process would be 
 necessary and essential, or would contain mere fact or accident, 
 is simply to ask whether a true account may not perhaps be 
 false. All truth is necessary in as far as it is rationally known. 
 And if a scientific analysis were to lead to no truth at all, it 
 would simply lead to nothing. Whether in any particular 
 instance such a nothing may have resulted is a matter for 
 consideration on the merits of the individual case. But in 
 general I must protest that there is no more reason in asking 
 
introd.] Naming 7 
 
 what evolution of thought we are studying.^ than in asking 
 what laws of motion are studied by mechanical science. The 
 laws of motion express the characteristics of moving bodies 
 qua moving ; and the laws of knowledge express the charac- 
 teristics of knowing subjects qua knowing. It is no more 
 necessary to specify in what particular cases you find know- 
 ledge, than to specify in what particular cases you find motion. 
 If knowledge has a nature that can be studied t» — and if not, 
 there is no logic — it can only exist where that nature is realised ; 
 and however the progress of the race may have prepared the 
 intellectual inheritance which is devolved upon successive 
 individuals, those individuals can only make it their own by 
 fulfilling the conditions which constitute its nature. I do not 
 deny that the type and content of knowledge must change 
 with the advance of evolution ; I only affirm that any such 
 change depends on the modes and degrees in which the general 
 conditions of knowledge are fulfilled in successive generations 
 and not in any difference between knowledge in its essential 
 nature, knowledge as developed in the race, and knowledge as 
 a process within the individual intelligence. 
 
 4. To give a name is for civilised thought the first step in The act of 
 knowledge. It at once depends upon, and in a sense creates, ^'"^"g- 
 a recognisable arrangement of things, qualities, and relations. 
 Wherever new ground has to be appropriated, whether actually 
 or in metaphor, the first necessity is to find recognisable points, 
 by which, being named, we can observe and communicate our 
 whereabouts. 
 
 The value of this first step is only to be estimated by expe- 
 rience, now necessarily exceptional, of the attempt to attain 
 knowledge without it. We do not experience this simply by 
 going where a language is spoken that we do not understand. 
 
 * Genetic theorists say, if I understand them rightly, that it is mainly 
 or wholly the evolution of thought as an adaptation to social or external 
 needs. It is all very well to illustrate the stimuli of thought in this 
 way, but to restrict them in this way does seem to me ridiculous. There 
 is nothing in the universe of experience which cannot act as a stimulus 
 to thought. See ii, pp. 271, 275. 
 
 "Of course this does not mean 'studied apart from reality'. The 
 world of knowledge is one of the worlds of reality, organised according 
 to its law, under certain limitations. 
 
8 Introduction [Introd. 
 
 No doubt, in the long run, lack of communication with our 
 fellows would affect our reasoning power ; but we are now 
 looking for an instance in which we ourselves, within our 
 minds, have no names to aid us in distinguishing and recog- 
 nising things. We find such an instance in our attempts to 
 deal with any new region of knowledge of which we have 
 not mastered the rudiments and in which we have 
 neither books nor teachers to guide us. This is merely indi- 
 vidual ignorance ; but the great pioneers of knowledge must 
 be in the same predicament when, going beyond established 
 distinctions and taking note of new phenomena, they lay the 
 foundations of a fresh structure of science. Great discoverers 
 are able to add fresh names to language ; ordinary men con- . 
 tent themselves with learning the meaning of those in common 
 use. The limitations of popular nomenclature form the limita- 
 tions of popular observation. When we are brought face to 
 face with a scientific classification and the terminology it in- 
 volves, we are astounded at the blindness in which we had 
 contentedly been living. Every yellow ranunculus we call 
 a buttercup, every myosotis a forget-me-not, every large white 
 umbellifer a hemlock ; not merely as an epithet, but because 
 we really see no difference. So in the history of architecture 
 or of fine art, popular knowledge is confined for the most part 
 to the application of two or three terms which have gained 
 currency. Few people are able to observe without the help 
 of names. 
 
 It is true that there is something ludicrous in the tendency 
 of common minds to cling to a name ; in the insistence of an 
 inexperienced art-critic on superficial characteristics which 
 happen to be nameable, when he ought to be looking into the 
 special significance of a work of art ; in M. Jourdain's delight 
 at the discovery that he conversed in prose, or in the sudden 
 zeal of Strepsiades for the correct employment of the masculine 
 and feminine terminations. Nevertheless, the current censure 
 of verbal knowledge is itself largely founded on ignorance, and 
 actually on the same ignorance which creates the risk and 
 opprobrium of mere verbal knowledge. In the annals of 
 philosophy there is nothing more tragi-comic than MUl's 
 condescending excuse for Plato's discussions about related 
 
introd.] Naming 9 
 
 existence — discussions which laid the permanent foundations 
 of scientific logic ; the modem logician showing his superiority 
 to verbal quibbles by an attempt to dissociate existence from 
 attribution based simply and solely on the fact that existence 
 is sometimes expressed by a peculiar kind of attribution. The 
 condemnation of a knowledge which rests in mere words too 
 often means that the word and no more has reached the 
 understanding of the critic. It is probable that we think too 
 little rather than too much of Naming as a first step in know- 
 ledge. To give names which endure is with few exceptions the 
 prerogative of genius. The number of terms which we inherit 
 from Plato and Aristotle is among the most striking proofs 
 of the immense advance which they won for the human 
 intellect. These two great minds mapped out the world of 
 knowledge in its essential features much as we have it before 
 us now, and gave to its main divisions the names which 
 they still retain. Or, again, what a gigantic advance was 
 made by the work of Linnaeus, though it now serves as the 
 stock example of an ' artificial ' classification ! It was the 
 indispensable starting-point for the more profound and rational 
 researches of modern times, and thus if not one of the most 
 arduous, at least one of the most valuable, of scientific 
 achievements. 
 
 I spoke of Naming as the first step in knowledge /o;" civilised 
 thought. Plato recognised the operation much as we recognise 
 it. And yet there must have been a time when it was not easy 
 thus to isolate a single word from the sentence. Indeed, even 
 now, the single word is not really isolated. Except in the 
 instances in a logical text-book, the utterance of a single word 
 always implies a sentence, and usually a judgment. We now 
 print the title of a book or the description of a species of flower, 
 contrary to older custom, without a verb ; but none the less 
 they are read off into propositions or judgments. The artificial 
 nature of the supposed concept which is thought to correspond 
 to a name and to be generically other than a judgment is 
 curiously illustrated by the fact that Linnaeus was the first 
 to omit the verb in the descriptions of flowers. Such descrip- 
 tions, though in appearance reduced to logical names, are of 
 course understood as sets of judgments. No doubt however 
 
10 Introduction [Introd. 
 
 all these habits, including the use of dictionaries, familiarise 
 us at least with the appearance of the significant noun in 
 complete isolation from the sentence, and lead us to imagine 
 that in such isolation it is still a fair representative of some 
 individual object or quality (also isolable) in a way in which 
 the complete sentence is not. But I must repeat that under 
 no circumstances does a man in his senses make use of an 
 isolated noun, except to indicate an assertion, wish, or com- 
 mand. A dependent sentence, as its name shows, cannot stand 
 alone ; and a name is for grammar in this respect like some 
 form of dependent sentence. If a man were to say ' the sun ', 
 the difference between this and a given proposition like * the 
 sun is low ', is not that in the first case we have a mere name 
 and in the second a proposition, but that in the second case 
 we have a given proposition, while in the first we are set 
 to make propositions at random. The same is true of 
 any logical noun, i. e. descriptive or appositional sentence 
 — and a noun may, we shall see, be equivalent even to a 
 conditional sentence — ^such that it can stand as subject or 
 predicate in a proposition. No such sentence is ever used 
 independently ; for all thought, if not optative or imperative,^ 
 is categorical. 
 
 Thus it would seem that the isolation of the significant name 
 from its context, which is even now more apparent than real, 
 must in very early stages of language have been a wholly 
 unfamiliar process. The history even of proper names shows 
 a tendency to illustrate this ; though proper names for human 
 beings would be, one would suppose, among the earliest pro- 
 ductions of language. As we go back, we find the ' proper ' 
 name less purely distinctive, less ' proper ', and more significant 
 or predicative. The animal names borne by some savages 
 must be significant, though how or of what may be doubtful. 
 The Roman Agnomen and the Athenian Deme name were 
 directly significant, as of course are many modem surnames 
 in their recent origin. The addition of a name of father (also 
 husbcind or master) in the possessive case was not originally 
 
 ^ Whether optative and imperative forms can or should be analysed 
 into categorical propositions is a psychological rather than a logical 
 question. 
 
iNTROD.] Isolation of the Name ii 
 
 a mere appellation ; it was an assertion of ownership.^ It is 
 well known that among the Romans the gentile name {notnen) 
 was the name par excellence, as indeed for most purposes the 
 smname is now. It is less well known that the ' fore-name ', 
 which, if any, was individual, was not at all freely chosen to 
 serve as a distinctive sign ; it was characteristic of family, 
 and the choice was exceedingly restricted. Among all the 
 Roman patricians only about thirty * fore-names ' were in 
 use, and the ' fore-name ' of women was constantly omitted 
 in Cicero's time. It would be interesting to find parallels for 
 some of these features in modern usage ; a small number of 
 Christian names no doubt serves to name by far the greater 
 number of individuals in one country, and the selection of 
 Christian names is to a certain extent characteristic of families 
 or of family. But on the whole it is now admitted that the 
 chief purpose of a proper name is to be a name, i.e. a constant 
 sign, and even the surname, although significant in many 
 respects, is not really to be relied on as an indication of family. 
 The law lets a man bear what name he pleases and change it 
 as he pleases, so long as he makes his desire sufficiently well 
 known ; in other words, the law accepts no purpose in the 
 name beyond that of mere recognition. 
 
 And in the case of the common or significant name the same 
 thing is more evident. Even so highly modernised a language 
 as classical Greek has no imambiguous expression for ' a word ', 
 though ' noun ' and ' predicate ' or ' verb ' were familiar terms 
 to Plato and Aristotle. The latter has to describe a ' word ' 
 by the periphrasis, ' the least portion of discourse which is 
 significant when taken by itself.' The Greeks did not separate 
 their words in writing ; and in their inscriptions a terminal 
 consonant is affected by the following initial consonant, as it 
 would have been in a compound word. I do not think it is 
 fanciful to refer to these facts in illustration of the closer 
 cohesion of sentences in ancient than in modem speech. The 
 solvent of the sentence is obviously writing. You cannot take 
 
 * Mommsen, Romische Forschungen, vol. ii, p. 5. He shows good 
 ground for supposing that the original form was ' Marcus Marci ', used 
 equally of wife, slave or son, and that Marcus Marci filius (no correspond- 
 ing form was adopted in Greek) was a later modification. 
 
12 Introduction [Introd. 
 
 to pieces the spoken sentence as you can that which lies written 
 before you. If you ask an uneducated man about some one 
 point in what he told you, he will say it all over again. But 
 this enquiry hardly belongs to logic, though it helps to rouse 
 us out of the analytic abstractions in which we are now at 
 home. I only wished to guard myself against asserting that 
 the conscious selection of an individusil object and the appro- 
 priation to it of an element of language common to all sentences 
 in which that object is referred to — that this act of Naming 
 comes first in history as it does in modem science. It appears 
 to me that the descriptive sentence must have furnished the 
 material for a subsequent appropriation of names ; and that 
 the appropriation of names by habitual description must have 
 been quite a different process from methodically searching for 
 new ' points d'appui ' and fixing their appellations at one blow. 
 What the 5- The act of Naming implies in the first place ' Logical 
 Namine Significance '. i. A name then is a sign which rouses the mind 
 implies, to a set of activities having an identical element. In the 
 Logical purely artificial case, when a name is spoken in my hearing 
 can^e. without any context expressed or implied, such activities 
 may probably take the shape of interrogation or suggestion ; 
 i.e. as is commonly supposed (but see sect. 2, above), a review 
 of matters which we might employ in judgments, but do not 
 yet know how to, being unable to attach any of them to 
 our real world. The meaning of the name consists in its 
 power of suggesting and controlling these activities, these 
 judgments completed or inchoate. If, to return to the example 
 suggested above, I hear some one say ' The sun ', my first idea 
 is that the speaker is thinking aloud, and that I have caught 
 the fragment of a sentence which he has completed in his mind. 
 But with a view to logical theory we may neglect the speaker's 
 intention (though no theory should forget that it has neglected 
 this feature of the case), and simply consider what the word 
 does for the hearer. It makes him think of something, and in 
 this case of what is called far excellence a thing : had the word 
 been * red ', it would have suggested a quality ; had it been 
 ' parallel ', a relation. We have not to do just now with the 
 difference between these three kinds of signification, but only 
 with what signification is as such. In thinking of something 
 
iNTROD.] Logical Significance 13 
 
 without more guidance than a significant name, we find our- 
 selves involuntarily thinking not merely of it, but about it. 
 And this is inevitable. That which the name signifies is, for us 
 at all events, an identical character exhibited by different 
 contexts, or different contexts united by a common character. 
 Any one who has been told, by an old-fashioned mesmerist, 
 to ' think of nothing but ' a copper and zinc disk which is put 
 in his hand, and which he is expected to contemplate for some 
 minutes, must have found (supposing that he attempted to do 
 what he was told) that his thoughts traversed in a series of 
 judgments the various ways in which the thing affected his 
 perceptions, or reacted in the comparisons that suggested 
 themselves.-^ These judgments, if expressed in language as 
 propositions, would all contain the same name, that of the thing 
 which they described. But although connected with different 
 standards of comparison in the different judgments, the thing 
 spoken of in them all is not different things, but the same 
 thing. If you persevere and try to elicit the root and basis of its 
 identity, you may indeed fix more or less arbitrarily upon 
 certain ' essential ' attributes, but these attributes represent 
 the thing in different contexts, and are also themselves, as Mill 
 has explained,^ elements of identity between different contexts. 
 You may judge the thing to be round, hard, heavy, flat, cold, 
 and to be on the palm of your hand, and you may define 
 circular form, hardness, weight, etc. as you please ; but you 
 will not express either thing or attribute as other than an ele- 
 ment of identity which is exhibited and takes shape in different 
 aspects or relations. Mr. Bradley^ has pointed out that 
 
 1 I suspect that the particular mesmerist to whom I refer was in- 
 fluenced by the fallacy which has been combated in the text, and 
 imagined that to think continuously of an individual thing involved 
 an immobility of thought, as though the thing were for thought like an 
 image in space fixed and isolated. In attempting to attain such an 
 immobility (which attempt, on this hypothesis, the operator intended 
 to be made) the patient would simply arrest the operation of his intelli- 
 gence, and would thus approach to that withdrawal of attention from 
 all specific stimuli which is perhaps a condition of the mesmeric sleep. 
 How far this principle is connected with that of Braid's and similar 
 experiments, I am not expert enough to say. Cp. Lotze, Metaphysik, 
 sect. 304. 
 
 ^ See Mill's Logic, i. 201 (sixth edition). 
 
 ' See Bradley's Principles of Logic, p. 44. 
 
14 Introduction [Introd. 
 
 extension in space or duration in time are sufficient to invest 
 that which has them with the character of an identity into 
 which differences enter. This — an identical element which 
 enters into and is entered into by differences — is what we 
 might call the logical significance, the significance which must 
 be postulated in all cases, of a name as such. 
 
 The process of Naming, as known to our reflective thought, 
 is to adopt an individual element of language as the instrument 
 of intellectual reference to an individual identity in the know- 
 able world. The conscious adoption or appropriation of the 
 linguistic sign is the same thing in principle, whether the sign 
 is employed solely within my own consciousness, or is applied 
 to communication with other intellectual beings. The ' con- 
 vention ' ^ or agreement which has been said to give language 
 its meaning, would be the same thing between other persons 
 and me that the employment of significant signs is between me, 
 so to speak, and myself. It is as wonderful, and as much 
 a proof of ' convention ', i. e. of the power to agree, that 
 ' goodness ' should mean the same to me yesterday and to-day, 
 as that in this sentence it should mean the same to me and to 
 my reader. It may be said, and here we anticipate a difficulty 
 which must be treated later in this chapter, ' But goodness 
 does not mean quite the same to you and to your reader, or 
 to you at different times.' Then I will change the phrase and 
 substitute ' refer to '. It will be seen at once that if ' goodness ' 
 in my mouth and in yours does not refer to the same charac- 
 teristic, it is not intended to mean the same, and its meanings 
 however different cannot be conflicting. In that case the two 
 characteristics referred to are ' homonymous ', and the same 
 word goodness is used for them only by accident ^, as glass is 
 for a telescope and a tumbler. The point and purpose of 
 a name is, always to refer to the same ; it is on this reference 
 that the whole possibility of mutual intelligence depends. 
 The connection between isolated reference, or meaning, and 
 reference to a system, or affirmation, has been explained 
 above (sect. 2). 
 
 ^ A name is speech which has meaning according to convention (kotA 
 (TvvOfiKTjv). Arist. n^pt 'Ep/i7]vtias, sect. 2. 
 
 ' By accident as regards present use ; there may be a common history, 
 but this is rather a source of deception than of clearness. 
 
introd.] Rational Convention 15 
 
 Identical reference or rational convention is thus the root 
 and essence of the system of signs which we call language.^ 
 The act of Naming, i. e. of establishing such a reference, and of 
 appropriating a sign to it, has been elaborately analysed into 
 a number of processes or aspects. In my opinion such an 
 analysis should be regarded mainly as a mere analysis — as 
 a distinction of aspects and not as a history of acts. Historical 
 conclusions may flow from it ; but the analysis is the first 
 thing. We are here met by a difficulty which besets all the 
 higher sciences, and which I shall endeavour in the first instance 
 to grapple with in its general form. 
 
 ii. The distinction of stages in a continuous growth has Meaning 
 always a degree of artificiality. It is hard to say precisely pijgg - 
 when an embryo becomes a chicken, or a boy a man. It is 
 impossible to say at what point feeling appears in the organic 
 world, or when a child acquires a will, or a primitive tribe the 
 instinct of religion or of fine art. Characteristics which 
 attract general notice only when full-grown, are traceable far 
 back when we come to look for them ; and further, they are 
 frequently implied by the nature of an individual long before 
 any scrutiny can detect them. It is a cheap and false accuracy 
 to express such a growth in successive stages according to the 
 definite emergence of obvious features, without scrutinising 
 the continuous identity which is present from beginning to 
 end. But it is a fatal carelessness, on the other hand, to treat 
 rudimentary attributes as ipso facto equivcdent to their mature 
 form, or as necessarily identical therewith in the features of 
 chief concern. The labour of genuine science is to disentangle 
 the true continuity of processes, limiting it only by modifica- 
 tions which are certainly traced or inevitably implied ; never 
 assuming the existence of a highly developed attribute or 
 function where it is not seen in operation, or shown to be 
 
 ^ I can see no ground for restricting the logical conception of language 
 to written or spoken words. We must not argue from the possibility of 
 educating the deaf and dumb (cp. Lotze, Logik, sect. 6) that ' the logical 
 operation in the mind is independent of the possibility of linguistic 
 expression '. It is unfortunate that the German ' Sprache ' and 
 ' sprachlich ' make this inference appear a truism, while if we ask 
 whether the deaf and dumb can in thinking dispense with fixed signs 
 wholly or in part, the question, though still of interest, assumes a very 
 different complexion. 
 
i6 Introduction [Introd. 
 
 implied to the exclusion of all conceivable alternatives. In 
 fact, if ' conceivable ' means ' conceived up to a certain stage 
 of knowledge ', the last clause is not stringent enough ; a sus- 
 pension of judgment is often preferable to a conclusion from 
 disjunction which violates general analogy. Many complete- 
 looking disjunctions are imperfect ; and unless supported on 
 a thoroughgoing principle, a disjunction is worth nothing 
 at all. 
 
 It is hard to escape both the complementary blunders 
 which I have indicated, and the object of this digression is 
 to point out that though we may not escape them altogether, 
 their sting is removed if we are not too ready with our dis- 
 junctions, but discuss to the best of our power the principles 
 which underlie functions and attributes, and the consequent 
 limits and laws of their modifications. Have such and such 
 savages the instinct of fine art ? Probably Yes or No would 
 be no answer. We should find that they had some elements 
 or germ of such a tendency, perhaps the love of imitation, 
 or earlier still, the instinct of construction. Then we should 
 have to estimate the value of this and its connection with 
 aesthetic capacity ; and the correctness of our whole reading 
 of the facts would probably depend on the rightness of this 
 estimate. The act of naming presents such a problem. Does 
 Naming, for instance, imply the processes of Comparison and 
 Distinction ? Does it imply a Judgment, such as the Judg- 
 ment of Perception ? If we look at the activity of highly 
 reflective thought, we must unhesitatingly answer both ques- 
 tions in the affirmative. It is a serious matter to introduce 
 a new word into language, or to christen a new phenomenon 
 or a new species. All that science can do to verify and 
 determine is being done when, and is largely done before, 
 such an event occurs. Or if we go to the extension of the 
 individual's knowledge, which is to him a creation of new 
 appellations, the same holds good for kindred leasons. The 
 individual profits by the work which language presupposes, 
 and all sorts of apparatus is at hand by which he can put 
 himself through the processes, in learning a name, which the 
 discoverer went through before him in conferring it. This is 
 the one extreme of the growth we have to watch ; the extreme 
 
iNTROD.] Ohjectification 17 
 
 at which the function we are discussing has become an instru- 
 ment of conscious science. 
 
 iii. In speaking of the opposite and lower extreme, we have Objectifi- 
 to depend on analysis and implication.a Let us think of the ^^*'°"- 
 feature of reference, which we found to lie at the root of 
 intelligent speech. A name always refers to something. (I 
 must repeat that the idiomatic ' something ' is not to be taken 
 as meaning an individual ' thing ' in space.) I avoid sajdng 
 that it refers to an idea in the mind, because, unless the name 
 explicitly proclaims itself the name of an idea, it does noi 
 refer to an idea in the mind as such.^ When I use the word 
 ' red ' I do not refer to or mean my idea of red considered 
 as my idea, though I do mean red as I understand it by 
 help of my idea. When I use the word, I mean a colour, a 
 quality of surface, or at least of light, which I represent 
 to myself by help of one or more reds which I have seen, 
 but which I think of as not dependent either for being or for 
 quality on my happening to know it. The fact that my 
 perception of red may be abnormal does not affect this refer- 
 ence. As I pointed out above, if it were not for the identical 
 reference there could be no conflict, no question of normal 
 or abnormal. This, then, if no more, is involved in naming. 
 That which is named is recognised as having a significance 
 beyond the infinitesimal moment of the present, and beyond 
 the knowledge of the individual. It enters into the ' con- 
 vention ' which he who uses language maintains with himself 
 and with others. It is, in short, characterised as an object 
 of knowledge.^ Under this aspect the act of Naming has been 
 well called the act of Ohjectification. 
 
 Let us further consider what is implied in the act of Naming 
 considered as an act of Ohjectification. 
 
 iv. In the first place, then, the matter which is invested A positive 
 
 content. 
 
 ' These sections on naming and ohjectification would be very mis- 
 leading if they impUed that contents, e.g. of sensation, which have 
 never been named or 'objectified', are not objects, but mere subjective 
 states. But it is quite true that a sensation takes a different rank 
 in knowledge when it has been attended to and named. For the 
 relation of mental states to objects of thought see p. 69 below, and 
 ii, chap. X. 
 
 * See below, chap, i, sect. i. ' Cp. Lotze, Logik, sect. 3, 
 
 1337 n 
 
i8 Introduction [Introd. 
 
 with the attribute of being such as to be known — which is 
 thus ' objectified ' — must be something positive, something, 
 so to speak, of affirmative nature.^ It must be presentable to 
 consciousness by help of some actual modification of con- 
 sciousness. I mean that it cannot consist simply and solely 
 in the distinction between itself and something else. It is 
 one question how we come to perceive a certain content — 
 contrast and distinction may be essential to perception — 
 another what it has in it when brought into perception. It 
 may be — the question is chiefly psychological — that if red 
 had been the only colour we should never have been aware 
 of it as red. But now, being aware of it, we find in it a positive 
 quality or character which is not exhausted by the distinction 
 between it and all other colours. This is the primary condition 
 of the act of naming. That which is to be referred to by a 
 name, which is thus erected into an object for intelligence, 
 must be at least a positive content, something with a nature 
 and character. It is not safe to clinch the matter by saying 
 * definite nature ', ' determinate character ' ; for though 
 scientific naming involves all this, yet it would be overbold, 
 and would beg a question which we shall soon arrive at, to 
 presuppose all this for every act of naming. * Definite ' and 
 ' Determinate ' introduce negation into knowledge, and so 
 are not words to be used lightly. We must if possible keep 
 to one thing at a time, and what we are sure of at this point 
 is this, that the identity in difference which is referred to by 
 a name is something positive ; not necessarily a ' quality ' 
 in the technical sense of an immediate unrelated matter of 
 perception, but necessarily a something. 
 
 It is obvious that for the general purposes of logic such 
 meaning is not confined to substantive and adjective nouns 
 or names. A positive content is also referred to by the material 
 or uninflected element in verbs, if we may for logical purposes 
 distinguish this from the formal or inflected portion, which 
 indicates the connection and function of the verb as such. 
 When I say ' it flows ', of course in the element ' flow ' I use 
 a significant sign which refers to a positive content. Very 
 probably as we go back into primitive speech the distinction 
 
 ^ Cp. Lotze, Logik, sects, lo, ii. 
 
introd.] The formative elements 19 
 
 between this and the grammatical Name would disappear. 
 Aristotle certainly treats ' is white ' as a verb.^ 
 
 V. Here we cannot escape raising a further question. Meaning 
 Granting that pronouns used independently rank as nouns, of verb- 
 
 , cLUO. C3.SC* 
 
 still there remain inflected elements of verbs, the case-endings endings, 
 of nouns, adverbs, prepositions and conjunctions. Does not 
 each of these indicate an identity in difference, a positive 
 feature in the world of meanings ? Why are not they too to 
 be treated as names ? There is no doubt that the words 
 in question are fixed signs which refer to positive features 
 of the world ; nor that their contents are such as can have 
 names given them which can be employed in propositions as 
 substantives or adjectives. Presence in time or space. Intention, 
 Direction, Proximity, Property, Attribution, Reference, and 
 the corresponding adjectives, these are all intelligible names 
 and designate familiar matters. Yet they are but another 
 shape of such linguistic elements as ' Here ', ' Now ', ' For ', 
 ' To ', ' At ', ' Of ', ' About ', the s in ' flows '. 
 
 It would be easy to answer that these elements are signs 
 whose content consists in the actual operations of thought ; 
 that therefore they are not at first names, because we are 
 operating directly and not reflecting on the operations ; but 
 that they become names at the stage of reflection in v/hich 
 we become aware of the part played by our intelligence in 
 connecting and comparing the data of sense-perception. 
 
 But this would not be true. There are names for intel- 
 lectual acts, such as Comparison, Measurement, Enumera- 
 tion ; but these just show the difference between the opera- 
 tions themselves, and the results gained by them. ' Similar ', 
 ' Equal ', ' To of ', * Present *, ' Near ', are not mere signs 
 of operations performed by the individual intellect. We 
 
 ^ He distinctly treats the prjua as capable of indicating time. So his 
 idea of it did not quite cover our Predicate, which he would call to 
 KaTrjyopovfievov, though on the other hand we do not recognise 'is 
 white ' as a verb. It is remarkable that he should have insisted on the 
 indication of time in face of the fact (constantly borne out by his own 
 instances) that the verb ' is ' could be omitted in Greek, and predication 
 conveyed by position only. It seems, therefore, that to say the verb was 
 understood would have been no empty phrase to him, but would have 
 expressed the fact as he regarded it. 
 
 C2 
 
20 Introduction [Introd. 
 
 unhesitatingly treat them as characteristics of matters which 
 we meet with in the objective world. We find them out by 
 combination, comparison and measurement, but we treat 
 them as independent of the acts of our individual mind. 
 ' Present ' may create a difficulty, if we think of it solely 
 as present to us ; but it is obviously a relation predicable 
 and constantly predicated of objects or occurrences with 
 reference to any self-conscious subject. Indeed, all names 
 are signs of thinking operations, so that this would be no 
 distinction between names like ' equal', ' near', and names like 
 * warm ', ' painful '. 
 
 But it is true that the inflectional and formative elements 
 in question have this much in common with mere signs of 
 intellectual acts, that we use them in propositions before 
 we make propositions about them ; and that when we 
 come to make propositions about them we still have to 
 employ them in one form, in order to make propositions about 
 their other and abstract forms. And further ; like signs of 
 intellectual operations, they cannot exist by themselves ; they 
 are not intelligible unless put in connection with substantive 
 elements. You might say ' " Of " is not " For " ' in the 
 sense that a man's legal property is not morally for his sole 
 benefit ; but then the related points are supplied in inter- 
 preting. The proposition is not intelligible in the same 
 immediate sense in which ' Red is not Green ' is intelligible. 
 
 Thus the formative elements of language are not complete 
 names on the one hand, nor mere signs of intellectual functions 
 on the other. They are however significant, and significant 
 of matters which are capable of being named. But the 
 matters or characteristics which they signify are such as 
 to presuppose related terms, and to be incapable not merely 
 of being, but of being understood, apart from those terms. We 
 find these meanings or attributes therefore, in the first instance, 
 in explicit dependence on the simpler contents which they 
 imply ; and we only find them treated as nameable or isolable 
 contents at a stage of reflection which can supply the pre- 
 supposed simpler, contents in a typical form. Thus their 
 apparently subordinate position in the simpler classes of 
 judgment comes not from their being so little significant. 
 
Introd.] Naming and Distinction 21 
 
 but from their being so much. They indicate, not indeed 
 mere acts of mind, but the realised wholes which arise for 
 knowledge through those acts of mind. Their names are names 
 for such wholes, and for nothing less ; as expressive of a 
 special relation within an individual whole they are not names 
 but auxiliaries.^ 
 
 It is quite true therefore that the formative elements of 
 language imply acts of mind ; but not true that what they 
 indicate are mere acts of the individual mind, such as Judg- 
 ment or Comparison. 
 
 vi. So far we have spoken of Naming as involving Refer- Naming 
 ence or Object ification, and of Objectification as involving an ^^ction 
 affirmative or positive content. Are we obliged by these 
 conditions to treat Distinction and Comparison as essential 
 to the act of Naming ? When we refused to apply the terms 
 ' definite ' and ' determinate ' to the positive something 
 which constituted the identity that can be named, we did 
 so in order to avoid begging the question of distinction 
 and comparison. We felt sure however of one thing, that 
 a positive content is what makes distinction possible,^ and 
 cannot itself consist in a mere distinction from something 
 else. I am speaking all through of being as it is for know- 
 ledge ; not of the ontological, and to my mind, fruitless 
 question, how being can be apart from a consciousness. What 
 I say is, that we cannot see how the characteristic quality 
 of a colour should be supplied by the distinction between it 
 and all other colours. And if the process of distinction does 
 in fact make us notice all the features of something present 
 to perception, this is only because contrast, in this case, 
 invests those features with an interest which they might 
 equally have obtained in some other way. 
 
 Mere distinction is not the essence of naming. On the 
 other hand, distinction is implied in the purpose of naming. 
 
 ' ' Here ' and ' now ' are peculiar. As iraplying relation to the 
 subject which judges they carry their points of application with them 
 even in their first and direct use, and can be used as logical subjects 
 even in perceptive judgment ; while for instance ' at ' and ' in ^ cannot. 
 But ' here ' and ' now ' generalised into ' Presence ' drop the special 
 relation to the judging subject, and indicate a relation to any judging 
 subject. ' Cp. Lotze, Logik, sect. ii. 
 
22 Introduction [Introd. 
 
 I do not say that the implication is always apparent. But 
 the least reflection, the least practice in the use of language, 
 must bring it to the surface. We shall constantly have 
 occasion to speak of the interest or purpose * which is essen- 
 tial to all judgment. And it meets us heie on the threshold 
 of intelligence. Why do we name ? Why do we refer to 
 an identity ? What do we want with a set of signs ? To 
 give voice to our positive wishes and feelings, we may reply. 
 Doubtless, in the first instance. But this very giving voice, 
 this fixing on a something, is selection. It answers the question, 
 ' What do you want ? ' and is meaningless except as an act 
 of choice. If there was only one thing in the world, we should 
 not want a name except to distinguish between having it 
 and not having it ; or if we wanted no distinction, we should 
 want no name. And when we use a name, we ipso facto 
 select, because we omit ; and we omit on a plan and with 
 grounds, because a purpose guides us in selecting. 
 
 Therefore I should state the relation between naming 
 and exclusion or distinction, as follows. Reference or Objecti- 
 fication, as represented by Naming, carries Distinction or 
 Exclusion with it formally. I do not mean externally or 
 explicitly, but just the reverse. The act of Naming is in the 
 abstract an act of selection, though we may not at first find 
 it out. It is therefore selective or exclusive in form, but is 
 not so materially, in any special relation, till we use it for 
 that purpose. And how soon this happens, how soon and how 
 far a material value is actually given to the implied element 
 of exclusion, is a question rather of anthropological psychology 
 than of logic. In the very beginnings of human thought 
 (which I take as equivalent to thought aided by speech) it 
 may be supposed that the sense of distinction would be chiefly 
 represented by the effort to identify and fix under a name, 
 
 * I call attention to this phrase, which indicates the interest proper 
 to judgment — the interest of complete expression. It seems to me that 
 the error of not recognising that judgment involves an interest rests 
 with those who assume its subordination to some alien interest, e. g. that 
 of external action, see ii, pp. 246, 275. The whole of the present work 
 is based on the conception that judgment develops in accordance with 
 its proper interest and purpose, which of course includes as applications 
 of it all sorts and sizes of partial interests. 
 
iNTROD.i * Essentially relative * 23 
 
 and by the feeling of success when the desired result was 
 attained by such means. It is clear that such effort or success 
 would represent a rudimentary work of distinction, which 
 combats the difficulty of fixing the content and of finding and 
 adopting the sign. Or if the sign-system grows without 
 perceptible effort on the part of individuals, there is still the 
 interest to which I have alluded. The distinction of man 
 and woman or meum and tuum must, one would think, invest 
 some contents with negative determination from the very first. 
 
 On the other hand, even our reflective thought is per- 
 plexed when its attention is first directed to the mutual 
 implication of very familiar facts, which seem to have inde- 
 pendent being because so familiar. The essence of objects in 
 space may not be in distinction ; we certainly however tend to 
 underrate the importance of distinction in knowing them. And 
 when we come to negations such as those implied in conscious- 
 ness or morality, for instance mind and matter, sin and the law, 
 the degree in which essence seems to consist in distinction 
 surprises us at first. Distinction then is formally involved 
 in Naming ; but the degree in which it is realised as dis- 
 tinction between ' this ' and a definite other, and as essential 
 to the character of ' this ', is not determined by the mere use 
 of a significant sign. It may not be so realised at all. And 
 when it is so realised, it involves logical forms which go 
 beyond the Impersonal or other nuncupative Judgment ; 
 forms such as negation, disjunction, and classification. 
 
 There are indeed facts which are such as to be essentially 
 relative — {Kad' avrd Tipos ri) — a pregnant conception of Aris- 
 totle. And obviously all facts partake progressively of this 
 character as they are united with the whole of knowledge, 
 and as, in this process, their centre of gravity, so to speak, is 
 shifted outside them by their connection with larger systems. 
 We can scarcely understand a curve except as distinguished 
 from a straight line ; nor sin except as distinguished from 
 a good will. Nor can we know even red light or violet light 
 scientifically without including in the conception of each its 
 wave-length and degree of refrangibility or place in the 
 spectrum — a disjunctive knowledge which involves a number 
 of precise reciprocal distinctions. As thought grasps more of 
 
24 Introduction [Introd. 
 
 its object, the object takes more of this coherent character. 
 And in an object thus coherent, it may seem that distinction 
 or negation takes the place of affirmative nature. Straight 
 is the line which is not ciu-ved. Sin is the wiil which is not 
 good. Red is the light at the other end of the spectrum 
 from violet. Here we are in the region of the complicated 
 contents described above as relations. Distinction has here 
 a value which it had not before, but it is not mere distinction 
 or mere negation. The distinction is valuable for its positive 
 ground, and the negation for what it affirms. The point is 
 not that the essence of a fact can be given by mere distinction, 
 but that positive matter finds it necessary- to take the shape 
 of distinction and negation. I shall retiu^n to this subject in 
 treating of negation and disjunction. The distinction from 
 straight is the essence of curve, only because or as far as the 
 positive spatial nature of line and direction is involved in 
 straight ', and this same spatial nature is also involved in 
 the opposite curved. It is not really that ' Not straight is 
 curved '. but that ' Whatever is a line and not straight, is 
 curved '. It is the nature of space, as kno^^'n in line, and in 
 constant and varWng direction, that forms the positive 
 content of both determinations. 
 
 Thus it is never true in the plainest sense that a thing or 
 matter of fact has its essence in mere distinction from another; 
 but it is true, as we shall see more fully, that all reality is so 
 entangled and intersvoven, or rather is so coherent in each 
 of its several regions, that in mastering the positive essence 
 of one fact we are forced to master that of many more, all of 
 them being branches of the same stem. Even in the simplest 
 cases there is at least an element of content common to the 
 facts distinguished, like the stem up to the parting of the 
 branches ; and every distinction made between them has this 
 at least for its positive content, as in distinguishing red from 
 violet we imply that both are light. But no doubt in more 
 intricate cases, the alternative or alternatives may be essential 
 to their subject ; and in that case the metaphor of the tree 
 breaks do\\"n, for the nature of the whole is such that one 
 branch perhaps cannot be seen, or perhaps cannot exist, apart 
 from the perception or the existence not merely of the stem 
 
iNTROD.] Comparison, or Identification 25 
 
 but of the other branch. Still we must think of the positive 
 nature of the whole revealing itself in this peculiar form (say 
 the nature of a mojal being revealing itself in the good and bad 
 will) ; mere distinction or negation is no characteristic at all. 
 
 Distinction then is involved in the purpose and essence of 
 naming, but primarily as a consequence. Meaning, or the use 
 of names, is never mere distinction ; though proper names 
 are used for the sake of mere distinction, and so with no care 
 for positive meaning except as subservient to that end. And 
 though in the deeper grasp of reality Distinction, Exclusion 
 or Negation comes to be an active and prominent property 
 of fact, yet this exclusion depends for its value always on its 
 positive ground or motive, and never, as such, constitutes 
 the essence of anything. 
 
 vii. And what is true of Distinction is true of Comparison, Naming 
 or rather, as I shall use the terms in future, of Identification, ^^^j^^^"^" 
 Formally, in the light of analysis, and in respect of purpose 
 and interest, to use or give a name is Comparison. For it 
 is identification, the establishment of an identity which holds 
 good in spite of differences. We may illustrate by the German 
 word ' Vergleichung ', which is usually rendered ' comparison ', 
 and which seems to be used in logic (I am not speaking 
 philologically) to mean the establishment of a ' Gleichheit ' 
 or immediate identity between the terms compared. This 
 applies — cannot but apply — to the use of names as we have 
 described it. But if we take Comparison at the other extreme 
 of its meaning, which ' Vergleichung ' shares with it, we 
 must say that it is a distinct reflective operation, which 
 presupposes naming and is not implied in naming. Com- 
 parison par excellence is a process which starts from the 
 content of recognised names, and reacts upon it with a view 
 to the interest which may have provoked the operation. 
 Ultimately as a scientific method, it involves measurement, 
 and is the instrument of classification ; whereas the use of 
 names must be prior to number or measure, and classification 
 as a method of science arises so late that its genesis is almost 
 within our ken.^ 
 
 ^ In Western thought, it was probably first analysed and its import 
 pointed out by Plato. In practical life it must have arisen in the earliest 
 
26 Introduction [Introd. 
 
 It would be easy to say, in the tone which I deprecated 
 above, that Identification as a method of science presupposes 
 Distinction, and therefore is a process naturally later than 
 Distinction, and not to be looked for concurrently with the 
 latter in the earlier stages of knowledge. But this would be 
 merely a commonplace blunder. It would be as easy to 
 show that Distinction presupposes Identification, as that 
 Identification presupposes Distinction. Before you can dis- 
 tinguish colours as red and green, you must identify them as 
 coloured surfaces ; and before you can identify the surfaces 
 in respect of colour, you must distinguish them as separate 
 areas in space. We can come to no good result in this way. 
 We are merely pointing out, not any special relation between 
 Distinction and Identification, but that every level of reflec- 
 tive observation presupposes a previous level on which it 
 improves. How do we begin then ? It may be hard to say 
 how matters get into consciousness, but all that is in con- 
 sciousness seems to present both difference and identity. 
 And we shall find how closely they are connected, and reveal 
 the true relation of Distinction and Identification in the 
 germ of knowledge — the act of Naming — if we look closer at 
 the nature of. Comparison itself, taking this as a process which 
 may end either in- Distinction or in Identification. 
 
 If, in order to effect a comparison, we trace two shapes, 
 say the shapes of two leaves, one upon the other, it is clear 
 that we shall have a repetition at every minutest step of what 
 takes place in the act of naming. Coincidence, deviation — 
 curve and straight — ^jagged or uncut — ^notched or entire ; the 
 discrimination of universal characters like these, with, if worth 
 while, accurate measurement of differences, will mark the 
 process as it goes on. In respect of each of these points we 
 may infer an identity or a distinction ; we express an identity 
 by a single judgment, either ' The outlines coincide ' or ' Both 
 outlines are slightly serrate ' ; a distinction either by the 
 single judgment, ' The outlines are different ', or by the two 
 judgments, ' One outline is serrate and the other simple '. 
 We should notice that if any portions of the two outlines 
 
 society by the effect of social rules ; see above on distinction. Exogamy 
 is an instance of an early custom which operates through classification. 
 
iNTROD.] Complementary aspects 27 
 
 absolutely coincide, we can only predicate identity of them 
 within that portion by bearing in mind the ideal continuity 
 of that bit of line E C with the two differing out- 
 lines E C F and E C A. If we leave this out of 
 account, judgment and identity disappear. Hence 
 it seems to follow that complete comparison must 
 always resolve the terms compared, in the respect 
 in which they are compared, into cases under a ^ ^ 
 universal, or differences within an identity. Identity without 
 difference, or difference without identity, destroy the meaning 
 of comparison. It is for this reason that the single judgment 
 will not contain a complete comparison. We shall see that 
 a disjunctive form is really required. But it is true that the 
 conclusion in these processes moulds its result into apparent 
 opposition to its starting-point, or rather, causes us to read 
 into the starting-point the complementary aspect to that 
 which is proclaimed in the result. This is simply because 
 the result is a modified form of one element in the starting- 
 point ; of the identity if it is an Identification, of the differ- 
 ence if it is a Distinction. The complementary element is 
 thrown into relief by the explicit exhibition of the new deter- 
 mination, so that Difference always seems to be predicated of 
 Identity, and Identity of Difference. But really the judgment 
 has done nothing more than to develope further either the 
 identity or the difference of the datum. ' X and Z are like ; ' 
 here we take X and Z as distinct objects, though we know 
 well enough that if they are like, they were comparable. 
 ' X and Z are different ; ' here we take X and Z as instances 
 of some class or rule and so far identical, though we know 
 that if they are different they were distinguishable. ' " Sorrow " 
 and " Sorry " have quite different et5miologies.' ' " Sorrow " 
 and " Sorry " have the same meaning.* The former pro- 
 position assumes sameness of meaning, in spite of which it 
 asserts difference of etymology ; the latter starts from a differ- 
 ence of form, perhaps intensified by a difference of etymology, 
 in spite of which it asserts identity of meaning. And yet the 
 former also treats the words as two, and the latter as prima 
 facie the same in their significant part. 
 
 I do not think that distinction can be effected except by 
 
28 Introduction [Introd. 
 
 developing differences which are presented, or identification 
 except by developing an existing identity. But of course 
 either element may be very faint at first. It is of no use to 
 say that we may be artificially set to search for distinctions. 
 No motive will help us in science unless it guides us ; and if 
 it guides us to a distinction, then it contains the distinction 
 in germ. The same is true in searching for identities. Thus 
 it would be hopeless to distinguish the two sodium lines in 
 the spectrum while they look single as a small instrument 
 shows them. And we could never distinguish Ricardian 
 rent from common farmer's rent (e.g. including interest 
 of capital) except by pressing home the differences which 
 are given with, and in, the two kinds of cases. This, like 
 many considerations in logic, will help us to understand 
 the childishly tardy progress of early intelligence, and 
 the cumulative rapidity with which knowledge generates 
 knowledge. 
 
 Naming then implies some degree of Distinction and 
 Identification. These two processes might, as we have seen, 
 conveniently be included under Comparison. But Com- 
 parison, Identification, and Distinction, as involved in naming, 
 are not the developed methods of which I have spoken.^ 
 In developed knowledge their organa are measurement and 
 counting, in which it becomes mere pedantry to separate 
 Identification from Distinction.^ I shall return to this point 
 in speaking of the value of Judgments, and shall there treat 
 the eeirliest distinct judgment of Comparison as the transition 
 to number and measurement. But the keyword of mere 
 naming is Recognition ; and this is the limiting purpose of all 
 functions qua subservient to naming. And as regards the 
 affinity between Distinction and Identification, they are 
 obviously two sides of the same process, and it is idle to ask 
 which came first. So far as we can see. Consciousness, or at 
 least Intelligence, must begin with both. 
 
 * See further Book II, chap, i, on ' Immediate Inferences '. 
 
 * I mean that it is pedantic to restrict measurable identity to the case 
 of absolute equality, but that if you do not, you must admit a degree of 
 distinction to be present in all cases. A distance of 400 miles and 
 another of 400 miles i yard are as we say ' the same to a yard ' ; and 
 this is the true way of putting it. 
 
iNTROD.] Succession of logical activities 29 
 
 6. Enough has already been said to make clear my general Concept 
 view of the growth of logical fmictions. While I would spare ^q^I^ ^' 
 no pains to ascertain the precise order in which and differentia 
 with which logical activities make their appearance, I have 
 never been able to doubt that the central function of the 
 intellect, I would even say of consciousness, is one from 
 beginning to end.^ In speaking, therefore, of the connection 
 between impressions and ideas, and again between ideas or 
 concepts and the judgment, I am obliged to reject the easy 
 partition into distinct operations which finds place in many 
 text-books.a More especially, I cannot at all follow Lotze in 
 his treatment of this connection, and I select his work, as 
 probably the most permanent in value of those which adopt 
 these views, to comment upon when comment is necessary. 
 
 As I read Lotze, the act of Naming coincides with that 
 shaping or moulding of an impression which is required to 
 convert it into an idea, as a stone requires shaping to make 
 it fit for use in a building. And then, subsequently, the 
 ideas so shaped are fitted together, and the result, I suppose, 
 is a concept ; while it is not till the simpler concepts come to 
 be combined that the judgment takes its rise. Ideas, it will be 
 observed, are thus subsequent to impressions, concepts to ideas, 
 and the judgment is subsequent to the simpler concept. 
 
 It is worth while to notice the nature of the analysis by 
 which this account is defended. Impressions must be shaped 
 like stones before they can be fitted together.^ Judgments 
 must presuppose at least simple concepts,^ because judgments 
 consist of concepts, and if such concepts presuppose judg- 
 ments, where are the concepts to come from which make up 
 these latter judgments ? It is hard to think that such argu- 
 ments as these really expressed Lotze's mind ; they must 
 rather have resulted from over-eagerness to present a perfectly 
 clear arrangement to his readers- The thought of a germ 
 which unfolds differences, of the elementary sensation as 
 
 * Cp. Bradley, Principles of Logic, p. 455 ff. Mr. Bradley's views on 
 this question have influenced mine, but rather in the way of moderating 
 than of suggesting or intensifying the view adopted in the text. 
 
 * See Keynes, p. 8, and my Preface to Ed. 2. 
 
 * Lotze, Logik, sect. i. * Ibid., sect. 8, 
 
30 Introduction [Introd. 
 
 already containing, in the features which make it a state of 
 consciousness, rudimentary distinctions which are shadowy 
 at first but receive form and fixity by degrees, — such con- 
 ceptions seem at once to destroy the application of argmnents 
 drawn from mechanical processes. If metaphors are indis- 
 pensable, we should rather call to mind such processes as the 
 formation of structure in an embryo, as the separation of. 
 a double star by successively higher powers of the telescope, 
 or indeed as the discernment of features in a distant landscape 
 which prolonged attention even without optical assistance 
 has the power to effect. 
 
 And, though the suggestion is hazardous, I cannot but 
 think that Lotze allowed himself to confuse change as process 
 in time with the rectification of error in knowledge.^ There 
 is nothing whatever in the concept or idea, as Plato thought 
 of it, to interfere with its expressing the laws of process in 
 time. The constitutive equations of curves, read in con- 
 nection with the law of gravity, have, so far as we can see, 
 precisely fulfilled one of the grandest aspirations embodied in 
 Plato's view of science, the establishment of the true laws 
 of motion as they are in general, and not solely or specially 
 for the heavenly bodies.^ And these equations are the in- 
 stance which Lotze gives of the highest order of concept? 
 Such a concept or idea embodies the very essence of process 
 in time, or change. It is true that change is also a principal 
 vehicle of indications that our concepts are erroneous, and 
 therefore often requires them to be changed, but this is not 
 because the concepts are concepts, but because they are 
 wrong. It is wholly an illusion, founded I presume on the 
 doubtful idea that predication involves reference to time, or 
 even that the judgment is a transition in time, to suppose 
 that the judgment as such can represent change or ' Becom- 
 ing ', while the concept cannot. To make this in the least 
 probable it would be indispensable to confine the judgment 
 to narrative judgments which use tense, and thereby to 
 abandon all scientific knowledge. 
 
 I cannot but think that the reasons alleged by Lotze for 
 
 * Lotze, Logik, sect, 34. * Plat, Republic, 530-1. 
 
 * Lotze, Logik, sect. 117. 
 
iKTROD.] Judgment and its parts 31 
 
 the transition from Concept to Judgment are wholly vision- 
 ary ; and merely conceal the mireality of the entire arrange- 
 ment which made such a transition necessary. There is 
 truth, indeed, in the remark that the judgment reconstitutes 
 the concept with a reason ', but is there any possibility that 
 the act which reconstitutes the concept is fundamentally 
 other than that which constituted it at first ? 
 
 I will summarise the criticism which I think essential on the 
 whole point of view indicated by the ordinary successive 
 arrangement, and especially by Lotze's form of it. 
 
 If a Sensation or elementary Perception is in Consciousness 
 (and if not we have nothing to do with it in logic) it already 
 bezirs the form of thinking. I will not say that it is a rudi- 
 mentary judgment ; but it is certainly an act, for it is a change 
 within a percipient subject ; it has identity in itself, or it could 
 be nothing for consciousness, and difference, or it could not 
 have identity ; and it stands out against other elements of 
 the momentary consciousness in a way that approaches to an 
 attribution. An Impression or sensuous idea becomes a logical 
 idea when it is fixed and referred ; — fixed and referred if we 
 like to say so by receiving a name, though this is rather a sign 
 of the act than the act itself .» We have here the explicit form 
 of judgment given to what before must have been a mere 
 actual extension of sensations by idea, depending on a general 
 identity, but not consciously referred to an identity other than 
 the sensation as an object.^ 
 
 Judgment is not, in relation either to impressions, ideas or 
 concepts, a mechanical combination of parts Avhich remain 
 outside each other. It is an expression — perhaps at bottom 
 the only expression — of the imity in which consciousness con- 
 sists. I do not mean that it is nothing more than an idea or 
 impression ; but I incline to think that it is better described 
 as an idea or impression writ large than as a combination in 
 which ideas or impressions are units. Judgments may contain 
 
 * Cp. p. 1 7 above, note a. We listen at night, half awake, to a sound 
 which we do not at first identify, and then name it by saying, ' Surely, 
 a motor standing still.' 
 
 ^ In Ed. I the words ran, ' than the psychical image.' But there 
 would be no discrimination of a psychical image at the stage we are 
 speaking of. 
 
32 Introduction [Introd. 
 
 complex ideas, but every Judgment qua Judgment exhibits the 
 content of a single idea. Ideas and Impressions, as I have 
 tried to show above, are not found lying apart as words lie on 
 a page, although, by a reflective abstraction, we can regard 
 them as so lying apart, and when thus regarded they form the 
 world of meanings or of objective references — the identities 
 symbolised by logical ideas. 
 
 We have then Judgment or some analogous operation of 
 Consciousness, from the first ; ^ and in naming and all subse- 
 quent operations we certainly have Judgment. What we are 
 watching all along is the development of an act, a function. 
 
 Thus Judgment and Idea go pari passu. An Idea is not 
 presupposed by Judgment any more than vice versa. And 
 it is, as I have explained, an extraordinary confusion to 
 account for the advance from concept to judgment by the 
 inability of the concept to represent change. 
 
 And indeed the whole question of advance from concept 
 to judgment is meaningless to me, for I think of the concept 
 as existing only in the act of judgment. I have tried above to 
 explain the deception which language practises on us in this 
 respect. The question is not easy, and is all-important. I shall 
 therefore return to it for a moment. 
 
 If a man were to say in our presence ' The Sun ' and no 
 more, we should either suppose that he meant ' The Sun is 
 visible ', or, if circumstances excluded this interpretation and 
 furnished no other, we should turn upon him sharply and ask, 
 * Well, what about it ? ' This implies that the words have 
 conveyed a meaning to us, but that the meaning is incomplete. 
 I will speak of the second point first. It may be said that our 
 impatience of the incompleteness of the thought is ethical and 
 not logical ; that it arises from annoyance at the waste of an 
 intellectual effort, or at the interruption of other thoughts, 
 seeing that nothing is to result from it ; and not from any 
 inability to think the thing ' sun ' by help of our idea of it, 
 without judging. 
 
 This explanation would have much truth, and only needs 
 pushing further. We should in such a case miss the ethical 
 
 ^ Cp. Bradley, p. 455 ff. And see below, Book II, chap, i, on the 
 lower limit of Inference. 
 
iNTROD.i What is a tentative judgment ? 33 
 
 purpose which all thought implies. But this defect would 
 have a logical side, which would be this ; that we should be 
 started upon an intellectual exercise not only objectless, but 
 also and for that reason endless. Thus the meaning is incom- 
 plete because undetermined. We are left to traverse an 
 indefinite series of judgments. 
 
 And yet (I return to the first point) a meaning has been 
 conveyed. In what shape does it exist ? The natural answer 
 would be that an incomplete meaning must exist in the shape 
 of questions or suggestions — of tentative judgments. But 
 a tentative judgment lacks, it would seem, the differentia of 
 a judgment. It does not assert, it does not claim truth. 
 Therefore we have prima facie in the idea or conception some- 
 thing that will not go into the form of the judgment. An idea 
 in this stage seems to be in a position corresponding to that 
 of a relative or dependent clause or clauses without a principal 
 clause ; a form of language which certainly can exist, but 
 which has not an independent right to existence. Or it may be 
 taken as corresponding to a question. ' The sun, around which 
 the planets revolve, which is hot and bright ; ' ' The battle — 
 lost or won ? ' These instances give different cases. In the 
 former the attributes are all constant, and we might if we 
 chose say that we first judge, affirm certain attributes of 
 a thing, and only leave it undecided what attribute is in 
 question here. If this was so, we should have something like 
 a disjunctive judgment. In the latter case, that of the ques- 
 tion, the form of sentence is considered absolutely to exclude 
 a judgment, although we have assumed the material for 
 a disjunction to be furnished by the prevalent interest of the 
 moment. What is the thought corresponding to a question ? 
 I do not find any sufficient discussion of this subject in the 
 logic books.^ 7s a question a peculiar act of thought at all, 
 putting language aside ? The test for this is to see whether 
 we can genuinely ask ourselves a question, or whether it is, 
 
 ^ Cp. Bradley, Principles of Logic, pp. 13-14. His treatment is 
 definite though brief, and I cannot agree with it. I cannot think it 
 possible that the content of a doubt or negation should be the same as 
 that of the corresponding affirmation. Cp. Sigwart on the Question, 
 Logik, i. 231. Eng. Trans, i. 177. 
 
 1337 D 
 
34 Introduction [Introd. 
 
 like a lie, only a form of speech which has the object of pro- 
 ducing a certain effect on others. I am disposed to doubt 
 whether we can interrogate ourselves. It appears to me that 
 a question directed to oneself for information which one has 
 is always rhetorical, is a concise summary of the interest which 
 the information has for us. But we too often have to ask 
 ourselves questions which we cannot answer, and know that 
 we cannot answer. I do not see how these, again, can be 
 genuine questions. While in the former case we know the 
 answer already, in the latter we know that there is at present 
 no answer possible. A question addressed to another person 
 in such a case, i.e. knowing that he cannot now answer, has 
 not the differentia of a question ; it is a mere guide to him as 
 to the information which we wish to possess, a memorandum 
 for future use when he may have the information. But, if we 
 are speaking with ourselves, this leads to the former ground of 
 rejection ; the question becomes, as before, merely rhetorical. 
 And thus there is not even a prospect of genuine self-question- 
 ing ; to treat oneself as another may react powerfully on the 
 imagination, but is impossible in strict thought.^ 
 
 Thus a question cannot be an act of thought as such, just 
 as a lie is not, and for the same reason, that it is not an attitude 
 that the intellect can maintain within itself. A question is not 
 merely doubt ; nor merely doubt plus the knowledge that the 
 doubt can be resolved in a particular way. It is a demand for 
 information ; its essence is to be addressed to a moral agent, 
 not ourselves, in whom it may produce action. It is closely 
 analogous to the imperative, which also cannot be addressed 
 to ourselves except by mere metaphor. Thus to say that the 
 mere mention of a name leaves us questioning or fills us with 
 questions, is not to say what it does for thought. 
 
 I suppose that the thought, on which a question is based, 
 must always partake of the nature of disjunction. Where the 
 interest lies wholly on one side of the alternative this is hardly 
 noticeable, ' Are you going to see Hamlet ? ' We scarcely 
 think of the possible negation as an alternative at all, but rather 
 
 * I now think this is nearly true, but overstated. It seems to me 
 a mistake of principle to deny that a man can have social relations with 
 himself, see p. 14, above. 
 
iNXROD.] Question and Disjunction 35 
 
 as a bare nothingness, a rejection of the idea proposed in the 
 question. A more difficult case is ' How much did you give 
 for that horse ? ' In this case, as in asking ' Where ' or 
 ' When ? ' we assign the general principle of the Disjunction 
 under which the answer is to fall, instead of selecting an 
 alternative and demanding information about it. 
 
 I should therefore be inclined to think that when a man 
 says ' The battle ' — and then stops, and we ask ' Lost or won ? ' 
 our thought is really a disjunctive judgment with reference to 
 which we express a desire for an action ab extra that will enable 
 us to accept one of the alternatives. The same result follows 
 if we describe an act of thought as doubting. It is impossible 
 to doubt without knowledge, and a definite doubt, apart from 
 a moral or religious sense of the term (for a degree of failure of 
 will may pass for doubt in these spheres) is unquestionably 
 a disjunctive judgment. 
 
 And if now we return to the case of the sun and its constant 
 attributes, we may find that a similar account is possible. 
 The speaker has uttered what is the equivalent of a dependent 
 sentence ; he sets us judging in distinct affirmations about 
 reality which form our resources for estimating what he can 
 mean (or suppose we judge about his mind, it is no less true 
 that we judge), and the indefinite series of these affirmations 
 may be treated as an imperfect disjunction. It makes no 
 difference whether we conjecture as to his meaning or as to 
 the fact which may underlie it ; whether we think ' He either 
 means the sun is just visible, or that it is hot, or — ', &c. ; 
 or again, simply, ' Either the sun is just visible or,' &c. 
 
 Such judgments are prima facie substantive or independent 
 judgments. But if it is our express purpose to regard what 
 has been communicated as nearly as we can in the light of 
 a mere idea, mere concept, or mere possibility, then we must 
 be taken to affirm the universal mecining which pervades these 
 judgments to be true of Reality under specific but unknown 
 conditions, amode of affirmation which we shall find to be the 
 essence of the problematic judgment. Such a point of view as 
 this is rendered inevitable, in the case supposed, by the 
 absence ex hypothesi of any ground for restricting our affirma- 
 tion to any special element of the universal content, unless, as 
 
 D2 
 
36 Introduction [Introd. 
 
 in the example of the question about a battle, a determinate 
 or partly determinate disjunction is provided by the context. 
 A mere idea then as distinguished from a judgment, but con- 
 sidered as the mere meaning of a name or as an objective 
 reference in the world of meanings — an isolated idea — is the 
 content of a reflective problematic judgment, and is referred 
 to reality as true under unknown conditions or among unknown 
 alternatives. But every idea has its existence in the medium 
 of judgment. 
 
 The judgments which embody ideas may have many 
 degrees of unity. The identity which pervades a set of judg- 
 ments may be quality, thing, or complex attribute. When 
 the identity is a quality the judgments in which it appears are. 
 but slightly connected, and one member of the group will not 
 necessarily be accompanied, opposed, or conditioned by any 
 of the others. In the case of groups of not very coherent 
 attributes, such as form concrete things in space, the result is 
 exceedingly curious, and it is very doubtful whether the judg- 
 ments into which the thing enters should be treated as single 
 rather than as multiple. For the judgment which is made is 
 often related to the others which the identity binds to it, not 
 as consequent to conditions or grounds, nor as conclusion to 
 premisses, but as if joined with them either by a copulative 
 or even by an adversative conjunction. ' The strongest men 
 were afraid of him,' i. e. The strongest men, though much 
 stronger than him, yet were afraid. Or, The strongest men were 
 very much stronger than him ; and yet, &c. Or, again, The 
 Venus of Milo is in the Louvre ; in this any number of judg- 
 ments may be supplied out of the subject, and linked by 
 a mere ' and ' to the one given. There are all degrees of con- 
 junction ; it is well known that even ' and ' may carry either 
 adversative or inferential meaning. But where it carries pure 
 conjunctive or pure adversative meaning, there must be 
 a question how far the proposition represents a single judg- 
 ment. It is from this ambiguity that the judgment is freed 
 by assiuning the hypothetical form. 
 
 To analyse these degrees of unity here, under the head of the 
 concept, would be superfluous. The whole work of logic is to 
 depict them in the order of judgment and inference. 
 
iNTROD.] Petrified Concepts 37 
 
 It should be mentioned that there is unquestionably a re- 
 action of judgment on the actualimage or appearance presented 
 to perception. No doubt, all arrangement in space has been 
 learnt, but I take it that the disposition of points on surfaces 
 perpendicular to the axis of the eye, even if a result of inter- 
 pretation applied to feelings of motion, is when once learnt 
 an inevitable process, for every detail of which there is a special 
 distinct sense-stimulus. On the other hand, in the perception 
 of depth it appears to me that we have a generically different 
 case. The interpretation of certain dispositions of colour, 
 and of certain feelings in the ocular muscles, to mean ' if 
 I want to touch that point, I must put my arm out as far as 
 I can ' — this would cause me no surprise, and would simply be 
 knowledge brought to bear on perception, just as it is when 
 certain appearances indicate that one has food or poison 
 before one. What is noticeable in the case I now speak of, is 
 that the interpretation reacts on the image, that we seem to 
 see depth exactly as we see height and breadth ; and that, in 
 learning to draw, the counteraction of this interpretation, and 
 the reduction of objects to their places on a plane surface is 
 a matter of extreme difficulty. The solid images in which 
 a mere interpretation is thus made visible as a fact, do realise 
 the popular notion of what I might call a petrified concept, 
 a group of attributes and relations which stands still to be 
 looked at.* Ultimately, however, even this petrified concept 
 is a judgment — a perceptive synthesis. 
 
 I will recapitulate our results so far : — 
 
 i. Naming, or the appropriation of fixed signs for meanings, 
 always marks a first step in the thought which acts so ; 
 scientific naming e. g. marks a first step in a region of science, 
 though a late stage in the history of the human mind. 
 
 ii. The formative elements of language are significant, but 
 qua formative elements are not names, because their meaning 
 is incomplete without that of other elements. At a later stage 
 of reflection names are assigned to their entire significance, 
 that is, to the classes of complex wholes which they imply. 
 
 iii. A name has meaning only in a sentence or by suggesting 
 a sentence. The sentence is the significant unit of language. 
 * See further, ii, p. 292. 
 
38 Introduction [Introd. 
 
 This is most easily seen in ancient speech, but is equally true 
 of modern and analytic tongues. Dependent or appositional 
 sentences can enter into names. It is probable that the 
 thought corresponding to a sentence is always assertory, if not 
 optative, or imperative. 
 
 iv. Naming involves Objectification — the treatment of that 
 which receives a name as an object of knowledge, as recog- 
 nisable, that is, in a world which exists for all thought as such, 
 and is not dependent on the thinking of the individual mind.*^ 
 
 V. Objectification involves being as a positive somewhat on 
 the part of that which is to be treated as an object of know- 
 ledge, but this does not amount to the exhibition of a ' definite ' 
 and ' determinate ' nature. 
 
 vi. ' Being as a positive somewhat ' includes in a formal 
 sense being known by Identification and Distinction, which 
 are the two sides of Comparison. But as processes of real or 
 material import, these methods presuppose number and 
 measurement, and are posterior to fixed names. 
 
 vii. That which is named is always an identity in difference, 
 and must disappear if either element is neglected or removed by 
 abstraction. This is illustrated by the relation of names to 
 sentences. 
 
 viii. Every name refers to such an Identity treated as an 
 object of knowledge, whether thing, quality, or relation. 
 
 fx. The meaning of every name is in what it refers to or 
 is meant to mean ; but this is represented to the individual 
 intellect by the significant idea which the name causes it to 
 produce. 
 
 X. An idea or concept is not an image, though it may make 
 use of images. It is a habit of judging with reference to 
 a certain identity. 
 
 xi. There is no correspondence between Concepts as such 
 and Quiescence, or between Judgments as such and Change. 
 As the fundamental form of Knowledge the Judgment tends to 
 overcome change, and to view phenomena sub specie aeferni- 
 tatis, and is in this respect at one with the Platonic ' forms '. 
 
 * This is not the transformation of a subjective state into an object. 
 ' Subjective ' states only become ' subjective ' as the objective world 
 developes for consciousness. 
 
iNTROD.] Work of the individual Mind 39 
 
 xii. The giades of unity and complication of ideas and 
 concepts are the same as those of judgments and arguments.- 
 
 xiii. The relation of the concept as representative of the 
 meaning of a mere name, to the assertory judgment, is illus- 
 trated by the relation of the dependent sentence and of the 
 question to the assertory judgment, and depends upon the 
 possibility of making the identity in a group of judgments the 
 content of a relatively reflective judgment. 
 
 7. It will be observed that having spoken at first of what Logical 
 I may call the logical meaning of names, i. e. of their reference ^^^f +1° ^ 
 in the general world of thought, I have digressed in the last mind, 
 few pages into discussing the act of judgment by which the 
 individual mind realises that meaning. The purpose of this 
 was to show that the acts set in motion by the name and by 
 the proposition were the same, and therefore the logical 
 function of these forms could not be generically different. 
 
 But before further considering the logical meaning, it will 
 be well to say something on the relation between the universal 
 or logical meaning and the act of the individual mind. 
 
 Logical meaning we have treated all along as taken to exist 
 in the world of meanings,** the world which is common to 
 thinking beings as such. Not merely London and Mont Blanc, 
 but virtue, redness and pleasure, have their being in this 
 objective world of meanings. And yet the meaning which on 
 the one hand belongs to a world independent of the individual 
 peculiarities of our thought and perception, is on the other our 
 meaning. It is dependent on our private experience and our 
 private intellectual endowment in two ways. 
 
 First, the psychical ' ideas ', the images which our mind 
 generates from moment to moment and which never recur,'' 
 
 * It is not admitted, the reader should remember, that the world of 
 meanings is separable from the world as affirmed. It is merely the 
 latter looked at in a fragmentary way, see p. 5 and p. 36 above. 
 
 ^ See further on ' Mental States ', ii, ch. x. The view of the present 
 work was from the beginning that a human intelligence has in principle 
 the form of a continuous judgment, in which no psychical elements 
 -escape from contributing to meaning, and no meanings are ultimately 
 unaffirmed (see pp. 70-1 below, with the observation as to how we 
 are aware of ideas as mere facts). The important point is to avoid 
 the conception that judgment is a transition from mental state to 
 mental state, by distinguishing the use of mental contents from their 
 
40 Introduction [Introd. 
 
 are only such as our memory, conjoined with the suggestions 
 present at the moment, will supply. Mr. Bradley has well 
 explained how, as images in our minds, these are not ideas 
 in the logical sense, not significant, not meanings. We use 
 these images, make them starting-points of thought, treat 
 them as containing approximations to what we mean ; we 
 direct ourselves to omit parts of them, or to note that they 
 require weakening or intensification. We may illustrate this 
 by the way in which we attempt to communicate a qualitative 
 impression ; but it is only an illustration, because we cannot 
 employ as an instrument of communication a particular 
 momentary psychical image ; it is not transferable, not 
 capable of being reawakened with precision by language in 
 another individual mind, nor in our own. We must employ 
 then an image which is already so far universalised as to be 
 subordinate to a meaning ; but which may be diverted from 
 its original meaning and applied to another in a way that 
 illustrates the employment of a psychical image. ' Not quite 
 sky blue, but a little darker ; ' ' Between pleasure and pain ; ' 
 ' A baritone is in quality something like a tenor, though with 
 points of resemblance to a bass.' 
 
 Now though, after this fashion, we can deal freely with our 
 particular psychical images, and make them do duty in very 
 various contexts, yet there are limits to the modifications 
 which can be effected in them. To take a well-worn instance, 
 we cannot suppose that a man blind from birth can ever make 
 judgments involving the quality of colours, although he can 
 obviously learn the mathematical theory of undulation and 
 refraction. But the whole region of particular psychical 
 occurrences, immediate impressions of colour, which are made 
 
 mental existence. It does not matter that they are already determined 
 in a context of meaning. The point is that in judging we take them 
 out of their context, and identify them with a new one, in which they 
 become part of a new whole in the real world, and give and receive new 
 characteristics. I do not mean that novelty is essential to judgment ; 
 but when a judgment is well established in our minds it is less easy to 
 see where the predication came from, and what, as a content, it originally 
 was. When I first say ' Reality is solid ' we see that I am using a piece 
 of my mental equipment, the adjective ' solid ', in a special way. But, 
 if approved, it grows into its place, and we forget that it was torn from 
 a number of other applications. 
 
iNTROD.] Reference and Content 41 
 
 use of in referring to the recognised colour-system, would 
 simply be absent from his mind. Structure, on the other hand, 
 involves mainly relative conceptions, such as movement and 
 position, in which the nature of the particular images employed 
 is indifferent ; or, if we mean the structure of an argument 
 or institution, the notions required are such as condition and 
 consequent, function and purpose. Structure therefore can 
 be reproduced by. any intelligence furnished with the chief 
 capacities of an intelligence as such. 
 
 But, secondly, ideas, even in the sense of meanings, are on 
 one side individual and peculiar. The intellect, at least the 
 individual mind of which we are now speaking, does not move 
 wholly in the objective world of meanings to which its acts 
 bear reference. In extreme cases Content and Reference are 
 in contradiction ; in less extreme cases, in veiled contradiction. 
 ' Oh I see, my dear sir,' said a theological disputant, ' your 
 God is my Devil.' Both parties had made the same reference, 
 viz. to God ; neither took what he was speaking about for an 
 idea merely in his mind ; but nevertheless, in making the 
 reference, each of them had employed a peculiar and special 
 act of thought, determined by his own intellectual conditions 
 and history. The opponent in the dispute maintains that 
 your reference is inconsistent with your content ; that one or 
 the other must be wrong. But the possibility of conflict is 
 gone if the reference of both disputants is not the same, and 
 the retort quoted above is an ironical suggestion of a basis 
 of agreement on the score of different reference. The antagonists 
 refer to, or mean to mean, the same thing, but they cannot 
 bring their notions of it into agreement. 
 
 If we go lower into mere quality we obtain good illustra- 
 tions of the line between meaning and psychical idea. It is 
 possible, on certain assumptions which do not concern us here, 
 to compare some of the colour-perceptions of individuals, and 
 it appears that there are various degrees of sensitiveness to 
 red light. Now if we take a case, not of absolute red-blindness, 
 but of over or under-sensitiveness to red light ; we see that 
 the eye which is thus abnormal can produce, presumably, all 
 the images which the normal eye can produce, excepting only 
 the very weakest in the one case and the most intense in the 
 
42 Introduction [introd, 
 
 other. But these, as we rarely meet with or think of them, 
 we may neglect. Now the mind of a man whose eye is thus 
 abnormal has the same furniture of images as our own, but 
 the meaning in each external reference in which they are used 
 must always be slightly different from ours, though such 
 differences pass undetected in common life. If I speak to him 
 of the red of a Doctor of Divinity's hood, he may indeed repre- 
 sent it to himself by any shade of red which springs to his 
 mind's eye ; but he will mean a weaker or a more intense 
 colour than I mean. In this case the abnormal condition has 
 not interfered (as in absolute blindness) with the supply of 
 images, but only with the occasions on which they are pro- 
 duced, and therefore with the meaning attached to each, 
 external influence, to each red object. 
 
 This paradox — that in using names we refer to matters as 
 independent of our individual thinking which in this very 
 reference are only represented to us by an act of our own 
 individual mind, certainly inadequate and possibly contra- 
 dictory to the reference — this paradox is inevitable if we 
 maintain the ordinary line between the mind and the world. 
 No doubt the reference demands some one correct or at least 
 recognisable element of meaning, or else we should set down 
 the name employed as a mistake, and thus if the reference 
 contradicts the content, the content must also contradict 
 itself. But this does not alter the fact that what we refer to as 
 independent of our intellectual act exists for us when referring 
 to it wholly in that intellectual act. 
 
 An effort of imagination might help us to see the real nature 
 of this paradox. We might try to think that the world, as 
 known to each of us, is constructed and sustained by his indi- 
 vidual consciousness ; and that every other individual also 
 frames for himself, and sustains by the action of his intelli- 
 gence, the world in which he in particular lives and moves. 
 Of course such a construction is to be taken as a re-construc- 
 tion,* a construction by way of knowledge only ; but for our 
 
 * This expression was not intended to involve, and I believe does not 
 involve, the notion of an actual external world, similar to, but distinct 
 from, that of our perceptions, by copying which, well or ill, we have 
 truth or falsehood. See ii, ch. ix, below, and compare the criticism 
 referred to in the following note. 
 
Introd.] The World as a Construction 43 
 
 present purpose this is indifferent. Thus we might think of 
 the ideas and objects of our private world rather as correspond- 
 ing to than as from the beginning identical with those which 
 our fellow-men are occupied in constructing each within his 
 own sphere of consciousness. And the same would be true even 
 of the objects and contents within our own world, in as far as an 
 act or effort would be required to maintain them, of the same 
 kind with that which was originally required to construct 
 them. We should know that correspondence ^ implies a degree 
 of identity, but also that every degree from mere correspond- 
 ence upwards had to be won and justified by intellectual work ; 
 the onus, so to speak, of establishing it would be thrown on the 
 intellect ; and the progressive coincidence of our separate 
 worlds would be the reward of knowledge. The moral of such 
 a view is not a bad one ; for it places the solidarity of mankind 
 in the intellectual life. 
 
 Thus the paradox of reference would become clearer. We 
 should understand that we refer to a correspondence by 
 means of a content. We should soften down the contradiction 
 of saying that a name to meet which we have and can get 
 nothing but an idea, nevertheless does not stand for that idea 
 but for something else. We should be able to say that the 
 name stands for those elements in the idea which correspond 
 in all our separate worlds, and in our own world of yesterday 
 and of to-day, considered as so corresponding. Even when we 
 say, taking the most subjective of feelings, ' Pleasure is the 
 accompaniment of activity,' we refer to pleasure as a point 
 in which all separate worlds correspond ; which occupies the 
 same relative position in all the worlds which are framed by 
 the consciousness of individuals, or, what is technically the 
 same thing, a constant position in the world framed by our 
 own. But we should not pledge ourselves to any special 
 
 * The unity of elements which correspond of course does not He in an 
 abstract idea made by eliminating their differences, but in the total 
 structure of which different aspects appear in the different corresponding 
 views. A poor man and a rich man may know the same things and 
 places in London, but their ideas of each place or thing would have to be 
 put together if we wished for a really comprehensive account. Contrast 
 the criticism in Chicago University Decennial Publications, 1903 
 (Miss Thompson on ' Bosanquet's Theory of Judgment ', p. 99).- 
 
44 
 
 Introduction 
 
 [Introd. 
 
 Exten- 
 sion and 
 Inten- 
 sion, 
 
 Insepar- 
 able. 
 
 Their 
 nature. 
 
 degree of correspondence or of identity resulting from com- 
 parison ; only to the bare justifiability of the reference. This 
 suggestion may be considered, if the reader chooses, as a mere 
 simile ; but even so it may assist him in seeing the true relation 
 between the idea which a name arouses, and the object to 
 which that idea refers. The distinction between objective 
 reference and actual affirmation depends, as we have seen, on, 
 the difference between the analytic consideration of a connected 
 group of judgments, and the affirmative of one among them. 
 
 8. I now return to some further characteristics of the logical 
 meaning of names, and shall follow Mr. Bradley in using ' idea ' 
 for a fixed content or logical meaning, not for the psychical 
 images which pass through the mind and never recur — for 
 the signification, so to speak, of the signal flags, not for the 
 particular flags themselves, whose meaning is not affected if 
 different bits of cloth are used on every occasion. 
 
 i. Intension and Extension are complementary and insepa- 
 rable, a. If an idea is the meaning or fixed logical content 
 indicated by a name, how does it come to pass that ideas or 
 names are said to have two kinds of meaning, known as 
 Intension and Extension ? The meaning proper, the fixed 
 content, is obviously the Intension of the name or idea, some- 
 times inadequately defined as the meaning which the name 
 implies, in contrast with the Extension considered as the whole 
 range of individual objects or instances to which the name 
 applies. But it is clear, as Mill has well insisted, that the 
 intension is the primary meaning, or, as we have said, the 
 meaning. To speak of it as implied or connoted, or as the 
 connotation, seems therefore to be a terminology which Mill's 
 own view should condemn. 
 
 But if Intension is the meaning of a name, or is the idea 
 which is this meaning, what is Extension ? How can a name 
 mean anything beyond its meaning, or how can an idea, which 
 is a meaning, yet have a further meaning ? The answer is so 
 familiar in practice that it seemed worth while to observe that 
 it is not free from paradox. Extension or Denotation consists 
 of the instances, ideal or actual, in which any content is con- 
 sidered as realised or realisable. That is to say, extension is 
 the aspect of a content as particular, or as an exclusive unit. 
 
iNTROD.] Intension and Extension 45 
 
 The plural of a noun substantive affords the simplest illustra- 
 tion. ' Men ' form the extension or denotation corresponding 
 to the content intension or comprehension of the name or 
 concept ' man '. But ' a man ', the singular meaning cor- 
 relative to ' men ', is extensive, just as is the plural itself. 
 
 If there are two or more instances of the one content, the 
 distinction between these particulars and the content itself is 
 obvious ; * if there is only one instance, and still more if there 
 can be only one,^ the relation is obscured. But in every idea 
 the distinction between universal meaning and particular 
 embodiment or exclusive self-identity can be traced, and neither 
 aspect can be lacking in any idea. A name or conception with- 
 out Intension would be a name without meaning, and therefore, 
 also, without Extension ; for it is only the meaning that pre- 
 scribes the Extension. And a name or conception that should 
 have no Extension would be one that would not apply to any 
 particular thing or case, and therefore could have no Intension ; 
 for the attributes which are thought of as embodied in par- 
 ticular cases are what constitute Intension. 
 
 ^. This latter conclusion might be objected to on the ground Fictitious 
 that names of fictitious ideas or vain imaginations, or again ' ^^^' 
 nonsensical or self-contradictory expressions, have a sort of 
 meaning, or at least find a place in would-be significant speech, 
 and yet apply to nothing, i. e. have no Extension. ' Nothing ' 
 in this objection must mean nothing actual, if the objection is to 
 
 * We should further note the distinction between what might be 
 called the extension under a name or universal, and the extension of 
 the name or universal. ' Under a universal ' would refer to cases like 
 the same colour on different objects, or different coins of the same date 
 and denomination. ' Of a universal ' would refer to differences which 
 develope in a necessary way the content of the universal itself, such as 
 the kinds of triangles. In this latter case the extension seems merely 
 the specification of the intension (Nettleship, Remains, i. 218). But 
 extension cannot really be reduced to intension (Bradley's Logic, 155), 
 There is always a difference between the content and the fact. And 
 this is what the difference between extension and intension depends on. 
 
 * Sigwart, vol. i, p. 351, gives as an instance 'The centre of the 
 material universe '. There cannot be two points, of which this content 
 is true, but the meaning is still distinguishable from the particular 
 instance, and is theoretically capable of having further particulars sub- 
 sumed under it. Of course there may be two such points in succession 
 — the centre may shift. 
 
46 Introduction lintrod, 
 
 be true in fact ; but actual in any determinate sense is a limita- 
 tion or factor in Intension, and if we introduce it into an 
 imaginary conception we create a contradiction and bring the 
 fictitious idea or name under the head of self-contradictory or 
 nonsensical expressions or conceptions, of which we shall 
 speak directly. But if we do not take nothing to mean nothing 
 actual, then the objection is not true in fact, and imaginary 
 ideas, the content of absolute fictions, have their extensions in 
 the instances, particulars, or units, or in the aspect of unity 
 which they naturally imply. Chimeras, four dimensional space, 
 Gulliver's voyage to Lilliput, have all the same complementary 
 aspects of meaning and particularity that are involved in man, 
 horse, or triangle. 
 Nonsensi- y. On the other hand, a word — for under this head we can 
 ureSons ^^ longei speak of an idea — which is unintelligible whether as 
 a mere noise or as a contradiction in terms with no rhetorical 
 significance, is of course not a name, and cannot enter into the 
 discussion ; for it has, strictly speaking, neither intension nor 
 extension, so cannot illustrate the existence of the one apart 
 from the other. Only it must be observed that even as a name 
 or sign for a certain noise ^ the combination of letters has still 
 its dual aspect of universality as an identifiable sound, corre- 
 sponding to Intension, and particularity as a momentary and 
 unique utterance corresponding to Extension. 
 Names of 8. Another case is that of abstract names of attributes, 
 
 f;**"' such as ' whiteness ', ' virtue.' It is quite clear that these 
 butes. ^ 
 
 abstractions are true of particular instances. The simplest 
 rule is to adopt as extension the meaning of the plural of the 
 noun ; thus virtue becomes a generic conception, and has its 
 extension in the virtues, i. e. the kinds of virtue, courage, tem- 
 perance, &c., and its intension in the generic meaning ' a habit 
 of volition directed to distinctively human ends ', or whatever 
 our definition of virtue may be. Whiteness is not obviously 
 a generic term, but has unquestionably a possible plural either 
 in the sense of kinds of whiteness ^ or in the sense of instances 
 of whiteness. In Latin as in English it is somewhat of a rarity 
 to use the plurals of very abstract abstractions ; but yet 
 
 * See Bradley's Principles of Logic, p. 157. 
 
 ^ Cp. Shelley's line, ' White with the whiteness of what is dead.' 
 
iNTROD.] Names of Attributes 47 
 
 they are sometimes used ; and besides, the difference between 
 singular and plural only illustrates and does not constitute the 
 distinction between Intension and Extension. As in the line 
 quoted from Shelley, the singular whose meaning is on all-fours 
 with that of one case among those indicated by the plural is 
 itself a particular, and accentuates the extensional aspect of the 
 idea. I may add that it has been well pointed out ^ that such 
 abstractions are ' doubly adjectival ', for they not only apply 
 to real cases or kinds of the abstraction, ' whites ' or ' white- 
 nesses ', but they actually mean the abstraction of a concrete 
 thing or subject that has the attribute. They imply not merely 
 particular whites, but particular things that are white. 
 
 The intension of the simple abstraction ' whiteness ' is hard 
 or impossible to state in general terms, if we leave out of 
 account the theory of light, which has not been available for 
 this purpose till a comparatively late date in the history of 
 logic. A parallel difficulty caused Plato to say, at least at one 
 stage of his views, that he could frame no ei8os of a smell, i.e. 
 he could find no general determinate attributes by which to 
 formulate its definition. Such difficulties are plainly matters 
 of the state of knowledge. A content which is recognisable 
 and identifiable in different contexts always has a meaning 
 and intension. We are about to turn to two extreme cases, 
 that of proper names and that of number, which will illus- 
 trate the lowest grade to which the intension of a significant 
 name can be reduced. No attribute, however hard to define, 
 can be so indifferent to intensional meaning as the significance 
 of a strictly proper name and the denomination of a number. 
 
 e. Proper names have sometimes been pronounced non- Proper 
 connotative, i.e. without intension; because their meaning ^"^^^• 
 is not fixed and generalised. On the other hand, Jevons, 
 rightly rejecting this view, which is absurd because as we 
 have seen intension and extension are inseparable, goes 
 into the other extreme by refusing to distinguish Proper 
 from Singular names, and therefore ascribing to the former 
 a maximum of intension. By a proper name I understand 
 primarily a name that merely serves to distinguish a place 
 or person, or, in exceptional cases, a thing. As a rule, a 
 * Bradley, Principles of Logic, p. 156. 
 
48 Introduction [Introd. 
 
 thing which is neither place nor person has not the indi- 
 vidual interest independent of fixed content which is the 
 root of the employment of proper names. We name a thing 
 according to its species, its type or function, not with reference 
 to its absolute particularity. Cases like that of a favourite 
 animal, e.g. a horse, to which a proper name is usually given, 
 or even a favourite thing, such as Henry Smith's hammer 
 Samson in ' The Fair Maid of Perth ', are exceptions that 
 prove the rule. We can see that in such cases as these a 
 special interest has come to be attached to the particular 
 individual independently of its specific nature. By a ' singular ' 
 name as contrasted with a proper name I mean a name that 
 indicates content as such, but content that is in its nature, 
 or at any rate assuming it to be located in the actual world, 
 unique. Such is the instance given above, ' The centre of 
 the material universe ; ' or, again, ' The king of England 
 in the year 1832.' There is a certain difficulty in finding 
 instances of these names, unless as in the last case we limit 
 them in time, or as in ' The chief murderer of Caesar ' confer 
 uniqueness upon them by relation to a true proper name. 
 When we come to speak of the singular judgment we shall 
 see^ that there is a good reason for this difficulty. It is 
 prima facie impossible for any content into which time does 
 not enter to stand as the subject of a singular judgment. 
 The centre of gravity of the material universe may shift its 
 place and thus become in one aspect plural, though in another 
 it remains unique. No idea can guEirantee its own uniqueness, 
 which is only given by reference to a position in the actual 
 sensuous series. Still there is a difference between the singular 
 and the proper name ; which I proceed to state as shortly 
 as I can. 
 
 Every name has intension and extension. But the extension 
 naturally follows the intension, and the intension attaches 
 to the name, without reserve ; that is to say, the name as 
 such has a meaning, and is applied to all objects of which 
 this meaning is true. Now the term ' proper ', which means 
 in this usage ' peculiar ' or ' individual ', is in contradiction 
 with the above-mentioned characteristic of significant names, 
 and imposes upon them a function with which the nature 
 
introd.] Proper and Singular Names 49 
 
 of intension is essentially at variance, viz. the recognition 
 of individuals as such, in their particularity, and without 
 primary reference to their attributes. Intension thus becomes 
 a means and not an end, A significant general name is used 
 of many objects in the same sense ; and a significant singular 
 name is used of one object only, because there is or can be only 
 one object to which its meaning applies ; but a proper name, 
 though used of many objects, is used of each in a different 
 sense. Its rudiment of general meaning is in such an implica- 
 tion as that John is the name of a man and not of a mountain 
 or a steam-engine ; or again, some one of the thousand 
 different applications of a proper name may become typical, 
 and so set up a general meaning, which however does not 
 attach to the name in its remaining 999 applications, but 
 only elevates it into a term of ordinary language in respect 
 of one application. I refer to such cases as * a Daniel ', ' a 
 Croesus ', ' a Solomon ', ' the Rupert of debate ', &c. 
 
 But these are abnormal uses in which the proper name 
 ceases to be proper. The particular Johns, on the other 
 hand, to whom the name John is applied as a proper name, 
 do not form one extension corresponding to a single intension 
 of this name. Each of them forms by himself a separate 
 extension corresponding to a separate and distinct intension 
 of the name John. The men called John are not related to 
 their name as ' men ' to ' man ' or as ' towns ' to ' town ', 
 but as Salviati's glasswork and the Pentateuch to ' Mosaic ', 
 or as a human being, and a cairn in the Lake Country, to 
 ' man '. The subject is not without historical interest, but 
 to pursue it would take us too far from logic. No doubt 
 it might be maintained that in early language Intensional 
 and Extensional meaning must to a great extent have 
 coalesced. Whatever sound was appropriated to a sensible 
 incident would at first, very possibly, attach itself only to 
 the concrete or confused perception as a whole, and it might 
 be long before pointing out the occurrence could be in any 
 way distinguished from saying in what it consisted. Thus 
 it might be said that language must have begun with proper 
 names for everything, and advanced to general names, and 
 only then had to face the problems arising from the necessity 
 
 1337 E 
 
50 Introduction [Introd. 
 
 of identifying individuals by help of symbols whose nature 
 is to be general. The problem is now solved to a considerable 
 extent by a peculiar convention as to mode of writing and 
 amount of signification to be expected. We know that to 
 find a town in Ontario called by the name of London justifies 
 no single inference as to points of identity between it and the 
 metropolis of England. We must keep etymology out of the 
 question. A word means what it is used to mean, not what 
 it once meant. The derivation of proper names justifies no 
 inference at all as to their meaning. The Remington type- 
 writers bear the stamp of Ilion. In the same way intensional 
 meaning cannot justly be ascribed to Christian names or 
 surnames, at least in modern England. There is now no 
 legal monopoly of such names (though there may be of trading 
 designations), and if we are taken in by ascribing intension 
 of birth and breeding to a particular name, it is our own 
 fault. But probably this state of things is modem, and 
 the existence of proper names of persons in the full sense 
 would in that case be modern also. If legal or social rights 
 depended on bearing a particular name, then such a name 
 had as an element of true intension those general relations — 
 patriciate, legitimacy, civic birth — in which the right to 
 bear it and the incidents of bearing it were involved. * The 
 art of giving names,' it has been said, 'is lost.' It is certain 
 that the purpose of mere recognition, to which all attributes 
 are in their nature indifferent and serve only as a means, 
 tends to destroy the picturesqueness of nomenclature by 
 dissociating it from interest in a general and so significant 
 intension. The close relation between mere extensional 
 meaning and the use of number is nowhere more strikingly 
 illustrated than in the custom of numbering not only houses 
 but streets, as in great American cities. In the proper name 
 there is still the semblance or fiction of a general Intension — 
 the special name-word seems indicative of distinct meaning ; 
 in the number even this fiction has disappeared, and nothing 
 remains but the place of the particular in an aggregate of parti- 
 culars, united solely by a common denomination. 
 
 Thus the distinction between a proper name and a significant 
 name (whether singular, as God, or general, as ' man ') is 
 
iNTROD.] Decline of Significance in Names 51 
 
 that in the use of a proper name signification is a means to 
 identification ; in the use of a singular or general name 
 signification is predicated for. its own sake. ' But the identi- 
 fication of a person or thing is signification,' it will be said. 
 This raises the question of the nature of personal or individual 
 identity, which is not in place here ; it is enough to point 
 out that mere identification is a very barren kind of significa- 
 tion, since there is hardly a single attribute of actual content 
 as distinguished from mere external relations that is 
 necessarily conveyed by it. Macaulay after his mind was 
 gone was still Lord Macaulay and his father's son, but what 
 else was he that he had been ? -^ 
 
 C If pure Extension were to be found anywhere, it would Names 
 be found in a general name or idea determined by number, nu^Jber 
 or of which number is predicated, attached. 
 
 An extensional whole is an aggregate of individuals sharing 
 a common nature, but regarded as particulars, i.e. as each 
 identical with itself and external to all the others. This is, 
 as we shall see more fully from the analysis of Enumeration 
 (Book I, chap. 4), the nature also of a numerical whole. The 
 unit of number and the particular of extension are closely 
 allied. Each of them consists in the identity with itself of 
 a concrete thing or discernible particular in spite of differences 
 which it includes. Proper names also depend on this self- 
 identity, but have for their purpose to single it out and mark 
 it apart from the whole universe besides. Number does not 
 seek to single out one such identity par excellence, but to 
 formulate the relations which arise between such discrete 
 identities as factors in a sum or aggregate. In the first place 
 then,, number, though an attribute and so an element of 
 intension, yet by accentuating the embodiment of a content in 
 units external to one another, demands an extensional rendering 
 of the idea. And in so far as depth of meaning is indifferent 
 when we are thinking of aggregate units and not of connected 
 attributes, so far the intension of a concept may be reduced to 
 
 ' See Kejoies, p. 45, note. My main point about proper names is that 
 the element of meaning in them is auxiliary to individual identification, 
 and therefore, in principle and not merely in fact (as with general 
 names), arbitrary and variable. 
 
 E2 
 
52 Introduction [Introd. 
 
 the denomination of a numerical aggregate. But if this 
 remnant of intension, which determines the range of the 
 aggregate, is removed, the thought is destroyed in both its 
 aspects. 
 
 And further, in the second place, a numerical determination, 
 although itself an attribute, tends to contradict intension 
 proper, and so force the attribute of extension or particu- 
 larity into importance. It is obvious that in every concept 
 the intension dictates the extension. And the extension so 
 dictated must as an aggregate of instances be theoretically 
 at least capable of representation by a number, or if not, 
 it must be in conflict with any and every number. We may 
 omit the consideration of parts of space and parts of time, 
 which seem to constitute a series that theoretically defies 
 enumeration ; but no actual content of our real world can 
 be thus infinite, so far as we can understand. The human 
 race itself must, as we are bound to suppose, have a limited 
 career, and the limitation, however far beyond our knowledge, 
 must be immanent in man's nature in its relation to his 
 environment. Thus the intension even of man, colour, gold, 
 or other ordinary general names, must ultimately and theo- 
 retically imply a finite numerical aggregate of instances.^ 
 
 This number, which in such cases as the above we can 
 never know, could be of no possible interest to us, were it 
 not that it affects the import of any other number by which 
 any such concept may be determined. In other instances the 
 knowledge, which in the above cases seems not worth serious 
 thought, is actually ours, or treated as being ours. Such 
 instances are the three persons of the Trinity, the three sides 
 of a triangle, the ten decemviri, the 670 members of the 
 House of Commons, the five regular solids, the ninety degrees 
 of a right angle. It will be observed that these illustrations 
 display the number in very different relations to the inten- 
 sion. A member of the House of Commons is no less a member 
 
 * This is, in so far as the instances are true individuals in a known 
 system. Mere ' observations ' on the other hand, successive presenta- 
 tions to sense, must always be taken as entering into an infinite series, 
 for no power can tell how often they may recur, nor what constitutes 
 a single one. Nor do they by mere repetition tend to generate a system. 
 
iNTROD.] Number and Extension 53 
 
 if some units are withdrawn from the legal number of 670, 
 as, in consequence of death or resignation, is often, perhaps 
 always, the case. The number in which he is a unit does not 
 directly affect his position, atlhough no doubt, if an immense 
 proportion of seats were to become vacant owing to some 
 extraordinary catastrophe, the House would be unable for 
 a time to act as a House of Commons. The same is the case 
 with the decemviri or the two Roman consuls, for the authority 
 of one member of these boards was independent of that of 
 the others or other. But if we take the case of twelve English 
 jurymen the matter is altered, for the number is essential, 
 though only made so by specific enactment, and if ' a juror is 
 withdrawn ' the others ipso facto lose their powers of trying 
 a case, i.e. cease to be in the full sense jurymen. 
 
 And it is possible for the number to enter even more deeply 
 into the essence. Two sides without a third cannot be two 
 sides of a triangle ; and an angle of one degree is not, con- 
 sidered in itself, a degree in a right angle. The nature of 
 space as an ideal whole does indeed introduce a difficulty 
 here, for it may be said that a degree can only be understood 
 with reference to the circle, and therefore involves the concep- 
 tion of a right angle ; and that in space, a figure is all that it 
 involves. The objection draws attention to a principle which 
 holds good of all units without exception, viz. that every 
 unit ultimately involves the whole in which it is a unit, but 
 it does not alter the fact that we have no right angle unless 
 we have ninety degrees, while we have a House of Commons 
 (unless Parliament is dissolved) so long at least as it has enough 
 members to form a quorum. In other words, the whole 
 implied in the unit in the one case involves a precise numerical 
 determination, and in the other case does not. And it will be 
 observed that as instances tend to approach the former type, 
 the number ceases to be truly extensional, becoming as we 
 shall see (Book I, chap. 3) a result due to measurement rather 
 than to mere enumeration. The content, that is to say, no 
 longer falls chiefly within each unit of the enumeration, so as 
 to make the number a mere sign of the repetition of embodi- 
 ments of the content, but in some essential respects is gene- 
 rated by a repetition of the parts and does not exist in each 
 
54 Introduction [Introd. 
 
 taken alone. Thus, as was said, the character of being a right 
 angle is not present in every degree of angular measure- 
 ment, nor is the character of being a commonwealth present 
 in every individual person — not, at any rate, in the same 
 sense in which the character of being a man is present in 
 every person. A name or idea which, while involving a 
 number of identical parts, is not truly predicated of each 
 such part singly, was called in the old logic a collective as 
 contrasted with a general name. Army e.g. is a ' collective ' 
 name as regards the individual soldiers in it, but a general - 
 name as applied to the English, German, French and other 
 armies. The distinction indicated by the term was not 
 valuable, for it was not explained. But it is obvious that a 
 ' collective ' name or concept like ' army ' is a halfway house 
 between the mere common nature of units like men, horses, 
 books and the like, in which the enumeration of the particulars 
 repeats the intension in every item of the extension, and 
 wholes like nation, Parliament, triangle, plant, in which the 
 parts are bound together by other relations than that of 
 number, and therefore their number does not form the 
 extension of the whole, so much as an intensional attribute 
 of that whole. Thus the enumeration of Englishmen is not 
 so much the extension of the English nation, as it is at the 
 moment an attribute of the English nation to contain such 
 a number of Englishmen. The question is whether the content 
 falls within the unit, or only within the synthesis of units. 
 
 But whether mere units in an aggregate or elements in a 
 numerically determinate whole, numerable parts must have 
 a number, which must directly or circuitously depend on 
 intension. And every numerical determination other than 
 that which thus springs from intension has the effect of 
 erecting a mere whole of enumeration which, as regards 
 the intension of the general name, is arbitrary and irrele- 
 vant. An exceptional instance will illustrate this. Any 
 two sides of a triangle are together greater than the third 
 side. Here the two sides are not a mere whole of enumera- 
 tion, and are not irrelevant to the conception of the three 
 sides of a triangle. What is here predicated of them is a result 
 of analysis applied to the triangle with its three sides, and is 
 
iNTROD.] Collective Names 55 
 
 a consequence of the three-sidedness of the triangle. The 
 three sides might indeed be named as subject in the pro- 
 position. But if we say 'There were 10,000 men in H^^de 
 Park last Sunday ' we have constructed a whole of enumera- 
 tion prima facie irrelevant to the concept man and having 
 an extension that conflicts with the extension of that con- 
 cept, and therefore with the intension that dictates that 
 extension. In other words, we have depressed the term 
 ' man ' into the denomination or designation of the unit 
 employed in counting. The number may if we choose be 
 stated as a predicate, and the limit * in Hyde Park ' taken 
 into the qualificgition of reality which forms the subject ; 
 all that concerns us here is to point out that we are speak- 
 ing of an aggregate framed ad hoc by enumeration, i.e. 
 by taking men one after the other in their particularity up 
 to a limit which does not prima facie present itself as implied 
 in their nature. We not merely count men as particulars, — 
 we count particulars if we count the angles of a pentagon, — 
 but we divorce them from their natural intension by excluding 
 the greater portion of the extension which it indicates. It 
 is true then that number, qua mere enumeration, is, like 
 the proper name qua mere identification, in a large measure 
 antagonistic to intensional meaning. 
 
 ii. The two cases which have just been discussed are Alleged 
 enough to show that not every variation of intension involves J.^^j^'^^of 
 a corresponding variation of extension, or vice versa. The Exten- 
 essence of proper names and of numbers is to mark the i^ntension. 
 same extension or the same amount of extension as persistent 
 through intensions partially at any rate varying. Never- 
 theless,- the demand for a formal rule of inter-dependence 
 between these two obviously connected aspects of concept 
 and of judgment was satisfied in traditional logic by the 
 doctrine that intension varied inversely as extension. This 
 idea was an early development of the Aristotelian definition 
 by genus and species, from which it obviously followed that 
 whereas the generic attributes were contained together with 
 others in the definition of the species, the individuals belonging 
 to a species must be contained together with others among 
 those belonging to the genus. Aristotle noticed this conse- 
 
56 Introduction [Introd. 
 
 quence of his own views, but the false accuracy of the tradi- 
 tional rule was a later development of the forms which he 
 established, when their life was beginning to fail. Recent 
 logicians have more or less completely condemned the doctrine 
 in question ; perhaps the latest well-known writer who ascribed 
 to it first-rate importance was Professor Jevons. His account 
 excludes one obvious objection, viz. that a multiplication of 
 identical instances cannot affect intension, by a proviso that 
 only logical change of extension could affect intension. But 
 this makes the view a truism ; if logical change of extension 
 means admission into extension of a new kind as opposed 
 to a mere multiplication of instances, it is obviously equiva- 
 lent to some change, of whatever kind it may be, in meaning 
 as such or intension. But even so, even accepting this proviso, 
 it remains doubtful whether the doctrine of the inverse 
 relation is important in any sense in which it is true. I am 
 inclined, however, to think that the recent logicians to whom 
 I have alluded, e. g. Sigwart, Wundt, and Bradley, and also 
 to a smaller extent Lotze, err by sheltering themselves under 
 a point of form, and avoiding the question of import. It is 
 true, no doubt, that you may have any arrangement of con- 
 cepts ; but it is hard, in view of our gigantic natural classifica- 
 tions with their unrivalled grasp of reality, to place any other 
 arrangement of concepts on a level in real import with that 
 of genus and species. 
 
 I will begin, however, by going briefly through the weak 
 points of the supposed law that the Intension of a concept 
 or name varies inversely as its Extension. 
 The a. The quasi-mathematical phrase ' inversely as ' is wrong, 
 
 mathe- j^ asserts a ratio, and a ratio is a numerical relation. 
 
 matical 
 
 phrase is But in the case before us, one side of the matters com- 
 
 wrong. pared does not lend itself to enumeration at all. The 
 
 parts of extension may be counted, as we have seen, but it 
 
 is inept to count the parts of intension. For they are not 
 
 external to each other, and they form a whole such as cannot 
 
 be divided into units except by the most arbitrary dilaceration. 
 
 And if it were so divided, all its parts would vary in value, 
 
 and there would be no reason to expect that ten of them 
 
 (i.e. ten attributes) should have twice the amount or value of 
 
Introd.] The inverse ratio 57 
 
 five. We must constantly bear in mind, e. g. in estimating the 
 
 false doctrine of analogical inference, that there is absolutely 
 
 no sense in counting attributes. 
 
 /3. Mr. Keynes (p. 36 note) admits the objection to a nu- Assump- 
 
 merical sense. But he considers that no error is committed ^ "j-d^jng 
 
 if we speak merely of the enlargement or restriction of the Inten- 
 ... f . sion. 
 
 m tension of a term. 
 
 This appears to me to be purely a question of assumptions ; 
 and it would not be worth discussing if it did not seem to 
 be the case that the common assumptions, which Mr. Keynes 
 for example embodies in his theory, rule out important 
 elements of our knowledge. These assumptions all spring 
 from the belief that the meaning of terms belonging to wider 
 classes is naturally formed by abstraction from that of terms 
 belonging to narrower classes. And this belief falsifies our 
 whole conception of knowledge and of the nature of things. 
 The assumptions rooted in it, so far as intension and ex- 
 tension are concerned, seem to me to be three. 
 
 (i) The comparison of co-ordinate adjectives, not belonging Neglect 
 to the same ascending series of class-ideas, is ruled out. Yet ^ate ad-^' 
 it is clear and important that such an adjective as 'visible' has jectives. 
 both wider extension and deeper intension than an adjective 
 meaning ' perceptible by smell ', (Bradley's Logic, p. 158.) 
 
 (2) It is assumed that the terms of the smaller class have Addi- 
 properties additional to those of the terms in the larger, and pj-oper- 
 not merely qualities which are variations of those charac- ties, 
 terising the larger class, each to each. This is Lotze's well- 
 known suggestion (Logic, sections 23 and 31) and would 
 overthrow Mr. Keynes's formal argument on p. 39. 
 
 ' Let X be determined by the set of examples Q j . . . Q„ , and 
 Y by the set Q^... Qn + j which includes the additional object 
 
 ' Then Q„ ^ j either does or does not possess all the pro- 
 perties common to Q^ . . . Q„ . ' 
 
 If the former, X and Y have the same comprehensions 
 and the same denotations; if the latter, Y has the lesser 
 comprehension ])y the properties which Q^...Q,„ do possess 
 and Qn + i does not, and at the same time has the greater 
 denotation by Q„^i at least. (I compress the statement.) 
 
58 Introduction [Introd. 
 
 But, I suggest, the fact is that Q„ ^ j- possesses in the form 
 a a property which Q, . . . Q„ possess in the form Oj. 
 
 Then Qn^, possesses an equivalent amount of properties 
 to Qi-.-Qn, and the comprehension of X and Y is therefore 
 equivalent (more carefully analysed, the one would exceed 
 in some respects, and the other in others) ; . while, as there is 
 a distinctive variation between some properties a, of Q^.. .Q^ 
 and some a belonging to Qn + v both of which fall within A, 
 a property of Y, the denotation of Y remains greater than 
 that of X by Q„ ^ , at least. 
 
 Or consider Mr. Keynes's sentence, p. 36 note i, ' There can 
 be no doubt that intension is increased when we pass from 
 animal to man, or from man to negro.' Does not common 
 sense receive a sharp shock at the second instance, even 
 though unable to escape from the belief that every sub-class 
 has additional intension, on the top of the whole intension 
 of its over-class ? Surely it is better to take it that the negro 
 has qualities which are distinctive variations within the 
 qualities of man, and which are compatible with his falling 
 short of the full intension of man as such. For minute 
 analysis, it might be said, he would have excess in some respects 
 and defect in others ; but that is only what every variation 
 in quality would exhibit. So as regards the relation of animal 
 and man. 
 
 It is easy to say that animality is common to men emd 
 beasts, while rationality belongs to men only, and in place 
 of it animals have either instinct or nothing, and that there- 
 fore animality is the intension of the class which includes 
 beasts and men, while each of these sub-classes has a separate 
 and additional intension. But in fact the animality of men 
 is quite different from the animality of beasts, and is not an 
 attribute common to both in the sense in which a tree-trunk 
 is the common support of two of its branches. While on the 
 other hand the thorough modifications which distinguish the 
 intelligence of man from that of animals do not suffice to 
 dissociate them beyond identification ; and the class-con- 
 ception which simply omits all reference to intelligence is an 
 inadequate class-conception for men and animals. Therefore 
 the notion or abstraction which is to include both men and 
 
Introd.] Increase of Intension 59 
 
 animals must on the one hand provide for a variable animality ; 
 must be considered, that is, not in the light of a fixed mark, 
 but as a scheme of modifiable relations ; and must, on the 
 other hand, find room for some reference to intelligence, 
 and not simply strike it out as a mark in which the kinds 
 to be classified are not the same. Prima facie then the content 
 of the superior class-conception is made up of the very same 
 elements as those of the conception nearer to individual 
 reality, only that it must represent each attribute schemati- 
 cally, by limits of variation, instead of embodying a fixed 
 system of amounts or values. 
 
 (3) Either the increasing concreteness of intension due to Concrete 
 inter-relations among individuals is wholly ruled out, or it ^^q^' 
 must be assumed that such intension can be reduced to common unac- 
 predicates of terms in classes, and ought, like such predicates ^^^^ ^ 
 in general, to be presupposed in the intension of every term 
 which possesses them. But the fact is, that the meaning 
 which accrues to a term from its functions or relations in 
 a whole cannot be represented as a class-predicate which it 
 shares with other members of that whole. As Lotze pointed 
 out with regard to humanity, that in it you have inter-relations 
 which make it more than the class concept * man ', so it is with 
 the state in regard to the citizen, or the army in regard to 
 the soldiers. 
 
 The old logic would retort here that the extension of ' state ' 
 is made up of particular ' states ', not of persons, or that that 
 of ' nation ' or ' army ', consists in the several nations and 
 armies, not in individual men and soldiers ; or that the exten- 
 sion of God is in his particular existence (as we do not here 
 admit a plural) not in elements within God's being. But this 
 would only meet the objection at the cost of narrowing the 
 idea of universality to that of mere abstraction, in contrast 
 with the sense — synthesis of differences — in which we have 
 taken it throughout. Moreover, even the aggregate of men, 
 nations, or animals which is indicated by an abstract universal 
 name has in virtue of that universal a common nature which 
 is a germ of concreteness. A crowd is not an army, but it has 
 in it always the elements of a mob. As we saw above, collective 
 names mark a mere half-way house from aggregation to 
 
6o Introduction [Introd. 
 
 individuality, and it is a purely arbitrary procedure when 
 examining the nature of universals, to restrict our notice to 
 such as have attained to no higher embodiment than an aggre- 
 gate of particulars. But in fact our prejudices would cause us 
 to neglect a concrete nature if any such were apparent within 
 the aggregate. We should insist that the idea which should 
 include the states or nations of the world must have less 
 import than the idea of England or France, and should there- 
 fore look for this idea in the abstraction ' state ' or ' nation ', 
 neglecting to consider whether, e. g. as the source of inter- 
 national law, the aggregate of nations has not in it some- 
 thing beyond the elements common to various peoples, or 
 whether, if this is not so, the absence of such a central unity . 
 is not at least a defect which we might hope to see amended. 
 
 So with the conceptions which might be supposed to be 
 the emptiest of abstractions because the widest of ideas. 
 Being, Reality, the Whole, the Universe. The entirety of our 
 profoundest science and speculation attaches to them, because, 
 in their enormous extension, all kinds of problems and inter- 
 dependences present themselves. You might urge formally 
 that as the widest classes they should have an intension prior 
 to and included in that of all common objects. And no doubt, 
 if we completely knew the flower in the crannied wall we 
 should know the universe. But no sane man surely would 
 maintain that the profoundest thoughts about the universe 
 are presupposed in the comprehension or intension of every 
 flower, because it is a member of the universe, or of the class 
 of existents or reals. Plainly these thoughts arise with the 
 increasing extension, as we pass from the plant to its functions 
 and relations in ever wider provinces of the w^orld. 
 Subsump- (4) The whole idea that judgment and reasoning naturally 
 or exclusively depend upon subsumption, i. e. upon taking 
 attributes as connected simply within and by the unity of 
 individual subjects, has of late been rejected, and with good 
 reason. And with this idea disappears any formal or universal 
 necessity that may have been supposed to attend the arrange- 
 ment of attributes as designations of successively wider 
 aggregates of individual subjects. It is important that we 
 should dismiss the notion that the higher degrees of knowledge 
 
 tion 
 
iNTROD.] Truth of the ' inverse ratio ' 6i 
 
 are necessarily and in the nature of intelligence framed out 
 of abstractions that omit whatever has interest and peculiarity 
 in the real world. Nothing has been more fatal to the truth 
 and vitality of ideas than this prejudice, which I do not admit 
 to be a just representation of the principles of Plato and 
 Aristotle, although certain salient features of their doctrine 
 gave it an unfortunate advantage. If the present reaction 
 against formal logic should end in establishing a more vital 
 conception of universality than that which sets it down to 
 mere abstraction, a fundamental reform will have been made 
 in philosophical first principles. 
 
 iii. Nevertheless, subsumption and abstraction play a Truth of 
 part in knowledge. It is not quite certain that there is any j.^tio^-'^^^ 
 judgment 6r argument which is incapable of being exhibited 
 in subsumptive form. It is certain that to abstract and to 
 distinguish — to know what belongs to one relation, and 
 what, again, though conjoined with that relation, yet does 
 not arise out of it, but out of some other condition or cause 
 — is the first duty of the scientific intelligence. In conse- 
 quence of this activity, arrangements of individual objects 
 under a series of abstractions, each applying to a wider 
 aggregate than the last, meet us on every hand, and most 
 obviously of all in family relationships as estimated among 
 civilised nations. The question before us cannot be dis- 
 missed until we have treated it from this more real point of 
 view. Is the ' pyramidal ' arrangement of concepts, sub- 
 ordinating the less to the more abstract, scientifically con- 
 venient, or, what in an ultimate sense comes to the same 
 thing, is it true ? In answer to this question I will mention 
 two further points of interest. 
 
 a. Sigwart reminds us that every concept may be regarded Altema- 
 from different points of view, and classification or abstraction gj^^a^. ^^" 
 may therefore have different lines open to it : e. g. do we tions. 
 class a square first with four-sided figures, and then, subject 
 to that limitation, with equilateral figures, or vice versa ? 
 It is obvious that we put the square in quite different company 
 according to the order in which we apply these points of view. 
 The point is that in this and similar cases we seem to have 
 bona fide alternatives. No serious attention would be needed 
 
62 Introduction [Introd. 
 
 by the mere fact that we can class a copy of ' Paradise Lost ' 
 either as a black or as a rectangluar object. But if genuine 
 alternative classifications are possible, it is clear that we 
 may have a hundred objects before us, and being forced to 
 divide them into classes from each of ten unconnected points 
 of view, may be left with ten different classifications for each 
 object, and apart from some peculiar ground there will be 
 no reason for subordinating each object decisively to one 
 classification rather than to another. 
 
 The first remark that such a suggestion invites is that the 
 idea of alternatives only touches the subordination of every 
 object to one class or series of classes, but does not touch 
 the alleged necessity of successively emptier abstractions 
 within any one point of view which may be selected (as 
 some one must always be selected at least fro hac vice) and 
 adhered to. And, secondly, the mere difficulty of alterna- 
 tives is inherent in the nature of intelligence, meets us in 
 the problem of giving names, and is overcome in some degree 
 whenever we venture to affirm a fact. In its most genuine 
 form it is met by the theory of the relation between different 
 sciences, to each of which the same individual thing obviously 
 presents a different aspect. Sigwart's suggestion ^ of an 
 inference to Pantheism from the doctrine of essence combined 
 with that of subordination — because only the essence of the 
 highest abstractions is in no relation accidental — seems to 
 me perfectly wild. We should by this time be well aware 
 that all essence is relative, but that relativity does not exclude 
 absoluteness. One set of attributes are a man's essence 
 qua citizen, and another qua parent. I may add that his 
 argument depends on assuming that any class may be re- 
 garded in its tiurn as genus and as species. But this is an 
 obsolete conception belonging to purely formal logic. The 
 successive abstractions of classification have distinct charac- 
 ters expressed by definite titles and not interchangeable. A 
 genus is not a species of an Order, and a Class is not the genus 
 of a Division. 
 Inverse j3. Thus I Cannot think that Wundt is right in tracing the 
 tfaiiy ms- relations between class-idea and individuals to the mere effort 
 tified. 1 Logik, i. 355. E. Trans, i. 274. 
 
Introd.] Truth of Successive Abstractions 63 
 
 of language to economise its store of words. The whole fabric 
 of the organic and even of the inorganic world creates prima 
 facie an overpov/ering impression that natural classification 
 can correspond to reality. The perceptible fact of graduated 
 affinity has in all ages taken precedence of its causal explana- 
 tion. The facts of human or animal descent, so far as imme- 
 diately observed and as embodied in systems of relationship, 
 supplied a name, if not a thorough-going explanation, for the 
 affinities observed in nature.^ The degrees of family connec- 
 tion, at least in mature European society, are the simple 
 prototype of the ordinary process of classification ; and the 
 analogy has extended since the earliest days of Logic to the 
 inorganic as well as to the organic world. Now the alleged 
 relation of Intension and Extension may be simply illustrated 
 by the characteristics shared by a group of first cousins, 
 i.e. persons descended from the same grandparents, compared 
 with those shared by second, third, or fourth coiisins, whose 
 common descent is more remote by one or by several genera- 
 tions. In the human race, indeed, individuality of mind and 
 disposition has so much to feed it in special knowledge and 
 experience that the phenomena are but irregularly observable ; 
 but in the evolution of plants and animals their characters have 
 the same graduated identity without the same deductions on 
 the score of special training and mental development. And it 
 is not only evolution by descent that will produce these per- 
 vading affinities. Cognate processes of causation result in 
 kindred formations all through the world of inorganic sub- 
 stances ; and even in the sphere of necessary ideas, of number 
 and geometrical figure, identical relations, under varied con- 
 ditions, produce the appearance of graduated kinship or 
 affinity. 
 
 Granting, therefore, in accordance with what has been said 
 above, that the v/ork of abstraction should be represented not 
 as selective omission hut as constructive analysis, and that the 
 blanks in a schedule of attributes common to a large range of 
 existence are not mere blanks, but zero values that may become 
 positive in some cases ; still we cannot on the whole deny that 
 
 ^ See Lotze, Logik, sect. 30, on the probable original meaning of '^ivos 
 and efSos. 
 
64 Introduction [Introd. 
 
 the graduated operation of natural causes is very conveniently 
 embodied for some purposes of knowledge in a hierarchy of 
 abstractions. But it must be remembered that the working 
 idea of the evolutionary science of life is not represented by 
 the classified organic world, but by the interdependent play 
 of creatures upon each other and their environment in a con- 
 crete universe — a conception which, as explained above, 
 cannot at all be represented in the form of a classified system. 
 And the largest conceptions of thought will not be the summa 
 genera of a hierarchy of abstractions, but ideas of a self- 
 determining totality, comprising an enormous intension 
 corresponding to their immense extension. 
 
 So, again, as has been shown above, where the higher con- 
 cept is not a mere law, but a concrete real whole, the idea of 
 diminishing Intension has no application whatever. It is for 
 special knowledge to determine how far these different points 
 of view are respectively to be taken. Psychology subordinates 
 the human soul to a set of laws which include, as they 
 grow more abstract, a larger range of animal and organic 
 existence.* Political science treats the same spiritual being 
 in its concrete relations within an actual community of 
 such beings — not as a mere member of a class. To which 
 of these two sciences that of Ethics ought to assimilate its 
 procedure is a vexed question which illustrates the problem 
 of deciding in what regions the rule of diminishing Intension 
 applies. 
 
 One more suggestion may be ventured which aims, it will 
 be said, at rehabilitating an old fallacy. I am unable, however, 
 to persuade myself that it does not appeal to an unquestion- 
 able truth. I assumed above, for the sake of simplicity, that 
 regressive abstractions such as figure in classification could 
 represent in respect of their abstractness no character of 
 
 * Yet even in this case a deeper intension tends to present itself along 
 with the larger denotation. We can hardly argue (cp. p. 60) that the 
 wider intension belonging to the word soul in the universe falls within 
 the class-predicates of the human soul, as a stratum below its distinc- 
 tively human properties. You may urge that if it is true we might 
 have known it from the human soul alone ; but the same argument 
 would require us to take the metaphysical theory of the universe as 
 a prior basis for the intension of every flower. 
 
iNTROD.] From Abstract to Concrete 65 
 
 reality. The grandparents from whom a cousinhood is 
 descended have often a more real, marked, and individual 
 character than their grandchildren, though what these latter 
 retain of that character can only be represented by an abstrac- 
 tion, much of it having been lost and supplemented from other 
 sources. The grandparents are represented by an abstraction, 
 in the existing first cousinhood, but were not themselves in 
 any way more abstract than their descendants. But when we 
 look at long intervals of evolution the matter undergoes a 
 change, as is easily verifiable in the case of human character 
 and intellect. A savage has not the individuality of a modern 
 European ; he is more abstract ; his nature includes fewer 
 differences, less profound feelings, less grasp of fact, and less 
 definiteness of imagination. Or to take a more tangible 
 instance (for the facts of savage life are always subject to 
 dispute if not to doubt), even the Greek intellect in its prime, 
 or Greek art at its best, has not the many-sided concreteness 
 that belongs to Shakespeare or Goethe, Raphael or Turner. 
 And indeed, if we go to natural history, and say that ' Organism 
 in the abstract ' never existed, really the Amoeba or the white 
 blood corpuscle seem to contradict us. It is hard to see how 
 every successive generation or epoch of evolution, so long as 
 growth is not counterbalanced by decay, can avoid adding 
 import and significance to the content of things. With the 
 mind this is admittedly the case, and the course of evolution 
 seems to show it in nature too. It may be said that the ante- 
 cedent is no more abstract than the consequent, and that the 
 universe as a whole cannot grow either more or less concrete. 
 But it may be doubted whether this formal argument applies 
 to a system which has individuals within it. In bringing to 
 bear its total content upon such individuals there seems to be 
 scope for infinite grades of concreteness. In this case the 
 advance from abstractness to concrete individuality would 
 have grounds in historical fact. In one form or another this 
 idea has often been maintained, and I think that it bears 
 witness to a truth. 
 
 We have now considered the primary aspects of the materials 
 or instruments of logical thought — ^the idea and the name. 
 This discussion seemed appropriate to an Introduction, be- 
 
 1337 p 
 
66 Introduction [Introd. 
 
 cause it is impossible to admit that the name, concept," or 
 idea, is a portion of the content of Logic, in the sense in which 
 such a position is assigned to the Judgment and to Inference. 
 We do not enter upon logical development proper till We come 
 to deal with the evolution and affiliation of judgments. 
 
 "^ Nettleship (Lectures on Logic) and other writers have insisted that 
 the concept, as the point in which judgment has rest and unity, ought 
 to be definitely recognised in Logic. I see that we possess a relatively 
 solid world of our own construction. But I do not see that this can 
 avoid being maintained within the general form of judgment by being 
 referred to its place in our universe of experience. See ii, p. 292. 
 
BOOK I 
 Of Judgment 
 
 CHAPTER I 
 
 Of Judgment and Judgment-forms in general 
 
 I. Judgment is coextensive with affirmation and denial, or, i. The 
 which is the same thing, with truth and falsehood. True and ^ature of 
 false are not indeed terms applied exclusively to judgments ; ment as 
 but yet in all their applications their essential meaning depends ^^^^' 
 upon judgment. The sensations of a diseased organ may be 
 abnormal, but cannot possibly be false unless, on the strength 
 of them, we judge erroneously. A false note is a real sound, 
 a false man is an actual individual. It is not their existence, 
 but a judgment implied in their nature, that gives meaning 
 to the censure of falseness. The musical note is not what its 
 place demands ; the man is not what he pretends or aspires 
 to be ; it is the demand or pretension, ascribed actually or by 
 metaphor to thing or person, which condemns them as false in 
 as far as it is unrealised. 
 
 Thus truth and falsehood are coextensive with judgment, 
 and depend on the fact which is its primary condition ; the 
 fact that a thing may have an ideal relation to reality over 
 and above its own particular existence ; so that its existence, 
 though in itself real and actual, is empty and valueless in the 
 absence of the further reality that such a relation demands. 
 Truth must belong to something whose unreality is not simply 
 non-existence ; or how could falsehood exist ? The essence 
 of falsehood or fiction is that there should be an actual some- 
 thing that pretends to be something else. 
 
 Thus if we describe Judgment as the act of thought which 
 is capable of truth and falsehood, the description, although 
 tautologous, is not unsuggestive. It tells us that we are to 
 
 F 2 
 
68 Judgment and Judgment-Jorms [Book i 
 
 look for the differentia of judgment not in a mere mental fact, 
 but in some further value with which the mere mental fact is 
 invested. 
 Symbolic i. This primary condition of judgment recalls us to the 
 ideas. subject of the Introduction. In judging, we use ideas, but 
 the ideas which we use are not mere particular mental images, 
 the perishing existences which pass through consciousness, 
 and which, qua particular psychical states on a level with mere 
 sensations, never recur. Ideas,-"^ according to Locke, though 
 particular in their existence, are general in their signification. 
 In judgment, ideas are employed solely for the sake of their 
 • general signification, and without reference to their particular 
 
 existence. An idea, considered as a general signification, is. 
 what was described in the Introduction as the meaning of 
 a word. It is not without effort, as we all know, that we can 
 find in our consciousness any intermediary between the word 
 on the one hand, and the reality on the other ; and when it is 
 brought to our notice that a reality cannot as such be a state 
 of our individual consciousness, we are sometimes tempted 
 to deny that it has any representative there beyond the name. 
 We see from this how utterly the symbolic and secondary em- 
 ployment of psychical images obliterates all consideration of 
 their particular existence as mental occurrences. We no more 
 take note of them than, on meeting a welcome friend, we give 
 ourselves a detailed account of the peculiarities by which we 
 recognise him. The word and its reference — a reference to 
 some continued identity in the world of meanings ^ — are in- 
 extricably welded together. It is only by reflective analysis 
 that we discover, within and auxiliary to the meaning of a 
 word, the particular psychical images by help of which we 
 symbolise it. 
 
 And the meaning tyrannises over the psychical image in 
 another respect. Besides crushing out of sight its particular 
 and exclusive existence, it also crushes out part of its content. 
 The psychical images that pass through our minds might be 
 compared to a store of signal flags. Not only is it indifferent 
 whether your signal flag of to-day is the same bit of cloth that 
 
 ' Essay on Human Understanding, Book III, chap. 3, sect. 11. 
 ^ See Introduction, sect. 7. 
 
Chap. I] SymhoHc Ideas 69 
 
 you hoisted yesterday, but also, no one knows or cares whether 
 it is clean or dirty, thick or thin, frayed or smooth, so long as 
 it is distinctly legible as an element of the signal-code. Part 
 of its content,"' of its attributes and relations, is a fixed index 
 which carries a distinct reference ; all the rest is nothing to 
 us, and, except in a moment of idle curiosity, we are unaware 
 that it exists. The well-known difficulty of detecting misprints 
 arises from the same despotism of the meaning. Let the main 
 index-letters of a word be correct, or even the main index- 
 words of a sentence, and we are off at once in thought to the 
 word or sentence which is indicated, and remain unaware of 
 minor variations in the content employed as index. 
 
 Thus the idea, as used in judgment, is a general signification, 
 or in other words, a fixed reference. And because fixed, it is 
 limited ; limited to portions of content which serve as indices 
 of the reference, and are compatible with psychical accompani- 
 ments that vary with the series of images. I will give another 
 instance. Some one speaks to me of the Aegean Sea, which 
 I have never seen. He tells me that it is a deep-blue sea under 
 a cloudless sky, studded with rocky islands. The meanings of 
 these words are a problem set to my thought. I have to meet 
 him in the world of objective references, which as intelligent 
 beings we have in common. How I do this is my own affair, and 
 the precise images at my command will vary from day to day, 
 
 * I can see no difficulty in this conception, if we bring in the acquired 
 content, e.g. of a word. Critics might say that this equals meaning, 
 and that the text explains meaning by meaning. But here, perhaps, 
 they supply the answer. For a word, they point out, has a psychical 
 fringe, which, they again point out, is not meaning (cp. Stout, Ar. Proc, 
 1903, p. 13, and Hoernle, Mind, 6i, p. 8i ff.). For my own part (see 
 p. 40 above, and ii, p. 298), what I take to matter is the use. In an 
 original or acquired content (though already symbolic, as in my view, 
 all ideas are ; see p. 70 below), when not being used in definite judg- 
 ment, the aspect of mental existence- becomes prominent. The use in 
 judgment I take to be a question of degree (p. 5 above). I may add 
 that I am aware of the passage about Mr. Bradley's phrase ' acquired 
 content ' in Professor Stout's paper above referred to. But I continue to 
 think that the term is explained by the words ' The meaning may be part 
 of the original content, or it may have been discovered and even added 
 by a further extension ' (Bradley's Logic, p. 3). And it appears to me 
 clear that with this explanation it is true that the content of a sign, 
 though not, of course, the whole content, always qualifies for us the 
 thing signified. See Nettleship, Remains, i. 23. 
 
70 Judgment and Judgment-forms [Booki 
 
 and from minute to minute. It sounds simple to say that 
 I combine my recollections of sea and sky at Torbay with 
 those of the island-studded waters of Orkney or the Hebrides. 
 Even so, there is much to adjust and to neglect ; the red cliffs 
 of Torbay, and the cloudy skies of the north. But then again, 
 my recollections are already themselves S3'^mbolic ideas ; the 
 reference to Torbay or the Hebrides is itself a problem set to 
 thought, and puts me upon the selection of index-elements in 
 fugitive images that are never twice the same. I have_^;'S^ to 
 symbolise the colour of Torbay, using for the purpose any 
 blue that I can call to mind, and fixing, correcting, subtracting 
 from, the colour so re-called, till I reduce it to a mere index- 
 quality ; and then I have to deal in the same way with the 
 meaning or significant idea so obtained, clipping and adjusting 
 the qualities of Torbay till it seems to serve as a S3anbol of the 
 Aegean. '^ 
 
 Here then we have the first essential of judgment. The 
 ideas used in judging are not particular existences but general 
 significations, or objective references. No mere mental 
 occurrences as such, no series or combination of particular 
 images, can by any possibility be a judgment. It is the 
 essence of judgment to claim a value which is beyond the mere 
 mental act itself, and which is therefore liable to be divorced 
 from the mental act ; and this divorce, as we have seen, is 
 what falsehood means. That is false, which zs, but like a false 
 coin, has not the significance which it claims. In judgment, 
 then, all ideas are symbolic, that is to say, have a constant 
 reference. 
 
 Can ideas be symbolic apart from judgment ? ** If no ideas 
 in a human consciousness are apart from judgment (see 
 Introd. 2. ii) this question falls to the ground so far as concerns 
 
 " Then, it has been said, my test of truth is correspondence, i. e. how 
 far my idea is like the original. I reply, to me this is meaningless. 
 There is no given original. Sense-perception gives no original. How 
 can it, when its main task is self-amendment ? A man may have seen 
 the Aegean, and yet have a worse idea of it than a man who has not. 
 The ultimate ' original ', got by amending our perception till it could 
 be amended no more, would involve the Absolute, and would be like 
 nothing in our world of percepts. But the working test for us is what 
 idea does most justice to all the experiences concerned. 
 
 ** For the significance of this paragraph see p. 39 above. 
 
Chap. I] Non-SymboUc Ideas 71 
 
 that consciousness. But the discussion referred to made it clear 
 that apart from ultimate analysis we do entertain ideas without 
 judging them true, as in the question and in the negation, 
 and that these ideas are symbolic. The further problem may 
 then be pressed upon us : ' Are there at all ideas which are 
 not symbolic ? ' In identifying the human intelligence with 
 a continuous judgment we seem to have denied in advance 
 that non-symbolic ideas are, for that consciousness. The 
 answer is that a. In judgment itself the idea can be distinguished 
 qua particular in time or psychical fact, and so far is not 
 symbolic, and ^. In all those human experiences from which 
 we draw our conjectures as to the animal intelligence, when 
 in languor or in ignorance image succeeds image without 
 conscious judgment, we feel what it is to have ideas as facts 
 and not as symbols. 
 
 ii. Granting that symbolic ideas cannot ultimately be enter- Reference 
 tained without judging, it does not follow that to judge is °''^^' ^■ 
 merely to entertain ideas. In what does the act of judgment 
 consist ? An act it undoubtedly is ; an act which is as cer- 
 tainly present, and which we find as hard to describe, as the 
 much disputed act of volition itself. 
 
 I shall attempt in the first instance to make the essentials 
 of the matter quite clear in a simple case, with which we shall 
 afterwards find that all more elaborate instances agree in 
 fundamental structure. 
 
 If I say, pointing to a particular house, ' That is my home,' 
 it is clear that in this act of judgment the reference conveyed 
 by the demonstrative is indispensable. The significant idea, 
 ' my home,' is affirmed, not of any other general significant 
 idea in my mind, but of something which is rendered unique 
 by being present to me in perception . In making the j udgment , 
 ' That is my home,' I extend the present sense-perception of 
 a house in a certain landscape by attaching to it the ideal 
 content or meaning of ' home ' ; and moreover, in doing this, 
 I pronounce the ideal content to be, so to speak, of one and 
 the same tissue with what I have before me in my actual 
 perception. That is to say, I affirm the meaning of the idea, or 
 the idea considered as a meaning, to be a real quality of that 
 which I perceive in my perception. 
 
72 Judgment and Judgment-forms [Booki 
 
 The same account holds good of every perceptive judgment ; 
 when I see a white substance on a plate and judge that ' it is 
 bread ', I affirm the reference or general meaning which con- 
 stitutes the symbolic idea ' bread ' in my mind, to be a real 
 quality of the spot or point in present perception which 
 I attempt to designate by the demonstrative ' this '. The act 
 defines the given but indefinite real by affirmation of a quality, 
 and affirms reality of the definite quality by attaching it to the 
 previously undefined real. Reality is given for me in present 
 sensuous perception, and in the immediate feeling of my own 
 sentient existence that goes with it. The real world, as a 
 definite organised system, is for me an extension of this present 
 sensation and self feeling by means of judgment, and it is the 
 essence of judgment to effect and sustain such an extension. 
 It makes no essential difference whether the ideas whose 
 content is pronounced to be an attribute of reality appear to 
 fall within what is given in perception, or not. We shall find 
 hereafter that it is vain to attempt to lay down boundaries 
 between the given and its extension. The moment we try to 
 do this we are on the wrong track. The given and its extension 
 differ not absolutely but relatively ; they are continuous with 
 each other, and the metaphor by which we speak of an exten- 
 sion conceals from us that the so-called ' given ' is no less 
 artificial than that by which it is extended. It is the character 
 and quality of being directly in contact with sense-perception,* 
 not any fixed datum of content, that forms the constantly 
 shifting centre of the individual's real world, and spreads from 
 that centre over every extension which the system of reality 
 receives from judgment. 
 
 Waiving then this distinction, though as a matter of degree 
 it may find a place in the enumeration of judgments, we find 
 the same general features in all judgments of perception. 
 There is a presence of a something in contact with our sensitive 
 self, which, as being so in contact, has the character of reality ; 
 and there is the qualification of this reality by the reference to it 
 
 * This has sometimes been remarked on as if it implied a sensationalist 
 view of Reality. But the point is merely that in the ' this ' of sense 
 Reality appears in a quasi-satisfactory form, having a sort of self- 
 completeness. When we begin to explain and define it, of course it 
 breaks down, and demands the effort to complete it by way of thought. 
 
Chap. I] The Constfucted Real World 73 
 
 of some meaning such as can he symbolised by a name. It 
 cannot be alleged in theory that a name is essential to judg- 
 ment. At least for ' name ' it would be necessary to substitute 
 in such an allegation ' some symbol '. The spatial order of 
 things which we see whenever we open our eyes, is, qua order 
 of things, the content of a perceptive judgment, in which 
 universal ideas are presented through sensuous symbols. 
 
 The subject in every judgment of Perception is some given 
 spot or point in sensuous contact with the percipient self. 
 But, as all reality is continuous, the subject is not merely this 
 given spot or point .^ It is impossible to confine the real world 
 within this or that presentation. Every definition or qualifi- 
 cation of a point in present perception is affirmed of the real 
 world which is continuous with present perception. The 
 ultimate ^ subject of the perceptive judgment is the real world 
 as a whole, and it is of this that, in judging, we affirm the 
 qualities or characteristics. 
 
 The claim to be true, which as we saw belongs primarily to 
 judgment, indicates the same relation. In every judgment, 
 as Mill incisively contends, we profess to speak about the real 
 world and real things. ' The Sun ' means ' the Sun ' ; and 
 whatever that may be, it is not anything merely in my mind ; 
 not relative purely to me as a conscious organism ; not 
 a psychical fact in my individual history. Every judgment, 
 perceptive or universal, might without altering its meaning be 
 
 introduced by some such phrase as * Reality is such that ', 
 
 * The real world is characterised by .' 
 
 Thus in the Perceptive Judgment at least we find the 
 meaning or objective reference of an idea — such a content as is 
 indicated by a name — affirmed to characterise some reality 
 present in sense-perception, and through it, reality as a whole. 
 We shall find that all Judgments of every kind share the main 
 elements of this description ; only that the reference to an 
 indeterminate element of present sense-perception is gradually 
 displaced by the introduction of explicit ideas to describe 
 
 * See Introd. 2. i. 
 
 * .See Introd. 2. i. Analysis and cross-examination readily verify this 
 as a fact. After admitting any judgment to be true, you cannot deny 
 its modifying effect on any portion whatever of your real world ; i. e. it 
 has been admitted of the real world as a whole. 
 
74 Judgment and Judgment-forms [booki 
 
 the immediate subject. Such ideas disguise but do not remove 
 the reference to Reality as the ultimate subject in every 
 judgment ; they have, however, important effects in modify- 
 ing both the act of affirmation, and the nature of what is 
 affirmed. When I come to examine the chief types of judg- 
 ment, I shall have to consider the nature of these effects. But 
 I intend in the first place to say something of the proposition, 
 from the analysis of which many current views about judgment 
 are derived. 
 Judg- iii- The enunciative sentence — the unit of language which 
 
 ment and represents a judgment — is called a proposition. Language, as 
 sition. we saw, supplies the fixed symbols which stand for ideas. It 
 would be rash to say that there can be thought without 
 language — if language includes every possible system of 
 recognisable signs — and wholly perverse to imagine that the 
 ideal of intelligence lies at all in the direction of a severance of 
 thought from words. The Introduction, in dealing with 
 Names, showed us the absurdity of any such conception. But 
 yet the spoken or written proposition differs fundamentally 
 from the judgment. 
 
 I do not think that it is convenient to rank the narrative 
 or temporal affirmation as a ' proposition ' (German * Satz '), 
 and reserve the name of judgment for an act of thought which 
 has some purpose in the way of classification or definition. 
 To do so is in English terminology at least to confuse a dis- 
 tinction of degree with one of kind ; but it is worth noticing 
 that such a nomenclature has been proposed,^ and that 
 according to it judgment proper would begin at the point 
 where inference and necessity become explicit. For against 
 any doubt, judgment maintains itself as an inference,^ and 
 this is exactly the test that has been held to distinguish 
 a judgment from a proposition. To affirm that a carriage is 
 passing the house, Hegel says,^ is not a judgment unless there 
 is a question, e.g. whether it is a carriage or a cart ; i.e., I sup- 
 pose, unless some general connection of attributes is inten- 
 tionally affirmed. Now a general connection involves a ground, 
 and so an inference. Thus the classification in question would 
 
 ' Hegel's Logic, Wallace's Translation, pp. 258-9. 
 ' Bradley, Principles of Logic, p. 404. 
 
Chap. I] What purts has the Judgment ? 75 
 
 have the merit of suggesting that judgment begins with 
 inference. But the point of commencement taken is really 
 arbitrary ; though judgment and inference begin together, 
 yet both begin before this point. 
 
 I prefer then to take the proposition all through as the 
 actual spoken or written enunciative sentence ; while the 
 judgment is the intellectual act which depends in various 
 degrees upon words or other symbols, but is different from 
 any mere combination of words or symbols whether heard, 
 read, or remembered. 
 
 The essential differences between judgment and proposition 
 may be arranged under two heads, which cannot however be 
 wholly separated from each other. \ shall first speak of the 
 so-called parts of the judgment, the current conceptions of 
 which are derived from grammatical analysis of the proposi- 
 tion ; and then pass on to consider how far the idea of a 
 transition in time, which is inseparable from the apprehension 
 of a sentence, is applicable to the judgment as such. 
 
 a. The division of the Judgment into Subject Copula and The parts 
 Predicate is obviously derived from the analysis of the enuncia- jude-^ 
 five sentence. The finite verb, which is a proposition in ment. 
 miniature, contains all these elements within itself ; and the 
 history of their being distinguished within the sentence is the 
 history partly of linguistic evolution and partly of gram- 
 matical or quasi-logical analysis. Even the separation of the 
 substantive from or within the verb, is, I suppose, an early 
 analytic development of language ; and it is the tendency of 
 modern speech, no less than a supposed convenience of 
 thought, that has finally transmuted Nominative and Verb into 
 Subject Copula and Predicate. The Copula in the modern 
 sense was unknown to Aristotle, although the use of the predi- 
 cative Veib 'to be ' attracted his attention and drew from 
 him a somewhat inadequate explanation. If we return, how- 
 ever, to Aristotle's main position, and, in agreement with 
 students of English grammar,^ regard the Judgment as made 
 up of Subject and Predication {6vo\ia andp^/xa), we have got 
 rid of one fiction in the separate Copula, but the distinction 
 
 ' Cp. Mason's English Grammar, Jones's Analysis of English Sen- 
 tences, and Wrightson's Functional Elements of the Sentence. 
 
76 Judgment and Judgment-forms [Booki 
 
 which we retain may still be challenged. It is plain that the 
 judgment, however complex, is a single idea. The relations 
 within it are not relations between ideas, but are themselves 
 a part of the idea which is predicated. In other words, the 
 subject must be outside the judgment in order that the content 
 of the judgment may be predicated of it. If not, we fall back 
 into ' my idea of the earth goes round my idea of the sun ', 
 and this, as we have seen, is never the meaning of ' The earth 
 goes round the sun '. What we want is ' The real world has 
 in it as a fact what I mean by earth-going-round-sun '. 
 
 This view, stated thus extremely, would not only annihilate 
 the copula with separate content, but also the whole distinction 
 of Subject and Predication, and it is an argument in its favour, 
 that, in doing' so, it would seem only to lay bare in all judg- 
 ments the elementary type which forces itself on our observa- 
 tion in the simplest perceptive apprehension ; at a stage, that 
 is to say, before the grammatical subject, which creates our 
 present difficulty, appears explicitly in the proposition. But 
 we shall see in tracing the evolution of judgment, that it is 
 impossible to dispense with the distinction of Subject and Pre- 
 dication, and that the appearance of contrast between propo- 
 sitions which have and which have not grammatical subjects, 
 is caused by the necessity of representing immatiure thought 
 in developed language ; so that the thought in which dis- 
 tinctions are rudimentary must either be mutilated by the 
 omission of an element, or transformed by explicit articulation. 
 It is impossible to represent a judgment by a single noun 
 belonging to a modern language, though such a noun is often 
 all that we utter. Such a judgment should really be represented 
 either by a rudimentary sentence, that is, by some element of 
 language not yet reduced to the position of a part of speech, 
 or by a miniature sentence, i.e. by a verb. 
 
 In other words, although the ultimate Subject extends 
 beyond the content of the judgment, yet in every judgment 
 there is a starting-point or point of contact with the ultimate 
 subject ; and the starting-point or point of contact with 
 reality is present in a rudimentary form in the simplest per- 
 ceptive judgment, as it is explicitly in the later and more 
 elaborate types. 
 
Chap. I] Subject, in Logic and Grammar yy 
 
 Then it would come to this. Subject and Predicate in the 
 actual judgment are really distinct, as a real identity from 
 or in its differences. The relation of their contents is itself 
 ideal, and not a relation between ideas ; but nevertheless 
 the judgment demands this relation ; for the judgment is my 
 consciousness qua judging, and my consciousness in judging 
 identifies the ideal or symbolised reference which constitutes 
 the predication with its own construction of the Real 
 world. ^ 
 
 The difficulty is that you cannot affirm without introducing 
 a distinction or reference into the content of the affirmation ; 
 and yet such distinction or reference, being part of what is 
 affirmed, and not a relation between what is affirmed and 
 something else, cannot, it would seem, be the essence of the 
 affirmation. What is the connection between the two things ; 
 between the reference of ' is-building-a-wall ' to ' Balbus ', 
 and the affirmation that the whole idea ' Balbus-building-a- 
 wall ' is true of reality ? What has the action of Balbus to do 
 with my affirmation that Balbus acts ? The latter seems wholly 
 unconnected with the former, and yet they are inseparable. 
 
 And the answer is that the real world is primarily and 
 emphatically my world. I take it to be real in virtue of its 
 contact with me. Therefore though the ideal relation within 
 a judgment is not a psychical fact in my mind but a fact 
 affirmed objectively of the real world, yet, the real world for 
 me being the world that hangs from my present perception, 
 I identify my assertion about it with its assertion of itself. In 
 every judgment the ultimate subject Reality is represented by 
 a selective perception, or idea, which designates a something 
 accepted as real. This something, taken as standing for 
 reality, is the actual subject of the judgment, and is qualified 
 by the ideal content which forms the predication. No judg- 
 ment can be found in which Subject and Predicate are not 
 apparent. Reality is one, but its presentation varies ; and 
 it is impossible to judge without explaining where and how 
 Reality accepts the qualification which we attach to it. The 
 presentation of Reality, qualified by an ideal content, is one 
 aspect of Subject and Predication ; and my individual per- 
 ^ Cp. Introd. 2. i. 
 
yS Judgment and Judgment-forms [Booki 
 
 cipient consciousness determining itself by a symbolic idea, is 
 the other. That the latter is identified with the former follows 
 from the fact that in entering upon the world of thought my 
 consciousness enters upon the experience of logical necessity — 
 the nisus towards complete expression. 
 
 Thus I am of opinion that Subject and Predication are essen- 
 tial elements in the Judgment. But whereas in the judgment 
 they are differences within an identity, in the proposition they 
 are isolated parts of an extended whole ; and the copula, 
 which in Judgment is merely the reference that marks predica- 
 tion, and has no separate content, becomes in the proposition 
 an isolated part of speech. When therefore the analysis of the 
 proposition controls the interpretation of the judgment, each 
 of these parts of the sentence is treated as a separable content, 
 and perhaps as a separate psychical existence ; and we are 
 told of two ideas or two ideal contents, and a variable copula, 
 itself also an ideal content, which indicates the varying 
 relations ^ between them. In this sense Subject and Copula 
 and Predicate are mere fictions. The judgment is not a relation 
 between ideas, nor a transition from one idea to another, nor 
 does it contain a third idea which indicates a particular kind 
 of connection between two other ideal contents. 
 
 The real nature of the copula we have seen already. It is 
 the mere sign of affirmation, and, though usually conveyed 
 by a finite verb in languages which possess one, does not 
 depend on tense. Aristotle, who was inclined to include 
 ' indication of time ' in the differentia of affirmation, was 
 nevertheless aware that judgment could take place ' abso- 
 lutely ' {airXSis) as well as with note of time {Kara xP<^^(>^)- 
 Moreover a verb can exist without definite tense, and predica- 
 tion can exist apart from a distinctly formed verb. 
 
 The reason why the verb, where there is a verb, is appro- 
 priated to the act of predication, is not that the verb signifies 
 time, change, or action, but that it is, as has constantly been 
 repeated, a miniature sentence. Not merely does the verb 
 * agree ' with its subject — the adjective also agrees with its 
 
 ' Lotze, Logik, sect. 52. It is very doubtful whether in this passage 
 Lotze escapes the error which he imputes to others, of ' reducing 
 a logical operation to a mere psychical occurrence '. 
 
Chap. I] Is Judgment a change in time ? 79 
 
 substantive — but by convention, or explicitly in the person- 
 ending, it includes within itself a reference to given reality, 
 and can therefore stand alone as an enunciation, which no 
 other part of speech can do.*^ In other words, the verb is 
 prima facie a content referred to a real individual subject, and 
 though the subject may be by the help of additional phrases 
 defined, set down as imaginary, or even denied, the verb has 
 always in itself the force of this demonstrative reference. An 
 adjective implies a reference to something else, but the some- 
 thing may be a mere idea ; it is only the verb that professes 
 to select an element directly related to the speaker's appre- 
 hension, and to attach a significant content to that element. 
 
 It is in the demonstrative force of the verb that we must 
 look for its fundamental predicative force. I suppose that the 
 collocations which in Greek, and more or -less in many lan- 
 guages, have power to turn the epithet into a predicate, owe 
 their significance to a quasi-demonstrative emphasis. In 
 ' the white horse ' (6 AevKos itttios) there is nothing that can be 
 taken as a reference to a special point in reality ; no indica- 
 tion of a real existence, either in the ideal content or out of it, 
 which we propose to qualify by its meaning. In ' the horse 
 (is) white ' (0 itt-ttos kiVKos) there is an indication of a line 
 between a an individual that may be real and j3 a content 
 that may be attached to him or it, and therefore the instinct 
 of reason which sees a judgment wherever a judgment is 
 possible, takes the individual named as if it were an appeal 
 to perception, i.e. a demonstrative reference to reality, and the 
 content as a quality ascribed to the real subject so obtained. 
 In the universal judgment this demonstrative reference 
 becomes merely formal ; but it continues in all language to 
 supply the symbol of judgment. 
 
 /3. It has been proposed to distinguish Subject and Predi- Judg- 
 cate simply as earlier and later in time, and the above instances j-giation 
 of demonstrative reference appear to support this notion. But to Time, 
 rather than admit it to be correct, I should surrender the 
 distinction altogether and adopt the view that there is no 
 subject in the judgment as such. For it is absolutely impossible 
 that priority in time should subsist between the parts of a com- 
 * See, however, p. 99 below. 
 
8o Judgment and Judgment-forms [Booki 
 
 pleted judgment. But if not, the priority of the subject would 
 exist merely in memory ; and an act of thought cannot be 
 characterised by a mere recollection of the process that 
 generated it. 
 
 In what sense is it true that the Judgment is in time, and in 
 what sense not ? It may be convenient to distinguish between 
 arriving at the judgment, and subsequently modifying the 
 judgment, although the two processes are, as we shall see, 
 really continuous. 
 
 In what follows I do not identify the aspect of Judgment 
 as in time with the series of images qua psychical occurrences 
 that pass through the mind while we judge. It is probable 
 that the view which defines Judgment as a change is influenced 
 by the particularity of ideas qua events of consciousness as 
 well as by the constant transition from judgment to judgment. 
 But the former element ought to have been eliminated by 
 what has been said above. 
 Arriving I. In arriving at a Judgment, as when we hear a sentence 
 at Judg- ^^^ < ^g^j^ £qj. ^j^g Yerh ', or scrutinise an approaching person 
 until his name comes into the mind, we undoubtedly appear 
 to begin with a ready-made Subject, to which a Predicate is 
 added by a subsequent transition. But closer attention will 
 show us that this is not the case. We have always some 
 anticipation of the meaning of a sentence, and this anticipation 
 takes the shape of a provisional judgment or judgment in 
 outline, very probably disjunctive in type, the shape of which 
 becomes more definite as we follow the sentence, until the 
 final clause determines its ultimate content. In the first place, 
 consciousness, when any ideal content whatever is presented 
 to it, absolutely refuses to abstain from judging ; and in the 
 second place, what comes first could not have (as it undoubt- 
 edly has) the significance of a subject, unless with reference 
 to something already referred to it in the way of predication. 
 
 The case of perception leads to the same conclusion. You 
 can come to no judgment by help of perception unless you 
 interrogate perception ; and you cannot interrogate percep- 
 tion unless you have in the mind some general idea as a basis 
 for further specification. 
 
 Thus, in reaching a particular apprehension or perception. 
 
Chap. I] Judgment is extended in time 8i 
 
 there is a transition that occupies time. But the transition 
 is not from Subject to Predicate, which we will call S and P 
 respectively, but from s-py (where y indicates superfluous 
 detail, which is omitted when the perception becomes clear) 
 through 2-11, to S-P. To speak of a transition from S to P 
 is wholly false. We never have an S first, and then tack a P on 
 to it ; we have always an inchoate judgment or a choice of 
 judgments. The process is not like adding one piece in 
 a mosaic to another ; it is more like enlarging a hole, which 
 has centre and circumference from the beginning. 
 
 2. What has been said of the transition by which we arrive The 
 at a judgment cannot but apply to the judgment when arrived ju^g-^ ^ 
 at. It is clear indeed that we are thus led to regard the com- ment. 
 pletion of the judgment as an arbitrary distinction, dependent 
 solely upon our momentary interest. The completed judgment, 
 like the process by which it is obtained, obviously possesses 
 duration. It is absurd to suppose that a judgment cannot be 
 dwelt upon, and only exists as a momentary transition from 
 S to P. Such a conception arises from the confusion of two 
 points of view, either of which may be taken as a presup- 
 position, and reconciled with the other by a mistaken com- 
 promise. It may be assumed that the judgment, as such, is 
 not in time, and then this assumption has to be reconciled with 
 the obvious fact that judgment as an intellectual process is 
 a transition that occupies duration ; or it may be taken as 
 certain that the judgment is a transition in time, and then we 
 have to face the experience that its essential parts do not fall 
 outside each other in succession. To treat it as an instan- 
 taneous transition is a ridiculous attempt to combine the 
 character of occupying duration with that of not being in 
 succession. It recognises both principles, and satisfies neither. 
 
 As we have seen in the process of arriving at the judgment, 
 the act of judging as an occurrence in consciousness presents 
 itself in the aspect of an interval of consciousness extended in 
 time, and therefore including successive differences within it. 
 But it does not include succession because the nature of the 
 judgment is to be successive, but because the flux of sensa- 
 tions and ideas is always pressing new material upon conscious- 
 ness, and a perception, once attained, satisfies no interest by 
 
 G 
 
 1337 
 
 lO 
 
 (^0 
 
82 Judgment and Judgment-forms [Booki 
 
 being further dwelt upon unless it gains in content from 
 moment to moment. Thus tlie duration of the judgment as 
 a transition in time is, so to speak, its external aspect, the 
 aspect which, as a whole, it presents when compared with other 
 occurrences in consciousness ; and this duration is theoretically 
 capable of any degree of extension. On the other hand, as 
 between Subject and Predication, that is to say, within the 
 judgment, there is no transition at all. 5 and P are modified 
 pari passu, and so, as a relation between them, the judgment is 
 not in time. This relation is a continued identity S-P which 
 includes within it the differences s-p, S-n, and so on. The 
 transition is not from 5 to P, but from s-p to 2-n within the 
 general signification S-P. The idea of mere momentary 
 existence has therefore thus much truth, that if you cut across 
 the interval of consciousness occupied by a single judgment at 
 any point whatever, you will always find in the plane so laid 
 bare both 5 and P in one or other of their forms. They are in 
 every minute part, but they are not confined to such a minute 
 part. Judgment breaks up into judgments as rhomboidal spar 
 into rhomboids, but nevertheless it is one through its whole 
 extension. 
 
 But if a judgment can be thus extended, what do we mean 
 by a judgment, and how do we know when we enter upon 
 a new one ? The question is in each case a material one, being 
 in fact the question of continued identity, and it is impossible 
 to give it a formal answer. As a first approximation we might 
 say that a single judgment is any extent of judging activity 
 that can be summed up in a single proposition. But as the 
 proposition takes its value from the judgment, .and not vice 
 versa, this is no more than an appeal to the fact that we suc- 
 ceed in distinguishing single judgments. The question is one 
 of continued identity, and therefore must be dealt with as 
 concerning organised wholes or systems. A mere extension of 
 a system, or a mere omission within a system, does not bring us 
 to a new and different system. The clearest cases of transition 
 from judgment to judgment are those in which language uses 
 a mere conjunction. When, on the other hand, we have 
 propositions united by the inferential particle, it is a matter 
 of degree how far they stand for separate judgments. Ulti- 
 
Chap. I] Continued identity of Judgment 83 
 
 mately perhaps every inference may or should be represented 
 as a single judgment, as being a mere extension of an existing 
 whole of thought, and not a transition to a different one. Such 
 an idea conflicts with the traditional differentia of inference, 
 that it should lead to a new judgment ; but this only means 
 a bona fide extension of the previous whole, such that, if taken 
 in abstraction from the process that generates it, it would appear 
 a perfectly new judgment. At least in elementary cases it is 
 easy to see how inevitably inference shrinks up into single 
 judgments, if we look at the actual life of thought. 
 
 Take such an e very-day judgment of mixed perception and 
 inference as ' He is coming downstairs and going into the 
 street '. It is the merest chance whether I break up the 
 process thus, into two judgments as united by a mere con- 
 junction, or, knowing the man's habits, say, when I hear him 
 half-way downstairs, ' He is going out.' In the latter case 
 I summarise a more various set of observations and inferences 
 in a single judgment ; but the judgment is as truly single as 
 each of the two which were before separated by a conjunction ; 
 for each of them was also a summary of a set of perceptions, 
 which might, had I chosen, have been subdivided into distinct 
 propositions expressing separate judgments ; e.g. 'He has 
 opened his door, and is going towards the staircase, and is 
 half-way down, and is in the passage,' &c. If I simply say 
 ' He is going out ' I am not a whit the less conscious that 
 I judge all these different relations, but I then include them 
 all in the single systematic content ' going out '. ' Cromwell 
 Road runs east, and the Brompton Road north-east,' are two 
 judgments ; but if the road happens to be thought of qua 
 continuous, one would say, ' Cromwell Road turns from east 
 to north-east, where it becomes the Brompton Road.' Again, 
 ' Knightsbridge and Kensington Gore run east ' may be 
 generalised as ' The street from Kensington Church to Knights- 
 bridge Barracks runs east '. 
 
 Thus a judgment is one in respect of the continued identity 
 of its Subject and Predication, and this identity cannot be 
 defeated by the inclusion of difference, but enly by the failure 
 to recognise continuity. It is obvious that the generalised 
 forms in the above instances presuppose a work amounting to 
 
 G2 
 
84 Judgment and Judgment-forms [Booki 
 
 colligation of facts, if not to elementary induction and analogy. 
 If the included judgments were never separately made, the 
 inferential work of colligation has not been explicitly done ; 
 but it would be found absolutely impossible to draw the line 
 between cases where it has been done and those where it has 
 not. Every judgment would on scrutiny reveal differences 
 which had more or less been absorbed into its formation. It 
 follows inevitably that every systematic inference considered 
 as a judgment is single and not multiple. However this may be, 
 it is clear that extension in time is no bar to the unity of 
 judgment. 
 Scheme II. Judgment, as we have seen, is primarily the intellectual 
 
 arrange- ^^^ ^^'hich extends a given perception by attaching the content 
 ment of of an idea to the fact presented in the perception. The whole 
 inen^s '^^ consciousness, in as far as it is the consciousness of a single 
 world that shares the reality of our waking self, may be 
 regarded as a continuous judgment, which qualifies our present 
 feelings and surroundings by the knowledge of what is more 
 remote in space and in time. From the point of view of 
 common logic, that is of individual knowledge, the intellect 
 sustains its world by continued effort, as Atlas held up the 
 sky.^ Every judgment is an effort of this kind, affirming on 
 the one hand that the same reality which we touch in the 
 present is rightly described by such and such an idea, and on 
 the other hand that such and such an idea is real with the 
 same reality as that which we touch in the present. The 
 ' idea ' of which I am speaking is, of course, not the particular 
 existence or single occurrence of a psychical image ; it is the 
 general signification for the sake of which we use the psychical 
 image. 
 
 The object of this Book is to analyse judgment into its 
 principal kinds, and, as a necessary consequence, to trace their 
 
 * This seems to me prima facie a plain and obvious fact. Every one's 
 world is relative to his capacity and energy of mind at a given moment. 
 If you ask ' What, then, becomes of the real world ? ' the answer is that 
 that is a metaphysical question, but by no means specially hard to 
 answer from this point of view as compared with any other. The real 
 world lies, I suppose, or rather lives, in the efforts of all spiritual beings 
 to sustain a unity of experience, taken in their completeness as success- 
 ful. Of course it does not live merely in judgment. 
 
Chap. I] Linear series inadequate 85 
 
 affiliation. We shall find that no linear arrangement will 
 represent these affinities. Judgment, as the effort of thought 
 to define reality, must vary with the kinds of reality to be 
 defined no less than with the degree of its success in defining 
 them. An equation is to one kind of whole what a definition 
 by genus and species is to another, or an appreciation of 
 aesthetic value to a third ; the function of judgment is present 
 in each of these activities, and the difference between them 
 is the difference of the wholes which they respectively analyse. 
 They are divergent developments of the same relation, in each 
 of which an aspect has become predominant that remains 
 subordinate in the others. 
 
 But we shall have to deal with convergence no less than with 
 divergence. The unity of the judgment excludes no com- 
 plexity of synthesis, and in determining the species of a plant 
 or the character of a man we may be obliged to employ, among 
 others, accurate determinations of number, time, and space. 
 That is to say, the treatment of a content by abstraction as 
 a spatial or numerical whole may be re-absorbed in a more 
 concrete treatment of it as an organic, aesthetic, or moral 
 whole. 
 
 It might indeed be urged, from the point of view of meta- 
 physics, that every kind of judgment must have its value 
 and no more as a contribution to the whole of Reality, and 
 that therefore the series of judgments, arranged according to 
 the degrees of their significance for knowledge, must after 
 all be linear. In other words, if a whole in number or 
 a whole in space is not final in itself, but demands some- 
 thing further to complete its significance, this might be 
 enough to show that we ought not to represent it as the goal 
 of an independent series, but rather as a stage or phase of con- 
 struction, subordinate to the more concrete forms of know- 
 ledge.^ I should not greatly object to such a \iew, and shall 
 endeavour in some degree to meet its requirements by ex- 
 hibiting the more complete and concrete syntheses as involving 
 the reunion of aspects which have been developed in the 
 abstract. But though the forms of space and time are involved 
 
 ' Cp. Plato's arrangement, in the Republic, of the mathematical 
 sciences in an order proceeding from abstract to concrete. 
 
86 Judgment and Judgment-forms [Booki 
 
 as a fact in the perceptive construction of the world of indi- 
 vidual things, yet the mathematical analysis of these forms is 
 an effort of the same scientific spirit which recognises the 
 principles of order in the world of things itself. The two 
 aspects of constructive science are co-ordinate and comple- 
 mentary activities of reason, and it would be ridiculous to 
 treat geometrical analysis as prior to the perception of charac- 
 teristic size or proportion. Intelligence is many-sided, in spite 
 of its unity ; and its aspects, which are correlative to each 
 other, lose their true interdependence by being drawn out 
 into a linear series. 
 
 SCHEME ILLUSTRATING AFFILIATION OF JUDGMENTS 
 AS DESCRIBED IN BOOK I. 
 
 Rudimentary or Intermediate 
 Series of Judgments 
 
 (Judgments of Quality.) 
 
 Impersonal Judgment ; 
 
 Demonstrative Judgment ; 
 
 [beginning with ' this ', ' here ', &c.] 
 
 (Judgments of Quantity.) 
 
 Comparative Judgments, &c. 
 
 (Judgment of Proportion.) 
 
 Measurement, &c. 
 
 Concrete or Categorical | Abstract or Hypothetical 
 
 Series. Series. 
 
 (Singular Judgments.) (Enumerative Judgments.) 
 
 Individual Judgment, &c. Plural or Particular Judg- 
 
 (Universal Judgments.) ments. 
 
 Quasi-collective Judgment. Collective Judgments. 
 
 Equation. 
 
 True Generic Judgment. Abstract relations of Space 
 
 I and Time. 
 
 I 
 Hypothetical Judgment. 
 
 Disjunctive Judgment. Infinity in Space and Time. 
 
 Purpose i- I subjoin a scheme of the arrangement which I propose 
 
 of scheme ^q follow in the remainder of the present Book. It is simply 
 
 intended to assist the reader in apprehending the views which 
 
 I submit, and is not meant to be a bed of Procrustes for the 
 
Chap. I] Infiovatiofis tfi scheme 87 
 
 facts of logic. I take it that variations of arrangement and 
 nomenclature are as inevitable in logic as in botany, and are 
 not undesirable in either science ; for they force upon our 
 minds the truth that species are but sections of evolution, and 
 that their arrangement is merely subsidiary to a correct appre- 
 hension of the process which we divide into such intervals. 
 
 ii. I will begin with a few words in explanation of the Explana- 
 scheme which I have adopted. scheme. 
 
 There is no need to apologise for describing some types of 
 judgment by appellations which are not to be found in Mill, 
 Whately, or Hamilton. Recent attempts to restore to logic its 
 hold on living concrete thought, a direction in which Mill was 
 himself an able and adventurous pioneer, have made us 
 familiar with a whole chaos of psychological, grammatical, and 
 quasi-mathematical titles applied to phases of the judging 
 activity. All that I have done has been to concentrate in 
 a single review the best estimate that I could make of the 
 tjrpical character and true affiliation of such phases, attempting 
 to give each judgment its appropriate place in relation to all 
 the principles employed in the classification, and eschewing 
 the too common habit of adducing various groups and appella- 
 tions in two or three successive chapters, without any distinct 
 reference of the one grouping to the other. 
 
 But besides adding to the traditional scheme of judgments, 
 the arrangement suggested involves a dislocation of its parts, 
 and the omission of one familiar antithesis. These innova- 
 tions, though by no means original,^ may conveniently be 
 indicated and justified in a few introductory remarks. 
 
 a. ' Categorical ' and ' Hypothetical ' are taken to designate Categori- 
 fundamental characters of knowledge, and not mere gram- Hypo- 
 matical appearance. It follows that the natural series ofthetical. 
 judgments commonly known as singular, particular, and 
 universal, cannot wholly fall within the genus categorical, but 
 at a certain point and in a certain degree assumes a, hypo- 
 thetical character. More especially, the formal equivalence of 
 
 1 The treatment of the universal judgment as fundamentally different 
 from the singular in categorical character was really initiated by Mill in 
 so far as he analysed the content of affirmation into coexistence of 
 attributes ; and has been adopted and accentuated by Lotze, Sigwart, 
 and Bradley. 
 
88 Judgment and Judgment-forms [Booki 
 
 the singular to the universal judgment is replaced by a pro- 
 found distinction of kind between the two. The disjunctive 
 judgment again has a place and value of its own, and is not 
 a mere proposition or grammatical form. 
 Diver- /3. The true quantitative judgment — not the ' universal ' 
 
 gent judgment of ordinary thought, which derives only its name 
 
 from quantity — reveals itself as a divergence from the central 
 development of the judgment by reason of its extreme abstrac- 
 tion, in which one element of the relation essential to judgment 
 almost disappears. 
 Analytic 7- The familiar terms ' analytic ' and ' synthetic ' are not 
 and Syn- made use of in the classification, because they belong to the 
 theory in general and are not distinctive of any particular 
 types. 
 
 I subjoin a short explanation on each of the above subjects. 
 Cateeori- «• ^ categorical judgment asserts an actual fact absolutely, 
 cal and A hypothetical judgment asserts only the consequence that 
 thetical. follows on a supposition. The distinction between the two 
 seems clear. It is the difference between ' There is a bad 
 smell in the house ' and ' If there is an escape of gas there will 
 be a bad smell '. But when we come to the ' Universal ' 
 Judgment the line of demarcation is at once blurred. Hamilton 
 gives ' Rainy weather is wet weather ' as an instance of 
 a categorical proposition, and ' If it rains, it will be wet ' as 
 an instance of a hypothetical. In the former, according to 
 him, ' rainy weather ' is ' unconditionally thought to exist '. 
 But is it ? Prima facie the two propositions represent the same 
 judgment, that is to say, their difference is grammatical only, 
 and their meanings are identical. It may be that the cate- 
 gorical shape conveys a presupposition which is absent from 
 the hypothetical enunciation — the presupposition that rainy 
 weather exists in rerum natura — and into the question thus 
 raised we shall have to enter at length later on. But it is 
 clear at all events that the ' categorical ' form conveys in this 
 case a meaning which is in a large measure, if not entirely, 
 hypothetical. 
 
 By referring to our account of judgment as such we shall 
 see that the distinction before us involves a fundamental 
 difficulty. Every judgment affirms an idea of reality, and 
 
Chap. I] Abstract is Hypothetical 89 
 
 therefore asserts the reality of an idea. Now an idea is neces- 
 sarily abstract, because determinate ; and therefore all judg- 
 ment involves abstraction. And abstraction is the essential 
 element of hypothesis ; it consists in taking up into an idea 
 some elements out of the content of experience, for the sake 
 of consequences which attach to the elements so taken up. 
 Therefore it seems, as the real world for us is maintained and 
 extended by Judgment only, that in all extension and even 
 maintenance of the given reality there is involved an element 
 of abstraction, which is the same as to say that in all categorical 
 judging there is an element of hypothesis. The relation of 
 these characters to each other throughout the history of the 
 judgment will be the main principle of the evolution which I 
 shall attempt to describe. But we must accept as the usage of 
 thought, which we are to explain, that the assertion of actual 
 fact coincides as a rule with the individual or singular judg- 
 ment, and that the universal affirmative of formal logic, on the 
 other hand, may in every case be taken as purely hypothetical. 
 
 The categorical character of a judgment in the above simple 
 sense may be tested by the possibility of expressing its meaning 
 by an impersonal proposition, however awkward may be the 
 necessary grammatical transformation. For ' Caesar was 
 crossing the Rubicon ' we may substitute ' There was Caesar 
 crossing the Rubicon ' ; but for ' All men are mortal ' it is 
 impossible to frame such an equivalent, for the reference to 
 given reality in the impersonal expression would be at once 
 contradicted by the abstract ' all ', which = ' any ' or ' if a- ', 
 and so points, in the absence of any more effective assertion 
 of the limited unity of the race, to an infinite series. If it is 
 possible to say ' These are all the men who, &c., &c.', the 
 ' all ' cannot be the true generalising ' all ', but must indicate 
 a sum of known individuals. It will be necessary however 
 to point out hereafter that the distinction between these two 
 senses of ' all ', or in other words the limit of individuality, is 
 not absolute, but is a matter of degree. 
 
 These instances suggest the principle to which we shall 
 adhere, viz. that every assertion is as absolutely categorical as 
 the nature of its elements will permit ; and that demonstrative 
 or individual judgments are in the plainest sense categorical, 
 
90 Judgment and Judgment-forms [booki 
 
 because the realities indicated by their subjects are of a nature 
 that can be given, in a way in which the realities indicated 
 by more definite abstractions cannot. In every case the real 
 subject is the reality indicated ; in every case this subject is 
 alleged to exist ; but the question is how and in what way it 
 is capable of existing ; in other words, what is the kind and 
 degree of its individuality. For only what is individual can 
 have actual existence as a whole. An infinite series cannot 
 have such existence,**^ and therefore cannot be taken to have it. 
 The ' all ' in this latter case remains a demand with which we 
 cannot comply. 
 Divergent /3. The content of a judgment is always a significant idea, 
 species, ^jjg^^ jg ^Q gg^y^ g^ iccogniscd ^ identity in differences. The 
 varieties of judgment correspond to the forms which identity 
 in difference is capable of assuming. 
 
 An identity in relation to its differences may always be 
 regarded as a whole in which they are parts. An expanse of 
 the same colour includes the changing lights and several points 
 of space through which the one identical colour extends ; the 
 policy of a government includes the details into which its 
 principles are developed ; the moral character of a man is 
 a whole in which his several acts of volition are the variously 
 dependent parts. In this wide sense, as a synthesis of differences, 
 not as a sum of units, the relation of whole and parts is a funda- 
 mental relation of all j udgment . It is only when the differences 
 or parts assume the maximum of homogeneity, and conceal, so 
 far as is possible, the individuality of their relations to the 
 whole, that the parts become units, and the whole a total or 
 a sum. The relation of unit to sum total, that is, of quantita- 
 tive part to quantitative whole, is thus obtained by abstraction. 
 It is not the complete natural relation of concrete identity and 
 differences, but is a device of knowledge which by sinking all 
 other aspects of a given content is enabled to regard it as a sum 
 of units, that is to say, as a whole of magnitude. 
 
 * See p. 163 below. 
 
 ^ ' Recognised ' is necessary to restrict the description to significant 
 ideas. For a sequence of images in elementary reproduction, such as we 
 ascribe to the animal mind, is an identity in difference, though we do 
 not suppose it to be an objective reference, i.e. a recognised identity. 
 See Book II, chap, i, sect. 3, The Reproduction of Ideas. 
 
Chap, i] ' Analytic ' and ' Synthetic ' 91 
 
 For this reason it seems right to consider the judgments 
 of number, with the kindred judgments of magnitude in 
 space and duration in time, as belonging to an outgrowth 
 of thought which diverges from the complete evolution of 
 judgment. All these judgments begin as qualitative, but 
 become quantitative by intentional abstraction, and end in 
 the creation of ideal totalities (abstract number, abstract 
 space, abstract time^) which we are unable to think of as 
 complete, and therefore are debarred from treating as actual 
 totalities. This, I may point out, is a case of the connection 
 between individuality and actual existence, which I spoke 
 of under the last head. 
 
 y. Every judgment is both analytic and synthetic. This Analytic 
 would not by itself be a sufficient ground for refusing to thetic^" 
 employ these terms as heads of classification, for it is more 
 or less the case through the whole of Logic that terms must 
 be employed to mark predominant aspects rather than ex- 
 clusive characters. Nor do I find a sufficient ground of 
 objection in the psychological comment that the judgment 
 which adds a fresh predicate to a subject to-day must become 
 tautologous or analytic if repeated to-morrow, and that 
 therefore it merely depends on individual knowledge and 
 memory whether a given judgment is synthetic or analytic. 
 Any conception of dominant quality, function, or essence, 
 is enough to make this comment futile, and without such 
 a conception it would seem that science is impossible. It 
 is a superstition to suppose that the progress of theoretical 
 explanation in terms of general law threatens the doctrine 
 of essence, form, or function. However clearly an individual 
 thing may be explained as a section of evolution or a meeting- 
 point of forces, there will always be a definite continued 
 identity conferred by characteristic form or function. No 
 explanation can destroy the actual relations of whole and parts 
 which form the essence of everything that is real. Knowledge 
 has quite enough fixity to give meaning to the contrast of 
 analytic and synthetic judgments wholly apart from the 
 progress of individual minds. 
 
 The reason why I no longer care to lay emphasis on the 
 
 ' Cp. Locke's Essay, II. xiv. 21, on ' Duration '. 
 
92 Judgment and Judgment-forms [Book i 
 
 antithesis in question is not that it is purely ' subjective ' — 
 for this is not the case — nor even that it is only a distinc- 
 tion of degree — for that is the character of most distinctions 
 in Logic ; but simply that it is not a sufficiently specific 
 antithesis to be of practical value in classification. I suppose 
 that if the terms were to be employed, we should call those 
 judgments analytic which attain to an adequate explanation 
 or appreciation of a complex whole. The best instances 
 might be the definition or the disjunction, the equation, and 
 judgments passed upon moral and aesthetic value. In all 
 these cases we have the whole completely given in its parts, 
 the identity in its differences, and therefore we are entitled 
 to consider not so much the nature of the whole reconstructed, 
 as the exhaustiveness of the reconstruction. But, as the 
 above instances show, adequacy or exhaustiveness exhibits 
 itself in contents whose nature is wide apart, and therefore 
 it has no convenient place as a general character in a classi- 
 fication. 
 
 On the other hand, as terms belonging to the general 
 theory of judgment, analytic and synthetic are of profound 
 significance. I said at the beginning of this section that 
 every judgment is both analytic and synthetic. This asser- 
 tion demands no explanation, if we remember our account of 
 judgment as always involving identity in difference. But 
 I will attempt to illustrate its meaning more fully. 
 
 If I say ' Caesar crossed the Rubicon ', I start with an 
 individual Caesar, whose continued identity extended through 
 a certain space of time and revealed itself in a variety of acts, 
 and I exhibit his identity in one of the acts and moments — 
 its differences — through which it persisted. What I mean 
 by the affirmation is that he, the Caesar ^ who had before 
 conquered Gaul, and who was afterwards murdered on the 
 Ides of March, displayed his character and enacted part of 
 his history by crossing the Rubicon. This is a clear case of 
 exhibiting an identity in difference. But the process has 
 inevitably two aspects. On the one hand, I analyse the 
 individual whole that is called Caesar by specifying one of 
 the differences that may be considered as a part within it ; 
 ' Contrast Lotze, Logik, sect. 58. 
 
Chap. I] Purts and whole 93 
 
 on the other hand, I construct or make synthesis of the 
 individual whole in question, by exhibiting it as a whole that 
 pervades, and absorbs in itself, each or all of its differences. 
 It is only an individual whole that is obviously present in 
 each as well as in all of its differences, as the individual Caesar 
 in the act of crossing the Rubicon. A totality whose unity 
 is incomplete, such as ' all men ', is only implied in each of 
 its differences, and is not given as a whole in anything short 
 of all. But this does not alter the fundamental nature of 
 assertion. Every judgment exhibits a whole jn its parts, 
 and parts as contributory to a whole. 
 
 Much has lately been said of Kant's celebrated instance, 
 the equation 7 + 5 = 12. We have here a total, twelve, 
 which can be compounded in an immense variety of ways, 
 and we display this total as identical, whether expressed by 
 its place in the series of numbers (which implies one and the 
 simplest mode of its formation) or treated as the sum of two 
 other totals, each of which is expressed in the same simple way. 
 It is obvious that if analytic and synthetic were reciprocally 
 exclusive characters, the question * Is this equation an analytic 
 or a synthetic judgment ? ' would be wholly unanswerable. 
 If 12 were not the same number as 7 + 5, the judgment 
 would not be true ; if 7 + 5 gained nothing by being defined 
 as 12, the judgment would cease to be a judgment at all. 
 7 + 5 is one of the differences which constitute the nature 
 of the total 12, and by constructing 12 in this way we ipso 
 facto analyse it. 
 
 The relation of these two processes, or rather two aspects 
 of the same process, is so fundamental in all knowledge, being 
 in fact the relation which especially characterises knowledge 
 as such, that I may be pardoned for continuing to insist on 
 it by help of another set of considerations. The notion of 
 a plain difference between taking to pieces and putting 
 together arises from actual operation on material things. 
 This origin of the metaphor involved in * analysis ' and 
 * synthesis ' has reacted and still reacts injuriously on our 
 conceptions of intellectual processes. In mechanical opera- 
 tions we cannot pull to pieces and put together the same 
 thing by the same act, and which of the two we can do is 
 
94 Judgment and Judgment-forms [booki 
 
 determined by the material handed to us. If a thing is 
 complete already, we cannot put it together any further ; 
 the only alternative then open to us, as between these two 
 processes, is to pull it to pieces ; and so vice versa. But this 
 feature of material operation cannot be transferred to thought, 
 and for this reason, that the essence of thought is to show 
 the process in the result, and exhibit each as necessary to the 
 other. Therefore, if we construct in thought, the materials 
 out of which we construct have not lost their separateness 
 when the fabric is finished ; the fabric as it is still issues 
 from them as they were ; if not, we have dropped a link, 
 and our construction is unwarranted. The synthesis, one might 
 say, is based on the analysis ; but this would ascribe a false 
 priority, because the fragments supplied to us only become 
 an analysis as the synthesis, which relates them to a whole, 
 progresses. Apart from the synthesis they are mere fragments, 
 and therefore are not an analysis of anything. The workman 
 who puts together the parts of a watch has first the handful 
 of wheels and springs, and then the completed watch ; he 
 cannot have both at once, and in as far as he has one he has 
 not the other. Moreover, when he has made the watch the 
 wheels and springs are together and are not separate, nor 
 are they separable consistently with the existence of the watch. 
 S5nithesis in this sphere is incompatible with analysis, and 
 vice versa. But a man who wishes in thought or calculation 
 to construct any instrument out of parts has a very different 
 task. Every element of the handful of parts must have its 
 place and functions clearly retained in the intelligence which 
 constructs the whole ; for the whole, as a whole of intellectual 
 synthesis, exists no longer than its parts are clearly appre- 
 hended in their relations. ' Yes,' it may be said, ' but the 
 distinction must remain that even in thought you may either 
 begin by considering detached wheels, &c., and finding out 
 how they must act in the watch, or by looking at a watch and 
 detecting, within its completed system, the separate parts 
 and their relations. The former process is synthesis, the 
 latter analysis.' 
 
 This is true so far as judgment or inference is an activity 
 in time, and includes within itself a transition in time. In 
 
Chap. I] Syuthesis in fact and in thought 95 
 
 so far as it has this character, the process of thought can 
 simulate or share the characteristics of material operation. 
 But this does not affect the internal nature of judgment, 
 as I have pointed out in discussing its temporal character. 
 The question is not whether you begin with the whole or with 
 the parts, but merely what sort of whole and what sort of 
 parts you begin with. Given an escapement wheel, I may 
 chance even to be ignorant that it belongs to a watch at all ; 
 but none the less I judge of it as a part in a whole, which 
 whole I can at first only think of, perhaps, as * some piece 
 of mechanism that depends on a catch playing into a delicately 
 toothed wheel '. The further intellectual construction of this 
 mechanism and the ultimate definition of it as a watch, is, 
 according to the views of the passage just referred to, not a 
 transition from S to P, but a transition from the judgment 
 s-/) to the judgment S-P, We therefore find analysis no less 
 than synthesis to be the internal essence of every minutest 
 section of the judgment or inference in question. In the 
 same way, if a watch is put into my hand with instructions 
 to find out what makes it go as it does, I have primarily 
 a thing in space as the given whole, and indefinite wheels, 
 springs, &c. (which as yet I cannot distinguish by position 
 or characteristic shape) as given psirts. No doubt in space 
 all the parts which I shall need to learn are given in position 
 within the whole, and so we tend to describe the problem 
 as one of analysis, in contrast to the other (in which I had to 
 find out or imagine the position of the parts in the whole) as 
 synthesis ; and these titles serve well enough as superficial 
 descriptions of certain cases to which judgment and inference 
 are applied — not of any judgment or inference as such. But 
 the whole is not, in the latter case any more than in the former, 
 given as an intelligible machine, nor are the parts given within 
 the whole of knowledge because they are within the whole of 
 space. In other words, to see the escapement wheel lying 
 inside the watch does not ' give ' me this wheel as a part of 
 a mechanical arrangement ; to know it as a part of such 
 a whole I must understand it ; and in understanding it, i. e. 
 in my analysis, perform the synthesis of the watch as a definite 
 mechanical contrivance. 
 
96 Judgment and Judgment-forms [Book i 
 
 Therefore not only is every judgment both analytic and syn- 
 thetic, but it is analytic only as far as it is synthetic. It can 
 only be called analytic or synthetic par excellence if, by the same 
 confusion that causes the judgment to be regarded as a transi- 
 tion from S to P, we consider the joint analysis and synthesis 
 of one whole as the analysis or synthesis of another ; because 
 in that case we seem to have a fixed and given whole, and to 
 predicate of it nothing but parts, or vice versa. In this con- 
 fusion there is an element of truth. Though s must become 
 S when p becomes P, yet s has continued identity with S and 
 P with P, and therefore the transition in time from s-p to 
 S-P does all that could be done by the unreal transition 
 from s to P. Present me with a pattern s which is a tissue 
 of intersecting curves p, and when I have analysed it into 
 the thistle design P, the pattern s is transformed to my eye 
 into a distinct and beautiful design S ; but S is the same 
 that was s, and in that sense we have connected s with P, 
 and we may represent P as the analysis of s, only not for- 
 getting that it is the synthesis of 5 which is the same as s, 
 and that therefore in predicating P of s we ipso facto trans- 
 form s into S. And thus the complete understanding of a 
 watch as a mechanical system, expressed in the joint analysis 
 and synthesis S-P, may be accepted as happening to involve, 
 Par excellence, either the intellectual analysis of the watch 
 as a given whole in space s, or the intellectual synthesis of 
 the watch out of given separate parts in space Sj, s^, S3, &c. 
 The given whole, or given parts, can be thus allowed to pass as 
 merely whole, or merely parts, because they are not respec- 
 tively whole and parts in the sense contemplated by the 
 judgment S-P, and therefore it does not press home their 
 relation to one another. The watch seems to be from the 
 first a ready-made whole, a round thing s in space, which 
 can only be analysed, and not constructed, by the judgment 
 S-P. But it is further constructed, not as a round thing 
 in space, but as a mechanical system, by means of that 
 judgment. 
 
CHAPTER II 
 
 Quality and Comparison 
 
 I NOW turn to examine specific types of judgment ; but 
 in doing so, I must beg leave to remind the reader of the 
 principle which I have laid down as governing any enquiry 
 into a continuous development. ■"■ What we wish to master 
 is the nature of a process, the scientific history of a function. 
 To do this, we must of course study and arrange its detailed 
 manifestations ; mere generalities are valueless. But we 
 need not be disheartened if our subdivisions and specific 
 names are different here and there from those adopted by 
 better authorities, nor even by the possibility (which can 
 hardly be absent from a highly detailed treatment) that we 
 may misinterpret some phase of evolution, or lay down some 
 inconvenient demarcation. If the main problem is thoroughly 
 faced, and the analysis of some chief typical forms accurately 
 conducted, the reader will be in a position to correct blunders 
 and to supply omissions by the light of the knowledge so gained. 
 If we can help him to sound principles and practice of 
 morphology, he will make short work of particular varieties 
 of type. 
 
 Judgment, we have seen, is, speaking generally, the in- 
 tellectual function which defines reality by significant ideas, 
 and in so doing affirms the reality of those ideas. I use the 
 term ' define ', because to define implies something given 
 which is to be defined ; and it is an essential of the act of 
 Judgment that it always refers to a Reality which goes 
 beyond and is independent of * the act itself. 
 
 I. We will now look at the judgment in its simplest form. The 
 
 which I have ventured to call the Judgment of Quality, and ^^^'^f 
 
 which, with its immediate sequel, the Judgment of Com- Quality. 
 
 parison, finds linguistic expression in the Inter jectional or 
 
 Impersonal Proposition. 
 
 ^ See Introduction, p. 15. 
 
 * On a criticism which this expression has attracted, see vol. ii, ch. ix. 
 
 1337 H 
 
98 
 
 Quality and Comparison 
 
 [Book 1 
 
 Meaning 
 
 of 
 
 Quality. 
 
 Judg- 
 ment of 
 Quality 
 proper. 
 
 i. By Quality I understand, not all attributes without 
 distinction, but the unanalysed content of any idea, when 
 treated, in its unanalysed simplicity, as a feature of reality. 
 It may be that all qualities are capable of being analysed 
 into relations ; but for our present purpose the question is 
 not whether a quality can he, but whether it is so analysed. 
 Even the diagrams familiar to. us in Euclid, which exist for 
 the very purpose of being analysed, have each its peculiar 
 look or effect, lopsided or symmetrical, solid or slender, 
 circular or bristling with angles. Qualities of shape, how- 
 ever, are as a rule quickly analysed into relations of propor- 
 tion, so that the commonly cited phenomena of colour and 
 sound give better instances for our purpose, while percep- 
 tions which are named, like softness and sweetness, with 
 some reference to pleasure and pain, are the best instances 
 of all. It might indeed be suggested as a definition of quality 
 that it is that aspect of any perception or idea in which it 
 gives rise to pleasure or pain. 
 
 ii. The Qualitative Judgment proper affirms a nearly 
 simple content directly of present Reality. An absolutely 
 simple content is indeed an impossibility ; every ' red ' or 
 * sweet ' or ' pleasant ' belongs to some context and includes 
 some differences. But, as I have attempted to explain in 
 the last paragraph, a qualitative content is very nearly 
 simple. The context which makes its difference is the context 
 for the sake of which we affirm it, and is thus presupposed, 
 and not itself affirmed as a further complication. If I exclaim 
 ' How hot ! ' I do so because the weather or the room is hot, 
 or perhaps if I am feverish, because I am hot for no obvious 
 reason. In all these, no doubt, the content ' hot ' belongs 
 to something ; it is not isolated from the varied surroundings 
 of my position, but exists in and extends over some of them. 
 But I affirm it without specification, or rather as a first effort 
 to make specification, of my position and surroundings in 
 general, and neglect to analyse its relations, or only analyse 
 by implying that it has some relation or other. 
 
 Thus much for the Predication. As for the subject of 
 a pure Qualitative Judgment, there is prima facie no assign- 
 able subject within the judgment. No ideas are employed 
 
Chap. II] Qualitative Content 99 
 
 to limit the aspect of reality to which the predication refers. 
 The whole of what is perceived at the moment, or more 
 probably some unspecified aspect of it or element within it, 
 is the subject, and it is of this that the content is affirmed. 
 By ' unspecified ', I do not merely mean unspecified in words 
 spoken aloud, but undefined by any such act of conscious- 
 ness as employs symbolic ideas and tends to call up words. 
 But if thus unspecified, how can the subject be indicated, 
 limited, or selected ? I answer, simply by the concentration 
 upon it of perception or attention, the exclusive gaze which 
 might be represented by pointing with the finger, and which, 
 though it has limits, is definitely aware of none. In this 
 sense, confining what is ' present to perception ' within the 
 limits of what more especially arrests attention and is taken 
 as ' This ' par excellence, we might say that the subject of the 
 Qualitative Judgment is always the whole of what is present 
 to perception. 
 
 The best illustrations of this rudimentary Judgment are 
 drawn from significant Interjections, or from significant 
 phrases used as Interjections. A distinction must be observed 
 between the true Interjection/ the outcry which relieves the 
 urgency of feeling, and the affirmation which refers the con- 
 tent of feeling as a quality to the surroundings that evoke 
 it. The cry of an animal is often significant for us ; it tells 
 us what the animal feels, and why ; but we do not therefore 
 reckon it as the expression of a judgment. What makes 
 the judgment is the idea that exists in our minds and yet 
 that only has truth as referred to Reality. And therefore 
 if we doubt whether we have a judgment before us, we 
 should ask if it is anything that could intelligibly be denied. 
 It is impossible to deny the animal's mere expression of its 
 feeling ; and although we may see a reason for its feeling 
 which we know to be an illusion (e. g. if a dog barks joyfully 
 in expectation of being taken out, when he is not going to 
 be), yet there is nothing which we can deny unless we can 
 suppose that this illusion exists in the animal's mind as an 
 idea distinguished from and referred to reality. If we could 
 believe this to be so, we should have to admit that the animal 
 
 ^ Cp. Lotze, Logik, sect. 48. 
 H2 
 
100 Quality and Comparison [Booki 
 
 judges. Bat short of this, there is nothing to deny. The 
 dog sees me take my hat and stick, he has a set of mental 
 images connected with going out, and he expresses pleasure. 
 I cannot deny that he has the images or that they give him 
 pleasure. It would be only if he could take these images as 
 standing for something other than themselves, and so distinguish 
 their meaning, a future event in reality, from their existence, 
 as present images in the mind, that anything could possibly 
 arise which I could intelligibly deny. The ideas used in judg- 
 ment must exist before they can be denied, and therefore 
 their existence cannot be denied, but only the affirmation of 
 their meaning.^ 
 
 Coming to human interjections, we might think that 
 ' Alas ! ' characterises the present as grievous ; and it is 
 certainly sometimes answered, though hardly denied. But 
 the answer, even if it takes the form of a denial, is usually 
 rather prohibitive (imperative) than negative ; though if self- 
 deception or hypocrisy are suspected, ' alas ! ' may be inter- 
 preted as ' I am sorry ', and in that sense denied. The distinc- 
 tion to be kept in mind is here one degree more subtle than 
 in the last case, for the objective content of the judgment is 
 the fact of a feeling in the mind of the person who judges. 
 Thus we have, if ' alas ! ' is a true interjection, the emotion 
 of grief present in the mind of the person, which merely forces 
 him to utterance by way of relief. But if it is to be taken 
 as a judgment, then we have in any case the symbolic idea 
 of sorrow, existing in psychical images, but having its meaning 
 beyond them, and a reference of this meaning to the present 
 perceived being of the person in question. And above all this, 
 if the judgment is true, there must be, as before, the actual 
 felt emotion of sorrow, though if it is false, this element of the 
 complication is absent. It is possible that this peculiar 
 complication, of the idea with the actual feeling behind it, 
 
 * These remarks are made purely for the sake of illustration. I have 
 not the least prejudice against admitting that animals can judge, if the 
 admission can be warranted by fact, and does not involve truncating 
 the theory of judgment. Domestic animals certainly seem to use the 
 imperative, i. e. to insist on the realisation of their ideas. Cp. Bradley, 
 Principles of Logic, p. t,;^. On an idea without forethought or image, 
 see Bradley, Appearance and Reality, p. 607. 
 
Chap, u] Interjection and Judgment loi 
 
 is responsible for the curious duplication of personality which 
 is sometimes experienced in protracted pain or anxiety. The 
 person whom we analyse and judge seems other than the person 
 who all through the process has the feelings which are being 
 analysed, or rather are forcing their disagreeable peculi- 
 arities on our attention. ' If / were suffering so, how horrible 
 it would be,' we repeat to ourselves. Just as the comple- 
 mentary image comes between our eyes and the sun, so the 
 idea of our feeling comes as the object of knowledge between 
 us and the feeling itself, which remains in the background 
 and resists our successive efforts to include it in an adequate 
 idea. The sufferer remains to us distinct from the person 
 whose suffering we conceive and affirm. 
 
 However this may be, when we come to such quasi-inter- 
 jectional expressions as ' Bad ! ' ' How ugly ! ' ' Such pain ! ' 
 ' Oh horrible ! ' we are unquestionably dealing with judg- 
 ments. 
 
 The Impersonal Proposition is cdso a suggestive counter- 
 part of the judgments in question, which have even been 
 treated as Impersonal Judgments. But the impersonal form 
 of sentence has become in developed language so purely a 
 grammatical fiction, that it no longer illustrates with special 
 appropriateness any one type of assertion ; although it 
 exhibits a certain coincidence with the range of the concrete 
 existential or singular categorical judgment. 
 
 A few instances however occur to us at once — and philology 
 might be able to furnish more — of impersonal sentences 
 that really seem to have stood for judgments whose subjects 
 were not especially designated by means of ideas, but were 
 accepted as merely the given in perception. Such may be 
 ' Methought ', ' Him list ', ' Mir traumt's ', ^ ' Es trieb mich ', 
 ' Taedet ', ' piget ', &c., ' It rains ', ' es macht heiss ', mi. As, 
 
 ' In Greek, a conservative though flexible language, ' I dreamt,' is 
 never, so far as I know, impersonally rendered : but on the other hand, 
 in Homer the dream is personified. The principle is the same in so far 
 as my dream is not referred to me as my act. Indeed the coincidence 
 is curious with the view of those who have held that the subject of an 
 impersonal proposition is the content of the verb itself as in ' the rain 
 it raineth every day '. It is much the same to say ' Es traiimte mir ' 
 and to say ' A dream came to me '. 
 
102 Quality and Comparison [Booki 
 
 in the plastic Greek imagination, Athene may suggest a man's 
 thought, and the actual Dream stand over him in sleep, so, 
 it would seem, in the beaten track of language, the thought 
 and the dream are simply referred to ' it ' or to ' something ' ; 
 to the present reality or to an indefinite element within it. 
 Though the formed verb presupposes a distinct reference of 
 ideal contents to real subjects, yet the habitual use of ex- 
 pressions in which this reference is blimted and neutralised, 
 testifies to a survival, in certain preeminently obscure relations, 
 of a rudimentary type of judgment. This, 1 think, is the only 
 connection that we can safely assume between the Judgment 
 of Quality and the Impersonal Proposition. 
 
 The Qualitative Judgment is the germ and simplest case 
 of the Perceptive Judgment. Perception is a wide word, 
 including, as frequently used, any so-called immediate 
 apprehension ; even that, for instance, by which we are 
 supposed to see the necessary truth of one of Euclid's axioms. 
 But if we are to give the term a distinctive logical meaning, 
 we should do well to restrict it to so-called immediate appre- 
 hension when dealing with the portion of reality which is in 
 contact with the individual through the senses. Perception 
 thus defined deals primarily with what is present, but extends 
 it by ideas which go beyond the present. When we recognise 
 a man and call him by name, we are said to ' see who he is ', 
 i. e. to perceive. In this case our perception is expressed 
 by an idea that goes a long way beyond the present and brings 
 in the man's entire personality. 
 
 The Qualitative Judgment does not differ from the judg- 
 ment which recognises an individual, by being shut up within 
 a minute interval of present space or time. It is not minute- 
 ness of extension or of duration that distinguishes the refer- 
 ence of this simplest case of the perceptive judgment ; the 
 qualitative affirmation may deal with what is really a con- 
 siderable area of space or interval of time. The distinction 
 is not one of magnitude, but of definiteness. There is always 
 a risk of construing the absence of quantitative determinate- 
 ness into determinate minuteness of quantity. This is just 
 what we want to avoid. The qualitative judgment knows 
 nothing at all of duration or of extension, and can have no 
 
Chap. II] Analytic and Synthetic Judgment of Sense 103 
 
 specified individual for its subject. It is thus confined within 
 the given presentation in so far as the universality, whether 
 abstract or concrete, is absent that alone could extend it 
 beyond. The Reality which is the subject is the given as given, 
 not as a universal that reaches before and after ; the content 
 of the predication includes no negative element, summarises 
 in itself no diverse manifestations, and thus neither refers to 
 anything beyond the present, nor in any specific way to the 
 present itself. It is attached to the present, by the mere fact 
 of its actual reference to presentation, not by anything within 
 its explicit content. The first specification, the first establish- 
 ment of an identity that can be called by a name, is the work 
 of this judgment, and is not presupposed by it. We must 
 take it, I think, after the discussions of the Introduction, 
 that the establishment of a name — a permanent identical 
 symbol of a meaning — must on the ivhole have coincided with 
 the establishment of meanings as such, distinct from psychical 
 occurrences, and capable of being referred to reality. I have 
 attempted in the discussions in question to qualify the rash- 
 ness of this unverifiable ^ historical allegation, by pointing 
 out that the two co-ordinate processes — the constitution of 
 symbolic ideas and of linguistic symbols — must be regarded as 
 processes of gradual and unconscious adaptation, widely differ- 
 ing from the methodical extension of nomenclature according 
 to modern ideas. But the logical track is the same, whether the 
 historical evolution is quick or slow, conscious or unconscious. 
 Perception as above defined would include two species 
 which have been called respectively the ' Analytic ' and 
 the ' Synthetic ' judgments of sense. If these distinctions 
 are to be seriously treated, and we are to speak of any judg- 
 ments as merely analysing a presentation of sense, without 
 going beyond what is given within it, then, I think, we must 
 identify the Analytic Judgment of sense with the Judgment 
 
 ^ Of course there can be verification by analogy ; and it is liard to 
 draw the Une between this and actual verification. The characteristic 
 cries of animals and children have significance -for us, and we cannot 
 suppose that they do not react upon the intelligence of those who utter 
 them. It would be far easier to understand how animals should acquire 
 language, if, like children, they did so in fact, than it is to understand 
 how they stop short of it. 
 
104 Quality and Comparison [Booki 
 
 of Quality. It appears to me quite idle to treat a description 
 of an ordinary scene, such as ' The blacksmith is at his forge 
 mending the ploughshare ', as a case of a judgment confined 
 within present perception. Every element of the description 
 is a concrete individual, including innumerable differences, 
 involving elaborate categories, and extending indefinitely 
 into past and future. If ever there was a constructive or 
 synthetic judgment, this is one. It would surely be more 
 appropriate to treat these common perceptions, which we deal 
 with lower do^vn, as Synthetic judgments of sense, because 
 they interpret what is given by ideal contents that go beyond 
 it. And then we might reserve the title ' Anal5rtic Judgments 
 of sense ' or ' Judgments of Quality ' for the activities repre- 
 sented by the Inter jectional and Impersonal propositions 
 of which I have spoken, and the true Demonstrative proposi- 
 tions of which I shall speak below. 
 
 The difficulty of identifying simple forms of judgment is 
 intensified for modern reflection by the definite and diverse 
 articulation of the elements of modern speech. The lan- 
 guages which embody the reflective thought of Europe, both 
 ancient and modern, resist the expression of elementary 
 perception in two ways. First, for a germinal thought we 
 need a germinal word. But the languages which mould 
 our ideas have no germinal words. Every word, in the 
 languages of European culture, is a particular ' part of speech '. 
 That is to say, it is adapted to fulfil some one function in a 
 sentence, whether substantive, verb, pronoun, or conjunction, 
 and, if used alone, has an air of incompleteness which forces 
 us to ' understand ' supplementary words. The existence 
 of the Judgment of Quality is but slightly corroborated by the 
 fact that a single word often conveys a judgment. Many 
 such single words are conventional symbols for quite definite 
 sentences. But the judgment of which we have been speaking 
 corresponds to a whole sentence in the bud, with its differences 
 unevolved. How far phUology could furnish authentic repre- 
 sentations of the sentence in such a stage — words which 
 are not ' parts of speech ', but entire though undifferentiated 
 units of speech — it is beyond the limits of the present work to 
 enquire. Even the verb of ancient Greek or Latin, which 
 
Chap. II] Subject in and outside Judgment 105 
 
 required no supplementary pronoun to represent its subject, 
 is one degree more appropriate for the purpose than any 
 element of modern speech. 
 
 And the second difficulty is really a case of the first. Most 
 judgments are expressed by help of a verb, and if we employ 
 a substantive or adjective alone, it urges us to ' understand ' 
 a verb. But a verb is in our languages above all things a 
 tense ; and for a rudimentary judgment like the judgment 
 of Quality, a tense is exactly what we do not want, least of 
 all the elaborate duration-tense of the present (rpe'xet, amat, 
 ' he is acting '). We want to affirm neither duration nor yet 
 point of time ; we simply want to qualify the given by a 
 content, without specific limitation or extension. It is true 
 that the logical present, the absolute present of the universal 
 judgment, marks no limitation of time, and it depends on the 
 nature of the content involved whether universality of time 
 as an infinite series is asserted in such a case. But whether 
 it claims universality in time or by negation of time, such 
 a judgment implies the conception of time as an abstract 
 whole and is posterior to this conception, while the reference 
 of which we are speaking is prior to the origin of the systematic 
 idea of time. 
 
 These properties of developed language, — and prior to 
 developed language it would scarcely be possible to have 
 analytical reflection, — may be compensated, but cannot be 
 cancelled. The fact that sometimes thought is behind language, 
 and at other times struggles to pass it (it would be hazardous 
 to complete the antithesis by saying that thought can really 
 outstrip speech) is a fruitful source of misinterpretation. 
 Children learning to speak, or savages learning a European 
 tongue, are like the wizard's apprentice uttering a spell ; 
 they are incapable of grasping the significance or controlling 
 the effect of their words. And all human beings perpetually 
 oscillate between limits, different in every case, on the scale 
 of intelligence ; for not only is the student's or politician's 
 world of thought very different from that of an illiterate man, 
 but every man varies in the level of his intelligence according 
 to momentary conditions of interest and capacity. The same 
 difficulties of interpretation which are found by a student in 
 
io6 Quality and Comparison [Booki 
 
 the speech of a child or Anglicised savage, subsist in a less 
 degree as between every man and every other, and as 
 between every man and himself. 
 
 Up to this point the constituent elements of the Judgment 
 have been naked before us. There was the Subject, — the 
 actual contact in which reality pressed upon our sense- 
 perception, — and there was the significant idea by which 
 we defined it. It is this case that affords the strongest support 
 to the view which denies all meaning to the distinction of 
 Subject and Predicate, as a distinction of elements within a 
 judgment. The Reality to which we ascribe the predicate is 
 undoubtedly self-existent ; it is not merely in my mind or in 
 my act of judgment ; if it were, the judgment would only 
 be a game with my ideas. It is well to make this clear in the 
 case before us, for in the later forms of the judgment it will 
 be much disguised. Still the reality which attracts my 
 concentrated attention is also within my act of judgment ; 
 it is not even the whole reality present to my perception ; 
 still less of course the whole self-existent Reality which I 
 dimly presuppose. The immediate subject of the judgment 
 is a mere aspect, too indefinite to be described by explicit 
 ideas except in as far as the qualitative predication imposes 
 a first specification upon it. This Reality is in my judgment ; 
 it is the point at which the actual world impinges upon my 
 consciousness as real, and it is only by judging with reference 
 to this point that I can refer the ideal content before my mind 
 to the whole of reality which I at once believe to exist, and am 
 attempting to construct. The Subject is both in and out 
 of the Judgment, as Reality is both in and out of my con- 
 sciousness. 
 The de- iii. We have now to consider a slightly more definite 
 tivrfiidg- ^yP^ °^ judgment, which we may still rank among the judg- 
 ment, ments of quality, although we can detect in it the beginning of 
 a further growth. 
 
 When we say, * This is hot,' ' Now it is raining,' ' Here it 
 is dark,' the demonstrative pronoun or particle designates 
 the point in given Reality to which the affirmed content is 
 to refer. The point is designated, but seems, prima facie, 
 not to be described. The demonstrative has a meaning, 
 
Chap. II] Spuce and Time brought in 107 
 
 no doubt, but its meaning seems to consist of a mere refer- 
 ence to what is presented before perception, and therefore 
 does not seem to introduce any abstract limitation that 
 qualifies the given subject. Compare, for instance, ' This 
 is hot ' with ' This metal is hot '. The latter judgment may 
 possibly be met with ' This is not metal at all ', and by such 
 a reply the judgment is cut in two, and the more significant 
 half becomes a conditional assertion whose condition does 
 not apply to the ' this ' in question. But ' This ' alone is on 
 a different footing. You cannot say, ' There is no this at 
 all.' There is always a this, as there is always a that ; and 
 the same applies to here, there, now, and then. 
 
 One of these demonstratives indeed appears at once to 
 take us over a boundary, ' Then ' requires a past or future 
 tense in the predication ; and in referring to the past or 
 future we get beyond analysis of the present, which is the 
 province of the analytic judgment of sense. The problem 
 is one of real importance, but its point is not where we are 
 most likely to look for it. It is not that the Judgment of 
 quality refers to a point of time, and that ' then ' takes us 
 outside this point ; it is that the Judgment of quality is prior 
 to the idea of duration, and that we have now introduced the 
 idea of duration definitely into the subject. The effect on 
 tense, which happens to be the vehicle of predication, pro- 
 duced by taking ' then ' as the subject, calls our attention 
 to the fact that every present includes a past. The contrast 
 of ' here ' and ' there ', not happening to affect the verb, 
 did not force on our notice the equally real universality 
 of the present in space. Every ' here ' is made up of ' there's ' 
 as every ' now ' is made up of ' then's '. And thus in designa- 
 ting a given subject as ' now ' or * here ', we have unawares 
 included in the subject a ' then ' and there ', and by introducing 
 universals of space and time have set our faces to leave the 
 region of the qualitative judgment. The demonstratives 
 stand for ideas, and it is therefore through ideas that in the 
 judgments now in question we refer to reality. But the 
 demonstratives have the peculiarity that their application 
 cannot be denied, as can that of a determinate idea such as 
 metal, and therefore, though they characterise the given 
 
io8 Quality and Comparison [Booki 
 
 Reality as appearing in space or time, yet they can specify 
 no nexus, introduce no condition, which may be absent in 
 fact, and through its absence may save the judgment from 
 falsity by rendering it inapplicable. If heat is not present 
 in the ' this ' to which it is ascribed, the judgment ' this is hot ' 
 is false without reserve ; but if to ' this ' we add ' metal ' 
 then the absence in fact of the condition ' metal ' makes 
 the whole judgment ambiguous and inapplicable. Thus we 
 have in the demonstrative judgment of quality, as in the 
 simple or pure judgment of quality, a perfectly categorical 
 judgment ; the Subject must, in its nature, exist, and the 
 Predication must therefore be alleged to hold good of actual 
 existence. It is noteworthy that of this perfectly categorical 
 judgment we cannot say whether the existence of the Subject 
 is affirmed or presupposed. Where we are dealing with the 
 given qua given, the difference between affirmation and pre- 
 supposition has not emerged. 
 The 2. The contrast between 'now' and 'then' suggests to 
 
 inen^ of "^ ^^® Consideration of such judgments as are expressed by 
 Compari- 'Now it hurts less than then ', ' This is redder than that ', 
 ' Here it is hotter than there '. The form of these judgments 
 indicates as their appropriate title the Comparative judgment, 
 or the Judgment of Comparison. They arise naturally out 
 of the Demonstrative judgment of quality, because, as we 
 saw in the case of 'now' and 'then', it is impossible to prevent 
 the present subject from revealing differences within itself. 
 * This,' as more clearly defined, will display itself as a part, 
 ' not-that ' within 'this and that', 'now' as a part 'not-then ' 
 within ' now and then,' ' here ' as a part ' not-there ' 
 within ' here and there '. The whole, when thus resolved, 
 displays differences of quality between its parts, or 
 rather the given reality reveals itself as a whole for 
 the first time when it breaks up into parts united by an 
 identical but varying quality. Even if we forget that the 
 ' this ' and ' that ' ever entered into a single whole, yet 
 the identical quality because of which we compare them 
 contains in itself the essential of the comparative judgment, 
 viz. the explicit recognition of difference in identity. ' Redder,' 
 ' hotter/ ' less painful,' are terms that go beyond mere 
 
 son. 
 
Chap. II] Comparison involves Quantity 109 
 
 quality by introducing the conception of more and less, that 
 is to say, the beginning of quantity. I give instances, bracket- 
 ing the explanatory words which would be superfluous in 
 presence of direct perception, and which belong to a higher 
 level of judgment than that which we are discussing. ' This 
 [paper] is green, and this [part of it] is lighter green than 
 that.' ' Now [all to-day] it ^ hurts less than it did [yester- 
 day] ; but [just] now it hurts more than it did [a moment 
 ago].' But in cases like these we are apt not to notice that 
 we are predicating differences within a single identity, the 
 green paper, or the whole of to-day ; though we must be 
 aware that we imply them in the comparison of quality. 
 And therefore, having pointed out the underlying character 
 of such a simple analysis as the above, I will pass at once to 
 a case which is one degree more complex, but which dis- 
 plays the essence of comparison beyond possibility of mistake. 
 I refer to the case in which a given whole of perception 
 designated by one demonstrative has parts distinguished 
 within it by means of the others, and differences assigned 
 to it conditionally upon these distinctions. There is no 
 difference of principle between defining ' this ', within ' this 
 and that ', and defining it within ' here and there '. The only 
 advantage is that a demonstrative of another kind is more 
 readily taken as a condition, while one of the same kind is 
 apt to be understood as a jump to a wholly new subject. We 
 will therefore merely change the farts, which might be new and 
 substantive wholes, into conditions. ' This is redder now 
 than it was then.' ' This is hotter in this part than in that.' 
 ' This [green paper] is lighter here [in this part of it] than there 
 [in that].' These instances clearly show the primary datum 
 revealing itself as a whole with parts distinct yet bound 
 together by a common quality. 
 
 i. Let us now examine the essential nature of the com- Quantita- 
 parative judgment in one of the above instances. It is not par^ison"^' 
 my intention to enter upon the niceties of quantitative com- 
 parison at the present stage. 
 
 * The ' it ' in this instance is on the verge of introducing an identical 
 subject. I did not, however, mean it to stand as a definite subject, but 
 merely as the grammatical complement of the impersonal verbs. 
 
no Quality and Comparison [booki 
 
 We will take the instance, ' This is redder now than it 
 was then ; ' or in the simpler form, ' This is redder than it 
 was.' We will take the Predication first, and then consider 
 its reaction upon the subject. 
 
 That which is redder is also red. The red and redder 
 are both red, and yet differ from each other, not, or not 
 merely, in other ways, as in time or place, but in respect of 
 their redness. It has been sufficiently insisted on that there 
 cannot be difference without some identity, as for instance a 
 red and green surface are identical in respect of reflecting 
 light. But these, though the same in as far as they reflect 
 light, are not the same in the light which they reflect. There 
 is a break between the two colours, considered as colours,^ 
 which nothing can bridge, and the immediate perception 
 of their discontinuity supplies the terms which indicate the 
 difference between them. The surfaces which are both red, 
 but one redder than the other, are separated by no such 
 break. If one changes into the other, it does not cease to 
 display the same quality that it displayed before. But 
 a quality that changes, and yet remains the same quality, 
 has passed into quantity, which might be defined as difference, 
 not merely in identity as its meeting point, but consisting 
 of identity as its material. 
 
 Thus the fundamental identity and difference of judgment 
 are specified by the comparative judgment as whole and 
 parts in the simplest form of that relation : viz. the form in 
 which the whole differs from any part by an interval which 
 consists of other homogeneous parts. Parts in this sense 
 differ from units only by lack of precise comparison ; but 
 precise comparison is posterior to the conception of a whole, 
 of which we are just considering the first establishment. 
 We do not measure or count until we know of some totality 
 that requires definition by these processes. 
 
 The reaction of comparison upon a simple subject indi- 
 cated by a demonstrative, that is, on a mere spot or point 
 
 * It is possible that, considered as amounts of light, red or green may 
 share a continuous element and so have quantitative relation. If so, 
 this is another case in point. For the difference is then in respect of the 
 characteristic which forms the identity. 
 
Chap. II] Analysts of the Subject iii 
 
 upon which perception is concentrated, is an essential step 
 towards the recognition of an individual totality. The 
 present of space or time is as we saw in its nature continuous. 
 Therefore the spot or point on which perception is fixed, and 
 which we indicate perhaps by ' this ', will undoubtedly exhibit 
 differences under analysis. Such analysis is brought to bear 
 by the judgment of Comparison. The spot or point ^ in which 
 a change of degree is observed forces itself on by that fact 
 from being a mere spot on which the eye is fixed to the first 
 stage of individuality as a synthesis of differences. Change 
 is not necessary to this result, though negation in some form 
 is. The observation of parts differing in degree within the 
 spot which we have in view is as effective for the purpose as 
 the detection of succession within the time which we call 
 ' now '. The mere spot fixed by perception begins under such 
 analysis to assume the character of a Thing ; and by a parallel 
 process, the distinctions of Time and Space begin to emerge as 
 parts within homogeneous systems. 
 
 It is obvious that such a point in the evolution of thought 
 would correspond to the first distinction of Noun, Finite Verb 
 with Tense system, and the more elaborate spatial and tem- 
 poral adverbs and prepositions. But it would not be fair 
 to test the correspondence strictly by negative instances, 
 Language fits thought as a very loose glove ; and if it were 
 the case that we could find several languages in which our 
 familiar parts of speech, more especially the tense system, 
 do not exist, we should still no doubt find that the distinctions, 
 whose origin we are examining, are represented in some other 
 way than by linguistic signs, or are thought even if not 
 represented. It would be ridiculous to contend that the 
 Chinese do not think of self-identical and independent things, 
 
 ^ It is hard to escape the dangerous pitfall of speaking as though 
 there were no perception but sight, and therefore as if the germ of the 
 judgment were always fixation of the look in space. The focus of 
 attention may operate through any sense, and is characterised at any 
 moment by that identity which the judgment makes explicit. But the 
 identity is referred in rudimentary judgment not to a special content as 
 subject but to what could only be paraphrased as ' That which engrosses 
 my attention ', the present feeling which the judgment determines into 
 thought. 
 
112 Quality and Comparison [Booki 
 
 even if it is true that their language has no special class of 
 nouns substantive. Nevertheless, the contrast of develop- 
 ment between different languages has or has had its meaning ; 
 and it appears to me absolutely impossible that a people 
 whose sole language was Hebrew could have had the accurate 
 consciousness of time as a system which came easily to the 
 Greeks and Romans of the classical age. I believe, indeed, 
 that the origin of the Aryan tense-system is not beyond the 
 ken of philology, and that its probable history reveals an 
 evolution much like that which has been here suggested — 
 a transition from simple unspecified reference, to reference 
 differentiated by a temporal system. 
 
 ' This,' then, as the subject of a continuous Quality in- 
 cluding differences tends to acquire an individual name. I 
 have pointed out in the Introduction that the process of 
 Naming in a world distinctly organised by knowledge cannot 
 be that which belongs to the unrefiective epochs of thought. 
 A natural name must be a petrified description. The linguistic 
 element which stands for the content of the Judgment of 
 Quality is already a name. And some such element, in the 
 simplest case perhaps that element itself, will emerge in later 
 forms as a description of the newly distinguished individual, 
 which in the Judgment of Quality is only known as ' this '. 
 ' This red (leaf) is redder than it was.' And when the individual 
 is once revealed as a whole with parts by this judgment of 
 Comparison or synthetic judgment of sense, the ascription 
 of other differences to it cannot but follow. It seems obvious 
 that an adjectival appellation, or at least an appellation 
 of unspecified grammatical class, would come first, and the 
 hardening into a substantive be a later process. I incline 
 to think that the hardening of a description by usage, and 
 the isolation of its elements by employment in different 
 judgments, must have been the real and natural process of 
 naming. 
 Compari- ii. It is evident that judgments which assert distinctions 
 sonm q£ Spa^ce and Time, without proceeding to measurement by 
 and Time, units, must be ranked among comparative judgments, or, 
 as these might otherwise be called, judgments of continuous 
 quality. It is not the business of Logic to analyse the means 
 
Chap. II] Quality in Spatial Perception 113 
 
 by which the consciousness of extension or succession is 
 obtained. Logic only deals with the nature of such a con- 
 sciousness, and not with its psychical genesis. But we cannot 
 entertain a doubt that position in Time or Space can only 
 be indicated to consciousness by qualitative marks that fall 
 outside the content which is perceived as in Time and Space. 
 Our inability, in many or most cases, to detect these marks 
 by immediate observation (I have never been able to analyse 
 my seemingly direct perception of the quarter from which 
 a sound comes), cannot, I think, outweigh the possibility 
 of showing other means by which the eye can judge distance, 
 the ear direction, and the memory recall a series in its serial 
 order, and no other. 
 
 The only logical importance of this psychological analysis 
 lies in its confirmation of the idea, suggested by the facts of 
 language and the very nature of quantity, that Space and 
 Time must imply qualitative discrimination as an element 
 of quantitative comparison. Nearer and further must be 
 qualitatively distinct spatial perceptions, as red and redder 
 are qualitatively distinct chromatic perceptions. Thus, the 
 abstract totalities of Space and Time have their germ in 
 comparisons effected by perception co-ordinate with the 
 perception of continuous quality and of its differences. 
 
 But the demonstrative judgments have forced upon our 
 notice a further and peculiar distinction within space and time 
 as continuous qualities, which is known in space as difference 
 of direction, and in time as difference of past and future. 
 ' Nearer ' and ' further ' are different spatial perceptions ; 
 and it is possible that ' this ' and ' that ' may be naturally 
 equivalent to ' nearer ' and ' further ', as ' here ' and ' there ' 
 must be, or must soon have become. ■'■ But besides ' this ' 
 and * that ' we have in space the distinction of ' that ' and 
 ' that ', ' there ' and ' there ', just as in time besides ' now ' 
 and ' then ' we have ' then ' and ' then ' — a distinction which 
 may apply to points equally removed in past and future, and 
 therefore cannot be reduced to quantity, i. e. degree of 
 remoteness. ' That ' and ' that ', ' there ^ and ' there ', imply 
 
 * Even if, prior to a spatial distinction recognised as such, there may 
 have been a less defined distinction as between ' by me ' and ' not by me '. 
 1337 I 
 
114 Quality and Comparison [Booki 
 
 no difference or remoteness, nor indeed do ' this ' and ' that ' 
 necessarily do so. 
 
 All these may just as well mean on the right hcind and 
 on the left as nearer and further. They must indeed he 
 comparable in distance, but it need not be distance that 
 furnishes the distinction between them. With other qualities 
 the case is different. There cannot be two different reds 
 that match ; all reds that match, i. e. that are ' equal ', are 
 the same. And if there can be two or more different musical 
 sounds that have the same pitch, this is because the distinction 
 between them is one of kind, not of simple quality, because, 
 that is, they are composite perceptions which are estimated 
 with reference to one element within them taken as dominant 
 or essential. 
 
 Thus it seems that (i) Space and Time appear in the germ 
 as mere qualities whose continuity is displayed in the judg- 
 ment of comparison like that of any other qualities. If 
 apprehension of Space and Time really depends on ' local ' 
 and ' temporal signs ', we must suppose that the peculiar 
 definite externality which characterises extension could only 
 appear by degrees, and that perception must have been 
 transformed from perception of contents plus local signs, 
 to perception of contents arrayed in extension by means of 
 local signs, that the logical character of spatial perception, 
 its continuity and homogeneous differences, must have been 
 present from the first in any system of apprehension which 
 could develope into our spatial world. The judgment of 
 continuous quality admits of this.^ And (2) the distinctions 
 which first present themselves within a given spatial or 
 temporal perception are not simply and solely differences of 
 quantity, though in time more so than in space, and in both 
 capable of quantitative expression. They are more analogous 
 
 * See Professor Stout, Mind, 77. 7, ' The essential fact is that colour 
 presentations and touch presentations, both as actual sensations and as 
 images retained or revived, are diffused in a continuous quantum within 
 which it is possible to distinguish parts outside of each other, beside 
 each other, and between each other. ' I am sure this is right. Then the 
 question is whether the local sign theory is consistent with it. All that 
 concerns us in logic is to maintain that the quantitative differences have 
 a qualitative basis, both of identity and of distinction. 
 
Chap. II] Qualities as such are disparate 115 
 
 to differences of kind. We must therefore take the spatial 
 and temporal demonstratives, apart from explicit quantitative 
 comparison in space and time, as in themselves comparative 
 contents involving continuous quality. 
 
 The divergence from the main progression of the judg 
 ment, by which space and time are erected into totalities 
 having a special structure of their own and a peculiar mode 
 of existence, must be taken as beginning with the resolution 
 of a given ' now ' and ' here ' in the judgment of comparison. 
 In this resolution we have the two grades, corresponding to 
 distinctions of direction, or to the distinction of past and 
 future, and to quantity respectively ; first that in which ' this ' 
 and 'that' may be e.g. to left and right (not nearer and 
 further), where the spatial comparison is implied rather than 
 expressed, corresponding to the judgment, ' This is red, and 
 that is green ; ' and, secondly, that in which a true spatial 
 comparison is introduced into the content, as in 'This is nearer 
 than that ', which is analogous to ' This is redder than that '. 
 
 iii. Under the head of Comparison it is usual to treat of So-called 
 
 like and different in kind, as co-ordinate with more and less. Qualita- 
 
 . . tive Com- 
 
 But it is to be observed that such a co-ordination is not parison. 
 
 accurate. Mere qualities, as such, are disparate, incom- 
 parable with each other. The judgment of quality pure 
 and simple, as we have seen, excludes comparison. This 
 is red, this is black, this is golden, this is sweet, this is sour. 
 These are successive and isolated judgments of quality ; and 
 the semblance of comparison which they now bear is due 
 exclusively to the advanced point of thought at which language 
 places us to begin with. 
 
 Comparison of degree, as we have seen, includes difference 
 or elementary negation within the limits of a single quality, 
 but the differences themselves, in regard to the aspect which 
 makes them distinct, remain disparate or incomparable. 
 In other words, every part of a quantitative whole is dis- 
 tinguished by a peculiar quality as well as united with the 
 rest by an identity of quality. Every shade of red, besides 
 being a degree of red in general, is also a particular hue and 
 produces a distinct impression. Every perception of warmth 
 is qualitatively peculiar, and often it is not without an effort 
 
 I 2 
 
ii6 Quality and Comparison [Booki 
 
 that we can recognise the character in respect of which it 
 can increase or decrease. Every inch in a yard measure, 
 every cannon ball in a heap, in thus distinguished ; and if it 
 were not so, the parts would have no stability and the quanti- 
 tative whole would cease to exist. 
 
 We therefore are driven to conclude that quantitative 
 comparison is not prima facie co-ordinate with qualitative, 
 but rather stands in its place as the effect of comparisoti on 
 quality, which so far as comparable becomes quantity, and 
 so far as incomparable furnishes the distinction of parts 
 essential to the quantitative whole. It is with this latter 
 aspect in which qualities are incomparable that qualitative 
 comparison as such must be connected. It is thus, prima 
 facie, comparison of the incomparable. Any two shades 
 of red, regarded as shades of red, are respectively more and 
 less. But they must also be, as we have insisted, different 
 reds, and if regarded simply thus are pronounced incom- 
 parable as a result of comparison. If we pass, as we can, 
 by slow transitions, along the complete solar spectrum, 
 comparing each colour with that which formed our starting- 
 point, we shall arrive first at differences which may, and then 
 at differences which must, be thus regarded. The difference 
 between red and green, for instance, is not to ordinary percep- 
 tion a difference in the same quality ; and if it can become 
 measurable, can only become so by reference to an identical 
 quality, such as brightness of illumination, which falls outside 
 the peculiarities of red and green as such. 
 
 I believe that it is futile to attempt the measurement of 
 difference except in respect of a continuous quality. And 
 the mere affirmation of difference, without the attempt to 
 measure, appears to me absolutely devoid of meaning. The 
 mere judgment, ' These two colours, — ^these two sounds, — or, 
 these two perceptions (a colour and a sound), are different,' 
 is an imperfect and unreal judgment, which in this form, and 
 apart from a meaning which I shall explain below, is as I believe 
 to be foimd nowhere but in logical text -books. It may best 
 be considered as an incomplete quantitative comparison, in 
 which the parts are distinguished, but their place in a 
 continuous whole has proved impossible to determine. In 
 
Chap. II] Quality and Kind 117 
 
 this sense, the mere judgment of difference would mark the 
 initial effort of quantitative comparison. Such a relation is 
 illustrated by the well-known fact that qualitative difference, 
 e. g. between two musical notes, is perceptible before its 
 quantitative nature (their relative pitch) is ascertained. 
 Such a judgment of qualitative difference may be regarded 
 as a first determination of quantity ; for its point is merely 
 to deny identity of quality, and in matters of simple quality 
 to be identical is to be equal and vice versa. In this sense 
 the judgment of qualitative difference, such a judgment as we 
 make when we see that two colours do not match, is an aspect 
 of the initial stage of quantitative comparison. 
 
 But another judgment of sameness or difference, which it 
 is almost impossible to avoid confusing with the above, has 
 its true place in classification and analogical inference, and, 
 if explained as mere qualitative comparison, is an unreal 
 fiction. Such judgments are : — ' These two instruments are 
 not in tune \ ' ' Gladstone and Chamberlain are very different 
 men ; ' ' That victory is uncommonly like a defeat ; ' ' The 
 globe-flower is just like a hellebore, only it is yellow.' Here 
 we are not speaking of an immediate qualitative identity and 
 difference, but of essential and dominant qualities or rather 
 attributes, in other words of differences valued by a pre- 
 supposed standard or purpose. The idea of a standard 
 involves the idea of kind, and kind goes beyond quality. 
 Therefore, we come to a conclusion which I think frees us 
 from much sham accuracy and pretended precision. The 
 judgment of difference is never made apart from a standard 
 of difference. The apparent exception, when such a judg- 
 ment denies identity of quality, is simply the first step in 
 quantitative compaiison, and it is by quantitative com- 
 parison that precision must in such cases be obtained. But 
 the class of judgments from which our later instances are 
 drawn do not refer to identity of quality, but identity of 
 kind. They presuppose classification, and affirm difference 
 or likeness with reference to this classification. All attempts 
 therefore to introduce a quantitative estimate into these 
 generic judgments of difference are founded on a confusion 
 between judgments of quality and judgments of kind, on an 
 
ii8 Quality and Comparison [Book i 
 
 attempt, that is, to reduce the latter to the former. This 
 does not deny that the latter may imply the former in 
 addition. 
 
 It is a futile introduction of psychology into logic to speak 
 of measuring difference by the difficulty or duration of a 
 psychical transition ; the measure of the difference is what 
 we mean by the difference, and what we mean by it depends 
 on the series or classification within which we affirm it. Apart 
 from such a standard the judgment of difference is nonsense ; 
 it becomes like ' The soul is not square '. How idle to inform 
 us that Gladstone and Chamberlain are different ! How 
 superfluous to affirm that one plant is like another ! Any 
 assertion like these, if it is not referred to a ground of distinc- 
 tion, in these cases to political and botanical classifications 
 respectively, is as destitute of content as a bare negation. The 
 instance of two instruments pronounced out of tune with 
 each other may seem not to be in place under this head, and 
 to be a judgment of true qualitative comparison. I inserted 
 it expressly to indicate the line of demarcation. Different 
 colours are such as do not match, i.e. are not discernible in 
 simple quality. But in comparing musical notes we have not 
 to do with simple quality,^ but with dominant quality,^ i.e. 
 kind. ' A note ' is identified by its pitch, and different notes 
 are sounds differing in pitch. Therefore in pronouncing notes 
 to be different we do not merely deny that they are indis- 
 cernible ; we deny something further than this, we deny that 
 they are indiscernible in their dominant quality, viz. their 
 pitch. That the pitch is itself a quantitative attribute 
 makes no difference ; for it is a quantitative attribute, which 
 has become characteristic, and therefore stands logically 
 in the same position as any other basis of classification. 
 
 In short, then, we must not confuse quality and kind. 
 Kind is dominant or characteristic quality and involves 
 a series of ideas which we have not yet discussed. And 
 whereas comparison in respect of simple quality is prior to 
 and absorbs itself in quantitative comparison, comparison 
 in respect of kind is subsequent to quantity and involves 
 
 ' I use quality in the logical sense, in which it includes timbre (musical 
 quality), pitch, and loudness. 
 
Chap. 11 J Klud IS EsseuUal Qualify 119 
 
 other ideas. An isolated judgment of difference can have 
 no meaning except as the first stage of quantitative com- 
 parison, the negation of identity ( = this and that are unequal). 
 The attempt to assign gradations to the mere judgment of 
 difference rests on a confusion between quality and kind, each 
 of which has in itself an adequate and objective principle 
 of measurement independent of psychical transition, and in 
 the case of kind, incapable of reduction to quantity. 
 
CHAPTER III 
 
 Measurement — Quantity and Proportion 
 
 Measure- I- MEASUREMENT is the equation of any whole, by com- 
 ment and parison, to a numerical aggregate of determinate parts, 
 ality. The parts may be determinate through reference either 
 outside or within the whole to be measured ; but if the 
 reference falls within it (as when we say a man's whole height 
 is so many times the length of his head) the whole must be 
 complex and contain subordinate systems. The reference 
 may also take the shape of relations which are not purely 
 quantitative (as a tone or semitone in music, apart from its 
 physical cause, is simply a difference between two peculiar 
 sounds) ; but in that case we are passing out of the region 
 of pure measurement. Some reference, however, there must 
 be in measurement beyond that to the simple whole which 
 is to be measured. It is no measurement of a line to divide 
 it into 100 or looo equal parts. We must know tvhat else 
 they are parts of, besides being parts of the line to be 
 measured. The length of a line is measured when it is 
 equated to feet and inches — to the length, that is, of some 
 actual piece of metal agreed upon as a standard — the pitch 
 of a note is measured when we have determined its place 
 in the scale or the number of vibrations per second that enter 
 into it ; the specific gravity of a substance is measured 
 when we have stated the ratio of its weight to that of an equal 
 volume of distilled water at a certain temperature. Here 
 a verbal difficulty may be cleared away. If the weight of the 
 substance before us is twelve times that of water, our definition 
 of measurement applies straightforwardly. We equate the 
 whole substance in respect of its weight to a numerical aggre- 
 gate of twelve parts, each of which is determined by equation 
 to a known volume of water.^ But if tlie substance is 1^2 of the 
 
 ^ Practically of course we do not heap up volumes of water in one 
 scale till they balance a substance in the other scale. The process 
 
Chap. Ill] Measurement and Comparison 121 
 
 weight of water, we seem not to be breaking up the whole 
 which is being measured into an aggregate of parts, but to 
 be representing it as a part within another aggregate. This 
 is a mere matter of practical convenience. The equation of 
 a whole to a numerical aggregate is as much involved in the 
 expression iV (a twelfth part), as in the expression ' twelve 
 times '. In measuring, we bring two terms into precise 
 equation, and the entire relation of whole and part is in- 
 volved in each. The numbers in which the same part enters 
 into two or more wholes are in every case the organon of 
 measurement. 
 
 i. Measurement is to begin with Simple Measurement, Simple 
 ,,. . ^ ... measure- 
 
 resultmg m pure Quantity. ment. 
 
 Simple Measurement consists in judging of a perceived Quantity, 
 object that it is a whole containing a certain number (one or 
 more) of a determinate unit. Measurement is thus a develop- 
 ment of comparison, which is the first revelation of the unit, 
 or equal part — the result of successful equation — within 
 continuous quality. Simple qualitative identity, for instance, 
 such as that of colours which match, may be set down to 
 comparison or to measurement according as it is or is not 
 ideally referred to a scale of degrees. In pure qualitative 
 identification we have sometimes no idea of possible degrees, 
 and such identification must be regarded as the earliest germ 
 at once of measurement and of comparison. Thus ' The taste 
 of this is the same as the taste of that ' is mere identification 
 or comparison if it only means that the tastes of the two 
 things are indiscernible, but is measurement if we are consider- 
 ing whether the one taste is sweeter than the other. We have 
 seen that qualitative identification is only the germ of quanti-- 
 tative comparison, and that the two pre not co-ordinate.-^ 
 
 How is the unit fixed ? It is fixed, as we have seen, by 
 equation or identification of it as the same throughout the 
 various wholes or aggregates into which it enters as a part. 
 
 employed is equivalent to weighing first the substance, and then the 
 water which it displaces, against known standard weights, and taking 
 the two results as a ratio ; i.e. by help of the balance we state the two 
 things to be compared in terms of an aggregate of already known and 
 determinate parts ; one thing will = 12 oz. and the other i oz. 
 'p. 116 ff. 
 
122 Quantity and Proportion [Booki 
 
 This process of equation tends to repeat itself ad infinitum. 
 Pure quantity is an essentially relative attribute. Hence in 
 Simple Measurement the paradox of knowledge takes an 
 extreme form, for every measurement presupposes and pro- 
 vokes others ad infinitum. The tables of weights and measures 
 of our arithmetic books are enough to illustrate this. Ihey 
 are long lists of equation after equation, by means of which 
 all objects that are measured or weighed are ultimately 
 equated with some single portion of matter or relation in 
 nature,^ arbitrarily selected as a basis of the division and 
 multiplication that facilitate comparison. The substitution of 
 a determinate physical motion supposed to be constant for 
 a particular portion of matter makes no change of principle so 
 long as it is taken qua a term in a fixed ratio or mere ratio, and 
 not qua a term in a generalised ratio or proportion. But in 
 fact the two ideas are at bottom inseparable. Everything 
 fixed is qua fixed, potentially generalised. The wave-length 
 of what is a particular red to a normal eye does not vary (so 
 far as I know), but this is so to speak an accident ; and if we 
 take in non-normal eyes, all that is certain is that this wave- 
 length preserves its place in the colour-series above some wave- 
 lengths and below others. Its fixity for red judged by the 
 healthy eye has however caused it to be suggested for an unit 
 of length. Weight — the relation of a portion of matter said to 
 weigh I lb. to all other portions of matter in respect of their 
 gravity — becomes a generalised relation or proportion the 
 moment we consider distance from the earth's centre. ' i lb. 
 at earth's surface : 2 lbs. at earth's surface : : i lb. five miles up : 
 2 lbs. five miles up.' When a thing is described generically by 
 the number of its own parts this is more obvious, for the ratio 
 is then ipso facto generalised by the mere recurrence of indi- 
 vidual things. But simple measurement of perceived objects 
 gives simple ratios expressed in singular judgments with 
 
 ' Such as a fraction of the earth's circumference. But any sucli 
 relation is likely to be variously determined at different times, while it 
 is not convenient to alter the basis of a system of measures. I believe 
 that practically all systems of measures depend upon the actual material 
 standard, which as a mere piece of metal, not capable of being tested by 
 any general relation in nature, must be reckoned as a purely arbitrary 
 standard. 
 
Chap. Ill] Generalised Measurement 123 
 
 external reference. As the judgment becomes general the 
 ratio becomes first formally proportional, because the ratio 
 is generalised as against instances in which it occurs, and then 
 really proportional, because this generalisation comes to apply 
 to cases in which the corresponding terms are different magni- 
 tudes. The ratio between measures ^ is formally proportional ; 
 that between weights, explained as above, is really pro- 
 portional. 
 
 ii. Thus measurement necessarily becomes complex, ideal, Complex 
 or mediate ; i. e. in short generalised. In this aspect it first ^g^ji^^g 
 appears within the singular judgment, and then breaks loose measure- 
 from it. Propor- 
 
 Every relation established by measurement is a ratio, or tion. 
 relation between magnitudes ; and as incommensurable magni- 
 tudes [Me for logic a contradiction in terms, every ratio can be 
 expressed in so far as it is a true ratio (in so far as its terms are 
 magnitudes) by a relation between two numbers. Number 
 refers the relation to an abstract whole of quantity, and there- 
 fore determines the identity of the relation by its place in a self- 
 identical articulate system. But the effect of such expression 
 is to generalise, while the results of simple measurement can 
 warrant no generalisation, and therefore are not spoken of as 
 a ratio, and often not reduced to their simplest numerical 
 expression. Nothing would be gained by saying that a given 
 plant 5 ft. high had a height which was to i ft. as 5 : i, nor 
 by judging that this piece of lead is to this piece of gold in 
 weight as 11 to 19. The ratios so affirmed would still be 
 destitute of general significance, would be mere facts, alleged 
 of a particular reality present in perception, and would there- 
 fore gain nothing, but might lose their truth, by abstract 
 expression. 
 
 But thought always tends to coherence and necessity, and 
 we cannot even employ a determinate idea to assist us in 
 pointing out an object of perception without creating the 
 impression that the ideal content which we use will be charac- 
 
 ' By ultimate refinement, this too is really proportional. Suppose all 
 measurable things to expand and contract preserving their ratios, we 
 could never know it. Given a foot-rule, we could still construct a yard- 
 measure, however the absolute length of the foot-rule might vary. 
 
124 Quantity and Proportion [Book i 
 
 teristically connected with the content of our predication. 
 When this occurs in the judgment of measurement, ratio passes 
 into proportion ; that is to say, the ratio enunciated as true 
 of the particular given subject becomes a universal rule 
 applicable to all variations compatible with the determinate 
 idea which conditions the subject. Such measurement is 
 complex, because the unit on which it is based is no longer 
 single and fixed, but variable in absolute magnitude, though 
 determined by a condition. It is ideal, because no longer 
 a mere fact of sense-perception, but enunciated as flowing from 
 a content intellectually defined. It is mediate, because the 
 reference to reality which constitutes this as every judgment, 
 is not direct, but has to pass through a condition before it can 
 attach to reality. 
 
 Therefore if we take one of the above simple measurements, 
 and even without removing the demonstrative ' this ', insert 
 a determinate condition into the content, we shall find that the 
 whole affirmation is greatly modified in its nature. Let us 
 judge that ' This piece of lead and this piece of gold, being of 
 the same volume, are found to be in weight as ii : 19 '. Then 
 we at least suggest the erection of the ratio 11 : 19 into a law 
 of proportion : ' The weights of equal volumes of lead and 
 of gold are as 11 to 19.' 
 
 So again, we may have simply counted the leaves on a plant- 
 stem, going round the stem in the same direction, till we find 
 a leaf immediately over or under that from which we began. 
 If we do not know that these ratios are characteristic, or if we 
 suspect the plant to have been injured so as to make its ratio 
 undiscoverable, we may simply judge, ' On this plant I find 
 five leaves in going twice round the axis.' Whereas if we 
 insert the name of the plant or tree, and use an abbreviated 
 expression for the ratio of divergence, we at least suggest the 
 idea of a characteristic law of the leaf spiral. ' This oak shows 
 a divergence of f ' (i. e. the sixth leaf is directly over the first, 
 and in counting from i to 6 you have gone twice round the 
 stem). It is obvious that here generalisation and characteristic 
 attribution have begun. Granting that we have not yet any 
 assertion about the genus oak, or even about the species in 
 question, for the ' This ' hinders such an interpretation, yet 
 
Chap. Ill] Characteristic Ratio 125 
 
 we unquestionably are awakening to the expectation that the 
 tree before us will present the ratio in question in all its different 
 parts and from time to time, and to the problem whether and 
 how far we may drop the ' This ' which indicates particularity. 
 When the ' This ' is dropped the judgment ceases to be singular, 
 unless it is attached to a proper or in some way individual 
 name. Whether and how far, failing these refuges, it ceases to 
 be categorical and becomes hypothetical, or how far indi- 
 viduality continues or even revives after the loss of particu- 
 larity, as a factor in the evolution of thought, is a question 
 which will frequently occupy us in the sequel. 
 
 Characteristic ratio, or proportion, may refer to standards 
 external to the whole which it qualifies, or to relations within 
 that whole. In the former case the qualitative quantity 
 remains subject to relativity and eked out by equations ad 
 infinitum, hardly less than in the case of simple measurement. 
 
 In any table of specific gravities, for instance, we have 
 a number of substances each severally characterised by the 
 ratio of its density to that of distilled water at a temperature 
 of about 39.1° Fahrenheit. Now in the first place, each of 
 these several ratios may obviously be regarded as a proportion 
 in so far as it applies without variation to any volume of the 
 same substance, in the sense that the weight of any volume of 
 any substance is to the weight of the same volume of 
 water ^ in the ratio of the specific gravity of the substance. 
 Proportion is defined as ' equality of ratios ' ; and equality of 
 ratios obviously is identity of the ratio, and exists between 
 every ratio and all cases in which it applies. 
 
 But in the second place, although in these cases we have 
 
 proportion, yet we have also relativity ad infinitum. Select 
 
 the specific gravity of some one body, and suppose that of all 
 
 the rest except water itself to be erased from knowledge ; 
 
 the significance of our one fragment of information would then 
 
 be all but gone, were it not for the accessory idea, which we 
 
 cannot now get rid of, that the rest could easily be recovered. 
 
 * I omit for the sake of brevity in this and parallel cases to repeat in 
 every sentence the precise determinations by which the standard unit 
 is made a standard. But it is all-important to remember that there 
 are such determinations, and that they in turn need re-determination 
 ad infinitum. There is no ultimate unit. 
 
126 Quantity and Proportion [Booki 
 
 Apart from this accessory idea, the supposition makes it plain 
 that the ratio between the density of silver. or flint glass and 
 that of water is not sought out as valuable per se, but is valued 
 as a means of equation with all measurable densities. In such 
 instances as these we have the first grade of characteristic 
 quantity or proportion, still subject to an external relativity 
 which extends into an infinite series. 
 
 Now though this relativity never disappears as an aspect of 
 human knowledge, yet characteristic quantity C2.n assume 
 a more self-sufficing position than that which has just been 
 described. Instead of developing the this and that of the 
 comparative judgment into separate units connected only 
 by an abstract identity of quality, we may consider them as 
 structural elements within a concrete whole. As before, we 
 shall find ourselves at first in the stage of simple measurement 
 and pure quantity. But the tendency to advance to proportion 
 is in cases of this type much more pronounced, because the 
 parts of an individual whole are more likely to vary in con- 
 nected ways and therefore lend themselves to proportion, than 
 the elements of wholes external to one another. Still we begin 
 with pure quantity. ' This plant has petals exceeding the 
 calyx segments,' or ' has radical leaves half the height of the 
 stem ', or ' has twenty-one carpels and forty-two stamens ', or, 
 as we said above, ' has a divergence of f between its stem- 
 leaves.' In the first instance such judgments as these are mere 
 judgments of perception, or at the outside of direct historical 
 fact, and the ratio which forms the content of predication is 
 therefore not a proportion, because it has no extent of applica- 
 tion. In proportion, the ratio is to the cases of the ratio as 
 Intension to Extension. 
 
 But the moment thought has seized a significant ^ idea, it is 
 committed and must go wherever the idea carries it, in despite 
 of the demonstrative ' this '. And the moment that any such 
 internal ratio as those which I have suggested is taken to be 
 characteristic, i.e. to be involved in the significant idea, it 
 becomes a proportion, i.e. a law of structure which holds in 
 spite of varieties of size, shape, and number, although, at least 
 
 * I have here altered the term ' designative ' into ' significant ', 
 because of the contrast between designation and ideas. See ii, pp. 260 ff . 
 
 1 
 
Chap. Ill] Proportion and Individuality 127 
 
 in natural objects, always subject to limits which as regards 
 the proportion itself are arbitrary and external. 
 
 Proportion is the simplest expression of individuality.^ 
 All intelligent recognition of individual objects depends either 
 on proportion or on some principle which involves proportion. 
 It is in this that the truth lies of the well-known Pythagorean 
 doctrine that all things are embodiments of number. All 
 things have aspects and effects which find generalised expres- 
 sion in number. Shorten a snipe's beak, take one from the 
 divisions of the horse-chestnut leaf, or misplace the accent 
 (a variation of loudness and duration) in an English word, 
 and recognition falters or fails. Even a human character or an 
 artistic inspiration, though not in itself susceptible of numerical 
 expression, leaves traces in all its acts and products of an 
 individuality that takes shape in proportion or qualitative 
 quantity. An exhaustive statistical treatment of a man's life 
 in all its tangible aspects would give, by the graphical method, 
 not indeed his character, but a set of proportions penetratingly 
 significant of his character. 
 
 It may seem indeed that in common hurried thought 
 recognition simply attaches to some pre-eminent quality, 
 a bright colour, a marked outline, a peculiar movement ; and 
 that such elements as these, without extension into propor- 
 tional systems, furnish the practical meaning of words in 
 ordinary life. But in the first place, this is perhaps a super- 
 ficial analysis cf perception. I very strongly doubt if the 
 element of proportion, both external as in size compared with 
 surroundings, and internal as in shape, symmetry, or harmony 
 of sound or colour, is ever absent in a recognitive perception 
 of an individual thing. A really abstract quality would hardly 
 mean anything : we should be able to place it nowhere in our 
 world ; and if we even recognised its degree of intensity, that 
 would at once constitute a quantitative element. It has 
 indeed been observed that a familiar scent (one of the least 
 articulate of qualities) has a notable power of stirring asso- 
 ciated memories. But this seems so noteworthy just because 
 the scent does not recall any individual thing, but rather brings 
 
 * That is to say, when once we have abandoned or transcended the 
 uhanalysed ' this ', which has individuality in a different sense. 
 
128 Quantity and Proportion [Booki 
 
 back a general state of feeling connected perhaps with entire 
 scenes and incidents, but especially with emotions. 
 
 And in the second place, if an abstract or mere quality were 
 used designatively * in judgment, it would not grasp or enter 
 into the nature of a real individual ; it would simply be 
 a falling back towards the demonstrative affirmation with its 
 ' This ', which may on occasion be eked out by any element 
 that draws attention. 
 
 But all ordinary recognition of individuals undoubtedly 
 depends on the judgment of proportion. We cannot indeed 
 tell the specific gravity of a metal by the mere sense of pres- 
 sure or of resistance, but we know how a sovereign ought to 
 feel when we lift it on the palm of the hand ; and though we 
 may call this effect on the hand a quality, it is plainly a quality 
 pervading differences and so quantitative, and moreover taken 
 as characteristic and so proportional. Consider once more the 
 effect of altering an accent in English (I do not speak of 
 languages in which accent depends on pitch) as exemplified in 
 the change of ' conquer ' into * concur ' by transferring the 
 stress from the first to the second syllable, or the utter un- 
 recognisability of such a term as ' sleeping-car ' when pro- 
 nounced with a heavy stress on the second syllable,^ and a 
 light stress on the first. Here it is the internal proportion 
 that is modified, with the result of destroying the peculiar 
 rhythm by which in a great degree the ear instantaneously 
 recognises a word. The more marked an individuality is the 
 more it depends on internal proportion. Every instrument 
 fitted for a purpose has internal proportions dictated by its 
 purpose ; a knife is sharp at the edge and blunt at the back ; 
 the thickness of the blade in its transverse section depends on 
 the requirement of strength on the one hand and on that of 
 dividing without displacement on the other, and these require- 
 ments together dictate a certain set of proportions character- 
 istic of a blade suited for some particular purpose. The length 
 of the blade compared with its width depends on such another 
 
 * See notes on pp. 126-7. The argument here amounts to saying 
 that a quality cannot be used designatively. 
 
 ^ The author once heard the words thus mauled at Calais, and could 
 not imagine what was being said, though no elements of the sound were 
 omitted. 
 
Chap. Ill] Internal and External Proportion 129 
 
 set, and its temper on a third. All of these being on the one 
 hand relative to each other and on the other hand relative to 
 a purpose are internal proportions subject to limits prescribed 
 by external proportions. It is by acquaintance with the 
 perceptible character impressed by such proportions as these 
 that we readily pronounce on the use of objects made by the 
 hand of man, and that we detect, somewhat less readily, the 
 actual purpose served by adaptations in the organic world. 
 Such attributes as are expressed in these proportions form, 
 for perception, the content of individualities. 
 
 It follows from these considerations that the question of 
 individuality in contents the main attributes of which arise 
 from external proportions is not an easy one. Such are nearly 
 all inorganic substances, except where adapted to a purpose 
 by man. External '^ proportions -per se produce no effect of 
 individual unity, and though it is true that all substances 
 occur in particular fragments which have definite characteristic 
 forms, yet the ratios which would express these forms are not 
 absolutely typical or essential (though perhaps all substances 
 prefer some shapes to others, and have typical fractures, &c.), 
 nor do the particular masses of substances or volumes of gases 
 demand or receive individual names. Professor Jevons has 
 called attention to this curious fact, which goes deep into the 
 nature of individuality. Below the level of organic form, or 
 form given by human interference, what do we mean by 
 a thing ? Of course we may take a lump of metal or an ounce 
 of water, a handful of sand or a jarful of chlorine, and speak of 
 it as a thing ; but we shall be puzzled to find any name that 
 recognises its separate-identity as ' lion ' or ' spade ' or * house ' 
 recognise that of the contents that form their meaning. Is 
 gold a class-name, say a specific name, and are the actual 
 pieces of gold individuals under it ? This does not seem to 
 be right ; a class-name is true, without further determination, 
 of the individuals under it. ' This is a lion,' ' This is a spade,' 
 &c. But you cannot say ' This is a gold ' : you can only say 
 * this is gold ', where ' gold ' almost = ' made of gold ', i.e. is 
 
 * There seems no meaning in this word except in contrast with the 
 inner proportions of an organism. It must be understood of a difference 
 of degree between organic and inorganic structure. 
 
 1337 K 
 
130 Quantity and Proportion [Booki 
 
 adjectival, and has no plural, or if it has one, uses it for different 
 kinds, not for different pieces, of gold. 
 
 It is enough at present to call attention to this difficulty as 
 illustrating the place of structure in individuality. It should 
 be noticed that a structure however complex which repeats 
 itself homogeneously throughout all atoms of a certain 
 substance tends to confer individuality, if at all, on the minute 
 units in which the complex structure exists, but neither on 
 the substance as such nor on its larger fragments ; the sup- 
 posed minute structure is not the structure of it or of them, 
 but only a structure repeated within it or them. A heap of 
 corn is, qua heap, no more organic than a heap of sand. But 
 it may be for instance that, in virtue of a common structure, all 
 the iron that anywhere exists is united by reciprocal reaction 
 in a common magnetic world ; if so, it is then up to a certain 
 point single and individual. The further consideration of this 
 difficult subject belongs to the discussion of the Individual 
 and Generic judgment. 
 Qualita- ill. The relation of Quantity to Quality results at this point 
 *7i"fr^^'^^" a further problem. Assuming that a thing which has 
 duals. marked individuality has always a number of pervading 
 qualities, each of which contains gradations and a distribution 
 expressible by a ratio or proportion, what are we to say of the 
 interconnection of these various systems of proportion with 
 one another ? Is it necessary that there should be a general 
 proportion of proportions which, whether our actual appre- 
 hension of it be rough or exact, must be taken as capable of 
 expressing the various systems of attributes as gradations 
 within one and the same totality ? Is there any sense in 
 talking of the proportion not only of length to length and of 
 colour to colour, but of length to colour ; or of the proportion 
 not only between rhythm and rhythm or pitch and pitch in 
 a melody, but between rhythm and pitch as elements of the 
 musical effect ? 
 
 The view which we took above of the effect of comparison 
 upon quality forces this suggestion upon us. //, in other 
 words, a single qualitative effect pervades any and every 
 totality which we apprehend, and if within such a quality 
 there are parts perceived as differences of it, then these 
 
Chap, iiij Disparate Qualities how combined ? 131 
 
 differences must in respect of that quality be regarded as 
 gradations. It is not necessary to press this conception home 
 at present. It is possible that there may be individuals whose 
 unity lies in an idea only and not also in a quality, and that 
 an idea may hold together without crushing them into grada- 
 tions, antitheses which a quality could only admit as quanti- 
 tative. But it is worth while to bear in mind* that there may 
 be a quality of ' effect ', or secondary quality, within which 
 even form and colour or pitch and rhythm may take their 
 place as degrees, just as the repetition of analogous though 
 different forms in a picture or design gives the impression of 
 a pervading character which is more and less intense in 
 different parts of the work. Take for instance a picture about 
 which there is a question whether Turner painted it, or a song 
 which is ascribed without certainty to Shakespeare. In such 
 cases we point to this and that characteristic as more or less 
 Turneresque or Shakespearean ; and the elements so desig- 
 nated need not be in actual sensuous quality comparable with 
 each other. It might even be suggested that the exhibition of 
 such a pervading quality was a condition of aesthetic thoug*h 
 not necessarily of actual individuality ; a suggestion which 
 would raise the fundamental problem whether all actual 
 individuality has, for those who have eyes to see, a thorough 
 characteristic unity. It would seem not improbable that true 
 individuality is attained by actual individuals in very different 
 degrees. 
 
 iv. In explaining the apprehension of individual things,^ Change 
 which I have set down to the sense of proportion, it is usual to ^^^ ^°' 
 lay stress on the fact of change, including motion. Change in reference 
 time and place is no doubt a primary instrument in revealing duaUtv^'' 
 the fact of individual existence. The moveable and modifiable 
 Thing proclaims itself unmistakeably as distinct and perma- 
 nent. Nevertheless, for logical purposes change is only a case 
 of difference or negation ; or if in fact the two are coextensive, 
 yet change is not the essence of all difference. It may be that 
 
 ' I have here cancelled a sentence which implied that zero of a quality 
 was a degree of that quality. See Bradley, Mind, 74, 184. 
 
 ^ All the ' individuals ' here discussed are of course only prima facie 
 individuals. See ii, p. 253. 
 
 K2 
 
132 Quantity and Proportion [booki 
 
 every apprehension of difference requires lapse of time, but 
 this is only because our activity is in succession, and does not 
 mean that the differences themselves must be (though they 
 may be) successive. 
 
 What the whole matter comes to is this. Difference is the 
 principle which when generalised is known as Negation ; in as 
 far as contents merely differ, they are merely not each other. 
 Every continuous quality includes negative determination, 
 i.e. differences, elements which are not each other. Among 
 other continuous qualities, duration and extension charac- 
 terise a large part ^ of the world of sense-perception, and 
 duration characterises in one aspect everything that comes 
 before the human intelligence. It is not, therefore, surprising, 
 that not only the parts or elements of individuals, but the 
 individuals themselves as parts or elements of our perceived 
 world, should bear a negative relation to each other and to 
 themselves in time, in space, or in time and space together. 
 
 Now if we contrast change and motion on the one hand with 
 mere perceived difference on the other, as influences bearing 
 upon the apprehension of individuality, the distinction between 
 the two cases amounts simply to this, that in the latter we 
 have a single set of differences, which can go but a short way, 
 as a rule, to exhaust any identity, while in the former we have 
 at once a summary of innumerable differences or negative 
 relations. These differences, in virtue not of their mere spatial 
 or temporal distinctness, but of their positive content, are 
 read off in judgments which may ^ coalesce into one or may be 
 distinguished into several determinations of the individual. 
 These judgments may have a negative or positive iorm, but 
 must always express a partly negative element of apprehension, 
 viz. that * what is not B is not A '. 
 
 When we see a moving animal against a variously coloured 
 background, different elements of its outline and colouring are 
 successively thrown into relief by successive contrasts, and 
 perception traces its form with increasing completeness by 
 
 * I cannot think that sonorous bodies appear to be clothed with 
 sound as luminous bodies are with colour. To me sound is an unex- 
 tended perception, though referred to a cause in space. 
 
 ' See the general theory of judgment in time, chap, i, above. 
 
Chap. Ill] Change and Difference 133 
 
 the negations which these contrasts furnish, i. e. by the cor- 
 rection which is effected when a line or colour, which the 
 moment before ran into the background, is sharply defined by 
 a change of contrast. The perceptive judgment resulting 
 from this change will take the shape ' That (the dubious border 
 of colour) was not B (a particular part of the animal's outline) 
 and therefore is not A (does not belong to the animal).' More 
 elaborate interpretations than this may of course attach them- 
 selves to the motion of a separate material thing ; thus, for 
 instance, that which moves all together must in all probability 
 have mechanical cohesion, for it is unlikely that in presence of 
 varying friction at its different points the parts of a moving 
 appearance should keep together apart from such a condition. 
 But cohesion is for our present purpose merely a definite con- 
 tent assigned to unity, and the negative relation of the moving 
 thing to what does not partake of its cohesion is established 
 by just the same logical process as its relation to that which 
 does not partake of its distinctive shape or colour. Change in 
 time without motion has the same effect ; nothing is more 
 readily detached from its background and apprehended as 
 individual than an object whose transformations take place 
 before our eyes in surroundings which do not share them. The 
 judgment or judgments ^ ' What is not a,, a^, a.^, &c. is not A ' 
 seems to form itself in such a case almost without an effort of 
 mind. We shall be told indeed that ' What is not a^, a.^, &c. is 
 not A ' is a mere inference from ' A is a,, a.^, &c.' This objection 
 would raise questions which cannot be dealt with till we treat 
 of negative and of inductive inference. Here we need only 
 insist that however we may elect to describe the process of 
 the negative instance, it is easily seen to be the most effective 
 instrument of definition. When we inject a system of vessels 
 with coloured fluid, in order to observe them under the micro- 
 scope, it is not the particular colour, red or blue, that we 
 look for, but the contrast between the artificial colour and 
 the dull grey or yellow of the background. Even granting 
 that we start from ' The vessels which are to be traced (A) are 
 the red lines (aip a.^, &c.),' stni this judgment cannot have 
 scientific precision apart from the determination of the 
 * See the account of judgment as an act in time, p. 79 ff. 
 
134 Quantity and Proportion [Booki 
 
 detailed not a-^, not a^, &c. ; and when the not-a's assume 
 a positive character, the negation ceases to be an inference 
 from the affirmation A is a. And change is an infinite succession 
 of such contrasts, that gives every element of the complex 
 individual before perception its chance of being sharply 
 defined, and by successive negations defines each of them both 
 against its own permanent elements and against the back- 
 ground. Instead of the simple change of colour by injection, 
 let us think of the effect produced by rotating the polariser or 
 analyser while observing an object that modifies polarised 
 light. The successive but gradual changes of colour, illumina- 
 tion, and background which are thus obtained bring out the 
 details of a structure as clearly as if we could handle it and 
 move it freely in space. Change and motion merely do for 
 a single individual identity what a comparison of instances 
 does for an abstract identity. That is to say, they show 
 through what contrasts the individual can pass, to what 
 negations it can be subjected whether within its content, or 
 between its content and the background from which it is 
 distinguished, without losing characteristic identity. Change 
 and motion have their logical value simply as embodiments of 
 difference. 
 Abstrac- V. In the Judgment of Measurement we find ourselves face 
 
 tion and |q {^^.g ^^|-j^ ^j^g element of abstraction and necessity, the 
 Necessity. '' 
 
 medium in which exact science moves, and the occasion of the 
 
 most fundamental crux for logic as for ethics. We are no 
 longer, as in the Judgment of Quality, simply ascribing the 
 meaning of an idea to an unspecified reality given in perception. 
 We are indeed, as always in judgment, defining the reality 
 which perception presents to us ; but we find that in trying 
 to define any special feature or element within it, we are under 
 constraint, not merely as always from the pressure of percep- 
 tion, but from the inability to select and connect at pleasure 
 within the presented content. Judgment — so far as it escapes 
 from the distractions of mere association — proceeds in grooves 
 or along threads which are always leading it across and out of 
 the picture. It cannot, in the present stage at all events, 
 simply characterise a given identity by differences related to 
 it and to nothing else. Such differences, as we have seen, would 
 
Chap. Ill] Measurement leads to Necessity 135 
 
 have no stability, and could characterise nothing; although 
 the more highly organised and individual the identity the 
 more capable it is of prescribing a necessity to subordinate 
 wholes which appear as differences within it. The course of 
 judgment within the present whole of perception is determined 
 by connections which refer beyond that accidental whole, to 
 other more comprehensive totalities, and ultimately, in every 
 case, to the system of the known world. The connections 
 thus prescribed between part and part within some systematic 
 whole are necessary connections, and judgment, in so far as it 
 is controlled by them, is abstract or hypothetical judgment. 
 
 But the appearance of this element in the judgment of per- 
 ception makes it simply self-contradictory. The specification 
 of a subject by means of an idea, which is only meant to point 
 out a feature in present reality, brings the judgment into a 
 ^oove of necessity, and all but makes its affirmation con- 
 ditional. A speaker who has affirmed that ' This execrable 
 ruffian should be hung ' will probably, if convinced that the 
 man is not a ruffian at all, consider that the non-existence of 
 the condition precludes the application of the judgment ; 
 i.e. in spite of the ' this ', he will maintain that his judgment 
 was essentially conditional. We shall not find it easy to decide 
 whether the idea in question was really a condition or a predi- 
 cated content. In the latter case the judgment is falsified by 
 the non-existence of the fact indicated in the subject, in the 
 former it is not. There can be little doubt that we must follow 
 the analogy of ' this ', ' here ' and ' now ', by treating ideas, 
 which characterise '^ the subject, as presupposed rather than 
 affirmed ; but seeing that in this case the idea which forms 
 the presupposition is such as may or may not be realised, and 
 yet is welded together with a presupposition — the ' this ' — 
 which cannot but be realised, there is an inevitable ambiguity 
 in the judgment, — the ambiguity between absolute and con- 
 ditional assertion. 
 
 vi. In logic as in ethics, Individuality or Absoluteness is at Absolute 
 first sight opposed to Necessity or Relativity. That which is ditional 
 individual or absolute claims to be self-sufficing ; that is to Affirma- 
 say, to be an Identity which determines and is determined by 
 * See note on p. 126. 
 
136 Quantity and Proportion [Booki 
 
 its own differences, but is not dependent on anything outside 
 itself. Every content partakes of this character in so far, but 
 in so far only, as it has a unity or an interest for its own sake 
 or in itself. A material ' thing ', an organism, a work of fine 
 art, possesses such unity in a degree that forces its individuality 
 upon perception and ensures it universal recognition in 
 language. But every content without exception that is 
 exhibited in judgment has such unity or interest in some 
 aspect or to some degree. Even the abstract idea that qualifies 
 * this ' in a perceptive judgment such as ' This cold is intoler- 
 able ' is taken as the key to the interest of a presentation, as 
 a predominant feature that arrests attention in our momentary 
 surroundings. That the distinctive character which makes 
 the unity of the presentation is abstract and indeterminate 
 follows merely from the judging function being in a rudi- 
 mentary stage to which a concrete synthesis is stUl unattainable. 
 On the other hand, every judgment may also be regarded 
 under an aspect of relativity or necessity. In so far as a 
 content is necessary it is not self-sufficing, but is a conse- 
 quence of something else, and in so far as it is relative it 
 fails to explain itself, and refers to something else for ex- 
 planation. Every content, every identity in human know- 
 ledge is on one side wholly of this character. How the two 
 sides, the absoluteness and relativity of the objects of know- 
 ledge, can coexist without interfering may be considered if 
 we please, though in my judgment erroneously, as a desperate 
 problem. But that they do coexist we may convince ourselves 
 by the evolutional history of any flower, by the analysis of 
 any ornamental design, by the study, in its genesis and with 
 a view to the influences that conditioned it, of any human 
 mind. And, in one sense, necessity is more universal than 
 what I call absoluteness, or if I may coin a phrase significant 
 of the sense in which I speak of absoluteness, morphological 
 unity. Morphological Unity has degiees, but relativity or 
 necessity has none. The only escape from relativity is 
 in the exhaustion of relations. If, for instance, we can in- 
 telligibly speak of the universe as a whole, we must take it, 
 I presume, as the totality of relations, and therefore as bearing 
 no relation to anything outside itself. But this speculation 
 
Chap. Ill] Relativity and Explanation 137 
 
 is unprofitable, because what is out of relation is out of know- 
 ledge ; or it has at most a negative value as against doctrines 
 which extend the relativity which holds within the totality 
 of relations to the ideal totality of relations itself, and so 
 discuss its origin 01 the possibility of it not having been. 
 This is futile, from the very nature of explanation. All 
 explanation is within the universe, not of it. Therefore every 
 content that qualifies a subject invites consideration as an 
 antecedent in necessity in a judgment ' if a is, then h is ', 
 while it is not every content that has morphological unity 
 and so is given as a whole in each and all of its differences. 
 And only such a content as this is adequate to reality, 
 or can stand, without special symbols of reference, for an 
 individual reality. What is not individual can only be 
 a fragment of the real. 
 
 The above considerations were touched upon in chap. I, 
 in explaining the pregnant distinction between Categorical 
 and Hypothetical judging, and are to govern, as was there 
 indicated, the application of that distinction in the remainder 
 of the present Book. We start from the principle that all 
 judgment whatc ir is an attempt to make explicit the nature 
 of Reality, and is directly or indirectly attached to the reality 
 which is presented through perception. The ultimate subject 
 of all Judgment is the Real, and any idea which appears as 
 characterising or even as in lieu of the subject of judgment 
 must be taken as simply indicating or calling attention to 
 some aspect of the real world. That is to say, such an idea 
 must be taken as morphologically corresponding to the ' this ', 
 ' here ', or ' now ' in the demonstrative judgment, to the un- 
 named direction of perception in the pure judgment of quality, 
 or to the significant ideal content which expands the ' this ' or 
 ' here ' in the elementary judgment of measurement. It follows 
 from this that in every judgment the immediate subject is 
 prima facie taken to be real, and therefore every judgment 
 is prima facie taken to be categorical. This does not mean 
 that in the strict sense it asserts real existence of the subject, 
 for its real existence is presupposed,^ but rather that it defines 
 the reality of a real existence presupposed as subject. 
 ^ See last section. 
 
138 Quantity and Proportion [Booki 
 
 But this prima facie semblance of the judgment must be 
 qualified. The explicit content which characterises the real 
 subject may be inadequate to the nature of reality. In 
 ' this red thing ', ' this metal ', even ' this man ', the explicit 
 contents ' red ', ' metal ', ' man ' are t5^ical and general, not 
 single and individual ; and still more is this the case if we 
 think of such judgments as ' Red is a colour ', ' Metal is lus- 
 trous ', ' Man is mortal '. These contents stand for imperfect 
 and incomplete realities ; realities that could only be com- 
 pleted in an infinite series of time and space. The difficulty is 
 not that they go beyond present perception and beyond our 
 knowledge. Caesar is not in present perception and we do 
 not know all that he did, yet in ' Caesar crossed the Rubicon ' 
 no one doubts that Caesar is a reality. Caesar is an indi- 
 vidual,*^ and his entire identity is present in his every act 
 and attribute. Man is no doubt a definite concept, but its 
 instances or manifestations have not prima facie individual 
 identity one with another. The centre of morphological 
 unity is in each separate human being, not in the idea of 
 the race as such. The concept, as we commonly think it, is 
 an abstract idea, and the reality that corresponds to it is a 
 series of individuals, which not merely is not yet actual as 
 a whole, but is not in our predication treated as an actual 
 whole. The reciprocal relations which bind together say the 
 English nation or the Roman Empire into a historical indi- 
 vidual may be present also more or less in the case of humanity, 
 but when we say 'Man is mortal ' this is not the light in 
 which we look at the Subject ; we are speaking of individual 
 men whom we designate by help of the concept man, not 
 of humanity or mankind as such, for which it might be main- 
 tained that morphological unity is possible. No doubt 
 however, if we push the matter home, even the predicate 
 mortality is affirmed of all individual men in virtue of a oneness 
 of nature running through them all ; and therefore we must, 
 as I have said, take the individual unity to be a matter of 
 degree, and to be wholly absent in no content that can be 
 presented to thought as characterising a subject of judgment. 
 When, in view of cases like these, we qualify the principle 
 
 * See note ^ p. 131. 
 
Chap. Ill] Individuality and Reality 139 
 
 laid down above that in every judgment the subject is taken 
 as real, we must do so by the emendation, ' The subject is 
 taken as possessed of that kind of reality of which it is capable, 
 subject to any alteration which the predicated content may 
 declare in such reality '. The first part of this sentence pro- 
 vides for judgments introduced by abstract ideas and not re- 
 ferred toactualindividuals, thesecond for all kinds of judgments 
 which formally affect, reality and which are alleged ^ as proofs 
 that content and reality cannot depend upon one another. 
 First among these come the Negative Judgment which sets 
 up an aspect of Reality in order to demolish it, and then all 
 such peculiar cases as ' The chimera is a fiction ', ' Nothing 
 is here ', ' A wise knave is a contradiction in terms '. 
 
 The view to which I have just alluded might raise an 
 objection at this point, which I will only mention in this 
 place, as the real answer to it, if any, can only be found 
 in the whole conception of the judgment which we have 
 adopted. * Whether an idea stands for a reality or not 
 does not depend on its content, but on that content being 
 recognised as somehow and at some distance or other belonging 
 to the world continuous in quality with the object of present 
 perception — i.e. to the actual world'. My answer to this 
 would be that I have accepted this identification in quality 
 as the abstract logical or rather as the psychological condition 
 of all judgment ; but that this identification is empty apart 
 from the specific kind and degree of reality assumed or alleged, 
 and this, as it appears to me, is a matter of content and of 
 content alone. 
 
 The Hypothetical Necessary or Relative aspect of judgment 
 is a consequence of the characterisation of the subject by 
 any determinate ideal content. It is the universal connection 
 of attributes within systems, as opposed to the morphological 
 unity of individual systems upon which that connection 
 rests. This aspect is undoubtedly perceptible from the 
 moment that the immediate subject is made explicit by help 
 of ideas, but as long as there is a gulf between the ideal content 
 and the latent reality which it designates — the ' this ' — the 
 necessary aspect of the judgment is absolutely dissociated 
 * Bradley's Principles of Logic, p. 14. 
 
140 Quantity and Proportion [BookI 
 
 from its categorical aspect, and the divergence almost amounts 
 to a duality of the judgment. In some cases indeed the 
 contents employed to designate the subject will have only 
 a partial connection with the predicate, as in ' This flower 
 is a rose '} Such a judgment has been called a double appella- 
 tive judgment. But I incline to think that affirmation of 
 this type is always on the road to necessity ; ' flower ' does 
 not indeed tie down the predicate to ' rose ', but the thread 
 of botanical classification runs through both. If it were not 
 a flower it could not be a rose. So the two designations are 
 undoubtedly chosen with reference to one another, and the 
 true duality of the judgment is not in christening the rose 
 twice over as rose and as flower, but in the ambiguity between 
 ' This is a rose ' and ' This, if (or ' in as far as ') it is a flower 
 at all, is a rose ', which might well be said of the Tudor rose 
 as it appears in some decorative designs. 
 
 The judgment whose subject is designated by a proper 
 name is at first sight devoid of necessity. For in it deter- 
 minateness of content is sacrificed to the indication of actual 
 continued individuality, and therefore the relation of neces- 
 sity or hypothesis, which depends on determinateness of 
 content, is not easily traceable. Yet a name is always capable 
 of acquiring a definite content, which at once brings such 
 a relation into prominence. The indignant denial, ' Gladstone 
 never said that,' ' Socrates never gave immoral advice,' is 
 obviously hovering between the sense of ' A. B. did not go 
 to town to-day ' and that of ' An honest man cannot say 
 what is certain to mislead', that is to say between the assertion 
 of fact and that of necessity. And again, if, as explained 
 in the last paragraph, the content which characterises the 
 subject has not the nature of a complete or individual whole, 
 then its reality must be taken as that of which alone it is 
 capable, viz. indefinite presentation in the series of space 
 and time ; and this amounts to so little (for the presentation 
 may be as rare as is consistent with occurring at all) that the 
 element of necessity or relativity dominates the element 
 of unity or actuality, and the judgment appears to have 
 as its essential content a necessary sequence or connection 
 ^ Cp. Sigwart, vol. i, p. 69. E, Trans., I. 57. 
 
Chap. Ill] Necessity in Judgment 141 
 
 about the presence of which in reality little or nothing is 
 affirmed. Such a judgment, and every judgment in as far as 
 it can be thus regarded, is hypothetical, that it to say it runs 
 wholly or partly along a line which may be formulated as 
 ' If fl is (or in as far as a is), then b is (or so far b is '). 
 
 On the other hand, even those perceptive or historical judg- 
 ments, including ordinary assertions about people or places 
 called by proper names, which betray in their content no 
 tendency to enter a groove, i. e. to exhibit a universal con- 
 nection of attributes, nevertheless must be held as bound by 
 this ideal, which is involved in the employment of contents 
 which have a meaning, and therefore can acquire a determinate 
 meaning. If then, as in such instances we may assume to 
 be the rule, the contents actually employed in judging embody 
 no principle, but merely exhibit irrelevant differences as 
 coexistent in a concrete subject, such judgments, even when 
 true in their first meaning as mere statements of fact, are yet 
 fundamentally false. That is to say, they are true in their 
 categorical aspect but false in their hypothetical or relative 
 aspect, from which, being definite judgments, they cannot 
 escape. They do not express an a, upon which, within some 
 real system, the content of predication follows as b. But it 
 is important to remember that we are dealing from beginning 
 to end with aspects and not with total differences. I believe 
 that a misapprehension on this head has of late years given 
 rise to an erroneous conception regarding the tendency and 
 goal of knowledge. 
 
 vii. It is a great thing to have raised the notions of Logic Know- 
 to a level with the ideas of exact science. This has been done |®^.f® ^^ 
 by Mill and subsequent writers,^ and the work had become solute 
 necessary, though the views to which it led were not in prin- ^^ ^ 
 ciple new. The essence of judgment was by them declared to 
 lie in the coexistence and rational connection of attributes, and 
 the ideal of science to consist in the knowledge of the fewest 
 assumptions, from which, if given, the whole course of the 
 
 ^ Mill's Logic and Lotze's earlier Logik seem to have appeared in the 
 same year (1843). Lotze, I presume, was largely influenced by Herbart 
 on the point in question. I have in my mind also Sigwart, Wundt (whose 
 doctrine of ' Gegenstandsbegriff ' does not, however, seem to me perfectly 
 clear), and Bradley. 
 
142 Quantity and Proportion [Booki 
 
 world might be deductively derived. As a consequence of these 
 ideas, the universal judgment was, in part by Mill himself and 
 more distinctly by later writers, identified with the hypothetical 
 or abstract afifirmation of necessary connections ; and, further, 
 by identifying this type of judgment with the extreme case of 
 supposition for the sake of argument, the universal judgment as 
 such was denuded of all afifirmation having real content. It was 
 still treated as affirmed of Reality, but was held to be related 
 thereto as a known consequent to an unknown antecedent. 
 It was pointed out that in supposal for the sake of argument 
 no element of the content supposed or of its consequence is 
 affirmed either to be actual or even to be possible, and that 
 nothing more is alleged as fact, in judgment based on supposi- 
 tion, than that Reality, which itself does not appear within 
 the judgment, is such as under the supposed conditions to 
 exhibit the inferred consequent. Truth, it might therefore 
 be concluded, may be taken to illustrate, but it cannot be taken 
 to define, reality. The strong implication of actuality which 
 attaches to the content of many ordinary universal judgments 
 was dismissed as explicable on grounds of habit and confusion. 
 Thus the categorical judgment, in the sense of a judgment 
 which asserts any specific content to be actual, was primarily 
 confined within the limits of affirmation about individuals in 
 space and time, although in disjunctive judgment, and in 
 judgments, if any, dealing with existences beyond time and 
 space, a categorical character was admitted to reassert itself. 
 In contrast with the conception of logical progress and 
 with the ideal of knowledge which I have just described, it 
 appears to me that a somewhat modified form of the views 
 in question might yield less one-sided conclusions. I should 
 prefer to regard the normal and central evolution of judgment 
 as categorical * from beginning to end, and as gaining, not 
 
 * The truth of this matter cannot really be grasped except by care- 
 fully considering such a catena of judgments as forms the basis of 
 Mr. .Bradley's Principles of Logic or of the present work. I do think 
 it remains firm that the intention of the Judgment is categorical 
 throughout. It desires to say something true about something real. 
 But the point to master is its twofold nature, in which fact and necessity 
 are in conflict, so that in all its phases there is an unsatisfied implication, 
 and it never expresses either a self-contained fact, or a really perfect 
 
Chap. Ill] Univevsal = Hypothetical ? 143 
 
 losing, in this characteristic as it passes from perception and 
 history to the more complete forms of science. The implica- 
 tion of real existence which attaches to the content of ordinary 
 generic and universal judgments seems to me to be of the 
 same kind as the implication of existence — for it is no more 
 — which accompanies the demonstrative ' this ', ' here ', or 
 ' now ', or its expansion by a significant idea, or a proper 
 name, or the significant name of any actual, even if not in 
 the full sense individual, totality, such as the English nation, 
 or the Natural Order Rosaceae. 
 
 The main function of judgment would then be identified 
 with the exhibition of individual totalities at once in their 
 absoluteness and in their relativity. We should thus not 
 wholly subordinate classification, type, and individuality to 
 the claims of explanatory theory, but endeavour to repre- 
 sent the two as complementary and indispensable aspects of 
 knowledge. Abstract and ideal judgments like those which 
 embody the necessary connections of geometry we should 
 rank as an indispensable divergence, but still as a diver- 
 gence, from the natural track and tendency of reason, and 
 as attaining their truth most fully when, returning towards 
 that track, they are taken up into the precise determination 
 of typical structure in space, or even of individual realities. 
 We should refuse, in spite of identity in linguistic expression, 
 to take supposition for the sake of argument as the type of 
 universal judgment, and should point out that as supposition 
 passes from selection within reality into free imagination it 
 becomes detached from the real ground of all relations, and 
 ceases even to exhibit a necessary relativity. 
 
 It is in accordance with these views that I have treated 
 measurement as involving both the revelation of Individuality* 
 (morphological unity) through characteristic ratio, which is the 
 same thing as proportion, and the exhibition of relativity by 
 the reference of the unit to something outside the individual. I 
 now proceed to speak of kindred judgments, which present the 
 essential aspects of measurement in one-sided modifications. 
 
 connection. And so in the end undoubtedly ' Judgments are con- 
 ditional in this sense, that what they affirm is incomplete '. Bradley, 
 Appearance and Reality, ed. 2, 361. * Cp. note ^, p. 131, above. 
 
CHAPTER IV 
 
 Measurement {continued) — Abstract Quantity 
 
 One-sided 2. INDIVIDUALITY as revealed in measurement may be 
 forms of simple or complex, and, if complex, it must involve a variety 
 ment. oi simple factors. In a simple individuality, or the simple 
 factor of a complex individuality, the qualitative distinct- 
 ness of the parts is at a minimum ; for any exceptional 
 qualitative difference in any part would challenge measure- 
 ment and constitute a complication within the unity. When 
 an individual is thus taken in its simplicity, in a single aspect, 
 and yet considered as being a whole complete in itself, it is 
 treated as a whole of quantity ; that is to say, such a content 
 as is exhibited in the predication of the comparative judg- 
 ment, but taken as standing in the place of the individual 
 Subject, now that the conception of individuality is attained. 
 Enumera- i. In such instances we find the simple quantitative whole 
 tion. which is thought of as constituted by absolutely homo- 
 geneous parts — an idea which we have seen to be never 
 strictly true, for without some distinctness of quality the 
 parts would cease to be. Such a whole differs from the 
 normal individual by the lack of anything that can be called 
 dominant, essential, or characteristic within the content 
 itself. There is, for instance, no need to consider its unity 
 in the light of a secondary or aesthetic quality. The unity 
 is already that of a continuous quality, and in the attempt 
 to define it, it lapses almost wholly into relativity, for the 
 determination of the whole depends on the equation of the 
 parts, in an unending series, with other and independent 
 standards. Thus the purely quantitative whole is character- 
 ised by being capable of construction by ideal repetition 
 of a unit or fixed part ; and such ideal repetition is enumeration. 
 Enumeration may seem prior to measurement or identical 
 with it ; in measuring we enumerate units, and whenever we 
 enumerate units we measure some totality. When we count 
 
Chap. IV] Enumeration and Measurement 145 
 
 the carriages in a railway train we are measuring the train, 
 when we count the sheep in a flock we are measuring the 
 flock, just as when we count the feet and inches in the length 
 of a room we are measuring the room. But usage, as we feel 
 at once, does not bear us out in speaking of the two former 
 instances as measurements, and the reason is plain. In 
 measurement we start from a whole which we characterise 
 by its differences ; in enumeration we start from a distinct 
 unit, out of which we desire to construct a collective or 
 aggregate whole — a sum total. The whole in enumeration, 
 which is a predicate, is a weakened form of the individual 
 whole in measurement, which is a subject ; and the unit in 
 enumeration, which is a subject (generally distinguished by 
 a natural individuality), is a strengthened form of the 
 distinct unit, ideal part, or constant difference, which forms 
 the predicate in measurement. 
 
 Enumeration is therefore in one sense posterior to measure- 
 ment, because it presupposes, as a naturally distinct unit, 
 the ' thing ', the idea of which can only be furnished by a sense 
 of proportion or perception of limit ; but, on the other hand, 
 enumeration is an instrument of precise measurement, which 
 involves the notion of a scale of degrees or aggregate of 
 homogeneous parts. The two processes are constantly con- 
 current, and only differ in the respective values of the parts 
 and wholes with which they deal. It would be futile to dis- 
 tinguish them from one another, but for the consequences 
 which result from the possibility, first exemplified in abstract 
 enumeration, of systematising the synthesis of parts without 
 relation to a whole. The whole of enumeration is depressed 
 into a mere aggregate, or not even a definite aggregate, and 
 therefore the part into a mere unit, or even into the mere 
 place in which a unit might be. The process with all its 
 corollaries, including the three unreal infinities of Number, 
 Time, and Space, must be regarded as belonging to a form 
 of the judgment-function in which the relation of whole 
 and part is denuded of all structural variety, and therefore 
 the aggregate or sum which is the outcome of that relation 
 lacks predominant unity. This principle is expressed in 
 the saying that in a numerical system the sum of units is 
 
 1337 L 
 
146 Abstract Quantity [BookI 
 
 the same whatever may be the order in which they are 
 counted, i. e. any part {qua part of a total formed by enumera- 
 tion) can be interchanged with any other part without modi- 
 fying the whole in which they are parts. 
 
 Corol- I proceed to state and illustrate some corollaries which 
 
 laries. follow from the above idea of enumeration. 
 
 Simple a. Simple counting always consists of a series of singular 
 
 counting, j^dg^g^is^ ^^^ is {^ f^is respect on a level with simple measure- 
 ment. 
 
 However abbreviated or abstract each step in counting 
 may be, it can always be expanded into a singular judg- 
 ment which records its own position in a coherent series. 
 In counting the birds in a covey, or the stitches in a bit of 
 needle-work, we often merely repeat aloud the words ' one ', 
 ' two ', * three ', and the real nature of the judgment which 
 accompanies them is open to question. In fact, each of 
 these numerals in such a case implies a separate singular 
 judgment, though extreme abbreviation tends to conceal its 
 structure. The essence of counting is in just such a pro- 
 gressive distinction as is conveyed by ' this ', ' that ', and 
 * the other ' ; ' alter ' and erepos have almost the value of 
 numerals. The exclamation ' One ! ' when we are beginning 
 to count any set of objects means ' This unit is a part in the 
 whole which interests me ', e. g. ' One — ^two — three — eight 
 birds in that covey '. The bird is the naturally distinct unit 
 by which in so simple a case we proceed as a matter of course, 
 and the covey is the total up to which we wish to count. 
 If birds get up belonging to another lot, we shall probably 
 desire to keep them distinct, and so count them separately, 
 beginning ' One ', ' two ', &c., over again. It is plain in this 
 or any similar instance that we do not count right on as long 
 as units can be found, but that every step of the enumeration 
 is made with reference to a limit as well as to a unit. This 
 limit, however disguised by our caprices and interests, is 
 simply the common or continuous nature of the unit in so 
 far as it interests us, and in every enumerative judgment 
 without exception the elements of separate unit and common 
 nature may be traced. The unit need not be externally 
 distinct or physically separable ; and the common nature, 
 
Chap. IV] What do we count ? 147 
 
 instead of being hard to trace, may all but obliterate the 
 differences that exist within it. But it is the nature of the 
 unit that furnishes both rule and limit of enumeration, which 
 is a process unmeaning without a limit and impossible without 
 a rule. If we are told to count even all the ' things ' in a 
 room, we shall find ourselves obliged to ask what is to be 
 reckoned as a ' thing '. Is a bookcase with 500 volumes 
 in it one thing or 500, or 501 ? ' In a room ', however, is a 
 kind of limit, and assigns a totality to be constructed by 
 synthesis ; but if we are asked simply to count, we should 
 reject the request as pure nonsense, because it assigns no 
 totality to be constructed by counting. 
 
 What, then, is the meaning of counting ' One ' ! ' Two ' ! 
 ' Three ' ! in starting a race, or of — 
 
 ' And still stood all who saw them fall 
 While men might count a score ' ? 
 
 In the latter case, the idea is that of counting the names of 
 the numbers up to a fixed limit at a rate determined by 
 habit or by the time which is required to pronounce the 
 words distinctly. In the former case the object is perhaps 
 not merely to let time elapse, but to set attention in a certain 
 rhythm, so that the tendency of rhythmical anticipation 
 may assist in seeing or hearing the starting signal at the 
 moment it is given. For this purpose the periods should be 
 exactly equal, and in fact at the Oxford boat-races every 
 boat has some one beside it who counts aloud the last few 
 seconds before the gun fires. Of course, finally, the names 
 of numerals may be repeated, as any words may, without 
 a meaning. But to do this is not to count. 
 
 Thus even simple counting always involves the elements 
 of the judgment — of an identity exhibited in differences 
 and affirmed of reality ; which elements present themselves 
 in the shape of a distinct unit within a continuous nature, 
 its relation to which nature is indicated by number. And 
 that the simple enumerative judgment is always singular 
 follows from the nature of the unit, which is theoretically 
 nothing more than the content to which we ascribe dis- 
 tinctness pro hac vice ; in other words, the unit is the difference 
 or part that is taken as distinct by one act of judgment, 
 
 L2 
 
148 Abstract Quantity [Booki 
 
 and it may be said that what we count '^ in enumeration are 
 primarily the acts of judgment, as acts of distinction and 
 relation within a certain continuous quality. 
 
 Does it follow from this view that Number arises essentially 
 out of the sense of time or succession ? I answer, Not ' essen- 
 tially '. The connection between number and succession is 
 a psychological and not a logical question. If it is impossible 
 for two related acts of judgment to be simultaneous, as we are 
 naturally inclined to suppose that it is, then two enumerative 
 judgments must always be successive, and in this sense 
 enumeration may depend upon succession. Nor do I think that 
 this connection is necessarily disproved by such observations as 
 that perception can take note of six balls at once being 
 dropped into a box. Such a perceptive judgment, in my 
 opinion, is probably one, and applies the result of previous 
 counting, as an attribute resting on experience, to the 
 perceived content, just as we can judge the number of 
 pips on a card from the mere form of the pattern which 
 they make. So if we count by twos, fours, or more, 
 I think that this is complex counting, the unit being 
 the mass of two or four, known to be such by previous 
 experience ^. A logical order among the units, i. e. an 
 order in which the apprehension of each unit has a place 
 in the series conditioned by the separate apprehension of 
 other units, is of the essence of enumeration, although a 
 material order among them, i. e. such an order that a unit 
 changes its value by changing its place in the series, is in 
 contradiction with the essence of enumeration. Unless 
 there is what I have called a logical order, we have no security 
 that the unit as such is appiehended at all, and what we 
 take for enumeration may really be an inference like that 
 which detects from the pitch of a note the number of vibrations 
 
 * This view has been treated as an assertion that what we count is 
 our own counting, which has no meaning. I understand it as holding 
 number to be the general schema of the relation of parts in any whole, 
 taken as homogeneous so far as the distinctness of parts permits. In 
 counting, as I understand, we apply this general schema to a given 
 whole, and are consequently put in possession, with regard to that whole, 
 of all the relations which the schema involves. Cp. p. 156, below. 
 
 * See the Author's Knowledge and Reality, p. 92. 
 
Chap. IV] Number and Magnitude 149 
 
 per second which generate it. But whether a logical order 
 of succession can only be realised in temporally successive 
 acts of apprehension, is a purely psychological question ; the 
 more so, that, as we have seen, succession and time do not 
 exclude unity of judgment, and the acts of judgment which 
 constitute an enumeration might even, like an inference, 
 be brought under the head of a single continued state of 
 consciousness. In any case, succession in time would be 
 a mere psychical condition of number, following from the 
 unity of the intelligence as forbidding (if it does forbid) two 
 judgments to be made at once. There is no sort of ground 
 for connecting enumeration with the apprehension of equal 
 parts in time, unless the equality of such parts be the material 
 purpose of the apprehension in hand. 
 
 13. It follows from the nature of enumeration that the Discrete 
 distinction hetiveen discrete and continuous magnitude and tipuou" 
 the opposition of number as discrete to space, time, and other 
 kinds of quantity as continuous, rests on a confusion. Number 
 as mere names or mere sounds may be discrete, i.e. dis- 
 connected, but then it has nothing to do with magnitude, 
 but is a set of mere words destitute of meaning. On the other 
 hand, number considered as the vehicle of magnitude or 
 quantity is both discrete and continuous ; and the same is 
 true of all quantity, as we saw in examining the comparative 
 judgment, and it is the essence of quantity to be so. The 
 distinctness of natural units such as reciprocally exclusive 
 material things does not make any difference of principle. 
 They, like all units, are numbered in virtue of a continuous 
 quality or identity which pervades them, and every unit, 
 though it may only be suggested by a momentary purpose, 
 is, like them, a distinguishable part, within a whole or aggregate 
 consisting of such parts. The books on a shelf are not merely 
 discrete, and the inches in a yard or the units of weight in a 
 gravitating body are not merely continuous ; in every case 
 the unit is a distinct or discrete part, and the sum is a self- 
 identical or continuous whole. It is nonsense to speak of 
 counting without saying what is to be counted ; and in 
 specifying what is to be counted we specify at once the nature 
 of the continuity and the rule of the discretion. 
 
150 Abstract Quantity [Booki 
 
 Juilg- ii. Judgments affiliated to the Enumerative Judgment. 
 
 affiliated ^^^ Enumerative Judgment is the root of all quanti- 
 to Enu- tative determination ; and, as we have seen, all the matter 
 Judg- of knowledge above the stage of pure quality is either in 
 ment. itself or in its conditions accessible to quantitative deter- 
 mination. But the judgment in question also contains, that 
 is to say, is, though in a depressed form, the universal essence 
 of judgment in the principle of identity and difference ; and 
 it is possible for this to be revived by one kind of abstraction 
 into a different relation from that of unit and sum, as it is 
 for it to be further specialised, by an opposite abstraction, 
 into an idealised form of the latter relation. But before 
 indicating the genesis of other types of judgment out of 
 enumeration, we must glance at those which it necessarily 
 generates, and which must be regarded as species of itself. 
 These are, a. the Plural or Particular, and /3. the Collective 
 judgment. 
 The a. The Plural Judgment, or the Particular of traditional 
 
 Particu°'^ Logic, differs in no essential respect from the singular. It 
 lar Judg- is not however accurately described as a mere aggregate 
 of singular judgments, and indeed this description does not 
 explain itself, for is such an aggregate several judgments or 
 only one ? I cannot doubt that the plural judgment is a single 
 act of thought, which determines a certain whole or aggre- 
 gate, given at the moment, though, it may be, in process of 
 modification, by an attribute or condition such as two, three, 
 or some other number which expresses the reciprocal relations 
 of its homogeneous parts. Thus the plural judgment is not 
 an aggregate of judgments, but a judgment about an aggre- 
 gate. Therefore the number is to be regarded as a predicated 
 content or determining condition, attributed to a whole 
 consisting of the units which have been counted up to the 
 point at which the plural judgment is taken. That the 
 element of continuity, or designation of the whole whose 
 parts are to he counted, must quarrel with a determination 
 by any number short of this whole,^ and demand a continuance 
 of the enumerative process, is only a case of what happens 
 in every judgment of perception. Such judgments, as we 
 * See Knowledge and Reality, p. 65, and above, Introduction, pp. 5 1 ff. 
 
 ment. 
 
Chap. IV] Pluval implies Ratio 151 
 
 have seen, never embody ' pure cases ', i. e. they never fit 
 precisely into a groove of necessity, that is, a sequence of 
 reason and consequent. There is always something relevant 
 omitted, or something irrelevant retained. 
 
 Thus the particular judgment from the very first implies a 
 ratio ; and the implication may be so strong as to take the 
 judgment out of the category of particular judgments and 
 place it in that of collective judgments, e.g. ' 335 members of 
 the House of Commons are Liberals.' As every one knows 
 that the House of Commons contains altogether 670 members, 
 this is just the same as to say ' half of the House of Commons 
 are Liberals '. It depends for its meaning on a completed 
 enumeration, and therefore is essentially a collective judgment. 
 It may even be regarded as an instance of simple measurement, 
 i. e. of ratio treated as pure historical fact, in as far as its purpose 
 is to measure the voting power of the Liberals against that of 
 other sections of the House. The Liberals and the whole House 
 are equated in respect of numerical strength ; the whole House 
 minus half of the whole House = the Liberals. In short, as 
 we have seen, the completed judgment of Enumeration passes 
 into Measurement, though the idea of Measurement is prior 
 to the act of Enumeration. If on the contrary we say that 
 ' Two Cambridge men are coming down to lecture ', the 
 number two is prima facie non-significant ; the judgment tells 
 us nothing of the ratio borne by two to the whole number of 
 Cambridge men, nor even to the whole number of local lec- 
 turers. Nevertheless if we think of it, we shall see that either 
 it was wholly superfluous to mention the number, or else some 
 context or latent allusion must imply a ratio. Number has 
 significance only by comparison with number. 
 
 The Plural Judgment is equivalent to the Particular of 
 traditional logic in the form ' Some men are mortal '. There 
 is no essential difference between ' some men are mortal ' and 
 ' four men are mortal ' ; the two assertions, if interpreted 
 literally, belong to the same logical class. It will appear 
 however below that this literal interpretation does not render 
 the true meaning of the old ' Particular Judgment '} 
 
 But we must distinguish from the above a form which has 
 ^ See on ' Modal Conversion ', chap, vii, below. 
 
152 
 
 Abstract Quantity 
 
 [Book I 
 
 The Col- 
 lective 
 Judg- 
 ment. 
 
 been employed in quasi-numerical arguments, viz. the form 
 ' Most men are mortal ', or ' The majority of the House of 
 Commons that has just been elected is Conservative '. These 
 judgments are not merely particular even in immediate 
 appearance. They present on their very surface the relation 
 to a collective judgment which we saw to be at least latent 
 in every particular affirmation. ' Most ' or ' The majority ' 
 means more than half ; and when we speak of half or a quarter 
 or any ratio we assume a completed enumeration of the whole. 
 We must therefore now pass to the Collective Judgment or 
 judgment of completed Enumeration. 
 
 /3. The Collective Judgment has of late been rightly dis- 
 tinguished from the Generic and from the Hypothetical Judgr 
 ments, which correspond to the real meaning of the Universal 
 Judgment known to traditional logic. It has been justly 
 pointed out that the ' All ' of mere extension or numerical 
 totality does not really express what is intended by such an 
 allegation as ' All men are mortal ', or ' All triangles have their 
 three angles equal to two right angles '. In such cases com- 
 plete Enumeration is inconceivable, and something quite 
 different, viz. the universal connection of attributes which are 
 not results of enumeration (for number is also an attribute) is 
 really the matter affirmed. So far all is clear, and Logic has 
 greatly gained by the distinction. 
 
 But when we come to erect a difference of kind, and to treat 
 the collective judgment as purely on a level with the singular 
 or particular judgment, and as in fact a mere aggregate of 
 singular judgments, and as thus separated by an impassable 
 gulf from the universal judgment ; and when we further 
 maintain that enumeration cannot warrant its own complete- 
 ness, then we fall into difficulty and confusion. Even the 
 Plural Judgment, as we saw, is not a mere aggregate of 
 singulars. 
 
 The Collective Judgment I understand to be a judgment 
 made about a definite group or limited class of individuals, 
 which individuals are taken to have been exhaustively 
 enumerated, or to be capable of exhaustive enumeration. It 
 is not necessary that the individuals should all be together in 
 space or time ; it is not necessary that they should all exist or 
 
Chap. IV] Meaning of " AW 153 
 
 have existed with any specific degree of reahty ; but it is 
 necessary that every one of them should be brought before the 
 mind, or should be capable of being brought before the mind, 
 in a distinct and separate enumerative judgment. Such 
 judgments are ' All the books on that shelf are German ', 
 ' Every horse that I have bought in the last three years has 
 gone lame ', ' All the kings of England since the Conquest but 
 three have died natural deaths '. 
 
 When it is said that such judgments as these are on a level 
 with the singular or the particular judgment, I take it that 
 we must exclude from the meaning of singular or particular 
 judgment all dependence, whether latent or explicit, on com- 
 pleted enumeration ; otherwise our account of the collective 
 judgment becomes circular. But if so, then we have the 
 ' allness ' of the collective judgment staring us in the face as 
 a distinction between it and the particular. And this dis- 
 tinction becomes an absolute severance if we are to insist that 
 the process of enumeration, a process which consists in singular 
 and particular judgments, cannot furnish the warrant of its 
 own completeness. 
 
 I have maintained elsewhere,^ and it follows from my whole 
 conception of the judgment, that enumeration cannot be made 
 intelligible on such a view. It is impossible for enumeration 
 to go on apart from the discriminative control exercised by the 
 pervading nature of the totality under construction upon the 
 successive apprehension of the units. It is this control which 
 takes the form of an inchoate perception of ratio as the count- 
 ing advances, and of the warrant of exhaustiveness when it is 
 completed. Apart from such an influence of the whole there 
 can be no purpose in enumeration. No doubt therefore com- 
 plete enumeration is in one sense on a level with the singular 
 and particular judgments, because they present though in an 
 imperfect form (as we have excluded the case of definite ratios 
 such as ' Half A are B ') the same relation to totality which 
 the collective judgment completes. 
 
 But for the same reason it is impossible to justify an absolute 
 separation between the collective and the generic or universal 
 judgment. The collective judgment, we may say, must 
 * Knowledge and Reality, p. jy. 
 
154 Abstract Quantity [Booki 
 
 emanate from an enumeration of actual individuals, or at least 
 of individuals actually brought before the mind, one by one. 
 But how can we carry a genetic distinction like this into the 
 interpretation of judgments whose actual content is precisely 
 the same ? It is the commonest thing in the world for a judg- 
 ment to be taken as exhausting a group or set of distinct 
 individuals, without resting in any way upon direct enumera- 
 tion ; in other words, a judgment that might be obtained by 
 enumeration constantly is obtained in some other way. The 
 fact is, that when we have gone beyond sets of individuals 
 present to perception or within the power of the mind to 
 represent at once as distinct individuals (and it would be im- 
 possible finally to limit the collective judgment to such sets of 
 individuals), we have entered on a process which is plainly and 
 obviously mediate and hypothetical, and the fact that many 
 judgments thus mediated are taken to refer to a finite group 
 of individuals is a mere instance of our general rule that every 
 content in judgment is taken to have the reality of which it is 
 capable. 
 
 Is there then no difference between a collective judgment 
 and a true universal ? Certainly there is a difference, and 
 it is illustrated though not constituted by the connection of 
 the former with complete enumeration. It is simply this, that 
 a collective judgment deals with a content which can be 
 presented to thought as possessing the character of an aggre- 
 gate of exclusive units, or finite whole of enumeration. This 
 point of view would involve identification of the collective 
 judgment with the aggregate of singulars only if all enumera- 
 tion were simple enumeration. But a numerical whole may be 
 obtained by mediate enumeration, and it is to a whole so 
 obtained that the content of many collective judgments is 
 equivalent. It is true that a collective judgment is not 
 a genuine universal, but it is not true that such a judgment 
 must be equivalent to a mere aggregate of singulars. This 
 conception is, in the first place, irreconcilable with the unity 
 of the judgment ; ^ and, in the second place, is not warranted 
 
 ^ No doubt there is a difficulty here. ' George and John have gone 
 to school,' ' The two boys have gone to school.' Does the former 
 sentence convey two judgments and the latter only one ? The latter 
 
Chap. IV] Unity of an Aggregate 155 
 
 by the plain meaning of the propositions in question. It is 
 impossible to characterise a number of individuals by a common 
 name as the subject of a judgment without implying a signifi- 
 cance in the characterisation. Even if the predication is true 
 of the different individuals for different reasons, the common 
 interest of the judgment must give it unity of purport. An 
 arbitrary limitation either of number or of time tends, no 
 doubt, to interfere with this significance, and to force an 
 extensional meaning upon the judgment ; but, as we know, 
 the purest extensional meaning is only a minimum of inten- 
 sional meaning. And there are collective judgments which 
 could not possibly be taken as mere aggregates of singulars. 
 Such are reflective historical judgments. ' All States of the 
 North American Union are prohibited from interfering with 
 the tenure of property.' I need not know this by simple 
 enumeration ; I may know it mediately, as a provision of the 
 Constitution of the United States. I need not even be actually 
 able to enumerate the States which are included in the Union. 
 But I know that they are numerable, because I know that they 
 are an actual limited group, and so I judge it as a historical 
 fact, though I may know it also as rooted in the nature and 
 tendencies of the Union. 
 
 The fact is, that superficial as is the view which makes 
 ' allness ' the adequate expression of logical necessity, it is 
 if possible, more superficial to deny their connection. From 
 the first use of the characterising idea, necessity makes itself 
 felt ; and ' allness ', or the aspect of a finite totality as an 
 aggregate of exclusive units, is never without a warrant and 
 significance however arbitrarily the totality may be taken. 
 It is by the certainty of complete enumeration that counting 
 becomes, as was said above, the organon of precise measure- 
 ment. For instance, the series of enumerative judgments, 
 ' One, two, three, four, five, six ounces are in the scale balancing 
 this packet,' is convertible, in virtue of their exhaustiveness, 
 into the judgment of measurement, ' This packet weighs 6 oz.' 
 
 We saw that the act of counting tends to assume indepen- 
 
 only one, certainly ; the former conveys two at first sight ; but if we 
 bear in mind our account of the Judgment as an act in time, we shall 
 see that these two may readily pass into one. See p. 79, supra. 
 
156 Abstract Quantity [BookI 
 
 dence, as if it could have a meaning apart from any continuous 
 nature in the units, i, e. in short, apart from an identity 
 presented as a totality. This is not merely owing to the 
 customary abbreviation of the enumerative judgment, as when 
 we seem to count by saying ' One, two, three,' &c. ; rather 
 such an abbreviation is made possible by the apparently 
 independent reality of number. This appearance of reality 
 depends on the fact that the numerical series does furnish 
 a generalised scheme of the relation of whole and part when 
 envisaged in the form of total and units.**^ Such a generalised 
 scheme, though meaningless except as applied to a positive 
 content of thought, contains nevertheless definite and necessary 
 relations which are imposed by it on any content to which 
 it is applied ; and the presupposition that it is taken as applied 
 to an adequate content fades into forgetfulness that it need be 
 applied to a content at all. But need it ? We may surely 
 investigate the numerical series for its own sake. When we 
 say that twice 50 is 100, need we mean that twice 50 of some 
 particular kind of thing are 100 of it ? We may surely mean 
 that in the numerical series 100 is separated from 50 by the 
 same number of places as 50 from o, which relation involves 
 a variety of consequences, all true of the numerical series 
 as such. No doubt this is so, but it will be observed that 
 we have to appeal to the idea of places in the series, and 
 these places are the abstractions of enumerative judgments 
 and imply relation to a content. Such places contain in 
 themselves no reason for stopping at any point of enume- 
 ration, are applicable hypothetically to every content, but 
 can yield, in their abstraction, no conclusion about any. 
 It is a well-known fallacy to obtain a concrete estimate by 
 multiplying an amount by the number of times its cause as 
 given has to be repeated. Hardly any concrete quantity is 
 unaffected in the ratio of its increase by a great addition to 
 its absolute magnitude. To say that the stock or trading 
 capital of England is worth so many hundred millions sterling 
 is a graphic expression for the fact that its amount is a million 
 times as great as an amount worth so many hundred pounds. 
 But in the economical sense of ' worth ' the conclusion is 
 * Cp. p. 148, above. 
 
Chap. IV] Abstract Number 157 
 
 nonsense. A thing is only worth what it will fetch, and who 
 is going to buy the whole stock of England if thrown on the 
 market at once, at the rate which is commanded by the 
 amounts of stock which change hands in the common way of 
 trade ? 
 
 The numerical series is an ideal scheme of the relations 
 of units within totals, but is itself unreal apart from its 
 applications, not because it is ideal, but because it has in 
 itself no element of limit or totality ; i. e. its units make no 
 choice between belonging to one total and another, and so 
 naturally belong to an infinite series. 
 
 This aspect of the enumerative judgment — the system of 
 number — ^leads to the consideration of complex counting 
 and of numerical infinity. But before pursuing the enquiry 
 in this direction I pause to indicate a reversion or conver- 
 gence to which the simple enumerative judgment tends in its 
 other aspect. 
 
 y. Every concrete enumerative or collective judgment Enumera- 
 bears reference to an identity which controls its selection of coming 
 units and fixes the limit of its enumeration. This identity Generic, 
 is the pervading nature of the units. Now if this nature ^^^g^^^ 
 consists in the characteristic quality of an individual thing, Judg- 
 then it is possible that on the one hand it suggests no con- "^^*^t- 
 ceivable limit of enumeration, while on the other hand the 
 characteristic individuality claims completion in respect of 
 its positive connections of content. In such a case there is 
 no true whole of repetition concerned ; no whole, that is to 
 say, which in its nature draws nearer completion by every 
 repetition of an individual. The books in this room are 
 a true whole of repetition ; the human race, to our present 
 knowledge, is not. Thus a problem which is first attacked 
 by enumeration may transform itself unawares. Meeting 
 with a series of individuals in which we perceive some im- 
 portant attribute, we enumerate them as cases of it. But 
 soon their characteristic nature reacts on the function of 
 thought, and we find our successive judgments attempting 
 to grasp a connection of content and not to exhaust a sum 
 total of cases. Now as enumeration is on one side selective 
 analysis, we continue to give our judgments enumerative 
 
158 Abstract Quantity [Booki 
 
 form, and even couch them by anticipation in the shape of 
 exhaustive totality. Then we have what has been called 
 Induction by simple enumeration, with its results embodied 
 in the Judgment of Allness, which to avoid an un-English 
 expression I shall venture to speak of as the Exhaustive 
 Judgment, 
 
 The most varied opinions have prevailed as to the nature 
 and value of this process, obviously because it forms a tran- 
 sition between two distinct lines of thought, marking the 
 revival within mere enumeration of the sense of characteristic 
 individuality which belongs to the judgment of proportional 
 quality and the kindred judgments of individualising thought. 
 We meet, for instance, with the question whether the judg- 
 ment * All men are mortal ' claims to represent completed 
 enumeration or not. The answer is that its form and its 
 meaning are at variance ; in form it does make this claim 
 and in meaning it does not. Such a judgment indicates 
 that the spirit of analogy and of characteristic quality has 
 reawakened within the form of mere enumeration, and is 
 sweeping the line of evolution back towards judgments 
 which predicate individual and generic character. When 
 we come to speak of Induction as a phase of Inference we 
 shall see that there are good reasons for such an awakening. 
 At present we have only to note that the exhaustive judg- 
 ment ' All men are mortal ' is a transitional form between 
 a collective judgment on the one hand, and the generic 
 judgment * Man as such is mortal ', also couched in the form 
 * All men are mortal ', on the other hand ; and arises from an 
 incipient reaction of positive content upon ideal schematic 
 form in the process of making number, before an external 
 separation has been effected between the two elements. It 
 is idle to demand the perfection of complete enumeration 
 from the exhaustive judgment ; for this latter is a popular 
 and unstable form of thought, and must simply be recog- 
 nised as such. It is better to treat the collective judgment 
 as inevitably leading up to a connection of attributes and 
 as therefore having its ideal in the spirit of the exhaustive 
 judgment, than to interpret the exhaustive judgment ac- 
 cording to the letter, as having its ideal in the collective 
 
 1 
 
Chap. IV] A further meaning of ''All" 159 
 
 judgment. We shall have to recur to this subject when 
 we return to the central development of the judging function. 
 
 We have now to trace the further abstractions which have 
 their root in enumeration. 
 
 8. On the side of the relations between units and total as Judg- 
 such, abstraction being made from the positive nature of the Mediate 
 contents submitted to enumeration, the judgment of com- Counting, 
 pleted enumeration is an ideal or generaUsed scheme of all 
 possible constructions of such purely numerical totalities. 
 It starts from a measurement or collective judgment of 
 the tj^e ' All the books in this room amount together to 
 a thousand.' The further abstract development of such a 
 predication may be brought about by the most various 
 occasions, but it essentially consists in this, that the positive 
 concrete units of enumeration which stand as subject in a 
 judgment like the above are replaced by generalised rela- 
 tions of ideal units equated to a total which also becomes 
 ideal and generalised. This substitution reveals the fact 
 which alone makes it possible, viz. that in the numerical 
 scheme all units, being abstract, retain the same value in 
 every part of the series ; e. g. the units between 50 and 60 
 count for as many as and no more than those between 30 
 and 40 or between o and 10. Thus a series of units may 
 safely be named by the number of places which it occupies 
 counting from the zero of the whole numerical series, but it 
 is the same wherever and however often it recurs. It is on 
 this characteristic of number that the possibility of mediate 
 or complex counting and of equation, which is implied in 
 these processes, depends. If, for instance, we desire to re- 
 compose the sum of books in the room by equating it to 
 component sums or to factors, we do so by conducting a 
 number of enumerations separately from the beginning of 
 the numerical series, and then combining their totals according 
 to the rules of that series, which are known to us simply by 
 eicperience. Thus, if we count 700 English books, 200 German, 
 and 100 Italian, we find that these sums, considered merely 
 as numbers, are equal to the total 1000 obtained by direct 
 enumeration. ' Considered merely as nmnbers,' because the 
 rules of the numerical series cannot warrant us against any 
 
i6o Abstract Quantity [Booki 
 
 material influence of the actual individual things upon each 
 other. Some of them may cancel each other, or may produce 
 more by combination ; but this has nothing to do with the 
 properties of number, except for the fact that, when known, 
 it is capable of numerical expression. The component numbers 
 in the subject of a judgment like the above (These 700 English 
 volumes with these 200 German and those 100 Italian make 
 up 1000 volumes) correspond to the characterising ideas in an 
 affirmation like 'This execrable ruffian should be hung'. It 
 is hard to say if they are general conditions, or if they are 
 specifications of fact taken as true merely in the present 
 instance. 
 
 But it is clear that in such enumerations we are on the 
 brink of mediate counting, that is to say of the abstract 
 equation 700 + 200 + 100 = 1000, just as in the individual 
 judgment mentioned above we were on the brink of the 
 generalisation ' Every execrable ruffian ought to be hung '. 
 ' Mediate counting ! ' it will be said ; ' then we are in the 
 region of inference, and no longer in that of judgment.' It 
 is certain that when we speak of necessary connection between 
 attributes, of hypothetical or mediate judgment, we are in 
 the region of inference ; but it is not the case that we are 
 therefore out of the region of. judgment. By * mediate ' in 
 the present connection I only intend to indicate a judgment 
 which has for explicit subject a generalised or abstract attribute, 
 and being free from any demonstrative or sign of perception 
 must be taken as conditioning its predication by that attribute. 
 Such a predication is mediated, i. e. is affirmed of any particular 
 individual only through and in virtue of the attribute ex- 
 pressed in the subject. Mediate counting forms the transition 
 between ratio and proportion just as mediate measurement 
 does. Logically speaking every equation expresses a ratio, 
 and a ratio becomes a proportion directly it is applied — 
 directly its unit is taken as variable. Thus an algebraical 
 equation, which exists with a view to a variety of applications, 
 is ipso facto a proportion. 
 
 Complex counting is a case of mediate counting ; that 
 case in which we count by units which are themselves sets 
 of numerical places, i. e. by multiplication and division, which 
 
Chap. IV] ' Mediate ' and * Abstract ' i6i 
 
 may for the purpose be taken to include addition and sub- 
 traction. The only difference between multiplication and 
 division on the one hand and addition or subtraction on the 
 other is the equality to each other of the subordinate totals in 
 multiplication and division, which enables them to be counted 
 as units and their number indicated like any other number, 
 by its place in the series counting from o upwards. In this 
 sense multiplication is a mere abridgment of addition ; it is 
 only a question of form whether we say 2 + 2 + 2 + 2 = 8 
 or 2 X 4 = 8. This latter equation represents what is essential 
 as well in addition and subtraction as in multiplication 
 and division, a total analysed into factors and a process. 
 Complex counting, as a case of mediate counting, shares its 
 abstract, hypothetical, and necessary character. 
 
 e. The processes of mediate counting deal with the con- Abstract 
 struction and reconstruction of any given numerical total, ^nd"*^"^ 
 Even the quantitative relation of part and whole in its infinite 
 extremest abstraction retains thus much of structural unity, ^^^^^* 
 that, given a total of units, it can only be dissolved or recon- 
 structed according to certain rules of combination or analysis. 
 But the quantitative unit per se, or rather the one-sided 
 abstraction of the quantitative unit, the mere numerical 
 place which no positive identity links with the other places 
 of the series, has in it no principle of totality or limitation, 
 that is to say no reason for stopping short after one set of such 
 places rather than after another. Enumeration of units as 
 such may be continued at pleasure, and the process of so 
 continuing it without limit is summarised in the conception 
 of numerical infinity. 
 
 We have here tracked to its genesis this paradoxical con- 
 ception, in its right place so powerful for good, and in its 
 wrong place for evil. It would not, perhaps, be beyond 
 the province of logic to comment on its use in its right place, 
 that is to say in mathematical science ; nor could a more 
 interesting subject readily be found. But lack of mathema- 
 tical knowledge deters me from attempting such a comment 
 with any degree of detail ; for a logician is aware of the risk 
 incurred by venturing beyond his knowledge, and as he 
 preaches that there is no royal road to truth, must keep clear 
 
 1337 M 
 
i62 Abstract Quantity [BookI 
 
 of the delusion that he himself has found one. But any 
 one may offer a suggestion, and this I propose to do by 
 saying that it seems to me most probable that the scientific 
 use of the conception of infinity rests in every case on a 
 justifiable neglect — justifiable, because that which is neglected 
 has a known nature, and may be set down as insignificant 
 either altogether or from the point of view of a specific 
 purpose. 
 
 If, to take a coarse and non-mathematical instance, we 
 set about any task in a way which is demonstrably perverse 
 and inadequate, a looker-on is justified in disregarding our 
 efforts. He will tell us that we shall not get it done in that 
 way if we live to the age of Methuselah. Translated into 
 logical phrase, his comment means that our way of going to 
 work has not the element of totality ; the successive efforts 
 which make up the series of our activity, bearing no relation 
 to the nature of the work to be done, do not include in them- 
 selves successive parts of it, and therefore, as regards it, have 
 no tendency to come to an end and will (unless we choose to 
 leave off) go on to infinity. We may even apply this illustration 
 to a simple mathematical idea, say to the case of parallel straight 
 lines. We may consider as the task to be accomplished such 
 a change of direction in either or both of a pair of parallel 
 straight lines that they should cease to be parallel to one 
 another. And we may consider as the means adopted to 
 bring about such a change the production of the two straight 
 lines in their original direction. Then our supposed on -looker 
 would say, * You might go on for ever at that game ; ' ' You 
 cannot change the direction of a straight line by producing 
 it in its original direction.' Therefore it would be justifiable 
 to neglect the production of parallel straight lines to infinity, 
 in other words to pronounce that such production cannot alter 
 their character as parallel straight lines, i. e. that even, if 
 produced to infinity (which they can never actually be) they 
 do not meet. Probably such a case as this would hardly be 
 recognised as an instance of the mathematical use of infinity, 
 but in as far as it introduces the conception of quantitative 
 infinity as a term in a positive definition it would seem to be 
 at least analogous to such a use. 
 
Chap. IV] A ctuul infinite sevics 163 
 
 (. I may insert at this point some additional observations New 
 upon the question of an actual numerical infinity.* j ^fi°i7 °^ 
 
 The previous paragraph expresses the essence of my argu- 
 ment. It still seems to me sound, so far as it goes, and while 
 fully admitting my own want of mathematical knowledge, 
 I cannot see my way to cancel it, or the discussion which 
 depends upon it. 
 
 Professor Royce,^ I think, in his reference to this discussion, 
 has done me less than justice by assuming that I insist, in 
 the vein of Hegel's satirical digression, •= on the mere tedious- 
 ness of numerical infinity. But my treatment contains no 
 reference to this topic (unless it were on pp. 191-2 ed. 2 where 
 I reject such a treatment), and in considering the numerical 
 series as the abstract schema of membership in a whole I 
 have implied and stated that it has laws and properties which 
 give it a character and interest of its own. That, taken by 
 itself, it fails, as a consequence of its abstractness, to fulfil the 
 conditions of an individual whole, seems to me obvious ; and 
 no less obvious that Professor Royce, in using it as a type of 
 individuality, lays stress on possible incidents of the repetition 
 of positive contents, rather than on the essential nature of 
 repetition to infinity. 
 
 With regard to the present state of the question, I will 
 venture on three remarks. 
 
 (i) I observed in the first edition of this book that ' relations Problem 
 may be given as actual which only an infinite series could ^ "^ * 
 represent on their quantitative side ' (p. 168 ed. 2). The same 
 point presents itself to me with regard to the conceptions 
 employed in the recent theory of infinity. I see that certain 
 problems and definitions are given, and that if their require- 
 ments could be carried out in actual series an actual infinity 
 would be given ; but I am unable to see that this latter 
 condition is fulfilled. The character of givenness does not 
 appear to me to be brought to a point beyond that illustrated 
 by Spinoza in the case of a circle within a circle and not 
 concentric. The figure, which would need an infinite analysis, 
 is given. But it does not follow that the series which would 
 
 ' Ed. 2, 191 1. •• World and Individual, i. 508 ff. 
 
 •= Hegel, Wiss. d. Logik (ed. 1841), p. 257. 
 M 2 
 
164 
 
 Abstract Quantity 
 
 [Book I 
 
 Split in 
 Whole. 
 
 analyse it is given in and with it. I suggest that this analogy 
 might apply to the conception of self-representative series 
 and of transfinite numbers. I note that the latter cannot be 
 reached by enumeration. I do not know what characters 
 they share with numbers of the natural series ; but it is 
 obvious that they can hardly be given in the same sense. 
 
 (2) In the definition of an infinite whole, it is obvious, and 
 I suppose intentional, that the relation on which the infinity 
 depends, the one-to-one correspondence of a true part with 
 the total of parts forming the whole, expends the material of 
 the whole, if I may speak so grossly, at an immensely more 
 rapid rate than the whole itself progresses. I am thinking 
 of the case in which prime or square numbers are taken as 
 a part of the series of natural numbers. This answers 
 well enough so long as you have an enumeration ad infinitum 
 to draw upon. But it seems to me that if you had anything 
 approaching a given totality this spending in advance must 
 produce a contradiction at once. At any point of the con- 
 sideration, the part is miles and miles outside the whole. 
 While you appeal to infinity as incomplete, this cannot matter. 
 But the moment you seek to apply the character of totality, 
 the arrangement seems to split in two. It is one thing, I 
 repeat, to have a definition which if fulfilled would involve 
 a given infinity, and another thing to show that it can be and 
 actually is fulfilled. 
 
 (3) I believe Mr. Russell would agree with me that funda- 
 o Logic, jj^gj^^ai principles of Logic could not be overriden by the 
 
 practice of mathematics. If they really conflict, he would 
 admit, some condition has been tacitly imposed ^ in the 
 transition to mathematical conclusions, though as conclusions 
 in mathematics they may be perfectly sound. But he holds 
 that they do not conflict. His view is that a true Logic is 
 one with the principles of mathematics, and carries the conclu- 
 sions of the latter without reserve. I cannot see my way to 
 escape from the former conviction. We may be given some- 
 thing else of great interest and value, but unless it fulfils our 
 simple requirements, we cannot accept it as an actual infinity. 
 On the other hand, we can show an actual infinity, in one 
 
 * On the nature of mathematical abstraction see pp. 182-3 below. 
 
 Demand 
 
Chap. IV] Infinite Number 165 
 
 sense of the word, in the character of wholes with parts such 
 as to embody and reproduce the spirit of the whole. Such 
 parts, in some degree, are the organs of an organism or the 
 institutions of a nation. And in some degree, by what seems 
 to me like special pleading, the character of such wholes is 
 discovered in the mathematical concept of self-representative 
 series.* But I cannot think that the two conceptions can really 
 be united, except in the sense that it is probably true that a 
 real infinite, or self-contained individual whole, could not be 
 numerically represented except by an infinite series, which 
 I take to be the same as saying it could not be numerically 
 represented at all. 
 
 7]. I will now continue the discussion from which this was Infinite 
 a digression. ' -gteTai. 
 
 More subtle and interesting are cases in which the con- 
 tinuance of the series makes a difference in the task to be 
 performed, but the whole possible difference can be shown 
 to fall within certain known limits. These cases, which I 
 presume to be of the nature of infinitesimals rather than 
 of infinites (both of which must fall under the head of infinite 
 enumeration), may be reduced to the same class as the former 
 if we reflect that in the former also the difference fell within 
 known limits, but these were limits of kind, whereas we are 
 now speaking of limits of quantity. In cases of this second 
 type we know that a series could be continued to infinity, 
 and that some difference would be made to the problem before 
 us by this being done ; but, on the other hand, we are aware 
 of a limit within which the whole series must fall, and we are 
 therefore able to pronounce that the difference which can be 
 made by its continuance after a certain point is, at ISast for 
 our immediate purpose, a negligible quantity. Such, I take it, 
 must be the principle of any process which determines e.g. the 
 area of a circle by treating it as between the area of a polygon 
 inscribed in the circle and that of a polygon described about 
 it. So far as I follow the exoteric utterances of mathematicians,^ 
 the principle of abstraction based on a positive knowledge of 
 
 ' A. E. Taylor, Metaphysics, p. 1 16 ff. 
 
 ^ I have in mind more especially Mr. Spottiswoode's Presidential 
 Address to the British Association, which unluckily I cannot refer to. 
 
i66 Abstract Quantity [BookI 
 
 the capacities of a series must be at the root of the employ- 
 ment of mathematical infinity. 
 
 But our immediate business is with infinite number con- 
 sidered logically, i.e. with a view to its general place in 
 knowledge. And from this point of view we have to notice — 
 
 (i) That the idea of infinite number has its genesis in a 
 one-sided abstraction, viz. in the notion of counting without 
 having anything in particular to count, ^ which corresponds 
 to the idea of difference without identity, and of parts without 
 a whole. By such an abstraction the enumerative judgment 
 is destroyed, the essence of judgment as such — the exhibition 
 of identity in difference or of the whole in its parts — being 
 withdrawn from it ; and the names of the numbers are turned 
 into a meaningless repetition, the purpose of enumeration 
 having disappeared. We are no longer saying ' One tree, 
 two trees, three trees ', &c., but we are merely saying * One, 
 two, three ', and it is for this reason that we need never stop. 
 
 (2) Being one-sided, the idea of infinite number is self- 
 contradictory. The essence of number is to construct a finite 
 whole out of homogeneous units. The idea of numerical 
 infinity arises from neglecting the continuous nature of the 
 unit, and therefore omitting the element which alone arrests 
 computation at one number rather than at another. Thus 
 an infinite number would be a number which is no particular 
 number, for every particular number is finite. 
 
 (3) It follows from this that infinite number is unreal. 
 This does not mean that there may not actually be more 
 units of one kind or another than we can count in the time 
 at our disposal or in any finite lapse of time. The statement 
 deals with the nature of number, not with the extent of the 
 sensuous universe. If, to put a common idea coarsely, we are 
 asked, ' Supposing that you could travel through space for 
 ever, and never come to an end of it, must not space contain 
 an infinite number of units ? or even if you can go on sub- 
 dividing a given portion of matter for ever, must it not contain 
 an infinite number of parts ? ' to such questions we could 
 
 * A series which is ex hypothesi infinite comes under the head even 
 if it seems to have a positive nature. For its nature ex hypothesi does 
 not determine the number of its units. 
 
Chap. IV] Aft ' infinite series ' 167 
 
 only reply, * Things or the parts of things may quite con- 
 ceivably transcend our power to count. But except in view 
 of a finite goal, number does not help us, does not tell us 
 anything, grounds no ratio of parts to whole. We should 
 in fact never give up counting any units that had interest 
 for us, and should in doing so always be at some finite number. 
 But if it could be miraculously revealed to us that there was 
 no end, then I think we should stop counting, unless the units 
 in question entered into subordinate or graduated totals 
 which had an interest for us. Thus we -go on counting the 
 stars for definite reasons. Their relation to us is graduated, 
 and several subordinate totals within their number have 
 already been completed by enumeration ; e.g. stars of the 
 first eight magnitudes have been identified and counted. In 
 counting them we have always in view some definable total to 
 be constructed or to be corrected. Who counts the waves of 
 the sea ? The hope of complete enumeration is the justifi- 
 cation of counting.' 
 
 Then why do we count the years and centuries ? Do we 
 pretend to know that they will have a numerable sum ? and 
 when they have reached it, do we imagine that the race will 
 survive to take an interest in the completed enumeration ? 
 In the first place, for each of us time seems to have an end ; 
 and in the second place, all history is parcelled out in over- 
 lapping epochs which we have an interest in measuring. We 
 do not in fact ordinarily know or compute the whole numerable 
 series of years that has elapsed since the first events of ascer- 
 tainable date in history ; we adopt this or that era according 
 to some overpowering historical interest which makes it seem 
 to mark a fresh beginning. We do not count the years to 
 ascertain their total quantity, but to give them names by 
 which we can fix events ; and as a means to fixing the relations 
 of events we no doubt desire to note the quantitative relations 
 within the total of historical time which has elapsed down 
 to any given present. If we are pressed further, and told, 
 ' But, after all, the years may go on for ever and the human 
 race may go on counting them for ever', we can only reply that 
 the faculties with which We are endowed refuse to express 
 this ' ever ', that at any point taken in the series we should 
 
i68 Abstract Quantity [Booki 
 
 be at some finite number, and that if a conviction of the 
 endlessness of the series could be miraculously impressed upon 
 our minds we could only conclude that, except as a record 
 of the past, counting the years was an unmeaning form, 
 seeing that the nature of the series could not be represented 
 in niunber. A very simple case of enumeration ad infinitum 
 would be that in which, by persistent errors of identifica- 
 tion, we should count the same objects over again, round and 
 round, without being aware that we were doing so. In such 
 a case it is obvious that the conception of number would be 
 destroyed so far as these objects themselves were concerned, 
 though if they were at known intervals of space we might none 
 the less use them as a measure for other things. \Vhen we 
 measure with a foot-rule we do in fact count the inches 
 marked on it over and over again in this way, not for their 
 own sake or the process would be infinite, but only for the 
 sake of some other quantity which we characterise by them. In 
 this respect the inch-marks on the foot-rule correspond to the 
 physical changes which indicate the day and year, and which 
 serve as a measure for occurrences other than themselves. 
 
 An infinite series, then, is not anything which we can 
 represent in the form of number, and therefore cannot be, 
 qua infinite series, a fact in our world. Relations may indeed 
 be given as actual which only an infinite series could represent 
 on their quantitative side, such as the ratio of the diameter 
 to the circumference of a circle. But for this very reason 
 they never are adequately represented on that side, although 
 we may know and argue from the positive character of the 
 series, which ex hypothesi its prolongation to infinity is not 
 to change. Our constructive judgment requires parts and 
 a whole to give it meaning. Parts unrelated to any whole 
 cannot be judged real by our thought. Their significance is 
 gone, and they are parts of nothing. 
 
 Thus it is nonsense to speak of any definite number, say 
 100, as a portion of number, in the sense in which a foot is 
 a portion of a yard, or a minute of an hour. The question 
 * what portion ' ? at once disposes of any such relation. 
 Number as such cannot be identified with any particular 
 total such that a given number is a definite fraction of it. 
 
Chap. IV] What is Unvarying Duration ? 169 
 
 Closely allied to infinite number, and in a great measure 
 depending upon it, are the conceptions of abstract or ideal 
 time, and of abstract or ideal space, tending respectively to 
 generate ideas of infinite time and of infinite space. 
 
 Q. In speaking of Comparison we saw that every ' now ' Abstract 
 tends to become a part within ' now ' and ' then ', and every nittT^me. 
 ' then ' again within ' then ' and ' then '. This analysis is very 
 gradually brought about, speaking historically, in the evolu- 
 tion of the tense-system. The sense of Time is in the first 
 instance the mere consciousness of continuity in succes- 
 sion, that is, the mere perception of a succession or process 
 of change. This sense however being only possible through 
 setting off the succession against a comparatively permanent 
 background of consciousness, is in embryo the comparison 
 of successions, with the development of which comparison 
 measurement of Time, and with this the abstract idea of Time, 
 are brought into existence. The measurement of Time consists 
 in the equation of one set of perceptible changes identified 
 by a common nature, to another set of perceptible changes, 
 in the sense that the beginning and end of a numbered series 
 of the one coincide with the beginning and end of a numbered 
 series of the other. The enumeration of phases of one series 
 that coincide with one or more phases of the other series 
 might conceivably be undertaken apart from any belief that 
 either series has a constant duration in time, i.e. if repeated, 
 would occupy the same amount of duration as before ; but 
 in enquiring whether such a belief actually exists we must 
 distinguish between the reasonable doubt whether any portion 
 of any series ever can or will be repeated absolutely without 
 physical modifications which may affect its duration, and the 
 unmeaning doubt whether a series assumed to be repeated 
 without physical or causal variation may not nevertheless 
 have varied in the absolute amount of duration which it 
 occupied. The former kind of doubt will only lead to a demand 
 for criticism and reciprocal adjustment of our time-measures, 
 together with the temperate scepticism which our lack of 
 exhaustive knowledge must produce about our acquaintance 
 with even those natural conditions which we have most fully 
 investigated. The latter kind of doubt, if pressed to its con- 
 
170 Abstract Quantity [BookI 
 
 elusion, would reduce the enumeration of successive changes 
 to a statement of mere numerical fact wholly devoid of signifi- 
 cance. Such enumeration would not be impossible, but would 
 scarcely fulfil the requirements of judgment. It would be on 
 a level with the mere repetition of the names of numbers. It 
 is hardly necessary to give instances ; every one can see at 
 once that if we entertain the idea of variation in the measures 
 of time occurring without any reason, all equation of succes- 
 sions becomes futile, and ceases to afford any ground of 
 expectation or of inference. 
 
 But though a doubt of this nature has been mentioned 
 by great writers, yet it has never been extended to affect the 
 only element of our time-perception which is essential to its 
 utility, viz. the constant ratio obtaining between the succes- 
 sions employed as measures of duration. This limitation of 
 the doubt arises from the confusion in which it originates, 
 the confusion which consists in treating the whole as if it 
 were a part. Time, for us, is a relation, a ratio, and its con- 
 stancy is the constancy of this ratio. If all processes in time 
 maintain a constant ratio to one another so far as they are 
 unaffected by physical modifications, then there is no meaning 
 in suggesting that tried by some unknown or impossible 
 standard^ they may be variable. But yet this suggestion 
 is a natural suggestion arising out of a natural confusion. 
 We naturally frame an idea of duration in itself, as that which 
 has successive parts really and absolutely equal, because 
 equality of successive parts m terms of one of our time-measures 
 is what we are always endeavouring to ascertain about some 
 other time-measure. And we forget that equality, if we 
 exclude from it the idea of measurement, ceases to be an 
 intelligible conception. This ideal of duration then, whose 
 successive parts, though ex hypothesi not measurable, are 
 assumed to be equal, we actually set up as an imaginary 
 measure against the totality of consenting measures and 
 processes the ratio of which to one another forms our world 
 of time, and is merely represented in an abstract and ideal 
 form by ' duration in itself '. ' Duration in itself ', says 
 
 * E. g. by measurement of successive phases against each other, which 
 is ex hypothesi impossible. 
 
Chap. IV] * Duration- ' and ' Thing-in-itself ' 171 
 
 Locke/ ' is to be considered as going on in one constant, equal, 
 uniform course. But none of the measures which we make use 
 of can be known to do so ; nor can it be assumed that their 
 assigned parts or periods are equal in duration one to another'. 
 But ' duration in itself ' not being a relation of successions, 
 could not be perceived as time, nor could any being that 
 perceives as we perceive be aware of equality or the opposite 
 in its successive parts ; for equation is necessary to equality. 
 If, on the other hand, we set it against our time-measures, 
 then it becomes one measure among many, and in case of 
 a discrepancy that should remain unaccountable it is only 
 caprice that could choose which we should regard as right. 
 The question in fact would be unmeaning, for the whole 
 discussion obviously originates in the attempt to transfer an 
 attribute which depends on a comparison to a set of terms 
 considered in themselves and apart from comparison, and then 
 to suggest a comparison between them (the supposed equal 
 parts of ideal duration) and the totality of our time-measures 
 of whose reciprocal relations those parts are an idealised form. 
 
 But this confusion does not naturally originate a doubt 
 of the constant ratio, physical disturbances being allowed 
 for, of our measures of time compared with one another. For 
 it is this constant ratio from which the idea of duration as 
 such, hypostasised by abstraction into duration in itself 
 with equal successive parts, is derived ; and to doubt the 
 constancy of this ratio would be to deprive ourselves of that 
 idea of duration on which the confusion itself depends. If 
 oscillations of a pendulum of fixed length, such as are normally 
 equal when measured by the rotation of the earth, may vary 
 without a physical cause affecting either of the compared 
 motions, the conception of uniform duration is destroyed, 
 and no equation of successions is more than an isolated fact. 
 On such a hypothesis there would be nothing to generate the 
 idea of uniform duration, and no measure of time with which 
 to compare that idea. 
 
 The antithesis between duration in itself and our measures 
 of it is merely a case of the antithesis between the thing-in- 
 itself and our knowledge of it. It is possible, though un- 
 ^ Essay, Book II, 14, 21. 
 
172 Abstract Quantity [Booki 
 
 meaning, to doubt whether our knowledge as a whole is real 
 knowledge — i.e. corresponds to some test or condition which 
 we may imagine as imposed upon it from without. The 
 possibility arises from our possession of an ideal of knowledge, 
 which by an act of abstraction can be set in antithesis to the 
 actual whole of knowledge from which it is abstracted. But 
 it is impossible when operating in detail upon the matter of 
 experience to doubt the existence of rational connection in 
 any one particular group of appearances ; for by so doing 
 we paralyse the understanding, which can only act in the 
 search for causes, and leave neither knowledge to condemn 
 nor an ideal by which to condemn it. We shall have to return 
 to this subject in a later chapter, when we speak of the 
 postulates of knowledge. 
 
 We have just seen that it is idle to treat the whole as if 
 it were a part — our reciprocally adjusted measures of time 
 as if they were one measure among many. It is also worth 
 whUe to observe in the same instance the impossibility of 
 making a part do duty for the whole, which is strikingly 
 exemplified in the ultimate data of time. No process of 
 perceptible change is a trustworthy measure of time except 
 in as far as it is equated with other processes of known con- 
 stancy, and observed to be in itself free from physical causes 
 of variation. That is to say, the part can only be taken as 
 a definite standard when it has been criticised in the light 
 of the whole. This is true of all premises of knowledge. 
 
 Amount of Time, like all quantity, is measured by the 
 enumeration of units which have a known value. But, 
 unlike any other kind of quantity with the exception of space, 
 it follows number not only into mediate counting (all quantity 
 does this), but into enumeration ad infinitum. 
 
 Simple enumeration in the case of Time gives such judg- 
 ments as ' He died three years ago ', ' It is seven days since 
 I saw him ', — which expand by reference to a standard of 
 succession the mere indications — probably of various nature 
 and origin ^ — conveyed by the tenses. 
 
 ^ Tense need not have originated in the idea of succession at all ; and 
 may often have arisen out of the expression of emotions or anticipations 
 or out of the mere negation of presence as a perception of a certain kind. 
 
Chap, ivj Reality of World in Time. 173 
 
 Mediate or complex counting in Time gives such judg- 
 ments as the equation ' 365 days = one year '. Such judg- 
 ments deal with our real and ideal time as the result gained 
 by comparison and equation of actual processes in expe- 
 rience. But the abstraction which stands as subject tends 
 to assert itself as a something apart from the actual pro- 
 cesses whose relation it is, and thus as we have seen generates 
 the conception of ' duration in itself ' or ' absolute time ', 
 which again having lost the element of totality precipitates 
 us into the idea of infinite time. 
 
 Enumeration to infinity, when applied to the parts of 
 time, has characteristics analogous to those of infinite number, 
 but more striking, inasmuch as time is closely bound up with 
 the attributes of actual existence. Infinite time is, like infinite 
 number, an unending whole, which is a contradiction in terms. 
 That is to say, we are prevented by the nature of our minds, 
 if by no other cause, from attaching any meaning to infinite 
 tim.e as a quantitative expression indicating an aggregate 
 expressible by enumerative judgments. Whether the problem 
 (for so we must consider it) which is put before us in this form 
 is capable of becoming, not a problem, but a fact, in some 
 other form, is a question which does not concern us here. The 
 instances which are alleged to show that an infinite series may 
 be given point somewhat in this direction; I allude to such 
 an instance as that of the relation between diameter and 
 circumference. However this may be, it remcdns true that 
 infinite time, as a mere quantity of duration, is a phantom 
 generated by a meaningless abstraction. 
 
 But, as we asked whether there may not he endless numer- 
 able units, so we may be challenged to ask, May there not 
 or must there not have been an endless chain of actual occur- 
 rences in succession ? And if we are prepared to deny reality 
 to every endless series, must we not first of all deny it to the 
 actual world as in time, and we may add by anticipation of 
 the next section, as in space ? There can be no doubt that 
 the relativity of events and appearances in time and space 
 does involve for our minds an infinite progression in the way 
 of referring one thing or appearance to another as its cause 
 or explanation, or at least as in some way its determinant. 
 
174 Abstract Quantity [Booki 
 
 We can hardly conceive that we are really counting in a circle, 
 but our position is just as hopeless as if we were. Our ideas 
 of reference, determination, causation, do not allow us to 
 fancy a first event, a beginning of time, or a limit of space. 
 On the other hand, so far as we can understand, it is impossible 
 for such a succession as we postulate to be actual in the sense 
 in which a known section of history is actual. It is not merely 
 something more than we do construct as a whole ; it is some- 
 thing the essence of which is to be incapable of construction 
 as a whole. We may say if we like that we are bound to think 
 of such a succession as actual in the sense that it is a problem 
 inseparable from the relativity of our world ; but we cannot 
 take the endless series qua endless as a positive element in 
 oiu: organised experience. 
 
 In dealing however with the succession of actual events 
 having positive character and content we are in spite of 
 their serial appearance on different ground from that of 
 abstract time or equable succession as such. Actual events — 
 the history of our world — have more in them than a mere 
 series. We may say either that the world in time and space 
 is not mere succession and externality, or that the real world 
 which intelligent perception presents to us is not merely 
 a world in time and space. The human mind and will are 
 always busy in turning a series into a coherent and almost 
 individual whole, projected more or less definitely on a scene 
 of time and space, but not exhausted in its meaning by the 
 nature of that background. Greece for instance or England 
 are not mere ' geographical expressions ' ; and if they were 
 they would still have a physical unity of a deeper kind 
 than the juxtaposition of extended units or the sequence of 
 a series. They are historical realities, but their coherence 
 lies in their meaning. Therefore in denying that for us, in 
 our way of understanding, an endless progress can be a real 
 and controlling factor of organised experience, we do not deny 
 the reality of the phenomenal world as presented to intelligent 
 perception. 
 Abstract i. The nature of Space is in many respects analogous 
 Infinite **^ ^^^^ ^^ time, and bears on the whole a similar relation to 
 Space. the system of number, with its degrees of simple or categorical 
 
 J 
 
Chap. IV] A ctual Distances 175 
 
 counting, mediate or complex counting, and counting ad 
 infinitum. The corresponding grades of abstraction in dealing 
 with space may be identified as — 
 
 a. The measurement of actual distances. 
 
 h. The theoretical relations of spatial qualities, including 
 the whole of the mathematical sciences, excepting what may 
 be included in the mere system of number, viz. all forms 
 of simple and generalised (algebraical) arithmetic ; and 
 
 c. The conception of infinite space. 
 
 In defence of the subdivision here adopted, I venture 
 with a good deal of diffidence to suggest that the idea of 
 infinite space is not an idea belonging to geometrical science. 
 The emplojmient of the idea of infinity in geometrical reason- 
 ing belongs, if the account above given of it is correct, to the 
 second of the above heads, being really an abstract mode of 
 describing a geometrical whole. If enough space is given to 
 make manifest the positive nature of the whole before us, 
 it would seem that no addition can really affect the case. 
 Quantitative infinity may be a roundabout description of 
 a direction or a quality. That a certain straight line is 
 infinite may only mean that its direction is such that it can 
 never meet a certain other straight line. 
 
 a. The measurement of actual distances is prima facie a Measure- 
 case of simple measurement, and must obviously arise at ^^ual° 
 the point where positions distinguished by the comparative distances, 
 judgment are discovered to have relations of distance and 
 direction reducible to degree. Degrees of distance from 
 assigned points, and proportions of such degrees, considered 
 as properties of objects, pass into the determination of con- 
 crete individuals and of their characteristic attributes. In 
 this respect we have considered them above. But also, 
 receiving their significance from a system of equations by 
 which all spatial magnitudes are brought to a common 
 denomination, they contribute to reflection upon space in 
 the abstract, a reflection which is developed by the process 
 of enumeration applied to the parts of space when thus 
 idealised and considered for their own sake. The system of 
 measures, as we have seen above, is a connecting link between 
 simple and complex measurement. It is prima facie a system 
 
176 Abstract Quantity [Booki 
 
 of ratios, and requires an arbitrary starting-point to give it 
 meaning. But when taken as general and typical it passes 
 into a system of proportions, as we see in such a judgment as 
 ' This map is on the scale of twelve inches to the mile '. 
 There need not be twelve inches in any direction in the actual 
 map before us ; the phrase expresses a proportion, not a 
 simple fact of enumeration. It is not necessary to know, for 
 the purpose of the scale, how much absolutely (i.e. in the mass 
 of other relations) an inch or a mile is ; we can interpret the 
 scale if we know how many inches there are in a mile. The 
 abstract numerical expression i : 63360, which is a proportion 
 as governing the relation between every part of the map 
 and the corresponding part of reality, represents what the 
 formula ' one inch to the mile ' really means to say. We may 
 compare this case with the financial expression ' five per 
 cent ' ; some newspapers will print this as 5^5 per cent, 
 which is a confusion between singular or merely actual, and 
 generalised or proportional ratio. They do not really mean 
 that £5 need be concerned ; their predication is as true if 
 the interest in question only amounts to five shillings. The 
 expression five per cent is simply a fractional or proportional 
 expression. 
 
 Now, when, e. g. in the two instances just quoted, the 
 reference to an arbitrary magnitude is dropped out, and 
 when moreover the generalised equation is taken as expressing 
 the relations between distances in space combined in a certain 
 way, then we have ideal or mediate enumeration as it exists 
 in geometrical science. ' Mediate ' because the proportion 
 contained in the equation is affirmed of reality as qualified 
 by definite spatial attributes, which therefore enter into the 
 content of the equation as interrelated conditions. The 
 equation of an ellipse is a hypothetical judgment asserting 
 that the axes of an ellipse (or other quantities involved in an 
 ellipse) being treated in a certain way will be always equal 
 to themselves treated in a certain other way. It is obvious 
 that being mediate this geometrical enumeration or computa- 
 tion is also complex ; ^ for the conditions by which it is 
 mediated may involve units of any degree of numerical com- 
 * See pp. 1 60- 1 above. 
 
Chap. IV] Geometrical Equation 177 
 
 plexity. Thus judgments dealing with squares and cubes, 
 still more with conic sections, presuppose, on their numerical 
 side, more or less elaborate enumerative processes as involved 
 in the formation or apprehension of the spatial unit. 
 
 b. The generalised relations of spatial attributes form a Geome- 
 systematic science with a distinctive object-matter. '^^' 
 
 (i) ' Any two sides of a triangle are together greater than indiyi- 
 the third side.* ' Triangles upon equal bases and between spatiall ° 
 the same parallels are equal to each other.' ' The square of Figures, 
 the hypotenuse is equal to the squares of the containing 
 sides.' ' The angles at the base of an isosceles triangle are 
 equal to one another.* 
 
 Such judgments as these are among the simplest results of 
 mediate enumeration ^ as applied to space, and they present 
 an obvious peculiarity shared with them in a high degree 
 by complex judgments of mere number, and in a less degree 
 by judgments that compute time. Although geometrical 
 science proper consists, as a science, exclusively of the equation 
 with each other of variously described spatial units, which, 
 if we further consider the sciences of motion, we must take 
 as referred to units of time, yet under this ' variously described ' 
 there lurks a whole classiiicatory science of forms possessed 
 of structural unity and quasi-organic relations between part 
 and whole. Thus in the definitions and definitory judgments 
 of geometry, as in the inductive judgment of enumeration, 
 there is a revival of that structural subordination of part to 
 whole which, though dormant, yet is never dead so long as 
 judgment has a meaning. The triangle, the square, the circle, 
 the ellipse, though each of them capable of being exhaustively 
 defined by generalised enumerative processes dealing with 
 homogeneous units, have also an aspect of structural unity 
 and subordination of parts to the dominant quaUty of the 
 whole. Both clauses of this statement are however subject 
 to reservation. 
 
 In the first clause, the expression ' homogeneous units ' is 
 not entirely adequate to the facts. Distances in the three 
 spatial dimensions are indeed as distances homogeneous, 
 
 ^ For the further distinction between arithmetical and geometrical 
 reasoning, see II, chap. ii. 
 
 1337 K 
 
178 Abstract Quantity [Booki 
 
 but it can hardly be said that an angle is homogeneous with 
 a distance or direction, although a proportion of distances 
 is an exhaustive measure of an angle. Therefore, though an 
 angle may be represented in terms of distance, yet in con- 
 sidering the elements in the spatial structure of a square or 
 triangle we must assume the angle as well as the straight line. 
 The apprehension of converging direction is hardly given in 
 the mere apprehension of direction. 
 
 In the same clause we must quaUfy the assertion that all 
 geometrical shapes can be exhaustively defined by equation 
 of quantities. I presume that the impossibility of squaring 
 the circle implies a difference of kind between circle and 
 straight line which is disguised but not destroyed by the 
 efficient methods employed to express the one in terms of the 
 other.^ Here again, in the adequacy, as distinguished from 
 exhaustiveness, with which quantitative equations represent 
 characteristics of kind not wholly reducible to quantity, we 
 find an analogy with the various systems of necessity which 
 are superimposed upon one another in the organic and 
 moral worlds. 
 
 And the truth of our second clause would be a good deal 
 interfered with, if not annihilated, by enlarging our list of 
 geometrical figures, and by regarding every figure in all its 
 possible variations. As to the first point, every spatial figure 
 is a geometrical figure ; and those which we mentioned, 
 together with others that occur to the mind at once as com- 
 monly considered in plane and in solid geometry, have no 
 real prerogative of existence to the exclusion of trapeziums 
 or any other irregular figures, even if partly curved and partly 
 rectilinear in outline. The world would be easier to explain 
 than it is (or so it seems to a superficial glance) if irregularity, 
 ugliness, and disease did not, as they do, exist by law and 
 necessity ^ just as much as symmetry, beauty, and health. 
 It may be said in defence of treating the regular figures as 
 
 ^ The quadrature of the parabola shows that the impossibility of 
 squaring the circle does not arise from the mere difference between curve 
 and right line. 
 
 • I do not say by the same necessity ; I only mean that they result 
 mechanically from natural conditions. Any limitation of which this 
 statement may be capable must refer to a distinction of kinds of necessity. 
 
Chap. IV] Continuity destroys Species ? 179 
 
 if there were no others, that all others are reducible to them, 
 — all rectilineal figures to triangles, and so on. But this is 
 a mere ideal reduction by measurement, and in no sense a 
 deduction of the existence of the one from that of the other. 
 
 And again, most ' figures ' of which we speak are really 
 classes of figures, even if we take all * similar ' figures as the 
 same, i. e. disregard size and only look to characteristic pro- 
 portion. I do not know why we should not take the conic 
 section as ' a figure ' and treat the circle simply as a case of 
 it. Anyhow the ellipse comprises in itself a whole class of 
 figures which are qualitatively quite different from each 
 other, and pass by imperceptible gradations into figures 
 which are not elliptical. By insisting on facts like these 
 we might melt away the individuality of typical figures, 
 and exhibit every group of geometrical shapes as destitute 
 of common characteristics beyond those which flow from the 
 mere genetic relation itself. Thus, for instance, an ellipse 
 when just passing into a circle or into a straight line has none 
 of the characteristics which we associate with elliptical form, 
 although the analytic relation by which its nature is theoreti- 
 cally determined may be within the limits which must as a 
 matter of geometrical classification be assigned to that figure. 
 Such a treatment would be the triumph of explanatory theory 
 and necessary connection over individuality and character- 
 istic quality. But it is a treatment of which, in geometry, 
 the facts admit, and which even in the organic world is 
 rendered indispensable by the idea of continuous evolution. 
 
 It is right that attention should be drawn to the above 
 reservation. No habit is more pernicious than that of assuming 
 what is obvious and familiar in a certain sphere to exhaust 
 the contents of that sphere. Every figure is geometrical ; 
 and even if all irregular figures can be reduced for purposes 
 of reckoning to the more regular types, this does not justify 
 us in speaking theoretically as though there were no figures 
 in space besides those which have been selected as typical by 
 geometricians. 
 
 We must meet such conceptions now as we shall have to 
 meet them again, perhaps more than once, in the evolution 
 of the judgment, by the reflection that one positive existence 
 
 N2 
 
i8o Abstract Quantity [Booki 
 
 cannot, by tb'^. mere fact of its existence, cancel another. 
 There may be non-elliptical ellipses, figures which fulfil one 
 set of conditions that mark the ellipse, but lack attributes 
 without which we hardly recognise the figure ; and there may 
 in the same sense be or have been (time makes no difference) 
 non-human human beings. And explanatory theory may be 
 able in both cases to trace step by step without saltus or miracle 
 the transition from the one phase into the other by develop- 
 ment of elements fundamental in both. But this will not 
 obscure our perception of the elliptical shape of a character- 
 istic ellipse, or of the humanity of a typical human being. 
 The typical human being is made typical, as we shaU see, by 
 real teleology. The typical ellipse is only typical through a 
 subjective quasi- teleology. This is the difference between the 
 two cases. 
 
 Thus, in spite of the above reservations, it remains true 
 that in complex enumeration as applied to Space the antithesis 
 of individuality and necessity is strikingly illustrated. A 
 generalised relation of distances, not obviously differing in 
 kind from any other generalised enumerative relation, when 
 interpreted into an actual figure, may at least produce a 
 structural totality complete in itself and of a marked individual 
 character. It is enough to mention such simple instances as 
 the equilateral triangle, the square, and the circle. These 
 totalities do not refer outside themselves for definition in the 
 obvious sense in which simple magnitudes are forced to do so. 
 They are primarily cases of internal proportion, of proportion, 
 that is, between one and another element of a single totality. 
 Relativity appears in them in another shape than that of 
 simple equation with absolute (in the sense of arbitrary) 
 standards of magnitude. A particular triangle or ellipse is 
 relative and finite chiefly in the sense of being derived from 
 arbitrary conditions, no one value of which has any preroga- 
 tive of existence as against any other, and an extreme modifica- 
 tion of which will always destroy the essence of the figure. 
 There is also a further sense in which all natural existences 
 are finite as compared with mind, because they cannot refer 
 to themselves, but only are referred whether to themselves or 
 to external conditions. 
 
Chap. IV] Is Geometry categorical ? i8i 
 
 The subordinate totalities of Time, such as the hour, day, 
 and year, are not really cases of the same principle, for they 
 are mere aggregates of units without a limiting totality, and 
 are simply formed by arresting enumeration at intervals 
 prescribed by external interests. A better parallel may be 
 found in the numbers of the numerical series which are 
 distinguished by any peculiarity, e. g. prime numbers, squares, 
 cubes, &c., if we consider these peculiar cases in their relation 
 to the one unvarying process of adding together homogeneous 
 units. This simple synthesis of number may be regarded as 
 analogous to the mechanical or necessary aspect of an individual 
 thing or figure, and its peculiarity as square or cube to struc- 
 tural totality. 
 
 (2) Figures in space then, and numerical relations, al- Existence 
 though abstract and ideal, and arbitrarily selected out of \^ Space.^ 
 continuous sets of value of which no one has existence by 
 preference to the other, yet seem capable in a sense of posses- 
 sing characteristic quality and self-sufficing totality. What 
 is to be thought of their existence ? Do such judgments as 
 are mentioned on p. 177 involve the assertion that the quali- 
 fications of Reality which form their subjects are actual, and 
 if so, in what sense are they actual ? The difficulty of the 
 question is only displayed in its true extent if we add to the 
 above instances some ideas for which actual existence, as 
 diagrams in books or as thoughts in the minds of individual 
 students, cannot with probability be claimed ; e. g. the idea 
 of a polygon with a thousand and one equal sides, of any 
 trapezium chosen at will, or of any irregular figure or high 
 number. 
 
 It is clear that the square or triangle qua spatial figure 
 has no actuality which does not equally belong to all such 
 less familiar shapes, and therefore mere presence in the 
 individual mind is not the existence in question. And indeed 
 to speak of it as such would be to enter upon a vicious circle 
 which would stultify the judgment ; for it is essential to the 
 judgment to affirm a reality outside itself, and it would be 
 too ridiculous that your judgment should refer merely to the 
 content of mine as the reality asserted, and mine in turn to 
 that of yours. It is obvious that the two manifestations of 
 
i82 Abstract Quantity [Book i 
 
 the thought -function are on a level, and if each refers to the 
 other, each might just as well refer to itself, i. e. find its truth 
 in the simple fact that it is made.^ A triangle must be just as 
 real ^ when no one is thinking about it as when many students 
 are engaged upon the conception of one. This is of course 
 not the same as to say that spatial figures do not depend on 
 the spatial consciousness, or on consciousness at all. We are 
 only saying that they cannot depend for actuality on one 
 particular reflective consciousness of those particular figures. 
 The world as it is for perception and intelligence is the object- 
 matter of our whole enquiry, and we have no occasion to raise 
 a question that assumes the destruction of the object which 
 we are considering. 
 
 The absence of material existence and also of any mode 
 whatever of particularisation in determinate forms (the 
 selection e. g. of a typical ellipse not being justifiable on 
 purely geometrical grounds) must however make a distinction 
 between the actuality of the contents under discussion and 
 that of material things or their sensible properties. Admitting, 
 as we must admit for logical purposes, that Space is to be 
 reckoned with as having a peculiar actuality of its own, still it 
 is not clear in what relation geometrical figures, apart from the 
 shapes of actual objects, stand to actual space. Geometrical 
 figures as such, the subjects of judgment in geometrical 
 science, are not the shapes of actual objects ; they are not 
 identical with any perceptible figure ; they are not distributed 
 through space nor present as special characteristics in any 
 portion of it. I do not know how to describe them better 
 than as a peculiar class of laws or attributes of the spatial 
 relation as such, which are concrete in the nature of their 
 content, though abstract in their medium of presentation. 
 And in the same way the characteristic totalities of number 
 must be taken as laws — embodied laws — of the enumerative 
 relation of part and whole. 
 
 ' Reference to the world of meanings or objective reference (Intro- 
 duction, sect. 7) is not merely reference to judgments in fact made by 
 others. It is an inadequately conditioned reference to reality. 
 
 * This is overstated. Every thought, we must suppose, contributes 
 something, however practically inappreciable, to the reality of what 
 it thinks of. 
 
Chap. IV] Are Spatial figures real ? 183 
 
 We may illustrate the nature of such attributes by com- 
 paring them with any piu-ely imaginary ideal content which 
 bears (so far as an imaginary content can, for it is always, in 
 my opinion, found wanting somewhere) the character of self- 
 sufficing totality. Such an ideal content for instance is 
 Shakespeare's Hamlet,^ or the material spheres of ancient 
 astronomy, or, to come nearer to our present subject, the 
 conception of ' Flatland ' as space in ' two dimensions only, 
 with sentient beings confined to it. These conceptions, though 
 doubtless based on elements of fact and illustrative of real 
 conditions, yet exist only in the minds of those who read 
 and think about them, or more strictly in the identical refer- 
 ence which these minds are stimulated to make to a world 
 of meanings, but a world of meanings explicitly discontinuous 
 with and detached from the actual world of fact, or what we 
 call in short an imaginary world. Such a world is indeed 
 maintained by judgment, but it is judgment of a peculiar 
 kind and under peculiar conditions — subject, not like the 
 common world of meanings to a wholly indeterminate, but 
 to a conscious and explicit, abstraction from reality, which 
 becomes semi-conscious in artistic fiction, and utterly lost 
 and obliterated in mere error and superstition. 
 
 The figures which represent the properties of actual space 
 are not imaginary in this extreme sense of the word. It might 
 however be a question whether the difference between them 
 and such ideas as have been mentioned is one of kind or one of 
 degree. Both kinds of ideas it might be said involve abstrac- 
 tion from concrete perceived reality, both kinds are therefore 
 hypothetical and not actual existences, and how far the 
 abstraction is carried cannot be a question of principle. Nor, 
 I must add, do I mean to insist on the manifest contradiction 
 with experience, or self-contradiction when viewed in the 
 light of experience, that some of my instances of imaginary 
 ideas may be held to present. The distinction which I desire 
 to draw is simply between abstract but real, and purely 
 imaginary contents, when employed as subjects in judgment. 
 
 ^ Omitting the considerations which arise out of the artistic truth of 
 the conception, and taking it merely as an illustration of an imaginary 
 idea. 
 
184 Abstract Quantity [Booki 
 
 Perhaps the distinction might be found as above suggested 
 to consist formally in the nature of the abstraction to which 
 the two kinds of contents are severally subject. A merely 
 abstract content is subject only to the abstraction which its 
 ostensible nature implies. The name of a figure in space is 
 the name of a figure in space and not the name of a man or 
 a mineral or of any material object. But the name of Hamlet 
 for instance is and yet is not the name of a man. The name 
 of a knot tied on an endless string is and yet is not the name 
 of a reality in space. These imaginations are subject not 
 merely to the abstraction which separates every content from 
 all that is not included in it, but to a further abstraction 
 which says, ' This is a meaning, but not the meaning you would 
 take it for : ' in other words, it is conditional within a world 
 which itself can only be predicated conditionally and not 
 directly of the reality with which we are in contact by means 
 of perception. 
 
 Thus we may say, if we choose, that our ideas of actual 
 space have for their meaning only possibilities, but these 
 are at least real possibilities, that is to say, their fundamental 
 generating relations actually exist in the world which centres 
 in present perception. They are therefore as real as colour 
 in the dark or as sweetness which we do not taste. And if 
 we pronounce these attributes unreal outside the moment of 
 perception, we have laid the axe to the root of the perceptible 
 world. We might as well say that the wall in front of me is 
 actual and that behind me is not. But what corresponds 
 with these ideas to the actuality which colour and taste do 
 partake of when perceived ? Here we find a real difference. 
 Such actuality in sensuous presentation they cannot have. 
 But we do not of course admit that Reality is restricted to 
 sensuous presentation. All we can say is that in all relations 
 of actual things these spatial attributes make themselves 
 evident as controlling conditions, and are introduced as con- 
 ceptions without which the mind fails to construe the pheno- 
 mena. They are abstract characteristics of the actual spatial 
 relations of things, and are as much a fact for logic as any 
 secondary quality, qua general quality ; and they are not 
 on a level with mere imaginations and fictions, even if 
 
Chap, ivj Generic and Quasi-generic ' 185 
 
 these are consistent, or not notoriously inconsistent, with 
 
 reahty. 
 
 (3) The judgments mentioned on p. 177 are thus found The 
 
 to display in their own line of abstract evolution which we ^"^^1- 
 ^ ■^ . . generic 
 
 are now pursuing a character analogous mutatis mutandis judg- 
 
 to that which the Generic Judgment will be found to display ™^"*- 
 in the concrete evolution of thought. The subject of each 
 such judgment is Reality qualified as a structural whole 
 which embodies properties rooted in an actual relation and 
 controlling the consequences of that relation at every turn. 
 The figures in question do not claim sensuous particularity 
 and are not capable of it. The judgment therefore is a degree 
 less generic and more hypothetical than classificatory judg- 
 ments which retain much of the meaning of the collective 
 judgment. 
 
 Yet the judgment in question is generic. In the first place, 
 the particular figures which arise if particular conditions 
 are assumed are individual totalities, not indeed having 
 sensuous singleness, but self-identical as laws of space. And 
 in the second place, although no doubt any series of such 
 figures (triangles, ellipses, &c.) is in one point of view an 
 infinite series ^ (the transition from value to value of the 
 generating conditions being absolutely continuous), yet the 
 whole falls within known limits, and is bound together by a 
 characteristic quality which might probably be found to vary 
 with the variations of the generating factors.^ 
 
 Therefore a judgment like this presupposes, not as do 
 the judgment of zoology a limited even if very large number 
 of actual individuals forming a real historical unity though 
 spoken of mediately and by help of an abstract qualification 
 of Reality, but a series of laws regulative of form, or rather 
 
 * 'Then there are infinite series,' a critic may say. The case illustrates 
 my point. If you could make actual all the cases of a continuous series, 
 it would be a given infinite series. But I presume you cannot. 
 
 ^ It seems obvious that as one generating factor, e. g. one axis of an 
 ellipse, approaches disappearance, we should expect the characteristic 
 quality to diminish. But any such conception is not easy to carry out. 
 E. g. if we take equality of the axes as the characteristic point in a figure 
 of the conic section class, we get the circle as the characteristic type 
 to the exclusion of the ellipse. The question has perhaps only an 
 aesthetic interest. 
 
i86 Abstract Quantity [Booki 
 
 a law expressed in a series of forms, having positive common 
 characteristics and bounded by definable limits within which 
 the whole series must fall. ' All triangles ' is hindered from 
 meaning every particular triangle (i. e. variety of triangle — 
 I abstract from particular sensuous presentations all through 
 this discussion) not only as ' all men ' is hindered from meaning 
 every particular man, by the practical impossibility of dealing 
 with such a meaning, but also by a theoretical absurdity, for 
 all particular triangles would be an infinite series, which need 
 not theoretically be the case with all particular men. But, 
 as we saw above, a series which has a known positive character 
 or falls within known limits may be treated as an actual 
 unity in spite of its infinity. ' All triangles have their 
 angles equal to two right angles ' is a judgment about what is 
 really a single continuous relation, but embodied to the 
 mind's eye in certain salient types resulting from geometrical 
 classification. It resembles the generic judgment more 
 strikingly than appears at first sight, for the generic judgment 
 too deals with a section of evolution in which a vast though 
 not infinite array of transitional types has really bridged the 
 gulf between the marked species which are familiar. 
 Infinite C- Infinite enumeration applied to the parts of space is 
 space. the last result of abstraction in this region. Here, as in j;ime 
 and number, we have the idea of the absolutely homogeneous 
 part, i. e. the part whose repetition has no tendency to generate 
 a whole. The idea of infinite space is the idea of the endless 
 synthesis of such parts, which must always present to us the 
 appearance of an unsolved problem. If the problem has a 
 solution, it must consist in changing the point of view from 
 which we regard it, as if, to repeat an illustration which I 
 employed above, we were suddenly to awake to the fact that 
 we had been counting parts extended in a circle and not in 
 a straight line. 
 
 Will not the doctrine known as the subjectivity of space 
 and time help us to explain the nature of this contradictory 
 reality ? Up to a certain point it has undoubtedly done 
 good service by showing that the difficulties which attach 
 to sensuous reality are rooted in the nature of the percipient 
 intelligence itself, and must be reckoned with as inherent in 
 
Chap. IV] Subjectivity of Sense-forms 187 
 
 sensuous experience. But I am unable to see that the ' subjec- 
 tivity ' of these forms of apprehension can carry us further, 
 unless or until we are enabled to put something better in their 
 place. At present we seem only to have learnt that the 
 difficulties of knowledge are not external to it, but are inbred 
 and inevitable, at least so far as concerns the series of sensuous 
 phenomena. But we gain nothing, so far as I can understand, 
 by attempting to erect a world beyond as a non-sensuous 
 counterpart of the sensuous series. If a counterpart, then it 
 would seem to share the difficulties attaching to this series, 
 while as non-sensuous it lacks the compulsory reality of sense- 
 perception.-^ Our present knowledge rather points to the 
 conclusion that if we are to attain something less contra- 
 dictory, more capable of self-sufficing reality, or if we like to use 
 the phrase, more above sense, we must look for it 'in facts 
 and purposes which deepen the significance of life, not in a 
 shadowy counterpart which repeats the world of sense without 
 enhancing its value. Mere series, mere space and time, we 
 must always remark are mere abstractions ; and though 
 no human knowledge is free from relativity, i. e. from the 
 reference to what falls outside it ; yet on the other hand no 
 actual human knowledge is, like the abstract infinities, mere 
 relativity and nothing more. There would be some justification 
 for saying that, as contrasted with the concrete structure of 
 individual things, a ' subjective ', i. e. artificial and unreal, 
 character might be attributed to number, space and time as 
 infinite wholes ; on the ground that they conflict with the 
 nature of actual fact however comprehensive, and that the 
 extension to infinity deprives them of relation to the pheno- 
 mena in which they are known to us. But the distinction is 
 hardly sound, for it is at best one of degree. The difficulties 
 of relativity do not wholly cease as soon as we turn away 
 from the abstract infinity of mere number, time, and space ; 
 in common ideas of causation they affect the actual content 
 of phenomena. From the very beginning of knowledge, as 
 I have tried to point out. Absoluteness co-exists with Rela- 
 ^ Lotze has well brought out the difficulties attaching to the con- 
 ception of an ' intelligible ' counterpart to the world of sense. The 
 strange thing is that they do not appear in any way to make him dis- 
 contented with that conception. 
 
i88 Abstract Quantity [Booki 
 
 tivity ; but it is impossible to form categorical judgments 
 of a comprehensive type until the idea of causation has been 
 freed from its primary implication of an endless series. 
 
 The question might be asked, why are we exclusively 
 tempted to demand the reality of infinite time and infinite 
 space when there are other abstract conceptions of homo- 
 geneous parts not subordinate to any whole, which might 
 in the same way be pushed to infinity ? In the first place, 
 it may be replied that abstractions of this class are not so 
 common as might appear. The essence of them is that 
 progressive enumeration shall not tend to modify their 
 character. Thus intensive quantities, such as infinite force, 
 infinite velocity, are conceptions of a heightening the later 
 stages of which would modify the earlier and not remain in- 
 differently beside them. Therefore although the phenomena 
 of velocity or of force do suggest the idea of quantitative 
 infinities of those kinds, yet they do not impel us to judge 
 those infinities to be real, because the perceived forces do 
 not in their nature refer to and presuppose infinite degrees 
 of themselves, but rather each manifestation per se excludes 
 the infinity which would involve a qualitative change in 
 itself. Infinite force or velocity is as contradictory an idea 
 as infinite space, but is not in the same sense a problem 
 or 'a paradox, because it does not in the same sense claim 
 reality. 
 
 And secondly. Space and Time may be called the Categories 
 of sense. That is to say, they are the only principles according 
 to which the world of sense-perception, both of our own 
 immediate feelings and of external objects, appear to us to 
 be possible. The question is not merely whether we can 
 imagine the absence of either or both. I take it that experience 
 would reply to this by saying that we cannot seriously imagine 
 (i. e. conceive with full consideration) the absence of either 
 m a world of sense-perception} 
 
 * Psychologically speaking, I should suppose that we may lose con- 
 sciousness of either, perhaps more readily of space, e. g. when listening 
 to music. Time is perhaps the more importunate of the two ideas 
 because it extends to our inner feelings, &c., and I suspect this to be the 
 reason of Lotze's notion that time is more ' objective ' than space. Yet 
 we may, of course, in a fit of absorption lose consciousness of time. I do 
 
 \ 
 
Chap. IV] Space and Time why so importunate 189 
 
 But the .real point is not merely psychological, although 
 of coiu-se in dealing with it we must appeal to facts of the 
 mind. The point is that the very character and essence of 
 sense is isolation, and therefore in apprehending variety, 
 series. So extreme is this character of isolation that the 
 presentation of sensuous contents even as a series is due to 
 an intelligence that goes beyond sense. Space and Time 
 are /or us the first work of knowledge, as the conquest of them 
 is the second. But all we are concerned with here is that, 
 assuming the impulse to construct out of our sensuous per- 
 ception a whole of the same nature as itself, we cannot but 
 attempt to erect space and time also into wholes, an attempt 
 which is frustrated as we have seen. 
 
 iii. But, lastly, reflective science in pursuing an analogous Mechani- 
 attempt does meet with analogous difficulties. It assumes ^^^ ^^^^ 
 as further characteristics of the sensible world the abstrac- Universe, 
 tions of matter and motion. Matter and motion are the 
 abstractions in which the sensuous world is reduced to 
 homogeneity in order to be susceptible of quantitative treat- 
 ment, and in this treatment they are able to a large extent 
 to represent genuine and actual relations of that world. In 
 this respect they correspond to the structural classifications 
 of geometry, and form the content of mechanical science. 
 It would hardly be true I suppose to say that the infinity 
 of matter and motion in space is an inevitable paradox to 
 the scientific consciousness. It appears possible to conceive 
 of the universe as a coexistent finite mechanical whole, 
 demanding no determination from without. But this is only 
 because the determination from without is thrown back in 
 time by the doctrine of the eternity of motion, which, with 
 a similar doctrine applied to matter, introduce the infinite 
 series under the guarantee of the law of causation. Here 
 again we have the insoluble problem which arises from the 
 relativity of the sensuous world and presses upon us in its 
 naked form as soon as, by reduction to homogeneity, the 
 element of absoluteness or totality which helped to balance 
 it is destroyed. It is to the latter element that we really look 
 
 not suppose that these half-illusory states are at all perfect in their 
 neglect of the non-obtruding element. 
 
1 90 Abstract Quantity [BookI 
 
 for a solution in the degree in which it is possible. The infinite 
 series cannot itself be reality, but so far as we can transmute 
 the series into an articulated whole, so far we can gain a reality 
 out of it. 
 
 This distinction suffices to justify the well-grounded con- 
 clusions of science respecting the past and future of the 
 material universe. Such conclusions are contributions to the 
 projection that forms the actual world in which as percipient 
 and intelligent beings we live. But with eternity in the shape 
 of infinite regress and progress such a projection can have 
 nothing to do. 
 
 We have thus traced to its climax in mechanical science 
 that form of identity and difference in which an identity 
 is regarded as the sum of the differences in which it is pre- 
 sented. This one-sided aspect of identity and difference is 
 what takes the shape of whole and part in the strict or 
 quantitative meaning of those words, the meaning in which 
 the whole is taken as equated to a relation, whether par- 
 ticular or generalised, of homogeneous parts. 
 
 It naturally occurs to us to ask at this point, how, if quantity 
 is homogeneous, and if proportion is, as we have reckoned 
 it to be, generically a quantitative relation, the concrete 
 individual (see. p. 127) whose characteristic quality takes 
 the shape of proportion differs in content from a relation in 
 number, figure in space, or system of motions which, though 
 purely quantitative, is also, as we have seen, characteristic 
 and self-contained. In the first place, we have spoken of the 
 quasi-individuality which does attach to the structures that 
 embody geometrical and, we may now add, mechanical laws. 
 And we must remember that their quasi-individuality is only 
 made possible by a certain revival of the qualitative element 
 within the whole of quantity, even if the quality so present 
 throughout the parts is, like the curvature of a circle, constant 
 in all of them. And in the second place, we have to point 
 out that in a true concrete individual its individuality exists 
 in the form of a conscious purpose, a real teleology, and is 
 the cause of its homogeneousness, the proof of this being 
 that if the elements are isolated and removed from the indi- 
 vidual they fall back into disparateness. The proportion in 
 
Chap. IV] Concrete and Abstract Individuals 191 
 
 which its parts are held together is as we saw '^ secondary and 
 not primary ; it is a proportion between proportions. And 
 though it is true that in the simplest forms of comparison, 
 such as matching a colour, judgment and equation are 
 hardly to be distinguished, being in fact as yet in their common 
 germ, yet the peculiar secondary unity of a complex whole 
 characterised by internal proportions is not fully expressed 
 by reciprocal equation of its elements. Thus the concrete indi- 
 vidual is from the first characterised by rather than equated to 
 pure quantitative relations of parts. With abstract totalities 
 just the reverse is the case. Their elements, homogeneous to 
 begin with, are placed arbitrarily in any whole (in as far as 
 the elements of various curves resist such construction they 
 are not pure quantity), and only acquire the semblance of 
 a relation to a whole by their non-resistance in such a con- 
 struction ah extra. In the former case the differences involve 
 the character of parts as the concrete involves the abstract ; 
 thus head, arms, legs in a man have quantitative relations 
 to each other and to his whole figure, which vary only within 
 narrow limits, and which sculpture or painting must not 
 violate ; or again, his whole life is only possible subject to 
 definite quantitative relations of energy supplied to work 
 done. In the latter case the parts, indifferent in themselves, 
 are forced by construction into the function of differences. 
 The reservations to which this last assertion is subject have 
 been explained above (see pp. 177-8). 
 
 Thus equation and judgment are no doubt closely re- 
 lated in their origin ; and this is further illustrated by the 
 facility with which judgment drops back or crosses into the 
 equational form, which demands altogether less effort and 
 insight than the attempt to grasp the differentiated structure 
 of things. I cannot refrain from quoting in illustration a 
 paragraph from a powerful and sensible writer whose one fault 
 is the love of moving in the lower categories and avoiding 
 the effort to grasp entire realities as they are. ' As to the 
 general result ^ [of human progress] what is it ? Say, roughly, 
 three hundred million Chinese, two hundred million natives 
 
 ^ See p. 131, above. 
 
 * James Fitzjames Stephen, Liberty, Equality, and Fraternity, p. 177. 
 
192 Abstract Quantity [BookI 
 
 of India, two hundred million Europeans and North Americans, 
 and a miscellaneous hundred million or so, — Central Asians, 
 Malays, Borneans, Javanese, South Sea Islanders, and all 
 sorts and conditions of blacks ; and over and above all 
 the rest, the library at the British Museum. This is the 
 net result of an indefinitely long struggle between the forces 
 of men and the weights of various kinds in the attempt to 
 move which these forces display themselves. Enthusiasts 
 for progress are to me strange enough. " Glory, glory : the 
 time is coming when there will be six hundred million Chinese, 
 five hundred million Hindoos, four hundred million Europeans, 
 and Heaven only knows how many hundred million blacks 
 of various shades, and when there will be two British Museums, 
 each with a library." ' The numbers here are not merely 
 descriptive ; they are essential ; otherwise the element of 
 progress could not consist in their augmentation. Of all 
 instances that show in what thin abstractions a writer who 
 prides himself on contact with realities may live and move, 
 I know none more grotesquely striking than this ; and it 
 cannot be defended by suggesting that its absurdities are in 
 some degree imputed rather than adopted. For they can only 
 be so imputed because they are adopted. The faith in progress 
 need involve no assumption of numerical increase of population. 
 Had the writer ever heard of virtue or knowledge ? ^ That his 
 main thesis in the passage is somewhat of a truism does not 
 justify so gross a misconception in supporting it. The more 
 we examine the more we shall find that it is indolence which 
 makes us drop into the equation when our subject-matter 
 demands the judgment. 
 
 I have finished the account of the equation before pro- 
 ceeding with the judgment proper chiefly with a view to 
 coherence in treatment, and not with an intention of repre- 
 senting the former as inferior to or less ultimate than the 
 latter, though in a sense which may appear from p. 85 above, 
 such a representation might be held justifiable. But the 
 
 ^ Contrast Dante's lines : — 
 
 ' Considerate la vostra semenza ; 
 Fatti non foste a viver come bruti 
 Ma per seguir virtude e conoscenza.' 
 
 Inferno, xxvi. 118. 
 
Chap. IV] Truth and falsehood of Quantity 193 
 
 conception of divergence, of a co-ordinate evolution gener- 
 ated by abstraction, seems more appropriate to the matter 
 before us than that of linear development.^ The equation 
 is, as we saw, hardly even a momentary phase in the growth 
 of genuine judgment ; the two functions part company almost 
 as soon as their significance reveals itself. 
 
 And quantity is more than one among many categories ; 
 as the simplest point of view which admits of difference and 
 system it aspires to be, and in one sense is, the sole category, 
 or ultimate ideal of knowledge. It may be treated as sole 
 category falsely or truly. It may be sole in the sense that 
 though abstract, yet, subject to the reservations involved in 
 its abstractness, it has universal applicability. Every science, 
 as we read in Aristotle, assumes its subject-matter, and does 
 not give an account of it. The schematic world of space, 
 time, and mass is in this sense, as an object of science, beyond 
 question ; it has only to serve as an abstract postulate in 
 working with perceptible facts, and from this point of view 
 is a truth, if not the truth about the universe as a whole. As 
 enabling a coherent reflective view to be obtained of perceptible 
 phenomena as a quasi-totality (always encumbered indeed by 
 the infinite series), it is of immense scientific value and co- 
 extensive with definite existence. For these reasons, again, 
 the equation — the judgment of quantity — is rather co-ordinate 
 with judgment than a phase in its development. And still 
 more is there reason for so considering it if we take account 
 of the false employment of quantity as sole category. This 
 false employment arises, or would arise, supposing the category 
 of quantity to be considered not merely as co-extensive with 
 determinate existence, but as, in its abstraction, the ultimate 
 reality of all determinate existence, and consequently as 
 furnishing the final ideal of science. It is obvious that the 
 true use of this as of every category slides easily into the false 
 one. Every science is occupied with its own abstractions. 
 Every individual mind tends to magnify that with which it is 
 occupied. The category of quantity, for reasons mentioned 
 above, lends itself to universal application. It seems a short 
 step from universal application to sole application, but it is 
 ^ Above, p. 85. 
 
 1337 O 
 
194 Abstract Quantity [BookI 
 
 the step from truth to falsehood. It is not made exclusively 
 by votaries of physical science, nor perhaps by them chiefly. 
 It meets us in theology and in philosophy under the- form of 
 the quantitative infinite as a sublime attribute of the Deity, 
 or of soul life, or of the universe as contrasted with the ' finite ' 
 mind of man. We find it again in barbaric or vulgar art, in 
 as far as this relies for effect on mere magnitude, mere 
 evidence of expended labour, or mere costliness of material. 
 And we do also find it no doubt in a formulated shape wherever 
 matter and motion are invested with the dignity of real 
 existence in a sense and to a degree that degrades the indi- 
 vidual and concrete realities of life into something secondary 
 and fictitious. But it is plain that no such tendency is neces- 
 sarily involved in the treatment of these abstractions as real 
 characteristics of the perceptible world. There is no special 
 virtue in non-atomic continuous extension, nor any especial 
 iniquity in the resolution of material objects into systems 
 of vortex-rings, if such resolution either is a good working 
 hypothesis or represents a real fact. The only error is in 
 taking either a hypothesis for a fact, or a fact for the sole 
 fact — in confusion, not in mere abstraction. 
 
 The category of Quantity is, as we have seen, in its nature 
 wholly relative. It is therefore incapable of furnishing an 
 absolute and ultimate account of things. It not only cannot 
 escape from the reference ad infinitum from term to term 
 and condition to condition, but is forced to make this con- 
 tradictory conception the very basis and postulate of its 
 scheme. We have seen that the moment characteristic 
 quantity or proportion makes its appearance in the judgment, 
 as in any quantitative judgment it may, the whole between 
 parts of which the characteristic proportions obtain is tending 
 to exhibit itself as an individual synthesis of true differences, 
 not as a mere aggregate of indifferent parts. The pure 
 quantitative judgment or mere equation ^ is possible only by 
 abstraction from one aspect of the essential judgment-function. 
 
 ' An equation that embodies a characteristic proportion is not purely 
 quantitative. It involves in its interpretation the material differences 
 between the parts which are in the assigned ratios, e. g. between angle 
 and arc. See pp. 177-8, above. 
 
Chap. IV] Divergent series 195 
 
 It is not easy to find a parallel to so comprehensive and 
 systematic an employment of a single class of abstractions, 
 except in any attempt which may have been made to regard 
 the world as simply a congeries of qualities, say of pleasures 
 and pains. No such system indeed exists — ^the point of view 
 excludes system ; but one may conjecture of some such state 
 of feeling as forming the consciousness of children and childish 
 adults who have no judgment to pass on things, persons, or 
 events beyond the expression of their likes and dislikes. 
 
 Thus I have thought it desirable to treat as in some degree 
 co-ordinate developments the two series of judgments which 
 diverge from the simplest measurement or equation such as 
 a colour-match. On the one side we have the full evolution of 
 concrete thought, as it builds up the actual and individual world 
 within the series of relativity ; on the other side we have the 
 truncated evolution which embodies relativity almost pure 
 and simple, but, as the abstraction is never quite complete 
 (for then it would annihilate itself), may in particular matter 
 revive its relation to totality, as we see in the exhaustive 
 judgment of enumeration, and in the quasi-generic judgments 
 of geometrical classification. And in the same way the more 
 concrete judgment may in particular phases and under 
 particular stimuli borrow determinations from or generate 
 approximations to the abstract series. This happens when the 
 life of a nation is subjected to statistical treatment ; when 
 the disjunctive judgment is taken in the weakened form of 
 enumerated alternatives, and so gives rise to the calculus of 
 probabilities ; or when any one of the grooves or threads 
 of relativity which compose the perceptible world is taken as 
 a problem per se and tracked to its consequences by means 
 of a pure hypothetical judgment. 
 
 02 
 
CHAPTER V 
 
 Singular and Universal Judgment 
 
 Singular 
 Judg- 
 ment, 
 
 Indivi- 
 dual 
 Judg- 
 ment. 
 
 Judg- 
 ment 
 with 
 Proper 
 Name. 
 
 I. The transition from the singular to the universal judg- 
 ment is the transition from the affirmation of particular fact 
 to that of general fact. This transition may be expressed 
 by distinguishing two forms of the singular judgment, which 
 may be called respectively the Individual and the Corporate 
 Judgment. 
 
 i. In approaching the Individual Judgment we are returning 
 from the one-sided offshoots of measurement to the normal 
 and concrete evolution of the judgment. We saw in chap, iii 
 that it is the judgment of proportion which first reveals 
 individual quality ; that is, quality which, although particular 
 and characteristic, yet does not refuse to admit diversity into 
 itself and itself to enter into various contexts. This quality, 
 however, we found, if merely indicated as the content of an 
 abstract idea, stood in antagonism to the demonstrative 
 indication of present perception which alone could attach it 
 to actual reality. We found ourselves entangled in such 
 judgments as ' This oak-tree has a leaf-spiral of | ', ' This 
 teasel has the bracts longer than the head ', ' This tower 
 diminishes in width from story to story '. Such judgments 
 as these must rank as singular, for it is of their essence to 
 qualify present perception by the meaning of ideas ; yet their 
 content is really ambiguous, for, as we saw, the characterising 
 idea which ekes out the demonstrative reference to the 
 concrete subject tends to grow into a condition and to make 
 the judgment abstract, and in that sense universal. 
 
 a. The ambiguity which tends to split in two the im- 
 perfect singular judgment of the above type, which we have 
 ranked among the judgments of measurement, is apparently 
 removed in the class of singular judgments which we now 
 proceed to consider, and which are avowedly based on the 
 fact of recognisable individuality. Such are judgments whose 
 
Chap. V] Proper Name indicates Universal 197 
 
 subjects are designated by Proper Names. Enough has been 
 said in the Introduction of the essential nature of Proper Names. 
 We have now only to consider the logical value of the judg- 
 ments which are made by their means. 
 
 The determinate idea, present in the judgment of pro- 
 portion, is omitted in the judgment made by means of a 
 proper name. On the other hand, the demonstrative particle, 
 which by itself is helpless, being only an indefinite reference 
 to presentation, is replaced in the proper name by the indica- 
 tion, not to be effected without some kind of meaning, 
 of a particular individual. Thus it might be said that 
 the two elements of the subject in such a judgment as 
 ' That young soldier is the victor of Actium ' are fused to- 
 gether in the subject of ' Caius Julius Caesar Octavianus 
 is the victor of Actium '. But the union is effected at the 
 cost of a mutilation of the significance ; although as in the 
 present example the diminution of determinate content may 
 be more than compensated by the accession of suggested 
 ideas. Identification no doubt involves ideas, but with the 
 proper name, as we saw, identification is the end and ideas 
 are only the means. In unfamiliar matter, say in a chronicle 
 of remote date, we might conceivably identify the unknown 
 possessor of some name as figuring in several scenes or incidents 
 without being sure what he, she or it might be ; whether a 
 man or a woman, or a favourite horse. In this sense the 
 judgment that deals with a proper name is merely particular. 
 It has no meaning that can carry its application beyond the 
 unique individual to whom it is taken to refer. 
 
 But, though subject to this imperfection, yet Singular 
 Judgments of the class now before us form a real advance 
 on the Singular Judgment of Proportion. They rest upon 
 the fact of characteristic individuality capable of change 
 and persistence without sacrifice of identity. Instead of an 
 abstraction limited by pointing as if with the finger they 
 refer us to a unique * concrete thing in its continuous perma- 
 nence. In this sense, because attached to a continuous element 
 
 ■■^ I say ' unique ' because that is the purpose of the proper name. 
 Of course it has a general nature of its own, and cannot really guarantee 
 uniqueness. 
 
198 Singular and Universal Judgment [Booki 
 
 of reality not shut up within a particular time or a given 
 perception, the Individual Judgment is universal, and as we 
 shall see leads up to a transition which takes us in one respect 
 beyond the Singular Judgment. But universality — concrete 
 universality — is not, we must understand, antagonistic to 
 individuality. ' Caesar crossed the Rubicon ' is an Individual 
 Judgment ; yet in it we are not ^ confining the reference of 
 Caesar to the moment in which he was engaged in fording 
 the river. If we thus refused to refei the predicated content 
 to the whole extended identity of Caesai the significance 
 of the judgment would be destroyed, and an eristic error 
 committed by reducing an assertion to a tautology. Where is 
 the significance of crossing the Rubicon it we do not affirm 
 it of the conqueror of Gaul, the rival of Pompey, and the true 
 founder of the Roman monarchy ? Thus the judgment 
 regarding a person, place or other object that bears a proper 
 name introduces a reference that is determinate without 
 being abstract, and particular without being confined to 
 present perception. It should be observed that not all classes 
 of objects are suited to be distinguished by proper names. 
 This fact is akin to the inapplicability of significant names 
 indicating a thing to many objects endowed with material 
 existence. The range of proper names fall within that of 
 significant names of things, and the spheres of application of 
 these two kinds of S5anbols compared with each other and with 
 the sphere in which neither applies have a curious bearing 
 on the subject of individuality (see above, p. 128 ff). 
 J udgment /3. With these Individual Judgments must be classed all pre- 
 Name dications dealing with particular events, individuals, or objects, 
 andldeas. in which the demonstrative particle is dispensed with and re- 
 placed by a symbol referring to the individual. It will be found 
 that these particular events, persons or objects have ultimately 
 to be designated by reference to a proper name, or to some 
 symbol which nearly approaches the nature of a proper name. 
 As such e. g. may be ranked all chronological indications — 
 ' Christmas Day, 1885 a. d '. 
 
 It is obvious that such a symbol, or a proper name, as a 
 fixed point in history, may be supplemented by any amount 
 * Contrast Lotze, Logik, sect. 58. 
 
Chap. V] Personal and objective era 199 
 
 of definitely significant ideas ; and as the proper name or 
 the date is often understood or presupposed, e. g. in a con- 
 tinuous narrative, we. are apt greatly to under-estimate the 
 part played in judgment by the content of such symbols. Page 
 after page of discussion about political or social tendencies 
 may chance to be found in a reflective history, say in Lanfrey's 
 History of Napoleon, without the mention of a proper name. 
 But in so far as these discussions are to be taken as significant 
 of the actual conditions of an actual epoch, they are under- 
 stood as ideal content predicated of the nation, age and persons 
 with whom the narrative is concerned. Chronological symbols 
 exhibit the transition from the demonstrative to the proper 
 name in a peculiarly clear light. ' To-day,' ' yesterday,' ' last 
 year,' are just on the line between demonstratives and proper 
 names. ' To-day ' seems naturally to = ' This day ', a demon- 
 strative indicating mere relation to the percipient subject.^ 
 ' Last year,' ' twenty years ago,' show the relation to the 
 percipient subject growing into an objective system. And 
 when we come to the employment of an era, A.U.C,, B.C., 
 A.D., we have the system transferred from the accidental 
 percipient subject, and attached to the content of a proper 
 name. Wherever we have ' I ' or ' my ' &c., as points of 
 reference in narration, we are dealing with something between 
 a demonstrative and a proper name. And every narrative 
 judgment which goes beyond a mere impersonal or demonstra- 
 tive reference to present reality or to my own perception may 
 prima facie be said to involve a reference to some proper 
 name. No mere abstract idea can form the subject of historical 
 predication. How far this prima facie conception must be 
 corrected by allowing for judgments which may be capable 
 of uniting without mutilation the powers of unique reference 
 and of determinate notions is a question which will occupy 
 us in the sequel. 
 
 ii. Closely allied to the Individual Judgment, and perhaps Corporate 
 in rigid technicality not distinguishable from it, is what for ]^^^^ 
 
 * I take what I believe to be the actual meaning in use. Philology 
 may or may not support it as the original meaning. We are bound to 
 take philology into account as evidence of evolution and as a guide to 
 observation ; but it cannot override present usage. 
 
200 Singular and Universal Judgment [Booki 
 
 want of a better name I call the corporate judgment. This 
 title is meant to include all such affirmations as deal with 
 comprehensive totalities or aggregates which we bona fide take 
 in their corporate or singular aspect, and do not consider 
 either as in the collective judgment, in the light of sums of 
 enumerated particulars, or as in the hypothetical judgment, 
 in the light of mere abstractions whose very existence is not 
 absolutely postulated. Such a judgment may be expressed 
 indifferently by a singular or by a plural enunciation, so long 
 as the name used in the plural is a bona fide designation of 
 a known or knowable unity in respect of its characteristic 
 features : e. g. ' The ancient Greeks were at once a most 
 scientifically and a most imaginatively minded race.' This 
 judgment obviously = ' The Greek race was ', &c. This is 
 not a collective judgment in the sense which has above been 
 given to that title. It is not capable of being obtained by 
 successive synthesis of the component units — by enumeration 
 — and retains therefore no special extensional reference to the 
 individuals who as an aggregate constituted the ancient 
 Greek race ; it starts from the idea of a common stock as 
 a historical entity with peculiar endowments and with its 
 own rise, decline and fall. Other instances are such as ' Europe 
 has acted harshly to the modern Greek nation '. Europe is 
 here not a geographical expression, nor even a mere body 
 of nameable states ; it is an organisation acting upon definite 
 resolutions and through a known combination and proportion 
 of forces. Several states in geographical Europe probably 
 do not count in political or concerted Europe. Again, we may 
 say 'The House of Commons detests a bore'. This might 
 be transformed into * All members of the House of Commons ' 
 &c., but the two affirmations are only equivalent if the latter 
 is understood of the members qua members, i. e. as engaged 
 in debate in the House ; otherwise this latter becomes a 
 mere collective judgment, dealing with the members as a 
 collection of individuals who share two attributes, viz. 
 belonging to the House of Commons and hating bores, but 
 wholly neglecting any reference to the House in itself as a 
 single body with its own functions and peculiarities, among 
 which is the one predicated in the judgment. The glacial 
 
Chap. V] Historical realities 20i 
 
 period, The French Revolution, The Italian renaissance, The 
 solar system, are ' corporate ' realities and subjects of singular 
 judgments of the species of which I am now speaking. 
 
 The distinction between such individualities and those of 
 really single objects or persons such as form the subjects of 
 individual judgments is not a matter of principle, for in both 
 the existence of the subject is affirmed, or, as I prefer to 
 say, absolutely postulated. Nevertheless, the fact that such in- 
 dividualities as we have now before us do on one side consist 
 of immense aggregates of particulars, and are therefore capable 
 of being regarded at any moment from points of view antago- 
 nistic to that of their individuality, either as abstract ideas or 
 again as series of numerable units, makes it desirable to mark 
 by a specific distinction the fact that in their unity they can 
 be regarded as individuals. 
 
 On the other hand, the subjects in question are again not 
 easy to distinguish absolutely from the content of scientific 
 class conceptions whose individual unity and actuality are 
 disputable. The line which I have drawn is intended to 
 correspond with the distinction between history on the one 
 hand and truly physical science on the other. History deals 
 on the whole with contents into the essence of which time 
 enters, and which therefore, however comprehensive, are 
 ultimately particular within the phenomenal series. Abstract 
 science as a rule deals with timeless connections and systems 
 of attributes, though it will be necessary in exhibiting this 
 tendency to make allowances for a considerable admixture 
 of and recurrence to the historical attitude, for in the light 
 of evolution, time, or at least amount of change, enters into 
 the essence of most things. And besides Abstract Science we 
 must not leave out of account Classificatory Science on the 
 one hand and Philosophy on the other, both of which, though 
 in different senses, may claim to deal with actual realities. 
 
 The Corporate Judgment marks the fullest development 
 of the affirmation of particular fact, and at the same time a 
 near approach to the affirmation of general fact. In other 
 words, the affirmation with which we have so far been deal- 
 ing is beyond possibility of dispute Categorical affirmation, 
 treating of contents which the judgments affirm, or at least 
 
202 Singular mid Universal Judgment [Booki 
 
 absolutely postulate to be features that have or have had 
 actuality in the world continuous with present perception. 
 But from this point onwards the Categorical character of judg- 
 ments becomes a matter of theory and of analysis. There 
 is indeed, according to the scheme here adopted, no absolute 
 separation between the Singular and the Universal Judgment. 
 Still the distinction, unknown to Formal Logic, which is the 
 ground of that separation as made by recent writers, is the 
 basis of our scheme also. The Historical or Singular Judgment, 
 and a fortiori the perceptive or imperfect singular judgments 
 that precede it in our scheme, are not on all fours with the 
 judgments of science, whether classificatory or anal5rtical, or of 
 philosophy. Before attempting to trace in these latter types 
 of judgment the elements which we have observed in the 
 former, though in other proportions and combinations, it will 
 be well to examine more particularly the one leading difference 
 between the two chief stages of affirmation. 
 Time and iii. The Judgment that asserts particular fact coincides 
 in Singu- ^^^ ^^^ Categorical Judgment in the primary sense of 
 lar Judg- the latter title. According to the standpoint which for 
 the present we have adopted, a judgment is Categorical 
 when it asserts some thing or event to belong to the actual 
 world in which we live. This assertion is made both by the 
 Individual and by the Corporate Judgment. For the subject 
 in these judgments is something that can exist as a particular 
 reality, and is therefore taken or presupposed to be a real 
 particular, while at the same time its reality is so far deter- 
 minate that it can intelligibly be denied, which we saw not 
 to be the case with the ' this ', ' here ', or ' now ' of the Im- 
 perfect Singular Judgment. In these judgments, therefore, 
 though not necessarily in them alone, we have existential 
 assertion. And the simplest test of the presence of such 
 an assertion is to ask whether the non-existence in reality 
 of the content which enters into the judgment renders that 
 judgment false. To such a question the primary answer is 
 that at least in all judgments where time enters into' the 
 content — i. e. which assert facts in time — the non-existence 
 of this content renders the judgment false. And these judg- 
 ments will be found to be coextensive with the Historical 
 
Chap. V] The time in Predication 203 
 
 Judgment, affirming as it does not necessary connection, but 
 particular reality within the phenomenal series. And thus, 
 as said above, the Historical or Singular Judgment is equi- 
 valent to the Categorical Judgment in the sense here under 
 consideration. 
 
 This answer, however, demands explanation and limitation. 
 If non-existence of the content or subject of a judgment 
 renders the judgment false, we have further to ask. Non- 
 existence when ? 
 
 In every judgment we must distinguish between the time 
 of predication and the time in predication. The time of 
 predication, i. e. the time at which some thinking being makes 
 the judgment, is relatively to the content of the judgment 
 a mere accident, and alters actually while we are occupied 
 in judging, and a fortiori when the judgment is rethought 
 after a lapse of days or years. The time in predication is 
 the relation of the predicated content to the total content 
 of the temporal series of events which we construct and 
 contemplate as objective. The time in predication, if any, 
 is affirmed as an attribute by the judgment ; the time of 
 predication is not affirmed as an attribute by the judgment, 
 which therefore is not made false by any relations whether 
 negative or positive between its content and that time. 
 Hence it follows that the non-existence of the individual 
 subject or content which falsifies a Singular Judgment is 
 non-existence at the time in the predication, not non-existence 
 at the time of the predication. ' Thucydides is among the 
 greatest historians of the world ' is not false, although Thucy- 
 dides is in fact, when we speak, not a living man.^ ' The 
 House of Commons is an integral part of the British Con- 
 stitution ' does not depend for its truth on Parliament not 
 being in dissolution at the moment of predication, but only 
 on the co-existence of a House of Commons with the British 
 Constitution in the sense and to the extent demanded by the 
 
 ^ It may be objected that it is false to say ' Thucydides is a general in 
 the Peloponnesian war ', simply because Thucydides does not exist at 
 the time of predication. Where we have true tense this is so ; we have 
 then not got rid of the personal era. See p. 199. It must be remem- 
 bered that in ' Thucydides was ' &c., Thucydides is non-existent, and 
 yet the judgment is true. 
 
204 Singular and Universal Judgment [Booki 
 
 import of the judgment. It appears to be a corollary from 
 this principle that if no time in particular is involved in the 
 import of the judgment, which is the case at any rate with 
 geometrical truth, it becomes all but impossible to convict a 
 judgment of falsity on the score of non-existence of its content ; 
 although the demonstration of utter non-existence, i.e. I sup- 
 pose of impossibility, would so convict it. This bears on the 
 categorical character of the generic and hypothetical judgment. 
 A subtlety is introduced into the problem by the phenomena 
 of tense which include the time of predication, or a relation 
 to that time or personal era, within the content of the judg- 
 ment, and so within the allegation of time in the predication. 
 The content so superadded is of the most fugitive and relative 
 nature, and is constantly neglected even by historical narrative. 
 Picturesque history neglects it by the use of the historical 
 present, and philosophical history by the use of the logical 
 present. Nevertheless where a past, future, or true present 
 tense (neither historical nor logical) is intentionally employed, 
 its relation to the personal era or date at which the narrative is 
 drawn up beyond a doubt enters into the judgment and makes 
 an assertion which demands a particular limited existence on 
 the part of certain objects and events, and is false if this 
 existence is not as affirmed. In the case of the present tense 
 there is a peculiar subtlety arising from the confusion between 
 the atomic or nearly atomic and the continuous or ultimately 
 non-temporal present. The former is the import of the 
 present as a true tense ; the latter of the present as it 
 approaches to a mere vehicle of affirmation. Compare the 
 following examples : ' The Derby is being run at this very 
 moment ' ; ' The horses are leaving the paddock for the 
 Derby of 1861 ' (from a narrative written in 1883) ; ' The 
 Derby is run once a year ' ; ' The Derby race in England 
 is an instance of those customs which owe nothing to govern- 
 ment but yet amount to national institutions '. The first 
 of these judgments if true now must be false after the lapse 
 of five minutes. The second is only false if there was no 
 paddock or no Derby in 1861. The third is only false if at 
 the time of its predication the race has altogether ceased to 
 be an annual event ; but its present is well able to compre- 
 
Chap. V] Tens 6 and Personal era 205 
 
 hend within itself the intervals of time which the import of 
 the judgments admits and requires, and is not falsified by 
 reason of the non-existence of the race during these annual 
 intervals. And the fourth is false only if there never was 
 nor will be such a thing as a Derby race having the im- 
 portance alleged in English life. I am discussing of course 
 only how far the respective judgments become false if we 
 assume non-existence of the content ; I am not raising the 
 question of the material truth of the attributes enunciated. 
 It is only in the first of these four examples that we see the 
 present operative as a true tense. In the case of the past 
 and future the difficulty of tense does not arise in its full 
 extent ; the tenses which indicate them must of course 
 introduce the personal era, but for that very reason cannot 
 be confused with a mere form of predication, for which they 
 have not the appropriateness that the present possesses. 
 Therefore they do not risk the reduction of every possible 
 judgment to a statement about a momentary date or epoch, 
 which would be the result of neglecting the above distinctions 
 in the use of the present tense. And moreover, these very 
 tenses ' was ' and ' will be ' prove that it is at least not neces- 
 sary to the truth of a judgment that its content should exist 
 in the moment of predication. It is however necessary for 
 judgments dealing with past and future that their content 
 should have the alleged relation, however fugitive and acci- 
 dental, to the time of predication. But at any rate in none of 
 these cases, neither in present, past nor future, need the content 
 be shut up within the time of predication or the time related 
 to that personal era. Past and future do not pretend to be 
 momentary, and the present cannot possibly succeed in being 
 so. It must be credited either with duration in itself or with 
 a continuity that shades by degrees into the past and future. 
 Thus, though the time of predication has the slightest 
 possible relation to the content of judgments, yet no doubt, 
 when predicated as an attribute by help of true tense, a re- 
 lation to the time of predication or subjective era enters 
 into predication. And in so far as history as a whole falls 
 in the past, the use of the past tense in narrative bears true 
 witness to the essential particularity and limitation of the 
 
2o6 Singular and Universal Judgment [Book i 
 
 existences with which history deals. But after all, the past 
 is not a point but a line ; and so for precise temporal im- 
 port even of narrative propositions in the past tense we 
 must go, not to the tense, but to the import of the judgment. 
 And a fortiori this is the case with the present, where the 
 true tense is difficult to distinguish from the same tense used 
 as the mere form of predication. 
 
 We have thus seen in what sense and to what extent 
 Singular and Perceptive Judgments are identifiable with Cate- 
 gorical affirmation. The Judgment whose content involves 
 a limitation of time is plainly false if in the time-relation 
 prescribed by such a limitation its content is non-existent. 
 This test shows that all such Judgments are assertions of 
 particular fact. Even the example (on p. 204) which goes 
 beyond common historical usage nevertheless asserts fact 
 which is essentially in time, although the truth of the assertion 
 is not relative to the date of predication. If the Derby race 
 never existed the judgment would be false, and its existence 
 involves a multitude of temporal relations which are necessary 
 to its being what it is. It is essentially a fact in time. 
 
 When we get away from the proper name and the relations 
 of events in the temporal series, we find it much less easy 
 to say what non-existence of particulars, if any, would imply 
 the falsity of the judgment, and in what sense therefore, if 
 in any, the judgment alleges actual fact belonging to the real 
 world. We must bear in mind that we have up to this point 
 been dealing with unanalysed perceptions and with proper 
 names and their expansions. We have therefore not got rid 
 of the element of irrational concreteness which attends all 
 judgment whose subject is given as if by simple pointing 
 with the finger ; for qua a mere symbol of identification the 
 proper name itself partakes of the character of simple pointing ; 
 and until we reached the proper name we were encumbered 
 with the demonstrative particle. 
 
 Therefore the judgments thus far considered, omitting the 
 one-sided forms that arise out of measurement, possess certain 
 peculiarities. They assert, to begin with, the existence of 
 things or events in time. In doing so, they restrict and burden 
 with irrelevant matter the application of determinate ideas. 
 
Chap. V] Singular Judgments are false 207 
 
 which, as the only symbols of meanings, they cannot avoid 
 employing. Taken therefore as rational connections of attri- 
 butes, a point of view which determinate ideas challenge, 
 and towards which, as we saw, the import even of proper 
 names tends to develope, the judgments which we have been 
 considering are false, being burdened with irrelevant and 
 deficient in relevant matter. This is the same thing as to 
 say that they present an aspect of necessity, in which aspect 
 they are defective and so false. 
 
 2. By the title of ' Universal Judgments ' I mean to desig- The Uni- 
 nate, in all their phases of import, the assertions usually j^d^g! 
 typified by such well-worn examples as ' All men are mortal ', ment. 
 ' All fire burns ', and ' All triangles have their three angles 
 equal to two right angles '. It has been shown above that 
 perceptive and singular judgments, and more especially 
 those which employ proper names, possess an element of 
 universality as predicating identities into which differences 
 enter or which persist through differences. But in spite of 
 this fundamental unity of the judging function, the distinction 
 between the ' Singular ' and the ' Universal ' Judgment has 
 an importance for us which it has not for traditional Logic ; 
 which indeed treats the Singular and the Universal Judgment 
 as on the same level in a strictly logical point of view, and 
 both, consequently, together with the particular judgment, as 
 species of Categorical enunciation. The attitude which we 
 have to adopt towards this arrangement was defined in an 
 early part of the present book,-^ where we saw that it was 
 impossible for us to retain these species of enunciation in their 
 traditional relations. It is beyond a doubt that the Universal 
 assertion must at some point of its development assume in 
 some aspect or in some degree a hypothetical character ; 
 while if the genus Categorical, which certainly includes the 
 Singular Judgment, extends into or over the domain of the 
 Universal, it can only do so subject to reservations which 
 are unnecessary so long as it is confined to the judgments of 
 present perception or of simple narrative. 
 
 The Universal Judgment, then, is not distinguished from 
 the Singular Judgment by the mere feature of Universality, 
 ^ See supra, chap, i, p. 87 ff. 
 
2o8 Singular and Universal Judgment [book i 
 
 but by a special phase of Universality, that is to say, by 
 the predication of a universal law of connection. It has, indeed, 
 been obvious to us throughout the analysis of judgment that 
 universal connection was everywhere at work in the back- 
 ground, exploiting any qualification expressed or implied in 
 the Subject, for the benefit of systematic connection or 
 necessity, and at the expense of the simple perceptive or 
 narrative conjunction of contents ; untU, surrendering for 
 the moment the task of intelligible qualification of reality, 
 we fell back, in the proper name, on an attempt at unique 
 designation.^ But here again we faU to escape from universal 
 connection or necessity, and in the names of illustrious indi- 
 viduals, as in those of nations, epochs, or movements, we have 
 found that every significance tends to break down the mere 
 conjunction of data, and to exhibit itself as a connection of 
 reason and consequent. We attempted to draw the line at 
 events and individuals into whose content time entered, and 
 to show that judgments dealing with such matters as these 
 were inevitably allegations of fact, and not of abstract connec- 
 tion. Now we adhere to this distinction, and it is perfectly 
 true that any fact which is especially involved in one portion, 
 however extended, of the temporal series of phenomena, must 
 have existence within that portion if an affirmative judgment 
 about it is to be true. The assertion of such a fact in its 
 accidental concreteness is therefore radically different from 
 the assertion of a mere law or relation, and if taken in this 
 latter sense would necessarily be false. But we found in the 
 corporate judgment that it was not perfectly easy to distinguish 
 the facts of history from the truths of science ; for sets of events 
 greatly extended in time appear to pass by a sort of sorites 
 into sets of events which, though in respect of existence 
 precisely on all fours with actualities limited in time, are 
 nevertheless either not treated as relative to time or really 
 are not held to be so relative. In order, while marking the 
 
 * I have said above (Introduction) that I do not give this as a his- 
 torical account of the genesis of proper names, which must no doubt 
 have been appUed and recognised by a gradual differentiation. But 
 none the less, wherever language has fixed them as a class of words, 
 they perform the function and are subject to the modifications indicated 
 in the text. 
 
Chap. V] Generic and Hypothetical 209 
 
 distinction demanded by the absence of limited particularity, 
 to give full weight to the continuity of import between these 
 types of judgment, I shall not follow Lotze and other modern 
 writers in identifying the universal ab initio with the hypo- 
 thetical judgment. I shall prefer to distinguish within it two 
 species, of which the first, the generic judgment, alone belongs 
 to the main evolution of thought, and the second, the pure 
 hypothetical, is regarded as an abstraction of a quasi-mechanical 
 character, and consequently as a divergence in the direction 
 of the arithmetical and geometrical judgment. 
 
 i. The generic judgment is the qualification of reality under The 
 the aspect of a Natural Kind by attributes or relations incident generic 
 to that Kind. A Natural Kind is for our purpose a Kind ment. 
 accepted and treated as such by any science. We have 
 already seen that the geometrical sciences are in this respect 
 in a peculiar position, and we have discussed the limits under 
 which their quasi-generic judgments may be taken to embody 
 truth about actual reality. The question of alternative 
 classification, which arises on account of the different points 
 of view introduced by different sciences, was treated in the 
 Introduction, and should cause us no difficulty if we are once 
 able to understand the nature of the truth embodied in any 
 science. For every science employs some abstraction and 
 idealisation, though there is an all-important difference of 
 degree between contents which are merely abstract as not 
 sensuous, and contents which are abstract as not concrete. 
 
 The restriction ' incident to that kind ' is not intended to 
 exclude relations which one kind shares with other cognate 
 kinds. A purist logic, following a suggestion to be found 
 in Aristotle, might indeed require that every generic judg- 
 ment should be ' commensurate ' or characteristic. It would 
 then have to deny that the possession of breathing apparatus 
 was incident to man, because he shares the respiratory 
 function with the whole organic world. Such a view would 
 be illustrated by the fact which was commented on above, 
 that e. g. the animal properties of man are, in man, modified 
 by their relation to his humanity ; so that in order to represent 
 them as features of man they ought ideally to have certain 
 modifications assigned to them, while in their abstraction 
 
 1337 p 
 
210 Singular and Universal Judgment [BookI 
 
 they can 'only be set down as characters correlative to the 
 no less abstract idea of animality as such. But this prin- 
 ciple seems needlessly purist. The attributes which man 
 shares with the animal world are elements of identity, however 
 partial, between him and it ; and there can be no reason 
 against characterising him by these identities which would 
 not tell equally against any knowledge which falls short of 
 perfection. The rule to be borne in mind about such cases 
 is that imperfect knowledge only becomes /a/se when mistaken 
 for perfect knowledge. In as far therefore as the form of the 
 judgment implies a truth completely adequate to its subject, 
 something may be said for the view which has just been stated. 
 But we shall find if we press the matter home that this ideal 
 is to be regarded as the vital principle active in knowledge, but 
 not as hostile to any genuine fact that is free from confusion. 
 
 Under ' incident to the kind ' then are included the attributes 
 and relations which lie at the root of the individuals' being, 
 although shared by them with individuals of other kinds, or 
 even with mechanical or geometrical wholes. It is only to 
 be borne in mind that such relations, e.g. the characters of 
 vertebrate organisms, are not thought as mere abstract 
 properties, when applied to specific kinds, but are regarded 
 as concrete schemes presenting both a general and a specific 
 aspect. It is in this characteristic of graduated identity that 
 the intelligible order of the world reveals itself to us. 
 
 The generic judgment has always been the battle-field 
 of confhcting logical tendencies, corresponding to actual needs 
 and features exhibited in various points of view by the 
 judging activity. I shall endeavour, on the same plan which 
 I have hitherto pursued, in some measure to satisfy these 
 tendencies by distinguishing as different, in phase and line 
 of evolution, intellectual acts which are often reckoned as 
 one and the same. But it follows from the nature of thought 
 that all such aspects have a real connection, and are in fact 
 rather distinguishable than separable. Thus in distinguishing 
 the generic judgment from other acts of thought we shall 
 also be analysing this many-sided judgment itself and justify- 
 ing to some extent the views of those who have recognised in 
 it only one or other of its many sides. 
 
Chap. V] Allficss and Necessity 2ii 
 
 a. The Generic Judgment — the Universal Judgment of The 
 common hfe and of classificatory science — was regarded by Vf^V- . 
 Aristotle, as is well known, under two connected aspects, as Judg- 
 a judgment of Allness and as a judgment of Necessity. The ™^"*- 
 former of these aspects has been seized on by formal logic, 
 and the doctrine of logical universality has been adapted 
 mainly to the consideration of subject and predicate as names 
 or ideas applicable to groups of individuals. We examined 
 the judgment from this point of view, as dealmg with an 
 aggregate arising out of enumeration, in a former chapter. 
 We there saw its actual goal in the Collective Judgment and 
 its reversion towards a more concrete and natural mode of 
 thought in the Exhaustive Judgment, which amounts to 
 nothing but a Generic Judgment very strictly taken in exten- 
 sion. It must however be remembered that we did not think 
 it possible for any judgment, however closely confined to an 
 aggregate resulting from enumeration, to avoid characterising 
 the individuals by a common attribute, and predicating an 
 attribute of them. Attributes are enunciated by extensional 
 no less than by intensional judgments ; but in the latter they 
 are connected with attributes, in the former they are centred 
 in the identity of individuals. Therefore it is possible to con- 
 sider the Generic Judgment as differing from the Collective 
 Judgment simply in degree, viz. by predicating attributes of 
 an unknown or unlimited and not of a known or determinate 
 aggregate, the actual means of predication being in both cases 
 alike a general attribute, though in the latter case attached to 
 reality by a proper name or its equivalent. But an unknown 
 or unlimited aggregate of individuals is a contradiction,^ a 
 numerical problem which proclaims itself insoluble by enu- 
 meration, and therefore the judgment which is couched in this 
 shape, and which in fact conveys a perfectly intelligible mean- 
 ing, must derive this meaning from some other source than 
 from such an enumeration as that on which the collective 
 judgment rests. The Exhaustive judgment must be inter- 
 preted by the Generic and not by the Collective. 
 
 Examples of the Quasi-collective judgment of which we 
 are speaking are — ' All men are mortal,' ' All organisms both 
 * See p. 1 66, supra. - 
 P2 
 
212 Singular and Universal Judgment [Booki 
 
 breathe and assimilate,' ' All unstriped muscle in the human 
 body is inaccessible to the control of the will.' Tliis last 
 example, however, is suggestive. The Exhaustive judgment, 
 i. e. the Generic judgment in its aspect of ' allness ', is helpless 
 in the face of the most trivial exception. Thus ' Nearly all 
 striped muscle is under the control of the will ', but the muscles 
 of the heart form an exceptional case, and, though striped, 
 are normally inaccessible to volition. Nevertheless there can 
 hardly be a doubt that the coincidence expressed by the 
 judgment must indicate some sort of connection, however 
 circuitous, between the appearance of the muscle and the 
 degree in which it is under control, and that the exceptional 
 case must be accounted for by special conditions. But on 
 its purely enumerative side the judgment has nothing to say to 
 this ; it only knows that the sum-total of Enumerative judg- 
 ments cannot be made, and the judgment of allness is therefore 
 unwarranted. It is obvious that the affirmation of universal 
 connection which in such an instance we feel to be all but 
 warranted is not approached from the side of the individual 
 units, but from the side of the common or continuous nature 
 which binds them into a whole. 
 True /i. As dealing with a common or continuous nature the 
 
 Generic Generic judgment may be more properly expressed in the 
 ment. form, ' Man is mortal,' ' Water boils, under one atmosphere, 
 at 212° Fahrenheit,' ' A society organised on a purely com- 
 mercial basis treats the working classes as little better than 
 slaves.' These propositions are accepted as practically equiva- 
 lent to ' All men are ' &c., ' All water ' &c., ' All societies ' &c. 
 Here however it is plainly the connection of attributes that 
 warrants the affirmation concerning individuals and not vice 
 versa. When thus regarded, the Generic judgment challenges 
 comparison with the Singular judgment in both its forms, both 
 as Individual and as Corporate. 
 Ordinary «. ' Man is an animal capable of social life,' ' The bacillus 
 OT^T"^' ^^ ^ septic organism,' ' Throughout the vast Orchidean order, 
 logical including 433 genera and probably about 6,000 species, the 
 nient' ^^^ °^ fertilisation is almost invariably left to insects.' These 
 are affirmations that unquestionably refer to something real, 
 but yet employ neither perception nor a demonstrative nor 
 
Chap. VI Abstract, in Form and Content 213 
 
 a proper name. Therefore, prima facie, it seems as if the 
 determinate idea had come to its rights, and were no longer 
 obscured by any irrelevant elements of the phenomenal 
 concrete. The act of thought ought, it would appear, to fall 
 at once into the groove of abstract necessity : ' // man, then 
 social; ' ' // Orchid, then insect-fertilised.' But ideas such 
 as those now before us offer a resistance to such treatment. 
 The determinate idea is abstract, indeed, as all thought is 
 abstract, but nevertheless it may have a content which is 
 concrete, and in the example before us we have such concrete 
 contents. These, therefore, bear the morphological character 
 of individuality, by which alone even the unique object named 
 by a proper name is made recognisable, persistent, and so 
 universal. Compared with such an individual subject the 
 Generic subject has lost unique reference ; but it has gained 
 abstract significance, with which the proper name was in- 
 compatible. And it is in virtue of this significance, the 
 significance of individual self-completeness, that the Generic 
 subject persists as an identity through the differences which 
 form its attributes. Now the individuality when reduced to 
 a content is not single, but exists in instances. Thus, in 
 attaching differences to the individually characteristic content 
 as such the judgment goes altogether beyond the synthesis 
 of differences in an actual individual subject, and affirms such 
 a synthesis mediately of a number of subjects, which may 
 be taken as endless seeing that its limit is at this stage not 
 held essential and not enquired after. Such a judgment, 
 which treats a concrete individuality as an abstract universal, 
 and extends its incidents to all individual instances, may be 
 described as an analogical judgment. And this is the funda- 
 mental nature of the ordinary Generic assertion. 
 
 The introduction of the term analogy into the theory of 
 judgment may indeed be objected to on the ground that 
 analogy is a kind of inference. But the fact is, that apart 
 from any general question of a connection between judgment 
 and inference, we are now at any rate on the threshold of 
 an activity of judgment in which inference is unmistakably 
 present. All that we can do in order to avoid a premature 
 discussion of inference is to approach the analogical judgment 
 
214 Singular and Universal Judgment [Booki 
 
 rather as a conclusion the content of which is open to analysis 
 than as a complete inference whose process lies before us. 
 It may be added, that logic is quite familiar with the idea 
 of ' necessary ' judgments. Yet necessity involves inference 
 far more explicitly than does analogy. 
 
 In the analogical or ordinary generic judgment, then, we 
 have neither implied reference to perception as in the im- 
 personal judgment-form, nor the demonstrative ' this ' or 
 * that ', ' here ' or ' there ', nor a conventional implication of 
 unique reality by means of a proper name. The subject — 
 I speak of the immediate subject or subject within the judg- 
 ment — is an idea, and qua idea, is abstract. But we must 
 distinguish between abstractness as incident to thought in con- 
 trast with sense-perception, and abstractness as a character 
 attaching to contents present in thought. In the former 
 way of speaking all thought is abstract. In the latter, 
 some is abstract and some is not. The ideas which form 
 the subject of the generic judgment in the phase now before 
 us are not abstract in the latter sense. They are ideas 
 of totalities, existences complete in themselves, to which we 
 cannot indeed venture to apply the conceptions of teleology 
 proper except in so far as the wholes in question are products 
 due to the human mind, but which must be regarded from 
 the standpoint of that secondary finality which may be 
 described as morphological unity or quasi-teleology. We 
 have thus a character or complex of attributes which is at 
 once general and indi\'idual, abstract in thought and concrete 
 in content. As abstract, it defies enumeration of instances, 
 and implies necessary sequence or connection of attributes. 
 As individual and concrete, on the other hand, it refuses to 
 be taken as a mere ideal antecedent in a relation of necessity, 
 i. e. of reason and consequent. The conciliation demanded 
 by these antagonistic elements of import is found in the 
 judgment of analogy. The essence of this judgment is that 
 it is neither purely subsumptive, as expressing a de facto 
 conjunction of attributes in a single subject, nor purely con- 
 structive as expressing a de jure connection of attributes inde- 
 pendent of the immediate subject in which they may exist, 
 but is something intermediate, as expressing a perception or 
 
Chap. V] MoYphological Unity 215 
 
 presumption that the content enunciated in the judgment is 
 bound up with the characteristic individualit}'' which forms the 
 immediate subject. 
 
 The ultimate foundation of any such insight must be the 
 final cause or teleological idea of the individual, which how- 
 ever, when considered as an immanent or embodied final 
 cause, is most prudently treated on the level of morphological 
 character. We may indeed safely say that the purpose or 
 final cause for which we make a microscopic lens is to combine 
 magnifying power with light and definition, and from this 
 purpose, by help of a number of further judgments dealing 
 with optical and mechanical truths, the physical attributes of 
 a good lens may be constructed. But in dealing with things 
 not made for a known purpose we cannot apply any such 
 abstract rule, and must fall back on the idea that the thing 
 discharges an actual function, or at least looks as if it had 
 a function, which must be taken as immanent and identified 
 with the thing in its concreteness. The judgment that 
 pronounces what is involved in this content and what is not 
 rests on the presumption of the individual unity of the content, 
 and on the capacity of discerning from the structure of this 
 unity aided by empirical knowledge of instances what is 
 essential to it and in what degree. The insight in question 
 has undoubtedly some kinship to aesthetic judgment, for both 
 depend on the power of seizing the concretely presented 
 import or principle of unity of a concrete whole. To judge 
 the structure of a fossil creature from a vertebra, or to detect 
 the affinity between two zoological species which are externally 
 much modified, is a sjmthetic apprehension of the same nature 
 as that which realises the construction of a picture or of a 
 drama. Such judgment, however, is merely the condition 
 precedent, and not the essence, of the true relation between 
 the mind and fine art. 
 
 The analogical judgment, like the aesthetic judgment, is 
 essentially outside relativity and necessity, and incapable of 
 being resolved into them. It is true that judgments of abstract 
 relation, drawn from the mechanical or geometrical sciences, 
 are perpetually coming in aid of analogical truth, by indicating 
 that this or that de facto service within the concrete individual 
 
2i6 Singular and Universal Judgment [Booki 
 
 can only be performed by its parts under this or that condition. 
 To support a certain weight the plant stem or spinal column 
 must have adequate strength. To impel a certain bulk and 
 mass through the air at a certain velocity the bird's wings 
 must have a certain area and striking rate, the arrangements 
 necessary to which of course react on the whole muscular 
 circulatory and respiratory apparatus. But even this merely 
 rhetorical selection of an abstract final cause is really unjustifi- 
 able. Which comes first ? why such a weight on the stem ? 
 why should the bird's body have such a bulk or mass ? There 
 is nothing to fix any one of these elements as a given final 
 cause to which the others must be adapted. Adaptation 
 to the bird's prey or the like is again simply de facto. An 
 animal might have to change its prey by reason of a change 
 in their relative powers, just as probably as it might develope 
 new powers to keep pace with those of its prey. And further, 
 in the background we may see such a law as that of the Conser- 
 vation of Energy dominating the entire system and operations 
 of everything that moves. In all these relations we observe 
 the ultimate character of necessity, viz. the reference of a 
 subject to a whole other than itself ; e. g. the treatment of 
 an animal as a part in the whole of moving matter, or as a 
 figure having properties in space, so that in each of these 
 relations it appears as determined by the character of a totality 
 other than its concrete self. The nature of space for instance 
 is per se a datum or fact ; but when it determines the results 
 entailed, e. g. by the shape of a leaf, it is exhibited as a whole 
 prescribing the relation of its parts, which relation as regarding 
 something that is not merely a part in space is external but 
 constraining and so necessary. 
 
 Yet even if the entire construction of an individual con- 
 tent were laid before us in terms of mechanical analysis, 
 still the analogical judgment would force itself upon us, as 
 the aesthetic judgment would in a parallel case. Analogy 
 would then indeed no longer be the chief instrument in dis- 
 covery, or at least in presumption of universal connections, 
 because these would be capable of constructive apprehen- 
 sion of a more direct and relevant kind. Such a state of 
 knowledge niay already in some degree be illustrated by 
 
Chap. V] Individuality as a Result 217 
 
 the Darwinian analysis, say, of an orchid-blossom, in as far 
 as it succeeds in tracing the mechanical modifications, which, 
 each of them representing a definite physical adaptation to 
 some external circumstance, have generated the present 
 structure of the flower. The same observation might even 
 be applied to the identification of types and their affinities. 
 The mechanical history of any organic structure would, if 
 ideally complete, include the nature, degree and physical 
 causes of its deviation from kindred structures. 
 
 But all this would not interfere with the import of the 
 generic or analogical judgment. For this import consists in 
 the identification of individuals with a concrete content, and 
 such an identification involves connections which differ in 
 kind from the identification of abstract relations which are 
 not Things. They take the content not in its external relativity, 
 but in its relation to self or to an immanent final cause — a 
 final cause identical with itself. We have examined this self- 
 relation in the more difficult case of geometrical figures which 
 are absolutely and adequately reducible to examples of general 
 conditions, and seem merely to mimic the self-contained 
 relation of the concrete thing. This relation is an element 
 of import which does not wholly disappear even in those 
 kinds of existence which are hardly ranked by common 
 language in the category of individual things — as we saw to 
 be the case e. g. with the elements, and in short with all un- 
 organised substances. I do not restrict the meaning of the 
 term unorganised to = ' inorganic ' in the technical sense ; 
 l3ut I employ it to designate any portion of matter, organic 
 or inorganic, which is not shaped into a whole by human 
 activity, or regarded in respect of its natural subordination 
 of parts with interest due to its unity for our intelligence. 
 Every element has no doubt its peculiar minute structure, 
 and every fragment or portion of matter has no doubt its 
 spatial or other relations which unite it into a whole. A pebble 
 or a bit of rhomboidal spar or a nugget of gold has a self- 
 relation, a characteristic peculiarity which makes it single, 
 and distinguishes it as a persistent universal from things 
 external to it. Much more has any organism a typical indi- 
 vidualitv which introduces the distinction of inner and outer, 
 
2i8 Singular and Universal Judgment [Book i 
 
 essential and relative, into what as a mere example of general 
 laws has no self-relation -^ and no inner or outer. 
 
 And in these last two sentences I have omitted the strongest 
 case, because it is so strong as to dispense with the reservation 
 which we were trying to illustrate. But when we come to 
 reflect on the conception of a thing, we must be struck with 
 the fact that by far the greater amount of what we most 
 readily recognise under that title are objects made by man 
 for purposes which he consciously embodies in their structure. 
 I cannot think that, apart from our familiarity with such 
 objects, the conception of a thing would seem so simple as 
 it does. A mountain, a waterfall, a wave of the sea, are things 
 chiefly to the aesthetic perception ; and if we left this percep- 
 tion out of account, it would not be easy to assign the bound- 
 aries of their individuality, or to single out its essence. Com- 
 plaint has been made ^ that those who lay stress on the 
 progressive interpretation of the idea in nature do not find 
 room in their theories for the achievements of the screw and 
 the lever, and for the laws of the equilibrium of fluids, of 
 pressure, and of tension. These examples may be regarded 
 in two aspects. The screw and the lever are best known to us 
 as tools, in which capacity they belong to the sphere of mind, 
 as objects endowed by human foresight with an immanent 
 significance depending on their adaptation to a determinate 
 purpose. But as mere characteristics of matter mechanically 
 considered they rank with any of its general attributes, — 
 rigidity, gravity, inertia, — attributes which are the basis of 
 all material organisation, but do not by themselves suffice 
 to give individual interest to any fragment in which they are 
 embodied ; and among such attributes must be ranked equi- 
 librium of fluids, and the effects of tension or of pressure. 
 
 But what are we to say of the shell that screws itself into 
 the sand, of the screw propulsion exerted by the porpoise's 
 tail, or of the levers which form the limbs of animals ? We 
 
 ^ Of course such a point of view is unreal in its abstraction. If the 
 thing were absoiutelj' regarded without self -relation, its external 
 relation would be gone too, for what would there be to determine it ? 
 Tlie point is that the centre of interest, in relativity, falls outside 
 the self. 
 
 " Lotze, Mikrokosmus, English Translation, vol. i, p. 17. 
 
Chap, v] DouUe Import of Mechanism 219 
 
 dare only speak, in relation to such phenomena, of a de facto 
 purpose or actual function. In virtue of this function, this 
 contribution to an obvious and real end, the total life and 
 motion of the animal in which they are found, we claim for 
 these arrangements a morphological unity which forces us 
 to grant them the character of elements in things that have 
 concrete individuality. We dare not ascribe to them the 
 unity of an ideal purpose, as we safely may to the screw of 
 a micrometer or to the lever of a balance ; but we treat them 
 as elements in a unity analogous to that with which M^e are 
 familiar in objects that represent the purposes of our mind. 
 The rudest mechanical contrivance is in this respect on a 
 level with the products of fine art and superior to those of 
 nature, that it unites the abstractness of thought with the 
 concreteness of sensuous existence ; i. e. while in one aspect 
 a mere material object, yet in another it embodies an idea, 
 and does so determinately and without irrelevancy. 
 
 Thus the conception of machinery has a double and not a 
 single import for logic. If on the one hand it accents the 
 fact that matter is indifferent to our purposes and simply 
 acts and reacts according to its own nature — and it is this of 
 which we are constantly being reminded as the mechanical 
 or uniform aspect of the world — yet on the other hand it is 
 the most obvious example of a concrete embodiment of mind 
 in matter, and corroborates if it does not awaken the reflec- 
 tions of the understanding on the rationality of things. Of 
 this rationality the existence of individual types as concrete 
 universals recognisable by the analogical judgment is a higher 
 phase, a phase more akin to individual intelligence, than 
 matter in its abstract and general modes. And therefore 
 the generic judgment resting on analogy, i. e. on the perception 
 of concrete identity of content, is not capable of being super- 
 seded by the abstract judgment of pure relativity. The latter, 
 if ideally complete, gives a true account of what occurs in 
 terms of mass and motion, but necessarily omits the teleo- 
 logical or quasi-teleological import which gives the content of 
 the judgment its interest and significance for knowledge. 
 
 I \\i\\ analyse a single example. Exogenous trees display 
 ' annual rings ' in the wood, which are due to the augmented 
 
220 Singular and Universal Judgment [Book i 
 
 pressure of the bark as each year's new wood expands the stem, 
 resulting in the flatter formation of the outer and later cells 
 in every year.-*- As this stands I call it a generic or analogical 
 judgment. It is indeed based on one of the above-mentioned 
 simple mechanical relations, the effect of pressure ; but it pre- 
 dicates this relation within a concrete individuality which gives 
 it an import that as a mere mechanical problem it would not 
 possess. Let us reduce its essential points, however roughly, 
 into the latter shape. We shall obtain some such residuum 
 as this : ' A fabric gradually constructed under increasing 
 pressure out of a material which hardens after a time will 
 show increasing effects of pressure in its later-formed portion.' 
 Here we have, in part at least, 'freed the direction,' to borrow 
 an expressive phrase from Bacon, i. e. stripped off circum- 
 stances which are irrelevant to the production of the effect 
 in question. But with these irrelevancies we have lost in the 
 case before us not merely confused concomitants of percep- 
 tion, but the interest which gave the example its place in 
 knowledge. The fabric is no longer wood, the gradation no 
 longer that displayed in the annual rings of timber, the subject 
 of the judgment is no longer reality embodied in the character- 
 istic individuality of the exogenous trees. The import of the 
 judgment is gone. ' But its content is subsumed under the 
 simple mechanical relation, if this is rightly understood.' 
 Perhaps ; but what does this mean ? If the import of the 
 concrete thought is to be saved, it must mean that the 
 analogical judgment is re-thought in its full depth, but with 
 the explicit knowledge that it includes the abstract mechanical 
 relation. The typical character of exogenous trees, though 
 we must not call it a final cause, yet prescribes the extension 
 and gives a definite reference to the content of the judgment. 
 And I must here put the reader in mind, that, wishing to gain 
 notliing from what may be called accidental ignorance, I have 
 laid no stress on the present impossibility of constructing any 
 living thing on purely mechanical principles. Individuality 
 rests on a difference, not on a confusion, of categories. I am 
 
 ^ Probably other causes concur in this process. I have purposely 
 simplified it. The rings are annual only if the period of growth in the 
 year is single. A second hot season may cause a second ring. 
 
Chap. V] Distinction of Categories 221 
 
 convinced that no organic nor spiritual movement accessible 
 to human intelligence is without a mechanical aspect. I have 
 therefore treated the present subject from a point of view 
 which admits such an aspect to be knowable in all vital and 
 spiritual processes. This point of view may seem absurdly 
 fictitious when we consider the present state of exact explana- 
 tion in the sphere of biology, or again of social science. The 
 generic or analogical judgment now has, and seems likely 
 long to retain, what we may describe as a secondary function ; 
 a function not merely of interpreting but of predicting — not 
 merely of resuming sensible facts under higher categories, 
 but of anticipating their actual occurrence. In- all science 
 that deals with subjects beyond our power to construct, we 
 draw our conclusions by means of analogical judgment in 
 this secondary sense. When we judge a particular plant of 
 deadly nightshade to be poisonous, or a particular red stag 
 to be dangerous at a certain time of year, we are judging on 
 analogy ; on an anticipation based upon a concrete character 
 whose particulars we cannot construct. The precise nature 
 of these inferences will occupy us in the theory of inference ; 
 it is plain that the larger part of inexact science consists of 
 them. 
 
 We must not confuse analogy in that secondary sense, 
 as a mere anticipation of nature,^ with the true generic or 
 analogical judgment which is compatible with complete 
 analytic perception of mechanical cause and effect within the 
 subject considered. We have perfect examples of these latter 
 judgments in the case of things made by man for a purpose ; 
 in which a complete and accurate perception of their structure, 
 interior causal nexus, and inevitable course of movement in no 
 way supersedes the summary of their import which a knowledge 
 of then: purpose enables us to embody in a generic judgment. 
 When we wind up a watch of which we know the construction, 
 we do not merely anticipate that it will go because we have 
 seen other watches go ; we can point to the specific causal 
 connections by which it must (excluding accidents) result 
 that the main-spring, unwinding itself, will draw round the 
 wheels ; that the motion passed through the wheels will at 
 ^ Anticipatio naturae. — Bacou. 
 
222 Singular and Universal Judgment [Booki 
 
 one point be regulated by the escapement, &c., &c. If we 
 knew nothing of the use of a uniform measure of succession, 
 but had some experience in mechanics, we should be quite 
 certain that the watch must go, but we should have no notion 
 of its generic content — we should not know ' what a watch 
 is,' i. e. what its purpose is. We could not therefore make the 
 pure generic judgment, ' A watch is a motion regulated by 
 an escapement so as to maintain a uniform rate.' In order 
 to this judgment we must know the purpose of the instrmnent, 
 viz. to maintain a uniform rate. With this knowledge however 
 we are in a position which, in strict theory, we can never 
 attain with regard to any natural product. We can dictate 
 the generic import of the watch ; we can say that if any watch 
 possesses this import imperfectly it is a bad watch ; if it 
 possesses it not at all, it is not a watch at all. 
 
 Judgments such as this form the ideal to which the universal 
 judgment in the form now under consideration always aspires. 
 The properties expressed in such judgments are not merely 
 anticipated or presumed ; they are, or at least may be without 
 altering the nature of the judgment, deducible with the utmost 
 rigour. Yet, again, they are not mere causal sequences ; it 
 is possible to have before us all the causal sequences concerned 
 in the object, and yet not to make the true generic judgment 
 which unites them into a coherent system. In this class of 
 objects we may fearlessly say that it is the purpose^ which is 
 the essence, and that generic judgment rests on the knowledge 
 of essence. In all other classes of objects such a view has 
 degrees of precariousness, and can only be applied to the 
 purpose as immanent, and therefore as not determinate, and 
 as uncertain in its boundaries. Nevertheless, when we predi- 
 cate in the organic world ' growth ', ' development,' ' self- 
 preservation,' ' irritability,' we are really referring mechanical 
 processes to an idea of life — an idea of self -relation, of ' inner ' 
 and ' outer ', which is a higher result, though it is a result, of 
 their purely mechanical nature. 
 
 " Such a purpose or essence, however, ia limited, and e. g. excludes 
 the means, and therefore part of the whole which embodies it. Teleology 
 in this current sense, therefore, cannot be used as a principle in explain- 
 ing any whole, e. g. the universe. 
 
Chap, V] Affirmation in Generic Judgment 223 
 
 The above is the best account that I can give of the normal 
 generic judgment, which represents the really central pheno- 
 mena that were designated under the title of Universal Judg- 
 ment by Formal Logic. The point of view which emerged 
 in comparing this Universal \\dth the Collective Judgment, 
 and which was suggested by the quasi-collective form of the 
 plural subject \vith ' All ', can never have been really felt to 
 include what the judgment intended to affirm. But, as was 
 said above, ' allness ' is undoubtedly an aspect of universality. 
 
 h. In order to bring to a focus the nature of this judgment Existeu- 
 we have now to consider how its affirmation is to be classed ^^ °ieaa- 
 — whether as asserting the existence of fact, or the connection 
 of attributes. 
 
 To determine this question, we must recur to the distinc- 
 tion laid down above -^ between abstractness as a character of 
 thought in contrast with sense-perception and abstractness 
 as belonging to a kind of thought as distinguished from con- 
 crete thought. Abstractness in the former sense is compatible 
 with individuality, while in the latter sense it is not ; and it is 
 in the former sense that we apply the term abstract to the 
 ideas which are subjects in the generic judgment. Thus 
 though we have no longer a proper name as in the singular 
 judgment, yet we have a concrete idea, which being as a whole 
 capable of reality, presupposes such a reality. We saw that 
 in the case of the demonstratives 'This', 'Here,' &c. the 
 reality which is the immediate subject cannot be intelligibly 
 taken as affirmed to exist, but only as presupposed. The 
 ideal qualification which sometimes accompanies such demon- 
 stratives showed us the point at which presupposition of 
 existence tends to pass into affirmation, simply because a 
 significant presupposition can be intelligibly denied. But this 
 tendency is never absolutely fulfilled. The union of actual and 
 ideal qualifications in the demonstrative judgment — e. g. ' This 
 bad man,' for though he were a good man he would still be 
 this — always leaves the ideal qualification the option of being 
 read as a condition. The proper name, again, in its primary 
 function, being void of determinate meaning, presupposes 
 rather than affirms the existence of its content. It only tells 
 * p. 214, supra. 
 
224 Singular and Universal Judgment [Booki 
 
 you that some individual is in question ; and you cannot deny 
 that an individual may be in question. But then as the proper 
 name becomes more charged with import, which may even 
 be made explicit in ideal contents as it is in the Corporate 
 Judgment, it also becomes as we saw capable of conditional 
 meaning. Now as the primary function of the proper name 
 can never be cancelled while it remains ' proper ', there arises 
 •within the singular judgment a parallel ambiguity to that 
 which arises within the demonstrative judgment. The pre- 
 supposition that reference is in any case made to actual 
 existence is at war with the determinate qualification which 
 can and will only refer to some determinate existence that may 
 or may not be forthcoming. A determinate, i. e. significant, 
 ideal qualification standing as or in the subject of a judgment 
 is never unambiguously affirmed to be an actual existence. 
 It may always take refuge in a conditional meaning. The 
 reference to actual existence is presupposed in the sense 
 possible for the subject ; in perceptive judgments because 
 we are never without perception, and in singular judgments 
 because the form of the subject-idea suggests an individual, 
 and reality consists of individuals. 
 
 The independence of these two kinds of qualification, ideal 
 and existential, and their consequent liability to contradict 
 one another, is the very root both of existential and of 
 conditional affirmation. In existential afiirmation the two 
 qualifications are taken as meant to coincide, though it is a 
 purely material assumption or assertion that they do so ; in 
 conditional affirmation the two are allowed to fall apart, i. e. 
 the ideal, qualification is not read as implying an individual 
 reality that possesses it. 
 
 Returning now to the concrete idea which stands as subject 
 in the generic judgment, ' society,' ' man,' ' art,' ' the bird,' 
 ' the rose,' ' a time-piece,' ' a telescope,' we find the same 
 elements of meaning, but in reversed proportions. The subject 
 here consists technically and primarily of ideal qualification 
 and nothing more. It has reference neither to an unnamed 
 perception nor to a unique individual undetermined by abstract 
 significance. Hence the presupposition that the subject is 
 an actual reality is less prominent, while the abstract con- 
 
Chap. V] Existential and Conditional 225 
 
 ditional import of the ideal content is more so. In the earlier 
 types of judgment we feel that we are referring to reality, 
 and we assent with reluctance to the analysis which shows us 
 that our reference is conditional. In the more abstract forms 
 at any rate of the generic judgment we feel that we are af&ming 
 conditionally, and we at once acknowledge our reference to 
 actual reality to be merely implied or presupposed. It will 
 be noticed that I do not admit this side of the antithesis to 
 be completely developed in the simpler generic judgments. 
 I do not think that in * The rose has pinnate leaves and 
 perigynous flowers ' the existence of the subject is merely 
 ' implied ' and not ' asserted '. It is not uncommon to find in 
 a manual of botany such and such a variety ' is no doubt 
 a mistake of the observer ', which shows that the observer's 
 description asserts existence so far as existence is asserted by 
 any judgment.^ All this however is a mere question of degree. 
 What I am here concerned to show is that the mere impli- 
 cation or presupposition of real existence, to which in one way 
 or another we do undoubtedly come in the Universal Judgment, 
 is not extraneous to the affirmation and dependent on a mere 
 fancy or habit of ours, but is the lineal descendant, mutatis 
 mutandis, of that so-called existential affirmation which we 
 have traced in perception and in narrative. And the strength 
 of this implication depends on the concreteness of the idea 
 which here forms the immediate subject in judgment. We 
 have then here as before two elements in the content, or rather 
 a content regarded in two lights. We have self-relation, 
 existence, or a categorical aspect, and external relation, 
 necessity, or a hypothetical aspect. But the nature of the 
 generic affirmation, as analysed above, shows for the first 
 time a trace of reconciliation between these two points of 
 view. The concrete self-relation is no longer void of meaning 
 and purely designative ; it is a system of assignable import, 
 and the analogy of which we have spoken is the anticipation 
 or the insight based on this import. But again, this analogy 
 introduces relativity and necessity, and as we saw interprets 
 
 ^ It may be said that in such a case the observer has alleged the plant 
 to have been found in a given spot at a given time. But this is not 
 essential ; he may simply send in the description. 
 
 1337 Q 
 
226 Singular and Universal Judgment [Booki 
 
 relations that unite the individuality in question with other 
 totalities which prescribe to it either conditions or purposes. 
 Thus the generic judgment is categorical in respect of its 
 concrete self-relation, and hypothetical or necessary in respect 
 of the analogical or constructive nexus to which the import of 
 that self-relation gives rise. 
 
 But, it will be objected, this might be all very well if we 
 were speaking of individuals, whose nature is to be unique, 
 like the present King of England, or the centre of the material 
 universe ; but here we are speaking of an indefinite set or 
 series of individuals whose common nature is nothing and 
 nowhere but in them. This is, it may be urged, Scholastic 
 Realism over again. What existence does a generic judgment 
 presuppose, when and where ? In reply to such an objection, 
 I insist in the first place that we cannot treat any imperfection 
 of knowledge as incident to knowledge unless we can prove 
 that it necessarily is so, and that to treat a natural kind as 
 an indefinite set or series of individuals is an imperfection of 
 knowledge which can be shown not to be necessary. This 
 consideration however belongs to the subsequent section. 
 
 But in the second place I reply that even without treating 
 a kind as an actual unity, and though in fact we do not treat 
 it so in judgments which are true of each individual singly 
 (as common generic judgments are), yet still the individuality 
 of the content dictates its own time, place and measure of 
 existence. And it is this time, place and measure, wholly 
 without reference to subjective era,^ place or fancy, that is 
 affirmed^ in generic judgment. It is characteristic of the 
 rose to exist in a certain epoch of evolution and within certain 
 limits on the earth's surface. Existence within this time and 
 place, subject to such variation as the nature of the content 
 allows, is what the generic judgment affirms (or implies) of 
 the rose ; that is to say, in affirming that ' the rose has 
 
 * See above, p. 204, discussion on tense in judgment. 
 
 " I should not object to replacing ' affirmed ' by ' implied ', in order 
 to mark the unquestioned line between the singular and the universal 
 judgment, if it were admitted that the implication is an integral part 
 of the judgment, and not a fancy of our own. The point is that existence 
 is implied or affirmed in these judgments, just as Necessary connection 
 is implied or affirmed in Perceptive and Singular judgments. 
 
Chap. V] Existence of a Kind 227 
 
 perigynous flowers ' we mean that individual actual roses, 
 found within these limits, have the attribute in question. If 
 there are none such, then the rose is like any genus or species 
 that has been imagined to exist by a mistake of identifica- 
 tion ; the kind in question would in that case not exist, and 
 the judgment would beyond question be false. Of course 
 in every-day subjective judging the place and time &c. of 
 existence is but roughly indicated by what we happen to 
 know or believe about the actual subject of judgment, but 
 it is never referred to the time or place in which we judge, 
 unless per accidens our knowledge is limited to, or the con- 
 tent especially concerns, that time and place. Rose in the 
 abstract does not exist. But it is a concrete universal which 
 has power, in the context of the real world to which we refer 
 it, to dictate the epoch, place and quantity of its individual 
 embodiment. 
 
 I need hardly guard myself against the misapprehension 
 that I am alleging that anything and everything exists which 
 we choose to fancy. I am maintaining just the opposite, 
 viz. that if we attempt to embody fancied realities in judg- 
 ment, such judgment is false ; for all judgment is a definition 
 of real reality. We can only escape this result if the fancied 
 content is such as is in its logical nature debarred from being 
 real, i.e. a mere abstraction, and is therefore incapable of 
 claiming to stand for a reality. 
 
 c. The reality involved in a concrete universal will be Indivi- 
 made plain by insisting on a third aspect of the generic judg- Generic 
 ment, viz. that in which it challenges comparison with the J"dg- 
 Corporate Judgment. For this purpose we must think of 
 generic judgments which are not merely analogical, but which 
 for want of a better term I may designate as Individual. 
 These judgments are characterised by not being true of any 
 and every individual singly, but only of the kind taken as 
 an individual. Such judgments are, ' The animal world 
 represents an evolution coordinate with that of the plant 
 world,' ' The Orchidean order includes 433 genera and probably 
 about 6000 species,' ' Space has three dimensions,' ' Humanity 
 is the object of worship to Positivists,' ' Monarchy disappears 
 with the advance of civilisation.' 
 
 Q2 
 
228 Abstract Quantity [Booki 
 
 In comparing such judgments as the above with that form 
 of the Singular Judgment which we called the Corporate 
 Judgment, we find at first sight little distinction between 
 them beyond the fact that these Generic Judgments do not 
 employ a proper name in the subject, whereas the Corporate 
 Judgments do. And even this distinction is in some degree 
 bridged over when we call to mind that such determinations 
 as ' now,' ' last year,' * this,' and ' mine ' appeared to us 
 essentially to rank either with proper names or with demon- 
 stratives ; and also that there is a tendency on the part of 
 proper names themselves to assume abstract significance, so 
 that a proper name is not always easily distinguished from 
 a generic name. The Greek race, Europe, are proper names ; 
 but it is more doubtful how we should class ' the Aryan 
 languages,' ' the North Pole,' and ' the Mahometan religion.' 
 Again, ' the earth,' * the solar system,' seem free from all 
 arbitrary reference ; but in speaking of them we really imply 
 ' our earth,' ' our solar system,' and so fall back into some 
 form of the singular judgment. 
 
 The difficulty is worth noticing ; but it is simply one of 
 those which must arise from the Sorites-like character of 
 any continuous evolution. It is hard to say whether ' the 
 Mahometan religion ', as we mean to employ the term, involves 
 a reference strictly of the order of a proper name,^ or on the 
 other hand is simply an ideal content, and, so far as ideal, 
 abstract. The reason of this is that the conception is in fact 
 on the border-land between the proper name and the mere 
 determinate content, and in all probability it is sometimes 
 employed in the one sense and sometimes in the other. The 
 question is whether the general meaning or the individual 
 identification comes first in the mind. As we saw above, it 
 is not improbable that in primitive careless and unscientific 
 thought the significant word is not made distinct from the 
 proper name — in other words, the intension which is the 
 
 * In every case we must keep etymology out of the question. The 
 reference to Mahomet as a historical individual is certainly not the chief 
 element, and perhaps hardly an essential element at all, in the direct 
 significance of ' Mahometan ' at the present day. Compare the rhetorical 
 antithesis that has been drawn between ' Christianity ' and ' the religion 
 of Jesus '. 
 
Chap, v] Propcv Name and Generic Name 229 
 
 mere means to identification is the only intension signified, 
 but for this very reason the purpose of identification is not 
 distinguished, so as to be considered primary, from the purpose 
 of definition. In fact, when we now speak colloquially of 
 ' the bay mare,' ' the low pasture-field,' we are using ' bay ' 
 and ' low ' merely as signs of identification, though of course 
 by help of their meaning. Such is the type of usage which 
 we may imagine to have been the common root of the signi- 
 ficant and the proper name. The terms of the Linnaean 
 arrangement of plants, in as far as they are subservient to 
 mere recognition, are a somewhat similar case in point. 
 
 But when all deductions are made, there remains a clear 
 distinction of principle between judgments which use proper 
 names, and judgments which do not. From this point of 
 view the generic judgments now before us agree with those 
 last discussed and contrast with the singular judgment. 
 They are able to convey their reference to reality by means 
 of a determinate ideal content. 
 
 On the other hand, in the nature of their reference to reality 
 they agree with the singular judgment and differ from the 
 common generic judgment. They do not rest on analogy. 
 The individual to which they refer is a real and a single 
 individual, and not a mere individuality. So far from being 
 mediated predications about a number of particulars they 
 are not even true of the particulars that enter into their content. 
 When we said, in the former section, ' The rose has perigynous 
 flowers,' we were treating the individuality of all roses as one 
 by analogy .-"^ But when we say, ' The rose family is a descen- 
 dant of X, a divergence from y, and a transition towards z,' 
 such a judgment is not made about each particular plant 
 
 1 Subtlety of transition must have an end somewhere in writing, but 
 in fact it has none. Thus the reader may object that if it is nonsense 
 to say that the rose family as an actual individual has perigynous 
 flowers, yet we may always safely say in such a case that it prescribes 
 that the particular rose shall have perigynous flowers. I can only 
 admit the objection ; the fact is so if we are bona fide regarding the 
 genus as a whole of evolution, whose actual individuality expresses 
 itself in this and in other common predicates. But if, as is most probable, 
 we realise nothing of the kind, but are merely going by analogy to 
 a common property of roses, then we are treating the kind as a mere 
 individuality, and must not pretend to be treating it as an individual. 
 
230 Abstract Quantify [Booki 
 
 within the tribe, nor even about each particular species. If 
 true, it is true of the whole section of plant-life in which every 
 particular rose-plant is a distinct and separate progressive 
 or divergent phase. There can be no doubt, I think, that from 
 an ideal point of view every natural kind in the concrete 
 sensible world must be thus regarded ; and of course when 
 we consider existences in which intelligence is more definitely 
 active — society, mankind or at least civilised man, fine art, 
 or morality — in these phenomena the totality is more real and 
 concrete, and the reciprocal relations of its parts exist not 
 merely for the microscope of analysis, but as patent every-day 
 facts. 
 
 Although universal, the Generic judgment in the aspect 
 now before us is fully Categorical. It is in this respect wholly 
 on a level with the Singular judgment, being in fact related 
 to the judgment of Analogy with its dual nature much as 
 the Singular judgment is related to the proportional or 
 comparative judgments that are introduced by a demonstra- 
 tive. The Singular judgment may be regarded as a premature 
 attempt to concentrate individuality — the ' characteristic 
 quality' which the proportional judgment had revealed — into 
 an individual ; resulting as we saw in the omission of deter- 
 minate quality from the individual content by the use of 
 Proper Names. The generic judgment raises (in its Analogical 
 form) and meets (in its Individual form) the same problem 
 m a more adequate way, concentrating individuality into an 
 individual by completion and not by omission. It is as a 
 system of such individuals, united perhaps in a yet more 
 concrete individual reality, that we must conceive of the 
 world known to us through space and time, if we are to assign 
 it any existence beyond the present of presentation. For us, 
 it is plain, such individuals are intellectual constructions, and 
 only attached to, not shut up within, the actual present 
 perception. The distinction between concrete realities and 
 abstract truths is not, for us at any rate, that the latter are 
 intellectuall}^ initiated and the former are not ; it is not a 
 question of origin, but a question of nature, i. e. of the degree 
 in which a content is capable of being regarded as something 
 that exists as a whole and can be considered in relation to 
 
Chap. V] Generic as Categorical 231 
 
 itself, or on the other hand is incapable of being given as a 
 whole and affords no matter for consideration in relation to 
 itself. All contents must theoretically be regarded as com- 
 bining these two characters ; and as an important application 
 of this idea I may instance the answer to a question which 
 arises when we make the categorical nature of assertion 
 depend upon the degree of concrete self-relation. 
 
 Is it possible, we shall be asked, to lay down a hard and 
 fast line, by which abstract shall be divided from concrete 
 contents ? And if not, does not our view surrender the self- 
 dependence of reality and make it purely relative to fancies 
 and notions in the individual mind ? Does it not enable us 
 to treat as actual any content however abstract or trivial, 
 and any however concrete or significant as a mere element 
 in hjqjothesis, simply by varying the point of view from 
 which we regard them ? And the answer is, that as reality 
 unites these two characteristics, we can always emphasise 
 either at will ; and further, we commit no error in so doing, 
 unless we assume and assert the relation which we happen 
 to be considering to be the only relation that there is. Our 
 knowledge always falls short of reality, and apart from false 
 identification of relations — with which false antithesis is at 
 bottom the same — we have a right to see all that we can 
 either of absoluteness or of relativity in any content what- 
 ever. Reality is such that any element or feature of it, how- 
 ever slight or superficial, can be raised by our intellectual 
 gaze to the position of a self-related significant whole. The 
 nature of mind is present in everything ; the only difficulty 
 is to see it there. And such an elevation is not false, except 
 in as far as it is exceptional ; in as far^ that is, as we fail to 
 view the remaining contents of reality with the same con- 
 structive insight. Not merely a fragment of stone or metal, 
 but a colour, a curve, a relation of size or weight, is ideally 
 capable of being passed through the stages of generic judgment, 
 of being regarded first as an individuality, and then as an 
 individual. What is false or forced in such a mode of con- 
 templation depends on the want of proportion between it and 
 our ordinary careless vision of organisms and fine art, of men 
 and of society. All contents are relative except the absolute ; 
 
232 Abstract Quantity [Booki 
 
 but the import and degree of their relativity is not the 
 same. 
 
 A further corollary may be worth drawing in a few words 
 from the above considerations. Our present treatment of 
 logic starts from the individual mind, as that within which 
 we have the actual facts of intelligence which we are attempting 
 to interpret into a system. But our consequent preoccupation 
 with the phenomena of the individual mind, with its imperfect 
 grasp of reality and the varying aims and tendencies of its 
 thought, brings with it a double danger which haunts every 
 phrase and every idea in a logical treatise. Either one may 
 speak as if reality were simply relative to the individual mind, 
 a ridiculous idea, but one which the very caution required 
 of a modern writer is apt to encourage ; for he hardly dares 
 to allude to Mind as such or in itself ; or one may become 
 interested in tracing the germination and growth of ideas in 
 the individual mind as typical facts indeed, but only as one 
 animal's habits are typical of those of others, and so we 
 may slur over the primary basis of logic, which is its relation 
 to reality. For mental facts unrelated to Reality are not 
 knowledge, and therefore have no place in Logic. The difficulty 
 is, in other words, simply that modern Logic has a hard task 
 to hold its own between Metaphysics and Psychology. I 
 entertain no doubt that in content Logic is one with Meta- 
 physics, and differs if at all simply in mode of treatment — 
 in tracing the evolution of knowledge in the light of its value 
 and import, instead of attempting to summarise its value and 
 import apart from the details of its evolution. My object 
 however in mentioning the difficulty at this point is merely to 
 protest that though I assume reality as the norm of the mind, 
 in constructing which it is reconstructing and not creating de 
 novo * out of itself, yet I can entertain no doubt that intelli- 
 gence is essential to the being of Reality, and that an abstraction 
 which tries to regard the one apart from the other is a hope- 
 less and helpless self-contradiction. As a working conception 
 
 * See ii, p. 319. Reconstructing, for me, never meant representing 
 or copying. And thought is as creative as anything in the universe 
 can be. But creation de novo is a contradiction in terms, because 
 it forbids the conception of a creative nature, and so of any interest 
 or continuity throughout reality. 
 
Chap. V] Logic and Metaphysics 233 
 
 in Logic we are forced to adopt some such idea as that of a 
 normal intelligence operative in all human minds, but subject 
 to the accidental limitations of each. The evolution of know- 
 ledge is, as Plato long ago portrayed it, the emancipation of 
 individual minds from their accidental limitations, and their 
 education into the knowledge of the one real and intelligible 
 world.* But the duty of modern science is to preserve the 
 continuity of this evolution, and to admit no saltus at any 
 point between the world in which we live and the world 
 which is real and intelligible. And in this continuity we 
 have a standpoint which Plato, although he reached it, did 
 not consistently maintain. Objective Intelligence presents 
 itself in Logic as the mere postulate required by such a 
 continuity, and, starting as we have done from the indi- 
 vidual consciousness in time, it is merely as a postulate 
 that we propose to treat it. To say that the real world 
 is the intelligible world is only to repeat what we found 
 ourselves obliged to suggest as an elucidation of the earlier 
 stages of judgment, that reality is something at which we 
 arrive by a constructive process.^ 
 
 We are now to consider the consequence of emphasising the 
 abstract or relative aspect of the Analogical judgment. We 
 are thus led to a form of thought which is antithetical to the 
 Individual Generic judgment of which we have just been 
 speaking, and consequently must be regarded as a divergence 
 from the concrete evolution of thought towards the mechanical 
 or analytic judgments which begin with enumeration. 
 
 " It does not seem necessary in Logic to develop this point further. 
 A ' first philosophy ' would have more to say about the sense in which 
 the one Real world is intelligible, and would not admit that the limita- 
 tions of individual niinds ought to be called, in principle, accidental, 
 little as we may be able to explain them. 
 
 ^ See above. Introduction, p. 38 ff. 
 
CHAPTER VI 
 
 Universal Judgment [continued) 
 
 ment 
 Its rela- 
 tion to 
 previous 
 forms. 
 
 Pure Hy- ii- The Universal Judgment, when pushed to the extreme 
 pothetical point of abstraction, becomes the Hypothetical Judgment.* 
 a. The Hypothetical Judgment is distinguished from all 
 which have thus far been spoken of, by its essentially abstract 
 character ; abstract not merely as thought is said to be 
 abstract when compared with sense-perception, but as the 
 
 * A word must be said on the distinction between Conditional and 
 Hypothetical propositions, to which Mr. Keynes, following Mr, W. E, 
 Johnson (Keynes, p. 249), attaches much importance. 
 
 Conditionals, as I understand, affirm a connection between pheno- 
 mena, and their elements are events or combinations of properties, the 
 connection of which in a subject or in time or place is affirmed. Hypo- 
 theticals have for their elements independent judgments, propositions 
 of independent import, a relation between the truth or falsehood of 
 which is affirmed. The characteristic phrases of Conditionals are 
 ' Whenever,' ' In all cases in which,' ' If any — then that.' The unam- 
 biguous form of a Hypothetical is ' If — is true, then — is true.' 
 
 I think this distinction tends to obscure the meaning of the pure 
 Hypothetical. I note some points : 
 
 ( 1 ) I do not see why the elements of a pure Hypothetical should be 
 taken as propositions or judgments. Its characteristic, I hold, is to 
 trace a tliread of logical necessity, and I see no gain in throwing the 
 sequence into the form of two or more propositions. And this opinion 
 encourages 
 
 (2) the idea that true Hypotheticals coincide with what I have called 
 'broken-backed sequentes ' (p. 236 below), the propositions retaining 
 their full meaning when separated from one another (Keynes, p. 251). 
 For the criticism of this view I may refer to my discussion on p. 236. 
 
 (3) It would have made a neat series if we could have said that 
 Categoricals (in shape) are only assertorical and existential ; Con- 
 ditionals (adding ' Because,' ' Since,' to the above-mentioned phrases) 
 unite modal, assertorical, and existential meaning ; and true Hypo- 
 theticals are modal only. But Mr. Keynes rejects any such distinctions, 
 which are indeed incompatible with usage. Therefore I see little or no 
 raison d'etre for the class of Conditionals. It is hard enough to dis- 
 tinguish Categoricals (in shape) from pure Hypotheticals. 
 
 (4) I am glad to agree strongly that it is not the differentia of propo- 
 sitions of the type If A is B, C is D, to imply doubt. 
 
 (5) The student will distinguish from the doctrine I am discussing 
 
Chap. VI] PuYC necessity 235 
 
 thought of an ideally isolated attribute is abstract compared 
 with the thought of a self-dependent and self-related indi- 
 vidual. It represents the fourth of the elements or aspects 
 which have been confounded, or at any rate have not been 
 duly distinguished, by traditional logic within the so-called 
 Universal Judgment. Its differentia is that it does not refer 
 to a concrete subject, not even to what we called an indi- 
 viduality or the concrete self-related content in its aspect 
 of self-relatedness ; and that consequently we do not consider 
 whether its subject is given in actuality or not. For it is 
 essentially the judgment of necessity or relativity, in which 
 the subject is taken, not given, and taken not for its own sake 
 nor with reference to its individuality, but for the sake of that 
 which is to follow from it, that is, for the sake of its relativity. 
 It is a judgment which follows out the single thread of a 
 nexus of attributes, and does not heed the import of the 
 pattern into which it enters. If a gravitating body is set free 
 to fall, it falls with an acceleration proportional to the squares 
 of the times, whether it is a drop of rain, or a tortoise with 
 the head of Aeschylus below it. Here we have, in an explicit 
 shape, the relativity of knowledge which has haunted us 
 throughout the evolution of judgment, forbidding us to feel 
 satisfied in connecting together any data whichwe might merely 
 chance to light upon in conjunction, and requiring that every 
 idea should always be limited and controlled by its reference 
 to something else, and not simply taken as we find it in percep- 
 tion or in ordinary life. And just because this principle has so 
 haunted us, the judgment that embodies it cannot be sharply 
 severed in meaning from the earlier forms of the universal 
 judgment, and even the quasi-collective ' All gravitating 
 bodies &c.' may, and most frequently in this case does, contain 
 what is really meant as a hypothetical affirmation. ' In this 
 case,' for the distinction really goes, as we have maintained 
 all through, not by the shape of the proposition, but by the 
 content of the judgment. The connection however between 
 all the t5rpes of universal judgment is intimate and essential, 
 
 Mr. Bradley's view that all judgments are conditional, i. e. that there is 
 always a supplement, which is never completely known, necessary to 
 make the predicate fully true of the subject. Appearance, ed. 2, p. 361. 
 
Form. 
 
 236 Universal Judgment [Booki 
 
 so that in popular usage one easily slides into the other, or 
 even combines the other with itself as its ground or conse- 
 quence. When I say ' All animals need food ' I am probably 
 expressing a quasi-collective conclusion about a property 
 shared by all species of animals, taking its significance from 
 an analogical perception of the generic function and immanent 
 purpose of animal life, but ultimately resting on the hypoihe- 
 tical judgment, expressing a necessary or relative principle, ' If 
 force is to be expended it must be supplied.' It will be observed 
 that the second type of generic judgment, which for want of 
 a better name I have called Individual Generic, is omitted 
 from this combination of aspects. It represents a tendency 
 divergent from that of the Hypothetical assertion, while 
 the Analogical judgment is undecided between the two. If 
 the Individual Generic judgment is capable of combination 
 with the Hypothetical, we must look for the result in the 
 Disjunctive and not in the Universal affirmation. 
 External ^. The type of the Hypothetical Judgment in traditional 
 logic, so far as it is recognised at all, is stated in one of three 
 forms : ' If A is B is ; ' ' If A is B, then C is D ; ' and ' If 
 A is B, then it is C The third of these forms is that which 
 guides us to the true import of the judgment, though con- 
 formably to the habitual irrelevancy of popular thought the 
 second is that most commonly in use. But this second is 
 obviously a broken-backed sequence, in which no point of 
 unity is formally recognised between the antecedent and 
 the consequent. When, indeed, significant words are sub- 
 stituted for letters, the unity would generally be obvious, 
 supposing the sequence to have scientific value at all ; but 
 in such a case the expression is not essentially distinguish- 
 able from that of the third form. The first form, ' If A is 
 then B is,' has been said to be an abbreviation in which letters 
 stand for clauses ; in that sense of course it must be reducible 
 to either the second or the third form. We get the same 
 result if we try to take it as a combination of single-word or 
 impersonal predications. Contents may undoubtedly be 
 ascribed in judgment to an unanalysed present, but an 
 unanalysed present can form no bond of union for a necessary 
 sequence. ' If guilty, then death ' is a mere linguistic abbre- 
 
Chap. VI] Exprcsston of Nexus 237 
 
 viation for ' If he is guilty then he will be put to death '. And 
 even ' Where there is smoke, there is fire ' superadds to the 
 impersonal ' There is ' a true local particle in the ' where ' 
 of the antecedent, and this reacts by a curious equivocation 
 on the impersonal ' there ' of the consequent. No doubt, 
 but for the unpleasantness of the sound, we should say, 
 ' Where there is smoke, there there is fire.' Here again, then, we 
 have in essential meaning the third type of the Hypothetical 
 judgment, ' If A is B, it (A) is C I will next illustrate the 
 transformation of type ii. into type iii. ' If the barometer (A) 
 falls (B), the weather (C) becomes stormy (D).' ' If the 
 atmosphere (A) decreases its pressure locally (B), it (A) must 
 leave a gradient for wind (C).' But now if we take the lines, 
 
 ' . . . when in Salamanca's cave 
 Him listed his magic wand to wave, 
 The bells would ring in Notre Dame,' 
 
 we find that the salfus from antecedent to consequent is all 
 but essential to the judgment ; the point of the mystery is 
 that we cannot get at the underlying unity. Thus we see 
 the extreme case of type ii. in a judgment which has for its 
 object to assert magical, i. e. irrational, connection. Of 
 course the general scheme of reduction would have to be, 
 ' When his magical power (A) was exerted (B), it (A) could act 
 at any distance (C).' It is in this sense that Schopenhauer 
 calls some of Euclid's demonstrations conjuring tricks, 
 because, although in a demonstration some unity of course 
 must be shown between antecedent and consequent, yet 
 the unity shown is often not central or fundamental,^ and 
 is therefore a causa cognoscendi, and not a causa essendi. 
 In the pure type, ' If A is B, then C is D,' we have no indi- 
 cation even of a causa cognoscendi. 
 
 Much more might be said about the forms of conditional 
 sentence ; but the subject is really grammatical rather than 
 logical, for the hypothetical judgment can be expressed 
 without a conditional sentence at all. Hypothetical and 
 Categorical Judgment, as we understand the terms, are 
 a question of content, not of grammatical form, and the 
 hypothetical judgment is found wherever we frame asser- 
 
 ^ Schopenhauer, Werke, i. 1 36 fif. 
 
238 
 
 Universal Judgment 
 
 [Book I 
 
 Assertion 
 made by 
 Hypo- 
 thetical 
 
 Judg- 
 ment. 
 
 The 
 idea of 
 Ground. 
 
 tions about an abstract content, in the above sense of abstract- 
 ness ; although there is a difference of adequacy in different 
 grammatical expressions for any kind of judgment, and the 
 conditional sentence resists any attempt to embody in it 
 a purely categorical meaning. ' If this man dies, our cause 
 is lost,' takes ' this ' as a sign of unanalysed content and not 
 as a point of attachment in reality. We know that the 
 reason is somewhere in the unanalysed content, and so take 
 it as an antecedent in the lump.-^ 
 
 y. What is the precise nature of the assertion conveyed 
 by a Hypothetical Judgment ? In answer to this question 
 I shall speak first of the idea of Ground or nexus in general, 
 secondly of Ground as compared with Cause, and thirdly 
 illustrate our view by the attitude of the individual mind in 
 hypothesis or supposition. 
 
 a. The contrast which we have anticipated throughout 
 the above account of judgment determines the central 
 attribute which we are now to consider. The content of 
 a true hypothetical judgment is abstract ; abstract in itself 
 and not merely by the absence of sensuous perception. In 
 other words, the subject of a hypothetical judgment is not 
 an individual, not a whole, nor anything considered as a 
 whole, i. e. as a self-related system. On the contrary, the 
 content of a hypothetical judgment is composed of ground 
 and consequent, each referring to something other than itself, 
 and hence essentially a part. For a system as a whole, such 
 as space, or the totality of gravitating matter, or the British 
 Constitution, is a mere fact, complete in itself, and neither a 
 ground for nor a conclusion from anything else.^ It is only 
 as parts within a system that elements can be so relative to 
 one another that ' if this is so, then that must be so'. 
 
 It is only a question of detail how far the system in and 
 by which the nexus subsists, is itself made explicit as a content 
 within the hypothetical judgment. We may say, if we like, 
 
 ^ I take this analysis, which appears to me exceedingly felicitous, 
 from Bradley's Principles of Logic, pp. 89-90. 
 
 " This applies to the examples given only when considered with 
 reference to their internal nature. It may be said that space implies an 
 intelligence ; but this is as within a further whole. There is, of course, 
 no ultirhately Absolute whole except the Absolute whole. 
 
Chap. VI] Gfound as Identity in System 239 
 
 that the ideal of logical sequence demands that the system 
 as a totality should be so made explicit, because the system 
 is the real ground of the nexus ; and if the system does not 
 appear in the content, the real ground does not appear in 
 the content. But this argument, from the comprehensive- 
 ness of the real ground, does not overcome the essential 
 principle which is inyolved in there being a ground, as ground, 
 at aU. Ground implies a consequent other than, though 
 fundamentally one with, itself. This transition or otherness 
 ceases to exist if the content does not formally present itself 
 as part to part. For say that the totality of the system is 
 explicit in the ground, still this totality is depressed into the 
 relation of a part by the fact that a part is selected to appear 
 over again as consequent, and so as formally at least external 
 to the ground. Thus it remains true that the elements of 
 content in a hypothetical judgment are related as other to 
 other within an identity which determines the one on the 
 basis of the other. Such an identity, as far as exhibited in the 
 one term that, in virtue of it, determines the other, is what 
 we mean by Ground. It is obviously capable of all degrees 
 of completeness up to the ultimate fact or whole which 
 embraces in itself as parts both ground and consequent 
 commonly so called. The various degrees of imperfection 
 or broken-backedness in Hypothetical judgments, such for 
 instance as were illustrated in the last section, are simply 
 the degrees in which the system that determines the nexus 
 fails to manifest itself within the content connected. It 
 must not be forgotten however that we have refused to 
 treat the grammatical form of propositions as decisive of 
 the character of judgments. Where no rational nexus is 
 traceable, but only a coincidence in fact, however general, 
 we cannot admit that the essentials of hypothetical judgment 
 are present. But then if we are impelled to make a judgment 
 in h5^othetical form, there always is some presumption of 
 a rational nexus. We shall consider in the following section 
 what attributes of true hypothetical judgments are shared 
 by analogical assertions such as ' If he is a negro, he has 
 woolly hair '. It is not worth while to insist more fully on 
 these degrees of imperfection, except in so far as they will 
 
240 Universal Judgment [Booki 
 
 come under our notice in dealing with the doctrine of causation 
 and with the kindred subject of the negative in hypothetical 
 judgment. 
 
 Let us attempt to make perfectly clear, before we go 
 further, the nature of the relativity within a system which 
 we ascribe to the contents before us. The simplest cases 
 of such relativity are drawn from the field of numerical 
 or geometrical construction. A Chinese puzzle or dissected 
 map may give us a first idea. Any selected piece out of 
 such an arrangement determines nothing by itself, but when 
 a second piece is given some relation between them emerges, 
 though perhaps only a negative one. It is further possible 
 for a piece entirely enclosed by others to have its place rela- 
 tively to them determined long before the whole arrangement 
 is completed ; but this determination will really be partial, 
 for the place of the whole group of pieces cannot be determined 
 till the whole puzzle is put together. Now the arrangement 
 as a whole is a mere matter of fact ; it is only within it and 
 by reason of it that each piece has a prescribed place in virtue 
 of its own shape combined with the shapes of all the other 
 pieces. All the pieces being given, of course the arrangement 
 is given too ; but if nothing is given, of course all is in the 
 air, and one arrangement and set of shapes is as likely as 
 another. 
 
 Or again in the region of number, we may take as equi- 
 valent to Hypothetical judgments those which in treating 
 of Enumeration we called Mediate. 50 x 3 = 25 x 6 would 
 run in conditional language, ' If 50 is multiplied by 3, the 
 product is equal to,' &c. Here we have one form of the 
 numerical whole 150 presented as a term from which another 
 term, viz. another form of the same whole, may be inferred. 
 The system within which the relation exists is of course not 
 the whole 150, but the system of number as such ; or we 
 may say if we prefer, the whole 150 as involving and exemplify- 
 ing the nature of the whole of number as such. This system 
 may be brought to bear either by simple counting, the process 
 which is so to speak the medium in which number exists ; 
 or by developing any of the relations which are embodied 
 in the several places of the series with their individual names. 
 
Chap. VI] TJic Basis of Necessity 241 
 
 Thus the above statement may at once be reduced to a 
 tautology by taking 50 as 25 x 2 and 6 as 2x3. The com- 
 binations which might be made with the same result might 
 be pursued as long as we cared to continue the enumeration 
 of places in the series, and from whatever point we started 
 in the system we should obtain the same result so long as 
 both sides of the equation were subjected to treatment that 
 was equivalent according to the rules of the system. On 
 the other hand, if we were to assume the invalidity of the 
 equation, we should at once make the whole numerical 
 system inconceivable — a unit, say, would have to be taken 
 as varying in value without being subjected to any arith- 
 metical process, and such variation is incompatible with the 
 fundamental principle of number. 
 
 The same may be shown in space, treating it not qua 
 extended whole of parts outside one another, but in respect 
 of the connection of its attributes. ' If two straight lines 
 have the same direction, they can never meet.^ This is 
 a consequence drawn from the conception of direction in 
 homogeneous space. If we destroy the idea of homogeneous 
 space, the relation, which only holds within a totality having 
 that attribute, is annihilated. If there can be a change of 
 direction which yet is not a change of direction — I do not 
 know how else to express the notion of direction in space 
 which is itself curved — then, I presume, the judgment from 
 which we started is no longer true. 
 
 The same characteristic might be pointed out in relation 
 to gravity, inertia, or any property which is the basis of 
 exact inference. The consequences of gravity hold only 
 within the totality of gravitating matter, of inertia in the 
 combination of motions, and so forth. Every sphere of 
 this kind, every set of relations within which certain nexus 
 of attributes hold good, is itself ultimately a fact or datimi, 
 relative no doubt within some further totality, but absolute 
 relatively to the inferences drawn within it. Hence we are 
 brought to a conclusion of the last -importance. All hypo- 
 thetical judgment rests on a categorical basis. That is to 
 say, all relativity rests on an absolute datum and all neces- 
 sity on fact. Why then is mechanism, necessity or relativity, 
 
 1337 R 
 
242 Universal Judgment [Booki 
 
 opposed to individuality, fact or absoluteness, if all mechanical 
 relations are themselves characteristics given in some indi- 
 vidual whole ? * The answer seems to be dictated by what 
 has been said. Individuality is in self-relation, Necessity 
 is in external relation. But as all relation is within some 
 whole, it follows that wherever we have necessity or relativity 
 we are concerned with more than one whole or individual 
 content ; that is to say, we have a whole or content 
 with its own import and significance taken as a part 
 within a wider or completer totality.^ The ground or necessity 
 which forms the affirmed nexus of attributes lies then in the 
 systematic nature of the wider whole, that within which 
 the terms of the nexus are capable of being opposed as part 
 to part. 
 
 We will examine two or three instances of ground and 
 consequent in the light of the above doctrine. ' A picture 
 6 ft. X 7 ft. cannot be hung in a space 5 ft. x 6 ft.' Here 
 we are taking the picture as a whole in itself, but as a part 
 within space, and as therefore having external relations 
 determined by the spatial system as including other objects. 
 The arrangement of other spatial objects so as to leave only 
 the area 5 ft. x 6 ft. is incompatible with the occupation of 
 the area 6 ft. x 7 ft. by the picture. But again, we may 
 judge that ' If the boat in the right foreground of the picture 
 were erased, the arrangement of the distances would become 
 confused.' In this judgment we stUl call attention to spatial 
 determinations, but only as involved in the concrete indivi- 
 duality of the work of art, which assigns them their meaning 
 and value. We are thus taking not space as such, but the 
 individual picture before us, as the totality or determining 
 system, and contemplating the necessary relations which 
 this fact or whole, from its nature and structure, imposes 
 on its several parts. Of course, apart from the effect of the 
 whole picture, there would be no such necessity or relation 
 between the parts. This is an illustration of the ultimate 
 
 ^ Space and Time are, as we saw, imperfect individualities. But it is 
 their individuality and not their imperfection that makes them sources 
 of general relations in things. 
 
 ' See' on Measurement, chap, iii, supra. 
 
Chap. VI] Examples of Necessity 243 
 
 nature of logical necessity or relativity and its relation to fact, 
 which is, if not specially felicitous, at least true in every 
 detail. In a true work of art we have the bearing of every 
 part on every other, the innumerable details, none of which 
 could be altered without necessitating the alteration of others, 
 all concentrated in a unity which is itself constituted by all 
 these parts, and yet, as a whole, prescribes the relations 
 existing between them. And yet the whole is itself a compre- 
 hensive /ac^, and apart from it or outside it all these prescribed 
 relations lose their necessity and disappear. 
 
 Again, take such a judgment as ' The sound of the violin 
 
 is of peculiarly piercing quality.' If we describe the sound 
 
 merely in terms of the mechanical system of vibratory 
 
 movements, it is governed by the necessary relation, ' If 
 
 a string be dragged by a bow, slipping from it at intervals, 
 
 its vibration is of highly angular form,' i. e. in terms of its 
 
 effect on the air, produces sharp and not gradual transitions 
 
 from increase to decrease of condensation. Omitting the 
 
 effect on our hearing, this is a nexus of attributes grounded 
 
 in the properties of vibrating bodies, and in the laws of friction 
 
 and of undulatory transmission. But here again the whole 
 
 system of physical properties, though comprehensive, is a 
 
 datum, and except in it no necessity could be shown why 
 
 motion communicated by a bow must have this particular 
 
 form, or why this particular form should find a correlative in 
 
 a peculiar type of impulse communicated to the air. It is 
 
 this system which as an identity in differences appears first 
 
 in the effect of the bow on the string, and then in the peculiar 
 
 impulses communicated to the air by the sounding-board. 
 
 It is only as having such a unity behind both of them that 
 
 the one of these phenomena can condition the other. And 
 
 here again we may obtain a relative absolute by considering 
 
 the compound tone of the violin string as perceived by the 
 
 mind through the ear, simply on its own merits. It then 
 
 becomes an ultimate fact, embodying certain relations between 
 
 musical sounds. And within this fact we may distinguish 
 
 the necessary relation, ' When a tone is piercing in quality, 
 
 the higher overtones are strongly marked in it.' And finally, 
 
 we may bring the physical and the musical system together 
 
 R2 
 
244 Universal Judgment [Book i 
 
 under the complex fact of the correspondence between the 
 shape of oscillations and the character of tones, and say on the 
 faith of this complex fact that where the oscillations are 
 angular, the higher overtones are audible, and proceed to 
 the whole system of deductions made possible by Fourier's 
 analysis of all vibrations into combined single oscillations. 
 
 The idea on which we have been insisting — that of a 
 system or unity which prescribes the relation between its 
 parts or differences — is the idea of Ground, which includes 
 the sphere of the Hypothetical Judgment, and indeed wher- 
 ever it appears may be said to involve a Hypothetical element. 
 It is difficult to express the essence of this conception other- 
 wise than by saying that the system is the same in the one 
 difference or aspect as it is in the other. We thus appeal 
 to the notion of identity in difference, which we have taken 
 throughout to be the content of judgment. Only, as Ground, 
 it is not mere identity, but systematic Identity,-'^ a notion easier 
 to illustrate than to define, but apparently equivalent to 
 * identity such that the differences in which it is manifested 
 have definite relations to one another.' Of course any such 
 definition only repeats the characteristic which the accoimt 
 of the Hypothetical Judgment presupposes. 
 
 Assuming however these characteristics as smmnarised 
 in the above definition, we can draw from them two con- 
 sequences that affect the idea of Ground. First, it is plain 
 that when once a Ground is rightly stated, in conformity 
 
 " The question has been raised (Keynes, p. 264) whether the conse- 
 quent in a true Hypothetical should be called an inference from the 
 antecedent. My answer is given by the doctrine of Ground. I certainly 
 agree that the consequent in a typical Hypothetical does not follow 
 from the antecedent alone, if that means that it would follow if the two 
 stood, without further implications, alone in a universe. On the other 
 hand, I hold that the warrant of the sequence lies in the relevance 
 and adaptation of the clauses to the systematic world which they 
 presuppose (see p. 245 below), and assuming this world as a basis, 
 I should say that the consequent is always a necessary inference from 
 the antecedent. It appears to me ofE the track of the distinctive 
 Hypothetical type to treat the consequent as inferrible only when it is 
 a sort of converse of the antecedent, or when the antecedent has the full 
 premisses of a syllogism put into it (Keynes, p. 264). Even here, after 
 all, you have to presuppose some law of identity or Contradiction, so that 
 you do not get rid of the assumption of a systematic world. 
 
Chap. VI] Can the whole change ? 245 
 
 with the true nature of the system which it presupposes, 
 and with which it is in fact identical, such a Ground is un- 
 alterable except by alteration of this system itself. With 
 what justification, theoretically, we refuse to contemplate 
 such alteration of the universe as a whole, or how far prac- 
 tically we permit ourselves to contemplate it in respect of 
 subordinate systems, e. g. man's moral nature or the t\-pe of 
 disease, are questions that must be reserved for a general 
 discussion of the postulates of knowledge. Formally, we 
 may say, the whole cannot alter, because any alteration 
 must be included in the whole. But we shall see that so 
 purely formal a postulate would not satisf\^ the purposes 
 for which a postulate is required. 
 
 And secondly, it is plain that a ground is not rightly stated 
 imless it either embodies the whole essence of the svstem 
 which constitutes the ground, or at least is exactly relevant 
 to or compatible ^^■ith that system, and to the particular 
 bearing which a given interest in an}' context imposes upon 
 it. In the former case it is clear from what has been said 
 that the hj'pothetical judgment must tend to expand itself 
 into a categorical one. ^\llen we go to the root e. g. of 
 geometrical truths we find ourselves affirming facts regarding 
 the nature of space, \^'e shall thus at a later stage have to 
 face the conception of judgments at once categorical and 
 necessarv" ', we have indeed anticipated something of the kind 
 in speaking of the indi\"idual generic judgments. The latter 
 case is that which gives rise to hypothetical judgments having 
 strict reference to a systematic ground, which they therefore 
 imply, but do not need to express. Such are the ordinary 
 statements of ' piure cases ' in exact science, or geometrical 
 truths as commonly treated without raising fundamental 
 questions of the nature of space. A ' pure case ' is a nexus 
 of differences reduced to their expression as the differences 
 of the system in which they have their nexus. \Mthout know- 
 ledge of such a system we may analv'se ad infiniium and yet 
 never be sure that we have obtained a ' pure case '. This has, 
 as we shall see, an important bearing on the theory- of Induc- 
 tion. I gave a rough instance of a pure case on p. 220 in 
 reference to the annual rings of exogenous trees. Such, 
 
246 Universal Judgment [Booki 
 
 again, are the mechanical and chemical elements in the vital 
 processes of man, e. g. the pumping action of the heart, the 
 oxidation of the carbon in the blood and so forth, in stating 
 any one of which as a necessary sequence of ground and con- 
 sequent it must be treated as belonging to its own mechanical 
 or chemical world, and not as an element in human life. 
 All such judgments are abstract in the fullest sense, and 
 analytic ; their very point is that they disregard the import 
 which constitutes the individual. On the other hand, a 
 system which is the combination of individuals in their full 
 import, i. e. the state in relation to moral beings within it, 
 is most naturally dealt with not in hypothetical but in 
 categorical judgments. For the subject is either the concrete 
 system itself, or an individuality subordinate to it, taken in 
 its full concreteness. It would be sheer pedantry to speak in 
 hypothetical language of man's moral being, its ground, and 
 its necessary relations. 
 
 It is a corollary from the idea of Ground as a relation purely 
 relevant to a positive determinate system that the hypothetical 
 judgment, when ideally complete, must be a reciprocal judg- 
 ment. * If A is B, it is C ' must justify the inference ' If A is 
 C, it is B '. We are of course in the habit of dealing with 
 hypothetical judgments which will not admit of any such 
 conversion, and the rules of logic accept this limitation as 
 they accept the custom of ordinary speech as to the compara- 
 tive range of subject and predication. Some cases of non- 
 reciprocal sequence and their justification will be considered 
 in the next section. But here we are only concerned to explain 
 the principle upon which necessary sequence must ultimately 
 rest ; and according to that principle, the unity of a system 
 in its determinations, it follows that if A B necessitates A C, 
 then A C must also necessitate A B. We are not now speak- 
 ing of causation, but simply of coherence in principle, and it 
 is obvious that the idea of coherence in a system is reciprocal. 
 A cannot cohere with B unless B coheres with A. If in actual 
 fact this is found not to hold good, and A B is found to involve 
 A C while A C does not in\'olve A B, it is plain that what 
 was relevant to A C was not really A B but some element 
 a j3 within it. ' But may not the irrelevant element be just 
 
Chap. VI] Hypothetical is reciprocal 247 
 
 the element which made A B into A B as distinct from A C, 
 so that by abstracting from it A B is reduced to A C, and 
 the judgment is made a tautology, i. e. destroyed ? ' 'If 
 he is drowned, he is dead,' e.g. is not reciprocal. But it may 
 be objected that the judgment I desiderate is really ' If he 
 is dead, he is dead'. The suggestion is tempting, because it 
 aims at cutting up by the root a troublesome scientific problem, 
 viz. the statement of connected attributes as purely relevant 
 to one another and yet as distinct. We constantly tend 
 either to insert irrelevancies by way of distinction, or to let 
 both attributes fall back into the undistinguished abstract 
 relation which connects them. To grasp a distinction in unity 
 is an effort, and we dislike effort. Nevertheless, if it were 
 impossible, the idea of system, of the one in the many, would be 
 gone. In the above instance, the reciprocal judgment re- 
 quired would be something like ' If his heart has stopped 
 for good, he is dead ', or 'If he is drowned, he is dead through 
 suffocation by water '. The former shape obtains reciprocity 
 through the expansion of the antecedent, the latter through 
 the limitation of the consequent.* A systematic relation is 
 always within an individual whole, and the priority or antece- 
 dence of its elements belongs to the imperfection of knowledge, 
 and not to the relation in itself. I am not sajdng that every 
 individual reality exists endlessly in time, but I am sajang 
 that every whole in as far as its parts form a system has a 
 nature which is independent of time, or (what really comes 
 
 "• Mr. Keynes's remark (p. 271) called my attention to my omission 
 of the case in which reciprocity is secured by dealing with the conse- 
 quent (see however p. 255 below). My use of the term expansion is not 
 his. Applying it to the consequent, which ex hypothesi in a non- 
 reciprocal Hypothetical is wider than the antecedent, he ought to mean 
 expansion of the expression, but limitation of the case. But from his 
 use of the phrase ' a more complete statement of the consequence ' as 
 equivalent to ' expansion ', I think he has in mind his cases in which 
 something like a middle term is introduced in the antecedent and 
 dropped in the natural statement of the consequent ; and that he 
 hardly notes the point that as a rule the consequent, as a case, has to 
 be cut down and not expanded in order to secure reciprocity. My 
 reason for insisting on the ideal of reciprocity has to do with my general 
 attitude to Logic and to the Hypothetical Judgment (Preface, and 
 p. 236 above). I do, as Mr. Keynes says I ought, maintain that the 
 proposition A is imperfect. See Knowledge and Reality, pp. 190-2. 
 
248 Universal Judgment [Booki 
 
 to the same thing) continues positively and actively through 
 the fugitive moments of time. 
 
 But apart from time on the one hand and irrelevant ele- 
 ments on the other, I cannot see how the relation of con- 
 ditioning differs from that of being conditioned. Every B 
 that is conditioned by A is the condition of A being such 
 as to condition B, i. e. of A being what A is ; and if the 
 being of A were wholly relevant to B, this would be equiva- 
 lent to saying that the existence of B involves the existence 
 of A. In other words, if there is nothing in A beyond what 
 is necessary to B, then B involves A just as much as A in- 
 volves B.^^ But if A contains irrelevant elements, then of 
 course the relation becomes one-sided, as if we were to say 
 that a plane section of a sphere has its radii equal. The 
 mention of the sphere makes the relation of coherence one- 
 sided ; the circle need not be regarded as a section of a 
 sphere. But, always assuming the homogeneous nature of 
 Space, the relation between equidistance from a central 
 point and uniformity of curve is inseparable, and it is im- 
 possible to see that either of these essential differences of the 
 circle is prior to the other. It may however be questioned 
 whether in an ultimate sense any incomplete case can be pure, 
 i. e, whether irrelevancy can be wholly avoided except by 
 including the whole fact to which the judgment belongs. What, 
 e, g. has distance to do with curvature ? The only answer 
 is in the nature of space. This amounts to a doubt whether 
 in the end any Hypothetical Judgment can be true, and 
 points us again to a further type of judgment in which such 
 deficiencies may be made good. 
 
 The relation of Ground is thus essentially reciprocal, and 
 it is only because the ' grounds ' alleged in every-day life are 
 burdened with irrelevant matter or confused with causation 
 
 " Mr. Bradley's remark should be noted. ' I certainly agree here that 
 if the judgments are pure, the relation holds both ways [ref. to this 
 place]. But if in the end they remain impure, and must be qualified 
 alwaj's bj' an unspecified background, that circumstance must be taken 
 into consideration.' Appearance and Reality, ed. 2, 362 note. I pre- 
 sume that the effect would be to demand great caution in asserting 
 a reciprocal, e. g. not to assert it unless we knew by experiment or other 
 special consideration that ad hoc the background might be neglected. 
 
Chap. VI] Irrele%mnce hinders Reciprocity 249 
 
 in time, that we consider the Hypothetical Judgment to be 
 in its nature not reversible. The habit of thought is to pro- 
 ceed by determining an undetermined datum ; and this habit 
 is never wholly laid aside even in the Hypothetical Judgment 
 which is theoretically its negation. But a given condition, 
 though interpreted in a single aspect by the judgment which 
 draws its consequence, may have other consequences just for 
 the same reason for which its consequent may have other 
 (alternative, not merely co-operative) conditions. The ' other ' 
 conditions arise through a variation of the irrelevancy present 
 in the given condition ; as, if a circle has been said to arise 
 through cutting a sphere in a plane, this condition may be 
 varied by altering the superfluous relation in which a plane 
 figure bounded by a line equidistant from the centre can be 
 regarded ; e.g. it may be taken as a section of a cone, or as 
 an ellipse with equal axes. And just as each of these irrele- 
 vancies would present the antecedent of circular curvature in 
 different garb, so the presence of an irrelevancy which is thus 
 capable of variation involves all the independent consequences 
 that follow from the irrelevant idea — in this case that of a 
 sphere-section — which has been included in the condition. If 
 we restrict ourselves to the relation of equidistance in a plane, 
 we can get no result beyond that of a circular figure with the 
 properties which belong to it in the geometrical system. 
 
 A ground that admits of such variation is not only partial 
 or abstract, i.e. one which leaves the true ground in a measure 
 to be understood, but is actually in part ' impure ', i. e. burdened 
 with matter which gives rise to diverging consequences, and 
 makes the ground itself one among many converging grounds. 
 
 We have thus seen the idea of Ground in three aspects ; 
 as an actual system, interpreted in its bearing upon its parts ; 
 as a ' pure case ', i.e. a factor within a system stated in terms 
 precisely relevant to the system and entering into a nexus 
 in virtue of that system; and as an 'impure case', i.e. a 
 condition v/eighted with irrelevant matter and so failing to 
 express the real nexus which is aimed at. The first of these 
 three is necessarily categorical in import, and may perhaps be 
 identified with Schopenhauer's ' Seyns-Grund ', or Ground of 
 Being ; the two others are primarily hypothetical and only 
 
250 Universal Judgment [Book 1 
 
 imply reality behind them, and correspond together to his 
 Erkenntnissgrund, or Ground of Knowledge. It need hardly 
 be remarked that the ground of Being is also the only genuine 
 and complete ground of knowledge. In respect of reciprocal 
 character they must be divided differently ; the first two, the 
 complete and the abstract ground, being necessarily reciprocal 
 with their consequents, and the third being as obviously not. so. 
 The idea b. Cause may correspond either to the complete form or to 
 o cause, ^j^^ incomplete forms of Ground. In the former sense it can 
 scarcely be taken to differ from ground at all. In the latter 
 sense it is a distinct species which is included in a common 
 genus with the incomplete forms of Ground. 
 Cause as (i) Cause ^ as corresponding in meaning to complete Ground 
 Ground .^ would Consist in the exhibition of some selected attribute or 
 event — the effect — in the totality of systematic relations 
 which constitute its necessity. And in such meaning it can 
 scarcely be taken to differ from Ground, because the temporal 
 succession, which seems the natural differentia of Causation, 
 disappears in the reference of the effect to a positive and 
 continuous system. Mere temporal relation is negative, is 
 nothing. It is only the unity behind the temporal relation 
 that can bind cause to its effect ; and in the real or complete 
 Ground this unity is made explicit. The cause of the earth's 
 being where it is at this moment may indeed be popularly 
 indicated by saying that it was, wherever it was, at the 
 previous moment ; but strictly of course the relation of 
 the present position to the last position when fixed before 
 the mind as discrete and successive in time is simply that the 
 one is not the other, which is so far the same relation that 
 subsists between the earth's present position and the sun's or 
 moon's last position, and amounts to nothing at all. The 
 cause of the earth's present position is the persistent velocity, 
 together with the persistent influences regulating the direction, 
 of its passage through space. This meaning of Cause is the 
 ideal logical import of the term, and is what Mill meant to 
 indicate when he defined Cause as the ' sum of the conditions '. 
 The word ' sum ' is unfortunate, because it indicates a special 
 
 ^ On the conception of Cause, see some very acute remarks of Pro- 
 fessor Clifford, Lectures and Essays, i. 150. 
 
Chap. VI] Cause US ' SuM of Conditions ' 251 
 
 way which may be inappropriate of combining the factors. 
 The totality of the relations would be a better phrase than the 
 sum of the conditions. 
 
 The only difference between Cause in this sense and Ground 
 would be that Cause, though not a sensible event, still retains 
 an import relative to the explanation of sensible events or of 
 attributes entering into events (character, health, &c.), and 
 is therefore not coextensive with Ground, which includes 
 e. g. geometrical relations where the phenomena of process in 
 time are wholly wanting. There would be no sense in saying 
 that the attributes of a triangle are the cause of those of 
 parallel straight lines, or vice versa} The distinction, how- 
 ever, is more one of usage than of theory. On the one hand, 
 the effect, subsequent in time, which is exhibited as one 
 relation or difference within a necessary nexus, is necessary 
 to the persistence of the whole system and to the evolution 
 of its significance, so that the parts of the unity or system 
 are reciprocally necessary in complete Cause as in complete 
 Ground ; and on the other hand, if in investigating a ground, 
 say in geometrical matter, we go back to the whole system 
 of fact which is at the root of the necessary connection, we 
 shall be justified in treating this fact as a Cause. We could 
 hardly be censured for saying that the nature of space is not 
 only the ground, but the cause, of the attributes of triangles 
 and of parallels alike. 
 
 Cause then, in its largest sense, is a real ground, and ulti- 
 mately there is no complete ground which is not a real ground. 
 Ground and Cause are thus not identical but convergent 
 conceptions, i. e. as they are completed they tend to coincide, 
 and the striking differences between them depend on a com- 
 parison of their imperfect and ultimately self-contradictory 
 forms. 
 
 Complete Cause, like complete Ground, corresponds to a 
 Hypothetical Judgment whose condition and consequent are 
 reciprocal. If, as is perhaps the case in Mill, the phrase ' sum 
 of the conditions ' is not limited to relevant conditions, and the 
 
 ^ Schopenhauer's ' Seynsgrund ' describes the relation of such cases, 
 supposing the rational connection to be central and fundamental to the 
 contents connected. 
 
Ground. 
 
 252 Universal Judgment [Book i 
 
 hypothetical judgment which expresses the nexus of such a 
 sum with its effect is consequently not reciprocal/ the notion 
 of sum of conditions loses the only merit which it appeared to 
 possess. But if it means, as it seems to mean, a persistent and 
 systematic fact, then it agrees with other indications in suggest- 
 ing that for the complete Ground or the complete Cause we must 
 go beyond the Hypothetical Judgment. 
 Cause as (2) Cause as an event in time is thus an imperfect concep- 
 dis^nct*' ^^^^- Indeed it is hardly possible to formulate the idea of 
 from one event in time as the cause of another that falls, in time, 
 wholly outside the first. Cause is always taken to be more 
 or less of a complication of relations and circumstances ; and 
 these, as acknowledged to bear on one another, are not mere 
 events in time. It may indeed be retorted that mere time 
 is an unreality and that no one ever said that causation was 
 in mere time, i. e. in succession taken as discrete ; but that 
 real time involves continuity as well as discreteness, and in 
 such real time causation really is. Such a retort might be 
 ill-founded as a statement of common logical opinion, but 
 would in substance express the principle which I am en- 
 deavouring to explain. Mere time is mere succession ; but 
 real time involves something that is not in succession, though 
 it remains through succession. The consciousness for which 
 there is time has begun a process which tends to abolish time. 
 To say that in this sense Causation is in real time is to say 
 that Cause corresponds to an incomplete ground, i. e. a partially 
 known unity including the factors which are in question as 
 Cause and Effect. But when we come to speak of an incom- 
 plete Ground, the difference between thought and reality 
 emerges, for it is only the complete Ground that is the real 
 ground. When the ground in thought is distinguished from 
 the ground in fact, then the cause is one with the ground in 
 fact and is separable from the ground in thought, which 
 latter is sometimes called by analogy the causa cognoscendi. 
 
 ^ Cp. Essays in Philosophical Criticism, p. 96 note. Of course if Cause 
 as = sum of conditions is compatible with Mill's plurality of causes, 
 the Cause as sum of conditions cannot = Ground. But it ought to be 
 incompatible ; for in any concrete circumstance that may be named as 
 condition, what is not relevant is not condition. So the sum of con- 
 ditions ought to be restricted to the relevant or minimum conditions. 
 
Chap. VII Cause as incomplete Ground 253 
 
 Of course the causa essendi ^ must be a causa cognoscendi, 
 but a causa cognoscendi need not be a causa essendi. As a 
 matter of fact the ground in thought or causa cognoscendi 
 often belongs to the effect in time,^ but may be any element 
 whatever related to the real ground, whether cause, effect, or 
 abstract principle. 
 
 The root of these distinctions is that the nexus of ground 
 and consequence is at this stage still charged with irre- 
 levancy. The cause and effect, ground and consequent, are 
 all of them at this stage concrete events, or groups of incom- 
 plete relations, among which the special aspects belonging to 
 any nexus that may be in question have not yet been freed 
 by analysis. As a result of this state of things the hypo- 
 thetical judgment which embodies such a connection follows 
 the analogy of singular judgments or of imperfect universals, 
 and has an antecedent which is not affirmed by affirming 
 the consequent, just as the subject of a singular or generic 
 judgment is not affirmed by affirming its predication. And 
 in so far as the hypothetical judgment is taken to be the 
 natural vehicle in which to assert causation, this characteristic 
 of it agrees with the popular view that the same cause always 
 has the same effect, but the same effect need not always be 
 due to the same cause. This doctrine, formulated by Mill under 
 the name of the plurality of causes, and wholly incompatible 
 with his view which treats Cause as * the sum of the conditions ', 
 is a mere translation into analytic science of the notion of sub- 
 ject and attribute, here quite out of place. The degree of truth 
 which the view possesses depends solely on an imperfection of 
 knowledge and not in any way on the nature of causation. 
 
 ^ Schopenhauer's distmctign between the Causa essendi (Seynsgrund) 
 and the Causa fiendi (Ursache, cause proper) is reduced by the view 
 taken in the text to a distinction of degree. Effect cannot be in suc- 
 cession to cause in the sense of faUing outside it ; there must be a real 
 whole which includes both. 
 
 ^ It is worth remarking as a matter of usage that ' antecedent ' in the 
 conditional sentence has absolutely no allusion to the temporal relation 
 of the events connected. Its name may have come from the usual 
 grammatical place of the condition, or from some profounder idea of 
 priority. But this would be a mere historical connection. Mill's appli- 
 cation of the term to succession in time creates quite an unfounded idea 
 of correspondence between Causation and the Hypothetical Judgment. 
 
254 Universal Judgment [Booki 
 
 It is an old story that if, having said that ' All men are 
 mortal ', you then further say that ' A. B. is a man ', you are 
 committed to the assertion that he is also mortal ; but if 
 you prefer to make the more cautious assertion that he is 
 mortal, you do not thereby pledge yourself that he is a man. 
 The same maxim in relation to the Hypothetical Judgment 
 is summarised in the formula ' Assert the antecedent or deny 
 the consequent '. It makes no sort of difference in the applica- 
 tion of this formula whether cause is antecedent and effect 
 consequent or vice versa. 
 
 Thus the reason why the law of Causation has beeii stated 
 in the form ' The same cause always has the same effect ' 
 rather than in the complementary form ' The same effect 
 always has the same cause ' is that popular philosophy 
 tends to start from the event which comes first in time, as 
 logical antecedent, because the primary source of knowledge 
 is simply to observe processes in time : and so the further 
 determination of any datum or circumstance when effected 
 by this elementary method corresponds to the succession of 
 events in time, and that event which comes first is taken as 
 the datum to be further determined, and that which comes 
 after is regarded as its determination. Of course then the 
 same datum always has the same determination, for every 
 content — and a datum is a content — is an identity, and 
 having attended to an identity in respect of one of its differ- 
 ences we are quite safe in saying that this identity — ^this 
 datum — will always have the same difference. For if it seems 
 not to have, we may say either that the difference is disguised, 
 or that the datum is not the same. And so we come first to 
 the principle that the same cause always has the same effect ; 
 and sometimes, to make quite clear that we are simply 
 regarding a real content in respect of a difference which we 
 have selected out of its concrete nature, we add ' the same 
 cause under the same conditions ', or ' in the same relation ' ; 
 thereby showing that we know very well that the concrete 
 cause has all sorts of different effects under different conditions 
 and in different relations. 
 
 It is usually presupposing the truth of the first principle 
 that we go on to consider whether the same effect always 
 
Chap. VI] Same Effect, same Cause ? 255 
 
 has the same cause ; and neglecting in the effect, which we 
 take at first as a goal in which thought can rest, the idea of 
 a limiting reference to a particular antecedent, we are im- 
 pressed by the variety of relations and conditions compatible 
 with the undetermined result, as contrasted with the single 
 aspect in which we watch the operation of a cause ; and we 
 forget that each set of these generates the effect in a slightly 
 different form. It seems so common-sense to say ' If a man 
 is drowned he is dead, but if he is dead he need not therefore 
 have been drowned ', that we forget that, if he is dead in the 
 particular way produced by drowning, then he has been drowned. 
 We might, from the very first consideration of an effect, draw 
 a parallel to the popular form of the Law of Causation, ' Same 
 cause in same relation, same effect,' by a Law of Effect which 
 should affirm, ' Same effect, in same form, same cause.' But, 
 as our first impression in starting from Cause is of the Identity 
 of Effects, so our first impression in starting from Effect, 
 because there is no simple guide to further determination, 
 is of the Plurality of Causes. Really however we have to 
 supplement these ideas by those of the Plurality of Effects 
 and of the Identity of Causes. It is, technically speaking, 
 an accident which of these four points of view attracts our 
 attention first. The knowledge that the same effect has the 
 same Cause is not necessarily later than or dependent on that 
 of the converse maxim. 'If a man is dead his heart has 
 stopped ' does not involve a knowledge whether stoppage of 
 the heart must always cause death. Still, as we saw, the 
 common law of Causation is most readily suggested by our 
 experience of simple observation, and has a certain real pre- 
 eminence because of this experience. Experimentally we 
 only follow up Cause into Effect, not Effect into Cause. And 
 thus the natural tendency is to identify Cause with Antecedent, 
 and the common law of Causation ' Same cause has same 
 effect ' is the resulting one-sided application to Cause and 
 Effect of the commonplace rules of the Hypothetical Judg- 
 ment. Of course, when we have both principles together 
 we have what is truer than either alone ; but in itself 
 neither prima facie involves the other. 
 We have seen, then, that even the incomplete or partially 
 
256 Universal Judgment [Booki 
 
 known Cause can always enter into a Hypotlietical Judg- 
 ment either as Ground or as Consequent. In thie same way 
 it is possible for Effect to be either Ground or Consequent 
 in Hypothetical Judgment. But Effect can never be Cause, 
 unless we go back to the doctrine of complete Ground in which 
 the boundary between Cause and Effect really melts away. 
 Effect can never be Cause, and yet Effect may be as inevitable, 
 as essential to the sequence, as necessary a Ground of hypo- 
 thetical nexus as ever Cause could be. It is a well-known 
 saying that we cannot conceive a storm to have been less 
 violent than it actually was without the difference involving 
 differences in a series of physical processes going back ad infi- 
 nitum in the causal nexus . Yet we cannot bring ourselves to treat 
 the storm as the cause of the previous physical processes which, 
 as we say, resulted in it. The distinction which is at the root 
 of our inability to do so is of course the distinction of Time. 
 The operation of this distinction has never been more tren- 
 chantly stated than by Aristotle,^ who lays down the general 
 doctrine of Ground with perfect clearness, but in going on 
 to deal with causation in succession doubts the security of 
 all arguments from cause to a subsequent effect. For ' in 
 the moment between the two, it would be false to say that 
 the second has taken place, although the first has already 
 taken place'. It may of course be rejoined that the cause 
 cannot have completely taken place if the effect has not 
 begun. This rejoinder however depends on the postulated 
 unity of the causal process and on the consequent con- 
 tinuity of time. If we press this point of view, it takes us 
 back to the doctrine of complete ground, which consists in 
 exhibiting the unity or continuity of causation regardless 
 of succession in time. But we are anxious at this moment 
 to do all we can in the way of elucidating the problem involved 
 in the natural conception of causation as sequence, and 
 therefore we will not simply fall back on this notion of complete 
 ground. Granted that time and sequence are continuous, 
 yet they are also discrete. There is indeed no empty ix^ra^v 
 or interval in which we can stand and say, ' The cause is past 
 and the effect is not begun.' But unquestionably we can 
 
 ^ Anal. Post. ii. 95 a, 30 fif. 
 
CiiAp. VI] Why is Effect not Cause ? 257 
 
 make a stand at any point in the continuous sequence and 
 say, 'So much is (or "has been ") real, the rest is not yet real.' 
 And what is not yet real cannot be the cause of what is or 
 has been real. 
 
 This appears to be the root of our whole conviction about 
 cause and effect in time. Even after the entire sequence has 
 been realised, and when all of it is alike real or unreal, as we 
 may choose to count the past, still the objective temporal 
 order into which we project our experiences embodies the 
 succession of relative reality and non-reality which attached 
 to the order in its original constitution. We remember that 
 this became real while that was still unrealised, and we 
 therefore feel that however certainly they may reveal them- 
 selves as parts of a single whole, we can never hold the event 
 which came after to be an element in the actual determination 
 of that which went before. It would involve to our minds 
 the absurdity of treating the existent as caused by the non- 
 existent. 
 
 I do not mean to deny the reality of this distinction. It 
 amounts to just what it is. Time is a condition, is the condition, 
 is we may almost say the inmost nature, of our sensitive 
 experience. The first operation of our intellectual synthesis 
 is to build up an ideal objective order which, though itself 
 not in time, yet contrasts as a more or less completed reality 
 with the sensitive experience which is always passing into it. 
 It is obvious that we can only construct our anticipation 
 of reality out of its positive content so far as known to us ; 
 and its positive content so far as known to us belongs to the 
 past. We may fill up gaps in the past out of other parts of 
 itself, but we can get nothing out of nothing, and therefore can 
 draw no anticipations from the future. Therefore at any given 
 moment we have no choice but to say that the future is 
 conditioned by the past, and the past not by the future ; 
 effect by cause, and cause not by effect. Cause, at any such 
 given moment, is what we have, and effect what we have not. 
 And further, taking the past as a representation of all that is, 
 for it is the only positive content that we have to represent any- 
 thing, we are right in saying that the past as a whole is the 
 cause of the future as a whole. What is, is, and will act as it 
 
 1337 s 
 
258 Universal Judgment [Booki 
 
 will act ; and what we already know of it is the only source 
 from which we can anticipate its action. But of course the 
 past as a mere series of events is past ; it has ceased to be 
 real just as truly as the future is not yet real ; the relation 
 between two nothings is nothing, and cannot cause any- 
 thing. The same applies to particular events ; it is hard 
 to find words which describe the negative relation of effect 
 to cause, and which do not apply equally to that of cause 
 to effect. Effect cannot be the cause of its cause, for the 
 reason that it is absurd to find the cause of something existent 
 in what does not (yet) exist. But is it less absurd to find the 
 cause of what is now entering upon existence in what does 
 not (any longer) exist ? Yet this is what we do if we take 
 cause as an event and effect as a subsequent event. Hence 
 we are driven to the second operation of our intellectual 
 synthesis, which is, after erecting an objective temporal order 
 not itself in time, to strip this temporal order of the importance 
 attaching to its successiveness, and to treat it more and more 
 as the expression of a plan or unity. Except as the expression 
 of such a unity, causation, as we have seen, disappears ; but 
 «s the expression of such a unity, the causal relation ceases 
 to be in time, because the positive connection between cause 
 and effect being made manifest, the two are united in the 
 complete ground. This must be carefully distinguished from 
 saying that time may be introduced anyhow without making 
 a difference ; it does not mean that eggs boil water, or that 
 death produces a revolver-shot. It simply means that the 
 order of succession, which has a largely negative- aspect, dis- 
 appears in the significance of a positive systematic connection, 
 and that we do not in fact, in considering a past sequence, 
 regard what came later in time as less fundamental or eluci- 
 datory than what came before. 
 
 Then is not Time real ? I answer that everything is real, 
 so long as we do not take it for what it is not. Time is real 
 as a condition of the experience of sensitive subjects, but it 
 is not a form which profoundly exhibits the unity of things. 
 And when we transfer the true judgment ' What has not yet 
 happened must be a manifestation of the same unity which 
 is involved in what I already positively know ' to a totality 
 
Chap. VI] Reality of Succession 250 
 
 which is already in all its parts equally real, we confuse, 
 and give ' time ' a reality which it has not. Such a confusion 
 is involved in the idea that there can be no more in the effect 
 than there was in the temporal cause, and in the tremendous 
 power consequently exercised by historical analysis over 
 common minds. The confusion is reinforced by another 
 aspect of causation. Practice, like sensitive experience, is 
 in time. In translating a plan into practice, the relations 
 of succession hold good. A sequence is what it is, and nothing 
 else ; and a reversed sequence would simply be different. 
 Therefore for practice the earlier event is more important, 
 in the sense in which the means is more important than 
 the end. For knowledge of the end does not give power to 
 produce, but knowledge of the means does. But this im- 
 portance begins and ends with practice, and even there it 
 only exists in virtue of the unity whose nature is expressed 
 for us in the fabric of ideal reality — a fabric which is not in 
 time. 
 
 Thus it is easy to see the relation between Cause and 
 Ground in the imperfect stage in which they are distinguish- 
 able conceptions. Ground is a content which is perceived, 
 by reason of any systematic relation whatever, to involve 
 the determination of another content. Cause is also a Content 
 perceived to involve the determination of another content, 
 and is therefore a kind of Ground, but is primarily confined 
 to the special case in which the determining content is real 
 and the determined content unreal. But as this is merely 
 a negative relation, even the first presumption of causation 
 in some degree supplements it by the postulate of a positive 
 nexus, and we know very well that in practice if no positive 
 nexus, no continued identity of process, can be alleged, we 
 do not allege causation. A familiar illustration is the sequence 
 of day and night. It is generally urged that if causation were 
 mere succession, day must be the cause of night, but that 
 really day is not the cause of night, because b)oth are effects 
 of a common cause, and either might very well go on without 
 the other. This is one of those trivial examples that seem 
 hardly worth arguing about, and yet, if argued about, must 
 be treated at length. I have shown that I at least think 
 
 S2 
 
26o Universal Judgment [Booki 
 
 ' Causation = mere constant succession ' plainly false and in 
 contradiction with facts ; but if I must discuss this case I 
 should like to have the terms defined. The question, as I take 
 it, is, Does ' day ' in the sense in which it is here used include 
 a unity, a system, a principle, which is continuous in and 
 responsible for night ? If so, day is the cause of night ; if 
 not, not. The reason why we think it wrong to call day the 
 cause of night is not because night has the same claim to be 
 called the cause of day. There is no contradiction here. 
 In our ordinary way of treating imperfect causation there 
 is no reason why the daylight hours of Monday should not 
 be the cause of Monday night, Monday night of Tuesday,. 
 Tuesday of Tuesday night, and so on. The difficulty does 
 not lie in the sequence being of this alternate nature — a single 
 oscillation of a pendulum is certainly the cause, though not 
 the complete ground, of the next — but that the persistent 
 unity which lies at the root of both phenomena does not fall 
 within the natural definition of either. If day meant not merely 
 the presence of light on the earth's surface, but, in relation 
 to any given point on the earth's surface, that portion of the 
 earth's rotation which carried that point from its sunrise to 
 its sunset, then I do not see how it could be denied that this 
 portion of rotation, in as far as it determined the position of 
 the selected point throughout the immediately succeeding 
 section of the rotation, was the cause or principal condition 
 of the ensuing night. But of course the name ' day ' is applied 
 e. g. to the six months' day of the poles only by metaphor, 
 being a chronological idea which has become largely inde- 
 pendent of the relation of a particular place to the sun's 
 illumination, and having legal and social meanings which 
 do not admit of an antithesis with night. So the true reason 
 why we do not like to predicate causation of this sequence 
 is simply that, owing to their varied accessory significations, 
 the terms day and night do not apply to successive stages 
 of a continuous natural process, but are mere chance distinctions 
 that are drawn, according to our shifting purposes, on the 
 surface of that process. 
 
 But though we do not allege causation where we cannot 
 allege a positive nexus, yet, as I pointed out above, there is 
 
Chap. VI] Histovy and Science 261 
 
 a considerable distinction of degree between the objective 
 temporal order and the intelligible unity of things. The 
 less we advance beyond the stage of perception and narra- 
 tive to that of science and intelligence, the more does the 
 negative distinction of time retain its significance. Strictly 
 speaking, the distinction between cause and effect in time is 
 only real at an arbitrary moment in which we draw an ideal 
 line across the temporal process of sensitive experience, 
 between the real and the unreal. When cause and effect 
 are both absorbed in the past, the distinction is only transferred 
 by memory into the content of reality, which thus takes the 
 form of the objective temporal order. This order would 
 be an intolerable chaos but for a certain presumption of 
 causation, i. e. of unity, which bind§ it together according 
 to some sort of system ; there is no real history apart from 
 the idea of causation. Nevertheless this unity remains for 
 the most part inchoate, i. e. only in some degree explicit ; 
 and so, though not itself in time, presents the scheme of a 
 de facto evolution in time as a sort of extended memory, with 
 the transferred character of determination of unreal by real, 
 i. e. of effect by cause. Now it is plain from what has been 
 said that the distinction of Cause and Effect is self-destructive. 
 It is utterly impossible to be successful in the investigation 
 of a causal relation without reducing it to the intelligible 
 unity of a complete ground. History therefore, in the sense 
 of the mere record of remembered fact, would seem to have 
 for its ideal to disappear into systems of hypothetical judg- 
 ment, in which complete ground should do duty for cause 
 and effect, and the relation of time should disappear. 
 
 This conclusion is true, in my judgment, in relation to 
 the mere phenomena of the past, and the resulting con- 
 nection between causation and ground. But as regards 
 what we really mean by history, such a conclusion is repug- 
 nant to our feelings and inconceivable to our understanding. 
 The reason is plain. History is not merely a name for the 
 recorded past. A series of astronomical observations is 
 not history ; it is science, and has no value but for science, 
 unless by chance it throws light on the observer's character 
 or on the state of science in his time as an element in the 
 
262 Universal Judgment [Book i 
 
 condition of man. What we mean by History is the revelation 
 of man's nature in action and intelligence. And when we 
 deprecate the reduction of history to a system of hypothetical 
 judgments founded in some single abstract individuality — to 
 a science like abstract mechanics or abstract economics — 
 what we really mean is that man's nature reveals itself in 
 individuals, in actions, in forms of intelligence, and we do 
 not want to lose these realities in abstractions of relativity 
 and necessity. But if we consider that hypothetical necessary 
 or relative judgment is entirely based upon categorical 
 judgments, that all nexus is within an individuality, we shall 
 see that history may be received into the intelligible unity of 
 knowledge without sacrificing its concrete import and charac- 
 teristic significance. This could onty be destroyed if we 
 insisted on predetermining within what whole or system we 
 should find the facts of history to be necessarily related. 
 
 And no doubt a suspicion of some such prejudice is opera- 
 tive in the reluctance to absorb history in ' science ' to which 
 I have adverted. If science meant exclusively the sciences 
 which grow out of the one-sided forms of measurement, 
 then we should rightly deny that there is a science of history, 
 and, for the same reasons, that there is a science of art, of 
 political form, or of religion. We escape however from such 
 suspicions if we remember that all connection is based on 
 fact, and all analysis on individuality ; and that the nature 
 of the facts or of the individual whole or system with which 
 a science deals can ex hypothesi be only for that science 
 itself to determine. 
 
 Thus the conception of Cause as an event in time anterior 
 to effect gives way on analysis, and forces us back to the 
 conception of the complete Ground ; and the conception of 
 incomplete Ground {causa cognoscendi) as distinct from Cause, 
 expands into the same unity, which, as we saw, is at once 
 the complete Cause and the real Ground ; i. e. the relation of 
 part to part within an actual and systematic totality. This 
 relation of part to part, either burdened with irrelevancy as 
 in the ordinary hypothetical judgment, or pure and relevant 
 as in the hypothetical judgment whose terms are reciprocal, 
 forms the content of the abstract universal judgment. And 
 
Chap. VI J SupposUion lu Judgment 263 
 
 this abstract judgment is a divergence from the concrete 
 evolution of thought, and joins with the mediate and quasi- 
 generic judgments of the sciences which arise out of one- 
 sided measurement.^ But it may also be regarded as an 
 element in or aspect of the popular or transitional quasi- 
 collective and the generic judgments which are enumerative or 
 individual in form but analogical in meaning. Analogy, as we 
 pointed out, is compatible with systematic necessary relation. 
 
 On the other hand, though a complementary aspect of 
 the universal judgment, the pure hypothetical is destitute 
 of finality, and incapable of standing alone. It demands a 
 reversion to concrete thought by the fact that it presupposes 
 a self-existent whole. Apart from such reversion it may 
 become a wholly arbitrary and meaningless play of fancy, 
 presupposing conditions which are not made explicit. 
 
 As I have not yet dealt with negation, I shall leave the 
 negative forms of the hypothetical judgment to be dealt 
 with in the same chapter as the disjunctive judgment, with 
 which they are closely connected. 
 
 c. The above appears to me to be a fair account of the Supposi- 
 hypothetical or abstract universal judgment considered from *^°P ^" . 
 a strictly logical point of view. In one important respect judg- 
 however it is prima facie at variance with conclusions which °^^'^*- 
 might be drawn from the grammatical shape of these pre- 
 dications as to the attitude of mind in which they are normally 
 made. The point in doubt is the existential significance of 
 the universal judgment. The account which I have given 
 treats the existential implication which attaches — vmdoubtedly 
 in very various degrees — to the different forms of the universal 
 judgment, as cognate with the existential affirmation involved 
 in the singular and in the perceptive judgments. But it has 
 been frenchantly laid down by Mr. Bradley that a different 
 view is suggested by the attitude of the mind in all purely 
 abstract judging — abstract be it remembered not necessarily 
 in content, but only as all thought is abstract when contrasted 
 with sense-perception, I am unable to reconcile this view 
 with the existential value of judgments about individuals 
 designated by proper names, in which there is no direct 
 ^ See Scheme, p. 86. 
 
264 Universal Judgment [Booki 
 
 reference to sense-perception nor to anything but a content^ 
 whose real existence is as I imagine taken to be asserted 
 owing to its concrete nature. But I proceed at once to discuss 
 the analysis of the abstract universal afhrmation, from the 
 point of view to which I allude. 
 
 It will be remembered that in the general discu^ion of 
 the nature of judgment, we agreed that the ultimate subject 
 in judgment was never an idea, — never that is to say even 
 a logical idea or content, for the particular psychical image 
 we found not to concern us in logic. The ultimate subject 
 in judging was always, we held, the Real, which in the act 
 of judgment is qualified by certain logical ideas. So long 
 as the immediate subject was present perception, whether 
 additionally qualified by significant ideas or not, all went 
 smoothly, for the immediate subject was then simply the 
 point of contact with the ultimate subject of judgment. Some 
 difficulty, indeed, arose in explaining the real reference of the 
 Singular judgment in which the subject may fall outside 
 present perception and may have to be united therewith by 
 a constructive process. Still, however, the immediate sub- 
 ject was a determinate element in the whole of Reality, 
 having individual existence manifested within the sensible 
 series, although e. g. in the case of an organism, stiU more in 
 the case of a man, not of a kind that could really be pre- 
 sented by sense-perception as such. So far therefore we 
 were, in judging, referring an ideal content to reality in 
 some particular concrete aspect, and therefore our Judgment 
 was still plainly existential, i. e. such as to become false if 
 the concrete element of reality described had no place in the 
 series of sensible events. 
 
 Now when we come to deal with the Universal Judgment 
 it must be admitted that at least as a question of form the 
 reference to reality becomes less easy to define. The pseudo- 
 collective and the analogical judgment at any rate (dismissing 
 the conception of the individual generic judgment, in which 
 the singular judgment revives) are unquestionably capable 
 of an interpretation which reduces them to the pure Hypo- 
 thetical Judgment. In our old acquaintance ' AU men are 
 mortal ' the ' all ' is too obviously not collective to stand 
 
Chap. VI] Idea as Subject 265 
 
 in the way for a moment. We certainly might be driven 
 to confess that in so judging we had only asserted ' If man, 
 then mortal ' or ' Where man, there mortal.' Such an inter- 
 pretation is involved no less in Mill's analysis of the import 
 of propositions than in Lotze's or Bradley's treatment of 
 the universal judgment. To affirm co-existence of attributes 
 is not to affirm existence of subjects.^ The analogical judg- 
 ment has this aspect even more plainly. ' An organism 
 as such is mortal ' means, it may be urged, if taken strictly 
 and without counting implications, ' If organism, then mortal,' 
 'Where organism, there mortal,' 'Whatever, is organic 
 is mortal.' If in consequence of such an assertion we take 
 it that organisms are actual elements of the real world, 
 this is implication — though very strong implication — and not 
 assertion. 
 
 According to this analysis, the essence of which is to 
 regard the implication of existence in these judgments as 
 outside the matter affirmed, all abstract affirmation — abstract 
 merely in the sense of not referring to present perception or 
 to particular sensible events — is on the level of hypothesis, 
 has for its immediate subject an idea not a reality, and 
 consequently has no existential import, or ' deals purely 
 with adjectivals.' ^ 
 
 The identification of the universal judgment as such with 
 affirmation based on hypothesis being thus made, the further 
 development of the view turns on the nature of hypothesis 
 or supposition. The essence of supposition is that it is qua 
 supposition, wholly arbitrary in its starting-point. Its con- 
 tent is taken, not given, is an idea, not a fact (if per accidens 
 a fact, is not used as a fact, i. e. its existence is not argued 
 from), and is considered not in itself, but for the sake of its 
 relativity, i. e. for what flows from it, for its consequences. 
 The essence of supposition is in short argument from content, 
 and not from existence of content. The consideration of 
 any proposed legislation, e. g. a Reform or Land Act, with 
 
 ^ This comes out very emphatically in Mill's account of Definition, 
 which when Real at all, he analyses into a meaning and a postulate of 
 existence. In this he is pretty much at one with Mr. Bradley's account 
 of universal judgment. See also Mill's account of mathematical truth. 
 
 * Bradley's Principles of Logic, p. 8i. 
 
266 Universal Judgment [Booki 
 
 reference to its consequences, is an example of supposition. 
 ' Suppose every adult male to have a vote, it will be impos- 
 sible to maintain indirect taxation ; ' * Suppose Ireland to 
 have a Statutory Parliament, the Imperial Parliament will 
 by this fact itself become statutory.' Or again, ' Suppose 
 beings endowed with perception but confined to a plane in the 
 exercise of it, they must see all figures as lines or points.' 
 
 The process is to select or to fabricate, apparently at 
 pleasure, an ideal content, to think of it as in connection 
 with some known reality, and to judge the result as a truth 
 conditional on such connection. 
 
 It is plain that in this operation, subject to a certain 
 reservation to be mentioned directly, the supposition selec- 
 tion or fabrication ^ of content is arbitrary, but the judgment 
 proper is necessary. 
 
 What then, precisely, it has further been asked, is in 
 such a case affirmed about ultimate Reality ? Plainly, not 
 the existence of the content as a fact in the context of our 
 world. We may take Sigwart's instance, reproduced by 
 Bradley. ' Si tacuisses, philosophus mansisses.' Something 
 is here affirmed, but not the actuality of the content, which 
 is by the strongest implication denied. Or again, ' All tres- 
 passers will be prosecuted.' The truth of this declaration 
 does not depend on there being trespassers, though it cannot 
 be tested unless there are trespassers. 
 
 When we have once accepted this point of view, and 
 excluded as unessential the various implications of existence 
 which attach to various Universal Judgments, the conclusion 
 is inevitable. Judgments so regarded do not affirm as true 
 of Reality any explicit content or even any connection of 
 explicit content. We have seen that it is no impeachment 
 of the judgment that its content never has been nor can be 
 actual. ' The necessary may be impossible or non-existent.^ 
 And as for the connection of content, though it is necessary, 
 yet it cannot be actual unless the content to be connected is 
 actual, and the judgment may be true though the content 
 
 ^ Selection and fabrication difiEer only in degree, not merely because 
 all fabrication is selection, but also because all selection is fabrication — 
 involves the constitution of an idea from a given or chosen point of view. 
 
 ^ Bradley's Principles of Logic, p. i86. 
 
Chap, vi] The natufe oj Sitpposition 267 
 
 be incapable of actuality. Therefore the truth of the judg- 
 ment, according to this extreme analysis, depends neither 
 on the actuality of its content, nor on the actuality of the 
 connection it alleges within its content. What then does such 
 a judgment assert of that Real which is the ultimate subject 
 in every judgment ? Simply this, that the Real is such that 
 under the ideal condition which forms the immediate subject 
 of the judgment it will furnish the ideal consequent which is 
 expressed in its predication. The hypothetical judgment 
 would then be illustrative but not enunciative of Reality. 
 The property of Reality which it illustrates may however 
 be accessible to knowledge ; or again, according to the view 
 before us, it may not. Sunple examples of the former case 
 form the best explanation of the conception which we are 
 discussing. ' If you ask him for money he will refuse you.' 
 The real quality of the real man, on which this prediction 
 rests, may be that he is a miser ; then his miserliness x is 
 the real fact, not apparent in the judgment, which the sup- 
 position and consequent a and h only illustrate by its effect 
 in an ideal case ; and which is categorically affirmed, but 
 only as an unknown x, in the Judgment. And it is conceiv- 
 able that the property of Reality which lies at the root of 
 the judgment may not be known, and wherever the connec- 
 tion envisaged as hypothetical is considered to be ultimate 
 and not susceptible of further explanation, the property of 
 Reality at its root is pro tanto unknown. Such a connection 
 would be, I suppose, ' \Vhatever is material, has gravity.' 
 The property x of reality which is here categorically asserted 
 as the basis of this connection, ' If a then &,' is, I presume, 
 and is likely to remain, unknown. 
 
 The real criticism which I have to offer upon this view 
 is contained in the whole account of judgment which has 
 been submitted to the reader. Its point and purpose have 
 been to exhibit the aspects of fact, and of relativity or 
 necessity, within the judging function as complementary 
 and inseparable, but as differently predominant in dealing 
 with different contents. Consequently, the abstractness on 
 which their respective predominance has hinged, has been 
 treated as the abstractness of contents, and not as that 
 
268 Universal Judgment fBooKi 
 
 formal abstractness which is merely the mark of thought as 
 opposed to sensuous perception. And the result has been to 
 exhibit the graduated existential implication of universal 
 judgment as falling within and not without the import of 
 those judgments, and as homologous with the aspect of 
 existential affirmation in perception and in historical narra- 
 tive. But I propose to comment very briefly on two special 
 problems raised by the view before us. 
 Simple (i) It is easy for any one to form for himself a catena of 
 
 condi- universal judgments, beginning where the proper name 
 tional becomes significant, as with Europeans, Christians, Peelites, 
 inents. ^^^ passing on through the generic conceptions of classi- 
 ficatory sciences, to physical and mechanical principles, 
 geometrical axioms or theorems, and finally to imaginary 
 and impossible but self-coherent hypotheses, like that em- 
 bodied in the ingenious jeu d' esprit entitled ' Flatland '. 
 Such a catena is at the root of the view of Universal Judgment 
 which I have endeavoured to formulate. Any one who will 
 take the trouble to follow up and to fill out with instances 
 familiar to himself the terms of such a series, will hardly 
 be able, I think, to avoid forming the conviction that no 
 single type of proposition is adequate in the same degree to 
 the content of all universal affirmations. If, however, we are 
 compelled to choose, the conditional proposition is the more 
 adequate. But it is not adequate. Such a judgment as 
 ' All Christians hold that God is a Spirit ' combines collective 
 and generic meaning with necessity. It indicates not merely 
 that the doctrine is of the essence of Christianity, i. e. that 
 ' If a man is a Christian he holds ' &c., but that there is 
 a Christian world, realised in many individuals, which is 
 united in this conviction. 
 
 And on the other hand, after our too laborious consideration 
 of the subject, it is not necessary to remind the reader that 
 relativity is operative within the judgment from the moment 
 of the first analysis introduced by perception into the data 
 of sense ; that is to say, even when the judgment assumes 
 the external form of the impersonal proposition, which indi- 
 cates that identifiable subjects are not yet constituted in 
 virtue of determinate qualifications. 
 
Chap. VI] Idea of Supposition criticised 269 
 
 The fact then is this. Speech can express no logical relation 
 except by making it the correlative of a word or clause. But 
 the common types of speech, which have been made the basis 
 of logical investigation, are direct and simple. They therefore 
 embody only one aspect of the concrete logical thought, and 
 leave all others to be guessed at from variety of context and 
 the requirements of content. The process of recognising 
 explicit linguistic correlatives of relations which in these 
 direct forms are only implicit is a slow process — ^Aristotle 
 did not recognise the conditional proposition on its merits — 
 and begins, as is usual in such cases, by substituting one- 
 sided abstraction for unanalysed confusion. Therefore by 
 adopting either the direct or the conditional mode of expres- 
 sion we ignore in the first case, and formally exclude in the 
 second, elements without which it is impossible for judgment 
 to exist. The direct or ' categorical ' form is used till it breaks 
 down under the burden of an import for which it was not 
 invented ; and the conditional form then takes its place, 
 to express the relative import, the determinate and restricted 
 reference from part to part within a whole, which now insists 
 on making itself predominant. But both forms, not one only, 
 are inadequate to their content. The content of categorical 
 assertion has relativity, and that of hypothetical assertion 
 has absoluteness. But categorical assertion (I am speaking 
 of grammatical form) leaves the former, and h5^othetical 
 assertion leaves the latter to be implied. The two forms 
 however have not an equal right to the ground they commonly 
 claim. The first comer has, naturally, occupied all it could 
 get, and more than it could adequately deal with. It is 
 against this encroachment of the categorical judgment-form 
 that modern logicians have rightly espoused the cause of the 
 hypothetical. The true frontier is, beyond a doubt, where 
 the singular judgment ends. After that point, if we dismiss the 
 Individual Universal and omit to consider the Disjunctive, the 
 purpose of assertion is relativity or sequence, and absoluteness 
 or existence is only its presupposition. Formal Logic granted 
 this territory, that of the pseudo-collective and the analogical 
 judgment, to the Categorical Judgment, simply because it 
 found the Categorical or direct Proposition in possession. 
 
270 Universal Judgment [book i 
 
 And the further analysis of the irrelevant connections 
 which encumber every perceptive and singular judgment, 
 and which, if understood to be generally affirmed, imme- 
 diately become false, may be regarded as a reprisal on behalf 
 of the hypothetical judgment, which, now that attention has 
 been drawn to the meaning made explicit in the conditional 
 sentence, threatens to dislodge the categorical judgment even 
 from the fields of perception and of history. The degree in 
 which such a claim should be conceded has been indicated 
 above.* 
 
 Thus the simple and the conditional ^ propositions are, the 
 one of them an indeterminate and the other a one-sided 
 type — both therefore imperfect expressions of thought. The 
 latter is borrowed no doubt from, or is at any rate most 
 appropriate to, the extreme and arbitrary attitude of mind 
 known as supposition. It is natural, as we have seen, that 
 the empire of the first comer should not be broken into unless 
 a forcible demand arose for something utterly incompatible 
 with its type. The representation which is correlative to 
 supposition is thus the sole representation in ordinary speech 
 of the aspect of necessary sequence within the judgment. 
 This is why, when logic awakens to this aspect, it is tempted 
 to find its essence in supposition. 
 
 But supposition is not the essence. Supposition is inten- 
 
 * See p. 261 above, and note Mr. Bradley's later statement, ' Thus 
 we really always have asserted subject to and at the mercy of the 
 unknown. And hence our judgment, always but to a varying extent, 
 must in the end be called conditional. ' To the word ' unknown ' he 
 adds a footnote, beginning ' Hence in the end we must be held to have 
 asserted the unknown. It is better, however, not to call this the pre- 
 dication of an unknown quality (Principles of Logic, p. 87), since quality 
 either adds nothing, or else adds what is false ' — Appearance and 
 Reality, ed. 2, 362. The following discussion of supposition and the 
 hypothetical judgment is not relevant to and does not deny Mr. Bradley's 
 general position as formulated above. I retain it mainly for its treatment 
 of illegitimate hypothesis, which seems to me an interesting point. 
 
 ^ The grammatical difference between the two is connected with their 
 logical import in that the conditional sentence provides for an express 
 analysis ad hoc of the subject-qualification of Reality, whereas the direct 
 sentence simply indicates a subject-content by a name. If we insist on 
 the name being the right subject name in the context, as in Aristotle's 
 KaOuXov, we have an intermediate stage. 
 
Chap. VI] Ufiknown basis of Hypothetical 271 
 
 tional abstraction or selection culminating in fabrication ; and 
 the essence oi the judgment is not in the fact of intention, but 
 in the logical groimd and justification of the intention. The 
 interference of the will is no differentia in a logical process. 
 All thinking presupposes will, but the guide of thought can 
 never be moral purpose, the purpose of will, but must always 
 be logical necessity. What remains then out of the fact of 
 supposition is that a content is taken, chosen, fabricated, if 
 we will, with a view to its relative aspect, to its consequences. 
 But what is presupposed in so taking it, and what are the 
 conditions under which alone it can be so taken — ^whether, 
 that is, it can be taken in the air and without either self- 
 relation or relation to an actual system, are questions in no 
 way touched by the mind's attitude in supposition. We shall 
 see that speech finds the embodiment of a necessity resting 
 on fact in the proposition which expresses the disjunctive 
 judgment. 
 
 (2) The character of Reality on which the sequence 'if a The basis 
 then b ' depends must be in the ultimate analysis of judgment °hetical° 
 admitted to be unknown.* This follows from the ultimate Judg- 
 reduction of all judgment whatever to judgment which is 
 conditional. But if this were so in the case of the hypothetical 
 judgment as commonly imderstood, the back of the sequence 
 would be broken. The ground would be absent. Every hypo- 
 thetical judgment is affirmed only within an actual system. 
 What then are we to do with our ultimate sequence, e. g. with 
 the nexus between resistance and gravity ? I cannot but main- 
 tain that, if we have no explicit ground to go upon, we must 
 either surrender the sequence altogether, or affirm it categori- 
 cally, i. e. not as a sequence, but as a datum ; not as a coherence, 
 but as a conjunction. ' All matter (i. e. aU that resists) gravitates ' 
 is no doubt a judgment in which we look for necessity. But 
 it does not follow that we find it. It presupposes the judgment 
 ' There is gravitating matter '. It is not adequately rendered 
 by ' If or wherever there is matter it gravitates '. We are 
 unable (or at least I am unable, which is all that my illustration 
 requires) to assign any system which acts as ground and 
 compels the sequence to be true within it. The world of 
 * See note, previous page. 
 
272 Universal Judgment [Book i 
 
 matter given as resisting and gravitating, as a systematic fact, 
 is the ground. And therefore it is on the other hand a true 
 hypothetical judgment to say, ' If a material object is set free 
 within range of a gravitating centre, it falls with a velocity 
 accelerating as the squares of the times.' For the content of 
 this judgment is within the system of gravitating bodies, and 
 the sequence is compelled by that system, whose existence as 
 a fact is required by the judgment, but not in this form ex- 
 plicitly asserted. In this case the unity of gravitating matter 
 is "the X on which the sequence a-b is founded. 
 
 May not the whole system be supposed, ground and all ? 
 Certainly not ; and this is the fundamental point at stake. 
 Every judgment is a qualification of reality by some ideal 
 content, and when the basis of a sequence is the content by 
 which reality is qualified, that basis is by the judgment 
 affirmed to be actual. So far Mr, Bradley and I are together ; 
 my further contention is that this ground or basis must be 
 known, and must be indicated in the judgment, of which it 
 forms the essence. The degrees in which it is so indicated 
 form the various complete and incomplete grounds which were 
 discussed above. But an ultimate ground must be actual ; it 
 is the fact which is judged in a hypothetical judgment. We 
 may of course freely suppose or imagine a system, as complex 
 as we please ; but if we proceed to judge about the consequences 
 or results of such a system, it must thus be related to these 
 consequences within some further system ; and this further 
 system must be actual. In other words, you can only 
 suppose an antecedent, you cannot suppose a consequent ; 
 the consequent must be judged, not supposed ; and in 
 judging the consequent you assert the underlying ground to 
 be actual. 
 
 This may be illustrated by the extreme cases in which we 
 refuse to entertain a supposition. This means that we are not 
 aware of any reality which furnishes a system such that the 
 supposed case is capable of entering into it. When supposition 
 begins to infect the nature of the reality, we are beginning 
 to suppose and not to judge our sequence. It is quite doubt- 
 ful whether the conclusions of ' Flatland ' can be taken as true 
 even qua hypothetical judgments. When your supposition 
 
Chap. VI] Illegitimate Suppositions 273 
 
 has knocked the keystone out of actual reahty, how is it to 
 support a conclusion ? 
 
 The appHcation of this conception would I think solve the 
 curious cases in which a sequence is true, though it is possible 
 for the content of supposition not to exist, or even impossible 
 for it to exist. What must exist is a system that, subject to 
 the supposition, necessitates the consequence drawn from the 
 supposition. Whether the content itself exists or not depends 
 upon whether it is an element essential to the system ; and how 
 it exists, on the nature and selfcompleteness of the system. 
 The former condition meets the case of impossible contents, 
 which are in every case illegitimate suppositions — i. e. sup- 
 positions in which the consequent has to be supposed and not 
 genuinely judged, because the supposed antecedent conflicts 
 with the nature of the real system on the basis of which alone 
 any conclusion about it can be drawn. 
 
 I will take some examples. ' Given a first cause, we can 
 dispense with the idea of a regress to infinity.' But Cause, in 
 any sense which it could be First, i. e. in temporal relation, 
 means an element in a system of relativity. Therefore the 
 idea of a first cause contradicts the whole actual system to 
 which the idea of Cause refers, and it is utterly impossible 
 to affirm anything about an idea which begins by destroying 
 its own basis of affirmation — the causal system. Or again : 
 ' If one man were throughout the whole period of his conscious 
 life alone in the universe, his moral purpose could be nothing 
 but to please himself.' Here we are judging on the basis 
 of an existing moral world — for it is only this that gives a 
 meaning to a judgment relating to moral purpose — but we 
 are putting a case which contradicts the nature of man as 
 a being existent in a moral world. I do not think that in this 
 case any judgment can reasonably be made. But the purposes 
 of supposition in argument are so various, for its object may 
 be in different degrees to emphasise the impossibility of the 
 content supposed, that the limits of legitimate supposal are 
 exceedingly hard to define. Undoubtedly its use is one of the 
 most fallacious if one of the most effective means of controversy. 
 * If A. B. were to turn coward ' — ' But he could not ' — ' But 
 I am only putting a case '— ' But if you put such a case I may 
 
 1337 T 
 
274 Universal Judgment [book i 
 
 put any consequence I choose as equally likely,' i.e. it is felt 
 that the real basis on which judgment rests is annihilated. 
 
 Some real basis can never be dispensed with in judgment. 
 The nearest approach to dispensing with it is made when 
 elements of reality which would conflict with the suggested 
 case are wilfully kept out of account by an act of abstraction ; 
 which act of abstraction may be either borne in mind, or 
 forgotten. If the act of abstraction is borne in mind, we 
 obtain such judgments as those in which mathematical 
 science deals with imaginary quantities.-^ Thus judgments 
 are subject to the reservation implied in the abstraction from 
 reality which enables them to be made. Yet, in as far as they 
 are judged at all, they must rest upon, and involve the affirma- 
 tion of, properties of reality. If the abstraction is forgotten, 
 we then obtain such judgments as apply imaginary conceptions 
 without reservation to the real world ; ' A conjuror can tie 
 a knot in a string whose ends are held, because he understands 
 the properties of four- dimensional space.' 
 
 I may further illustrate this last case by the example of 
 artistic fiction, which I have discussed at length elsewhere. 
 It consists of judgments both singular and universal,^ made 
 on the basis of human nature, but subject to a reservation 
 which separates them from the world of past sensible events. 
 While actually under the spell of romance or of the drama, 
 we forget or half forget this reservation ; but we do not and 
 cannot forget the true and ultimate basis of the judgments, 
 fundamental human nature, which is the ground and substance 
 of the whole matter. 
 
 ' See p. 165 ff. on mathematical infinity. 
 
 ^ It may be doubted how far the universal judgments in a fiction ought 
 to partake of the character of fiction. It depends on their grade of 
 universality. Judgments of a reflective order, about human nature for 
 instance, if not dramatic, are expected to be true without reserve. 
 Judgments about parties, nations, &c., may be fictitious. Dramatic 
 sayings are yet more complicated ; they are not judgments of the 
 author at all ; the author's (fictitious) judgment is that they were 
 uttered. Then their value or merit is compounded of their truth as 
 estimated by the limited reality of the drama in which they occur (i. e. 
 their appropriateness) and of their truth as estimated by real reality, 
 i. e. their weight or depth, which of course involves the whole relation 
 of the piece to real reality. See Knowledge and Reality, p. 140 ff. 
 
Chap. VI] Affirmation of Sensible Events 275 
 
 But we raised a question not only whether the content 
 exists, but how the content exists. This depends, we said, 
 on the nature and self-completeness of the system within 
 which it exists. Many universal judgments deal with sensible 
 events, which are not, within our knowledge, contained in any 
 really concrete whole in time and space. For these, according 
 to the principle which we have followed throughout, the 
 abstract universal or hypothetical judgment postulates such 
 existence as they can have, according to their nature and 
 that of the incomplete system to which they belong. There 
 is nothing which cannot ultimately be taken up into some 
 individuality by constructive thought. But as in ordinary 
 judgment no such actual construction is operative, we have 
 to substitute for it the mere assertion of the basis to which 
 the sensible occurrence in question is known to have some 
 relation. The imperfect explicitness of this relation is the note 
 of distinction between the hypothetical and the disjunctive 
 judgment. ' Pure red is ethereal undulation impinging on a 
 normal eye with x vibrations to the second.' Here the ground or 
 basis of af&rmation is the existence of hght, which is ultimately 
 dependent on the existence of sentient organisms in a certain 
 relation to the material world. Now this relation, though not 
 known nor explicit in the judgment, must be taken as knowable 
 and real. Space and Time indeed produce the illusion of endless- 
 ness ; but no special positive content like sentience or light is in- 
 volved in this illusion ; we rather assume every positive content 
 to have its own time, place and conditions within our actual in- 
 dividual system. No doubt we may be asked, Does the above 
 hypothetical judgment assert the existence of red, or not ? And 
 can we claim to assert the reality of what is for us an indeter- 
 minate endless series which as a whole cannot be real? To 
 these questions I should propose to reply : ' The hypothetical 
 judgment in question asserts the existence of light as the 
 categorical basis of the nexus which it selects. The existence 
 of red Hght is involved in the existence of normal light- 
 stimuli and normal eyes. Therefore the judgment in question 
 asserts the existence of red Hght as a feature of the reality 
 constructed by and for us, and subject to the reservations 
 which its position in that reality imposes on it. We do not 
 
 T2 
 
276 Universal Judgment [Booki 
 
 claim to assert the reality of an endless series of sensations 
 as such ; but in the first place a positive series as referred to 
 an actual system is already placed beyond theoretical end- 
 lessness, and in the second place it is not as an occurrence 
 in the way of sensation that we assert its reality, but as an 
 attribute of things in the whole of consciousness, which, as 
 constructed out of perception, is for us the only reality.' 
 This is in effect the answer which was given above to the 
 question whether the conceptions of geometry were judged 
 to be real ; and it follows inevitably from the considerations 
 to which we were led in treating of the doctrine of Ground. 
 We shall see that the real Ground, when made explicit, takes 
 us into the province of the disjunctive judgment. The 
 element of categorical assertion in the hypothetical judgment, 
 consisting as it does in some underlying real attribute, also 
 presents a close analogy to the positive basis of negation, as 
 will appear in the following chapter. 
 
CHAPTER VII 
 
 Negation, Opposition, and Conversion 
 
 r. The Negative Judgment presents at first sight a para- Negation 
 doxical aspect. We are bound to take it, qiia judgment, as \^rma- 
 playing some part in knowledge, and as at any rate capable tion. 
 of contributing some factor to the ideal fabric of reality. 
 But it assumes the external shape of ignorance, or at least of 
 failure, and the paradox consists in this — ^that in negation 
 the work of positive knowledge appears to be performed by 
 ignorance. The contradiction arises, as we have seen other 
 contradictions arise, from the adoption by thought of a shape 
 which at best expresses it but partially, and the retention of 
 that shape when the aspect which it did express has come 
 to be dwarfed by other aspects of knowledge. But of course 
 the shape could neither be adopted nor retained did it not 
 in some prominent aspect coincide with the requirements even 
 of developed thought. Here then, as elsewhere, the key to 
 our problem must be looked for in the conception of the 
 individual mind working out its participation in reality by 
 help of forms never wholly alien to this aim, but profoundly 
 transmuted in proportion as it is attained. 
 
 Negation is at first sight merely negative, It appears to 
 say nothing, but only to deny, i.e. to put away some ideal 
 content as other than reality or to express our inability to 
 recognise it as belonging to reality. The first step then 
 towards ascertaining its import is to ask, what does it deny 
 or pronounce unreal ? what does it presuppose to be present 
 before denial is possible? 
 
 It certainly does not presuppose an affirmation. Both 
 fact and theory protest against such a view. We have not 
 always judged a matter to be true before we deny it. And 
 if an affirmation ^ of the same content is to subsist as a con- 
 
 ^ Sigwart distinguishes ' affirmation ', as the conscious opposite of 
 negation, from ' Positive ' judgment, as assertion without consciousness 
 
278 Negation, Opposition, and Conversion [Book 1 
 
 dition of the negation, it seems doubtful whether a negation 
 would not always have to be self-contradictory. Although 
 Sigwart's account of double negation suggests this view, 
 yet he says explicitly^ that it is an attempted judg- 
 ment (' Ein versuchtes — Urtheil ') against which negation 
 is directed. And this seems so far to agree with experi- 
 ence. What is the nature of this attempted affirmation? 
 ' Suggestion ' and ' question ' come into the mind as possible 
 equivalents for it. It is difficult however to find a special 
 significance for either the one or the other on purely logical 
 ground. A question is closely related to a command, and 
 has its differentia in being addressed to the will of another 
 person. It is impossible in good faith to ask a question of 
 oneself. The power of the metaphor by which men are said 
 to question themselves rests on treating oneself as another 
 person. A question is a demand to the will to reveal some- 
 thing known to the person whose will is appealed to ; but 
 if I know the answer, I need not asl: myself ; if I do not, 
 I cannot ask myself. 
 
 A question then as such has not a logical differentia, and 
 cannot be the logical presupposition of negative judgment. 
 Still it may contain what we want. It is not merely an ideal 
 content floating before the imagination, even if we were to 
 grant that there are such floating ideas. It is an idea in 
 some way tested by Reality. A suggestion seems to be the 
 same. It is not a floating content ; it is suggested as some- 
 thing, as, so to speak, a candidate for a place in a judgment 
 already framed. That is to say, a question or suggestion 
 as it is on logical ground, omitting any demand upon or 
 incitement to another will, amounts at least to an idea whose 
 content is Reality qualified in a certain way. Is this all ? 
 This would not suffice to explain the import of suggestion 
 followed by affirmation or denial. It would not explain the 
 significance of the decision even when negative. There is 
 something more, and it is this. The content of the suggestion 
 
 of possible negation. We shall see in the sequel the value of this dis- 
 tinction, which can only be taken as one of degree. 
 
 ^ Logik, vol. i, p. 150, and 194 (with assent to Bradley's Logic, 
 p. 149 ff,). E. Trans. 119 nnd 149. 
 
Chap. VII] Negation and Suggestion 279 
 
 is taken within a whole in which we have an interest and which 
 is referred to actual ReaHty. Every suggestion enters into 
 a rudimentary disjunction. I mean by rudimentary disjunc- 
 tion an alternative whose limits are not made explicit. Where 
 there is a question or suggestion, there is always a something — 
 some general predicate — known to be true with reference to 
 the matter before the mind, and an interest which we have 
 in that something. It is within this something that the 
 attempt to state it more precisely, the question or sugges- 
 tion, falls. It is hazardous to obtrude analysis on the simpler 
 stages of consciousness ; but I do not see how we can have 
 a suggestion followed by denial cheaper than this. We might 
 even fall back on the principle which has been laid down in 
 previous discussions, that any consciousness for which a con- 
 tinuous real world exists, sustains that world by a judgment. 
 When a man first doubts and then decides, on such a question 
 as whether the river which he sees before him is safe to ford, 
 however simple the mental procees may be, there must be 
 in some form a positive basis of the two or more alternatives 
 as well as one suggested alternative. He must start with the 
 fact that the river has depth, or current, which he must deal 
 with in crossing, and within this fact the doubt ' too deep ? ' 
 ' too swift ? ' has its meaning for him. In simple cases this 
 embracing judgment of fact is hardly traceable except through 
 the interest in the question. This interest, if looked at closely, 
 betrays the nature of the alternative which the question in- 
 volves. 'Too deep?' 'What then?' ^I cannot get home 
 to-night,' i.e. the general fact is that the river is between me 
 and home. 
 
 Negation then presupposes an idea suggested as true of 
 Reality within a state of facts judged to be true of Reality 
 and interesting to us in respect of the matter suggested ; or 
 in other words, an alternative judged to be true of Reality, 
 but only so judged as one among a set of alternatives, and 
 therefore, in itself alone, problematically judged true of reality 
 — judged as a possibility, as one among a number of alterna- 
 tives, or as subject to unexpressed conditions. 
 
 We are now able to decide the disputed question whether 
 Affirmation is prior to Negation, or whether they are co- 
 
28o Negation, Opposition, and Conversion [Booki 
 
 ordinate types of Judgment. Negation is not, as such, the 
 denial of affirmative Judgment, and therefore does not pre- 
 suppose the affirmation of that which is denied. So far, 
 affirmation is not essentially prior to negation. On the other 
 hand, Negation does presuppose some affirmation, that is 
 the affirmation of a state of facts which, being judged true 
 as a whole, carries with it the problematic affiurmation, the 
 affirmation as a possibility or enunciation as a conception in 
 the world of meanings, of the idea ' suggested '. In this 
 respect, therefore, affirmation is in the beginnings of know- 
 ledge, at any rate, prior -^ to Negation. The world must have 
 positive content judged to be real as a condition of anything 
 following from the removal of a positive suggestion. But 
 I cannot believe that the consciousness of a positive world 
 could in fact exist for an appreciable time without the develop- 
 ment of negation.^ Further, however, it is also true that in 
 the beginnings of knowledge negation is a degree more remote 
 from reality than is affirmation ; ^ and this character of 
 ideality clings to the negative form through its whole develop- 
 ment, though without debarring it from the acquisition of 
 objective value. The remoteness consists in this, that the 
 suggestion which denial presupposes is, as we saw, not a mere 
 floating content, but a suggested qualification of reality, in 
 short ' a suggested affirmative relation '.■* An affirmation can 
 be, comparatively speaking, given as fact ; a negation cannot, 
 except in quite another sense, be given. It has to be made, 
 and made by setting an ideal reality over against real reality 
 and finding them incongruous. ' That fire is still burning ' 
 involves no doubt intellectual selection and is so far ideal, 
 but ' that fire is not out ' is one remove more ideal, because 
 it has to bring up the idea of ' that fire being out ' and test 
 it by the perceived reality, and then only proceed to judge 
 its exclusion to be a fact. We must not however exaggerate 
 this difference. Affirmation itself, or even positive Judgment, 
 cannot take place until the distinction between a mere idea 
 
 ' In this sense it may be called, if we prefer to do so, ' positive ' 
 judgment. 
 
 ^ See above, Introduction, p. 22, on t\\e fornml implication of distinc- 
 tion in objectification. 
 
 ^ Cp. Bradley's Principles of Logic, p. 116. * See Bradley, ib. 
 
Chap. VIII Affirmation prior to Negation? 281 
 
 and a fact of reality is recognised. And with this distinction 
 the idea of negation is given. It might therefore be argued 
 that Judgment, not to speak of affirmation, presupposes the 
 idea of a negative relation ; -^ just as negation presupposes 
 that of an affirmative relation. The fact seems to be that 
 affirmation presupposes the idea of negative relation in 
 general, while negation presupposes the idea 0/ ^ a correspond- 
 ing affirmative relation in particular. This apphes to the 
 beginnings of knowledge. In complete thought we shall find 
 the two more on a level. 
 
 Thus it is true, especially in the beginnings of knowledge, 
 that Affirmation is prior to Negation, both as one remove 
 nearer to reality, and as supplying the reality within which 
 alone Negation has a meaning. But it is no less true that 
 Negation has from the first its essential place in knowledge ; 
 and as Reality becomes for us an articulated system, the value 
 of negation approaches more and more nearly to that of 
 affirmation, with which it finally becomes equivalent. This 
 is however not to be understood in the sense that the import 
 of negation disappears from knowledge ; but in the sense that 
 affirmation and negation alike become double-edged, each in- 
 volving the other, 
 
 2. Negation then, in its primary shape, is the exclusion Bare 
 of a suggested qualification of reality. The bare expression and^in- 
 of this import, reduced to its minimum, would be found in finite 
 what has been called by a mis-translation of Aristotle, the ^q^^. 
 infinite judgment. 
 
 The infinite judgment was a term applied by Kant (fol- 
 lowing, I presume, the tradition of formal logic) to judg- 
 ments which had for their predicate what Aristotle called 
 an ' indefinite ' or ' undistinguished ' name or predication ; ^ 
 i.e. such a phrase as ' not-man ', 'not-good,' or the like. 
 More important however than Aristotle's expression ' in- 
 definite name ' was his distinct verdict that such phrases 
 were not names or predications. He gave them the title of 
 
 ' Cp. Bradley, Principles of Logic, pp. 2, no. I find some difiicult}' 
 in reconciling these two passages. 
 
 ^ Not ' presupposes a corresponding afiirniative relation as judged 
 true.' That view we have rejected. ^ pfll^°- or ovona dopiarov. 
 
282 Negation, Opposition, and Conversion [Booki 
 
 indefinite or undistinguished names or predications, ' be- 
 cause they may be truly predicated of everything ahke, 
 whether existent or non-existent.' ^ It is plain that Aristotle's 
 verdict is right, and that such names have no signification. 
 They are ' undistinguished ' because they are undistinguishing. 
 It may therefore be observed in passing that to attempt to 
 read all negation as affirmation of a negative name is an 
 unmeaning device, though possibly guided by a feeling of a 
 true ideal, viz. that negation, if it is to have a positive import, 
 must involve an affirmative element. Only by this contrivance 
 the affirmative element is ludicrously absent. We should be, 
 as Mr. Bradley says, denying, and then affirming that we have 
 denied. 
 
 It is for this reason that the ' Infinite judgment ' may be 
 fairly represented by examples in which the denial, though 
 undeniable, is unmeaning. ' Virtue is not square,' ' The soul 
 is not red,' 'Man is not a stone.' These, 5'wa negative, are 
 fully on a level with ' A monkey is not -man,' ' A stone is 
 not-Christian.' And so in illustrating the import of negation 
 we may disregard the pseudo-affirmative character of the 
 latter instances. Our interest in them is that, if strictly 
 interpreted, they display to us the nullity of bare denial. 
 ' Not-Christian ' literally interpreted includes not only heathen 
 humanity, but the fixed stars, the sea, and indeed, in Aris- 
 totle's words, ' everything whether existent or non-existent ' 
 except Christians. It refers to no one sphere in preference 
 to another, and thus says nothing definite enough to be 
 intelligible. The point being once established that negation 
 qua negation has no significance, we may disregard the attempt 
 to erect it into affirmation which draws our attention to this 
 fact. And we may then safely take as instances of the infinite 
 judgment, so far as its import is concerned, the judgments 
 typified by ' Virtue is not square ' . These show the true type of 
 bare denial, for they are the only negative propositions in which 
 usage does not irresistibly limit the sphere of the negation. 
 And when the sphere is limited, the denial is no longer bare. 
 
 ' Ar. n«pt "E^pn. 2. 3. Though the reading is doubtful in the appli- 
 cation of these words to ovk uvofxa, it is enough for our purpose that 
 they are applied to ov pfj/xa. 
 
Chap. VII] Bare Negation and Tautology 283 
 
 Thus it appears that bare denial, whether disguised as 
 spurious affirmation, or taken as the mere exclusion of mere 
 suggested predicates, amounts in the strict sense to nothing. 
 The judgments by which it is typified are the exact counter- 
 part of absolute tautology, and like such tautology, are not 
 really judgments at all. Identity and difference are insepar- 
 able aspects of all that exists or can be thought ; but in these 
 two classes of would-be judgments identity and difference 
 fall apart, and thereby the conditions of intelligible judgment 
 are destroyed. Pure tautology aims at mere identity, and 
 bare negation at mere difference. It will be found that any 
 meaning which in practice we attach to an apparent tautology 
 or an apparent bare negation is owing to the introduction 
 of difference into the former, or of identity into the latter. 
 ' Business is business ' qualifies a certain class of affairs by 
 the principles on which they ought to be conducted ; ' The 
 soul is not a machine ' qualifies the soul, not by the mere 
 exclusion of mechanical properties in favour perhaps of 
 absolute nothingness, but by some positive characteristic of 
 the soul which is incompatible with its being a machine. 
 
 3. We have seen that denial was not to be made into Signifi- 
 affirmation by the rough and ready method of the Infinite pgnjai. 
 Judgment. But we started, on the other hand, from the 
 postulate that denial, as a form of judgment, must be capable 
 of contributing something positive to knowledge. Whether 
 positive necessarily = affirmative is a problem that will solve 
 itself as we come to understand the full nature of negation. 
 I use it here simply as antithetical to ' nothing ', or as an 
 emphatic reiteration of ' something '. We must assume with 
 Plato that knowledge is the knowledge of something ; and 
 if the nature of * nothing ', as e. g. the abstraction of empty 
 thinking, can be known, then nothing is so far and in that 
 sense something. 
 
 All significance then is in this sense positive significance, 
 and significant negation must therefore convey something 
 positive. What is it that it does convey ? We shall find 
 the answer if we look at that which all judgment has in 
 common, viz. the interest or bearing of the judgment. What 
 is it that we really mean or wish to predicate when we make 
 
284 Negation, Opposition, and Conversion [Booki 
 
 an ordinary negative judgment ? There is always, I may 
 observe, something unreal in the analysis of isolated propo- 
 sitions. Apart from the context of a book or of a conver- 
 sation, or from the precise standards which involve the fixed 
 context of science, our interpretation of propositions into 
 judgments is almost entirely arbitrary. On the other hand, 
 it may be said that in a given context the ' bearing ' which 
 we ascribe to a proposition is not strictly within the limits 
 of what the proposition enunciates, but is read by us into 
 its meaning. It may be doubted however whether in actual 
 living thought there is any judgment that is not an enthy- 
 meme, i. e. an argument with a suppressed premise or a sup- 
 pressed conclusion. If we attempt to prune away from the 
 judgment all the implied and suggested bearings of the propo- 
 sition which conveys it, we shall find that we have whittled 
 away the meaning which is the judgment itself. We must 
 never forget the conclusion which we reached above, that 
 the unity of the judgment does not exclude systematic multi- 
 phcity within it. The logical content employed in any given 
 judgment is a many-sided although determinate idea, and is 
 gripped and attached to its actual place in the logical 
 mechanism now by some of its prominences and now by others. 
 Some reservations will have to be made in this respect when 
 we come to speak of judgments that deal with self-contained 
 systems, a type which we have more or less anticipated in the 
 individual and generic judgments. But in ordinary reflective 
 judging we are constantly referred away and away along a 
 series of grounds and consequences, and it is idle to attempt 
 to reduce the judgment to simplicity. What we really mean to 
 mean is only to be found in the explicit articulation of the 
 whole system of fact which the interest of the moment 
 covers ; and all ordinary judgment toils after our interest 
 in vain. But prima facie the positive judgment has an 
 advantage in this respect over the negative. A positive 
 content is at all events something ; it is an instalment in 
 satisfaction of our interest. If I say that the fire is burning 
 in the dining-room, this judgment is no doubt compatible 
 with various grounds and various consequences, and in the 
 judgment as I mean it some particular ground and some 
 
Chap. VII] The * Point ' of a Judgment 285 
 
 particular consequence are probably included. Such a state- 
 ment would not be made a propos of nothing, or if it were, it 
 would be resented just as talking gibberish would be resented. 
 There is some point or purpose to which it must be taken as 
 contributing, and some reason — though possibly falling out- 
 side the content of the judgment — which serves as a ground 
 for making it. But over and above all this there is, in the 
 affirmative judgment, the positive logical content itself, which, 
 though modifiable within very wide limits, yet cannot be 
 modified beyond certain limits. The judgment may be in 
 praise of some one's thoughtfulness, in condemnation of their 
 extravagance, in contempt of their effeminacy, or in alarm 
 at their carelessness. But there is a nucleus, not indeed fixed 
 nor free from ideal selection and synthesis, yet not quite inde- 
 finitely variable and containing a positive element of appeal 
 to normal perception. 
 
 In a negative judgment strictly interpreted as mere denial 
 this nucleus is lacking, as the consideration of bare denial 
 taught us. Therefore we have nothing left but those ele- 
 ments of meaning to which the interest of predication is the 
 sole clue. Let us take a plain every-day judgment such as 
 ' A. B, is not a dishonest man '. If we enunciated this pro- 
 position in the sense of the infinite judgment, meaning e.g. 
 that A. B. is not a man at aU, but a stone or a monkey, we 
 should unquestionably be held to have violated the conven- 
 tions of speech. The meaning of every judgment is to be 
 looked for in the attribute to which is attached the interest 
 that guides the selection of the content used in judging. 
 But this attribute must obviously have definite relations, at 
 any rate for some special purpose, to the content afiirmed or 
 denied. Whether it can precisely coincide with the content 
 affirmed is a point to which I shall have to recur ; but it cannot 
 precisely coincide with the content denied, for if so, no result 
 in which we had an interest would spring from the denial — 
 the whole reason of our interest would be cancelled and be put 
 away with the denial of the attribute on which it centred. 
 
 Now I may be interrupted at this point with the objection 
 that this is exactly what is always happening in negation. 
 When we have suspected a man or thing of having some 
 
286 Negation, Opposition, and Conversion [Book i 
 
 attribute which interests us, and then find that we were 
 mistaken, our interest in the individual may, and often does, 
 fall dead at once. A man may be pointed out to us in a 
 crowd as about to be our fellow-traveller on a difficult journey, 
 and we may regard him with some interest on that account ; 
 but if we learn that it was a mistake, and that we have nothing 
 to do with him, we shall probably after that regard him as 
 ' nothing to us '. This is in fact almost a recurrence to the 
 infinite judgment ; for though we must know that he is 
 a. man, yet so long as he is not to be our fellow-traveller We 
 do not care whether he is alive or dead ; i.e. for any positive 
 quality of his himianity. The judgment ' he is not coming 
 with us ' approaches then to a judgment of bare exclusion, 
 the attribute in which we have interest being the attribute 
 excluded. 
 
 In the first place, I think, we must to a great extent admit 
 this contention ; and simply refer it to a difference of degree. 
 Negative judgment does begin with a phase inappreciably 
 differing from the infinite judgment. But yet, of course, the 
 question ' Coming with us ? ' must have originated in some 
 such judgment as ' He is the sort of person who might be 
 coming with us ' ; and it is within this fact judged true that 
 the ultimate negation ' not coming ' has its meaning. The 
 interest is first awakened by the whole attribute ' such as to 
 come ', and could never have been aroused but for the presen- 
 tation of such an attribute. If the negative judgment were 
 reaUy one of bare exclusion it would apply equally well to 
 everything in the world, and no interest would have been 
 aroused which could have led us to make it of a particular 
 individual. But in the second place, it must be added that 
 in as far as, in the alternative which formally arises within the 
 attribute ' such as to come ', aU the interest practically falls 
 on one side of the alternative, this is an actual defect of 
 knowledge and morality, but has not, in the case supposed, 
 been pushed far enough to prevent the insistance on the 
 positive attribute ' capacity to come ' } And this attribute 
 
 ' It is a commonplace satire to say of a man that the universe interests 
 him only in as far as it is what his particular whim requires. What is 
 not money, or total abstinence, or woman's emancipation, as the case 
 
Chap. VII] Content of Denial 287 
 
 supplies in fact a positive content for the denial, though we 
 by the hypothesis happen to be now indifferent to it. The 
 denial reaUy contains the judgment, ' The man is one who, we 
 thought, might come, but is not coming.' The proximate 
 case in the ascending scale of knowledge may be illustrated 
 by supposing that instead of our interest dropping dead on 
 hearing that he does not come with us, this negative judg- 
 ment enunciates to us a regret that he is not coming, implying 
 that we ascribe to him some positive quaUty which causes us 
 to regret losing his company. In this case the positive 
 bearing of the negation ' He is not coming with us ' is primarily 
 a consequence of the negation operating upon the judged con- 
 tent * We should wish him to come with us '. This conse- 
 quence supplies the denial with a positive import, and may 
 be the only aspect of it prominent in the mind. 
 
 But there is something else to be considered. Every 
 judgment without exception challenges the question ' Why 
 is it so ? ' or at least ' How do you know it to be so ? ' the 
 former question demanding the cause or real ground, the 
 latter demanding the cause of knowledge or logical ground. 
 These two kinds of ground run into one another, as we saw, 
 and need not be distinguished for our present purpose. In 
 denial, then, there must be this element also of positive import, 
 the attribute which justifies the denial for us. It is plain 
 further that in case of the non-existence of the immediate 
 or apparent subject, this attribute may be judged directly of 
 Reality, which is the ultimate subject in Negation as in all 
 Judgment. ' The house on the marsh is not burnt down ' 
 may be true because there is no house on the marsh, and 
 although reality — ^positive fact — excludes the burning down 
 of any such house. ^ 
 
 may be, is nothing to him. This is a good illustration of the moral and 
 intellectual impotence indicated by any approach to bare negation. 
 Hegel has quaintly compared the distinction between bare and signifi- 
 cant denial to that between crime and civil dispute. If I steal, my act 
 says ' This is not yours ', without asserting that it is mine or any one's 
 by right, i. e. it ignores the whole sphere of property or reasonable 
 possession by alleging no ground for its denial. In a civil dispute I say 
 ' This is not yours, because it is mine,' i. e. I assert rights of property, as 
 you do ; but I deny your right on the ground of mine. 
 
 * It may be objected that in such a case to say ' The house on the 
 
288 Negation, Opposition, and Conversion [Booki 
 
 Thus in Negation we have two positive elements which 
 may be present together, or in various relations of prominence, 
 or may wholly or partially coincide. The third element of 
 import, the positive content explicitly employed in judging, 
 falls away in the negative judgment, being replaced by a bare 
 exclusion of an explicit content. This bare exclusion is what 
 we discussed on its own merits in the second section of the 
 present chapter, and found to amount in itself to nothing.* 
 We are therefore referred for the meaning of significant nega- 
 tion to the positive ground, or positive consequence, of the 
 exclusion which forms the outward and visible shape of nega- 
 tion. Thus we approach the solution of the problem how 
 knowledge can take the form of ignorance — how ' what it is ' 
 can be known through knowing ' what it is not '. 
 
 marsh is burnt down ', is not so much false as unmeaning ; in other words 
 that the negative ' the house is not burnt down ', has meaning only if 
 there is a house, and presupposes or asserts that there is one. I have 
 strong sympathy with this objection, which turns on the problem of 
 a real distinction between subject and Predication within the Judgment. 
 But an unmeaning judgment is clearly not true. The only doubt is 
 whether its not being true justifies any negative except one which should 
 brand it as unmeaning, e.g. ' There is no house to burn down.' The 
 more hypothetical judgments are, the less they present this difficulty. 
 " I think that Mr. Keynes' objection (pp. 122-3) to my account of 
 bare denial is sufficiently met by what has been said above, especially 
 on pp. 281-2 and 285-6. I will only remark (i) that I count two 
 elements of positive significance in the negative judgment viz. the 
 ground and the consequence or positive interest and not the ground 
 only ; (2) that wholly to separate ground from a judgment is always 
 to destroy in great part the meaning of the judgment — this is essential 
 to a sound theory of inference ; and (3) that our ready acceptance and 
 interpretation of such judgments as his examples shows how far we are 
 from bare negation when we accept them ; for their natural meaning, 
 which we accept, is conditioned by a whole system of context and 
 positive interest which we presuppose as always present with us. 
 Literally taken ' A.B. did not start by that train ' may mean there was 
 no A.B. in the world, or the man who started had not that name, or 
 that A.B. is a mountain in South America, and therefore could not start 
 by a train. How common it is for any careful speaker to say ' A.B. did 
 not start — at lea^t I looked and could not see him ', thus supplying 
 what we know the literal judgment wants. You may insist, ' but it 
 means at least the denial ; ' but I insist ' It does not tell you what the 
 denial means, except by assuming a context and positive interest, 
 which take it beyond bare negation. ' On the same passage in Mr. Keynes ' 
 book, see further, p. 297 below. 
 
Chap. VII] Positive Basis of Negation 289 
 
 The primary analysis of the significant negative judgment 
 presents therefore a close parallel to that of the hypothetical 
 judgment. ' A is not B ' may always be taken to = ' A is ^ 
 which excludes (or which is implied in excluding) B '. Or 
 in extreme cases we may have ' Reality is x, which excludes 
 or is involved in excluding A B '. Just thus we saw that ' If 
 A is B it is C ' may always be interpreted into ' A is a factor 
 in a real system x which given A B involves C ' ; or in an 
 extreme case, ' Reality contains a system x such that, if 
 A B were placed within it, C would result.' We examined 
 at length the conditions under which such a relation as that 
 enunciated in the hypothetical judgment could be made 
 intelligible, and we found that a real system within which the 
 separate terms should be interdependent was the bond of 
 union which alone could justify such a reference of one thing 
 to another. In the same way we saw that negation presup- 
 poses a real system — a system affirmed in judgment to be 
 actual — as a condition of its intelligibihty ; and if it is replied 
 that a system presupposes negation — for it presupposes 
 difference — we must answer, first, that negation in its pure 
 form as simple contradiction is the abstraction of difference, 
 and may be later in origin than, or at least presupposes as 
 coeval with it, the positive differences which all thought 
 involves ; and secondly, that in thought it is possible and 
 indeed is the rule for factors to presuppose each other, and to 
 grow into distinctness pari passu. In fact. Negation is 
 simply the logical, conscious expression of difference. 
 
 Significant negation, then, like hypothesis, is intelligible 
 within and with reference to a system judged to be actual. 
 It is only within such a system that something can be made 
 out of nothing by implying a positive ground or consequence 
 in a bare denial. In other words, the essence of formal 
 negation is to invest the contrary with the character of the 
 contradictory, or to raise mere discrepancy or positive oppo- 
 sition to the level of the absolute or contradictory alternative 
 which is the abstraction of difference. It is only contradictory 
 negation which allows a conclusion to be formally drawn from 
 the negative ; contrary negation does not admit of this. It 
 is only contrary negation which allows any import to be 
 
 13.37 U 
 
290 Negation, Opposition, and Conversion [Booki 
 
 materially attached to the negative ; contradictory negation 
 does not admit of this. The fact that contrary negation can 
 be given the force of contradiction, that a positive opposite 
 can be known as a sole alternative, and that unless this is 
 done knowledge remains inarticulate and chaotic, is simply 
 the fact that Reality is a system. It is in considerations of 
 this kind that we must look for a reconciliation of confhcting 
 ideas as to the ' subjective ' or ' objective ' place of negation. 
 We must ask in every case what negation ? The negation of 
 what and under what presuppositions ? Without going further 
 into extreme views about the objective import of negation, 
 I am most anxious to persuade the reader that the fruitful 
 question is not ' Can we conjure a meaning out of a bare 
 denial ? ' but ' Why is it that in knowledge we cannot do 
 without denial ? ' ' In your " system of differences ",' it may 
 be said, ' you put a significance into your negations, and then 
 pride yourself on finding there what you put in.' This is 
 true. What I want to insist on is the fact that this kind of 
 significance cannot be put into anything but negation, and 
 the light which this fact throws on the significance in question. 
 Reality is a system, and you cannot have system apart from 
 negation. This is the central fact from which all enquiry 
 must start. The connecting link between difference, contra- 
 diction, and contrariety ^ is that difference becomes contra- 
 diction when taken as mere difference or as the abstraction of 
 difference, that is, as expressed in a negative judgment which 
 (like the infinite judgment) professes merely to exclude a given 
 idea, or deny a given affirmation. If the denial were within 
 a self-identical system it would carry a positive bearing. As 
 ex hypothesi it has no positive bearing, it embodies mere 
 difference without identity, or the abstraction of difference. 
 Such a denial is the pure contradictory of the affirmation 
 which it denies. On the other hand, difference becomes 
 discrepancy or contrariety when not the formal abstraction of 
 difference, but positive differents claim the same place, and 
 the same place means the same relation to the same system. 
 Such contrariety exists between ' A is B/ and ' A is Bg '. 
 
 * See below, II, chap, vii, on the ' Formal Postulates of Know- 
 ledge '. 
 
Chap, VII] System and Negation 291 
 
 Thus the articulate arrangement of differences under their 
 systematic relations is the root of positive discrepancy. The 
 system as determined by one relation excludes, under that 
 relation, the system as determined by any other ; and the 
 system as a whole identifies any one of its positive relations 
 with the mere difference from, i.e. the bare exclusion of, certain 
 other positive relations. A is either Bj or B.^. This is the 
 combination of Contradiction and Contrariety. 
 
 It is not essential that the positive ground and positive 
 consequence of a denial should be different. Under conditions 
 of precise knowledge they must be the same. We shall see 
 that where only two alternatives are possible, and they 
 exclude one another, either of them is denied by the affirma- 
 tion of the other, and affirmed by its negation. Under such 
 conditions the denial of one alternative has the affirmation of 
 the other both for its ground and for its consequent. ' He 
 will either dissolve or resign ' permits us to understand under 
 the denial ' he will not resign ' the affirmation ' he will dis- 
 solve ' alike as its ground and as its consequent. It is plain 
 that in actual knowledge there are degrees of this coalescence. 
 The ground may be imperfect or extraneous ; it may be 
 replaced by any positive quality that excludes the predicate 
 denied, i.e. in this case, excludes resignation. This positive 
 quality might be even difficult to formulate precisely, and 
 might run as close as possible to a bare denial ; we might 
 feel sure that ' he is not the man to resign ' ; which means that 
 his general character as we understand it precludes the idea 
 that he will resign. Such a general ground would be at once 
 reinforced in its cogency and restricted in its result by the 
 consequence of the denial, the necessities of the case being as 
 supposed above. The two in their coalescence, * he is a man 
 who wUl not resign,' and ' not resigning, he must dissolve ', 
 would in that case form the complete analysis of the denial 
 * he will not resign '. 
 
 It has been necessary in this discussion to anticipate the 
 account of disjunction which will be given in the next chapter. 
 Perfect disjunction is of course a late form of knowledge. 
 But it is an ideal inevitably involved in the nature of negation. 
 All significant denial — all denial, that is, which rises above 
 
 U2 
 
292 Negation, Opposition, and Conversion [Booki 
 
 the level of the infinite judgment — corresponds to this ideal 
 in two respects at least. Every denial has its meaning within 
 an attribute or set of attributes judged to be real ; and every 
 denial affirms some positive matter which affects and is affected 
 by its relation to such a comprehensive attribute. This may 
 be illustrated in another way, which will also serve as a re- 
 capitulation of the stages of negation. 
 
 Negation is rooted in the fact of difference, but difference 
 is not enough to warrant negation. Mortality is a difference 
 within the identity of man, but we do not therefore deny that 
 man is mortal. Significant negation begins, we, said, when 
 positive differents claim the same place in the same system — 
 in the simplest case, when differents claim to be identical. 
 Man is not mere mortality, i.e. does not coincide with mere 
 mortality in the system of reality. As thus conflicting, which 
 of course can only happen in a judgment, differents are con- 
 traries or opposites, and the assertion of one is the negation 
 of the other. Now these contraries or opposites may be of 
 any number. There is nothing to limit them. Any colour is 
 the contrary or opposite of black, if asserted in the same rela- 
 tion ; and so would any sound or taste be, if asserted in the 
 same relation, which seems impossible for a sane man. If then 
 we consider negation at this stage as embodying contrary 
 opposition, what follows from it? 'This surface is not black' 
 has indeed a ground, viz. that it is some particular other 
 colour ; but what about the consequent of the negation ? 
 There is none, except that the surface is some colour other 
 than black, and therefore we lose by choosing the negative 
 expression rather than the positive, and the significance of 
 the negation qua negation is absent. What follows from the 
 absence of a consequent as definite as the ground ? Nothing 
 less than this, that negation cannot be explained on the basis 
 of mere exclusion of contraries. It is indeed possible to deny 
 intelligibly on such a basis, in virtue of the general consequence 
 of negation, but no reason can be assigned for in such a case 
 preferring negation to affirmation. For in the case supposed 
 we should be concluding from ' A is red ', through ' A is 
 not black ', to ' A is of some colour other than black ' — 
 a manifest loss. 
 
Chap. VII] Negation implies Contradiction 293 
 
 Negation can have no bearing, i.e. no interest or raison 
 d'etre, unless the contraries are limited so that something 
 follows from the negation. In other words, Negation always 
 involves Contradiction between contraries and not merely 
 Contrariety. There may be any number of alternatives, but 
 unless the number is limited or falls within some positive 
 characteristic however vaguely known, nothing can follow 
 from the denial either of one or of any number among them. 
 Therefore though negation originates in difference, which it 
 raises to contrariety by embodying it in definite relations, 
 and though it does not arrive at formal contradiction between 
 opposites till long processes of thought and language lie 
 behind it, yet I am unable to comprehend how any negation 
 can have interest apart from being taken within a positive 
 whole, however vague, which is of the nature demanded by 
 the relation of contradiction when established between oppo- 
 sites. Mere contradiction as between ' he is good ' and ' he 
 is not good ' is given in the nature of negation from the first ; 
 and its development consists in filling this unmeaning form 
 with significant opposites, so that from ' he is not good ' we 
 may be able to infer something more than that ' it is not true 
 that he is good '. 
 
 Significant Negation then combines in itself the absolute 
 Contradiction which was illustrated by the Infinite Judgment, 
 and the Contrariety which arises between differents when 
 referred to the same place in the same system. Without 
 contrariety negation would have nothing that it could mean, 
 but without contradiction it would not have in itself the power 
 to mean anything.* 
 
 * The above account was modelled so as to respect the distinction 
 made in Formal Logic between Contraries, both of which may be false, 
 and Contradictories, one of which must be true. But in common usage 
 the relation between Contraries is called Contradiction, no less than that 
 between Contradictories. And it is important to realise that Contradiction 
 in the metaphysical sense, i. e. a deadlock which reason cannot acquiesce 
 in, is rooted in what we defined as Contrariety, i. e. the unmediated 
 reference of different predicates to the same subject. See Bradley, Mind, 
 72, 496, and Appearance, ed. 2, 562. I think that the above account of 
 Contrariety and my account of Contradiction in the Companion to 
 Plato's Republic, p. 149 ff., are in harmony with Mr. Bradley's statement. 
 The ultimate nature of Contradiction is philosophically very important. 
 
294 Negation, Opposition, and Conversion [Booki 
 
 Opposi- 
 tion and 
 conver- 
 sion of 
 
 Judg- 
 ments. 
 
 Opposi- 
 tion. 
 
 Between 
 Singular 
 Judg- 
 ments. 
 
 Between 
 Plural 
 Judg- 
 ments. 
 
 4. The rules of the opposition and conversion of Judg- 
 ments, which have come down to us almost as Aristotle 
 formulated them, are founded on the classification of judg- 
 ments according to ' quantity '. They therefore lay down 
 the relations to one another of all classes of judgments which 
 this principle recognises, in as far as the truth or falsehood of 
 any one judgment affects the truth or falsehood of any other 
 which deals with the same content. But when we attempt, 
 as we have attempted above, to distinguish the kinds of truth 
 which various types of judgment embody, then the relations 
 between the various classes of judgment cease to be a matter 
 of mechanical rule-of-thumb, although not hard to understand 
 if we pay attention to the actual significance of the judgments 
 with which we deal. 
 
 i. The principle from which we must set out is that every- 
 thing which can be affirmed can also be denied. In some 
 cases the denial will be confined to a shape closely corre- 
 sponding to that of the affirmation, and in some there will be 
 two kinds of denial which will fall apart. 
 
 a. The Singular Judgment cannot be treated for the present 
 purpose as a case of the universal. It has, as we saw, a univer- 
 sal character, but not in the sense of referring to an aggregate 
 of individuals. If ' Caesar crossed the Rubicon ' is true, 
 ' Caesar did not cross the Rubicon ' is false ; and if the 
 negation is false the affirmation is true. Thus the relation of 
 Contrary Opposition, according to which the Universal 
 Affirmative and the Universal Negative of formal logic may 
 both be false, falls away in the case of a Singular Judgment in 
 our sense of the term. In this type of judgment we have the 
 simple relation of affirmation to formal negation which is 
 contradictory, i. e. presents an absolute alternative. The 
 reason of this we shall have further to consider in treating of 
 Double Negation. 
 
 /3. The Judgments of Enumeration, Plural or Particular 
 Judgments, including the Collective Judgment, present the 
 relations towards each other with which we are familiar in 
 the common scheme of opposition. The peculiarity of these 
 relations is that in them an absolute alternative or contradic- 
 tory opposition is only to be obtained by opposing judgments of 
 
Chap. VII] Pluval Judgments 295 
 
 different quantities. The reason of this is well brought out 
 in a phrase which Aristotle employs in his account of opposition, 
 where he states the contradictory of ' All are ' to be ' Not all 
 are ' — instead of using the expression of our text-books ' Some 
 are not ' ; or when he says that the contradictory of a pro- 
 position which affirms a predicate universally, is one which 
 asserts that of the same subject the predicate is not universally 
 true. What is affirmed in a collective judgment is the homo- 
 geneity in a certain respect of an aggregate still regarded as 
 an aggregate of enumeration, although endowed with sufficient 
 unity to warrant itself as a completed whole. The denial of 
 the judgment is the denial of this homogeneity, and is rather 
 a consequence of than identical with the partial counter- 
 enumeration which our logic-books take as its type. If, for 
 instance, we assigned a number to the coimter-enumeration, 
 the contradiction would no longer be complete, and we should 
 find ourselves in contrariety instead. To say that ' All these 
 books are German ' and that ' Two of them are not ' cannot 
 be a contradiction pure and simple ; for the falsehood of ' All 
 these are ' is compatible with the truth of ' Two — three — 
 or all of them are not '. This is enough to show that ' some 
 not ', if we take it as a sign of counter-enumeration, is less 
 safe in contradictory opposition than ' not all '. 
 
 As regards the ' contrary ' opposition of ' All are ' and 
 ' None are ', the doctrine of formal logic is true so long as we 
 confine ourselves to Judgments of Enumeration. * None are ' 
 asserts a complete counter-enumeration or its equivalent 
 based on some other ground, and besides this assertion and its 
 contrary there are as many alternatives as there are individuals 
 in the aggregate, minus one. 
 
 The particular or incomplete collective judgments ' Some 
 are ' and ' Some are not ' (sub-contraries) are of course com- 
 patible with each other so long as we do not determine them 
 numerically ; and continue to be so then if we consider that 
 incompleteness of enumeration debars us from all reference 
 to a sum total. If on the other hand we permit the comparison 
 with an assumed sum total, we pass at this point into calcula- 
 tion. The general conception under which we are enumerating 
 always, it must be remembered, implies a total ; so that 
 
296 Negation, Opposition, and Conversion [Booki 
 
 Between 
 Generic 
 Judg- 
 ments. 
 
 calculation lies very near to judgments of this type. ' Six 
 men were killed and ten wounded (but not killed) ' are judg- 
 ments perfectly compatible with one another if the number 
 of men on the -ground was sixteen or more ; but if there were 
 only fifteen or fewer, then the two judgments at once rise into 
 contraries. Both may then be false, but one must be. This 
 however is calculation. 
 
 This account of the matter includes all that need be said 
 of the Singular judgment if used in opposition to the Collective 
 judgment. In such a case the Singular judgment takes the 
 place and follows the rules of a judgment of Enumeration. It 
 must however undergo a transformation, even if only implied, 
 in taking on a relation to the basis of enumeration. ' How 
 many Liberals voted against the Bill ? ' ' A. B. did, C. D. did,' 
 &c., &c. These singular propositions are read oH into enumera- 
 tive judgments, ' One Liberal, two Liberals,' &c. 
 
 The further judgments which arise out of the Judgment of 
 Enumeration and Measurement follow the characteristics of 
 those forms of the true universal judgment to which, whether 
 as generic or as hypothetical, they severally approximate. 
 
 y. I will now point out shortly the characteristics of these 
 judgments themselves when placed in opposition. The 
 tendency of the higher stages of knowledge is, as we saw in 
 the last section, to fuse contrariety and contradiction into 
 one. This is obvious, for instance, in the individual generic 
 judgment, for the same reason as in the singular judgment 
 itself. And even in the analogical judgment the tendency 
 to fusion is strongly marked. The allegation of exceptions 
 against a generic character, whether in form of expression 
 positive or negative, must either be insignificant as when the 
 exceptions are apparent and not real, or else tend by analogy 
 to establish a contrary alternative or positive contradictory. 
 In the former case the judgments which emphasise the excep- 
 tions must be taken to be not generic judgments at all, but 
 mere enumerative judgments, which therefore cannot touch 
 the essence of the generic judgments they appear to oppose. 
 For we shall find the dominant principle in these relations to 
 be that a judgment of one type a cannot deny a judgment of 
 another type /3 ; although the former may suggest a judgment 
 
Chap. VII] The effect of Exceptions 297 
 
 of the type ^ which will constitute a full denial of the other 
 judgment of that same type.* Under the head of such mere 
 
 * Cp. Keynes loi, 122-3, and 259, and p. 369, "below. See also Essen- 
 tials, 1 16-17. Objection is taken to the views (i)that the Particular in 
 categorical shape is unscientific ; (2) that a judgment is in principle 
 effectively denied only by another of its own type. 
 
 The governing, principle of these views is the conception of the double 
 nature of judgment, which makes every actual judgment a battle- 
 ground between the existential and the necessary character. No form, 
 I take it, is quite unambiguous (see Preface to ed. 2), but the separate 
 types of import do tend to find appropriate expression, and it seems 
 only right in logical theory to insist on this tendency. And I think it 
 a counsel of perfection for practical life. 
 
 Thus ( I ) if what you want of the categorical particular is to contra- 
 dict the hypothetical or scientific universal, you are (p. 300, below) 
 fighting a theoretical principle with unanalysed judgments of perception 
 and enumeration. Do not nearly all popular errors rest on this practice ? 
 And you have an appropriate mode of denial in the modal particular, 
 which is intended for the expression of incipient analysis, when it falls 
 short of justifying a contrary universal. 
 
 If what you want of it is to assert existence, then you are falling back 
 on the assertory or existential side of judgment, and letting the aspect 
 of necessary connection slide into the background. ' But every judg- 
 ment includes in some degree both.' Yes it does ; and that is why we 
 are always confusing them with each other. ' Est hoc, ergo propter hoc ' 
 is a more general formula than ' Post hoc — ', and expresses much the 
 same fallacy. In Logic we might at least try to avoid both. 
 
 (2) If I were to say that a scientific judgment can only be denied 
 by a scientific judgment and an existential by an existential, that might 
 seem obvious, and would be all I want. A doctrinaire denies facts on 
 the ground of laws ill-understood. An empiric denies laws on the 
 ground of facts ill-conceived. M. Keynes says (p. 124) that I admit 
 that exceptions can overthrow a law, and the rest of my argument is 
 ignoratio elenchi. But of course I mean exceptions interpreted in terms 
 of a law. How am I to know that Volvox is not an animalcule, when 
 Ehrenberg says it is, unless I can tell more or less to what kind it really 
 belongs ? I need not know what precise kind ; but I must know ' some 
 kind excluding animalcule.' And from that it is only a step of degree 
 to knowing precisely what kind. 
 
 As to denying every judgment only by its own type, there is a pecu- 
 liarity in the disjunction (cp. vol. ii, 194). It is (see p. 328) a unity of 
 hypotheticals and a categorical, and, further, represents the whole 
 system which itself gives meaning to a negation. So, taking the last 
 point first, I should say that it is hardly natural to deny it, for in doing 
 so you must presuppose another disjunction to give meaning to your 
 negation. The place for negation is rather under than of a disjunction. 
 The natural course would seem to be to let it alone and begin again. 
 Cp. Essentials, p. 125, and below, 301. 
 
 But if you are able to specify and deny the categorical basis, e.g. to 
 
298 Negation, Opposition, and Conversion [Booki 
 
 enumerative judgments would come all observations of artificial 
 forms, mutilations, abortions, &c., in organic and spiritual 
 beings ; and all accidental juxtapositions rendered by judg- 
 ments whose subjects have no connection with their predicates. 
 The generic judgment ' Man is a creature with a sense of justice ' 
 is not invalidated by instances drawn from dead men, lunatics, 
 or idiots ; nor even, perhaps, from criminals, if there are 
 such, whose conscience is obliterated by lifelong war with 
 society. But I shall be told that a scientific law has no 
 exceptions. This is just what I am maintaining ; I am 
 sa5dng that exceptions are either apparent or real, and in the 
 former case, that now before us, do not deny the law ; in the 
 latter proceed positively to indicate another law. In the 
 second case, when the law is really impeached by the bearing 
 of the exceptional instance, this bearing must have a positive 
 import, which may not amount to a suggested law, but must 
 be in the same region of essential individuality in which the 
 characteristic that is denied has its import. 
 
 If I say that all exogenous trees are dicotyledonous, I am 
 opposed by a real, not merely apparent, exception in the case 
 of the Coniferae, which though exogenous have in many 
 species more than two cotyledons. Here we have one Generic 
 judgment (I use ' generic ' in the logical sense which I have 
 explained) opposed to another. It is not merely that here and 
 there an aborted or mutilated instance is to be found in 
 which a part of the plant is wanting ; but that an enormous 
 natural order with marked unity of habit, and in the strictest 
 sense -^ sharing the characteristic on which the analogy is 
 based, does not display the character required by analogy. 
 
 say, in denying ' X is red or green ', ' X. is not a colour ', that is one way 
 of disposing of the whole disjunction ; or if your objection is to its 
 exclusiveness or exhaustiveness you can deny that one of the two 
 special hypotheticals involved which alleges the necessity you desire 
 to impeach. In all this categorical is opposed to categorical, and 
 hypothetical or at least modal particular to hypothetical. 
 
 ^ Here an error is possible. The wood-formation of Coniferae, though 
 proceeding from a cambium ring outside the old wood, has differences 
 from that of Dicotyledonous Exogens. If these differences were of 
 importance the exception might break down as not a case under the 
 rule, Coniferae not being true Exogens. 
 
Chap. VII] Generic Judgment how upset 299 
 
 Now I am not aware that any importance has been attached 
 to determining the connection between exogenous wood- 
 formation and the mmiber of seed-leaves or cotyledons ; but 
 it is plain that the conflict of generic judgments so far as we 
 have followed it does not destroy the idea of such a connection, 
 which would be the effect of a mere contradiction, but suggests 
 that it may be characteristic of plants with two or more seed- 
 leaves. Supposing that monocotyledons were also found in 
 some cases to form wood externally, the question would still 
 arise whether any principle of development could be traced 
 according to which the characteristics under discussion might 
 arise together or owing to connected causes, as if e.g. there 
 was a point at which the one natural kind approached very 
 close to the other. If so, the supposed further exception would 
 still lead to a positive principle or contrary, and not to an 
 empty contradiction. Even if the first generic judgment were 
 a sheer blunder and confusion, as has been the case from time 
 to time with judgments propounded in science, it is scarcely 
 possible to rectify the confusion except by substituting for it 
 the true positive conceptions that arise out of the cases which 
 overthrow it. An example in point is Ehrenberg's inclusion 
 of a group of confervoid Algae (Volvox) under the class of 
 Infusorial Animalculae, or again, probably, his alleged detec- 
 tion of highly-organised structure in the Infusoria proper. 
 Enumerative exceptions are futile in such cases ; what is 
 needed is a re-interpretation of the character of the group as 
 such. Such a re-interpretation is at once contrary and con- 
 tradictory to the mistaken judgment which it corrects. But 
 in the process of interpretation it may and perhaps must pass 
 through a stage which may best be described when we are 
 speaking of the hypothetical judgment. 
 
 h. The contrary of the Hypothetical Judgment is as usual Between 
 a judgment of the same type. The complete contrary of^^°^j 
 ' If outdoor relief is refused the workhouses are crowded ' Judg- 
 would be ' If outdoor relief is refused the workhouses [caeteris ^^^^^ 
 paribus) are not crowded '. This denial means that the 
 condition expressed in the hypothesis * If . . refused ' is not 
 merely inoperative to cause pressure on the workhouse, but 
 is actively operative to decrease that pressure. I insert the 
 
300 Negation, Opposition, and Conversion [book i 
 
 limitation caeteris paribus merely to secure the judgment 
 being taken as truly hypothetical, because in such concrete 
 matter as this there is a tendency to interpret the judgment 
 as collective in the sense that ' Every case of a is a case of ^ ' ; 
 so that it may be objected to on the score of accidental in- 
 stances. In abstract matter, e.g. in geometry, where the 
 hypothetical judgment has an unambiguous import, these 
 objections are understood to be inadmissible. Parallel lines 
 are taken qua parallel when it is said that they do not meet, 
 and so forth. 
 
 This contrary is the form of negation to which all precise 
 thought aspires. If the condition is irrelevant and wholly 
 unconnected, then indeed the entire type of knowledge to 
 which we have aspired is a delusion and a snare, and the 
 mere contradictory which will express our ignorance must 
 be found in a judgment of a lower type. But if the condition 
 is relevant it must operate somehow, and we can only choose 
 between one view of its operation and another. Such a choice 
 is expressed by embodying mere contraries in an absolute 
 alternative or contradictory ; by considering ' If A is B it is 
 not C ' as the contradictory of ' If A is B it is C ' ; as it is 
 the only way of denying it by a hypothetical judgment. 
 
 But if we are to destroy the hypothetical judgment itself 
 as an expression of ground and consequence, we must -aim 
 our negation precisely at its form. The enumerative parti- 
 cular would not help us here. When we have said that * If 
 (i. e. in so far as) a man is good he is wise ', it is idle to 
 reply that some good men are not wise. This is to attack 
 an abstract principle with unanalysed examples. What we 
 must say in order to deny the above-mentioned abstract judg- 
 ment is something of this kind : ' If,' or * Though a man is 
 good, yet it does not follow that he is wise,' i. e. ' Though a man 
 is good, yet he need not be wise '. The particle ' though ' 
 introduces the condition as a supposal, but by its adversative 
 force prepares us for a denial that it has any connection with 
 the consequent. 
 
 This same form, which may be called the modal particular, 
 is the appropriate contradictory to a generic judgment which 
 has to be altogether surrendered and cannot be corrected by 
 
Chap. VII] The Modul Particular 301 
 
 a positive contrary. Its meaning is however not as clear as 
 that of the Generic or Hypothetical judgments. For it does 
 not assert a positive relation, but drops down into an un- 
 analysed quality of exclusion, and thus into the confused 
 concrete of phenomena. It may therefore mean that the 
 supposed condition is inoperative and irrelevant, or it may 
 mean that it is weakly operative and liable to be overcome 
 by normal counteracting conditions, or that it is operative 
 as asserted in the hypothetical judgment, but liable occasion- 
 ally to be overcome by exceptional conditions. This last is 
 a common meaning, but is not the true negation of the opposed 
 abstract hypothetical judgment, and ought to be discarded 
 from science, though there is no means of relieving the modal 
 particular negation from it. How then are we to treat the 
 correlative case, in which we deny ' If A is B it is not C ' by 
 ' Though A be B yet it may be C ' ? This seems to confirm 
 our view that the character of mere negation is incompatible 
 with that of the hypothetical judgment. For the former of 
 these two contradictories is of course the same judgment which 
 we have already considered in the light of a contrary and 
 positive negation ; and the latter seems therefore to retain 
 under its affirmative form the essential character of mere 
 denial. ' Though A is B yet it does not follow that it is not 
 C ' expresses the only sense in which the affirmative modal 
 particular is a true or mere contradictory to the negative 
 hypothetical judgment.^ This sense is not in itself satisfactory 
 if taken as the import of possibility, and real possibility 
 demands a nearer advance towards the affirmative contrary — 
 a recognition of some real operative condition making for the 
 connection alleged possible. That this is so only confirms 
 the suggestion made above that in significant negation contrary 
 and contradictory tend to become one. 
 
 I may anticipate the case of Disjunction so far as it here 
 concerns us by saying that the denial 0/ a disjunctive judgment, 
 though formally possible, is not a problem that naturally arises 
 in logic. The disjunction is the presupposition and the goal 
 of negation as an organon of knowledge. By denying it as 
 a whole we sweep away the fabric of knowledge relative to the 
 i See below, on Privation and Affirmation. 
 
302 Negation, Opposition, and Conversion [Booki 
 
 matter in hand, and must begin over again from the beginning, 
 as there is no sphere left within which anything can arise from 
 the denial of the disjunction. To deny a disjunction in this 
 sense we should not trouble ourselves with the alternatives, 
 but analyse them into their common basis and deny that. An 
 impersonal judgment, as expressing wholly inarticulate know- 
 ledge, is the appropriate form for such denial, unless we are 
 denying one disjunction under another. ' The soul is neither 
 square nor round ' may be denied by ' The soul is not in space ' ; 
 for this denial has a positive ground and consequence founded 
 on an implied disjunction, ' either in space or intellectual.' 
 But if we are presented with a number of alternatives about 
 a matter which seems to us to have no basis in reality nor 
 relation to actual knowledge at all, then we may reply with 
 the impersonal negative as the form of thought most suited 
 to mere absence of positive content. ' The disembodied 
 spirit in its earthly presence is revealed either by contact or by 
 signs.' To this an entire unbeliever would probably answer, 
 ' There is no earthly presence of disembodied spirits,' and here 
 he approaches, not wholly by his own fault, the infinite judg- 
 ment. He has merely said that reality is without the matter 
 alleged, and his saying has no positive import beyond what 
 arises from the imputation to reality of a character — whatever 
 that may be — not necessarily incompatible with, but rather 
 undistinguished by, the presence of disembodied spirits. 
 
 Specific denials of a disjunction on the ground of incom- 
 pleteness or superfluity ^ are of course either under a further 
 disjunction which the denial tends to make explicit, or in the 
 second case, prima facie, under the disjunction to be denied 
 itself, with the result of showing that a different one is needed. 
 Double ii. In treating of the contradictory relation, that namely 
 ega ion. bg^^gg^ two judgments of which one simply denies the other, 
 so forming an absolute alternative, we saw the results that 
 spring from double negation. We appealed to double negation 
 for instance in the case of the singular judgment, such as 
 * Caesar crossed the Rubicon '. This, with its simple denial 
 ' Caesar did not cross the Rubicon ', forms an absolute alterna- 
 tive, although the denial has a meaning and is not a mere 
 ^ See following chapter on this case. 
 
Chap. VII] Inference from Falsity 303 
 
 infinite judgment. So far as this is the case, the opposition 
 between the two is at once contrary and contradictory. 
 
 Do the two cases of inference from falsity in contradictory 
 opposition stand on the same footing ? The one is from the 
 falsity of the affirmative, the other from the falsity of the 
 negative. The former amounts to single, and the latter to 
 double negation. 
 
 The explanation of single denial which has been given above 
 may be briefly restated here. The abstraction of difference, 
 taken in respect of its contrast with identity, and so as mere 
 non-identity or otherness, is employed in negation as the 
 vehicle of a positive contrary, which contrary is thus in- 
 vested with the full alternative force that belongs to otherness 
 as such when contrasted in the abstract with sameness as such. 
 As regards the history of early thought on this question, of 
 course we are not to look for determinate abstractions in 
 primitive minds. But primitive minds probably are abstract, 
 though they do not deal with abstractions. We must look 
 for the germ of contradictory negation in mere repugnance or 
 repulsion, which, although a positive state, has a peculiar 
 aspect of negativity to which the inarticulate abstractness 
 of the primitive mind lends an aspect rather of contradiction 
 than of contrariety. Every one who has watched children 
 must have noticed the remonstrant ' No ' without any expressed 
 content, which is a sign of aversion to something done or 
 suggested. The absence of indicated reference to any particu- 
 lar matter is often surprising, and impresses an observer by 
 the difficulty of finding either the bearing or the ground of 
 the negation. Here it is rather the positive contrary that is 
 undeveloped and latent than the mere rejection or contradic- 
 tory. Therefore I cannot but think that the absolute alterna- 
 tive — mere generalised otherness or rejection — ^makes itself 
 explicit by the side of the positive contrary at a very early 
 stage of thought. 
 
 Thus though I do not take every negation to be necessarily 
 aimed against an affirmation of the same content, yet it seems 
 to me that the pair of judgments which form a contradictory 
 opposition embody an ultimate fact of knowledge. Single 
 negation is in form the substitution of mere difference, or 
 
304 Negation, Opposition, and Conversion [Booki 
 
 nothingness, for the combined identity and difference which 
 alone have meaning. This form is the basis of the alternative 
 in contradiction. It is the alternative antithesis between 
 something and nothing. That ' nothing ' is furnished with 
 a meaning in hunc effectmn does not appear from or affect the 
 form of contradiction. Single negation, then — the passage 
 from the falsity of ' A is B ' to the truth of ' A is not B ' — must 
 be regarded on its formal side as the abstraction of a universal 
 characteristic of knowledge. It means that A is, under the 
 conditions and for the purpose of the judgment in question, 
 in a relation of pure otherness to B. 
 
 The case of double negation — the passage from the falsity 
 of ' A is not B ' to the truth of ' A is B ' — is in my judgment 
 accounted for by the preceding remarks. The true problem, 
 to my mind, is not how negation should be the absolute 
 alternative of the corresponding affirmation, but rather how, 
 being in its exterior form and vehicle such an alternative, it 
 should become possessed of positive intelligible import. The 
 fundamental nature of negation, thus understood, may no 
 doubt be embodied in the principle of Excluded Third or 
 Excluded Middle, which asserts that of two contradictory 
 enunciations one must be true and the other false. Thus 
 stated, the principle is merely formal, because the question 
 immediately arises, ' What are contradictory assertions ? ' 
 The definition might be made plainer by substituting for the 
 phrase in question an expression such as ' the assertion and 
 denial of the same content ' ; but no definition can relieve us 
 from the task, which I have attempted to perform in this 
 chapter, of explaining what a mere denial of an assertion really 
 is. Excluded Middle is thus merely the abstract case of 
 Contradiction or simple negation, and the proof of the principle 
 lies in the analysis of negation. 
 
 I may illustrate this view, in the case of double negation, 
 by two conceptions that deserve attention. The affirmation 
 that admittedly results from double negation may be ascribed 
 to the reappearance of an original affirmation at which the 
 first negation must have been aimed, so soon as that first 
 negation is cancelled by the second. I take this view to be 
 true in substance, but false in the fact which its expression 
 
Chap. VII] Negation as Alternative 305 
 
 postulates. It was pointed out above that not every negation 
 presupposes an affirmation. Sigwart, in treating of double 
 negation in his second edition, correctly postulates as the con- 
 dition of denial only an attempted affirmation. But it is true, 
 and this is what Sigwart throughout meant to convey, that 
 every negation bears on its face the nature of an alternative, 
 so that, though we may not in fact have proceeded to it by 
 denying an explicit affirmation of the same content, we are yet 
 able to go from the negation of one member to the establish- 
 ment of another. It is one thing to say that every negation 
 is preceded by a corresponding affirmation, — for we may not 
 have judged on the subject at all, — but quite another to say 
 that every negation bears on its face that, if we judge, it is 
 the sole alternative to the corresponding affirmation. This 
 principle appears to me to be of the essence of the matter. 
 It is this that gives double negation its distinctive precision 
 and emphasis. 
 
 In opposition to Sigwart's idea, erroneously expressed as 
 I admit it to be, of re-establishing an original affirmation, 
 Mr. Bradley has maintained that the warrant of double 
 negation simply consists in this, that in order to deny a nega- 
 tion we must already be in possession of the corresponding 
 affirmation. We can only, he contends, deny A is not B on 
 the ground that, within our knowledge, A is B. This allegation 
 is made with good reason. We can indeed deny A is B on the 
 ground that A is a; or y, each of which excludes B ; but we 
 cannot assert A is B on the ground that A is not x or y, each 
 of which excludes B. We cannot deny the consequent not-B 
 on the strength of denying the antecedent x or y. The old 
 rule of the hypothetical judgment, ' Affirm the antecedent or 
 deny the consequent,' forbids this. 
 
 But on looking closer we shall observe that this impos- 
 sibility is based on the imperfect view of the hypothetical 
 judgment which assimilates its rules to those of the judgment 
 of enumeration. This view disregards the possibility of a 
 connection at once synthetic (i.e. not tautologous) and pure 
 (i. e. free from irrelevancy). For in this case the denial of the 
 condition is the denial of the consequent ; and it is this which 
 has been before us throughout as the essential and ideal 
 
 1337 X 
 
3o6 Negation, Opposition, and Conversion [Booki 
 
 meaning of judgment. This assertion of a pure connection 
 between condition and consequent becomes, in the case of 
 a negative consequent which is now before us, identical with 
 our position that all intelligible negation takes its meaning 
 from contrariety, though its form may be that of contradiction. 
 To say that in ' If A is :v it is not B ' we cannot go from ' not x ' 
 to ' not not-B ' (i. e. to B) is to say that there cannot be con- 
 tradictory opposition between contraries.* 
 
 Contradictory opposition between contraries ^ can of couise 
 exist only if the possibilities are limited by means of a disjunc- 
 tive judgment, and in this case Mr. Bradley admits that the 
 double negation may be got at otherwise than by the corre- 
 sponding affirmation. If we divide all Liberals into Unionist 
 Liberals and Gladstonian Liberals we can go from ' That 
 Liberal is not Unionist ' to ' He is not not Gladstonian '. So 
 too in a pure nexus with a negative consequent : ' If powder 
 is slow-burning (and in that case only), it does not strain the 
 gun unequally.' Under this judgment, if we know that the 
 powder is not slow-burning, we are able to say that it fails in 
 the quality of not straining the gun unequally. We can 
 unquestionably get this inference whenever we approach the 
 knowledge of a pure ground involving a reciprocal character 
 in the hypothetical judgment, which makes it, if either member 
 is negative, include the same cases as a disjunction.*' The 
 pure ground and the limitation of cases are merely different 
 aspects of the same form of knowledge. The ground is the 
 fundamental and operative character by which a system 
 imposes certain relations on its parts ; the limitation is the 
 external and formal consequence of these relations, which 
 may be mimicked for the purposes of common logic by an 
 arbitrary or conventional restriction of alternatives. 
 
 My only difference from Mr. Bradley consists therefore in 
 the view which I have maintained throughout, that apart from 
 
 * The negative character of not-B might raise the question of two 
 negative premisses (Muller in ' Mind ' Ixxx). But assuming reciprocity, 
 the hypothetical major has disjunctive force, and that adds a new factor. 
 See reference in note c. 
 
 •* See p. 293, note a, above. The Contradictory opposition here spoken 
 of is not Contradiction in the wide sense, but the relation between 
 Contradictories as recognized by Formal Logic, cp. p. 333, note, below. 
 
 *^ See p. 329, note, below. 
 
Chap. VII] The vulue of Double Negation 307 
 
 some limitation there is no intelligible negation — nothing but 
 the infinite judgment, and therefore in strict logic no negation 
 at all. Under such a limitation we can always go from denial 
 of a positive quality to a positive result which we may as a 
 matter of both theory and of fact approach from the side of 
 double negation, although of course the identity of double 
 negation with affirmation is in a reflective stage of culture too 
 immediate to admit of the two being really distinguished. 
 The reason for which I am anxious to insist on this not very 
 practical distinction will appear more clearly when I come 
 to speak of induction. It is, in brief, the importance of the 
 negative instance ; that is, of approaching any positive 
 content from the side of its limit, of the exact boundary at 
 which it ceases and some other content begins. For this 
 boundary is a negation by denying which we not only affirm 
 the content that lies within it, but affirm it in its conditions 
 and genesis, at least for knowledge. ' If a nation has no true 
 art it is not religious ' is a judgment that gives the analysis of 
 a group of ' negative instances ', which analysis passes into 
 an affirmation supported by those instances, in the form 
 ' A nation which has tnie art is not not religious '. The 
 conclusion thus obtained, ' This nation (having true art) is 
 religious ' may be bond fide arrived at through the double 
 negation I have described, and may be at first unsupported 
 by the direct observation ' This nation is religious '. 
 
 iii. Conversion is usually treated with opposition under the Conver- 
 head of immediate inference. It is primarily a transition ^^°°* - 
 from one grammatical form to another which introduces no 
 new elements into the content. Whether, or in what cases, 
 it really involves inference, i.e. a passage from one judgment 
 to another warranted by the first, is the main question which 
 arises in treating of it, and of course includes the problem what 
 inference, if any, is involved. 
 
 The unity ot the judgment, it will be remembered,^ does 
 not exclude a considerable measure of diversity. It is often 
 a mere chance whether a range of affirmative thought is 
 condensed into one proposition or comminuted into several. 
 And inference is working through the whole of such a range 
 
 * See above, chap. i. 
 X2 
 
3o8 Negation, Opposition, and Conversion [Booki 
 
 as the judgment gains depth and width, and defines its edges. 
 Thus, if we mean to say anything definite about the point 
 at which we pass from one judgment into ' another ', we must 
 look at what is bona fide impHed as the essential import of 
 the judgment -forms that we discuss, and not at the actual 
 transitions which attend our interpretation of any proposition, 
 and which vary with mental endowment in the interpreter, 
 and with the lucidity of expression of the given sentence. 
 That is to say, we must distinguish interpretative inference 
 from substantial inference — transition within the judgment 
 from transition between two judgments. 
 
 The question may seem indeed to settle itself at once. The 
 unity of judgment is determined frima facie bj^ the unity of the 
 Content judged. A new subject or a new predication, i.e. one 
 not related as part within whole to that of a given judgment, 
 is needed to constitute another judgment. But in immediate 
 inference there is no new content — at any rate no new positive 
 content. Can there then be a new judgment ? 
 
 The real interest of Conversion lies in the discussion which 
 it provokes of the precise relations imposed upon its content 
 by any given judgment, and of the boundaries which separate 
 the bona fide meanings of the various judgment-forms. In 
 arriving at these relations or at this meaning we use interpre- 
 tative inference ; it is only when we find ourselves able to go 
 from relation to relation by re-applying the same form of 
 judgment, or from meaning to meaning by passing from a 
 judgment of one type to a judgment of another, that we are 
 really employing substantial inference. It does not much 
 matter, however, where we elect to draw the line of transition 
 from judgment to judgment, so long as we understand the 
 connection of the imphcations concerned. 
 Simple a. I will begin with an accidental case of simple con- 
 
 sion^of version, not recognised in the text-books because the content 
 Singular, of predication in singular judgment is not necessarilj^ of 
 singular reference. ' The Duke of Cambridge is Commander- 
 in-chief.' I think it is beyond question that this proposition 
 might be met with * The Commander-in-chief is the Duke 
 of Cambridge ' in a tone which would give it the force 
 of a criticism or retort, although its content would be war- 
 
Chap. VII] Meve Transposition 309 
 
 ranted true by the proposition as first enunciated. I am not 
 prepared to abolish the distinction of subject and predi- 
 cate within the judgment, and if we retain the distinction, 
 then the mere transposition of the two makes a difference. 
 We understand the subject primarily as a designation and the 
 predicate primarily as an attribution. The idea of concrete 
 individuality clings to the subject, and that of specially 
 selected determination to the predicate. The second of the 
 above propositions might certainly be understood to mean 
 that the qualities of the office were limited in the relation in 
 question by those of the individual, and not those of the 
 individual adapted to those of the office. 
 
 If it is replied that this may be possible enough, but that 
 reaUy one who commits himself to the former proposition 
 has bound himself to know and judge the concrete synthesis 
 of qualities which the predication constitutes along with its 
 subject, I cannot deny that this is so. And I am therefore 
 content to rank such inference as is illustrated by the above 
 transition under the head of interpretative inference, i. e. 
 inference that falls within the logical unity of the judgment 
 as bona fide expressed by either propositional form. It is 
 true that in some simply convertible judgments, e.g. 'A = B 
 in weight ', the order of terms can make no possible difference 
 of import. But the reason of this is not that the proposition 
 is simply convertible, but that the content is of a highly ab- 
 stract character which annuls all individuality, and thus 
 destroys any significance that might attach to the difference 
 between subject and predication. A similar character belongs 
 in some degree to all quantitative judgments. 
 
 /3. The Universal Affirmative Judgment (under which, in Conver- 
 ordinary logic-books, the Singular Judgment is compre- Limita- 
 hended) is not admitted to be convertible simply, i. e. by tion. 
 mere transposition of subject and predicate, but is supposed 
 to be convertible ' by limitation', i. e. by transposition together 
 with reduction to the level of a ' particular ' judgment. 
 
 With reference to the first part of this rule, the whole 
 course of our investigation of judgment is a comment on the 
 degree and rationale of its truth. It is equally certain that 
 the prohibition of simple conversion is warranted by common 
 
310 Negation, Opposition, and Conversion [Book i 
 
 usage, and that the ' pure case ' (which does not mean mere 
 tautology) is an ideal operative throughout the judging 
 activity. I am confident that Quantification of the Predicate 
 and the Equational Logic owe much of their success to their 
 recognition of this ideal, though their forcing it upon the 
 ordinary judgment by truncating the meaning of the latter 
 is a blundering anticipatio naturae. 
 
 The second part of the above rule, the ' limitation ' of the 
 converse, has different values as applied to different classes 
 of judgment which correspond to the so-called ' universal 
 affirmative '. If we take a judgment of the collective type 
 and argue e.g. that because 'All houses in this street have 
 gardens ' therefore ' Some houses which have gardens are in 
 this street ' we do not seem to gain anything by the re-arrange- 
 ment. And we certainly lose something, for we cannot 
 recover the original judgment by re-conversion of the par- 
 ticular thus obtained. Of course re-conversion can only give 
 * Some houses in the street have gardens '. But we know, 
 to begin with, that all the individual houses in the street unite 
 with their other attributes that of having gardens. We 
 seem, then, only to have advanced to a doubt of what we knew. 
 There is however a shade of difference suggested, as in the 
 singular judgment examined above, by the mere transposition 
 of subject and predicate. The denomination of the individuals 
 is less emphasised than the content enunciated of it. The 
 former fills the place of pointing with the finger to an object 
 of perception, the latter that of the significant ideas by which 
 the perceptive judgment qualifies such an object. But this 
 transition seems to fall within the interpretative inference, 
 and not to amount to substantive inference. 
 
 In the case of the generic judgment of either type the 
 import of the change becomes more emphatic. ' The dahlia 
 is one of the Compositae ' tells me that this regular flower, 
 apparently a mass of petals like a garden rose or peony or 
 hollyhock, is really an aggregate of little florets like those of 
 the daisy or dandelion.^ In short, this judgment distinguishes 
 
 * In the double dahlia — the form till lately commonest in gardens — 
 every floret is developed into a one-sided corolla like those of the florets 
 which form the ray of the common daisy. 
 
Chap. VII] Cofiverston of Generic Judgment 311 
 
 the dahlia from flowers externally not unlike it, but having no 
 structural affinity with it whatever. ' The Compositae include 
 the dahha,' or ' Some Compositae are dahlias,' presents us with 
 the typical or generalised structure of a Composite flower deter- 
 mined and differentiated by the peculiarities of a dahlia. The 
 rose or peony would in this case never come into our heads ; we 
 should be occupied with some such individual as the daisy or 
 the thistle, and the object of the judgment would practically 
 be to distinguish the dahlia from other Compositae, not to 
 distinguish it from flowers which are in no way akin to it. 
 The one judgment qualifies the external appearance of a 
 dahlia by the internal structure of the Compositae ; the other 
 qualifies the diagrammatic type of a composite plant, as 
 admitting, among others, of the specific peculiarities of the 
 dahlia. 
 
 I have but little doubt that this account represents the 
 meaning of the two propositions in fact. But it may be said 
 that we have no right to separate them, and that we ought 
 to demand the explicit recognition of both these determinate 
 affinities as essential to the meaning of the generic universal 
 judgment itself ; and it may even be insisted that if the second 
 proposition contains more than the first in any respect — e. g. 
 in the more concrete appreciation of diversities of composite 
 structure — then it cannot be warranted by the first. This 
 latter suggestion would make short work of all conversion 
 whatever beyond the rank of grammatical change, unless — 
 TiXiov ijixLcrv irdvTos — mere selection can make the old into 
 new, or unless some principle is appealed to that goes beyond 
 the judgment itself. The former part of the objection may 
 be met by saying that undoubtedly the original judgment may 
 be made with the whole significance of the two propositions ; 
 but that when so made it is somewhat artificial, and that 
 the distinction of a specific adaptation within the Composite 
 type is naturally a different process from the qualification 
 of a given shape by the abstraction of that type. I may put 
 the antithesis thus : the generic judgment, which we took as 
 the convertend, if completed into identity, would determine the 
 composite type by limitations restricting it to the case of the 
 dahlia ; while the particular, in this case the converse, if 
 
Sion 
 
 312 Negation, Opposition, and Conversion [Booki 
 
 similarly completed, would extend the range of species by 
 disjunctive enumeration till they expressed the whole content 
 of the natural order of Compositae. 
 Modal y. This conversion of a generic judgment may be taken 
 
 ^inn^'^'^ either as interpretative or as substantial Inference. Tested 
 by common usage it is, I incline to think, a substantial trans- 
 formation, resting on some such principle as the possibility 
 of treating every content in turn as quasi-individual. Tested 
 by the logical ideal, it is a mere phase in the interpretation of 
 the judgment, which involves reciprocal determination in the 
 affirmation of a nexus. In either case it contains the only 
 fundamental principle on which conversion can really proceed ; 
 viz. that every content can be exhibited as a quasi-individual 
 element in a system. This is, for instance, the principle of 
 which ' modal ' conversion is merely a corollary. In the 
 typical example employed above modality has no real applica- 
 tion ; modality only appears where the disjunction is one of 
 ignorance. The particular judgment ' The type of the Com- 
 positae includes among its alternative modifications that of 
 the dahlia ' may be read into ' A composite may be a dahlia ', 
 i. e. the fundamental structure C is a real element compatible 
 with the modification D. But this is a mere consequence of 
 feigning ignorance when we have knowledge ; in order to get 
 the possibility we have to imagine that conditions are unknown 
 which in fact are distinctly known and enter into the content 
 of the judgment. 
 
 The pure Hypothetical Judgment differs from the Generic 
 by disregarding individuality, and therefore the above principle 
 is disguised in converting a Hypothetical, so that we appear in 
 this case to obtain pure modal conversion. ' If arsenic is taken 
 in such and such a quantity, it will cause death with such 
 and such symptoms ', which gives the converse ' Death with 
 such and such symptoms at least may have been caused by 
 arsenic '. This is a motived possibility or real possibility, not 
 a mere possibility, and forms a substantial conclusion and one 
 warranted by the convertend. But this result is still rather 
 a corollary from the converse, than the converse itself. The 
 example just quoted is one hardly deserving hypothetical 
 form. It involves no traceable modification such as to set 
 
Chap. VII] Modul Conversioft 313 
 
 up a clear nexus between antecedent and consequence. Thus 
 we cannot assign any precise conditions under which the 
 consequent is related to the given antecedent, and the possi- 
 bility that such death may result from such poison is merely a 
 fact plus unknown alternatives. In a true hypothetical there 
 is more than this. Grant that it is not simply convertible, 
 still we can bring the possibility home to the nature of the 
 consequent. ' If straight lines are parallel, they do not tend 
 to meet.' The real converse of this is, ' Straight lines in the 
 same plane which do not tend to meet are parallel.' But the 
 limiting condition is not given in the convertend. Nor do 
 I mean that we have a right actually to state it in the converse, 
 but yet we must think of the converse where such a condition 
 can be suggested as exhibiting a real if undefined attribute of 
 the content which is now the subject, in virtue of which this 
 content includes the case mentioned in the antecedent of the 
 convertend. The affinity between generic judgments and the 
 more valuable hypotheticals is very close, and we lose all hold 
 on the generic element in judgment if we insist on reducing 
 a definitely determinable content to one real alternative in 
 an unknown number of unknown ones. I cordially agree 
 therefore with Mr. Bradley's distinction between real and 
 mere possibility, and only insist that the true content even of 
 a modal converse is the positive nature in virtue of which the 
 subject-content is variously determinable, and not a mere 
 conjunction of attributes plus other unknown conjunctions. 
 
 h. We are now to speak shortly of conversion in which the simple 
 negative is employed. Every negation rests, as we have Conver- 
 seen, in its purely formal aspect, on the ultimate or absolute Universal 
 disjunction. But it does not follow from this that a real Negative. 
 process of substantial inference takes place where negation 
 intervenes. 
 
 I begin with the simple conversion ; ' A is not B,' therefore 
 ' B is not A ' ; 'No negroes have straight hair,' ' No straight- 
 haired man is a negro.' I should certainly prefer representing 
 this transition as a true process of argument to illustrating it 
 by a diagram of two separate circles, because by the latter 
 means we destroy all idea of the structure of the judgment. 
 But yet I cannot think that in our present stage of reflection 
 
314 Negation, Opposition, and Conversion [Booki 
 
 the argument if any is more than interpretative, i. e. more than 
 we are always using in arriving at the full meaning of any 
 sentence. We can formally trace out the process of inference, 
 but in using it we are like an engine running free and doing no 
 work. No doubt the formal steps are, beginning from the 
 ultimate disjunction between ' is ' and ' is not ', to say ' No 
 negroes have straight hair ' ; ' Straight-haired men are either 
 negroes or not ' ; 'If negroes, then they are both straight- 
 haired and not straight-haired ' ; ' Therefore it is false that 
 they are negroes', ' therefore they are not negroes.' But all 
 this is given in the meaning and practice of any civilised 
 language ; and though it might be possible to stumble in 
 using this converse,^ that is no more than may happen in 
 reading any sentence however simple. The elementary 
 meaning is simply that the two contents are in the relation of 
 abstract otherness to each other, and refuse to be brought 
 together in the modified or concrete otherness which subsists 
 within the affirmative judgment. 
 Contra- f. Contraposition seems to contain a more remote con- 
 posi ion. ^.^^gjQJ^ j^ gQgg from A is B, to Not-B is not A, e.g. from 
 ' Every negro has woolly hair ' to ' A man wlio has not woolly 
 hair is not a negro '. I remark on this process, i. that the 
 skeleton argument with symbolic letters seems far jnore 
 remote and obscure than the intelligible example ; ii. that we 
 are much hampered in the apprehension of our inference by 
 being forbidden to conclude that ' Not- A is not-B ', which the 
 ideal of judgment demands as the expression of the negative 
 instance, 'Just not-A is just not-B,' e.g. — the affirmative 
 being ' True freedom is virtue ' — ' If you fail to produce free- 
 dom, you fail so far and for that reason to produce virtue '. 
 And, iii. substantial inference is less likely here, for the unity 
 of the judgment is much greater in affirmation than in negation; 
 and when we have just, so to speak, dipped the object a in the 
 colour b, it seems idle to ask on the basis of that judgment 
 whether what is not of the colour b can be t)ie object a. We 
 are in fact no longer dealing with a and b, but with a b as 
 including all a. We may say of course, ' Oh yes ! noi-b is 
 
 ^ As e.g. if any one tried to argue that ' All not-straight-haired are 
 negroes '. 
 
Chap. VII] Elementary meaning of Negation 315 
 
 not-a, because if not-J is a then it is 6.' But this remark is 
 made ready to our hand ; we have just qualified a by 6 and 
 therefore are at least entitled to ' a is not not-& ', which brings 
 back our problem to the last head, that of simple conversion. 
 
 In short, then, in both these cases we employ the absolute 
 alternative ; but this is given in the/orw of negation or con- 
 tradiction, and needing no true limitation of alternatives, can 
 only rank as a formal principle of intelligible thought and 
 speech, not as a real addition to content of inference. Tran- 
 sition by help of such a formal principle I call Interpretative 
 Inference. 
 
 5. The external shape of negation belongs as we saw to Privation, 
 ignorance, and significant negation is knowledge disguised as Affirma- 
 ignorance. For bare denial would be devoid of meaning. excIu- 
 Now this external shape of negation seems really appropriate ^^o"^- 
 where positive knowledge fails, i. e. in the region of what has 
 been called Privation/ — the mere absence of positive deter- 
 mination. But this region is also the region within which 
 there falls the limitation of knowledge, a matter of the most 
 serious and positive import. Where knowledge simply fails 
 us, and consequently we seem to have nothing left but priva- 
 tion or bare denial, how are we to pronounce on any suggested 
 possibility, a. by way of affirmation, /3. by way of exclusion ? 
 
 The case a is the more complicated of the two. The priva- Privation 
 tion or bare denial is in this case the bare denial of an incom- poggi. ^^ 
 patibility with reality, i.e. of an impossibility. Exclusion, as bility. 
 we have seen, must rest on a positive quality, a ground of 
 negation. Here, ex hypothesi, we can find no exclusion of the 
 impossibility. We are supposed to know simply nothing, 
 either pro or co7i, about the positive matter whose possibility 
 is in question. Are we therefore bound to admit that it is not 
 
 ' ' Privation,' Privatio, used by Sigwart as equivalent to Aristotle's 
 artprjais, arfprjTiKos, and as contrasted with opposition, ivavrioTTii, and 
 distinct from negation, dnocpaais. :^Tfpr]<iis seems to be applied to any 
 negative enunciation, diro(paais only to the denial of an affirmation ; 
 see Aristotle's Organon, 38 b, 13, with Waltz's note. Unluckily the 
 distinction of privative and negative terms as given e.g. in Whately's 
 Logic has just the reverse meaning to that of privation and negation in 
 Sigwart and Bradley. ' Privative ' in Whately indicates a positive 
 opposite, and ' negative ' a mere absence. The association with active 
 ' deprivation ' implying a loss appears to be the cause of this usage. 
 
3i6 Negation, Opposition, and Conversion [BookI 
 
 not-possible, and, as a consequence of this double negation, 
 that it is possible ? If we are led to do this — and the trick is 
 often attempted, especially in popular theology— we feel that 
 we have been cheated. A possibility, in the usual sense of the 
 term, is something. We are foolish if we do not keep it in 
 view and let it influence our deliberations in any way which 
 its nature demands. Yet this something has here ex hypothesi 
 been created out of nothing. But in knowledge at least 
 nothing can come of nothing, and we are trapped in a contra- 
 diction. 
 
 What we have to remember is that our denial of the exclusion 
 of the positive content is or approximates ^ to a bare denial ; 
 or in other words, rests upon no positive ground. We do not 
 exclude the impossibility ; we only fail to find it. And there- 
 fore our denial is meaningless or nearly meaningless, and 
 amounts to nothing. In other words, the possibility which 
 we are asked to infer from mere not-impossibility has as so 
 inferred no foundation in positive reality. A real possibility 
 of any result consists in something given as actual, which, 
 under conditions of known nature and not known to be impos- 
 sible, would give that result. A gun forms a real possibility 
 of shooting, if there is no reason to suppose that cartridges 
 are not to be had ; an acorn is a real possibility of an oak, if 
 we know of nothing to hinder its being planted and growing. 
 But in the case supposed we have nothing like this ; we have 
 simply nothing — a failure to find incompatibility. Therefore 
 we ought, strictly speaking, to conclude not that it is possible, 
 which is an affirmation, nor even that it is not impossible, which 
 borrows the form of intelligible denial, and therefore presup- 
 poses a positive ground of denial, but simply that we do not 
 know it to be possible. This conclusion gives its true value 
 to the form of bare denial by making the ground of negation 
 what in the case of ignorance it really is, an actual state of our 
 own minds which excludes the knowledge in question. 
 
 ^ ' Approximates,' for a suggestion, if intelligible, contains some 
 ground in its mere conceivability, and thus affords material for intelli- 
 gible support or refutation. But by far the larger element in the 
 importunity of many suggestions is drawn from the fallacy of inferring 
 from non-impossibility to real possibility. 
 
Chap. VII] Does not-impossiblc = possible ? 317 
 
 Instances of assertion resting rnainly on this confusion 
 are to be found e.g. in expositions of the so-called modern 
 Buddhism, the elaborate dogmatic fabric of which is chiefly 
 protected from criticism by the impossibility of discovering 
 any ground on which it may be taken to rest, and against 
 which, therefore, a positive objection can be raised. 
 
 To put the point in other words, in the case before us it is 
 not true that double negation is equivalent to affirmation. 
 For the double negation in question is founded neither on 
 the affirmation itself, nor on the denial of a specific alternative 
 to the affirmation. If there were such a specific alternative to 
 the affirmation, it could only be denied on some positive 
 ground, and such a denial would not be the bare denial of which 
 ex hypothesi we are treating. 
 
 Or again, without appealing to the difference between 
 privation, i.e. bare denial, and exclusion — a confusion between 
 which processes however is the root of the fallacy — we may 
 simply lay it down that a real possibilit}'' is something actual, 
 and that a bare denial affirms nothing as actual, and therefore 
 a bare denial cannot affirm a real possibility. 
 
 And it must be added with reference to remote suggestions 
 generally, that a failure to demonstrate impossibility can 
 almost always be secured by a high degree of remoteness or 
 of abstractness in the suggestion itself. Thus, if accepted as 
 really possible because not demonstrably impossible, such a 
 suggestion would profit by its own wrong. Reality cannot, 
 for us, contradict a suggestion that has no point of contact 
 with reality. Things in themselves, according to the popular 
 notion of the Kantian doctrine, are the content of such a 
 suggestion. They made no claim to affect knowable Reality, 
 and therefore knowable Reality can present no quality which 
 excludes them. As a rule, to disprove the grounds on which 
 a fact is advanced is not the same thing as disproving the 
 alleged fact ; denpng the antecedent does not amount to 
 denying the consequent. But in the case of un verifiable sug- 
 gestions the grounds which are implied in the suggestion are 
 for a given state of knowledge the sole grounds conceivable, 
 or at least the grounds which can be stated are capable of 
 exhaustion, and the disproof of them may be taken as for that 
 
3i8 Negation, Opposition, and Conversion [Booki 
 
 state of knowledge disproving the suggestion. It must be 
 remembered that denying the antecedent does deny the con- 
 sequent qua consequent of the antecedent denied. At any rate 
 it is clear that in such cases as those under discussion the failure 
 to prove impossibility which arises from the emptiness of the 
 suggestions themselves must not be taken as amounting to the 
 establishment of real possibility. 
 Privation /3. We cannot go from bare denial, or privation, of an 
 and Im- inipossibility, to real possibility, because privation of im- 
 
 possi- ^ •' . . . 
 
 bility. possibility does not involve positive affirmation as the exclusion 
 of impossibility does. It may seem therefore that we have 
 decided in the negative by anticipation the question whether 
 privation or bare denial can ever justify exclusion. We denied 
 the claim of privation to establish real possibility, on the 
 ground that it could not exclude, as one form of the ground 
 that it could not affirm. Thus when we omit the incompati- 
 bility or impossibility, and consider merely the exclusion of any 
 positive content, it seems that we cannot predicate exclusion 
 on the strength of privation. Up to a certain point common 
 sense and experience support this result. Gold has never been 
 found in Northumberland, but that alone does not prove that 
 it never can be found there, unless the geological formation 
 forbids, i.e. is a positive ground of exclusion. 
 
 Still, the two transitions, from privation of impossibility 
 to affirmation of real possibility, and from privation of actuality 
 to exclusion of possibility or of actuality, do not stand on 
 quite the same level. The former is explicitly a passage from 
 denial to affirmation, or, as we saw, from nothing to something. 
 The latter retains its negative form and vehicle unchanged, and 
 leaves the change of its ground and hearing, the two other 
 elements of meaning,^ to be moulded by the context. Any 
 mere denial or privation when expressed intelligibly is given 
 a ground and bearing with reference to our cognitive state, as 
 we saw in dealing with the instance, ' We do not know that 
 there are things in themselves.' What is a bare denial with 
 reference to reality is a positive affirmation about our know- 
 ledge. We have agreed that we cannot transform ' We do 
 not know it to be impossible ' into ' It is possible '. Can we 
 ' See above, p. 289. 
 
Chap. VII] PHvation and Exclusion 319 
 
 transform ' We do not know it to exist ' into ' It does not 
 exist ' ? 
 
 It is plain, I think, that many beliefs become abortive and 
 cease to be regarded because we become convinced that 
 reality does not constrain us to accept them. And it seems an 
 unworthy shirkiiig of a theoretical difficulty to treat these 
 beliefs as shelved but not denied. If, whether in serious 
 speculation or in grave practical deliberation, some idea 
 cognate with the matters then before the mind has ceased to 
 exercise the slightest bias on thought or on action, it seems 
 idle to say that upon such an idea we have suspended judgment 
 as upon something that may be true in itself but is nothing 
 for us. It seems clear that upon such an idea — I may instance 
 the Swedenborgian hierarchy of spiritual beings — we have in 
 fact sate in judgment and have condemned it as unreal. But 
 I admit that the speculative expression of our relation to such 
 conceptions meets with serious difficulty from the necessity 
 of basing denial upon a positive ground. On what positive 
 ground can I base a denial that there are exactly seven heavens, 
 or that there are just seven orders of superior spirits ? I un- 
 questionably do deny it, that is to say, ' I do not believe it.' 
 The habitual use of such phrases as this,^ which refer gram- 
 matically to a fact of my intellectual state, but actually serve 
 as negations of something ascribed to reality, bears witness to 
 the connection which I am attempting to point out. 
 
 Incompatibility in the ordinary sense depends on the system 
 of reality. Differents which claim the same place are incom- 
 patible, and, in short, everything is incompatible with reality 
 which, while not conforming to our ideal system which stands 
 for reality, is yet without the power to modify it. But, as 
 I pointed out above, all this falls to the ground where the 
 system does not extend. Where ' we do not know ' in the 
 sense of having no knowledge — not merely in the sense of 
 lacking complete knowledge — ^we can say nothing, and ex 
 nihilo nil. ' Then,' it may be said, ' neither acceptance nor 
 rejection.' I cannot follow this. Knowledge is positive, and 
 acceptance and rejection are not co-ordinate alternatives. We 
 
 * Compare ov fijui, which means ' I deny ', or our common phrase 
 ' I don't think that ' — ^which is really equivalent to ' I think that — not.' 
 
320 Negation, Opposition, and Conversion [Booki 
 
 doubt, where we have a basis of fact to go upon, and presump- 
 tions that appeal to that basis ; but where we have nothing 
 to go upon we cannot doubt. 
 
 The only conclusion that I see open to us is of this nature. 
 Where privation seems to warrant exclusion, We must look 
 for the positive ground of exclusion in the determinate com- 
 pleteness of our ideal Reality. Such a ground may be hard 
 to state, and may amount in positive content to little more than 
 our experience of the persistency of the privation. But its 
 nature must be that the ideal Reality by its organised com- 
 pleteness excludes the matter which attempts to introduce 
 itself. This must not be taken to mean that we are nearly 
 omniscient. It means that the general plan and growth of our 
 knowledge is such as to afford no basis of attachment for the 
 proposed accretion, although for this very reason we are unable 
 to specify any definite antagonism between the content 
 suggested and the positive contents already accepted as part 
 of Reality. Reality is not especially incompatible with seven 
 heavens ; it could be so only if we accepted some kind of 
 heaven as a reality and were prepared, on the basis of our 
 knowledge about it, to reject either the particular number 
 seven, or the application of number to such a subject at all. 
 What we really have to say is that we do seem able to trace, 
 however imperfectly, something like a development of the 
 sensuous into the spiritual world ; and that the main lines of 
 this development appear to have a completeness of their own, 
 without growing out into a duplicate and quasi-material world. 
 
 It is not enough to destroy the grounds on which a suggestion 
 is explicitly based, unless we can show that they form not 
 merely the sole ground alleged, but the sole ground possible. 
 And in a region beyond our knowledge this ex hypothesi cannot 
 be done. It is often possible to show by what logical fallacy 
 or by what psychological tendency a suggestion was generated ; 
 but this is not a logical refutation. It may however grow 
 into a refutation if, besides the tendency which caused the 
 error, we can exhibit the satisfaction which reality offers to 
 the rational necessity embodied in that tendency. We thus 
 not only destroy the raison d'Ure of the error, but show a 
 presumption that there is an excluding ground. 
 
Chap. VII] IguoYance and Privation 321 
 
 Exclusion by Privation then rests on a conviction, won 
 by persistent lack of alfirmation, of the true negative limit 
 and external contour of knowledge, which limit, qua the true 
 limit, must be held true of reality. A privation cannot 
 ultimately be referred to our knowledge only. If persistent 
 in the history of thought and justified by the tendencies of 
 knowledge, it must sooner or later be taken as true of reality. 
 
 At best, we must remember, negation is always negative. 
 The last step from the positive ground to its formal expres- 
 sion by means of denial, retains the form of privation, i.e. of 
 ignorance. This is what the old saying means, * you cannot 
 prove a negative.' The negation is not after all quite the 
 same as the positive opposite latent under the negation. 
 You cannot prove that parallels never meet. In order to do 
 so, you would have, like the Irishman, to ' be there when it did 
 not happen '. You can only prove that they always do this, 
 that, or the other which in virtue of your geometrical experi- 
 ence you take as equivalent to not meeting. That is to say, 
 assuming your geometrical system to be ad hoc exhaustive, then 
 your failure to see, on the basis of that system, how parallels 
 can meet becomes knowledge though it retains the form of 
 ignorance. It expresses a limit or outline essential to geo- 
 metrical science. Thus the cases of persistent privation and 
 of true positive exclusion (genuine denial, not bare denial) 
 differ simply by the nature of the positive ground which 
 underlies them respectively. In privation this ground is 
 general, drawn from the character and tendencies of Reality ; 
 in true exclusion it is special, drawn from a system within 
 which the alleged reality would fall. It would seem fair to 
 concede to the former somewhat more and to the latter 
 somewhat less finality than common theory recognises. 
 
 1337 
 
CHAPTER VIII 
 
 Disjunction and the statement of Chances 
 
 The Dis- 
 junctive 
 Judg- 
 ment. 
 
 Its 
 
 Genesis. 
 
 I. The Disjunctive Judgment combines in an explicit 
 form the characteristics of the Generic and of the pure 
 Hypothetical Judgments. 
 
 i. It is nieedless however, and would be artificial, to lay 
 down rules for the precise mode of transition from these 
 judgments to the complete Disjunction. The whole assertory 
 state within which the simpler forms of judgment, at any rate 
 from Comparison upwards, have their import, is from the 
 first of a disjiinctive nature. Reflection may therefore be 
 stimulated to the explicit formulation of this type of knowledge 
 by very. various occasions. But the common ground which 
 must operate in all these occasions is the discovery of differ- 
 ences into each of which the identity underlying all of them 
 enters as a whole, and in all of which taken together its mani- 
 festations are exhausted. Every difference has the former 
 of these characters in some point of view. A conjimctive 
 judgment, or conjunction of judgments with an identical 
 subject, can always be made disjimctive by wilful abstraction. 
 A diamond is carbon, and crystalline, and very hard, and 
 highly refractive. This is a conjunctive judgment or set of 
 judgments.^ But if we limit the underlying identity, the 
 nature of the stone, bj'' the several conditions under which 
 it exhibits these several predicates, then each of these pre- 
 dicates may be regarded as not conjoined with but exclusive 
 of the other attributes enumerated. A diamond may be con- 
 sidered either merely as an element, or merely as a transparent 
 substance exhibiting crystalline structure, or in its power of 
 scratching other hard substances, or in its effect upon light. 
 This is disjunction — arbitrary and subjective, if we please, 
 but still disjunction. Any distinguishable attributes may be 
 regarded as reciprocally exclusive by our sunply refusing to 
 ' See above, chap, i, on the Judgment in Time. 
 
Chap. VIII] Transition to Disjunction 323 
 
 attend to more than one of thein at once, x may be both a 
 and b, but qua a it is not b. But in another respect also the 
 above instance of disjunction is bad and arbitrary. It makes 
 no serious attempt to exhaust the attributes. We stop 
 enumerating them simply because we do not care to go on. 
 
 It is clear that a disjunctive judgment may originate with 
 a conjunction of judgments like the above, which turn out to 
 have assignable relations to one another, or, again, with the 
 discovery of an error in a generic judgment ; e. g. ' Cereus 
 is a night -flowering plant.' ' No : Cereus grandifionts is a 
 night-flowering plant, but there are a hundred species of 
 Cereus, and not all are night -flowering.' Such considerations 
 would force upon us the disjunction, ' Cereus blossoms either 
 at night, or in the early morning, or &c., &c.' Again, the 
 attempt to convert a generic judgment naturally leads to 
 a disjunction.^ And so does the challenge thrown down by 
 the specific condition and consequent of a pure hypothetical 
 judgment. ' If we catch the train this morning we reach 
 London to-night.' In presence of such an assertion it is not 
 in human nature to abstain from asking, ' And if we miss 
 the train, what then ? ' so as to make explicit the disjunction, 
 ' We either catch the train or miss it ; ' and probably some 
 such further consequence as, ' We either get to London to- 
 night, or have to sleep at Crewe.' 
 
 All these are merely different ways of giving utterance to 
 the interest which attaches to some pervading identity and 
 compels us to pursue it throughout its modifications. Such 
 an interest, as we have seen, environs every genuine judgment, 
 and makes it an element in a system. And in proportion 
 as such a system is made explicit, negation enters into know- 
 ledge. For in every system the parts have an aspect of 
 negative relation to one another. 
 
 Thus the immediate occasion on which we form a disjunc- 
 tive judgment may vary. But the characteristics of true 
 disjunction do not vary. By true disjunction I mean a 
 judgment in which alternatives falling under a single identity 
 are enumerated, and are known in virtue of some pervading 
 principle to be reciprocally exclusive, and to be exhaustive. 
 
 ' See abovej chap, vii, on the Conversion of generic judgments, 
 
 ¥2 
 
324 Disjunction and the statement of Chances [bookt 
 
 Disjunc- 
 tions, 
 
 Not ex- 
 clusive. 
 
 This is the disjunction of which I shall treat, being convinced 
 that what seem to be different kinds of it are in fact nothing 
 but imperfect examples. 
 Imperfect ii. I will mention three of these. 
 
 a. First, there is the so-called disjunction in which the 
 alternatives are exhaustively enumerated, but are not taken 
 to exclude one another. ' He is either knave or fool ' does 
 not, it is said, exclude the possibility that he may be both. 
 On the question of the genuineness of these disjunctions 
 T must refer to Mr, Bradley's detailed discussion,^ which 
 appears to me to show decisively that we never really mean 
 to take into consideration under our judgment the conjunc- 
 tion of the alternatives specified in our ' Either ' — ' or '. 
 Without following him into the study of grammatical details, 
 I content myself with remarking that any Disjunction in 
 which the alternatives are not reciprocally exclusive must 
 of necessity fail to be exhaustive — the case or cases in which 
 any of them are conjoined being casus omissi. If, for the 
 purpose of the disjunction, such a case may be reckoned 
 under one of the other alternatives, then indeed the disjunc- 
 tion may be reckoned to be perfect ; but then the case of 
 conjunction does not rank as conjunction, but under one or 
 other of its component elements. Thus, ' To go by train 
 you must have either a first, second, or third class ticket.' 
 A man may of course buy all three, if he pleases ; but the pos- 
 session of them does not constitute a fourth case of liberty to 
 go by the train. He goes by the train in virtue of one or other, 
 though he may change carriages at every station if it amuses 
 him. The conjunction of all three tickets forms no separate 
 alternative as a particular way of going by train, and therefore 
 is rightly disregarded in the disjunction. It is not indeed 
 implied that ' If he has a first-class ticket he has not a second 
 or third ', but it is implied that ' If he goes in virtue of a first- 
 class ticket he does not go in virtue of a second or third '. 
 
 /3. Secondly, there are the troublesome cases often taken 
 
 as the true instances of Disjunction, which may be called 
 
 ' Disjunctions of ignorance ', The essence of these is that 
 
 they refer to an individual (actual or supposed) and not to 
 
 ^ Principles of Logic, Book I, chap, iv. 
 
 Disjunc- 
 tions of 
 Igno- 
 rahce. 
 
Chap. VIII] Ignonince on a specific point 325 
 
 an individuality, and consequently express doubt or indeci- 
 sion rather than knowledge. 
 
 ' A triangle is either isosceles, scalene, or equilateral,' A 
 triangle here can mean any individual triangle you may pitch 
 upon — ' any given triangle '. And with respect to such an 
 individual triangle the disjunction says that it must belong to 
 one of the three kinds mentioned, but that we do not know 
 to which. Lotze, for instance, appears to accept this expression 
 of indecision as the final type of disjunction. But it seems 
 obvious that this uncertainty is purely dramatic or fictitious, 
 and is a mere corollary from the true disjimction, which is, 
 ' A three-sided plane figure as such must have all its sides 
 equal, or two only equal, or all unequal.' Or we may take a 
 case where the doubt is real, as often in common life ; but 
 here also it is a mere application of or inference from the 
 true disjunction of knowledge. * Being an Oxford man, he 
 is either a University College man or a Balliol man, or &c.' 
 This judgment, which is a real expression of doubt or ignor- 
 ance, is based of course on the positive knowledge that the 
 conditions of University life require the student as such 
 (generically) to attach himself to some one of the corporate 
 bodies enumerated in the judgment. With disjunctions of 
 this type we must class the commonest of all expressions 
 of doubt or ignorance. ' He is either angry or jealous,' 
 ' He has either measles or scarlet fever.' These, like the 
 above, differ not in principle but only in perfection from the 
 ideal disjunction. What operates is something we know, 
 and know to contain the specified alternatives. We do not 
 however specify our knowledge in detail — it may consist in a 
 content hard to define — and we merely pomt to the concrete 
 individual, in whom it is embodied and from whom it takes 
 its interest. About this individual, as his complete state 
 goes beyond our knowledge, the judgment takes the shape 
 of doubt, just as in the case of 'any given triangle'. The 
 higher logical form may be imposed on the lower content ; 
 this is a possibility which follows from the nature of reason, 
 and which makes abstract distinction appear in some aspects 
 so valueless. Every thinkable content has in miniature all 
 the characteristics of reason, and in the abstract you can 
 
326 Disjunction and the statement of Chances [Book i 
 
 Disjunc- 
 tions re- 
 ferred to 
 point of 
 time. 
 
 hardly say anything of the self-conscious mind which is not 
 also true of a protococcus or of a pebble. The precise modes 
 and degrees in which the content fulfils the spirit of its abstract 
 form are what we must keep our eyes on in a true concrete 
 science. I cannot admit then that the mere inference from 
 om" disjunctive knowledge respecting that which an indi- 
 viduality implies, to a doubt respecting a given or supposed 
 individual, has a claim to rank as a genuine species of dis- 
 junction. 
 
 y. It is a similar vice to account for the exclusiveness of 
 a disjunction by referring it to a point of time. No judg- 
 ment whatever refers to an atomic point of time ; and no 
 universal judgment lefers to any time except that implied 
 in the content of the judgment itself. The time at which 
 the predication happens to be made has nothing to do with 
 the import of any judgment except in as far as it is taken 
 into the content by reference direct or indirect to present 
 perception.^ The denial of coexistence in time, which appears 
 in some disjunctions to be the principal meaning, is a corollary 
 from the nature of the disjoined contents, not a result of the 
 present tense employed as a vehicle of predication. ' A 
 railway signal shows to the same side either a red, or a green, or 
 a white light.' Now of course this judgment informs us that 
 at any given moment of time we shall only see one of the three 
 lights. But to interpret the judgment as if it essentially 
 referred either to the moment at which it is made or to ' any 
 given moment ' is a fallacy on all-foars with that pointed out 
 above of interpreting ' The triangle ' as = ' any given triangle '. 
 The judgment means that the nature of a railway signal is to 
 show one light to the exclusion of another and the other to 
 the exclusion of the one. From the naiiure of the case they 
 exclude one another in time and in spatial direction. But 
 the present of predication is coextensive, in its reference, 
 with the nature of the signal, and does not refer especially or 
 exclusively to the moment at which the judgment happens to 
 be pronounced, nor even hj^potheticallyto 'any given moment'. 
 
 We must clear out of the way, then, the above disjunctions 
 of ignorance, or dramatic disjunctions, and consider exclu- 
 ' See above, chap, v, ou Time in singular judgments. 
 
Chap. VIII] The Disjunctive Predication 327 
 
 sively the perfect disjunction as a form of knowledge. One 
 more peculiar type, indeed, will come before us later as the 
 statement of chances. 
 
 iii. A true or ideal disjimction is a generic judgment whose ^ffif^t 
 content is developed or inter-related by the aid of hypo- of true 
 theticals. ^^- 
 
 a. It is a generic judgment because it deals with an The 
 individuality, a content which is a whole or system in itself. Generic 
 So far, like the generic judgment, it is quasi-categorical, ment. 
 The subject is such as can be real, and the judgment assumes 
 its reality. But the predication made of this real and quasi- 
 individual subject is peculiar, and has points of analogy both 
 with the negative and with the pure hypothetical judgment. 
 The individuality is exhibited in the different forms which it 
 is capable of assuming as a whole, and which consequently 
 it cannot unite in itself under a single set of conditions. If 
 the individuality is considered as essentially affected by time, 
 these forms may be successive ; if it is a generic or specific 
 character, they may coexist in space and time with each other ; 
 all that is necessary is that the subject-content should enter 
 as a whole into each of the enumerated forms. What, then, is 
 directly predicated of the subject-content ? I see no theoreti- 
 cal reason to deny that the ' either — or ' considered as the 
 articulate analysis of a universal ■*• system of attributes can 
 be intelligibly and categorically predicated of it. Every 
 predication includes differences, and an extended present, and 
 therefore predicates as facts elements which can be regarded 
 as reciprocally exclusive. In fact, every imiversal is a synthesis 
 of such elements. But undoubtedly there will always be 
 positive qualities which are the condensed or summarised 
 expression of the total analysis, and may present themselves 
 as its ground, being thus in disjunction as the positive ground 
 or bearing in negation, and as the underlying quality in the 
 hypothetical judgment.. ' The triangle is either scalene, 
 isosceles, or equilateral ' contains as this condensed relation, 
 or synthesis of differences, * a plane figure bounded by three 
 sides, which may have any relative length so long as any 
 
 ' ' Universal ' not in the sense of abstract or generalised, but in the 
 sense of a concrete identity containing differences. 
 
328 Disjunction and the statement of Chances i^BooK I 
 
 two of them are together greater than the third.' Such an 
 attribute might be called the categorical or positive basis of 
 the disjunction ; * but it is an illusion to suppose that a basis 
 or ground is necessarily more real or more primary than its 
 consequences, and that therefore the implied predication in 
 disjunction is more categorical than the explicit ' either — or '. 
 The ground is to its consequences as whole to part ; but if 
 the consequences are fully stated in a connected system 
 this distinction falls away, and in disjunction such full state- 
 ment is the ideal. 
 
 The disjunction is therefore the only judgment-form that 
 in strict theory can stand alone. All connection is within 
 a system ; and only that judgment is self-sufficing which 
 affirms at once the system and the connections within it. 
 I do not say that every disjunction is thus ultimately self- 
 dependent, but relatively to a number of hypotheticals which 
 have their truth within it every true disjunction has a sub- 
 stantive character. Thus the disjunction which lays down 
 the nature and kinds of the triangle contains the ground and 
 basis of all the hypothetical judgments which expound the 
 properties of that figiue. In other words, if completed and 
 made explicit, any one of those h57potheticals would result 
 in that disjunction ; which however itself falls within the 
 ultimate judgment that would expound the nature and modes 
 of space. The above then is the generic or substantive element 
 in disjunction. 
 The Hy- )3. But we need in addition the reciprocal relations between 
 ^'°i*T^d ^^^ forms which constitute the explicit development of this 
 ment. predicated universal. For these relations we must go to the 
 hypothetical judgment, and to the hypothetical in a very 
 late and artificial form, viz. that in which the negation of one 
 content is known as the ground of the affirmation of another 
 content, and the affirmation of the one content is known as 
 the ground of the negation of the other content. The percep- 
 tion of the relations which these two types of hypothetical 
 judgment embody is essential to the exhaustiveness of the 
 disjunction and to the reciprocal exclusiveness of its members. 
 In order to know that the alternatives enumerated are 
 * See Appendix to this chapter. 
 
Chap. VIII] Reciprocal Relations 329 
 
 reciprocally exclusive, we must be able to say (using as an 
 illustration the simplest case in which there are only the two 
 alternatives B and C), * If A is B, it is not C And in order 
 to be sure that no possible alternative is omitted we must 
 be able to say (in the same example) that ' if A is not B, it is 
 C '. According to a rule of Conversion, or rather of Inference, 
 accepted for the case of Hypothetical Judgments (' Deny the 
 consequent ') the equivalent or converse judgments, ' If A 
 is C it is not B ' and ' if A is not C it is B ' are involved in 
 the two corresponding judgments above mentioned. If this 
 Conversion or Inference is disputed, then we must say that all 
 four cases, ' If A is B— ,' ' If A is C— ,' ' If A is not B— ,' ' If A 
 is not C — ,' must be perceived independently before the pre- 
 dication of disjoined alternatives is justifiable.-^ 
 
 * I insert here some details which are legitimate matter of curiosity, 
 but would needlessly overload the text. 
 
 i. It might be urged, on the analogy of the argument e"mployed above 
 (p. 324) — that a disjunction which is thoroughly exhaustive cannot but 
 have its members reciprocally exclusive — that the hypothetical which 
 prima facie secures exhaustiveness (If A is not B it is C) ought to afhrm 
 the reciprocal exclusiveness of the antecedent and consequent, i.e. to 
 exclude the case B C. If it did so, on the other hand, it would become 
 at a blow equal to the disjunction ' A is either B or C,' and would include 
 in itself the case ' If A is B ' — with its converse. In other words, it 
 would become a reciprocal judgment, correlative to a definitory affirma- 
 tion, and as such would admit of conversion or inference by denial of the 
 antecedent ; just as if we were to infer from ' A is B ' that ' not-A is 
 not-B '. This, as we have seen all through, is the ideal of the judgment ; 
 and a hypothetical judgment with negative condition or negative conse- 
 quent, that fulfils this ideal, coincides already with the disjunction. 
 But usage does not warrant the ascription to the hypothetical ' If A is 
 not B it is C ' of the meaning ' If A is not B-without-C it is C-without-B '. 
 As commonly employed, therefore, it lays down a certain outer limit, 
 but does not exhaust the subdivisions within the limit. This is just the 
 point of contrast between the hypothetical judgment in its ordinary 
 signification and the complete disjunction. But there is a certain 
 tendency on the part of the former to advance towards the latter. It 
 is plain that the reasons which induce us to give prominence to the 
 alternatives mentioned as the only ones to be specially considered may 
 readily transform themselves into reasons why only the alternatives 
 mentioned can be considered, or, perhaps, can exist. We have such 
 reasons just warranting a disjunction in the instance given above 
 (p. 324), where the case formed by the combination of the alternatives 
 considered exists, so to speak, in fact but not for the law, 
 
 ii. It may be worth while to point out that disjunctions with more 
 
330 Disjunction and the statement of Chances [Book i 
 
 The reference to these two or four hypothetical judgments 
 has its value in elucidating the natiire of the system which 
 a true disjunction embodies. It exhibits in the plainest 
 light the indispensable function of negation in articulated 
 knowledge, and the positive import with which in virtue of 
 that function the negative is invested. We have already 
 seen the nature of this import in the analysis of the signifi- 
 cant negation, where, however, the positive ground and 
 consequence of denial were matters of tacit understanding 
 and inference from context. In explicit disjimction, on the 
 other hand, we find them after they have been developed 
 independently and distinctly in the hj^othetical judgment, 
 and affirmed as actual attributes within a system that is 
 alleged to exist in reality. 
 When are iv. But, it may reasonably be objected, it is not in every 
 parts system that the parts are disjunctively related. As a rule 
 
 disjunc- •' r J J 
 
 tively the parts of a system are predicable in conjunction and not 
 
 related ? ^^ disjunction. 
 
 Apart from the case of intentional abstraction by which 
 any conjunction can be tinned into a disjunction — for in 
 the last resort within every system every part involves the 
 whole nature of the system — ^this criticism is just. A human 
 
 than two alternatives must be treated, as regards the hypothetical 
 judgments involved, as a succession of dichotomies. The hypothetical 
 judgments of each type involved in such a disjunction would therefore 
 be equal in number to the disjoined members, i. e. each alternative must 
 be made in turn the positive and negative condition of an hypothesis, 
 with a compound consequent, the disjunctive nature of which cannot 
 appear in the hypothetical judgment. A is either B, C, D, or E. Then 
 we have the negative conditions, ' If A is not B, it is within C D E ; ' 
 ' If A is not C, it is within B D E ; ' ' If A is not D, it is within C B E ; ' 
 ' If A is not E, it is within C B D.' The. positive conditions will corre- 
 spond severally to the above negative conditions. 
 
 Here we see a second defect of the hypothetical a? compared to the 
 disjunctive judgment. It can only handle one reciprocal relation at 
 a time, and "cannot master a whole system of such relations in a single 
 view. In the above analysis the hypothetical judgment does not enable 
 me to express more than a single contradictory relation, as between 
 a particular A and its not-A. The idea of a pervading contradictory 
 relation, characterising any one part as against all the others, cannot be 
 expressed in any one hypothetical judgment. By saying ' If A is not B, 
 it is either C, D,or¥ ' we should be pressing the hypothetical type beyond 
 its powers. 
 
Chap. VIII] Disjunction and Conjunction 331 
 
 body is made up of trunk, limbs, and head ; not of either 
 trunk or limbs or head. The government of a civilised nation 
 consists of the legislative and the executive power, not of the 
 legislative or the executive. A genus, again, may be said to 
 be identifiable with all its species, not merely with either 
 this or that, though here we are on more doubtful ground. 
 Triangles are isosceles, scalene, and equilateral. Men are white, 
 black, and yellow. We could hardly say however that * the 
 triangle is isosceles, scalene, and equilateral ', or that ' man 
 is white, black, and yellow '. The difference between con- 
 junctions of the kind here brought forward, and true (dis- 
 junctions, is formally speaking a difference of the aspect in 
 which a real system is regarded, but materially, therefore, has 
 an intimate dependence on the actual nature of the real system 
 in question, which may be such as to throw one aspect or 
 another prominently forward. Every universal may have its 
 differences conjunctively enumerated, whether they are in 
 time or in space, or merely distinct in thought. But in so far 
 as the universal itself enters as a whole into each difference, 
 which it can do in very different degrees, so far each difference, 
 if imposed as a condition on the universal, excludes all the 
 other differences. A man's having a hand does not interfere 
 with his having a foot. But a man's having a feeling in his 
 hand does begin to make a claim on the universal, the man 
 himself, which is to a certain limited extent incompatible with 
 his having a feeling in his foot or elsewhere. And when we 
 come to consider such acute interest or feeling as occasions 
 the absorption of the whole mind in the perceiving or suffer- 
 ing member, then it is true to say, ' The man perceives or feels 
 either with eye or with ear or hand or foot,' as the case may be. 
 So again if we think of a triangle as a mere abstract gener- 
 ality that describes a heap of Various figures, we may say 
 that it includes, or that — in a collective judgment — its in- 
 dividual instances are, this, that, and the other. But if we 
 think of it according to its complete conception as an in- 
 dividuality that must necessarily take individual' shape, and if 
 we follow the process by which such shape must be determined, 
 then we can only express our insight by the use of the dis- 
 junctive ' Either — or '. 
 
332 Disjunction and the statement of Chances [Book i 
 
 The conception of the whole as conditioned by one of its 
 parts takes the place of that imaginary reference to an 
 atomic point of time which has been supposed to be of the 
 essence of disj miction. ' A moving object is either here or 
 there ' means ' if here, not there ' and ' if not here, then 
 there '. It does not mean ' Within the indivisible moment 
 in which I am judging a moving object can be in one place 
 only '. For I cannot judge in an indivisible moment, nor 
 can I refer to a present that is an indivisible moment. In 
 any extended time a moving object traverses space, and 
 our ' present ' is always an extended time. And so the 
 disjunction if referred to our * present ' time would not be 
 true, and the moving object would be, like Sir Boyle Roche's 
 bird, ' in two places at once.' 
 Isthedis- V. When we have imderstood the nature of disjunction 
 reducible ^^^^^ ^^ ^^t much profit in asking whether the disjunctive 
 to Hypo- judgment can be * reduced ' to two or more hypothetical 
 t letica s. judgments. The mere fact that the hypotheticals in question -^ 
 are separate judgments, and that the disjunction is a single 
 judgment, is enough to show that we have in the latter a 
 combination of unity with reciprocal exclusion which we have 
 not in the former. I have endeavoured to express this unity 
 by representing the disjimction as a combination of the generic 
 and the hypothetical judgments. But it must be remembered 
 that at best we are dealing with grammatical types which 
 are only the symbols of states of knowledge ; and it is most 
 probable that any one who is able to make the two com- 
 plementary hypothetical judgments ' If A is B it is not C ' 
 and ' If A is not B it is C ', supplies out of his own mind the 
 systematic relation which the two taken together involve, in 
 a judgment equivalent to ' A is either B or C '. 
 
 Not to dwell longer than I can help on formal points, I 
 merely remark in addition to what was said above, ^ that 
 in any case these hypotheticals themselves presuppose the 
 ultimate or formal disjunction, ' A is either B or not-B,' by 
 their introduction of a negative relation into knowledge ; 
 and that further, if we wish to take the two h3^otheticals 
 above mentioned as implying the two which foUow from 
 * See footnote, p. 329. ^ p. 329. 
 
Chap. VIII] The Ultimate Disjunction 333 
 
 them by denying the consequent, we are once more relying 
 on this formal disjunction, which is essentially involved in 
 such a transition.^ The material importance of the whole 
 question lies in the process by which the fonn of disjunction, 
 in itself on a level with or consisting in the Law of Excluded 
 Middle, i. e. of contradictory opposition,^ acquires the 
 material significance of Disjunction between positive con- 
 traries. I have tried to show above that these two elements, 
 the bare rejection and the positive contrary, are probably 
 to be regarded as distinguishable from the first, but as tending 
 to coalesce, and not as later and earlier phases respectively of 
 the same movement. Or if, in history, earlier and later, then 
 the later, the abstract formal negation or bare rejection, is 
 to the earlier, the actual choice between positive alternatives, 
 as a separable outgrowth which consciously reunites with it 
 in the region of reflective intelligence. No anthropological 
 doctrine can affect — though it may elucidate — the above 
 logical analysis of the relation between the negative and its 
 material import as made explicit in the judgment. 
 
 2. The statement of chances is a case of the Disjunctive The state- 
 Judgment. ^,^"* o^ 
 "* ^ , , Chances. 
 
 i. The title which I place at the head of this section indicates Limits 
 the limits of the question which I propose to treat in it. The of the 
 calculus of chances, like all mathematical reasoning, has at ^i present 
 its root an inference that can be expressed in ordinary language, work. 
 In treating of inference it will be incumbent upon us to discuss 
 the differentia which separates calculation from ordinary 
 reasoning ; and we shall find the outward and visible sign of this 
 differentia to consist in the enormous abbreviation of reasoning 
 processes by their condensation into the import of recognised 
 s5nTibols. It is a further question in virtue of what peculiar 
 nature an inferential process can submit to such an abbrevia- 
 tion, and also to what extent the abbreviation has the effect 
 of substituting something else, e. g. application of a rule-of- 
 
 ^ See the account of Contraposition, above, chap, vii : the process 
 by ' denying the consequent ' is essentially the same with this. 
 
 * It is an unlucky confusion that the so-called law of Contradiction 
 only explains Contrary opposition, and that it is the law of Excluded 
 Middle that lays dowip the principle of Contradictory opposition. See 
 Book II, chap. vii. 
 
334 Disjunction and the statement of Chances [Book i 
 
 Affilia- 
 tion of 
 abstract 
 disjunc- 
 tion. 
 
 thumb/ for the reasoning process so ' abbreviated '. But the 
 value of any such abbreviation must ultimately rest in a 
 logical sense upon the reasoning which it represents, and this 
 reasoning must be in its nature explicable in language like 
 any other reasoning.^ Thus in the calculus of probabilities, 
 though I am obliged from mathematical incompetence to 
 omit much that might be of interest to an expert even from 
 a logical point of view, yet the principle of the statement 
 of chances is not a matter of technical method, but of funda- 
 mental postulates of knowledge. And also, no doubt, it 
 illustrates the necessity by which totalities of a certain 
 degree and kind of abstraction become subject to numerical 
 manipulation. 
 
 ii. The statement of chances rests upon a species of dis- 
 junctive judgment, but not on what we have spoken of as 
 the true or real disjunction — ^which might also be called, in 
 contrast with that which we are about to discuss, the con- 
 crete disjunction. The concrete disjunction, in as far as it 
 reaches its ideal, embodies differences that are distinct and 
 individual modifications of the underlying system, and pro- 
 vides in the nature of the common subject a complete account 
 of the conditions which determine it to each of these differ- 
 ences. In using such a disjunction we know precisely how and 
 why the whole or real subject must enter into each of the 
 differences which constitute it. And though it may be said 
 that we do not or need not know when or how far each 
 condition involved is or can be real, yet we must know some- 
 thing of the relation of such conditions to the reality of the 
 system which they affect (because their reality is partly 
 relative to its reality), and at least there is no sort of reason 
 
 * I have in my mind as an instance the use of tables of logarithms. 
 It does not appear formally essential that any one who uses them 
 should understand the reason of the rules he applies, i.e. (I presume) 
 the nature of Indices. 
 
 * A practical reservation must here be made in considering the higher 
 mathematical processes from this point of view, because they may pre- 
 suppose a number of stages consisting of subordinate processes, and be 
 inexplicable apart from these latter. But to explain the whole compli- 
 cation in ordinary language might involve a lengthiness that would 
 make it harder to follow such an explanation than to master the proper 
 mathematical language. 
 
Chap. VIII] Coficfete and abstract Disjunction 335 
 
 for supposing that the reaHty of these known conditions is 
 to be taken as an equal amount in the case of all the several 
 alternatives. The variety of the world and of all reality 
 throws the whole presumption the other way. The idea of 
 equally grounded alternatives is a negative idea, and can 
 only exist by a defect of knowledge, or by an abstraction 
 from what we kn&w. 
 
 The abstract disjtinction, on which alone a statement of 
 chances can be based, cannot be a system of alternatives 
 whose conditions and relations are thoroughly understood. 
 It is rather allied to what was spoken of above as the dis- 
 jimction of ignorance. The affiliation to the hypothetical 
 judgment is indeed the same in all disjunctions that are 
 formally perfect, i. e. both exclusive and exhaustive. But 
 on its other side the abstract disjunction does not, like the 
 concrete, descend from the generic judgment with its pene- 
 trating and dominating individuality, but rather fi'om a judg- 
 ment of enumeration such as the collective judgment, with 
 its homogeneous parts which do not occupy individual or 
 distinctive relations to the containing identity. It is true that 
 to give meaning to any disjunction, or to a statement of 
 chances founded upon it, the parts or members of the whole 
 must be distinct as well as homogeneous. But the distinction 
 is in this case mere distinction, interesting as a result, like 
 the differences between the six sides of a die, but on the side 
 of its relation to the whole not rooted in any known hetero- 
 geneous modifications of that whole. In other words, the 
 number of parts, or the fact that each is one among so many, 
 is the primary fact, and their nature is secondary. We may 
 illustrate this by contrasting an example of a concrete with 
 one of an abstract disjunction. ' The constitution of a modern 
 nation,' it may be said, ' is necessarily either democratic or 
 plutocratic' Here the fact that the species assigned are two 
 in number is of no importance. No one would think of trying 
 to infer anything from it as to how many nations were likely 
 to be democratic and how many to be plutocratic. The 
 whole weight of the judgment rests upon the component 
 elements implied in ' modern nation ', and upon the develop- 
 ment of those elements which the judgment indicates to be 
 
33^ Disjunction and the statement of Chances [Book i 
 
 Essence 
 of the 
 state- 
 ment of 
 chances. 
 
 necessary. But if we take such a judgment as ' A die must 
 turn up one of its six sides ' we here regard the individuality 
 of the several sides as indifferent with respect to the probability 
 of their recurrence, though not with respect to its results. 
 The important matter is the number of the alternatives. 
 For either we are unable to estimate the operative causes 
 which determine one alternative rather than another, or we 
 wilfully abstract our attention from them for the sake of 
 falling back on a more general process of estimation. We 
 are to suppose then that as the basis of our statement of 
 chances, we have before us such a formal disjunction as the 
 above, closely akin to the judgments which arise in the 
 process of enumeration, but with the addition of those known 
 relations between the enumerated parts which are embodied 
 in the hypothetical judgments with negative antecedent and 
 consequent respectively. 
 
 iii. We are then in a position to enter upon a process which 
 I can only describe as taking stock of our knowledge by 
 arithmetical methods. We know that the die has six sides and 
 no more, and that as the result of a single throw it must turn 
 up one of them. We know that we do not know of any cause 
 operative in the nature of the die or in the conditions of the 
 throw that should favour any particular side, nor of any 
 grounded presumption whatever in favour of any one side 
 in particular. In the case of the die, which herein differs 
 from many cases of the statement of chances, we may say 
 that we know that there is not any permanent operative cause 
 either in or outside the die that can favour one event in par- 
 ticular. Therefore — and here is the all-important step which 
 really constitutes the statement of chances — v^e go from ' no 
 known inequality of the grounds for affirmation ' ^ to ' equality, 
 so far as follows from this knowledge, of the grounds for affirma- 
 tion ' of the several' alternatives. Having made this step, 
 i. e. having placed the grounds for each alternative on a level 
 as equal, we are of course free to treat them as units, and a 
 
 * Judgment about the future, if we judge, is of course affirmation as 
 much as judgment about the past. But it is not essential to the state- 
 ment of chances to refer to the future. They can be stated on given 
 premises about any event, although its real issue be known. 
 
Chap. VIII] Physical Alternatives 337 
 
 ratio expressing the relation of each to all follows as a matter 
 of course. Each alternative counts for one, and none for more 
 than one. In other words, the ground for the affirmation of 
 each, assuming the reality of the common subject, is repre- 
 sented by a fraction of which i is the numerator and the total 
 number of alternatives the denominator. We do not attempt 
 to say what the ground is, but we say that, by the terms of 
 the disjunction, it is one out of so many equal and reciprocally 
 exclusive grounds. This transition from indifference of 
 formulated knowledge to equality of grounded affirmation, 
 and so to the relation of units within a sum total or fractional 
 parts within unity, is the logical foundation on which the 
 statement of chances rests. 
 
 iv. All its developments are applications of this principle. Applica- 
 a. For instance, it may happen that alternatives which are *|^J^ state- 
 separate units in respect of the ground for affirming their ment as 
 reality are identical in respect of that result of which the ^^ ^^_ "^' 
 chances are being stated. It follows that the chances of this tiv^Jand 
 result are represented by as many units out of the sum total Results, 
 as there are equal alternatives which produce it. In other 
 words, the chances of the common consequence of a number 
 of alternatives whose chances are known is the sum of the 
 chances of those alternatives. If you bet with me that you 
 will throw a six first throw with a single die, then all live 
 alternatives from one to five inclusive have annexed to them 
 the consequence that I win the bet. The total number of 
 alternatives being six, I have thus | of the chances in my 
 favour, or the chances against you are 5 to i. 
 
 The further processes of the calculus must always reduce 
 themselves to obtaining a correct enumeration of the equal 
 alternatives, and a correct estimate of the number of those 
 equal alternatives which have annexed to them the result 
 whose chances are to be stated. 
 
 /3. The combined chances of independent events illustrate Physical 
 both these principles very simply. ^j^^g 
 
 To find the physically different throws that are possible 
 with two dice, we must take into account which is which of 
 the two dice. It is obviously possible in a single throw for 
 any side of the one die to concur with any particular side of 
 
 1337 z 
 
33^ Disjunction and the statement of Chances [Book i 
 
 the other die, i. e. writing down the six sides of the one die 
 as headings, you will have to write down all six sides of the 
 other as possible cases under each of these headings. This 
 relation is of course expressed numerically by multiplying 
 the whole number of sides of one die by the whole number 
 of those of the other ; 6 x 6 = 36. This gives the correct 
 enumeration of the alternatives that are physically possible, 
 the chance of each in case of a single throw being — . General- 
 ising this process, we may say that in two or more independent 
 sets of alternatives the chance of the concurrence of two or 
 more particular events, as many as there are sets concerned, 
 is determined by the product of the numbers of alternatives 
 forming each separate set multiplied together. That is to 
 say, the chance of any particular concurrence of events, 
 consisting of one out of each independent set, is I divided by 
 the product in question. 
 Interest- y. But to return to the example of the two dice, it may be 
 results. ^^^^ *^® 3^ possible concurrences would not all count as 
 different^ because e. g. the throw 2 with the die a and i with 
 the die h may be treated as the same with the throw i with a 
 and 2 with h. Therefore the results which are the alternatives 
 according to this mode of counting have not all of them the 
 same chances in their favour, i. e. do not severally contain 
 the same number of physically distinct alternatives. Each 
 of the six throws i and i, 2 and 2 &c. up to double sixes 
 inclusive corresponds to one physical alternative only out of 
 the possible 36, and therefore has only the chance represented 
 by 3 g-. On the other hand, each of the fifteen ' throws ' i 
 and 2, I and 3 to i and 6 inclusive, 2 and 3, 2 and 4 &c. to 
 5 and 6 inclusive, is a result annexed to two physical alterna- 
 tives (i and 2 or 2 and i, &c.), and therefore counts as two 
 equal cases or units, and has a chance represented by the sum 
 of the chances of these equal cases, viz. by ^ instead of ~. 
 These 15 * throws ' then, answering to two actual alternatives 
 apiece, exhaust the 30 real cases that remain after deduct- 
 ing the six doublets, and the whole 36 alternatives are thus 
 accounted for. Or again, if we take into account merely 
 the number of points thrown, at each throw, without regard 
 to their distribution between the two dice, we get six com- 
 
Chap. VIII] Truc problematic Judgment 339 
 
 binations of throws that will give seven points, five for eight 
 points and six points respectively, and so on to one combina- 
 tion for two points and twelve points respectively. The chances 
 of throwing 7 are therefore 3^, and of throwing the other 
 numbers /g, 3^, and so on down to —^ respectively. 
 
 v. Logicians are not agreed as to the proper description What 
 of that which is expressed by the ratio that embodies a^^^^g. 
 statement of chances. Their disagreement arises more from ment of 
 the subtlety of the distinctions involved, wnich makes de- i-gpre- 
 scription difficult, than from a substantial difference of opinion sent ? 
 as to the relation between reality and the cognitive act in 
 question. It is not imnatural, for example, to say that the 
 ratio expresses our subjective expectation. But this is an 
 obvious slip, because the whole process of the statement is 
 undertaken in order to correct and control our subjective 
 expectation, and is futile unless it does so. The complete 
 coimterpart of this idea would consist in maintaining that 
 the ratio expressed an actual behaviour on the part of real 
 things. I do not know that this suggestion has ever been 
 made in this extreme form. Something of the same kind 
 however is commonly believed with respect to the realisation 
 of chances in a series, which I shall speak of directly. 
 
 The ratio of chance seems really to express the amount 
 of ground, which is afforded by the knowledge formulated in 
 the disjunctive basis of the calculation, for affirming the reality 
 of the result whose chances are in question, on the assmnption 
 that the general case, which forms the subject, is realised. 
 Instead of ' amount of ground ' it would be more usual to 
 say * degree of probability '. And by avoiding the expression 
 probability we do not really escape the tautology which it 
 would introduce. Foi the idea of a measurable amount of 
 logical ground, like the idea of a measurable degree of proba- 
 bility, is only intelligible with reference to the statement of 
 chances. 
 
 ' Expectation ' sounds more like a term which might 
 elucidate the definition, and if we say that the statement of 
 chances represents the expectation ivhich is justified by the 
 premise, we might not be far wrong. But I do not feel sure 
 that anything can be meant by a degree of expectation except 
 
 Z2 
 
340 Disjunction and the statement of Chances lbook i 
 
 the mood, whatever that may be, which is founded upon 
 a statement of chances. So that the chance would not come 
 from measuring the expectation, but the expectation from 
 measuring the chance. Even if we identify expectation with 
 judgment — a proceeding which is more than doubtful — we 
 cannot say that the chances necessarily represent the degree 
 of certainty ivith which we judge ** in a statement of chances ; 
 because the statement, giving due numerical weight to every 
 equally-grounded alternative, asserts in the proper ratio the 
 reality of all the alternatives, and is in this aspect a judgment 
 with its conditions made fully explicit, and therefore necessary 
 or apodeictic. Not that a statement of chances is usually or 
 ever true in fact ; but this divergence from fact, or abstract 
 character, affects the categorical aspect of the w^hole disjunc- 
 tive basis of the statement, the truth of which basis is in no 
 way affirmed or impeached by the ratio of chance founded 
 upon it. The chance that one side of a 6-sided die will turn 
 up is g ; but this says nothing about the certainty that 
 there is a 6-sided die. Paradoxically enough, the statement 
 of chances seems to measure, if anything, the degree of 
 certainty of a problematic judgment made without knowledge 
 of or in abstraction from the statement, as to the probability 
 of a single alternative out of a number without reference to 
 the remaining alternatives. Not that a statement of chances 
 can govern the meaning of a judgment made in ignorance 
 of it, and it is indeed hard to see any meaning in degree 
 of certainty apart from measurement b}^ the enumeration 
 \\hich gives a ratio. But on the other hand, the moment 
 we have the ratio, we have with it the iu'liole consequence 
 of the assumed reality, and the judgment which asserts the 
 ratio is mere arithmetical necessity, the nature of the assumed 
 reality being given. The judgment that ' the odds against 
 any one side of a (6-sided) die turning up at one throw are 
 
 * It is rather ' the degree of certainty which we judge,' i. e. alifirm. It 
 is beside the point to discuss the probabihty of the truth of the judg- 
 ment which states the chances. It is the degree of certainty of a par- 
 ticular alternative happening, not that of the judgment which states 
 the degree of certainty, that is represented by the chances. This is the 
 view of the text in the end, and I let the discussion stand, because it 
 illustrates a possible error. 
 
Chap. VIII] Gvound foY affirming 341 
 
 5 to I ' has not a probability as 5 to i, but on the premises 
 is necessary. But it determines what I ought to mean, when 
 I say, in ignorance of or not considering the calculation, 
 ' it is unlikely that a six will turn up the first throw.' If I 
 reflect and say, ' It is unlikely (with an unlikelihood of 5 to i) 
 that &c.,' then my judgment has ceased to be problematic, 
 and has become necessary, i. e. the conditions of its probability 
 are analysed and made explicit. Thus probability as a 
 character of judgment disappears when measured. 
 
 The ratio of chance then expresses the amount of ground 
 for affirming, that follows from the knowledge formulated 
 as the disjunctive basis of the reckoning. We may possess 
 knowledge that does not conform to the conditions of the 
 statement of chances, or at least that is not relevant to the 
 special disjunction which we are able to employ. Such 
 knowledge may cause us to distrust the reckoning slightly 
 or wholly as it affects some particular case. I may think for 
 instance that the calculated risk of being run down by a cab 
 in the streets of London does not apply to one man who is 
 in the prime of life and habitually alert, or to another who is 
 bedridden and never goes into the streets at all. But none 
 the less the probability of cab accidents for each individual 
 of the population on the data that are taken is a mere question 
 of calculation and can only have one correct answer. My 
 private notion that I have supplementary data which ought 
 to be considered, or that a more careful distinction should 
 be made between classes of persons in the data, does not in 
 the least affect the probability which flows from the premises 
 in any particular calculation. 
 
 The calculus of chances, in short, bears the character of 
 the judgments from which it is derived. Like the pure 
 hypothetical judgment, and the greater part of the abstract 
 judgments derived from the judgment of enumeration, it 
 affirms of Reality indirectly and conditionally. Its truth 
 is a truth of necessity, a consequence that follows from a 
 selected or fancied character when taken as real. Such a 
 consequence is not subjective or arbitrary. Given the premises, 
 it can only be drawn in one way, and every other result from 
 those premises is wrong. But yet it does not express actual 
 
342 Disjunction and the statement of Chances [Book i 
 
 concrete fact. It expresses a truth necessitated by the nature 
 of Reality, but not as it stands embodying a fact of Reality. 
 It is simply an arithmetical consequence of a highly abstract 
 disjunctive enumeration. 
 Chance vi. In every statement of chances we admit our partial 
 actual ignorance. If this were not so, the statement would involve 
 series, a flat contradiction. For our grounds for affirming rieality 
 are equal in the case of all the alternatives, and yet our state- 
 ment of chances is based on the assumption that only one of 
 them can be realised. 
 Fallacies a. But if we do not bear in mind the proportion of ignor- 
 tosems. ^"^^ which enters into our data, we are tempted into two 
 fallacious attitudes. 
 
 In the first place, we consider ourselves justified in being 
 astonished at the realisation of the alternative which has very 
 few chances in its favour. 
 
 And in the second place, we palliate the apparent con- 
 tradiction between equal grounds for reality and unequal 
 realisation by affirming that the statement of chances has 
 genuine truth only in an actual series which realises all the 
 equal alternatives equalty. To realise all the equal alterna- 
 tives equally is of course the same thing as to realise all the 
 interesting results ^ in the ratio prescribed by the statement 
 of chances. 
 
 First, then, we have very small ground for being surprised 
 at the actual occurrence of that alternative which had fewest 
 chances in its favour ; and absolutely none for being surprised 
 at the occurrence of a marked or interesting alternative which 
 has against it enormous odds, but only the same as against 
 every alternative which can possibly occur. In the former 
 case we are cherishing a private presumption that the know- 
 ledge embodied in our premises represented the actual operative 
 causes which determined the realisation of one or another 
 alternative, and this is ex hypothesi not the fact. In the latter 
 case we are misled by a special interest into comparing, as 
 if they were cases of which the chances should be equal, 
 cases which are not ' equal alternatives ', but ' interesting 
 results ' comprising unequal numbers of equal alternatives, 
 ^ See above, p. 337. 
 
Chap, viiij Actuul SeHes 343 
 
 viz. on the one side a single case which is in some way remark- 
 able, e. g. a hand at whist consisting solely of trumps, and on 
 the other side all other possible hands whatever, which we 
 implicitly contrast, as a single case, with the opposite ' inter- 
 esting result '. We are therefore surprised at the immense 
 adverse odds in spite of which this result has been realised, not 
 reflecting that there are precisely the same adverse odds 
 against any one of the alternatives which occur in everj'day 
 experience, though not, of course, against all of them together. 
 
 And secondly, the realisation of the ideal alternatives in 
 a series of real cases is confessedly a fiction unless we stop 
 the series at an arbitrary limit — say, for instance, the actual 
 limit of individual objects or events in question in space or time 
 — and even within this limit the series is not what we want. 
 
 There are under this head of an actual series two possi- 
 bilities which prima facie at least must be distinguished. 
 We may have to deal with a natural or deductive cycle 
 of alternatives, or with an arbitrary or inductive cycle. 
 
 In what may be called a natural cycle the alternatives are 
 ideal cases that follow obviously from the nature of the 
 general subject ; and are distinct from the real cases, the 
 actual instances or events, which may or may not continue 
 to present themselves beyond the one real case which is 
 postulated in the statement of chances. The sides of a die 
 or of a coin furnish ideal cases ; the throws of a die or tosses 
 of a coin are real cases. The natural cycle is the lowest number 
 of actual events in which the ideal alternatives could be all 
 realised equally ; i. e. six throws in the case of the die, two 
 tosses in the cases of the coin. Beyond this natural cycle 
 there is nothing to suggest a limit to the series of real cases. 
 We have therefore to ask, in considering the verification of 
 natural cycles by experience, whether the real cases correspond 
 to ideal cases (i) svithin every natural cycle that is observed ; 
 and (ii) in the series as a whole continued without limit. 
 
 In what, on the other hand, may be called an arbitrary 
 cycle the * ideal alternatives ' are derived from the enumera- 
 tion of real cases. The population of Great Britain at a given 
 date would be such a collection of real cases, and that these 
 real cases are identical with the equal ideal alternatives is 
 
344 Disjunction and the statement of Chances [Book i 
 
 shown by the fact that their number forms the denominator 
 in the fraction that states the chances. If e. g. the population 
 were 30,000,000, and 600,000 people died in the year, the 
 chance, assuming constancy of the average/ that any one 
 individual taken at random would die within the following 
 year would be 3§§§-5-o^o"o' ^^^- sV- ^^^ analysis of such a 
 statement of chances appears to me not quite simple, and 
 I doubt whether Mr. Venn, in maintaining that chance 
 essentially refers to series, has identified its elements rightly. 
 The individual human beings composing the population in 
 question, in whatever order we choose to take them (say, 
 in the accidental order of our enumeration), must correspond, 
 I think, both to the real case ^ — the throw of a die or toss of 
 a coin — and also to the ideal cases — to the sides ^ of the die 
 or of the coin considered as possible alternatives. And the 
 two general cases of dying or not dying within the year 
 cannot, I think, correspond to the equal ideal cases or possible 
 alternatives, but must be treated as those combinations of 
 alternatives which arise when several possible ' ways in which 
 the event may happen ' have an identical consequence in 
 which we are interested. Or, in short, we might put it thus, 
 following in part Mr. Venn's interesting discussion : — English 
 humanity is the ' event ' ; each individual is ' a way in which 
 the event may happen ' ; * dying and not-dying or male 
 and female ^ are general consequences or results each of which 
 emerges from a large number of ' ways in which the event 
 may happen '. Thus, as is right in theory, the ratio of chances 
 
 ' Or following what was said above of the independence of calcula- 
 tion and real event, we may neglect the constancy of averages, and say, 
 referring to the same year for which the enumeration is taken, ' the 
 chance that any particular individual will have died in that year.' On 
 the same premises, the chance is the same after the event as before it. 
 
 - This is what Mr. Venn describes (Logic of Chance, chap, i, sect. 6 ; 
 chap, iii, sect. 33), in the ordinary language of the theory, as the ' event ', 
 and in his own language as the collection of attributes. 
 
 ^ This is what Mr. Venn describes either as ' a way in which the event 
 may happen ', or as the ' occasional attribute '. 
 
 ^ Or a particular modification of the collection of attributes by 
 occasional attributes. 
 
 '•" Mr. Venn, Logic of Chance, chap, i, sect. 6. Male and female are 
 not the ' ways in which the event may happen '. This would give the 
 chance of each as ?,. 
 
Chap. VIII] Adherence to a Ratio 345 
 
 is determined by the number of ways in which the event may 
 happen, which in these arbitrary cycles = the number of cases 
 in which the event does happen. It is a consequence of the 
 inductive character of the cycle that this number of ways has 
 no obvious and necessary meaning, but is a mere inference 
 from the number of times that the event does happen. It is 
 as if there was a die of unknown structure thrown 30,000,000 
 times, and exhibiting a white side 29,400,000 times and a 
 black side 600,000 times. If then we chose to assume that 
 we had before us a die with 600,000 black sides and 29,400,000 
 white sides and to estimate all further chances on that basis, 
 we should be in an analogous position to that which we adopt 
 when we calculate chance on the basis of a ratio observed 
 de facto in a cycle of cases. The chances of white and black 
 respectively are then ^~ and /^ on the basis of this real but 
 arbitrary cycle, regarded as the foundation of an ideal cycle 
 of alternatives identical in content with itself. 
 
 Now the arbitrary cycle itself, the 300,000,000 individuals 
 and 600,000 deaths, being given as real, there is no question 
 of its correspondence with a pre-established ratio. If we 
 ask whether the ratio of ~j- which it prescribes is realised 
 in experience, we can only mean to enquire whether the 
 distribution of the deaths is regular within the observed 
 cycle, or whether the same ratio prevails outside this real 
 cycle, which latter question may be followed up if we please 
 by the same question as before about the regularity of occur- 
 rence. I am not quite sure that in speaking of the uniformity 
 whicli attends large numbers of instances our writers always 
 remember that such uniformity demands the comparison of 
 two or more cycles. The ratio of results within a single 
 group, even if embracing all hitherto observed instances, is 
 in the absence of an antecedent rule a mere fact and not a 
 realisation of anything. Every ratio is definite, and any two 
 numbers have a ratio, so that it is a truism to speak of a definite 
 ratio as prevailing between classes of cases in a single group.^ 
 
 ' Logic of Chance, i. 6. The distinctive characteristic of probability 
 is that occasional attributes as distinguished from permanent ones are 
 found on extended examination to exist in a certain definite proportion 
 of the whole number of cases. The italics are Mr. Venn's. How could they 
 exist in anything but a definite proportion ? 
 
346 Disjunction and the statement of Chances [Book i 
 
 Within a single large group if we speak of adherence to a 
 ratio, we can only mean regularity of occurrence. And in 
 the case of individuals that are not events in time the signifi- 
 cance of such regularity and its existence must depend simply 
 and solely on the order in which we consider and enumerate 
 them. 
 
 Thus the two kinds of cycles or groups of instances seem 
 to be quite differently situated with respect to empirical 
 verification, i. A natural cycle from the first corresponds 
 or does not correspond to its antecedent law, within the 
 limits which that law spontaneously prescribes, //we throw 
 all six sides of a die in every six throws there can be no doubt . 
 that up to the point when we break off the series is an empirical 
 verification of the chances as we stated them. It shows that 
 the unknown causes operate equally, and thus produce the 
 result, which we anticipated by neglecting them. But in treating 
 of actual experience we may practically disregard this kind 
 of correspondence, which is not common in fact and at all 
 events could hardly repeat itself through an extended number 
 of observations. 
 
 ii. We are thus referred to the second question which w^e 
 mentioned as capable of being proposed respecting a natural 
 cycle, viz. whether the law which it presupposes (e. g. every 
 side to turn up once in six throws of a die) is realised in' the 
 long run. It nmst be observed that to speak of realisation 
 in the whole set of actual cases, whatever their number may 
 be, cannot furnish a standard in this question, because this 
 number is constantly varying and is very different in different 
 subject-matters. There is nothing between realisation in 
 every natural cycle and realisation in an infinite series it we 
 keep clear of causal presumptions which do not belong to 
 the reckoning of chances pure and simple. There is no doubt 
 that the law presupposed by a natural cycle may be realised 
 in a great and increasing number of observations, and that 
 inferences may with the aid of causal presumptions be drawn 
 from this realisation. But for all that, it is simply nonsense 
 to speak as if the true and only true realisation of a ratio of 
 chance was in the series of real instances continued ad infini- 
 tum. Mr. Venn, who is consistent in regarding this as the 
 
Chap, viii] The arbitrary Cycle 347 
 
 solution of the antithesis between equality of ground and 
 inequality of reality, denies, as I understand him, that the 
 formula | ^ has any meaning as applied to a single real throw 
 of a die, except by association with the idea of a series in which 
 all sides should equally be exhibited. Here we come into the 
 province of fiction. There is no reason, in the cases before us, 
 that such a series should be a fact at all. And in these and in 
 all other cases alike it is impossible that the infinite series 
 could be a fact. And yet, if not a fact, it fails to solve the 
 antithesis as a solution of which it is propounded. It is not in 
 fact possible to go on trying for ever, and it is not in theory 
 true that supposing we did go on trying for ever (abstracting 
 from the contradiction involved) every alternative must be 
 realised according to the ratio. The ratio may be justly 
 erected according to our grounds of knowledge, even if some 
 of the alternatives are absolutely impossible and therefore 
 could never occur although, per impossible, the series of trials 
 should be prolonged to infinity. 
 
 In the case of the arbitrary cycle the answer to the question 
 is still less favourable. The primary interest of the arbitrary 
 cycle is just in that statement of chances affecting individual 
 real cases which is suggested not to be the true meaning of 
 the ratio. There is in this case no antecedent law between 
 which and the real cycle a correspondence could be observed. 
 The real cycle itself is and prescribes the law. And although 
 cycles of real events that fall outside it, or minor cycles within 
 
 * Mr. Venn seems to have been influenced by considerations such as 
 those of p. 340-1, above. It is true, as there shown, that the judgment 
 which measures probability loses ipso facto that isolated reference to 
 a particular alternative which marks the genuine, or at least the 
 natural problematic judgment. In every statement of chance we have 
 an apodeictic judgment involving the entire content of a disjunction 
 in the bearings of its members upon one another (as condition and 
 consequent). So far Mr. Venn and I are together. The question there- 
 fore reduces itself to that of the purport with which the reference to the 
 remaining alternatives is charged, whether it depends on the idea of a 
 completed series, or can be explained by the (assumed ) equal claim which 
 each alternative makes on reality in virtue of the (assumed) equality 
 of their grounds. The latter view seems to me to be demanded by the 
 nature of the abstraction on which the whole idea of stating chances 
 depends. 
 
348 Dispmction and the statement of Chances [Book i 
 
 it, can be tested and compared with it in respect of the ratios 
 they display — as we compare the ratios of deaths to population 
 in successive years — yet it is not easy to say on what ground 
 the first cycle that we happen to observe should furnish a 
 rule to which subsequent cycles are expected to conform. 
 The whole group of observed events or individuals is a com- 
 prehensive fact, within which the ratio of the ways in which 
 they happen or of their classes is also simply a fact. Any 
 comparison which we may make of the ratio exhibited in minor 
 cycles within this entire group has only the interest of the 
 comparison between different groups of actual occurrences or 
 individuals.^ On the assumption that the operative but un-. 
 known causes are not changing progressively, or that we 
 can allow for their progressive change, we may ]io doubt 
 expect to find that a ratio which we elicited from case i to 
 1000 will hold good for cases looi to 2000. But if what we 
 want is merely the serial form, we have it already in cases 
 I to 1000 ; while if what we want is the multiplication of 
 observations, why should the 2000 cases — a wholly arbitrary 
 number — be especially satisf3dng ? The fact is, that when 
 we have the serial form given to begin with, as in these 
 arbitrary cycles, or groups of instances limited only by our 
 ceasing to enumerate them, we see that it omits just that 
 peculiar transition which is the essence of the statement of 
 chance. It only presents us with this transition in so far 
 as, surrendering its serial form, it becomes the basis of a 
 fractional expression which summarises our knowledge, drawn 
 from the series, with reference to some instance or instances 
 whether within or external to itself. This criticism applies 
 to the serial form as such. The equal realisation of alternatives 
 considered as equal (i. e. apart from regularity and irregularity, 
 which are equality and inequality as judged by minor cycles) 
 destroys the peculiar relation of equal knowledge to unequal 
 fact, which is the ground of chance. 
 
 * Mr. Venn, Logic of Chance, ii. 8, seems thoroughly to accept this 
 result, and to conceive that all probability, even in what I have called 
 natural cycles (in his phrase ' a priori ' probability), is at bottom this 
 and no more. I cannot but think that if probability in a specific case 
 means anything, it must, even though dependent on an arbitrary cycle, 
 be stated as above in the form of a natural cycle. 
 
Chap. VIII] Interpretation of Series 349 
 
 On the infinite series, or approximation in the long run, 
 I can sa}'' no more than I have said above, and others have 
 said before me. The thing is simply a fiction, and the reference 
 of the realisation of a ratio to it proves, if anything, that it 
 is ultimately necessary to admit that chance is independent 
 of a real series. 
 
 /3. The true bearing of a series on the verification or Causal 
 corroboration of a ratio expressing probability must consist f"om^"^^ 
 in its relation to the causal presumptions which dominate Series. 
 our judgments about reality. All judgments that deal with 
 fact assume, though they may not explicitly assert, causa- 
 tion. Statements of chance do not proceed by following 
 causation into its ramifications ; we should thus have concrete 
 knowledge and not equality of alternatives. But when the 
 results of experience coincide with the predictions of the 
 calculus, this suggests to us not that we knew the right causes 
 or any causes at all, but that the actual causes at work have 
 a character compatible with the results which we obtained 
 through the indifference of ignorance. If, on the other hand, 
 the results of experience deviate widely, so far as experience 
 goes, from the ratio suggested by the calculus, then though 
 this deviation can never amount to a flat contradiction, yet it 
 suggests an arrangement of causes incompatible with the 
 results which were generated b}/ the indifference of ignorance. 
 If we cast six twenty times running with the same die, we have 
 no right to say that this theoretically speaking contradicts 
 the ratio of chance (unless we take as a standard, which no 
 one would ever do, the natural cycle of six throws), for in 120 
 throws the balance might be restored. In other words, no 
 sequence is impossible in such a case, nor is one more improb- 
 able than another, but of course any one sequence is immensely 
 improbable beforehand as against the whole remaining mass 
 of possible sequences. And in an}^ marked or so to speak 
 identifiable sequence this improbability strikes us as though 
 it had occurred in face of some enonnous probability in 
 favour of some one other sequence, all the less identifiable 
 sequences counting as if one in number, though n — l in proba- 
 bility. This is a partial accoimt of our surprise ; but as has 
 been well explained by Sigwart, there is in it the further 
 
350 Disjunction and the statement of Chances [Book i 
 
 element that whereas the twenty consecutive sixes are on the 
 assumptions from which we started but one among an enormous 
 number of equal possibilities, they happen to be of such a 
 nature that on another assumption, incompatible with those, 
 they would follow with absolute or all but absolute certainty. 
 We know that if the die is cogged it will always turn up the 
 same side, or to speak generally, if there is present an operative 
 cause which necessarily produces one alternative, that alterna- 
 tive will always be produced. This suggests the comparison 
 between one ratio, that with which we started, which gives 
 a very minute probability for the result found in practice; 
 and another ratio, formed on a different assumption, which 
 gives the observed result with something like certainty. 
 Nothing binds us absolutely to either, but it is plain that so 
 far as experience has gone the probability is with the latter 
 in the proportion in which it gives the result observed with 
 greater probability than does the former. It must be carefully 
 remembered that here, as all through this discussion, we are 
 dealing with hypothetical judgments only. The probability 
 I speak of is only on the data taken into account. If I am 
 playing with a most respectable friend who says he has got 
 the die from a good shop, I may prefer to believe in the 
 reality of a peculiar case rather than in a fraud. 
 Observed y. I do not see that it is inevitable, as has been maintained, 
 culatwi ^^^^ ^^ observed series must deviate from the calculated 
 seiies way ratio, as it passes through fragments of a fresh cycle. Of 
 course its coincidence with the ratio will not be demonstrable 
 while any cases are wanting to finish the cycle ; but if we 
 shrink from saying that the observed numbers can coincide 
 with the calculated numbers in a half cycle or less, we must 
 not, I think, say that they deviate, unless coincidence at the 
 next natural cycle is already impossible. Five complete 
 cycles of sides and three different sides in thirty-three throws 
 of a die surely form a case which should be distinguished 
 from the same five cycles of sides plus three repetitions of 
 the same side. 
 The series g. In speaking of the truth of chances based on statistical 
 forTome averages, we may illustrate what has been said by the different 
 purposes, positions of an insurance office and an individual customer 
 
Chap. VIII] Chances of Truth a priori 351 
 
 of the office. To the individual whose expectation of life is 
 in question the chance of Hfe gives but little information, at 
 all events so long as it is large. Whether he gains or loses by 
 insuring his life is for him practically a mere uncertainty. 
 He knows what it is reasonable to expect on the general data 
 of reasoning, but he has no sort of ground for being surprised 
 if it does not happen. For the office, on the other hand, so 
 long as the averages are constant, the fate of individuals is 
 wholly indifferent except in so far as they are more lightly or 
 more heavily insured. If the office could be sure that in each 
 class of customers (ranking them by the amount of their 
 insurances) the average of deaths would be maintained at the 
 same figure, it would make no sort of difference to it who in 
 particular died. Thus it is true that in a real cycle the ratio 
 of chance may in a certain sense become a fact. What is not 
 true is that in becoming a fact it remains a chance,^ and that 
 if it faUs to be realised in the short run it must be realised in 
 the long run. 
 
 vii. Before passing to the subject of modality I will mention Proba- 
 an interesting point in the theory of chance, which is cognate V^||ty °^ 
 to the above discussions on Privation, Affirmation, and in the 
 Exclusion.^ What statement of chances expresses the ^f ^"q^. 
 attitude which we ought to adopt towards an affirmation in ledge. 
 the absence of all knowledge ? The accepted answer appears 
 to be \, ' for if we make it less than this we incline to believe it 
 rather false than true,' or putting I suppose the same ground 
 into mathematical language, ' If we grant that the probability 
 may have any value between and i, and that every separate 
 value is equally likely, then n and i — n are equally likely, and 
 the average is always ^.' I am not prepared to deny this 
 conclusion, which of course follows from its data, but I think 
 that it may be instructive to discuss these data, which appear 
 to me somewhat superficial. It appears that the symbol % 
 has also been proposed, on the ground that ' the a priori 
 [formal ?] probability derived from absolute ignorance has 
 
 ' Cp. Adam Smith's attack on lotteries. You may see, he said, how 
 much the chances are against you, by the fact that if you take all the 
 tickets you are sure to lose. 
 
 * Chapv vii, supra. See Jevons' Principles of Science, p. 212, 
 
352 Disjunction and the statement of Chances [Book i 
 
 no effect upon the force of a subsequently admitted [real ?] 
 probability.' ^ 
 
 It cannot but strike the looker-on that these two suggested 
 values g and ^ seem to correspond with the conceptions of 
 non-impossibility and of real possibility respectively, and 
 that to take probability as having the value ^ in the absence 
 of all knowledge * is analogous to conjuring a positive favour- 
 able presumption out of an absence of counter-presumptions. 
 The question is, according to the analysis of chance which 
 has been stated above, whether the two alternatives ' true ' 
 and * false ' are sole and equal alternatives. Interpreting 
 absence of knowledge as Jevons interprets it, to include entire 
 ignorance of the meaning of an enunciation, I do not see that 
 they are sole alternatives. ' If I ask the reader to assign the 
 odds that a Platythliptic coefficient is positive, he would hardly 
 see his way to doing so unless he regards them as equal.' ^ 
 But to a reader who does not know what the words mean — 
 and this I suppose is what Jevons intended — ^there is no 
 judgment conveyed. The alternative ' unmeaning ' must 
 then be allowed for in addition to ' true ' and ' false '. This, 
 it may be said, makes nonsense of the problem. The unmean- 
 ing is not a judgment, and the problem is only about judg- 
 ments. Granted ; but then I must not include the very large 
 division of the unmeaning in the statement of chance without 
 recognising it as a separate alternative. And if I am to exclude 
 it altogether I must either be given a sentence which I am 
 able to recognise as a judgment, or the problem must refer to 
 any judgment as such without considering whether I know 
 beforehand what it is. The latter case is not that in question, 
 and could be treated perhaps better through statistics of error 
 in the sciences, than by deduction from the alternatives ' true ' 
 and ' false '. It includes in the reckoning all judgments known 
 to be true, whereas the present problem says nothing of these, 
 but only of judgments on which being presented to me I am 
 unable to return a verdict based upon positive grounds. 
 
 The real question then is this. Given a judgment which 
 I can understand, but which I have no positive ground either 
 
 ' Bishop Terrot, quoted in Jevons, 1. c. 
 * Cp. Appearance and Reality, ed. 2, p. 
 
 505, note. - Jevons, 1. c. 
 
Chap. VIII] Effect of Iguovance on Judgment 353 
 
 to affirm or deny, what are the chances in favour of its truth 
 and falsehood respectively ? The conditions of this problem 
 cannot of course be actually realised, because to understand 
 the meaning of a judgment theoretically involves some 
 consciousness of pro's and con's. Yet there are in the world 
 so many almost arbitrary judgments, that the question has 
 some importance. Truth and falsehood are in this case, the 
 case of intelligible judgments, sole alternatives, but I cannot 
 think that they are, under the supposed conditions, equal 
 alternatives. I cannot think, that is, that every separate 
 value of probability between and i is equally likely. For 
 the judgment being a form or indeed the form of knowledge, 
 the hypothesis of ignorance, in this case ' absolute ignorance ', 
 on which the statement of chances is erected, has a peculiar 
 relation to the content of such a statement when that content 
 is the judgment. If we knew there was a certain motion 
 below a certain limit of velocity, but had no further clue to 
 the velocity of the motion, it might be true I suppose that 
 every degree of velocity below that limit was equally probable. 
 But if we know that there is a judgment made, or proposed 
 to be made, and have no clue to any degree of positive proba- 
 bility in its favour, then for us the zero of probability is the 
 fact, and if we were to make the judgment in question it would 
 in our mouth be false even if in reality true. Thus, on the 
 basis of my individual knowledge, such a judgment qua judg- 
 ment is by the hypothesis prima facie false. But my know- 
 ledge is not all reality, and therefore I dare not say that falsity 
 holds the field as an absolute certainty. The possibility 
 however drawn from the mere difference between my know- 
 ledge and all reality, is an unmotived possibility ; for there is 
 at least no antecedent likelihood that my knowledge is always 
 wrong. And I am not entitled to raise this unmotived possi- 
 bility into an alternative having equal grounds with the 
 prima facie falsity which follows from the hypothesis. 
 
 I am not prepared to suggest any way of representing these 
 chances in numbers. Without equally grounded alternatives 
 we cannot state chances, and I do not see where in this case 
 these are to come from. If one read ' doctrines ' for judg- 
 ments, so as to restrict the question to matters of some depth 
 
 1337 A a 
 
354 Disjunction and the statement of Chances [Book i 
 
 and importance, one might obtain interesting enumerations 
 out of the history of science bearing on such relations as those 
 of false anticipations compared with true discoveries. But 
 it would all amount to very little, I only desired to point 
 out that the suggested symbols ^ and | seemed to lie in the 
 track of the fallacy discussed above.^ To say that objecting 
 to a judgment we do not know to be true is as unreasonable 
 as accepting a judgment we do not know to be true — and to 
 say that truth and falsehood have a chance of | each is to say 
 this — appears to me to be a sophism in the vein of Sir Anthonj^ 
 Absolute.^ If you have no reason for accepting a judgment, 
 you must decline to accept it. If you only decline provision- 
 ally, and say that in future, or to the knowledge of wiser minds, 
 the judgment in question may perhaps be proved true, then 
 you unquestionably are cherishing some distinct though 
 general presumption in favour of the judgment, and it is not 
 one of those whose chances ' in the absence of knowledge ' we 
 are discussing. We do not treat really arbitrary suggestions 
 with so much respect. It seems to me monstrous to say that 
 half the equal grounds are for truth and half for falsehood when 
 the fact is that you have no ground to think the thing true, 
 and require none to think it false. 
 
 This brings me to one further distinction. The reader 
 ought to reply, ' You do need a positive ground of denial in 
 order to deny, and in stating the chances as % you are denying, 
 which ex hypothesi you have no right to do.' But I suppose 
 that by the symbol ° we do not so much deny the judgment 
 as refuse to state the chances. It is only the logical interpre- 
 tation of this refusal that brings something like a denial into 
 the matter. You cannot obtain a denial out of a pure privation, 
 i.«. a mere profession of ignorance, but then in view of the 
 positive mass and far-reaching presumptions of knowledge as 
 
 * See chap, vii, p. 316. 
 
 * ' Absolute. " Sure, Sir, this is not very reasonable, to summon my 
 affection for a lady I know nothing of. ' ' 
 
 ' Sir Anth. " I am sure, Sir, 'tis more unreasonable in you to object 
 to a lady you know nothing of." ' 
 
 Sir Anthony wishes to represent the chances of attachment and non- 
 attachment to any unknown lady as J each, or even as more than ^ in 
 favour of attachment. This is really not a bad parallel to the view 
 criticised in the text. 
 
Chap. VIII] Symbols foY DouU and Denial 355 
 
 a whole, no privation however complete ^ can be quite pure^ 
 i. e. quite free from positive grounds of denial. A complete 
 and persistent privation must always, as I have tried to show 
 above, verge upon an exclusion. But if we had at command 
 a direct and positive ground of denial, then I imagine that 
 we should not restrict ourselves to refusing to state the chances, 
 i. e. to §, but should employ the symbol o. Or, in order to 
 indicate that a case has no chances in its favour because all the 
 possible chances are absorbed by another case which is certain 
 and which excludes the former, we ought I should think to use 
 the expression °-, i. e. negation grounded in positive certainty, 
 which is the remainder of ^, and so represents the total 
 certainty available for the two cases as entirely absorbed by 
 the one. Thus we should have three symbols representing 
 ideas which we ought not to confuse, f for demonstrable 
 impossibility, g for absolute ignorance (privation alike of real 
 possibility and of impossibility), ^ for a conflict of proofs, such 
 that truth and falsehood are equally grounded alternatives, 
 which in presence of absolute ignorance is not the case. 
 
 APPENDIX TO CHAPTER VIII 
 
 ON SOME RECENT DISCUSSIONS OF DISJUNCTION 
 
 Mr. G. R. T. Ross (Mind, N. S., 48) and Mr. Keynes (pp. 277 ff.) Are dis- 
 have recently supported the view that members under a dis- J""'^* 
 junction ought not to be considered as reciprocally exclusive, exclu- 
 I will comment on some of the arguments that have been ^^^^ ' 
 used, and will try to explain my own position further. 
 
 Is there really anjrthing to argue about ? If the whole 
 question is one of usage, and that is arbitrary, it would concern 
 grammar rather than Logic. But I. think that three points 
 of interest for Logic are involved : a the sort of guidance 
 which a logical instinct can follow in common speech ; /3 an 
 
 ^ By a ' complete ' privation I mean one in which we know absolutely 
 nothing in favour of the matter of which we deny all knowledge, while 
 I call a privation ' pure ' in as far as we know nothing positive against 
 the matter of which we deny all knowledge. And my suggestion is that, 
 looking at knowledge as it really exists, wherever we have the former 
 case it is almost impossible to have the latter. 
 
 Aa2 
 
356 
 
 Is Disjunction exclusive? 
 
 [Book I 
 
 Choice 
 involves 
 incom- 
 patibles. 
 
 A con- 
 junction 
 cannot 
 include 
 two 
 
 operative 
 alterna- 
 tives. 
 
 application of the theory of incompatibility, contradiction, and 
 negation ; y a substantial though not formal derivation of 
 the exclusive from the exhaustive character. 
 
 a One must not expect to find a definite theory governing 
 usage. If a moral is to be drawn from it at all, one must show 
 some simple character in the matter in question which could 
 serve as a guide through feeling and habit. And I think 
 Mr. Ross has helped me to put this in form, though his argu- 
 ment is directed against my view. His phrase, ' the nature 
 of the predicates,' is suggestive. 1 believe that usage favours 
 ' Either — or ' when predicates are coming which are felt to be 
 incompatible. They are the particles consecrated to choice, 
 and choice means incompatibles, i. e. that you cannot have it 
 both ways. Choice is always a special attitude, whether in 
 action or in judgment. When we feel it coming we adjust 
 ourselves to the situation by a special form of speech. No 
 doubt the area of choice — the space within which a right 
 choice must fall — is of interest to us. This is the exhaustiveness 
 of the ' Either — or ' = ' within these cases the right choice 
 must fall '. But the primary character, that which deter- 
 mines the very existence of a need for choice at all, is the 
 presence of incompatible alternatives — the exclusiveness of 
 the disjunct members. 
 
 ' Alternatives,' whatever else they may be, are surely 
 incompatible. No one was ever heard to say in presence 
 of a pair or set of alternatives, ' I choose them both or 
 all,' unless he means that it was an error to propose them 
 as alternatives. And it seems to me plainly erroneous 
 to speak of an alternative proposition while suggesting that 
 the alternants may both be true (Keynes, 277, 279). If you 
 may take both, you are surely not in presence of an alternative. 
 
 P Now incompatibility has degrees. And I wish next to 
 point out that there is a certain marked degree of it which is 
 present in the cases under any disjunction whatever, even on 
 the hypothesis that exhaustiveness is the primary assertion 
 which is intended. Take, for example, Mr. Ross's comment 
 (loc. cit.) on the argument (Bradley's Logic,, p. 124; above, 
 p. 324), that if the alternatives are not exclusive the disjunction 
 cannot be exhaustive, the case of their being conjoined being 
 
Chap. VIII] Cdses are changed if conjoined 357 
 
 a casus omissus. ' We might ask how it is that be can be 
 exclusive of b and c when as a matter of fact it includes them.' 
 For the possibility that be may really go under & or c (either 
 b or e being inoperative in it) I refer to my argument on p. 324 
 with the example of the railway tickets. In instances of that 
 type it is needless to mention be ; but this is because it already 
 falls under b or c, and therefore the cases are already both 
 exclusive and exhaustive. (This disposes of two of Mr. 
 Keynes's cases on p. 279 — the candidate for an appointment, 
 and the peer. The membership of more than one University, 
 in the first case, and the possession of more than one title, in 
 the second, are not special cases of eligibility and of peerage. 
 In either instance only one can operate, and the possession 
 of more than one constitutes no separate case under the 
 Disjunction.) 
 
 But if be is to be a distinct case under the disjunction, then 
 we have an interesting point. be then cannot include the 
 cases b and e, and for this reason. Each of these cases, qua 
 case of the disjunction, is proposed as capable of meeting the 
 requirements of the situation by itself and therefore completely. 
 Take it as a cause (Keynes, p. 278) ; (it might also be an 
 explanation or a consequent ; this makes no difference). ' He 
 has either used bad textbooks, or has been badly taught.' 
 Each of these suggestions is propounded as stating an adequate 
 cause of the existing situation. The mention of it as a separate 
 case makes this certain, even if we do not deny the possibility 
 of the fact contained in it being combined with another fact, 
 such as bad education. In the case put (the case b), the boy's 
 ignorance, or whatever is the matter, is accounted for by bad 
 textbooks. Now the case be cannot include this case b, 
 though it may include part of the fact suggested in it. In b, 
 bad textbooks are the cause. In be bad textbooks are not 
 the cause, but a co-operant cause. You cannot take two 
 causes out of a ' plurality of causes ', and treat them as co- 
 operant, without completely changing the operation of each. 
 It is a flat contradiction to predicate conjointly, without 
 special explanation, two predicates which are capable of being 
 predicated alone. When my builder gives me three explana- 
 tions of the same overcharge, it is not possible for me to 
 
358 Is Disjunction exclusive ? [Book i 
 
 accept them all, and this follows simply from the fact that 
 each claims to be sufficient taken by itself. The facts alleged 
 in them may in some way be combined, but the three sufficient 
 explanations cannot possibly be true together, though the 
 builder is inclined, like my critics, to say so. h and c are each 
 exclusive of b c. So with the well-worn case of rogue and fool. 
 If X is both rogue and fool, that excludes the cases of simply 
 rogue and simply fool. The man is different in every fibre of 
 his being. So if ' the witness is perjured or the prisoner is 
 guilty ' (Keynes, 279) you mean to say that you see two 
 possible explanations of the witness's evidence, constituting 
 incompatible cases. You can choose that which seems most , 
 probable ; but they are rival explanations, and you cannot, 
 having regard to the facts before you, accept them both. The 
 witness may be perjured and the prisoner nevertheless be 
 guilty, but that must be on further grounds, not present in 
 the facts so far to be explained. 
 
 Incompatibility of cases, then, is the primary meaning of 
 the words ' Either — or '. I will analyse Mr. Ross's curious 
 example (Mind, loc. cit.), pp. 492-3. The point of it is that if 
 disjunctions are both exclusive and exhaustive, ' A is either 
 not-& or not-c,' and ' A is either 6 or c ', mean exactly the same 
 thing ; e. g. if you say * a man who says he has seen a ghost is 
 either not sane or not truthful ' you can go from that to ' a 
 man, etc., is either sane or truthful '. 
 
 I note first, that this result is sound in the main. It looks 
 absurd, because contrast calls attention to the positive aspect 
 of the terms. Pronounced avec intention, it would be an 
 example of the phrases in which mere precision constitutes 
 effective irony, ' He is either sane, or truthful,' i. e. certainly not 
 both. I think that the effect of precision here really proves 
 the exclusiveness of the disjunction to be essential. 
 
 And secondly ; the instance with Mr. Ross's comment 
 itself shows clearly that what we primarily mean is the incom- 
 patibility of the positive terms. In a word, we mean to say 
 ' He cannot be both sane and truthful '. But there is a curious 
 point in the argument which might obscure this fact, and I will 
 take it to pieces. 
 
 Starting from the negative terms, not-sane and not-truthful, 
 
Chap. VIII] We asscH exclusiveness 359 
 
 what we want to assert is primarily exhaustiveness. But the 
 reason of this is that exhaustiveness as between them is the 
 same as exclusiveness between the two positives. 
 
 X is either not sane or not truthful, implies (i) If X is 
 not (not-sane) he is (not-truthful). 
 
 The type is, If A is not b, it is c, the hypothetical which 
 ensures exhaustiveness. This is clearly the right analogy, 
 expressing the meaning of the original statement, and keeping 
 the negative terms as such ; and I think, from his arrangement 
 of the propositions on p. 492, Mr. Ross recognises this. 
 
 But, being ' simplified ' by cancelling the double negative 
 (whether it is a true double negative is questionable), this 
 proposition results in 
 
 ' If X is sane, he is not truthful,' a proposition of the type, 
 If ^ is 6 it is not c, which is the hypothetical that secures not 
 exhaustiveness but exclusiveness. And this is undoubtedly 
 what the speaker meant primarily to assert, viz. exclusiveness 
 (incompatibility) between the positive terms, though this took 
 the form of exhaustiveness of the negative terms. Again, 
 
 (2) If X is (not-sane) he is not (not-truthful). This is of the 
 type. If .4 is 6 it is not c, the hypothetical which secures 
 exclusiveness. 
 
 This, ' simplified ' as above, gives 
 
 If X is not sane, he is truthful, of the type. If a is not b, it 
 is c, the hypothetical which secures not exclusiveness but 
 exhaustiveness. 
 
 This judgment, perhaps, as Mr. Ross says, we do not want, 
 and the disjunction ' Either sane or truthful ' is excessive 
 by that factor. And it arises, as he implies, from assuming 
 exclusiveness. But the point is that the exclusiveness assumed 
 is between the negative terms, and we have seen that this is 
 the same thing as exhaustiveness of the positive terms. But 
 it is this exhaustiveness which is the superfluous element. 
 What we asserted from the beginning and meant to assert all 
 along, was incompatibility, exclusiveness of the positive terms, 
 and it was only because we saw it meant this that we asserted 
 exhaustiveness of the negative terms. What we meant to say 
 was simply ' He cannot be both sane and truthful ' ; and the 
 ' Either — or ' saddled us with an unnecessary element, not in 
 
360 Is Disjunction exclusive ? [Book 1 
 
 the assertion of exclusiveness of the positives, which was the 
 whole point of our saying, but in the assertion of their exhaus- 
 tiveness, which is more than we needed to say. Taking the 
 positive terms, then, which are what we are really concerned 
 with, the argument proves my point, that a disjunctive pro- 
 position is primarily concerned to affirm the incompatibility 
 of the cases set out under it. 
 
 Now to predicate without distinction or reconciliation (e. g. 
 without explaining how and in what degree they co-operate) 
 separate predicates of the same subject is the definition of 
 contradiction. And therefore it is plain that the cases set out 
 under a disjunction, and prima facie meant to be separate and 
 sufficient for the situation, are not predicable conjointly 
 without special explanation and defence of their relations in 
 the conjoint case, which, if the several factors of it are really 
 operative, cannot possibly include the other full cases as they 
 are when separately predicated. The appearance to the 
 contrary has been shown to mean that the alleged conjoint 
 case satisfies the disjunction in respect of one of its elements 
 and no more. 
 
 The whole significance of the theory of negation lies in 
 showing how these independent cases, incompatible when you 
 offer to predicate them conjointly, become consistent when 
 arranged as the import of a disjunctive system (see p. 289 
 above). Every significant negative takes its meaning from 
 such an arrangement implied or expressed. 
 Exclu- y. I am convinced, then, in the first place that ' Either — or ' 
 
 folfows^ implies choice, that choice implies incompatible alternatives, 
 from inde- and that incompatibility or mutual exclusiveness of the cases 
 Wier^'^^ (otherwise than as the content of an ordered system) is the 
 criti- primary meaning of disjunction. But in the second place, 
 supposing it is maintained that the primary meaning is ' one or 
 other at least and, it may be, both ', I submit that the above- 
 mentioned considerations suffice to establish exclusiveness 
 as a logical consequence of the disjunctive attitude, even if it 
 is a consequence not always foreseen (as in the case of my 
 builder). If you assert ' either this or that ', even intending 
 to concede the possibility of both together, you clearly mean 
 that this or that by themselves are at least possible indcpcn- 
 
Chap. VIII] Unimportance of Classification 361 
 
 dent cases. You mean that each is a possible cause or explana- 
 tion or course independently of any other. 
 
 But if so, the nature of incompatibility or contradiction 
 determines the sheer impossibility of predicating two such 
 cases together. The joint predication can never include two 
 cases of the disjunction which have been offered as independent. 
 We have seen the two modes in which the appearance of such 
 a joint case may arise, and how in each of them we really have 
 no joint case of h and c at all. 
 
 I pass to other criticisms of my view of Disjunction. 
 
 Mr. Keynes (p. 283) criticises a statement in Essentials, 
 p. 124, that the proposition, ' The signal shows either red or 
 green,' asserts it to have ' some colour ', which is not asserted 
 by either of the hypotheticals entering into it. Mr. Keynes 
 objects that ' if not red, then green ', plainly makes this 
 assertion. The passage in Essentials is obscure from its 
 brevity. I refer for my meaning to p. 328 above and the 
 following pages. The disjunction unites the two characteristic 
 hypotheticals and the system within which they are true and 
 significant in a single survey and affirmation. You cannot 
 represent an assertion like ihis by two separate judgments, 
 each of them partial and hypothetical (cf. Essentials, 116, 
 and Bradley, Logic, 12 1-2). 
 
 On my general view of the logical rank of Disjunction, to 
 which Mr. Keynes (p. 283) objects that it gives an unreal 
 importance to classification, see besides 328-9, Vol. II, p. 194 ff. 
 These passages contain, besides an estimate of Disjunction, 
 a special reference to the subordinate importance of classifica- 
 tion. It is not classification, but the system of reconciled 
 incompatibles in which every universal when made explicit is 
 seen to consist, that I hold to be best exhibited in Disjunction. 
 It depends on the principle that in every system the nature 
 of the whole, differently conditioned, is in every disjunct mem- 
 ber. This seems to me a fundamental character determining 
 the explicit formulation of every universal, and therefore 
 necessarily prominent in logical theory. 
 
 Mr. Ross's argument that from a simple constructive dilemma 
 you can only get a conclusion of an exhaustive, and not one of 
 an exclusive nature (p. 495), seems to me to tell us nothing 
 
362 7s Disjunction exclusive ? [Book i 
 
 about the disjunction. The reason of the failure is plain. 
 According to the ordinary convention you can get no inference 
 from A\%d, (under the proposition if ^ is 6 it is d), nor from 
 A is not c (under the proposition \i A is c it is/). You have 
 barred the disjunction from transmitting its characters. If 
 you recognised reciprocal hypothetical you could go from 
 ^ is i^ to ^ is h, from A\%h (under the disjunction A is either 
 h or c) to A is not c, and from A is not c to ^ is not/. 
 
 The instance of the man at the top of the burning house 
 (at p. 495) seems to me to be spoilt by considering whether 
 the man's view is true or not. All we are concerned with, 
 surely, is what his view is, as expressed in the proposition . 
 ascribed to him, ' If I jump from the window I shall break 
 my leg, and if I do not I shall be burned to death.' Whether 
 he is right or not is a thing no one can possibly tell. But that 
 the whole motive for formulating such a proposition is the 
 intention to make a choice between alternatives taken as 
 incompatible, is surely undeniable. 
 
 I think, as I said above, that Mr. Ross is right in saying 
 that it is the nature of the predicates which makes them 
 incompatible. But it seems to me that this is the guide of our 
 instinctive usage of ' either — or ', that when we feel a choice 
 between incompatibles before us we confront it with, that 
 form of thought, although we may not always realize that it 
 debars us from conjoint predication, in the strict sense, of the 
 cases which are offered to our choice as severally independent 
 and sufficient solutions of the situation. I use ' the situation ' 
 as the most general term for the fact or idea with which we 
 are confronted, and which forms the disjunctive heading 
 under which the alternatives of our affirmation or action have 
 to fall. 
 
CHAPTER IX 
 
 Modality 
 
 I. I PROPOSE to conclude the discussion of the judgment Kant's 
 with a short treatment of Modality. For Modality, if it di^^ei""' 
 exists at all, is simply the degree in which individual judg- tally just, 
 ments participate in the certainty of that permanent and 
 all-embracing judgment by which the individual intelligence 
 sustains those qualifications of the Real which for it constitute 
 Reality. Our account of Modality must therefore resolve 
 itself into a recapitulation of the principal types of judgment, 
 having for its object to bring together in a single view certain 
 of their characteristics which have already been noticed. The 
 question before us is whether and in what sense there are 
 degrees of logical certainty ; not merely of habitual conviction, 
 or of readiness to act on a belief, which are psychological and 
 not logical,but of that characteristic which forms the differentia 
 of judgment, and which may be described as logical assertive- 
 ness. This logical assertiveness itself indeed includes a 
 psychical or psychological element which must be carefully 
 distinguished from the purely logical or rational element of 
 assertiveness. 
 
 One preliminary difficulty meets us on two sides. We find 
 Kant ^ maintaining that modality affects only the copula in 
 judgment, and that therefore, though a measure of assertive- 
 ness, it is indifferent to the content affirmed. And we find 
 it maintained against Kant that modality has no reference to 
 the copula in judgment, nor, consequently, to the assertiveness 
 of assertion, but is a peculiarity of the content affirmed which 
 does not affect the essential act of affirmation.^ Both of these 
 
 * Kant, Kritik der r. V., p. 97 (Hartenstein), ' Von der log. Function 
 im Urtheilen.' 
 
 * Sigwart and Bradley certainly agree in this. Lotze seems to say it 
 of the old Modality, in which ' " It must be so " counted as apodeictic ', 
 but does not distinctly say it of Modality as understood by himself (and 
 subsequently by the other moderns above mentioned), which requires 
 
364 Modality [Book I 
 
 views, it wUl be remarked, by separating the assertiveness of 
 assertion from the content asserted, represent judgment as an 
 arbitrary and irrational activity. It is not surprising that in 
 the ' Grammar of Assent ' ecclesiastical interest should have 
 thrown itself zealously on the side of such a conception. 
 
 The view which I have attempted to explain in the present 
 discussion is incompatible with both of the above-mentioned 
 ideas. Every judgment, as we have seeuj unites in it two 
 elements of certainty ; the formal or psychological element, 
 which consists in a reference of its content in virtue of a per- 
 ceived identity to the individual's personal world of perception 
 and experience, and the material or logical element, which 
 consists in the attachment of this content by rational necessity 
 to the organised nature which the Real possesses as already 
 qualified by the individual's knowledge. The former element 
 corresponds to memory and the latter to reasoning. All 
 reasoning is in the medium of memory, but memory as such 
 does not involve reasoning. The two activities however are 
 one in origin smd in ultimate nature. 
 
 Now the psychological element of certainty does not vary. 
 The unity of a content with the individual perceptive self 
 admits of no degrees. If it appears to vary in degree, we are 
 remembering by something, i.e. we are eking out memory by 
 reasoning. Memory as such is dumb in presence of questions 
 or comparison of grounds. It tells us nothing beyond the 
 mere content which it recalls. But material or logical cer- 
 tainty depends on reasoning, and is therefore capable of more 
 and less, and is the chief element of the assertiveness of 
 judgments. It foUows that modality is, as Kant said it was 
 not, a characteristic of the content affirmed, but is also, for 
 that very rccison, as the moderns say it is not, a measure of the 
 assertiveness of assertion. Whether modality must be said 
 to affect the ' copula ' at aU, or the copula only, depends on 
 what we mean by the copula. If the copula is formal and 
 empty, an unexplained act of reference like that of memory, 
 
 hypothetical or disjunctive form for apodeictic judgment. In his 
 suggestion as to ModaUty Lotze was of course anticipated by Hegel. 
 Sigwart and Bradley deny the superior logical certainty of the apodeictic 
 judgment, and Sigwart even disparages it on the ground of its mediate 
 character. Here, at any rate, he commits a gross blunder. 
 
Chap. IX] Kant ofi Problematic Judgments 365 
 
 then modality does not affect it, or rather it does not affect 
 modality. If, on the contrary, the copula is the act by which 
 grounded necessity is recognised, then it is the essence of 
 modality. The formal and indifferent copula of traditional 
 logic is the psychological copula, and when treated as the 
 logical copula becomes a logical copula indifferent to the logical 
 content,^ which is absurd. 
 
 As a matter of organic principle, therefore, I shall follow 
 Kant, although by what I must regard as a confusion, he 
 refers modality to the form of judgment and not to the content, 
 and although his ' problematic judgment ' is rightly pronounced 
 by later writers to be no judgment at all. His summary runs 
 thus : ' Because, then, in this aspect [i. e. in modality] every- 
 thing incorporates itself with the intelligence by degrees, so 
 that one begins by judging problematically, and subsequently 
 takes the matter to be true assertorically, and ultimately 
 affirms it as inseparably united with the intelligence, i. e. as 
 necessary and apodeictic, it follows that we may confer on the 
 three functions of modality the further appellation of so many 
 moments of thought as such.' ^ Here as throughout philo- 
 sophy it has been the task of later writers to realise in the 
 concrete a conception enunciated by Kant, but by him only 
 half liberated from the formulae of obsolete conventions. 
 Hegel's analysis of the hypothetical and disjunctive judgment, 
 adopted by Lotze and subsequent writers, is the realization of 
 Kant's idea of modality as progressive incorporation with the 
 understanding. 
 
 2. In order to begin at the beginning we must start from The Pro- 
 Kant's ' problematic ' judgment, which, as he describes it, is bletnatic 
 not a judgment at all. The problematic judgment according ment. 
 to him expresses mere logical possibility,* not ' objective ' 
 
 * Lotze does not fall into this trap. But he seems only to avoid it 
 at the cost of separating off a particular fragment of content to be 
 identified with the copula, at least when he is explaining the traditional 
 view. But as against this the traditional view was right. The copula 
 must have to do with all of the content or with none. In Lotze 's own 
 view of Apodeictic Judgment it has to do with all. 
 
 ^ Nearly equivalent to what I have often spoken of as non-impossi- 
 bility. See below. 
 
 * Kritik der r. Vernunft, p. 97 (Hartenstein's ed.). 
 
366 Modality I book i 
 
 possibility, and he gives as examples of it the antecedent and 
 consequent in hypothetical judgments, or the isolated members 
 of a disjunction. 
 Nature of i. But such elements of thought are of course by themselves 
 tion^or" ^^^ judgments, i. e. as Kant himself says, they are not asser- 
 Question. tory. It may be doubted however whether such elements of 
 thought exist by themselves at all, and whether they do not 
 of necessity enter into some judgments. Their nature is no 
 doubt the same as that of the genuine ^ Question, which 
 Sigwart has the merit of having discussed. I cannot think 
 however that his psychological expressions help us to grasp 
 the logical differentia of question or doubt. It is nothing to. 
 say that the idea merely floats ^ before the mind. It must, in 
 order to rank as a definite doubt or question, make some 
 specific claim, be a candidate for some definite place, in the 
 permanent judgment of consciousness. There is a nearer 
 approach to something intelligible in the suggestion that 
 a problematic judgment is a judgment about oneself, saying 
 that in the matter before us we are unable to judge. But this, 
 though often true in fact, is an evasion of the theoretical 
 difficulty. There must be some definite logical situation in 
 virtue of which we say this. When we judge that a judgment 
 is merely possible we must judge that its content has mere 
 possibility. The reduction of judgment of possibility to possi- 
 bility of judgment is an attempt to take refuge in psychology 
 from a logical difficulty. 
 
 ^ The question which expresses a real doubt or ignorance ; not one 
 to which we know the answer, but ask in order to force the interlocutor 
 to give it. This latter is an imperative, as Sigwart says (vol. i, 231). 
 But then the former hardly perhaps has the differentia of the Question, 
 which is just this imperative significance. So the ' genuine ' Question 
 is perhaps not a Question at all, but only a state of knowledge. What 
 state of knowledge ? Obviously one that presses for an advance, so 
 probably a disjunction of ignorance. Kant's problematic judgment 
 includes all supposition qua supposition, although known to be false 
 or known to be true. But I do not think that Sigwart's complaint of 
 a want of distinction between these cases and that of genuine doubt is 
 well founded, because a supposition qua supposition is considered by 
 an act of abstraction apart from the relations which constitute its 
 falsity or certainty. Therefore, as subject to this abstraction, any 
 supposition may rank as a doubtful judgment. 
 
 * ' In der Schwebe.' Sigwart, Logik, i, 230 ; E. Tr. i. 177. 
 
Chap. IX] ' Floating Ideas ' 367 
 
 Although then the mere idea of a judgment, floating before 
 the mind, is not, even if it exists, a judgment at all and there- 
 fore not a problematic judgment, yet every genuine question 
 and every judgment made subject to a ' possibly ' or * perhaps ' 
 represents a peculiar logical situation, and not merely a 
 psychological incompleteness of the act of judgment. It is 
 not true as a rule that we begin with floating ideas and advance 
 from them to judgments. I doubt if such a beginning is 
 possible ; * it is certainly not normal. Our thought consists 
 in the continuous modification of judgments — I had almost 
 said, of a single judgment. The question, considered as a state 
 of knowledge, is a disjunctive or hypothetical judgment used 
 as the premise of an inference. A groundless question is as 
 unreal as the ' infinite ' judgment. I cannot ask ' Are you 
 going home ? ' except on the basis ' You are possibly or 
 probably going home ', which means when analysed either 
 
 * If ::*; is the case you are going home ', or else ' Either you are 
 going home, or x is the case '. The question does not mean 
 
 * I have a floating idea in my head of you as going home,^ and 
 want to know if I am to refer this to reality '. It means 
 rather, ' I judge true of reality a definite situation in which 
 some conditions of your going home are included ; I want to 
 qualify reality by this situation more precisely defined ' or 
 to qualify a further element of Reality, viz. yourself, by it. 
 Thus Kant is not so far wrong in identifying a problematic 
 judgment, or, as we may call it, a genuine question, with an 
 isolated member of a complex enunciation ; but it is only 
 as a corollary from the complex thought or as an inability to 
 make its outline precise, and not as a mere isolated member of 
 it, that the problematic expression can be a judgment at all. 
 For in its isolation, ex hypothesi, it is not referred to reality. 
 
 ii. Possibility, then, as Mr. Bradley has told us, is a species Problem- 
 of necessity, and it seems to follow from this that the pro- ^^^"^ 
 blematic judgment is a form of the apodeictic judgment, and tic Judg- 
 that any series of gradations in which the two have separate ™®"*' 
 
 * Ultimately, there are no floating ideas. See above, pp. 4, 70, and 
 Bradley, Mind, 60, 445 ff. 
 
 ^ The idea is not ' of you as going home ' but ' that you may be going 
 home ' ; i. e. something is judged, which may result in your going. 
 
368 Modality [Book I 
 
 places — such gradations as Kant laid down — must be in 
 contradiction with the nature of the case. If the judgment 
 of possibility is the first form under which matters of knowledge 
 attach themselves to the understanding, then it can hardly be 
 a species of the final form, and ought to be verifiable in early 
 thought. 
 
 We must begin by admitting the difficulty indicated by 
 the last objection. All judgment, I have said, is in one respect 
 assertory. It is probable that very early thought may 
 present no other aspect. The distinction between memory 
 and intelligence is a late distinction. The old man in Homer ^ 
 who ' knows ten thousand things ' cannot but remind us of 
 the schoolboy whose friend ' knows an awful lot '. Whatever 
 is in the mind, such expressions seem to suggest, ranks alike 
 as knowledge. The asseveration, indeed, may be supposed 
 to begin as soon as man feels the danger of deceit ; and this 
 form of speech recognises a distinction in degrees of certainty, 
 and attempts to raise one matter of knowledge to the standard 
 of another. But on the whole, the distinction between" 
 memory and intelligence, and therefore that between mere 
 reference to perceived reality and systematically grounded 
 insight, would probably be found a vanishing distinction if 
 we could examine the earliest phases of the human mind. 
 Possibility, mere assertion, and necessity, as they exist for 
 the civilised mind, are based upon differences that concern 
 the material logical or systematic element in judgment. We 
 have to remember however that logical facts exist long before 
 the technical names for them, and we must not limit the 
 existence of modalities by that of words like possibility and 
 necessity, but only by that of speech-elements bearing the 
 power of ' may ', ' must ', ' shall ', or ' would that '. And we 
 must add that we cannot see how judgment should exist apart 
 from all sense of rational necessity. A mere instinctive 
 identification with reality, wholly without why or wherefore, 
 is rather a theoretical limit below which judgment cannot be 
 taken to exist, than a historical phase of the judging faculty. 
 
 * Homer is of course not primitive, but poetry is very conservative, 
 and Homer is full of ideas which are derived from vei y early strata in 
 the mind's formation, 
 
Chap, ixj Possibility and Necessity 369 
 
 The next difficulty is that possibility appears on the view 
 taken above to be a species of necessity, and yet to be prior 
 to necessity. In order to explain this we must refer back to 
 the doctrine of opposition and conversion. Strictly and 
 properly, a judgment can only be denied by another judgment 
 of the same nature ; a singular by a singular judgment, 
 a generic by a generic, or a hypothetical by a hypothetical. 
 But a very strong implication of denic' can be conveyed by 
 a judgment which being of a different t^-pe from that contra- 
 dicted denies the right of this latter judgment to the type 
 which it has assumed. If, however, the denial is to be prose- 
 cuted in earnest, the judgment of the lower type must be capable 
 of maintaining itself on the level of that which it assails. 
 Possibility, if not derivative or calculated, represents such a 
 first effort at denial, directed against a necessary judgment, and 
 may or may not go on to assume an explicitly necessary form. 
 
 a. Thus possibility as prior to necessity follows the meanings Particu- 
 and development of the Modal Particular, which, owing to J^^S" 
 the continuity in the evolution of thought, on which we have Excep- 
 so often insisted, has its roots far back in the quasi- singular tion and 
 or particular enumerative judgment. That is to say, the 
 consciousness of possibility begins — I do not mean in every 
 case, but in its most rudimentary logical form — with a rule 
 and an exception or with a positive instance suggesting a rule. 
 And it passes into a further type with the essentially negative, 
 or again with the essentially positive modal particular. The 
 latter, indeed, the positive modal particular, is hardly intelli- 
 gible apart from the explicit recognition of necessity. But 
 in accordance with a principle to which we shall have to recur 
 it is quite customary for thought to employ a derivative and 
 secondary judgment which is dependent upon a primary 
 principle remembered as a rule. Many j udgments of possibility 
 — those current in systematic thought — are after this fashion 
 corollaries from judgments of necessity, or rather from the 
 fact that certain judgments of necessity are accepted as true. 
 I now proceed to illustrate the development just described. 
 
 Possibility is at first negative. Bare negation indeed is 
 nothing, but possibility in its simplest case comes very near 
 bare negation. Such a possibility when veiled under the 
 
 1337 B b 
 
370 Modality [Book i 
 
 equivocal form of the particular judgment rests on an exception. 
 We must not suppose that the possibility is positive because 
 the exception is a positive case. The content of a mere excep- 
 tion as related to the rule which it impeaches is purely negative, 
 i.e. only contradicts, and suggests no contrary principle. 
 Suppose we have a half-collective and half -generic judgment 
 like ' All English railways are well managed '. Suppose that 
 then we come upon an English railway which is not well 
 managed, and embody our observation in the judgment 
 * There is an English railway which is not well managed '. 
 This may readily be interpreted as a judgment of negative 
 possibility, amounting to no more than this, ' It is not true 
 that English railways are in every case well managed,' or in 
 other words, ' It is not impossible for an English railway to be 
 other than well managed.' The principle is just the same if 
 the rule is negative, e.g. ' No crows are white.' An exception 
 would contradict this, but only by establishing little more than 
 mere possibility (not-impossibility) that a crow may be white. 
 ' There is a case in which a crow is white ; ' * It is not true 
 that no crows are white.' 
 
 The instance makes the step from negative to positive 
 possibility. Like the exception, it implies a generalisation, 
 at least incipient, but it supports this generalisation instead 
 of contradicting it. Supposing, what is always ultimately 
 the case, that the exception is a latent instance, the judgment 
 which expresses the exception will change, in coming to 
 express an instance, from a mere contradictory to a contrary 
 which is also contradictory. Let the original rule be ' No 
 secular education can be spiritual ' and the exception be ' In 
 the case of literary education we have a secular education 
 which is spiritual ', with the negative result ' It is not true 
 that no secular education can be spiritual '. Then when we 
 go on to treat the exception as an instance ^ we get a result 
 
 ^ Exception presupposes rule, and rule presupposes positive instance, 
 it may be said, so that our idea of negative possibility coming first gets 
 us into a circle. The fact alleged is true ; a positive rule must come 
 from somewhere, and probably from a positive instance. But prior 
 to the idea of denying the rule the generalisation is direct or naive, and 
 does not pass through the stages of modality except ou the embryo 
 scale on which it also implies negation. 
 
Chap. IX] DegYces of Possibility 371 
 
 hardly differing from the former in words, but charged with 
 the material distinction that we now see reason to think that 
 'secular education as such may also be spiritual', i.e. It is 
 possible that — or ' There is real ground for supposing that 
 secular education, &c., &c '. 
 
 j3. When we advance to the modal particular we have the Negative 
 same distinction in a purer form. The modal particular has ^[^^ ppg, 
 been treated above as the converse by limitation ^ of a hj^o- sibility. 
 thetical judgment, and at all events may always be treated 
 as the contradictory of another hjrpothetical judgment. ' If 
 A is B it is C ' becomes when converted by limitation ' If A is 
 C it may be B ', which latter is at least the contradictory of 
 ' If A is C it is not B '. Where the modal particular really 
 originates by the conversion of a hjrpothetical judgment, it is of 
 course an inference or corollary from a principle with reference 
 to another and opposite principle. But as usual the actual 
 or historical modes of initiation of the judgment are one 
 thing, and its logical essence another. Obviously the modal 
 particular may be generated either by inference from explicit 
 principles, or by the suggestion of rules through instances. 
 
 In any case the judgments '' A may possibly be B ' and 
 ' A may possibly not be B ' have two degrees of meaning 
 analogous to those of the exception and the instance. They 
 may be mere contradictories of the hypothetical judgment to 
 which they are respectively opposed, or they may be contra- 
 dictories growing into contraries. If they are mere contra- 
 dictories, corresponding to exceptions, then the judgment ' A 
 may be B ' merely means to overthrow the principle that ' A 
 cannot be B ' ; that is to say it asserts that if or though A is, 
 yet it does not follow, from that, that B is not. It is easy to 
 give the corresponding significance to ' A may not be B '. 
 But precisely the same judgments ' A may be B ' and * A may 
 not be B ' are capable of corresponding to the instance, and 
 their meaning then is that there is some positive connection 
 between an unspecified condition x, which is fairly conceivable 
 of A, and B or the negation of B as may happen. Under these 
 circumstances, even though we do not know that Ax itself is 
 
 ^ If the hypothetical j'udgment has a negative consequent, it is of 
 course needless to limit it in converting. 
 
 Bb2 
 
372 Modality [Book i 
 
 actually found in experience, yet we have ground for saying 
 that there is a rational connection or antagonism between A 
 and B. Many degrees of these connections are to be met 
 with. If X were the entire ground of B, and we knew x to 
 be true of A, then we should no longer have possibility but 
 certainty. But if x is part of the ground of B, and we know 
 X to be true of A, then we have a degree of real possibility 
 varying with the relation of :v to B. Or again, if x is not 
 the ground but a consequent of B, and we know categorically 
 that A is X, we have in effect an inference, from the hjrpothetical 
 ' If A is B it is a; ' converted by limitation into ' If A is a; it may 
 be B '. I will give a concrete example. 
 
 Plants (A) may possibly possess sentience (B). Taken as 
 the mere guess of an unscientific mind — ^prepared to say the 
 same no less of stones and metals, air or water — ^uch a judg- 
 ment would represent a mere negative possibility, or in other 
 words, it would express no more than the fact that having 
 considered the universal judgment ' Plants are not sentient ' 
 the individual mind happens to see in it no sequence of reason 
 and consequent, and therefore pronounces that * There is no 
 ground for asserting that plants are not sentient '. 
 
 But the same judgment ' Plants (A) may possibly have 
 sentience (B) ' is capable of conveying a more positive meaning. 
 It may rest on the conviction that ' If plants (A) have irrita- 
 bility (x) they must have sentience (B) '. Assuming ignorance 
 as to actual observations of irritabihty in plants we neverthe- 
 less have then a certain congruity ^ to go upon in saying that 
 A may, in a sense that has a certain basis of reahty, be B. 
 But still more strongly, if we could say ' If plants (A) 
 have sentience (B) they must have irritability (x) ', being 
 able to supplement this with the fact ' There are plants (A) 
 which have irritability (x) ', we should be able to affirm 
 There are positive grounds for maintaining that plants A 
 have sentience B '. 
 
 Possibility may therefore mean (i) the inability to make 
 
 ' We should not e. g. attach any such weight to the judgment that 
 if a plant had poetic genius it must have sentience. I claim throughout 
 that congruity is essential and not accidental in supposition. If we go 
 outside the system of fact which is our basis of supposal, we get results 
 analogous to the ' infinite judgment '. 
 
Chap. IX] Meanings of Possibility 373 
 
 a certain h5rpothetical judgment, so long as we bear in mind 
 that mere privation or inability is a limit which the judgment 
 must not actually reach if it is to retain significance. This 
 possibility is non-impossibility. Or it may mean (ii) the 
 inference from a h5rpothetical judgment, whether explicit or 
 suggested in instances, which {a) assigns an intelligible con- 
 dition (or makes us believe that there is such a condition), 
 which would if real establish the consequent whose possibility, 
 assuming the reality of the subject of judgment, is in question, 
 or (&) assigns a certain logical consequent to the attribute or 
 event in question considered as a logical antecedent, which 
 consequent is known to be real. This logical consequent may 
 be either an effect with alternative causes, or a consequent 
 with alternative reasons. The ideal or reciprocal form of the 
 hypothetical judgment excludes mere possibility and therefore 
 does not concern us here. 
 
 y. It is plain from the above examples that the terms Essence 
 ' possible ', ' probable', ' may ', ' might ', and ' must ', stand for Probfem- 
 more or less reflective estimates of certain kinds of knowledge, atic Judg 
 The essence of the problematic judgment is the substitution 
 of such an estimate for the concrete steps of inference really 
 involved in an affirmation. Possibility results in referring to 
 reality, without transition, but stibject to an estimate, what is 
 only connected with it by transitions. When the whole 
 transition is made explicit, the allegation of possibility is 
 superseded.^ The judgment which has all its conditions and 
 reservations fully assigned to it is of the apodeictic order ; 
 possibility arises from effecting the reference to reality apart 
 from the conditions. The idea of ' possibility ' is our substi- 
 tute for the omitted conditions. Obviously such an idea may 
 emanate from all degrees of confused perception or of reflection. 
 We may be silent about the conditions either because we 
 cannot clearly grasp them, or because we are explicitly 
 abstracting from them. But an estimated indirectness of 
 transition there must be if we are to judge problematically. 
 Disjunction can be treated in the same way, owing to the 
 hypothetical inter-relations of its members, and thus the 
 statement of chances is a clear and extreme case of the estimate 
 ^ Cp. p. 341, supra. 
 
374 Modality [Book i 
 
 in question. Its essence is to burden the reference to reality 
 of one alternative with a hindrance drawn from the number 
 of other alternatives. All possibility indicates a similar 
 tendency. But the statement of chances has measured its 
 own cloudiness and made certain of its own uncertainty.-"^ It 
 is therefore no longer problematical. It supplies a definite 
 predication of a hindrance to reality, and not a hindrance 
 to predication. 
 
 Thus the true problematic judgment is a judgment with 
 a peculiar and reflective content, which interferes with its 
 assertiveness. It is a hypothetical or disjunctive judgment 
 in disguise. All judgment whatever is within a real system, 
 but the problematic judgment has its relations to its real 
 system peculiarly obscured or neglected. In the question, 
 for instance, we only make explicit a part of the intellectual 
 state, ultimately affirmative, on which our desire for further 
 knowledge depends. A question indeed often vanishes when 
 we insist on its being clearly put. 
 
 Assertory 3. The other forms of modality may be briefly dismissed. 
 
 Judg- Every judgment may be called assertory, as we saw, in virtue 
 of its psychological reference to self-feeling. If any judgments 
 are to be called assertory in a strictly logical and material 
 sense, they must of course be the singular judgments which 
 depend on union of attributes within the concrete subject 
 of the judgment, and not on their necessary connection in 
 a larger subject falling outside the judgment. Such judg- 
 ments are even logically assertory in as far as the concrete 
 subject is merely individual as a synthesis of differences not 
 connected by abstract necessity. So far on the other hand 
 as it displays individual character and lends itself to analogical 
 affirmation, it stands for the present purpose on the same 
 footing with the subjects of necessary and apodeictic judg- 
 ments. The assertory judgment has a higher degree of 
 assertiveness than the problematical judgment as such, because 
 
 * This is the reason why the ' Thermometer of Probabihty ' (see 
 De Morgan, Budget of Paradoxes, p. 416) would not be of very general 
 application. What it measures is the ratio of the whole number of 
 equal alternatives arising on a certain condition to the number of 
 desired alternatives so arising. But in concrete knowledge we have no 
 security of finding equal alternatives. 
 
Chap. IX] AsseHory Judgment 375 
 
 its reference to reality though not apodeictic is direct and 
 open. It would be impossible to maintain Kant's view of a 
 progressive incorporation of contents with the understanding, 
 if he meant that every trivial judgment, say, of perception, 
 was preceded by a recognition and estimate of uncertainty. 
 But all experience supports his contention that imperfect 
 judgments in which only one element is clear, and in which 
 this clear element is attached to reality through others which 
 are not clear, belong to a less complete phase of knowledge 
 than judgments in which the reference is clear and complete. 
 If the problematic judgment arises by intentional abstraction 
 from precise knowledge, this makes no difference. We are 
 returning on purpose to an imperfect form of judgment from 
 a more perfect one, in order to exhibit a net result which the 
 more explicit form will not display. We must stand by the 
 result which we thus obtain. We cannot eat our cake and 
 have it. 
 
 Of course where an instance indicates a possibility, the 
 assertory affirmation of the instance and the problematic 
 affirmation of the possibility do not refer to the same content. 
 ' This Drosera shows irritability ' is a singular judgment of 
 perception. The problematic judgment ' There are conditions 
 though unknown in detail under which the nature of a plant 
 develops irritability ', i.e. 'A plant as such may have irrita- 
 bility ' arises from the analysis of the above instance into 
 a general suggestion. Such an analysis is probably concurrent 
 with the perception of individual identity on which the 
 Singular judgment rests, but the two are not identical. Imper- 
 fect insight into necessary connection may affect the same 
 content which is being erected into a thing, but is not one with 
 this process of erection. Assertory assertion and problematic 
 assertion may be and must be conjoined in every problematic 
 judgment, but they refer to different elements in the content 
 affirmed, the former to the system as a concrete real whole, 
 the latter to some element of the system as related by abstrac- 
 tion to the other elements. When the latter aspect of the 
 judgment is dropped or superseded we have the assertory 
 affirmation pure and simple. The assertory judgment has 
 no degrees of assertiveness except in so far as in virtue of its 
 
376 Modality [Book I 
 
 specific content the problematic or apodeictic judgments 
 inevitably show themselves within it. 
 The Apo- 4. Judgments of apodeictic character, i.e. hypothetical 
 deictic ^^^ disjunctive judgments, lay claim in virtue of their form 
 ment. to a higher degree of assertiveness than either problematic 
 or assertory judgments. The reason of this is that their 
 form has for its differentia the exact exposition of the transi- 
 tions, conditions, or alternatives subject to which the judgment 
 is true of reality. By such exact exposition the content either 
 becomes an articulated system, or at least reveals itself as 
 fitted to take a place in such a system. The former is the 
 ideal of the disjunctive, the latter that of the hypothetical 
 judgment. Reality considered as absolutely known is of 
 course ex hypothesi taken to be absolutely asserted. But 
 Reality is not by any sane person considered to be absolutely, 
 i.e. completely and precisely known. Degrees of certainty 
 in apodeictic affirmation arise from the consciousness — a 
 logical consciousness made explicit in the structure of judg- 
 ments — that the individual's knowledge is but imperfectly 
 identified with the ideal judgment which would qualify 
 Reality by the complete content of Reality. 
 The Hy- i. In the hypothetical judgment, as we have seen, though 
 '^^^^^dcr ™portant elements are made explicit, yet the connection 
 nient. which is affirmed implies an underlying reality which is not 
 expressed in the content of the judgment. Therefore the 
 hypothetical judgment is subject to two elements of uncer- 
 tainty, viz. its own reference to the limited reality the affir- 
 mation of which it implies, a reference which may be partial 
 or confused, and further the relation of that affirmed real 
 system to the content of Reality as a whole. ' The British 
 Parliament is able to alter a statute affecting its own duration.' 
 This is rather a generic than a hypothetical judgment ; but 
 for the present purpose these two types must rank as very 
 closely akin. About such a judgment there is first the question 
 whether it really follows, or how necessarily it follows, from 
 the facts which we are prepared to affirm of the reality known 
 as the British Constitution, and secondly, what opening these 
 facts themselves, as compared with the greater reality of our 
 entire experience on the ground of which they in turn are 
 
Chap. IX] Elements of Uncertainty 377 
 
 affirmed, leave for error or for unseen modification. Any 
 disjunctive judgment, as compared ^ with a given hypothetical 
 judgment of which it may be regarded as a development, 
 makes this underlying real system explicit, and therefore has 
 no source of uncertainty but that of a failure in the necessity 
 by which this system itself is attached to Reality as a whole. 
 But of course the disjunctions which we commonly use are 
 for the most part systems within known systems, and therefore 
 stand on the same logical level of certainty with hypothetical 
 judgments. Such e.g. is the disjunction which expresses the 
 number and nature of the conic sections, resting as it does on 
 the ultimate real system which we take to be the nature of 
 space . Only dis j unctions that embody a complete and coherent 
 sphere of knowledge, such e.g. as the nature of space, have the 
 character which has just been ascribed to the ideal disjunction. 
 But even with such a disjunction we still have the difficulty 
 in the background, ' Does the real system which we affirm ' — 
 in this example the nature of space — ' really emanate as a 
 necessity of knowledge from the whole reality which is forced 
 upon us by experience ? ' It appears to me to be quite idle 
 to maintain that all judgments, or even that all necessary or 
 apodeictic j udgments, are on a level in this respect . Ultimately, 
 we may imagine, nothing can be rightly known without know- 
 ing all else rightly, so that every isolated fact and principle 
 of knowledge would be implied in, say, the existence of morality 
 or in the existence of an intellectual world. But as knowledge 
 is in fact constituted its parts are fragmentary and incoherent, 
 and there is much that we affirm upon onty a partial or limited 
 necessity, while much again is so incorporated with the whole 
 fabric of our real world that we feel bound to maintain the 
 former if we would not fall into hopeless contradiction with 
 
 ' It is absolutely necessary, when we attempt to compare judgment 
 forms in respect of their essential import, to select instances which belong 
 to one and the same progression. A hypothetical judgment drawn from 
 an advanced phase of science has at once more content and more 
 precision than a disjunctive judgment drawn from everyday experience. 
 To judge the capacities of the two forms by instances so selected 
 would be like judging the powers of civilisation and savagery by 
 comparing a civilised infant without allowance for age to an adult 
 savage. 
 
378 Modality [Book I 
 
 the latter,^ The assertiveness of afhrmation is not indeed 
 measurable outside the calculus, but it is capable of being 
 perceived and to some extent compared. It is not a mere 
 feeling, but an insight into connections. It is absurd to main- 
 tain that in affirming the whereabouts of a friend, or the har- 
 monious or other effect of a combination of colours, or the 
 continuity or non-continuity of matter or of space, I am 
 pledging my intellectual existence to the same degree as when 
 I affirm the relations of the multiplication table, or (subject 
 to the requisite interpretations) the law of causation, or the 
 existence of moral purposes. 
 
 The uncertainty which may attach to apodeictic judgments, 
 arises then from the same cause as the uncertainty of problem- 
 atic judgments, but the cause is operative in a different mode 
 and in a slighter degree. We always feel certain when we 
 judge, for all judgments involve the same psychological 
 identification with self-feeling. But we know that this cer- 
 tainty is conditional on our expressing Reality with precision 
 and completeness, and this we are well aware that we never 
 do. Of course, to begin with, the apodeictic form of judgment 
 is no guarantee, any more than any other, against falsehood 
 or frivolity. There may be no underlying real system at all, 
 or that which is taken to be referred to may in no way justify 
 the sequence erected on it. Any false generalisation is an 
 instance of this. Or again, the necessary transition may be 
 quite incompletely set forth, so that the judgment sinks ipso 
 facto into a problematic judgment in spite of its apodeictic 
 form. Such are judgments in which a remote cause or conse- 
 quence taken as a sign is substituted for the ground of the 
 sequence, so that the judgment though not untrue in fact has 
 the appearance of a riddle. ' If the stick will beat the dog the 
 old woman will get home to-night.' Here we have no indica- 
 tion of the real arrangement on which the sequence rests, and 
 the condition, so far as can be seen without copious supplemen- 
 tation from ulterior knowledge, is irrelevant and equivalent 
 
 ^ This must be read subject to reservation as regards the actual 
 language in which abstract principles are expressed. It is a recognisable 
 function of the body of knowledge, not a limited set of stereotyped 
 ideas, which we may be justified in holding indispensably necessary to 
 our reason. See below, Book II, chap. vii. 
 
Chap. IX] Degrees of Apodeictic Assertion 379 
 
 to an unknown condition, implying as it does a number of 
 unknown conditions. This is the explanation of the examples 
 to which Sigwart appeals as showing that apodeictic judgments 
 are not in fact made with any peculiar certainty of conviction. 
 ' There is a common idea that the apodeictic judgment stands 
 for something higher than the assertorical. It is believed that 
 if we start from the problematic judgment and ascend to the 
 apodeictic we steadily increase the certainty of our knowledge, 
 and add to the worth and dignity of our assertions. This 
 idea must be relinquished. All mediate certainty must stand 
 in the end on immediate knowledge ; the ultimate premises 
 of every proof cannot be proved. The usages of life stand in 
 comic discrepancy with the emphasis we lay upon apodeictic 
 certainty. The sayings " It must be so ", " It must have so 
 happened" are judgments apodeictic; but the confidence 
 they express has most modest limits.' ■'■ 
 
 This is not the place to criticise the fundamental view which 
 Sigwart here expresses, but to which he is, happily, not 
 faithful throughout. In treating explicitly of the nature and 
 bases of inference we shall see that the distinction between 
 mediate and immediate knowledge coincides with the distinc- 
 tion between what is known and what is only on the way to be 
 known. If Sigwart meant what he said in this place, he would 
 have cut himself off from all possibility of believing in science. 
 As to the examples which he adduces, they fall into their 
 place, according to what has been said, as problematic judg- 
 ments. ' It must have so happened ' is an inference from 
 reality under a condition, to reality without an expressed 
 condition, and therefore is problematic. 
 
 The degrees of certainty belonging to the apodeictic judg- 
 ment itself are as we saw of the same kind as those which 
 characterise the problematic judgment. The whole of the 
 reality on which the sequence is intended to be based may not 
 have been brought to bear upon the sequence, and even if it 
 has, its own relation to the reality which is the ideal of know- 
 ledge may be so disproportionately trifling as to make the 
 judgment an especially inadequate embodiment of the ideal 
 Reality which alone is certain. 
 
 Sigwart, Logik, i. 238, E. Tr. 183, quoted in Bradley's Logic, p. 186. 
 
380 Modality [Book I 
 
 I may illustrate this conception by our present knowledge 
 of Hypnotic and kindred phenomena.^ The curative action of 
 Hypnotism, or the beneficent anaesthesia which may be 
 produced in some forms of the Hypnotic state, are now as it 
 seems matters capable of embodiment in empirical generalisa- 
 tions. These rules or laws can be exhibited, like all rules or 
 laws, in hypothetical or disjunctive form ; that is to say, as 
 consequents following upon conditions, or as alternatives 
 arising within a certain identical content. On a certain degree 
 and kind of hypnotic trance a certain anaesthesia is consequent. 
 A hypnotised subject is capable of some three or four recog- 
 nisable alternative states. In certain forms of nervous de- 
 rangement acquired, or, as it seems, congenital, repeated 
 hypnotic treatment exercises a sanative influence. 
 
 Now although I personally entertain no doubt that there is, 
 as the phrase goes, ' something in ' all these conceptions, and 
 though I am prepared to affirm them, i.e. to judge them true 
 of reality, as embodiments of an experienced content which 
 must be affirmed somehow and which I cannot affirm other- 
 wise, yet so far as I understand myself I do not stake my 
 intellectual existence upon them as I do on the existence of 
 causation, or morality, or beauty. On what I mean to say in 
 them, on the experienced content from which they are drawn, 
 I do stake my intellectual existence ; but this content, apart 
 from my explicit judgment, is to me an x, a thing-in-itself, 
 a nothing. I must stand or fall by my judgment as it is, not 
 merely by my ultimate intention to embody reality, which is 
 the common and formal feature of all affirmation. And I know 
 perfectly well that by my explicit judgment on such matters 
 as these I am very likely to fall. The reason of this is not that 
 the cases on which I rely are few in number, compared, e.g. 
 with ordinary cases of the operation of digitalis on the heart 
 or of mercury on the liver. One case is enough, as we all know, 
 
 ' I believe myself justified, when writing for purely logical purposes, 
 in treating the actual phenomena known to science as freely as may be 
 necessary to give them sharp outlines, and to avoid a mass of reserva- 
 tions and qualifications that would be only an encumbrance for my 
 present purpose. I on my side hope to keep clear of wilful distortion, 
 but the reader on his side must not accept my illustrations as citations 
 from a biological textbook. 
 
Chap. IX] Hypothetical Disjunction 381 
 
 where the framework of knowledge stands ready to receive it 
 with the grip of necessity. The reason is rather that the 
 organised system of reahty within which the sequences in 
 question have their force, lies or has hitherto lain outside the 
 great fabric even of biologiccd science, not to speak either of 
 deductive reasoning on the one hand or of philosophical con- 
 struction on the other. The principles of abnormal psychical 
 phenomena have not been as a whole identifiable either with 
 the principles of physical causation or with those of normal 
 psychical development. The judgment is therefore obstructed 
 by the want of contact or necessary relation between the 
 system of such abnormal phenomena, which it must in some 
 way refer to reality, and the entire cosmos of normal evolution. 
 Supposing, however (I speak merely by way of illustration), 
 that the abnormal states in question, even those which present 
 the apparent puzzle of a morbid origin combined with a curative 
 effect, could be exhibited as cases under the known principles 
 of evolution, the whole ground and certainty of the judgments 
 relating to them would be put upon a new foundation. It is 
 an old idea ^ that many states and susceptibilities of the soul, 
 which are commonly treated as mere freaks of nature or 
 capricious results of disease, may really have their place among 
 the phenomena of evolution no less than sleep and waking, or 
 the oneness, expressing itself through heredity, of parent and 
 child. If peculiar forms of sensitiveness and peculiar ' morbid ' 
 states or transitions to states could be brought under such 
 heads as survival, reversion, or analogous development, their 
 underlying reality would be grafted on the main stem of the 
 organised real world, and the necessity with which they were 
 affirmed would become more determinate and more concrete. 
 
 ii. Disjunction by its form aims at the standard of a com- The Dis- 
 plete and therefore of a real system. ' Real ' because it points l^'^g^*^^ 
 to nothing beyond itself as an implied ground of truth. We ment. 
 have seen sufficiently above that no objection can be raised 
 against the reality of the content of any judgment by reason 
 of its being extended in space or time. No judgment confines 
 its reference within an atomic ' now ', and no reality can display 
 itself as existent within an atomic now. It is grammatically 
 
 * See Hegel, Encyclopadie (Anthropologie), sect. 404. 
 
382 Modality [Booki 
 
 possible however for a disjunctive proposition to express a 
 judgment which is hypothetically disjunctive : ' A man who 
 would act so must be a knave or a fool.' This> shares the 
 character of all hypothetical judgments in implying an unex- 
 pressed real system as the basis of its truth, and its certainty 
 must be judged as the certainty of a hypothetical judgment. 
 But the disjunction according to the ideal prescribed by its 
 form is in itself an exposition of the reality that determines 
 its parts, and therefore is not a sequence within a presupposed 
 system, but is itself the content of a real system. It therefore 
 properly ranks with the generic judgment, to which it is 
 affiliated, as quasi-categorical ; and has only the imperfection 
 of certainty which arises from the comparatively minute range 
 of reality that is comprehended in any such simple system. 
 
 It is obvious from what has been said above that the 
 degrees of certainty here discussed are not numerically 
 estimable, because they are not reducible to ratios of equal 
 alternatives. It may therefore be justifiably complained that 
 the phrase ' degree of certainty ' is misplaced, and should be 
 transformed into ' stage of logical necessity '. I have no 
 objection to some such transformation provided that it is 
 distinctly understood that modality affects the assertiveness 
 of assertion, that this assertiveness is a matter of content and 
 not of the formal copula or reference to self-feeling, but that if 
 we extend the notion of the copula to include the material or 
 logical grasp by which a complex content is fitted on to a com- 
 plex Reality then we may say that Modality is a matter of the 
 Copula. In any case, the progressive incorporation of a con- 
 tent with the understanding,^ that is, with the organised ideal 
 system by which the understanding permanently qualifies the 
 Real, is the same thing as the progressive participation of that 
 content in the certainty that could only be complete in a judg- 
 ment that should exhaust Reality. 
 
 ' Cp. Whewell's account (see Mill's Logic, i, p. 279) of coming lo 
 perceive the necessity of a principle which he had before accepted as 
 fact. This is merely the acquisition of a precise and coherent insight 
 into its dependence on reality. Cp. Book II, chap. vii. 
 
A NOTE ON ERROR. 
 
 In the iii'st cditiuu of this work there was no treatment of Error co 
 nomine. The reason of this was that it appeared to me to be substan- 
 tially dealt with in the general account of the conditions of truth, in 
 the theory of negation and possibility, and in the account of the rectifi- 
 cation of judgment by scientific process. 
 
 It will be well, however, to sum up shortly the results of these views 
 in their bearing on Error co nomine. I acknowledge indebtedness to 
 Professor Stout for the distinct form which he has given to the question 
 (Aristotelian Proceedings, 1910-11, 'The Object of Thought and 
 Real Being '), and for his precise statement, amplified in private 
 correspondence with me, of the nature of ' relative possibility ' as 
 affecting conceivability. Yet I believe that I am advancing nothing 
 which does iiot fairly follow from the theory of this work. 
 
 The fundamental character of Error is always the assertion of a 
 merely possible alternative to be the alternative true of reality, i. c. 
 the assertion of something conditionally true, without regard to its 
 condition. (I should say ' unconditional assertion ' were it not the 
 case that in error there is rather a tendency to assertion under a false 
 condition.) 
 
 1 distinguish two main cases. 
 
 ( 1 ) There is what may be called ' Logical Error '. This is when the 
 condition, under which alone the affirmed alternative is realised, is 
 omitted or replaced by another, but not excluded by an incompatible 
 condition. A simple case is when we are drawn on to affirm the conse- 
 quent of a hypothetical judgment without thinking of its antecedent. 
 ' If that one little link were made out, I should be of royal descent,' 
 passes in cases of bias or failing mind into ' I am of royal descent '. 
 Here there is not necessarily factual error. The alternative affirmed as 
 actual is one relatively possible, i. e. conceivable from a certain point 
 of view, and may be in addition actually true, i. e. conceivable from 
 a complete point of view. But the limitation suggested by the incom- 
 plete point of view is not attended to and expressed, while, as in 
 ordinary everyday judgment, other more or less indifferent qualifica- 
 tions may be expressed. Such judgments may be what we call true 
 in fact (as the affirmed consequent of the hypothetical above may be 
 true in fact), but as in every judgment there is a presumption of neces- 
 sary connection (see vol. i, pp. 134-S), the indifferent qualifications 
 produce a false nexus and therefore a Logical Error. All judgments 
 except those, if any, which express absolute truth have some degree of 
 ' logical error '. What they assert does not ' hang together ' ; but it 
 may be a fact, and indeed all fact is asserted in this way. 
 
 (2) I call it ' Factual Error ' when the necessary condition for the 
 affirmed alternative being actual, not only is not expressed, but is 
 replaced by a condition or character belonging to an actual alternative 
 
384 A Note on Error [Book i 
 
 which excludes the one affirmed. ' The lady in the garden, wearing 
 a pink dress, is Mrs. A.' (when the wearer of the pink dress is Mrs. B., 
 and Mrs. A. really has on a blue dress). For the judging mind, this case 
 is much like the last. The status of the condition, which should attach 
 the alternative to reality, is unnoticed. And in this case it is a status 
 not merely of obscurity or irrelevance, but of hostility. But the point 
 of view of partial truth is preserved, and what is asserted is a conditional 
 element of reality taken as true without regard to its real condition. 
 The alternative affirmed is conceivable or possible from a certain 
 limited point of view (i.e. as ' lady in the garden '), but is a.ffirmed as 
 actual, i. e. as conceivable from a complete point of view, or, without 
 allowance for the limitation suggested by the point of view from which 
 it is possible. In factual error, the complete point of view involves a 
 hostile or excluding condition, a condition peculiar to a different 
 alternative, so that the alternative affirmed is no longer conceivable 
 nor possible. 
 
 We may say, therefore, that the alternative affirmed in factual error 
 ' belongs to reality ' (Green, Prolegomena, sect. 23, above, i. 327), but 
 not as affirmed. For the condition through which it is identified with 
 actual reality is a condition which, S and P being fully determined, 
 excludes it. Therefore from a complete point of view it is inconceivable, 
 and does not belong to reality. The judging mind has not fully deter- 
 mined the content of its own affirmation, but when this is determined, 
 the affirmation becomes a contradiction in terms. 
 
 End op Vol. I 
 
LOGIC 
 
 BERNARD HOSANI^VET 
 
6o 
 
 LOGIC >, 
 
 OR THE MORPHOLOGY OF '^^ 
 KNOWLEDGE K(l 
 
 BY 
 
 BERNARD BOSANQUET 
 
 M.A., LL.D., D.C.L. ; FELLOW OF THE BRITISH ACADEMY 
 
 IN TWO VOLUMES: VOL. II 
 
 SECOND EDITION 
 
 OXFORD UNIVERSITY PRESS 
 LONDON: HUMPHREY MILFORD 
 
i 
 
TABLE OF CONTENTS 
 Book II. Inference 
 
 CHAPTER I 
 
 The Nature of Inference 
 
 PAGE 
 I 
 
 4 
 4 
 
 1. The Essence of Inference ..... 
 
 2. Some Accidents of Inference ..... 
 
 i. Mental transition in Time .... 
 
 ii. Discovery or novelty . . . . . .8 
 
 iii. Omission of relevant matter ..... 8 
 
 iv. Selection, and omission of irrelevant matter? . . 12 
 
 V. Three terms ? . . . . . . .12 
 
 3. The lower limit of Inference . . . . . .14 
 
 i. The reproduction of Ideas ..... 14 
 
 ii. General necessity of Judgment . . . • IS 
 
 iii. Specific necessity of Judgment . . . .17 
 
 iv. The true immediate Inferences . . . .19 
 
 c. Comparison ....... 19 
 
 /3. Abstraction ... . . . . .20 
 
 7. Recognition . . . . . . .22 
 
 S. Discrimination, etc. . . . . . .24 
 
 €. Inferential character of above processes . . 25 
 
 f. Comparative Science . . . . -25 
 
 4. Species of Inference which have been erroneously identified with 
 
 its principle ......... 27 
 
 i. Inference from particulars to particulars . . . 27 
 
 ii. Subsumption ........ 28 
 
 iii. Calculation and equation ..... 29 
 
 a. Calculation proper ...... 30 
 
 )3. The Equational Logic . . . . -31 
 
 IV. Construction . . . . . . . -33 
 
 a. Physical ........ 34 
 
 j3. Imaginative . . . . . • -35 
 
 7. Intellectual, in geometry and mechanics . . 36 
 
 5. Intellectual, without limitation to geometry and 
 
 mechanics ....... 37 
 
 Scheme of types of Inference ....•• 39 
 
 Appendix on Symbolic Logic 
 The contrast of Formal or Mathematical Logic (Russell) with 
 
 Philosophical Logic ....... 40 
 
 I. The point of divergence between the two ... 40 
 a. As indicated above in this work (taking Quantity 
 
 as characteristic of Mathematics) ... 40 
 m. Taking pure Mathematics as= Formal Logic (as 
 
 study of implications) ..... 42 
 
vi Table of Contents 
 
 PAGE 
 
 The contrast of Formal or Mathematical Logic etc. (continued) 
 
 2. Precise nature of the divergence ..... 45 
 
 Contrast of Modes of Formal Deduction with ideal of 
 
 Logical Stability. ...... 45 
 
 a. Meaning of Logical Stability ... 45 
 
 /3. Formal Logic cares more for forms of Deduction 46 
 
 CHAPTER II 
 
 Enumerative Induction and Mathematical Reasoning 
 
 1. Enumerative Induction ....... 50 
 
 a. Syllogism in fig. 3 . . . . . .50 
 
 j3. Divergent tendencies . . . . -52 
 
 7. The Individual Judgment in Induction Lotze . 53 
 
 2. Mathematical Reasoning . . . . . . -55 
 
 i. Number and Analogy — Divergence . . . -55 
 
 a. Complete Enumeration as false Ideal. Syllogism 
 
 and Induction . . . . . -55 
 
 ii. Enumeration as Arithmetical computation . 58 
 
 7. Calculation compared with argument . . 60 
 
 ii. Applications of Calculation ..... 62 
 
 o. Substitutive Inference ..... 62 
 
 (j8. Apprehension of Connections in Space and Time) 64 
 7. Calculation applied to Geometrical Reasoning. The 
 
 Constitutive Equation ..... 68 
 
 5. Calculation applied to disparates. Proportion . 73 
 (i) Homogeneous Terms . . . -71 
 
 (2) ' a and a ' series ..... 74 
 
 €. Proportion, Analogy, and the Hypothetical Judg- 
 ment ........ 77 
 
 C. Consciousness and Conservation of energy . . 79 
 
 iii. The mechanical aspect of Knowledge . . .81 
 
 CHAPTER III 
 
 Analogy 
 
 Analogy and Enumerative Induction. Examples . . 86 
 
 Logical criticism of the Analogical argument ... 90 
 
 i. Fig. 2. Undistributed middle, Import of this defect 90 
 
 ii. Real value of Analogical argument .... 92 
 
 iii. No ratio of Identities to Differences . . . 100 
 
 iv. Concurrent Analogies. Negative confirmation . . 104 
 
 V. Divergent tendencies in Analogy .... 107 
 
Table of Contents 
 
 Vll 
 
 CHAPTER IV 
 
 Scientific Induction by Perceptive Analysis 
 
 1. Negative Inference .... 
 
 i. Its nature and conditions 
 
 ii. No conclusion from two negatives 
 
 iii. The negative instance 
 
 2. Scientific Induction .... 
 
 i. Induction and other Inference 
 ii. Induction as Perceptive Analysis 
 
 a. Sj'mbolic expression of the problem 
 
 /3. Establishment of ordinary Hypothetical Judgment 
 
 7. Establishment of reciprocal Hypothetical Judgment 
 
 ?. Conversion or Generalisation 
 
 iii. Logical character of Perceptive Induction 
 
 a. Its essence as Inference 
 
 P. Theoretical purpose of representation by symbols 
 
 7. Part played by number of instances 
 
 (i) In Perceptive Analysis proper 
 
 (2) In assigning known effects to classes of un 
 
 known conditions 
 
 iv. Observation and Experiment 
 
 a. Natural Experiment 
 
 /3. Observation with accurate instruments 
 
 7. Experiment expressed in logical symbols 
 
 5. Experiment with the Siren analysed 
 
 PAGE 
 
 109 
 109 
 112 
 
 "S 
 117 
 117 
 122 
 122 
 124 
 127 
 129 
 
 131 
 132 
 
 134 
 134 
 
 135 
 
 135 
 141 
 141 
 142 
 143 
 147 
 
 CHAPTER V 
 
 Scientific Induction by Hypothesis. Generalisation 
 
 Hypothesis and Postulate .... 
 
 i. Hjrpothesis falls outside Postulate 
 ii. But not if Hypothesis alleges Vera causa 
 Phases of Hypothesis ..... 
 
 i. Rudimentary Hypothesis 
 
 ii. Mediate Hypothesis .... 
 
 a. Hypothetical nature of Induction 
 0. Example of fusion between Hypothesis and data 
 Generalisation ...... 
 
 i. ' From many to all ' exploded 
 
 ii. By mere determination .... 
 
 iii. Material or Analogical Generalisation 
 General view of Induction .... 
 
 i. Difference from Jevons .... 
 
 ii. Ultimate nature of Induction . 
 iii. On a Defective Formulation of the Inductive Principle 
 
 151 
 151 
 154 
 15s 
 155 
 156 
 
 156 
 157 
 163 
 163 
 163 
 
 165 
 169 
 169 
 
 170 
 174 
 
Vlll 
 
 Table of Contents 
 
 4. General view of Induction (continued) 
 
 iii. On a Defective Formulation etc. [continued) 
 Inference and Repetition. 
 
 a. ' Same Cause Same Effect ' 
 
 0. A Tautology 
 
 7. The true Principle 
 
 5. Developing the Nexus 
 
 174 
 174 
 176 
 181 
 182 
 
 CHAPTER VI 
 
 Concrete systematic Inference 
 
 1. Philosophical Subsumption .... 
 
 i. Logical content of these Inferences 
 
 o. Real system 
 
 li. Apodeictic sequence 
 ii. Their form, Syllogism in fig. i 
 
 2. Disjunctive reasoning 
 
 3. The judgment of value 
 
 i. Real Teleology 
 ii. Mediation .... 
 
 4. Recapitulation of the main characteristics of Inference 
 
 i. No antecedent scheme of Inference 
 ii. Conditions of Inference ..... 
 iii. Relation of Syllogism to these conditions 
 a. The traditional syllogism 
 0. The syllogism as reasoned judgment 
 
 IBs 
 190 
 190 
 191 
 192 
 194 
 199 
 199 
 199 
 200 
 201 
 203 
 204 
 204 
 206 
 
 CHAPTER VII 
 
 The Relation of Knowledge to its Postulates 
 
 1. The formal postulates of Knowledge .... 208 
 
 i. The Law of Identity . . . . . .210 
 
 ii. The Law of Contradiction . . . . .211 
 
 iii. The Law of Excluded Middle . . . . .213 
 
 iv. The Law of Sufficient Reason and Law of Causation 215 
 
 2. The material postulates of Knowledge . - . . .216 
 
 i. The maintenance of life . . . . . .218 
 
 ii. The reality of values . . . . . .221 
 
 3. The ultimate nature of Necessity ..... 223 
 
 i. A priori necessity and mediation .... 223 
 a. Mediate nature of necessity forgotten in controversy 224 
 fi. Organised and unorganised experience, with am- 
 biguity of test by Conception . . . 226 
 ii. Rehabilitation of formal distinctions in Logic . .230 
 iii. Criticism of 'Aesthetic' necessity .... 233 
 a. Aesthetic necessity as a contradiction in terms . 233 
 0. Aestheti c necessity as a mere case of logical necessity 2 34 
 
Table of Contents 
 
 IX 
 
 Genetic Theory and Imitation . 
 i. Reason as an Adaptation 
 ii. Imitation plus Selection ? 
 iii. Meaning of Imitation 
 
 a. Imitation dist. Response 
 /3, Imitation why held a Vera causa ? . 
 7. False separation of Imitator and Inventor 
 iv. Truth or Belief due to Evolution ? . 
 a. Limits of Genetic account 
 &. The ' making of Truth ' . 
 
 PAGE 
 
 238 
 
 239 
 240 
 241 
 241 
 241 
 242 
 243 
 243 
 246 
 
 CHAPTER VIII 
 
 The Above Theory of Judgment in Relation to 
 Absolutism 
 
 Our theory treated as prejudiced. Answers to objections . 251 
 
 i. No finite real self -existent . . . . .252 
 
 ii. Degrees of Individuality . . . . . -253 
 
 iii. Experience of self fatal to doctrine of substances . -255 
 
 iv. Difficulty arising from conception of class-inclusion. 
 
 This conception foreign to S P judgment as such . 255 
 
 V. Imperfect Individual can be conditional Predicate . 257 
 
 vi. Absolutism rests on its own substantial grounds . 259 
 
 Freedom of expression in Judgment on this theory . .259 
 
 i. Traditional S P analysis rejected by it . . . 259 
 
 ii. Individuality said to demand Designation as opposed 
 
 to Definition — the reverse of the truth . . 260 
 iii. Doctrine of ultimate ' subject ' leaves philosophical theory 
 
 free, taking shape from the latter . . . 262 
 
 CHAPTER IX 
 
 Truth and Coherence 
 
 1. Disclaimer of Correspondence Theory .... 263 
 
 i. An expression which might be misleading . . 264 
 
 ii. The Criterion immanent ..... 265 
 
 iii. Truth its own test ...... 266 
 
 iv. Not all correspondence means copying . . . 267 
 
 2. The Logical world to-day ...... 268 
 
 i. ' Life,' ' Practice,' ' Feeling,' forms of Immediacy . 268 
 
 ii. The misconception which governs the movement . 268 
 
 iii. Fallacies of Genetic Logic according to a recent exposition, 
 
 Dualism, Occasionalism, Adaptationism . . 270 
 
 iv. How Psychology passes into Logic .... 274 
 
 V. Summeiry — defects of the new attitude . . . 275 
 
X Table of Contents 
 
 PAGE 
 
 3. Realism — a complementary form of Immediacy . . 276 
 
 a. The world of related simple things .... 277 
 Rejection of ' internal ' (relevant) relations . . 277 
 
 (i) Relations relevant to kinds . . . .277 
 
 (2) The meaning of terms relevant to their grouping 278 
 
 (3) Relations express behaviour of terms in groups. 
 
 ' Sense ' of relations ..... 278 
 
 b. Relations not asserted to be adjectives . . . 279 
 
 c. Truth and Error not absolute, because things not simple . 280 
 
 d. The illusion of simple fact . . . . .281 
 
 (i) Stating what is ' a fact ' may be telling a lie . 282 
 
 (2) or may be an error (' true ' conclusion from false 
 
 premisses) ....... 283 
 
 (3) How we come by ' simple ' facts . . . 284 
 
 (4) The facts are more not less than simple realities . 285 
 
 (5) In the ' reaUty ' the 'simple facts' are lost . 285 
 
 (6) The ' full facts ' or ' reality ' are comprehensive 
 
 systems ........ 287 
 
 4. Coherence is defective, like all theory, but not in a way that 
 
 implies correspondence as its standard .... 288 
 
 i. Coherence does not fall back on Correspondence . 289 
 
 ii. No ' approximation ' to an original . . . 290 
 
 5. Our quasi-solid world ....... 292 
 
 6. Does Truth copy this world ? No, it is plastic . . 294 
 
 CHAPTER X 
 
 The Relation of Mental States to Judgment and to 
 
 Reality 
 
 The Mental States in question . . . . . . 295 
 
 1. Doctrine of the present work ..... 295 
 
 a. All sense-content significant, and any of it may become 
 
 a ' state of mind '...... 295 
 
 H. The ' use ' of contents as ideas .... 298 
 
 2. The Real not arrived at by subtraction . . . 301 
 
 a. Knowledge involves mental states. . . . 302 
 
 (i) Reality lies ahead, not behind . . . 302 
 
 (2) Truth in ' Mind can only apprehend itself ' . 303 
 
 (3) What explanation means, viz. complete thinking 305 
 
 (4) Fallacy that ' independent of ' = ' apart from ' 305 
 
 (5) A simple real must duplicate mental being . 307 
 
 (6) If 'independent' == 'apart from', different phy- 
 
 sical objects are th» same for apprehension . 307 
 
 (7) The object of perception is conditionally, i. e. 
 
 for me . . . . . . . . 310 
 
Table of Contents xi 
 
 'Jhe Real not arrived at by subtraction (continued) — 
 a. Subjective Idealism insists on vital continuity of universe 311 
 7. ' Sustaining ' and ' constructing ' the world. Answer to 
 
 criticisms . . . . . . . -313 
 
 (i) Judgment involves a world, and one world . 314 
 
 (2) Both realists and pragmatists put mind outside 
 
 reality . . . . . . . .317 
 
 (3) Nature of object of cognition — strictly we neither 
 
 ' apprehend ' nor ' create ' it. We are organs 
 within the universe for ' eliciting ' its reality in the 
 form of truth. The true driving force of Idealism 318 
 
 ABBREVIATIONS 
 
 Bradley's Appearance = Bradley's Appearance and Reality, ed. 2. 
 Sonuenschein, 1897. 
 
 Bradley's Logic = Bradley's Principles of Logic. Kegan Paul, 
 Trench & Co., 1883. 
 
 Keynes = Keynes's Formal Logic, ed. 4. Macmillan, 1906. 
 
 Prichard = H. A. Prichard's Kant's Theory of Knowledge. Clarendon 
 Press, 1909. 
 
 Essentials = Bosanquet's Essentials of Logic. Macmillan, 1895. 
 
 Sigwart = Logik, von Dr. Christoph Sigwart. 2nd edition. Freiburg, 
 i88q. 
 
BOOK II 
 Of Inference 
 
 CHAPTER I 
 
 The Nature of Inference 
 
 I. Inference shares the essence of Judgment, but, at The 
 least qua exphcit Inference, has in addition ■ a differentia of o/j^^g^. 
 its own. The essence of Judgment is the reference of an ideal ence. 
 content to Reality ; the differentia of Inference affects the 
 mode of this reference, and consists in Mediation. Inference 
 then is the mediate reference of an ideal content to Reality. 
 If I affirm that I spoke to you in the street yesterday simply 
 because I find it in my memory that I did so speak to you, 
 that is, apart from refinements of analysis, simply a judgment. 
 If, as against your denial of the fact, I corroborate my recollec- 
 tion by pointing out that I must have spoken to you, because 
 you afterwards acted upon something that I then told you, 
 then I am reasserting the content of my original judgment, 
 but with an addition and modification that turns it into an 
 Inference. I then refer an ideal content to Reality, not as 
 directly given in memory or in perception, but on the strength 
 of a content distinguishable from the former content, bearing 
 a certain relation to it, and itself referred directly to reality. 
 
 By speaking of ' mediate ' reference to reality we have 
 mentioned the differentia of Inference, but have not ex- 
 plained it. Direct affirmation appears to explain itself ; but 
 mediate affirmation is even at first sight somewhat mysterious. 
 We are at once met with the old question, ' How are synthetic 
 judgments a priori possible ? ' The qualification a priori 
 adds nothing to the qualification ' true ' which is claimed 
 by all judgment as such. The question therefore is in plain 
 
 1337-2 B 
 
2 The Nature of Inference [Book ii 
 
 English, ' How can one content claim to be true of Reality 
 on the strength of another content distinct from the first ? ' 
 ' How can any synthetic judgment qua synthetic — i; e. going 
 from content to content and not simply accepting either a 
 mere occurrence or a mere conjunction — how can such a judg- 
 ment conceivably be justified ? ' The answer to this difficulty, 
 like all answers in philosophy, is at first sight a mere restate- 
 ment of it. Whether such a restatement is an explanation 
 depends on its congruity and coherence with reason and with 
 experience. It is possible — so the answer must run — to proceed 
 in knowledge from content to content, because the world as 
 known consists of universals exhibited in differences, and the 
 contents from which and to which we proceed are not shut 
 up within their respective selves, but depend on a pervading 
 identical character or universal of which they are the differ- 
 ences. ' Of which they are the differences ' * — for here is the 
 objection which meets us on the threshold. Suppose that I 
 find in a room a hundred different objects — ^books, guns, 
 china — all marked with the same label, say with the owner's 
 name. Well then, it may be said, here is your ' identical 
 character ' or ' universal ', but what can you infer from it 
 beyond itself ? It tells you nothing of the object to which 
 it is attached. You may go on for fifty cases affirming that 
 a having the label :v is a book, h having the label a; is a book and 
 so on, but you cannot teU in the least what the fifty-first 
 object that has the label will be, whether a sporting rifle 
 or a china teapot. There is an identity throughout all the 
 objects, but they are not, or seem not to be. Us differences. 
 They simply contain it, and are in no way leavened by it. 
 You cannot in any way determine their predicates on the 
 basis furnished by this pervading identity. 
 
 The whole of our previous and subsequent discussion 
 really deals with this radical difficulty. Logic is little more 
 than an account of the forms and modes in which a uni- 
 versal does or does not affect the differences through which 
 it persists. I can only point out that all turns on the dis- 
 tinction between the abstract or powerless and the concrete 
 or dominant universal. To interpret the latter by the former, 
 * Cf. vol. i., p. 45 note. 
 
Chap. I] Abstract and Concrete Universal 3 
 
 to reduce all universals to marks, i. e. to the level of the exam- 
 ple just mentioned, is a fatal tendency of popular logic. A 
 very elementary example of a relatively concrete universal 
 may be found in the nature of a geometrical figure, say of 
 the circle or the triangle. Given an arc of a circle, we have 
 the radius and centre, and can lay down the whole circum- 
 ference. The given arc is not simply repeated, it is continued 
 according to a universal nature which controls its parts, and 
 with a result which though involved in the given arc is yet 
 outwardly and as an actual content distinct from it. This is 
 clearer if instead of a circle we take an ellipse, in which the 
 given fragment of the curve cannot in any sense be said to 
 be simply repeated without change in constructing the re- 
 mainder. There is something in the curve as given which is 
 capable of dictating a continuation and completion of its 
 outline distinguishable from the given arc or fragment itself. 
 Just so with a triangle — given two sides and an angle, we can 
 find the third side and remaining two angles. 
 
 And we can now see that in the first example, which 
 seemed so hopeless, the same relation would be traceable as- 
 suming the label to have any meaning at all. A mere mark, 
 which conveys nothing, is not even a mark, for what is it a 
 mark of ? But supposing the label to indicate A's ownership 
 of the things, then we could infer all sorts of legal consequences 
 about them from this ownership ; and these consequences 
 would not be the same for all the objects, but would be 
 modified by their nature ; e. g. it is probable that some of 
 the things would be liable to seizure by a judgment creditor 
 and some would not. Thus here too the universal would be 
 an identity pervading different manifestations. 
 
 The universal in its differences is then the basis of mediate 
 judgment or inference. But it is also the basis, as we have 
 amply seen, of judgment as such, i. e. what would usually 
 be called immediate judgment. The above examples, however, 
 furnish the further distinction to which we shall find it 
 convenient on the whole to adhere. Mediate judgment or 
 inference is the indirect reference to reality of differences 
 within a universal by means of the exhibition of this universal 
 in differences directly referred to reality. The differences 
 
 B2 
 
4 The Nature of Inference [book ii 
 
 indirectly referred to reality may fall outside, or include, or 
 even consist exclusively of, the differences directly referred to 
 reality. Immediate judgment, according to its idea, would 
 be the mere reference to reality of differences as united 
 within the identity or universal. It might be more intel- 
 ligible if we were to substitute ' parts ' and ' whole ' for 
 ' differences ' and ' universal ' ; but then it would have to 
 be borne in mind that we are not speaking of quantitative 
 parts, i. e. that the kind of whole in question is not necessarily 
 the sum of its parts. Subject to this reservation, I have no 
 objection to defining Inference as the indirect reference to 
 reality of parts within a whole on the strength of the nature 
 of that whole as revealed in parts directly referred to Reality. 
 And the definition of Judgment would bear a corresponding 
 modification. Of course I do not mean that all the forms 
 which have already been discussed under the head of Judg- 
 ment are substantially confined within the definition of Judg- 
 ment and excluded from that of Inference. But for the present, 
 in order to obtain a clear view prima facie, we are considering 
 only explicit Inference and excluding all that takes the out- 
 ward shape of mere Judgment. 
 Some 2. The above account of the essence of Inference will be 
 
 .Accifidits 
 
 of Infer- ^^^^ illustrated by considering some accidents of inference 
 ence. which I have endeavoured to exclude from the definition. 
 Mental i. First among these comes the attribute of mental transi- 
 
 tion in ^^^^ ^'^ time, with which that of an advance from known to 
 Time. unknown may in one sense be identified. 
 
 The account given above ^ of the Judgment in time applies 
 also to Inference as a mental process in Time. The first and 
 most fatal error as regards both Judgment and Inference is 
 to introduce the idea of an actual and instantaneous transition 
 from content to content. This idea combines the error of 
 denying that inference, as a mental process, has duration in 
 time, with that of denying that as intellectual insight its 
 parts are inward to each other and exempt from temporal 
 succession. The universal itself, or intellectual S3aithesis of 
 differences, is not a fact in time ; and throughout the interval 
 which inference occupies as a psychical process the operation 
 ' Bk. I. chap. i. 
 
Chap. I] Real Advuncc in Time 5 
 
 of the universal as a growing insight is traceable in every 
 point of time, but is not shut up within any atomic moment. 
 But apart from the idea of instantaneous transition, there 
 is an idea of advance in time which has great appearance 
 of truth and which is indeed in one sense true. It is unques- 
 tionable that in inference we start from data, from facts 
 thrown down before us, it may be in chaotic disorder and 
 with no suggestion of a result. -"^ We go to work upon these 
 facts, and after the labour of hours, of days, or of a lifetime,^ 
 we light upon a conclusion which issues from them and to 
 which they are related as premises ; i.e. which exhibits them 
 as differences in a universal. How is it possible to deny that 
 we have here an advance in time from data without con- 
 clusion, at any rate to data plus conclusion, and, if we go 
 by the old syllogism, to conclusion minus a large part of the 
 data ? The difficulty which I find in stating the above 
 antithesis is a first indication of its fallaciousness. It was 
 impossible to write simply ' from data without conclusion to 
 conclusion without data '. A conclusion without data is an 
 obvious contradiction in terms, and if even part of the data 
 are dropped (as the middle term in the syllogism) the con- 
 clusion sinks pro tanto into a 6tl rather than a hiori — a fact 
 instead of an inference. No doubt we are apt to pluck off 
 our conclusion like a fruit from a plant and carry it away 
 for consumption. Practical life requires this procedure. But 
 we must remember that from the moment of severance death 
 has begun, and that the intellectual product can bear isolation 
 far less than the material. The idea of an actual transition 
 from data to result, so far as it is founded on this habit, is in 
 science simply a pernicious blunder. The case in which the 
 result is a systematic insight that includes the premises in 
 a transmuted form does not of course fall under this censure. 
 But this case is not as a rule contemplated by the traditional 
 forms of inference. 
 
 * I put the case at its extreme against myself. We must however 
 remember that we can only see in the facts what we are ready to see 
 there, what we bring with us. So however disorderly in fact, the data 
 are really from the beginning theorised upon by our apprehension, 
 because it can only apprehend them on the strength of its own existing 
 content. ^ See the famous preface to the ' Origin of Species '. 
 
6 The Nature of Inference [Book ii 
 
 And of course it might be correlatively maintained that 
 facts are not data, except by virtue of a result ; or if this is 
 not true of data but only of premises, then that inference 
 does not start from data but only from premises.^ At first 
 sight such a contention seems to blink the difficulty. The 
 conclusion, it seems, may be removed by a week's work from 
 the data or premises ; and granting that they are not rightly 
 called data or premises till the week's end when the conclusion 
 is won, still the facts concerned were present and active at 
 the beginning of the week and certainly entered into the 
 advance that has been made. 
 
 Two things are here to be distinguished, viz. mere repro- 
 duction and inferential reproduction. The universal active 
 in the mind is not apparent as a whole within the mere 
 psychical facts of the transition. Its operation is extended 
 throughout a series of the fugitive psychical facts or ideas, 
 and although in logical thinking its operation is conscious, 
 i.e. selects and modifies within the content of these ideas, 
 yet it is not in itself necessarily a conscious activity. It 
 acts in consciousness, but need not be conscious of its own 
 principle of action. In rudimentary reproduction we see 
 a man far off, and a name comes into our mind, apparently 
 as a detached fact, without any reason that we can assign 
 or think of trying to assign. It is only later, when we clearly 
 recognise the man, that we become aware either that we 
 recognise him, or how and why we recognise him. Logical 
 thinking consists of making this process conscious ; but 
 essentially and fundamentally the intellectual tendency which 
 controls reproduction need not be present as a distinct content 
 operating in reproduction. So" far the psychical process 
 might in theory begin with data alone and then go on leaving 
 them behind to result alone, not carrying throughout the 
 transition any conscious unity or continuity of content. 
 
 But in explicit inference, at any rate, this is not the case. 
 The essence of inference is to drag into consciousness the 
 operation of the active universal as a pervading unity of 
 content on which inference depends. The conscious operation 
 of the active universal in inference is what we have to dis- 
 
 * But then it would seem the data must be premises of the premises. 
 
Chap. I] Unity of Inference 7 
 
 tinguish from the mere implicit action of the universal in 
 rudimentary reproduction. Therefore when we speak not of 
 mere reproduction, but of inferential reproduction or passage 
 from data to conclusion, then it is true that you can no more 
 have data or premises without conclusion than conclusion 
 without data or premises. The appearance to the contrary, 
 which I have admitted to exist, arises from our fixing our 
 attention exclusively on the conclusion par excellence in which 
 and not before it we happen to rest. This conclusion, though 
 it may close a stage of science or set at rest a longing of 
 our hearts, is in no way different in logical character from 
 the first steps of preparatory activity with which reason 
 penetrates the facts laid before it. We meet the data with 
 a judgment when they are laid before us, and we modify 
 this judgment continuously throughout our inference. Any 
 section taken, so to speak, across the interval of intellectual 
 activity which elapses from first data to ultimate conclusion 
 would lay bare the whole structure of an inference, just as 
 a section across the time during which a chord is sounding 
 on the organ would exhibit the whole harmonic structure of 
 the compound tone. Of course we may draw partial con- 
 clusions, discard their data, and work with these conclusions 
 as with fresh data, and so far we make an advance from 
 content to content, discarding the old in favour of the new. 
 Bui this process, though necessary in practice, comes under 
 the observation made above upon a conclusion severed 
 from its proof, and is not typical of inference, but of its 
 limitations. 
 
 Transition in time from content to content as between data 
 and conclusion in inference is not really possible. But it is 
 true that the process of inference, though continuous and. 
 bound together by a conscious unity, is extended in time and 
 includes considerable modifications of the judgments from 
 which it starts. The appearance of a transition arises from 
 discarding data, which is unjustifiable, from transforming 
 data, which is right but is no transition, or from comparing 
 ultimate conclusions and primary data while neglecting the 
 intermediate phases which constitute the continuous and — 
 not transitional but — inclusive inferential evolution. It is in 
 
8 
 
 The Nature of Inference 
 
 [Book II 
 
 Disco- 
 very or 
 Novelty. 
 
 Omission 
 of rele- 
 vant 
 matter. 
 
 this character of transition without conscious continuity that 
 rudimentary reproduction differs from explicit Inference. 
 
 Thus our definition of Inference did not say that the differ- 
 ences which form the data are previously affirmed of reality, 
 although it is only from them as affirmed of reality that the 
 reality of the inferred differences can flow. 
 
 ii. Secondly, it follows from the above considerations that 
 discovery is an accident and not an essential of inference. 
 Inference is not essentially passage in time whether instan- 
 taneous or extended. Therefore it is not the case that a 
 conclusion ceases to be an inference the moment that it 
 becomes familiar, the moment, that is, that it ceases to be 
 a discovery. On the contrary, discovery without proof is 
 conjecture ; an element of proof is needed to constitute 
 inference, and indeed to constitute discovery. The activity 
 of inference cannot be identified with the perception of some- 
 thing new. It is quite a normal occurrence that the elements 
 which are indirectly referred to reality should also be directly 
 referred to reality. Whenever, indeed, as the ideal of inference 
 requires, the original data themselves are transformed and 
 freshly elucidated, this happens as a matter of course. When 
 the working of a machine is about to be explained we see 
 a wheel or piston to be there as a fact, and we ask what it 
 does. The answer tells us why there must be such a wheel 
 or piston, and this is not superfluous though we knew before- 
 hand that it was there. The part in question then becomes 
 to us an element or difference in the pervading identity or 
 universal which is the working of the machine. And if we 
 live fifty years and see the machine every day, understanding 
 it thoroughly, still the use of any one of its parts, considered 
 as necessitated by the nature of any other actual part or set 
 of parts combined with the working of the whole machine, 
 remains to us an inference and never becomes a mere fact. 
 Thus novelty or discovery is an accident of Inference. 
 
 iii. Thirdly, it follows from the above considerations that 
 omission in the conclusion of contents employed in the pre- 
 mises is an accident of inference. Inference is confined 
 neither to what is novel nor to what happens to interest us. 
 The appearance of a necessity of omission arises from various 
 
Chap. I] Omissiofi in Inference g 
 
 causes. The transformation of data is an ideal which is 
 likely to be misunderstood. It resumes the old data in a new 
 expression. Again, it is usual and in complicated matters 
 unavoidable to confine ourselves in dealing with any universal 
 to some aspect determined by context or by curiosity. And 
 the habitual omission of the middle term in the Aristotehan 
 syllogism is perhaps due in part to the above causes, and in 
 part to the vicious habit of severing the conclusion from the 
 premises which the rhetorical associations of early logic tended 
 to foster,-^ But the entire content of the universal, so far as 
 recognised in the necessity that unites its differences, is the 
 true content of every inference, and there is no logical reason 
 for neglecting to make explicit any portion of truth which our 
 perception of it generates. 
 
 A question arises on the margin of this subject of omission 
 with reference to the systematic realities of which we spoke 
 under the head of the hypothetical and disjunctive judgments. 
 If I directly affirm the reality of a complex system, such as 
 a railway, or a government, or a mind, and include in my 
 affirmation a mention of many parts and properties as sys- 
 tematically interrelated, am I in doing so rightly said to be 
 inferring ? It rather seems here as if the absence of omission 
 destroyed all semblance of a conclusion, and how can there 
 be inference without a conclusion ? ' Cannon Street railway 
 station has interlocking points and signals.' To any one who 
 understands the subject it is unnecessary to complete this by 
 the further explanation (which even if inserted may of course 
 be a mere qualification, not a fresh judgment), ' such that 
 opening any one line ipso facto needs the signals to be at 
 danger for all the lines that cross it.' In such a judgment, 
 regarding it, as we have every right to do, in the light of 
 a single affirmation, I am obviously embodying matter which 
 has an inferential character. But whether I am actually 
 inferring or not depends — not, as one might be tempted to 
 say, on the novelty of the conclusion implied, but — on the 
 degree of insight with which the judgment is made. It is in 
 
 ^ Because the rhetorician only wants to prove, not to understand. 
 If he reaches his conclusion, the steps by which he reached it cease to 
 interest him or his audience. 
 
10 The Nature of Inference [Book ii 
 
 short either an inference, or the allegation as a fact of relations 
 that must have formed the conclusion of an inference, although 
 the inferential connection may now be lost. If however we 
 go into such detail as proves that we have an insight into 
 the why and wherefore of the system, then we have no choice 
 but to say that we are inferring but are stating our inference 
 confusedly. The confusion is in not distinguishing data from 
 conclusion — how much is immediately affirmed of reality, and 
 how much is mediate. The judgment is a mediate judgment 
 simulating an immediate character.-"- 
 
 An ordinary hypothetical judgment is really an analogous 
 case to the above (which might be represented by a disjunctive 
 judgment). Inferential matter, a relation or nexus, seems to 
 be affirmed of reality ; but yet the omission, which would 
 leave as affirmed what seems to be the conclusion, cannot be 
 made. The groimd per se is not affirmed of Reality, and so 
 the consequent per se is not affirmed to be true. The moment 
 that 'If passes into ' Because ' you can omit the ground 
 and affirm the consequent per se. But retaining the ' If ' we 
 cannot affirm the consequent. We cannot affirm upon mere 
 supposition, nor can we infer without affirming. Yet cer- 
 tainly, as in the last paragraph, we seem to have before us an 
 inferential activity. ' In four-dimensional space (i. e. sup- 
 posing such space) a knot can be tied in a string whose ends 
 are held.' In this judgment the nexus between four-dimen- 
 sional space and tying a knot is undoubtedly inferential. 
 The moment we affirm the reality of the ground, we also 
 affirm the real possibility of the consequent. But the hypo- 
 thetical judgment as such affirms neither the one nor the 
 other. The entire judgment is no doubt itself a consequence 
 of an underlying reality, the affirmation of which it implies, 
 and on the groimd of which — a ground asserted to be real — 
 the whole complex content of the hypothetical judgment is 
 asserted to be real, subject to its own inherent reservation 
 
 ^ The existence of these ambiguous inferences — half inference and half 
 memory or authority — favours in appearance the restriction of inference 
 to -what has novelty. When an inference is just made, then, if ever, it 
 has definite data. When an inference is famiUar, it is too likely to rest 
 on the ground that it is remembered to have been approved of. Never- 
 theless, not novelty, but systematic necessity, is the true differentia. 
 
Chap. I] Hypothetical Inference ii 
 
 embodied in its own further ground. But this does not help 
 us to determine the presence or absence of inference within 
 the hypothetical judgment itself. 
 
 The fact seems to be that hypothetical affirmation is a 
 contradiction in terms, and so too is h57pothetical inference. 
 The whole process, apart from any categorical meaning 
 which it may make explicit, which is a matter of degree, is 
 a mere make-believe. You choose to treat as real in one 
 sense what you do not affirm to be reaUy real,^ and you 
 record the groove of necessity which manifests itself when 
 the artificial reality is considered as though forming part of 
 the real reality. Of the differences within the universal 
 which determine the remaining differences (in this case the 
 consequent) part (the hypothetical ground) are only sham 
 reality, and therefore although we seem to exert inferential 
 activity, yet we cannot affirm the conclusion of the inference. 
 Here then we have the two degrees of impropriety in omis- 
 sion. Even when the ground of inference is affirmed, as 
 with ordinary premises, the reality of the conclusion is 
 restricted to the precise sense imposed by that ground, and 
 it is therefore theoretically imsafe to affirm the conclusion 
 apart from the ground. But when part of the ground of in- 
 ference is not affirmed, then we have reaUy the case of the 
 problematic judgment, and if the consequent is affirmed with 
 omission of the supposed ground it can only be affirmed 
 problematically, i. e. cannot be affirmed as true, or in the 
 proper sense af&rmed at all. The reference to reality is then 
 incompletely mediated. But on a pure supposition no inference 
 can be erected. The element of supposed reality is the 
 element of reservation, and the element of real reality is the 
 element of affirmation. A pure supposition would be all reser- 
 vation and no affirmation. If I suppose that over a certain 
 spot of ground gravity ceases to operate, I can form some kind 
 
 ' This process has many degrees. The content of supposition may be 
 real all but some very minute relation. The conclusion from the 
 supposition can then be affirmed subject to-a very minute reservation. 
 The main content of the conclusion may depend on what is absolute 
 fact. • If that picture were I in. to the left it would hang symmetrically 
 with that other picture ' gives the conclusion. The picture A hangs 
 symmetrically to \ in. with the picture B. 
 
12 The Nature of Inference [Book ii 
 
 of conception of the consequence. I affirm the present state 
 
 of things with reservation for the modification introduced by 
 
 the limited absence of gravity. But if I suppose that there is 
 
 to be no gravity at all in the world, the reservation gets the 
 
 upper hand, and nothing, I presume, is left for me to affirm 
 
 — not even, as when part of the conditions only is affirmed, 
 
 a problematic conclusion. 
 
 Omission in inference is thus accidental and hazardous in 
 
 various degrees. It is, as we saw, in one form (as omission 
 
 of the condition or reservation in judgment) the mark of 
 
 problematic judging. Omission however as here discussed 
 
 is omission of matter relevant to the inference, or, which is 
 
 the same thing, falling within the conclusion. In this sense, 
 
 as within the relevant content, selection is the converse of 
 
 omission, and is equally an accident of Inference. If you 
 
 select, you omit ; and if you omit, you select. But you need 
 
 not do either. 
 
 Omission iv. On the other hand, actual data must always present 
 
 ofirrele- irrelevancies, and must be exhibited as transformed — ^not 
 
 vant 
 
 matter, necessarily he transformed de novo by an act of discovery — 
 
 in the inferential operation. Otherwise there could not be 
 the circuit through the universal which we have taken to 
 be the differentia of inference. It is natural therefore to 
 think of Omission and Selection with reference to the actual 
 data on which, as referred to reality in their crude form, a 
 given inference depends. Within these actual data Selec- 
 tion is of the essence of Inference, but Omission depends on 
 the existence of irrelevancies in the data, and although in 
 theory these disguises and superfluities cannot be wanting, 
 yet they may be reduced to an almost inappreciable margin, 
 and the element of omission in that case becomes inappre- 
 ciable also. There is then, apparently, selection without 
 omission ; there can never be omission without selection. 
 Three V. It has been maintained that the presence of three 
 
 terms. ' terms ', as required by the Aristotelian syllogism, is an 
 accident of inference and does not touch its essence. I must 
 leave this question, which is largely verbal, to decide itself 
 in detail from our whole account of the subject. Here I will 
 merely indicate the distinction on which in my opinion the 
 
Chap. I] Three Terms 13 
 
 answer to it depends. Of course an inference is constantly 
 drawn by the combination of very numerous facts and con- 
 ceptions. Aristotle's ^ or Lotze's Inductive syllogism, or a 
 Sorites, or a Euclidean construction, are familiar examples of 
 inference so drawn. The only question is whether these 
 numerous facts or conceptions correspond to phases or elements 
 in the logical act of Inference, and whether, if they do not, 
 they can claim the title of logical ' terms '. Must there not 
 always be (i) differences or parts directly referred to reality, 
 (ii) the universal nature or continuous identity which binds 
 these differences or parts into a whole, pregnant with a capacity 
 of accepting and arranging further differences or parts, and 
 (iii) further differences, identified as parts within the pregnant 
 whole which controls the inference, and, on the- strength of 
 this identity, referred to reality ? It may be observed that 
 this last ' term ', moment or element of inference, may 
 and ought to include the two former. But it contains them 
 in another sense than that in which they appear as isolated 
 elements of inference, and therefore is not superfluous nor 
 tautologous. We may have a thousand observations of the 
 places of a moving heavenly body, but these thousand data are 
 not a thousand terms. The thousand observed places fuse 
 into the law of the orbit, and the law of the orbit dictates 
 the remaining places which form the path that the body 
 traverses. Or, as the above instance really verges upon 
 geometrical construction, we may take an example more 
 cognate to what is commonly meant by Induction, though 
 it is hard to find a good example of a process which does 
 not exist. If typhoid fever attends a certain milk-supply 
 through a large portion of its ins and outs, including many 
 dozens of cases, then we shall no doubt be apt to suspect 
 that danger attaches to that milk supply as a whole, and 
 consequently menaces any localities as yet unexamined to 
 
 ^ TO Kad^ (Kaarov is a term in both premises of the Aristotelian Induc- 
 tive Syllogism. Obviously this means that each premise would be 
 a conjunction of judgments, or a conjunctive judgment. Such a group 
 of judgments would correspond to the so-called premises in Lotze's 
 Inductive Syllogism, which ' premises ' are really only a single premise, 
 out of which Lotze takes his conclusion per saltum. If the other premise 
 were filled in, his inference would show three terms. 
 
14 The Nature of Inference [Book ii 
 
 which this same supply extends its operations. Here again 
 
 the three elements of Inference are conspicuous, though, as 
 
 we shall see, they are in any such statement exceedingly 
 
 ill-defined and their connection ill-warranted. 
 
 The 3. I have thus far been speaking of explicit Inference, that 
 
 l?'^.®/ ^ is to sav, of inference in which three or more ' terms * or 
 limit of , .,,...,,, 
 
 Infer- intellectual elements are consciously distmguished and com- 
 
 ^^^^' bined. And it is true, as I said above, that the nature and 
 phases of implicit Inference must really be gathered from the 
 whole theory of judgment which I have stated in Book I to 
 the best of my power. But a few remarks and a few examples 
 may be useful in throwing light on the modifications which 
 have to be traced. 
 
 The function of which I have attempted, in the theory of 
 judgment, to write the later history, is the activity of the 
 universal in the mind, or in other words, of the mind as the 
 universal. 
 The re- i. I have at present neither space nor competence to enter 
 produc- ypQi^ psychological controversy with reference to the so-called 
 Ideas. Association of Ideas. But it is necessary to define my position 
 by explaining that in as far as any doctrine of Association 
 involves the hypothesis of reproduction by other ideas of ideas 
 as separate particular units, i. e. the denial of real identity or 
 of the active universal, I am unable to reconcile such a doctrine 
 with logical phenomena. And logical phenomena, if we include 
 in them the judgment from its very beginning, take in by far 
 the larger part of the known phenomena of mind. I cannot 
 suppose a discontinuity — in my opinion moreover wholly 
 unmotived by experience — between distinctly logical pheno- 
 mena and the quasi-intellectual activities of primitive and 
 animal soul-life. And therefore I shall treat the fundamental 
 activity of thought as the same throughout and as always 
 consisting in the reproduction by a universal or a real identity, 
 presented in a content, of contents distinguishable from the 
 presented content, which also are differences of the same 
 universal. 
 
 It may be that in early soul-life this reproduction is uncon- 
 scious, and that its results, the images which it brings before 
 the mind, are not used as ideas, i.e. are not distinguished 
 
Chap. I] Continuity of Soul-Life 15 
 
 from fact or known to be symbolic of a content other than 
 themselves. The results of experience may be made available 
 for the guidance of action in an animal through suggestion 
 effected by reproduction, but not distinguished as suggestion 
 from any presented reality. In this process we have some- 
 thing that does the work of judgment and inference, and that 
 has the same fundamental nature with them. But it is not 
 judgment, because the images which it causes to succeed one 
 another in the mind, not being distinguished from any reality, 
 as a mere meaning necessarily is,^ cannot be affirmed in quali- 
 fication of reality.* And a fortiori such early thought is not 
 inference, because it is not judgment. Inference as we saw 
 involves assertion. 
 
 To begin with, then, we may set down the lower limit of 
 inference as at any rate not prior to the beginnings of judgment. 
 Yet even this prima facie boundary is drawn subject to a large 
 reservation on account of the primitive reproduction or 
 redintegration to which I have just alluded. The unconscious 
 extension of a sensation by reproduction fulfils some functions 
 of inference. 
 
 ii. And when we come to judgment in the strict sense, the General 
 task of drawing a line between implicit inference and what ^^ judg- 
 is not inference at all becomes an impossible one. Fortunately ment. 
 it is also, in this rigid form, an idle one. What we have to 
 say upon it amounts to this. All Judgment, we are told ^ 
 with emphasis, claims necessity. That is to say, every one who 
 makes an assertion,^ though of course he has, as a rule, never 
 heard of logic or of a ground, yet believes that he cannot 
 think otherwise than as he asserts. In full-blown Inference he 
 backs up this belief by a distinct allegation of separate but 
 connected matters which he takes to justify his conviction. 
 In implicit Inference we must distinguish the feeling that there 
 
 ^ When psychical images come to be employed for the sake of 
 a meaning which they convey, they ex hypothesi are not treated as fact. 
 And their meaning is not itself a psychical fact, but is an intellectual 
 activity which can only enter into fact by being used to qualify reality. 
 
 * On the nature of an implicit idea, which is a mere qualification of 
 sensation or perception, see Bradley, Appearance, ed. 2, 606. 
 
 * Sigwart, vol. i. p. 237. E. Trans, i. 182. 
 
 * A conscious lie is only a sham assertion, except in as far as the 
 hearer is induced to judge it true. 
 
1 6 The Nature of Inference [Book ii 
 
 is a justification from tlie incipient selection of definite 
 matters as forming the justification. It is probable that, as 
 Sigwart implies, the feeling of justification is in one form or 
 another essential to judgment. An uneducated man or a 
 child, if his perception or his memory is doubted, will some- 
 times merely reiterate his assertion. This reiteration implies 
 on the one hand that he cannot formulate any inferential 
 support for his original judgment ; he does not know how to 
 travel outside the content of his assertion in order to invoke 
 external aid. Such a phase of the judging activity is well 
 illustrated by the impersonal judgment, in which the place of 
 the significant subject which develops into the pregnant genus- 
 idea, or ground, or condition, is devoid of all content. Yet 
 on the other hand such reiteration implies an effort and failure 
 on the part of the speaker to get beyond the original content, 
 and a consequent return to that content, which is the germ 
 of the motived inability to think otherwise that constitutes 
 the necessity of inference. In such a mind, we may suppose, 
 imagination and conception do not fall apart, and his think- 
 ing satisfies the criterion of necessary truth which Mill 
 criticised as defectively explained by Whewell, in that he 
 cannot even imagine (not to speak of conceiving) the matter 
 to be otherwise than as he asserts it to be. 
 
 An educated man makes a similar justification explicit 
 when he tells us that he relies on the evidence of his senses. 
 The phrase is perhaps primarily intended to be ironical, as 
 implying that the senses give the fact and not mere evidence 
 of the fact, but its irony fails because it is strictly true. Sense, 
 though it is a fact, cannot give the fact, and is strictly, as the 
 supposed speaker calls it, evidence — circumstantial evidence 
 or datum, not ' testimony ' ^ which implies assertion. The 
 phrase ' evidence of the senses ' then, if taken seriously, 
 conveys the consciousness that sense-perception has an 
 inferential character, and rests on a necessity arising out of 
 combinations of elements among which sensation is but 
 a part or datum. When this consciousness, which experi- 
 
 ' Evidence in this application may have originally meant obviousness 
 or intuitiveness, ' Evidentia,' ' Evidenz,' and would then have no close 
 connection with the common meaning of ' evidence ' as = ' testimony.' 
 
Chap. I] Divect and Indirect Affirmation 17 
 
 ence of illusions soon forces on reflecting men, is thorougWy 
 attained, then the perceptive judgment is known to need 
 justification, but it is not known in what this justification 
 consists nor that it may lie in a connection of content appa- 
 rently going beyond the observed conjunction. Attentive 
 observation and precise interrogation of the memory are the 
 engines which suggest themselves as securing the necessity 
 of judgment at this stage. Of course these processes imply 
 a reliance on certain principles. But the inference is so far 
 formal and general, not material and specific. It is rather a 
 general conviction that perception can be relied on, than an 
 individual inference that this particular perception is rightly 
 construed to give this particular content. And therefore 
 the inference falls apart from the judgment as such, and cannot 
 be taken as an element within it. When we pass this point, 
 we come to something much more like Inference proper. 
 
 iii. Prior to Judgment, as we saw reason to suppose, the Specific 
 operation of the universal or the real identity which governs of j^^dg^ 
 reproduction is unconscious. Of course it has a result in ment. 
 consciousness, but the mind is not aware of the limits and 
 pervading ground of the process from which this result 
 emanates. I cannot say on what definite stimulus my friend's 
 name rises to my mind when I see him at a distance, not 
 being yet aware that I have recognised him, nor what is the 
 operative content which makes a certain room recall a long 
 past incident which occurred elsewhere. In the phase of 
 judgment which has just been alluded to this real identity 
 emerges into consciousness as the meaning of sentences and 
 as the active guide of perception and memory. In this 
 capacity it is attended by a necessity at first actual and then 
 perceived, which at least reveals itself (when men talk of 
 the evidence of their senses) as a partly intellectual necessity. 
 But up to this point the real identity or meaning has simply 
 been suggested and affirmed, as this or that ideal content, to 
 be true of reality, and has not within itself displayed any 
 articulated or selective character. It has shown no systematic 
 organisation to which thought could appeal as a definite 
 individual compulsion prescribing the nature of the ideal con- 
 tent which it reproduced. The matters affirmed have simply 
 
 1337-2 c 
 
i8 The Nature of Inference [Book ii 
 
 been conjoined within a unity or identity, as philosophy and 
 self-conceit may be conjoined in the same man. They have 
 not been shown to cohere as parts in an intelligible whole, 
 not, that is, as the third angle of a triangle coheres with two 
 given angles and a given side, or as personal liberty in England 
 coheres with the supremacy of law.^ 
 
 But a further principle makes its appearance, as we saw, 
 with the judgments of individual character, of ideal measure- 
 ment or of ideal enumeration. Here the universal takes on 
 the character of a system, which governs its parts on the 
 basis of its pervading nature. From this point onwards we 
 have in fact the full essentials of Inference, and it is very 
 much a question of convenience whether the inference takes 
 implicit or explicit form. So long as we retain the form of 
 direct synthesis our definition forbids us the title of explicit 
 inference. For the identification of the subject-idea with 
 reality is presupposed and not affirmed, and the qualification 
 of reality by the predicated content is therefore direct in form, 
 though indirect to a large extent in substance. ' To a large 
 extent ' only, for according to the view which I take of judg- 
 ment the affirmation in all the more genuine and natural forms 
 of assertion is both direct and indirect even in substance. 
 If I affirm ' The Czar of Russia can throw Europe into a blaze 
 by lifting his finger ' I am judging both categorically of the 
 historical individual, and necessarily or inferentially of the 
 wielder of enormous forces. And the same holds good in some 
 degree if I speak of the British Constitution, or of the force 
 of gravity. The educated mind sees an argument in judg- 
 ments dealing with these matters even without the help of 
 vocal accent and inflexion which can be used to drive home 
 the inference. From the individual judgment then, through 
 the generic, as far as the pure hypothetical which has already 
 been discussed in this context, we have implicit inference 
 which verges upon explicitness in proportion as the operative 
 ground or reason is more clearly set out in the subject-idea. 
 
 ' See Dicey on the Law of the Constitution. I may venture to 
 remark that works of this class are a valuable study for logicians, 
 because they illustrate forms of necessary connection which are not 
 dependent on geometrical perception. 
 
Chap. I] Cross-veference 19 
 
 The generic judgment shows the union of the two types in 
 its fullest significance. The individual content here claims 
 to be a presupposed qualification of reality, and therefore, 
 as reality, has the predicated content directly identified with 
 it ; while the very same self-complete organisation which 
 entitles the subject-content to be taken as real, also enables it 
 to demand the predicated content as a necessary consequence, 
 and to act as a middle term attaching this content indirectly 
 to reality. ' Poetry is a form of art which employs ideas as 
 the medium of representation.' Here we are at once qualifying 
 a reality and drawing an inference. 
 
 iv. These principles may advantageously be elucidated by The true 
 the example of what might be called the true immediate ^-^^^^ j^. 
 inferences, which may properly be mentioned here on the ferences. 
 threshold of Inference. I refer to such processes as Recogni- 
 tion, Abstraction, Comparison, Identification, Discrimination. 
 All these titles are obviously drawn from characteristics 
 which in a certain sense no judgment or inference is without, 
 and which reciprocally imply one another.^ But they also 
 can be and are used as names of processes, of cases of the 
 judging activity, in which one or other of its aspects asserts 
 itself par excellence. They are cross divisions to the progressive 
 stages of judgment which were described in Book I, and 
 might be spoken of, though not with equal appropriateness, as 
 present in all these stages short of disjunction. They are 
 separated from one another and from other forms of judgment 
 rather by practical and methodological than by strictly logical 
 distinctions. 
 
 a. Comparison is a good example. The Comparative Compari- 
 Judgment, as described in Book I, fills an important place ^°°* 
 in logical evolution. The variations of a common quality 
 between more and less are the simplest explicit case of identity 
 in difference. But the reflective comparison of common life 
 both stops short of and goes beyond what I have called the 
 comparative judgment. Comparison in the ordinary sense 
 is a name applied to the intentional cross-reference of two or 
 more given contents, in order to establish, between those 
 contents as given, a general or special identity, difference, 
 
 '■ See Introduction,, sect. 5. 
 C2 
 
20 The Nature of Inference [Book ii 
 
 or partial identity (likeness). And with the establishment of 
 a relation of equalit}^ or of quantitative difference which im- 
 plies equality {a > h implies a = h-\- x), popular comparison 
 diverges into equation, in which the cross-reference is retained 
 throughout. The equation is essentially comparative. You 
 cannot say ' a is equal ' any more than you can say ' a is the 
 same '} In Comparison, identity &c. is stated as a result, or else 
 very strongly implied, in an abstract form. If it were made 
 concrete and definite the cross-reference to the contents as given 
 would be superfluous or impossible, other and profounder 
 standards being introduced and the contents having no longer 
 their original shape. The result required in comparison is such 
 as ' A is like B '. If we say ' A and B are both red ', this too is 
 comparison in virtue of the cross-reference implied in ' both '. 
 But if we say ' A is red and B is green ' w^e are passing out 
 of the process popularly called comparison into ordinary 
 investigation, aimed not at a particular cross-reference, but 
 at developing the facts which may come to hand. And if 
 we go to * All a (including a and h) are coloured surfaces ', 
 the original data have disappeared, and comparison in the 
 popular sense has become impossible. When the process has 
 justifipd in the concrete the abstract idea which guided it, 
 it has put an end to its own raison d'etre and passes into the 
 normal operations of knowledge. 
 Abstrac- /j. Abstraction, again, affords an example worth con- 
 sidering. Abstraction in general is the necessary conse- 
 quence of definite thought, and indeed of all definite activity. 
 All activity has its restrictions and limitations, selects and 
 omits, and is so far abstract. But though all thought is" abstract, 
 yet all thought need not be abstraction as a special process. 
 Abstraction in this sense is a methodic activity guided by 
 a special reflective idea, the idea of obtaining the part out of 
 the whole by omission of other parts. The whole is theoreti- 
 cally always, and practically often, more knowable than the 
 part. It is easier to say that 99 x 5 = five hundreds minus 
 five units, i.e. 495, than to multiply out ninety-nine by five. 
 Subtraction may be regarded as the specific term for abstrac- 
 tion when the latter deals with the parts of a homogeneous or 
 
 Cf. Sigwart, i. p. 85 ; E. Trans, i. p. 69. 
 
 tion 
 
Chap. I] Inference fvom Abstraction 21 
 
 quantitative whole. The hydrostatic explanation of the cup 
 which retains the juice in a fruit-tart is an example of abstrac- 
 tion ^ which obtains knowledge of one aspect of a hetero- 
 geneous whole by omittnig all the rest. But the examinee 
 who added that for the atmosphere to sustain the liquid within 
 the cup it was necessary that the cup should not be more than 
 thirty feet high had passed from mere abstraction within the 
 given whole to independent consideration of the hydrostatic 
 relation involved in the example. 
 
 Abstraction, then, like Comparison, when considered as a 
 method par excellence, is one of the processes by which Reason, 
 armed with reflective ideas, breaks into concrete data in 
 search of the unity of the universal. The reflective idea which 
 guides it is the equivalent in general knowledge of the mathe- 
 matical axiom that if equals are taken from equals the re- 
 mainders are equal. Withdraw a known relation from a known 
 system of relations, and the relations which remain are known. 
 It is plain that if the whole and its internal relations are really 
 known so as to justify such a process, the withdrawal is a 
 mere intellectual or ideal distinction. This is so even in 
 mathematics. To know the difference between two quantities 
 is the same as to know the greater as the sum of the lesser 
 and the difference. An algebraical sum treats subtraction 
 and addition as on a level. Abstraction would thus seem 
 primarily to restrict itself to instances where, as in mere 
 numerical conceptions, the withdrawal of a part leaves the 
 other parts unaffected. But as this is never within any real 
 whole theoretically the case, although by compensation or 
 in loose-knit wholes it may seem to be so, the instances 
 envisaged by abstraction occupy in truth no separate region 
 from those which form the matter of all definite knowledge. 
 Thus the guiding idea of abstraction is only a provisional idea. 
 It amounts to no more than this, that within known wholes 
 
 ' In saying this, I do not mean that the system of laws which an 
 investigation, beginning with such an abstraction, ultimately brings 
 to light, must be more abstract than the example which is the datum. 
 The semi-logical and almost arbitrary character of these methodic pro- 
 cesses as popularly limited is illustrated by the fact that abstraction, as 
 in the case before us, so easily slides into systematic construction which 
 leaves the example behind. 
 
22 The Nature of Inference [Bookii 
 
 known changes may appear to leave remainders known as 
 unchanged. For to say, as we said above, simply ' known 
 remainders ', really lets in all that positive knowledge can tell 
 us of the positive effects produced by the change on what 
 remains. In this we go beyond abstraction. The supposed 
 unchanged remainder, then, is predicated of the whole as 
 modified by the withdrawal of some parts. 
 
 But really of course the abstraction is not what operates. 
 Neither real nor ideal abstraction can help except by con- 
 ferring or illustrating knowledge of the real whole in question. 
 ' The Parnellites are chief men in Ireland, and were Ireland 
 separated from England would be chief men still.' But 
 li'oiild they ? The abstraction puts the question, but does 
 not answer it. The answer depends on our knowledge of 
 Ireland. ' He has lost his wife and yet goes on much as before, 
 therefore her loss has made no great change in him.' But 
 perhaps in removing one motive to his habitual acts the loss 
 supplied another. The inference even from this actual abstrac- 
 tion is utterly baseless except as a conclusion from our know- 
 ledge of the whole man, to which of course the new fact created 
 by the actual abstraction must contribute. But had we had 
 such knowledge before, we could have gone to the conclusion 
 without the actual abstraction ; and apart from such know- 
 ledge we cannot go to the conclusion on the basis of the actual 
 abstraction. 
 
 From the difficulty of bearing in mind the necessity, 
 often extremely obscure, of this circuitous route through the 
 nature of the whole, and the inapplicability of mere subtraction 
 in the complicated relations of non-mathematical reality, 
 abstraction is perhaps the most fruitful in mistakes of all 
 methods of knowledge. Knowledge in fact is one, and any 
 method which consists in the exaggeration of a mere charac- 
 teristic of knowledge is ipso facto hazardous. 
 
 Recog- y. Recognition^ is another of these curiously limited pro- 
 
 nition. 
 
 ' I restrict recognition to the elementary meaning of knowing again. 
 The ' recognition ' of a right or a principle, i.e. the admission of it, has 
 interesting connections with the former case both in Logic and in 
 Philology, and illustrates the ease with which these ' processes ' pass 
 beyond their normal sphere into knowledge in general. But it is truer 
 to usage to regard this latter import as metaphorical. 
 
Chap. I] Limits of Recognition 23 
 
 cesses. In its complete form it appears to be reflective re- 
 production under the influence of an idea of identity, followed 
 by comparison and identification of the content reproducing 
 with the content reproduced. Recognition differs from Per- 
 ception and from Inference as such both by dealing with 
 a reproduced content, and by always ending in a direct 
 comparison of contents. We do not speak of recognition 
 either where there is no reproductive process, or wheie the 
 process, though it may establish identity, does not end in 
 direct comparison. When we meet a friend whom we see 
 every day, there is no process of reproduction ; the extension 
 of the sensations is given along with them and the apprehension 
 of his identity is a datum of perception. For true recognition 
 to take place, it would be necessary that the first datum 
 should create a second, on which two data the further process 
 would operate. But in Inference the two data may just as 
 well be given ; and this is also the case of course with mere 
 Comparison. On the other hand, if I ask for a tune of which 
 I know the name, but fail to recognise it when it is played, 
 then I have inferential identification without recognition. For 
 of course I know, supposing that I am confident in my recollec- 
 tion of the name and in the pianist's knowledge, that it is 
 the same tune which I asked for ; but, when played, it fails to 
 reproduce the desired effect in my mind, and either there is 
 nothing to compare, or if I compare the tune I hear with my 
 idea of the tune I wanted, the result is distinction and not 
 identification. Thus recognition is absent, though inferential 
 identification is present. Inferential identification, however, 
 though ever so circuitous, may set up a direct comparison 
 ending in identification, and if so, then we have recognition. 
 This is too common an experience to need illustration. 
 
 The reflective influence of the idea of identity may be 
 active in recognition to very different degrees, and the idea 
 itself may be suggested in very various ways. Probably these 
 ways may all be included under imperfect reproduction. An 
 interest in identification is necessary to make the idea work ; 
 but an interest can only operate in logical thought by attaching 
 to a suggested content. Our interest in recollecting a man's 
 name operates through the natural but unsuccessful efforts at 
 
24 The Nature of Inference [Bookii 
 
 reproduction, in which a prominent syllable of the name, or 
 the like, occurs to us. And like the rest of these methodic 
 processes, recognition loses its differentia when the abstract 
 relation between the special contents in question ceases to 
 interest. It is recognition to say ' That is the man who was 
 with me in the train yesterday '. It may or may not be 
 recognition to say ' That is Professor Huxley ', for this is a 
 matter of fact which I may infer otherwise than by direct 
 comparison, and which may not at all be meant to indicate 
 an identity with a special content reproduced in my mind. 
 And when I go deeper into knowledge and say ' Professor 
 Huxley is one of the leaders of scientific thought in Europe ' 
 I have altogether got beyond recognition pure and simple, 
 because the interest is no longer that of mere identification 
 but of concrete description. 
 Discrimi- 8. Discrimination and Identification, and many other 
 ^^ ' methods or processes, might be analysed in the same way. 
 All of them are in one sense characteristics of Inference or 
 Judgment as such, and therefore enter into each other and 
 into the various processes which have just been described. 
 But each of them may also be regarded as a special though 
 transitional method, guided by a more or less reflective idea 
 of the result to be obtained, and subsuming under this reflective 
 idea all matters in the content which are favourable to its 
 purpose. Discrimination or Distinction is present in all judg- 
 ment, in all inference, in all comparison, and in all recognition. 
 But it would be pedantry to deny that we constantly set to 
 work upon a presented content or two contents as yet un- 
 examined, with the clearly envisaged purpose of making out 
 a contrast or difference which we expect to find between them. 
 Two Acts of Parliament on the same subject ought to deal 
 with different aspects of it, and we may fairly set ourselves 
 to distinguish the purpose and provisions of the one from the 
 purpose and provisions of the other. What we have to keep 
 clearly in mind is that the name Distinction is a title drawn 
 from a merely dominant and not exclusive characteristic, that 
 it therefore is not a desirable basis of logical discussion ; and 
 that the process of Distinction itself is transitory, because it 
 can only continue as such so long as the result is abstract, and 
 
Chap. I] Sctenccs of Cross-veference 25 
 
 so long as our interest attaches rather to this abstraction than 
 to concrete and material content. 
 
 e. There are thus two principles which limit the inferen- Inference 
 tial and non-inferential character of the practical processes t^ocesses 
 which we have been considering. As processes guided by 
 reflective ideas, they must necessarily involve grounded selec- 
 tion ^ resting either on presupposed subsumption ^ or on general 
 connection of content. And when we have grounded selection, 
 we have, as we saw, the essentials of -inference — we have at 
 least a suggested distinction between direct and indirect refer- 
 ence to Reality. On the other hand, the abstract and therefore 
 accidental character of the controlling ideas renders it impos- 
 sible that explicit inference should form the essence of these 
 processes. The moment we really found our argument on 
 an explicit ground going deep into the nature of the subject 
 we get a conclusion that must go beyond mere identity, like- 
 ness, or distinctness, which with one modification or another, 
 but always in more or less abstract form, are the guiding ideas 
 and interests of these subordinate methods of knowledge. 
 
 (. If the above processes, including Comparison, are Compara- 
 arbitrary and vanishing phases of knowledge, how do we come science, 
 to speak of Comparative science ? 
 
 The Comparative sciences are the sciences of organic and 
 intellectual evolution through its varied series and ramifica- 
 tions. Their data are thus, in the first place, actual, inde- 
 pendently of the operations of the science, and in the second 
 place are essentially types relative to definite functions, and 
 
 ' For the guiding idea operates through a selection within the content. 
 
 ^ When I recall a man's name on seeing him, this recognition is not 
 based on a necessary connection of content. But the accepted identi- 
 fication or subsumption of the man under his name in which I rest when 
 the name is reproduced is as good ad hoc as such a connection. The 
 reflective idea of identity guides me to select characteristic marks in 
 the presented content, which I subsume under that idea. ' That gait, 
 voice, gesture, is surely a help to his identity.' Then if I succeed in 
 reproducing anything not present, this reproduced content goes up to 
 fill up the idea of identity. 
 
 ' That face of his I do remember well ; 
 But when I saw it last it was besmeared 
 As black as Vulcan in the smoke of war,' — 
 and then a whole history comes up and mere identity gives place to 
 description of character. 
 
26 The Nature of Inference [Book ii 
 
 so not as a rule capable of being illustrated by the results of 
 direct ^ interference. Hence it follows that the sciences in 
 question (i) begin with cross-references between their actual 
 data — the method of ordinary comparison — and (ii) retain 
 their data untransformed in these cross-references — a leading 
 peculiarity of ordinary comparison. 
 
 On the other hand, the abstract ideas of identity, difference, 
 &c. which guide ordinary comparison could not form the 
 content of any science ; and the comparative sciences go 
 beyond ' comparison ' by seeking for definite concrete princi- 
 ples of evolution and affiliation between the types with which 
 they deal. 
 
 All science, of course, compares ; but chemistry, for example, 
 is not ' comparative ' in the above sense. It does not begin 
 by cross-references of mercury to carbon and of carbon to gold, 
 as philology does with Latin and Greek, and Greek and San- 
 skrit. Chemistry has to create its regular series of phenomena 
 by experiment before it can lay down principles that connect 
 them, and each series at first concerns the nature of a single 
 group of substances only. The data, as data of science, are 
 not actual. And chemistry does not in its generalisations 
 retain its data untransformed. The underlying principle, the 
 molecular or atomic hypothesis, is the essence, the element of 
 rationality and of interest. In its results, as at its starting- 
 point, it would be sheer distortion to call chemistry a com- 
 parative science of elements and their compounds. It is an 
 analytic enquiry into the fabric and behaviour of matter. 
 The elements and their compounds have no individual or 
 characteristic value like that of a language, or a polity, or a 
 group of myths. In short, in the sciences which are analytic 
 par excellence the rationality and interest are on the side of 
 the underlying principle, while in comparative science the 
 underlying principle serves rather to connect and illustrate 
 realities which have independent functional importance. 
 Science is one, and these distinctions are matters of degree. 
 But even should chemistry ever succeed in representing its 
 data as evolutionary products of an intelligible process and 
 
 * Variations of animals under domestication are hardly for this pur- 
 pose to be set down to direct interference. 
 
Chap. I] The Identity in Induction 27 
 
 so as thenceforward challenging comparison ah initio, still this 
 will be an ultimate achievement and not a method pursued 
 throughout. Geometry, as we saw in treating of the quasi- 
 generic judgment, mimics evolutionary procedure with some 
 success. But its data in their pure form are really made, not 
 given as realities of independent significance. 
 
 4. I will now attempt to exhibit in their true light some Species of 
 species of Inference, each of which has in turn been erroneously ^fJh"^* 
 identified with its principle. have 
 
 i. Induction in Mill's sense of the term, i. e. Induction by treated 
 
 incomplete enumeration, or inference from particulars to as its 
 
 particulars, is obviously to be identified with the species of ^ 
 
 inference in which a confused or implicit universal, indicated particu- 
 
 by a common name, is the ground in mediate assertion re- ^a^^s to 
 
 •^ . . . particu- 
 
 specting concrete things or events. I do not mean to examine lars. 
 
 here the case of Induction by complete enumeration, which 
 has in fact been sufficiently illustrated by the analysis of 
 enumeration in Book I.^ It is enough to remark that if this 
 Induction really relies on the completeness of its enumeration, 
 it ceases ex hypothesi to be Inference. If, again, it relies on 
 some discovery made during the enumeration, then the 
 completeness of the process is without influence on the result. 
 In the Induction by incomplete enumeration, or inference 
 from particulars to particulars, in which Mill finds the 
 fundamental process of inference as such, there is apt to be 
 at first sight nothing at all which binds these particulars 
 together. The pervading identity or universal, which we 
 affirm to be the operative power in inference, often appears 
 in popular practice as in Mill's theory, to be simply non- 
 existent. That is to say, it either creeps in under the shelter 
 of a mere common name, or may even be absolutely ignored 
 in the expression of our inference, because the common name 
 which would express it is presupposed, or perhaps is not 
 known or does not occur to us. ' Why do you think A likely 
 to be a good scholar ? ' ' Well, because B and C and D are 
 good scholars.' Here it is plain that something known to both 
 speakers is presupposed and not expressed ; perhaps for 
 example the fact that A, B, C, and D were educated at the 
 ^ See Bk, I. chap. iv. 
 
28 The Nature of Inference [Book ii 
 
 same school. But often the operative identity is left unex- 
 pressed not because it is clearly understood, but because we 
 do not think it definitely at all. ' Why do you think that 
 picture is by Mantegna ? ' ' Because it reminds me of some 
 pictures of his in the National Gallery.' Here the words 
 ' reminds me ' appeal to a merely psychical fact,* and express 
 in doing so my inability to produce a distinct formulation of 
 the ground on which I have gone. 
 
 Thus we are presented with something like an antinomy. 
 Identity is necessary to Inference, but some Inference takes 
 place without Identity. 
 
 The explanation of this contradiction, as distinguished frorn 
 the logical justification of Inference from particulars to 
 particulars, is afforded by what has been said about the 
 ultimate nature of Inference. The ' particulars ' are not par- 
 ticulars, but differences in a universal. The universal, however, 
 which in elementary reproduction operates unconsciously, may 
 in elementary inference be very far from explicit in thought ; 
 or, and this is by far the commoner case, there may be an 
 obvious deep-seated identity in the nature of the concrete 
 instances, which is not in its entirety relevant to the attribute 
 about which we draw our conclusion. Then, in accordance with 
 the principle of analogy, we follow the dominating identity, 
 and come to a result the precise or relevant ground of which 
 we are unable to ascertain. The conception of inference from 
 particulars to particulars is thus an illusion arising from the 
 activity in inference of presupposed, superficial, or unanalysed 
 universals. 
 Subsump- ii, Subsumption is the complement of inference from par- 
 ticulars to particulars. I speak here as above of the natural and 
 normal process, and not of the process by completed enumera- 
 tion, which is devoid of inferential character. Subsumption is 
 based on the conjunction of attributes in the actual concrete 
 nature of a subject or subjects. The identity of nature which 
 is implicit in inference ' from particulars to particulars ' is 
 here made explicit in the content of an individual or indi- 
 
 * I suppose it may be either a psychical fact or an indefinite meaning 
 — either a mood of mind, or a something in the actual painting which 
 I see but cannot express in words. 
 
Chap. I] SuhsumpHon and Calculation 29 
 
 viduality. But this identity, though seldom wholly destitute 
 of inferential significance, is in jespect of the conjunction of 
 attributes within it a confused and not a scientific concrete. 
 The connection of the attributes is proved by it not as a 
 principle but only as a fact. Of course, however, an inference 
 which is really matter of principle may borrow the shape of 
 subsumption, and in doing so may or may not continue to 
 imply a principle that really goes beyond subsumption. The 
 relation between inference from particulars to particulars and 
 its complement subsumption is thoroughly illustrated by 
 Mill's discussion of the subsumptive syllogism. Putting aside 
 the notion of a peiitio principii, which only applies when the 
 major premise in Barbara is regarded as a complete enumera- 
 tion, we find that the major premise consists in an explicit 
 enunciation of the common nature which really warrants the 
 conclusion. Mill regards this enunciation only in the light 
 of a summary of particulars, and as we have seen, the facts 
 of rudimentary reproduction and even of elementary inference 
 bear him out in the view that it is not indispensable. The 
 point however is, that though the enunciation itself is not 
 indispensable, yet the operation of that identity which the 
 enunciation formulates is indispensable. It is this which, in 
 the form of an ideal content considered as a subject qualified 
 by attributes, is the point of union in subsumptive inference. 
 Here again the nature of the active universal determines the 
 inferential form. 
 
 iii. Calculation is a divergent form of subsumption, in Calcula- 
 which, by passing through the stage of complete enumeration, ggu^t^on, 
 the universal operative in the inference has been transformed 
 from an ideal content existing in individuals to a totality 
 where parts are units. The concrete individuality, i. e. the 
 common generic nature of the individuals, has faded away 
 by abstraction into a mere denomination of units, and the 
 attributes which were conjoined within the generic content 
 have also become denominations of the numerical wholes. 
 These numerical wholes which have arisen out of the ' extension ' 
 of the ideal content by means of enumeration are related to 
 each other as measurable parts and wholes in the system of 
 number. Thus the subsumptive syllogism, ' All Englishmen 
 
30 The Nature of Inference [Book ii 
 
 are Europeans, all Londoners are Englishmen, therefore all 
 
 Londoners are Europeans,' may be seriously taken in the 
 
 aspect of extension, which through the affinity between the 
 
 individual and the unit is always closely allied to the aspect of 
 
 number. But to carry this aspect to a genuine result we must 
 
 not simply say ' Englishmen = English Europeans ', &c. &c., 
 
 for the insertion of ' English ' in the predicate makes the sign = , 
 
 which implies restriction to the aspect of number, superfluous 
 
 and meaningless. And if we do not use =, but retain the 
 
 copula ' are ', then the repetition in the predicate goes a long 
 
 way to destroy the meaning of the judgment by reducing it 
 
 to a tautology. 
 
 Calcula- ^ jf ^g seriously intend to draw a conclusion from the 
 
 tion 
 
 proper, relation of individuals as units, i. e. apart from their content 
 
 except in so far as it distinguishes them into groups, we must 
 first constitute each of our wholes into a numerical whole by 
 complete enumeration, and then refer these wholes to one 
 another in respect of their measurable identity or want of 
 identity, i. e. equality or inequality, which latter, as we saw 
 above, being assignable as an exact difference, involves the 
 former. Then we should get something like Englishmen = ^^ 
 Europeans, Londoners = \ Englishmen. That is to say, 
 Londoners, numerically considered, are a part that repeats 
 itself four times in the numerical whole of Englishmen, and 
 Englishmen numerically considered are a part that repeats 
 itself twenty times in the numerical whole of Europeans. 
 Thus the same numerical whole presents itself as thoroughly 
 identical with itself in its differences or different relations, 
 whether as the number of Englishmen, obtained by simple 
 enumeration, or as four times the number of Londoners, a 
 relation obtained by comparison of enumerations and analysis 
 of a sum into its parts, or as a twentieth part of the number 
 of Europeans, a relation obtained in the same way as the last 
 mentioned. The quantitative universal, which is the same 
 in kind throughout all its different aspects — not distinguish- 
 able as a subject controlling attributes and as attributes that 
 severally do not exhaust the subject — is thus an embodiment 
 of the rule, ' Things which are equal to the same thing are 
 equal to each other.' Calculation is mediate judgment, in 
 
Chap. I] Culculus at secoud-hand 31 
 
 which, from the nature of the whole that operates, there is no 
 distinction between subject and predicate. 
 
 It is obvious therefore that Calculation cannot be applied 
 to wholes that consist of heterogeneous or non-quantitative 
 parts, or at least, if so applied, can only deal with them in 
 their aspect, probably a subordinate one, of homogeneity. 
 If the number of lines in Macbeth is y^th of the number of 
 lines contained in all Shakespeare's plays together, what 
 then ? The relation of Macbeth to the other works of Shake- 
 speare's mind must be expressed by other universals than this. 
 There have always been logicians whose gaze has been fasci- 
 nated by the simplicity and certainty of calculative processes ; 
 but it is idle to place the ideal of argument in a type which 
 depends on the relations of identical units. The tendency 
 to acquiesce in this ideal has no doubt been strengthened by 
 the absolute reciprocity of the equational judgment, which 
 has been explained above. This reciprocity anticipates, 
 though at a long interval, a prominent attribute of notional 
 definition or of any complete and concrete knowledge ; and 
 this anticipation of a characteristic which is rightly ascribed 
 to the logical ideal has increased the attractiveness of com- 
 putative or quasi-computative processes as types of logical 
 method. 
 
 j3. The importance of the Equational logic is so great Equa- 
 that I will return for a moment to its principle, which has **°°.^1 
 been cursorily alluded to on the previous page. The point of 
 logical interest in regard to it is that it is not at first hand a 
 calculus at all, though it is a calculus, and a very effective one, 
 at second hand. In this respect it is of the same grade as 
 the calculus of chances, with which it is closely allied. By 
 saying that the logical calculus is not a calculus at first 
 hand, I mean that the judgments with which is deals are not 
 judgments that embody numerical or quantitative relations 
 as such, and therefore, as was shown above, have no fair 
 claim to the sign = as copula. This is absolutely clear of the 
 judgments which Jevons calls Partial Identities, in which the 
 employment of the sign = is not in accordance with usage. 
 It is not intelligible to say ^ that Iron = a metal, or that 
 * Principles of Science, p. 40. 
 
32 The Nature of Inference [Book ii 
 
 Diatomaceae = a class of plants, or that Mammalia = a class of 
 vertebrates. These judgments are obviously subsumptive 
 judgments, intended to express the conjunction of certain 
 attributes in certain individuals, or else the identity of 
 certain sets of individuals under certain different aspects or 
 descriptions. But the sign = does not express this conjunction 
 of attributes or identity of individuals, except as the attributes 
 or identity of a quantitative whole, and as on the other hand 
 the judgment suggests no obvious quantitative aspect, weight 
 or number or value, in which identity can be asserted, it 
 follows that the form of the judgment simply contradicts its 
 content, i.e. the judgment is not intelligible. 
 
 With Simple Identities the case is somewhat different. It 
 is not indeed intelligible to say that ' Lord Salisbury = 
 the Prime Minister of England ', or that ' St. Mary's Church 
 at Oxford = the University Church'.-^ But it is intelligible 
 — I now take Jevons' examples of simple identities — that 
 ' The smell of a rotten egg = that of hydrogen sulphide ; ' and 
 that ' The colour of the Pacific Ocean = the colour of the 
 Atlantic Ocean'. And the reason why it is intelligible is this. 
 It is possible to interpret these judgments as establishing 
 identity of degree ^ in a quality capable of variations ; i.e. 
 quantitative identity or an equation of colours or of smells. 
 And by a metaphorical usage based on this fact identical 
 conceptions, though not strictly quantitative, are sometimes 
 said to be equivalent, and this equivalence is rudely symbolised 
 by the sign of equality. But the point to note is that equiva- 
 lence cannot be affirmed on the ground of individual identity. 
 It means equal amount and kind of intension, and does not 
 
 * Unless we meant to affirm that Lord Salisbury when Prime Minister 
 retains, for example, his normal height and weight ; or that St. Mary's 
 when considered as the University Church suffers no diminution of size. 
 It might be urged that this is worth considering, for of Merton Chapel, 
 if I remember right, a parallel assertion would be untrue, the choir 
 being a college chapel, and the church as a whole a parish church. 
 
 ^ Jevons does not in the least distinguish true intensive equation, 
 as in a colour match, from identification of individuals or classes of 
 things in a sense quite beyond quantity. He fails to distinguish Quality 
 from Kind or Individuality. Hence ' Deal = Landing-place of Caesar ' 
 is to him a ' simple Identity ', no less than ' Colour of Pacific Ocean = 
 Colour of Atlantic Ocean '. 
 
Chap. I] Equutional Logic is subsumptive 33 
 
 mean identity of component individuals. Thus it is simply 
 false that * Exogens = Dicotyledons ', for the meanings are 
 not equivalent, though the individuals designated by the 
 names are, excepHs excipiendis, the same. 
 
 In the first instance, therefore, the judgment as formulated 
 by the Equational logic is not an equation, because it does 
 not restrict itself to a quantitative aspect, but predicates 
 individual identity. Although you say that Diatomaceae = a 
 class of plants, you may not go on to say that this class of 
 plants = another class x (meaning that the two are equal in 
 number), and that therefore the Diatomaceae = the class x. 
 The original judgment might indeed happen to justify this 
 calculation, but in passing through it would have entirely 
 lost its peculiar import. 
 
 The office of computation in the Calculus is not to compare 
 quantitative attributes of objects, but to secure complete 
 enumeration of possible judgments. In this office of secondary 
 import it somewhat resembles the translation of a material 
 disjunctive judgment into a numerical statement of chances. 
 But the statement of chances gives a numerical result, whereas 
 the logical calculus, after protecting itself by a computation 
 of combinations, returns to a result in the shape of identifica- 
 tion or identifications. Working as it does solely by the 
 identification of individuals under different aspects, i. e. as con- 
 joining in themselves different attributes, the equational logic 
 is obviously a species of subsumption, and rests ultimately on 
 the subsumptive principle that attributes conjoined in the 
 same individual are conjoined with each other. Thus in regard 
 to the nature of the universal which is operative in inference 
 through the calculus, there is little to say beyond what has 
 already been said in dealing with subsumption. The only 
 peculiarity of this species of subsumption is that in it the 
 undefined capacities of subsumption as such for conveying 
 connections of principles are cut down to the most abstract 
 expression of individual unity, without being allowed to 
 develope in the direction which such abstract unity naturally 
 suggests, viz. that of participation in a numerical whole. 
 
 iv. ' Construction ' * is a term frequently applied to a method 
 
 * Cp. ii. 3 19 note below on the relation of this passage to vol. i, p. 42 If. 
 
 1337-2 D 
 
34 The Nature of Inference [Bookii 
 
 Construe- or element of inference, a. It primarily indicates an auxiliary 
 Physical, process employed in geometrical or mechanical reasoning. 
 This process consists in making accessible to perception a 
 geometrical or mechanical complex of relations which embodies 
 a problem or theorem that is under consideration. The actual 
 physical construction — a diagram on paper or a model or 
 experimental machine ^ — though not ideal, but an object of 
 sense, is nevertheless abstract in its sensuousness, being pur- 
 posely cleared of the irrelevancies which encumber our 
 ordinary perceptions. And further, the nature of space is so 
 closely related to sense-perception, that ideal spatial relations 
 can be adequately sjnnbolised by actual figures presented to 
 perception, although the ideal relation underlying a theorem 
 is always both more and less than the visible or tangible lines 
 and points. * More,' because the visible lines can be but 
 a case of the ideal relation ; ' less,' because the perceptible 
 lines, though reduced to black on white, still include errors 
 and irrelevancies which the mind in working with them 
 disregards. The case of a working model or machine made 
 to experiment with is at first sight different from that of a 
 mere diagram. But the difference is only in degree. Both 
 the diagram and the machine are really in pari materia with 
 that which they represent to the mind ; the diagram with 
 ordinary perception, the machine with ordinary physical 
 causation. But it is harder to say where the line is to be drawn 
 between fact and representative of fact in the case of the 
 machine, which shades off gradually into the ordinary opera- 
 tions of nature. Such a thing however as a working model ^ 
 that illustrates the lever action of the limbs shows how 
 the machine as such stands between natural process and 
 abstract mechanics. It is the abstract physical expression for 
 
 ' An excellent example of construction in this sense, the solution of 
 a problem in actual physical embodiment, is the machine for drawing 
 sound curves of any shape by actual pendular oscillations. There is 
 such a machine, I think, with actual pendulums, which thus does not 
 merely mimic the curves (as the machine with cog-wheels may be said 
 to do), but actually constructs them in terms of the theory. 
 
 ^ A complete model of the ear or eye may seem not to be abstract, 
 but only magnified ; it is however abstract by its isolation from other 
 parts, its fixity, and its capability of being taken to pieces. 
 
Chap. I] Construction aids Abstraction 35 
 
 a natural activity, and paves the way for its abstract ideal 
 expression. 
 
 Construction in this first and simplest sense is not even a 
 case or species of Inference. The production of a visible 
 material figure or object does not even, strictly speaking, 
 enter into the essence of the inferential process. It is however 
 a peculiar auxiliary method which depends upon and throws 
 into relief the characteristic nature of the universal — the 
 abstraction of sense — ^with which Inference is concerned in 
 Geometry or abstract mechanics. The lines drawn on paper, 
 though peculiarly adequate symbols, are nevertheless only 
 symbols of the lines with which geometry actually works. And 
 of course we do not draw the lines on paper at random, and 
 they would be of no use if we did. We only draw them in 
 accordance with the requirements of the universal operative in 
 the inference, so far as these requirements are already known 
 and can guide us from moment to moment. The aim is to aid 
 intellectual reflection in fixing and following connections which 
 suggest themselves within that universal ; and as we have 
 seen, the material lines or even cords, pulleys, levers, &c. 
 represent an intellectual work already partly accomplished 
 in the exclusion of irrelevant elements. But the material or 
 physical construction is not the active element in the accom- 
 plishment of this work. This construction in the sense of actual 
 drawing or model-making is a process characteristic of geo- 
 metrical or mechanical inference, but not identical therewith. 
 
 ^. But this brings us to a secondary sense of construction imagina- 
 — secondary not in logical value, but, as I think, in usage and *'^^- 
 the growth of meaning. Of course actual lines on paper are 
 not essential to simple geometrical inference in which we can 
 ' carry the figure in our heads ', and if so, the visible external 
 figure cannot in theory be essential to any such inference. 
 Professor Clifford, it would appear, was almost independent 
 of external aids to realisation in considering geometrical or 
 physical problems. But when we work with ideas of lines, 
 and combine spatial elements in our imagination, and not on 
 paper, is not this still construction, and yet is it not now of 
 the essence of inference ? 
 
 I fear that at this point a further refinement cannot be 
 
 D2 
 
36 The Nature of Inference [Bookh 
 
 avoided. It seems to me obvious that the imaginative experi- 
 ment is a different thing from the intellectual perception of 
 unity. The imaginative experiment may be misdirected and 
 void of result, as a line drawn on paper in addition to an actual 
 diagram may be irrelevant and meaningless. The imaginary 
 line projected on imaginary paper, though necessary perhaps 
 to the intellectual apprehension, is it seems to me purely on 
 a level with the external line perceived through sense. But 
 when any line either given on paper or suggested in imagination 
 has been intellectually grasped as symbolic of a relation 
 relevant to the universal which we are developing, then it is 
 taken up into the inference and has passed from a step in 
 physical or imaginative construction to an element in necessary 
 apprehension. In looking for that point in an eUipse in which 
 the sun had to be placed in order that the ellipse might 
 represent a planetary orbit according to the theory of gravita- 
 tion it is easy either in imagination or on paper to select the 
 middle point of the longer axis. The question as to the nature 
 of the process is not whether I draw or only imagine, but 
 whether in doing either one or the other I am guided by 
 insight into the connection of the data and into the con- 
 ditions of the problem. If I seem to myself to have such 
 an insight, but am, as in the case above-mentioned, mistaken 
 in the connection which I fancy that I detect, then I infer, but 
 wrongly. If however, or in as far as, I put the sun in the 
 wrong place or in the right place by an isolated act of sensuous 
 fancy, then I may be constructing, but I am not inferring. 
 Intellect- y. The organised or articulated intellectual perception 
 ual, in itself, in contrast with the physical or imaginative experi- 
 and ment — or rather taken as including this experiment, for the 
 
 Mechan- ggnsuous ideas cannot be dispensed with — ^affords a third 
 meaning which may be put upon construction. Of course 
 this perception has the effect of a synthesis, of a putting 
 together as well as of a distinguishing. And especially when 
 the relations thus put together as having their unity in one 
 universal are spatial relations, readily symbolised by imagina- 
 tive pictures, there is a plausibility in translating the Greek 
 term ' synthesis ', which in technical logic expresses the unity 
 of differences inherent in all intelligible judgment, into the 
 
Chap, i] Intention in Inference 37 
 
 term of Latin origin ' construction ', which may be held to 
 express this same idea with the additional implication of 
 intentional operation in time, by which elements of intellectual 
 perception are put together like the parts of a machine. 
 
 Construction in this third sense, a sense largely insisted 
 on by Kant, is a hybrid idea. I cannot doubt that it designates 
 a true species of inference — inference dealing with the abstrac- 
 tions of sense — by a title actually drawn from and implying 
 an accident of inference, viz. intentional combination, successive 
 in time, of visible or imagined forms. Now the intention, 
 except in as far as it is a general intention to infer correctly, 
 falls outside inference. In inference nothing can guide us 
 but inferential necessity ; and a special intention, such as 
 that of drawing a line on a slate or on paper, or of constructing 
 a model of a joint, arises in some motive external to the 
 inference proper. And as with the intention, so with the fact 
 of material construction. It is a mere accident of inference. 
 Therefore the intentional combination of perceptible or 
 imaginable elements falls outside inference proper except in 
 so far as it is guided by inferential grounds. But it is true 
 that, especially wherever we have novelty or discovery in in- 
 ference,-^ imaginative or perceptive construction is an indis- 
 pensable auxiliary to thought. 
 
 8. And finally, by insisting on the ideas of synthesis, of Intellect- 
 intention, and of the value of imagination in inference, we "^^^ yith- 
 
 ° ' out Jimi- 
 
 arrive at a fourth meaning of Construction,^ in which it is tation to 
 alleged to be an essential element or even the essence of all ^^°™c 
 inference, as an intellectual combinative process, not confined 
 to the region of geometrical or mechanical abstractions. Thus 
 understood. Construction becomes a convenient expression for 
 the distinct realisation in inference even of universals which 
 are not numerical or geometrical, if they are more than 
 subsumptive. Transferring a spatial metaphor to such uni- 
 versals, it appears to explain the definite necessity which unites 
 their differences, by reference to the precise and unambiguous 
 coherence which belongs to geometrical relations. But we 
 have seen that even as applied to geometrical inferences 
 
 ^ See p. 8, supra. 
 
 See p. 8, supra. 
 
 Bradley's Principles of Logic, p. 235, and passim. 
 
38 The Nature of Inference [Book ii 
 
 construction is to a great extent a metaphor drawn from an 
 accident of those inferences, and when we deal with universals 
 which are not at all sensuous the simplicity of the expression 
 becomes actually deceptive. It is easy to say, for example, 
 that we intellectually ' construct ' such a whole as the British 
 Constitution out of isolated facts, principles, and accepted 
 ideas, and then proceed to perceive its nature. But it is plain 
 that anjTthing valuable in the ' construction ' is coincident 
 with and guided by the growing insight into the nature of 
 the content before us which constitutes the inference itself. 
 We must distinguish from this usage that by which we speak 
 of constructing a Utopia. Here of course we are ostensibly 
 not inferring, though we have really to use inference. Wc 
 are playing, employing the imagination according to arbitrary 
 interests and motives, and not under intellectual guidance, 
 until we begin to draw consequences from what we have said. 
 And the root of the whole usage which we have examined is 
 that in all inference, so far as it has novelty or is a process 
 modifying itself in time, there is an arbitrary and external 
 element which supplies guidance to the attention until the 
 true principle and the relevant details have been disentangled, 
 and operates throughout the inference by the side of the true 
 principle which gradually displaces and finally ousts it. This 
 arbitrary element may indeed be regarded as the universal 
 itself in an imperfect form, but for this very reason it contains 
 much in the way of suggestion or experiment ^ — ^much tentative 
 synthesis — that has to be dropped and erased before the infer- 
 ence can assume its true and final form. And the name 
 construction depends largely on the elements which, having 
 been intentionally and therefore tentatively inserted, are 
 ultimately dropped. 
 
 The outcome of our account of Construction then is this. 
 Construction is a term drawn from moral, physical, and 
 psychological adjuncts of inference. In the case of geometrical 
 and mechanical inference these adjuncts are so far akin to 
 the matter of the universal, that the term ' Construction ' 
 drawn from them may be held a fair designation of such 
 
 > Cp. the case above cited in which the focus of the ellipse was the point 
 required, but the middle of the longer axis was the first point selected. 
 
Chap. I] Construction not essential 39 
 
 inferential processes, e. g. of Kant's account of matter on the 
 basis of attraction and repulsion. In the case of other and 
 less sensuous universals this is not so, and Construction as 
 applied to them is a mere metaphor and not even a case of 
 Inference. Thus Construction should never be assigned as 
 the essence or as an essential element of Inferential activity. 
 
 The above account of four main cases ^ of Inference may serve 
 as an anticipatory sketch of the course which our discussion 
 wiU pursue in the following chapters. (See scheme annexed.) 
 
 SCHEME ILLUSTRATING AFFILIATION OF ARGUMENTS AS 
 DESCRIBED IN BOOK II. 
 
 Subsumptive Series. Constructive or Relational 
 
 Series. 
 
 Incomplete Enumerative Apprehension of connections 
 
 Induction in Space and Time : 
 
 (Syllog. Fig. 3). ' Construction.' 
 
 Complete Enumeration 
 Arithmetical Science. 
 
 Analogy (Syllog. Fig. 2), Geometrical and Mechanical 
 
 (Natural Classification). | ' Construction '. 
 
 I I 
 
 I Scientific Induction.'' ^j 
 
 Explanatory Theory. 
 
 Notional Subsumption 
 (Syllog. Fig. I). 
 
 I 
 Disjunction. 
 
 Judgment of Value. 
 
 ^ Or five, counting among them the process which Construction in its 
 fourth sense is abusively applied to designate. 
 
 ^ Scientific Induction is treated as a transition by which Explanatory 
 Theory may be reached from the side of Analogy. The scheme is 
 intended to represent each type of inference as a combination of that 
 vertically above it with that with which it is connected by a horizontal 
 line. This does not apply to the relation between Explanatory Theory 
 and Complete Enumeration, which stand where they do merely as being 
 intermediate forms. 
 
40 
 
 On Symbolic Logic 
 
 [Book II 
 
 APPENDIX TO CHAPTER I 
 
 On the Relation of Symbolic Logic to the Theory 
 OF THE Present Work. 
 
 I CANNOT pretend to give an adequate account of Symbolic 
 Logic in its present development. But there is a matter 
 connected with it which readers of this work may rightly 
 demand some attempt to explain ; and on which, moreover, 
 the co-operation of students working from the side of philo- 
 sophy (or, if this is held a question-begging phrase, from the 
 side of a monistic philosophy) and from the side of Formal 
 Logic respectively is highly desirable. I mean the ascertain- 
 ment of the precise point of divergence at which Formal 
 Logic, construed as including pure Mathematics, parts com- 
 pany from the sort of Philosophical Logic that is aimed at 
 by the present work, attempting to follow the tradition that 
 is one on the whole with that of Aristotle and Plato, 
 
 The problem thus arising in the first place (i) on a certain 
 point puts the theory of the present work on its defence, while 
 in the second place (2) as it involves the conditions under which 
 the divergence comes to pass, the answer to it would determine 
 the reservation or no-reservation subject to which Formal 
 Logic can be held from the monistic point of view to be true. 
 I. I will first say something about the theory of the present 
 work as it concerns the point of divergence of Formal Logic (in 
 Mr. Russell's sense indicating Symbolic Logic and pure Mathe- 
 matics) from Philosophical Logic in my sense of the term. 
 Point of a. The point of divergence in question, according to my 
 gence im- account given above, is where quality passes into quantity 
 plied in by the transformation of the judgment into the equation. 
 Here begins, according to that account, the transformation of 
 the wide and plastic logical idea of system and members,-^ 
 into the narrow and rigid idea of quantitative whole and parts, 
 passing through which it reaches the last abstraction in the 
 shape of denomination and numerical units. The denomination 
 appeared to be a last abstraction of the whole or system, 
 
 ^ Not yet explicit at the point in question — becoming in fact explicit 
 by contrast with the formal framework then brought to light. 
 
 Formal 
 dist. 
 Philo- 
 sophic 
 Logic. 
 
Chap. I] Mathematics and Quantity 41 
 
 the units, of the parts or members. The numerical series 
 seemed to be an ideal scheme of the relations of members 
 within systems * from a certain limited point of view ; that is, 
 when distinguished only by a logical order of progression 
 assigning every unit a place in relation to every other. ^ 
 
 Mathematics, then, seemed to be especially connected with 
 quantity, and to be characterised according^ by the homo- 
 geneousness of the wholes — ^space, time, and number — ^with 
 which especially it appeared to deal, their actual characteristics 
 being idealised to a point which made the nexus of their 
 relations a matter for almost purely hypothetical judgments. 
 Absolutely pure hypothetical judgment, an assertion of im- 
 plications following upon a supposition which is in no way 
 attached to an underlying real system, I do not believe to 
 have a meaning.** 
 
 The Logic which had the same origin as Mathematics when 
 thus conceived, was then familiar as Equational Logic, 
 founded upon the same transformation of the Judgment 
 which gave rise to Mathematics itself. This transformation, 
 when applied to Logic in general, was open to serious criticism 
 because of the inadequacy of the equational form, which 
 ought to indicate a purely quantitative relation, to the meEming 
 of a true logical judgment. It seemed to be neither Logic nor 
 Mathematics.*^ 
 
 * e.g. I. 168. 
 
 '' I think I am entitled to repudiate any suggestion (if really directed 
 against my doctrine ; see Russell, Principles, 1 14) that my view was 
 satisfied with the psychological conception of counting the acts of 
 counting. Number was for me always a relation of ordered series, 
 which we became aware of by counting. Cp. i. 168, 170. Andlshould 
 be wanting in courage were I not to admit, in spite of the authority 
 against me, that though every class has a number, yet the connotation 
 of every number seems to me to be determined by relations to a whole 
 independent of the class which has the number. 
 
 " See Russell, Principles, p. 14. This observation affects, I should 
 suppose, Mr. Russell's extreme use of the hjrpothetical proposition in 
 illustrating the meaning of implications. You cannot say, I should 
 urge, ' If a donkey is Plato, it is a great philosopher.' The hypothesis 
 scatters your underlying reality to the winds, and what I should call the 
 basis of implication is gone. I^ a real system, S qualifies P as well as P, S. 
 
 ^ Cp. Bradley's Logic, p. 24 ff.with Mr. Keynes's defence and reinter- 
 pretation of the equational form, pp; 189 90. 
 
42 
 
 On Symbolic Logic 
 
 [Book II 
 
 Point of 
 diver- 
 gence 
 on Mr. 
 Russell's 
 view. 
 
 (3. The conception of pure Mathematics has now, as I 
 understand, freed itself from all special relation to quantity, 
 and the view is affirmed that the science to which it applies 
 consists wholly in logical deduction from logical principles. 
 Thus its point of divergence from what is here treated as 
 Philosophical Logic is not that assigned in the account that 
 was summarised in the previous paragraph, but is rather 
 that to which my description finally traced the abstraction. 
 It deals, I gather, not at all with existents, actual space, actual 
 time, or actual characters of totalities represented by number, 
 but with the formal essence of propositions — ^not with facts, 
 but with the mutual implications of propositions, and these 
 propositions containing none but logical constants. It is, in 
 strict principle, to be defined as one with Symbolic Logic, 
 which again is one with Formal Logic* 
 
 The path which its conception traverses in attaining this 
 point may be illustrated by a quotation from Mr. Russell.^ 
 
 ' Whenever two sets of terms have mutual relations of the same 
 type, the same forms of deduction will apply to hoth.^ For 
 example, the mutual relations of points in a Euclidean plane 
 are of the same type as those of the complex numbers ; hence 
 plane geometry, considered as a type of pure mathematics, 
 ought not to decide whether its variables are points or complex 
 numbers or some other set of entities having the same type of 
 mutual relations. Speaking generally, we ought to deal, in 
 every branch of mathematics, with any class of entities whose 
 mutual relations are of a specified type ; thus the class, as 
 well as the particular term considered, becomes a variable, 
 and the only true constants are the types of relations and 
 what they involve. Now a type ^ of relations is to mean,^ in 
 this discussion, a class of relations characterised by the above 
 formal identity of the deductions e possible in regard to the 
 various members of the class ; and hence a type of relations, 
 as will appear more fully hereafter, if not already evident, is 
 always a class definable in terms of logical constants.^ We 
 may therefore define a type of relations as a class of relations 
 defined by some property definable in terms of logical relations 
 alone.' 
 
 * Russell, Principles, p. 9. '' Ibid., pp. 7-8. ■= My italics. 
 
 ■^ Mr. Russell's italics. ^ My italics. 
 
 ' [Mr. Russell's note]. ' One-one, many-one, transitive, symmetrical, 
 are instances of types of relations with which we shall be often con- 
 cerned *. 
 
Chap. I] Quantity not implied 43 
 
 Am I presumptuous in observing that we see here the 
 progress towards homogeneousness of the subject-matter and 
 pure logical implication much as it was set out in the account 
 to which the previous paragraph referred ? If two sets of 
 terms have mutual relations of the same type, the same forms 
 of deduction will apply to both ; but to be of the same type, 
 if I understand the passages rightly, has no other meaning 
 than to be such that the same forms of deduction will apply. 
 So, am I wrong in suggesting that very great and serious 
 differences between two sets of terms may be neglected (such 
 as differences between points in a Euclidean plane and 
 complex numbers) if only a common set of formal deductions 
 can be found which apply to them ? This is the course that 
 was described above, in pointing out the increasing homo- 
 geneousness of the subject-matter of Mathematics as the 
 characteristic differences e. g. of space and time come to be 
 neglected. The science has a right, I should say, to define 
 the same type of relations as it finds convenient. But in its 
 claim to truth the amount of difference which it has omitted 
 will have to be taken into consideration. 
 
 I gather, then, that any reference to quantity or to any form 
 of actual existence is now to be taken as excluded, and that 
 pure Mathematics is to consist, as we said, in logical deductions 
 from logical principles. And the province of Symbolic Logic 
 is practically the same. It claims, as I understand, to have 
 tlu-own off the limitation which offended us in the Equational 
 Logic, and is now prepared to deal with any type of relation 
 whatever, in no way implying a preference for statements 
 framed in quantitative form. And it is noticeable that the 
 Symbolic shape is treated as accidental and unessential. This 
 is more important than it seems. For the idea of a perfectly 
 and purely Formal Logic is necessarily, I presume, as we see 
 in the simple case of conversion, to deal with its terms as if they 
 were units unmodifiable except in position, expressions to be 
 combined or transposed as wholes, and without intrinsic 
 modification.* But the present symbolism is in itself more 
 
 * I am aware that in the most formal logic, when expressed in 
 ordinary language, grammar will hardly permit this rule to be carried 
 out. But there is no doubt, I think, that purely formal procedure 
 
44 On Symbolic Logic [Bookii 
 
 adaptable, as is shown for instance by its admitting a differ- 
 ence of ' sense ' * between a relation and its converse ; and 
 also, as we saw, the symbolism as a whole, which must always 
 be a check on the change induced in terms by change of 
 combination and inter-connection,^ is considered unessential. 
 Therefore the intrinsic modification of terms, demanded by 
 a sound theory of inference, though discouraged, as I think, 
 by the habitual use of a conventional symbolism, is not in 
 principle excluded. 
 
 Thus the point of divergence between Symbolic Logic, 
 including pure Mathematics, on the one hand, and what I 
 call Philosophical Logic on the other, is, if the views just 
 stated are to be held decisive, at the end and not at the 
 beginning of the quantitative development of the judgment. 
 The ultimate divergence would appear to take place at the 
 point where the theory of the hypothetical judgment has 
 been explicitly laid down, exhibiting for the first time an 
 embodiment of implication as distinct from mere subsumptive 
 con j unction. ° And it would consist in isolating the relation 
 of implication in such a judgment from the limitation 
 imposed on it and the extensions ascribed to it owing to the 
 doctrine that every hypothetical presupposes and depends 
 upon a systematic whole taken to be real. Thus the limitation 
 on illegitimate hypothesis, which forbids such an implication as 
 ' if the number 2 were Socrates, it would be a great philosopher ' ^ 
 is swept away ; and with it the suggestion that in a pure 
 hypothetical the implication is reciprocal. I give this latter 
 
 becomes uncertain in so far as a term is modified by its place in a 
 context. The preference for predication by ' is ' with a noun, over 
 a concrete verb, is a simple case. You cannot readily ' convert ' a 
 verbal predication. 
 
 * ' sens ', direction. 
 
 •• Cp. my remarks, p. 202, on the changes inevitable within a syste- 
 matic argiiment, where the meaning of the term develops. I therefore 
 deny that ' the syllogism in all its figures belongs to Symbolic Logic ' 
 Principles, p. 10. In my view it contains a principle of life and growth 
 which cannot be symbolically represented. 
 
 " In my scheme the meeting-point of abstract relation of Space, Time, 
 and Number, with the pure Hypothetical Judgment, and the develop- 
 ment of the latter as an expression of sheer relativity or implication. 
 See vol. i, pp. 86 and 233-4. 
 
 •* Principles, p. 14. 
 
Chap. I] Implication v. Stability 45 
 
 merely as an instance of a loss which seems to me to arise 
 from a non-philosophical interpretation of the proposition in 
 accordance with colloquial usage.* 
 
 This then is the acknowledged point of divergence ; not 
 the establishment of the quantitative judgment, but the 
 admitted emergence of implication as a relation between 
 propositions. If this view is to be taken as decisive, the account 
 of quantitative judgment in the present work shows first the 
 steps antecedent to the divergence, and next the full nature of 
 the divergence, rather than traces the divergence forward from 
 its critical point. To do this on the present basis would mean 
 to give an account of Symbolic Logic, which I admit myself 
 imable to offer. 
 
 2. In what, then, precisely does the divergence consist ? The di- 
 Surely in this, that S3anbolic Logic ^ is interested in the laws ^Hfl^^^ 
 of mutual impHcation between propositions — ^the modes of 
 formal Deduction — while Philosophical Logic is interested in 
 the conditions of logical stability. *= 
 
 a. I will first say what I mean by this latter conception. Logi- 
 I understand Truth to be that characteristic of a system of ^uity ex- 
 propositions which makes it free from self-contradiction and plained, 
 from contradiction with the rest of experience. This charac- 
 teristic (which I take to be what Plato means by d\7j^eta 
 ' trueness ') may be technically described as logical stability "^ 
 (Plato's jSejSaioVrys). It involves the conception that every 
 judgment is at once determined as to its meaning, and 
 criticised as to its non-liability to contradiction, by its place 
 
 * Even if the proposition is taken as itself non-mental, the assignment 
 of its import may be, and in Mr. Russell's case I think is, drawn from 
 colloquial usage. See below, p. 48. I do not feel sure whether the 
 statement that only judgment or belief, involving mind, can be true or 
 false, is an abandonment of the above position, or a concession to 
 popular phraseology. Cp. Principles, p. ix, and Philosophical Essays, 
 pp. 172-3. I think the difference is unimportant for my point, which 
 lies in the isolation of that, whatever it may be, which is true or false. 
 
 •" I omit henceforward, for brevity's sake, to add ' and pure mathe- 
 matics ', which I understand to be implied throughout. 
 
 " The sharp ruling out of Inductive Inference from the subject-matter 
 of Sjonbolic Logic is very significant (see Russell, Principles, p. 11) 
 To me, for example, it means that the ultimate principles which underlie 
 alike Formal and Informal Inferences, are ignored. 
 
 ^ See e. g. Rep. V and VI and notes in my Companion. 
 
46 On Symbolic Logic [Book 11 
 
 in the whole system of judgments which represents our 
 organised experience. Its degree of non-liability to contra- 
 diction, internal or external, is its degree of logical sta- 
 bility, and I take it to be the main interest of philosophical 
 logic, as r indicated from the beginning,* to analyse the forms 
 which are generated by the impulse towards such stability or 
 satisfactoriness, with reference to the various degrees in which 
 they embody its achievement. The rules of inference come 
 in rather as the modes of passing from grade to grade of logical 
 stability than as expressive of relations between this and that 
 or these and those propositions. How and under what reserva- 
 tions premisses yield a conclusion, for example, is the study of 
 the formation of a whole of relatively higher stability than its 
 isolated data, not a mere playing a game under given rules. 
 
 Now this conception at once brings the consequence that 
 there can be no unproved premisses or prior foundations ^ of 
 knowledge. For the proof of every judgment is ultimately in 
 the system as a whole ; and there can be no indefinables nor 
 colloquial interpretation of propositions in any sense of the 
 latter term, for every proposition and every judgment takes 
 its meaning as well as its certainty from the system. And 
 there can be no implication as a relation between isolated 
 propositions, for the only implication is that which at any 
 point is necessary to the avoidance of contradiction in the 
 system. If we intend to set out without reservations or pre- 
 suppositions, and investigate what is meant by the presence 
 of trueness or satisfactoriness in the forms of thought, this, 
 I suggest, is the only way to go about it. We start, in this 
 case, not from unproved premisses, but from minima of 
 experience, which are found to lead both in truth and certainty 
 beyond themselves, and possess, until they have so led, no 
 more than a provisional meaning and certainty. 
 
 /3. Symbolic Logic diverges from Logic as thus conceived by 
 omitting the conception of logical stability. It takes the 
 proposition primarily as an isolated unit — not mental — but 
 recognises the mutual implication of propositions. Its 
 interest lies in the study of the various general types of 
 deduction, or ' the general rules by which inferences are 
 * Vol. i, p. 3. '' Below, p. 266. 
 
Chap. I] Unproved Premisses 47 
 
 made ' ; that is, I presume, the rules by which you can 
 assert or deny a proposition of one general type when assum- 
 ing one or more propositions of the same or some other type. 
 It is recognised that true and false propositions respectively 
 have different relations of implication as regards all pro- 
 positions ; but I do not gather that these implications are 
 capable of degree, so that a proposition could be more or less 
 true because of being more or less supported by other pro- 
 positions. Its truth or falsehood I understand to be self- 
 contained, a private affair of its own, not lying in its coherence 
 or incoherence with a system.* 
 
 In a word, the resulting difference is twofold. As the 
 foimdation of the science you get a niraiber of indefinables 
 and of unproved premisses, assumed really "for reasons of 
 convenience — that is to say, with a view to leading proofs 
 from them in the simplest and neatest way.^ And as the 
 goal of the science you get an enormous command over the 
 forms of deductions applicable to propositions which them- 
 selves, though always general, are unchangeable units. You 
 have no such phenomenon as a system operating within 
 propositions ^ so that their ideal shape and certainty is always 
 ahead of their given form, and makes itself felt as an impulse 
 to self -transformation and completion in other forms. On 
 Mr. Russell's philosophy, I presume that a proposition would 
 not be an entity capable of embodying such an impulse (not 
 being in any way mental). But, as I admitted just now, 
 I do not know whether Mr. Russell's philosophy is generally 
 held essential to the logical doctrine which he shares with 
 others."^ In any case, whether the proposition is mental or 
 not, and whether or no we subscribe to pluralism, the pro- 
 position for Formal Logic is a fixture, in relation with others, 
 
 * I regret that, owing to want of acquaintance with the general 
 literature of Symbolic Logic, I am unable to say whether Mr. Russell's 
 philosophy is accepted by the principal authorities who agree with him 
 about Logic. His logic and his philosophy appear very precisely adapted 
 to each other, and he thinks them essentially connected (p. viii). It is 
 certainly not easy to discuss them apart. But I presume that his 
 logical doctrine might be held on logical ground only, by way of abstrac- 
 tion and not as final truth. 
 
 •> See e.g. Russell, Principles, p. 17. '^ See p. 266 below. 
 
 ^ He holds that it is so. Principles, pp. viii and 24. 
 
48 On Symbolic Logic [Book 11 
 
 but alike in truth and in import * independent of them. 
 Thus there is no idea of developing a system, or indeed any- 
 thing whatever, from a single point. The logician takes, as 
 it seems to me, whatever he wants in the way of first principles 
 without considering their relation to any single system, and 
 he makes usage and convenience, not systematic necessity, 
 govern the interpretation of single propositions. For example, 
 * by help of the first nine principles out of ten axioms,'' we 
 can prove the law of contradiction.' And again, he does not 
 raise, as a matter of principle, such questions, dependent for 
 us on the ideal of judgment, as the reciprocity of the hypo- 
 thetical or the exclusiveness of the disjunction, and he appears 
 to me wholly to leave out of account the problem of a cate- 
 gorical basis for the hypothetical and the disjunctive.'^ 
 In other words, he takes implication as a bare and ultimate 
 fact, an indefinable.* 
 
 I am not arguing against all this. It seems to me to be 
 natural, if we either deny, or choose to abstract from, the 
 idea of systematic coherence, about which I shall argue 
 below.® And I do not see why, if we find these assumptions 
 work in a special science, we should not make use of them 
 as a matter of ' taste and convenience ' (I extend the applica- 
 tion of Mr. Russell's phrase on p. 17 but I judge that it does 
 represent what with him is a great influence in the shaping 
 of his science) — ^whatever our doctrine of Reality may be. 
 
 Only, to those who hold a different philosophy, the assump- 
 tion that you may go forward without the idea of system 
 will always appear a reservation or special postulate, affecting 
 the truth or ultimate logical stability of sciences which need 
 it for their foundation. 
 
 This is the point at which controversy might arise. It would 
 
 ^ We must not say ' in meaning ', for Mr. Russell's proposition does 
 not have the meaning, but is it. '' Principles, pp. 16-17. 
 
 "= See above, p. 273, on illegitimate hypothesis. 
 
 ^ Principles, p. 14. Cp. Mr. Russell's explanation, Mind, 75, 375. 
 My only point here is that implication is taken as a relation between 
 two propositions, just as it is felt or found. We are not allowed, for 
 instance, to argue, from the nature of the system involved, on the 
 question whether if p really implies q, q must imply p. I think Mr. 
 Russell would accept this statement. * Cp. c. ix. 
 
Chap. I] Truth of Mathematics 49 
 
 be foolish and hopeless for an outsider to criticise the procedure 
 of these sciences on their own ground. What he not only 
 has a right to do, but is bound to do, is to attempt to indicate 
 the difference of attitude and presuppositions between them 
 and what he conceives to be Philosophical Logic. And this 
 attempt, however modest, must in the end lead to a different 
 opinion; or an opinion differently formulated, about the truth 
 of Formal Logic in the large sense here in question. 
 
 I say, an opinion differently formulated. For though Mr. 
 Russell holds that it is a merit of his philosophy to maintain 
 the complete truth of mathematics, yet he is too widely 
 experienced in all regions of culture not to admit the immense 
 prima facie difference between the kind of truth aimed at by 
 mathematics and that aimed at, say, by biology or by political 
 philosophy * or the philosophy of religion. He must, I imagine, 
 have his own account to give of the relation between a science 
 which stretches so far as his general science of inference in one 
 way, and sciences which include so very much more in another 
 way. I should call it the difference between a very highly 
 conditional system of propositions, dependent for their truth 
 on enormous reservations, and systems of propositions which 
 approximate very much more to categorical truth about 
 reality. But however this may be, every student must see 
 the problem, and it is not for me to conjecture the solution 
 which other students may propose. 
 
 * I hope the reader will treat it as irrelevant that I have myself 
 attempted to write about political philosophy. I am referring to the 
 place of the science as such in a hierarchy of sciences like that sketched 
 by Plato. Plato's reservations on the truth of mathematics are note- 
 worthy. 
 
 1337-2 
 
CHAPTER II 
 
 Enumerative Induction and Mathematical 
 Reasoning 
 
 In tracing the evolution and affiliation of the forms of 
 explicit inference, we begin with a more developed phase of 
 consciousness than that to which we went back in describing 
 the rudiments of judgment. The judgment-form in which 
 the universal first reveals itself as the simple unity of differences 
 must have given place to the articulate perception of things, 
 events, and relations, before we can grasp it as a system 
 whose parts are in necessary connection. In other words, 
 we have no longer to deal with the simplest judgments of 
 perception — ^the impersonal and the elementary comparative 
 judgment — ^but may go at once to the world of things with their 
 characteristic identity, and to the abstract relations of number, 
 space and time in which that world is constructed by the 
 mind. 
 Enumer- T. On the basis of a world of things and occurrences, which 
 ativein- involves a language, i.e. a more or less systematised nomen- 
 clature,-^ the articulate universal presents itself in the form of 
 individual objects having characteristic identity, in which 
 identity general attributes coexist. Language forces such 
 coexistence on our attention through its natural classifications, 
 and the first suggestions of inductive enumeration issue from 
 language — which has in fact gained its significance by the 
 same process conducted naturally and without explicit inten- 
 tion. Such suggestions are operative, as we saw, in the so- 
 called inference from Particulars to Particulars, of which 
 Incomplete Enumerative Induction is a form that has been 
 made superficially rational. 
 Syllogism a. Throwing this inference into the shape naturally pre- 
 in Fig. 3. g(;i-jbe(j i^y the tendency of the concrete individual thing to 
 
 ^ Cp. Introduction, sect. 4. 
 
Chap. II] Modal Conclusion 51 
 
 become the subject in judgment/ and making use, as Aristotle 
 
 also did, of the conjunctive judgment as representing a single 
 
 step in inference, we obtain an inference analogous to the 
 
 Aristotelian syllogism in the third figure : — 
 
 a, h, c, d, are rational ; 
 
 a, b, c, d, are men ; 
 
 . • . Are all men rational ? or, Men may be rational. 
 
 The ground of argument being the characteristic unity of 
 the unanalysed individual object or event, naturally takes the 
 place of the subject in judgment — of the concrete individual 
 which is taken as real — and therefore gives rise to that 
 syllogistic form in which the middle term is the subject of 
 both premises. 
 
 Experience bears out the view that some such type as this 
 represents the simplest operation of mediate inference. All 
 that is said for example by Stuart Mill about inference from 
 Particulars to Particulars must really be taken as applying 
 to inference of this type ; for it is impossible to state an 
 inference in a shape that will even appear to be convincing, 
 unless we supply by a second premise the element of unity 
 between the particulars, always operative in the mind, which 
 is necessary to bind the particular differences into the differences 
 of a universal. The use of symbolic letters brings to light 
 this formal necessity, which significant names satisfy without 
 acknowledging. From ' a, b, c, d are good books 'to ' e is 
 a good book ' no sort or kind of inference holds or is in any 
 way suggested. The gulf between mere d and mere e is beyond 
 the leaping powers of the boldest conjecture. These symbols 
 are true particulars, and we can see from them how far true 
 particulars will carry us in inference. But from ' Ivanhoe, 
 Waverley, and Rob Roy are good books ' to ' Guy Mannering 
 is a good book ' there is a self-evident passage by means of 
 the identity of authorship, which is too obvious to be expressed, 
 but which would form a premise in any explicit statement 
 of the inference. That this same ground would justify the 
 conclusion ' The Surgeon's Daughter is a good book ' is an 
 illustration of Bacon's remark that enumerative Induction 
 
 ^ See on categorical and hypothetical elements in judging, Bk. I, 
 chap. i. 
 
 E2 
 
52 Enumeration and Mathematics [Bookii 
 
 * precarie concludit, et periculo exponitur ab instantia con- 
 tradictoria'. 
 
 Speaking generally, the coincidence of several attributes 
 in one or more objects, or of several relations in one or more 
 events, is the usual starting-point of conscious conjecture 
 and investigation. And this starting-point is all that the 
 present form of inference embodies. Conjecture or pure 'dis- 
 covery ' differs only in degree from proof. Thus the conclusion 
 may be fairly represented by a question or a modal affirmation : 
 A, B, and C are great lawyers and had a classical education .*. 
 Has a classical education something to do with making great 
 lawyers ? ^ or ' A classical education may have something 
 to do with making great lawyers.' In the case of events, 
 which are designated more analytically, i.e. more with a view 
 to an intended inference, than individuals can be, a single 
 judgment is the natural form for elementary arguments of 
 this kind. 'He killed his bird every shot,' i.e. 'Such and 
 such times he fired ; all those times he lolled .*. When he fires, 
 he is likely to kill.' But in careful reasoning or experiment 
 ' such and such ' becomes an elaborate identification by 
 marks. 
 Diver- ^. In this argument by incomplete Enumeration we find 
 
 gent Ten- ^ ^nion of divergent tendencies. Plainly, it has no major 
 premise ; but no less plainly, the principle on which it primarily 
 relies is the principle of subsumption. Its conclusion is 
 therefore particular or modal, and affirms that in instances 
 or under conditions which we are not in a position to assign 
 explicitly, the attributes x and y are or would be united. 
 For the premises neither express precise conditions nor furnish 
 the basis of a complete inference by subsumption. In order 
 to assigning precise conditions, the form of subsumption, i.e. 
 of identification in unanalysed subjects, must be- surrendered. 
 In order to furnish a complete subsumptive inference, the 
 universal must appear in the form of AUness, i.e. in the form 
 of a totality of examples enumerated up to a limit which its 
 nature prescribes. Such an enumeration, or an allegation 
 equivalent to such an enumeration — ^the allegation might be 
 
 ^ The disjunctive import of this question, as is natural with a rudi- 
 mentary type of inference, is simply Yes or No. 
 
Chap. II] Which Figure suits Induction ? 53 
 
 of mediate origin — would be the major premise in a pure 
 subsumptive syllogism. In the present argument as it stands 
 we simply formulate the first impression made by this 
 discovery of an articulate-^ identity in difference, and the 
 first suggestion towards completing the articulation of the 
 universal thus indicated. This suggestion is most naturally 
 to be taken, in accordance with the type of the inference, as 
 quite abstract and superficial, consisting as it does in a single 
 pervading attribute, chosen, so far as we are told, at random. 
 
 y. It is obvious that the study of inference must retraverse, Indivi- 
 in part at least, the path taken by the study of judgment. ^^ _ 
 In the present form of inference the mind is at the same ment in 
 critical point at which it stands when in the Proportional ^^q^^' 
 Judgment it has become familiar with the identity of things 
 beneath their attributes. Only in the study of Inference we 
 see the actual process by which the judgment-forms pass into 
 one another — in this case, in the sphere of enumeration, by 
 the natural pressure of their own recurrence. Incomplete 
 Enumerative Induction is an obvious result of recurrent 
 individual Judgments, which accentuate the common dis- 
 tinguishable aspects prevalent in things and in their indi- 
 vidualities — i. e. in their characteristic natures. 
 
 In Lotze's representation of an argument akin to this, he 
 has set out the recurrent individual judgments as so many 
 premises of the syllogism ; ^ and, rightly recognising that the 
 number of such premises is not limited, he has thereby cut 
 the knot of the question whether inference essentially proceeds 
 through three terms. It is not worth while to dispute about 
 a matter of symbolic representation. So I have only to 
 explain the relation of his scheme of the argument to that 
 here given, by pointing out that his entire set of premises cor- 
 responds to either one of the two which I lay down, while the 
 
 ^ See distinction between explicit and implicit inference, in last 
 chapter. 
 
 * Lotze, Logik, Eng. Tr., p. loo : 'Now it often happens that the 
 same predicate occurs or does not occur not only in two but very many 
 different subjects, P, S, T, V, W, and the question is what consequence 
 can be drawn from the premisses PM, SM, TM, VM, .... which belong 
 
 in form to the second figure of Aristotle Our conclusion runs as 
 
 follows, " All 2 are M." ' 
 
54 Enumeration and Mathematics [Book it 
 
 relation of the individuals P, S, T, &c. to the common attribute 
 ^ forms the other of the two premises essential to the inference. 
 The use of a conjunctive judgment in inference of this type is in 
 accordance with the principles laid down in Book I ^ as regards 
 the unity of the judgment, and with Aristotle's practice in 
 his Inductive Syllogism, though not in the ordinary Syllogism 
 in figure 3 which I have treated as the inductive syllogism. 
 By using the individuals, not in a conjunctive judgment, but 
 as subjects to several premises, Lotze lias forced his inference 
 into the second instead of the third syllogistic figure, the only 
 common term being the common predicate, which therefore 
 must formally serve as middle term though it does not operate 
 as such. His transition from P, S, T, to 2 is effected without 
 an explicit judgment, and the whole process is more akin to 
 the colligation of a conjunctive judgment into a singular or 
 generic judgment as described in Book I,^ than to a process 
 of Mediate Inference. It is obviously more convenient to 
 use the third syllogistic figure, in which a common subject is 
 the middle term, for Induction, and to reserve the second, 
 in which a common predicate is middle term, for Analogy. 
 This was the scheme followed by Hegel, and I venture to think 
 that the deviation from this scheme,^ like other modifications 
 which Lotze has introduced into a logic largely resting on 
 Hegel's ideas, is far from being an improvement. 
 
 The critical point which is involved in the inference before 
 us is the point of divergence between the concrete and the 
 abstract forms of the universal. This is fundamentally one 
 with the divergence between subsumptive inference and 
 the inference which depends on the systematic necessity of 
 abstract relations. That these two types of inference unite 
 again in the systematic and definite concretes of the higher 
 sciences and of philosophy is obvious from the interconnection 
 of the hypothetical and the disjunctive judgment. But for 
 the greater part of their evolution they are distinct, though not 
 fundamentally discrepant. 
 
 * See Bk. I, chap, i, sect. i. iii. * 1. c. 
 
 ^ See Hegel's Wissenschaft der Logik, ii, pp. 131, 1^8-9. Hegel, 
 following the order which he finds convenient, calls Aristotle's figure 3 
 ' figure 2 ', and Aristotle's figure 2 ' figure 3 '. Is it possible that Lotze 
 was misled by this ? 
 
Chap. II] Numerical Totality 55 
 
 The abstract universal operates in all systems or totali- 
 ties that can be regarded as aggregates of homogeneous parts, 
 although this very word homogeneous indicates that the 
 whole has a nature which is also the nature of the parts. All 
 strictly mechanical science — all science, that is, which regards 
 its objects in the light of number, space, matter and motion, 
 is due to the operation of the abstract universal. And in a 
 certain sense, as we shall see, there is nothing which does not 
 in some degree correspond to these abstract relations ; nothing, 
 at all events, which in its analysis presents features discrepant 
 with their abstract necessity. 
 
 The concrete universal follows the track of the individual 
 totality, and displays itself, first, imperfectly, in analogical 
 inference, and then in the teleological conceptions which 
 govern the higher evolutionary sciences ; especially in those 
 sciences which have for their object-matter the achievements 
 and the intellect of man. 
 
 2. To assign the directions of this divergence in terms of Mathe- 
 traditional logic is not so easy as to describe their real nature. ^^^'^^^ 
 Logic has been compelled to adapt its types of inference ing. 
 to the false directions in which it has looked for them. Thus 
 in diverging towards the abstract universal we are leaving 
 the track of true subsumption, but yet we are following the 
 path on which Formal and Quantifying Logic have taught 
 us to seek the perfectly regular subsumptive syllogism. 
 Whereas by following the fortunes of true subsumption we 
 lose all hope of attaining the genuine syllogism of Allness, 
 and yet we go forward through syllogistic types — the second 
 and third figures — ^which we have been taught to regard as 
 only demonstrable by reference to that syllogism. 
 
 i. The lines of advance really suggested by Incomplete Number 
 Enumerative Induction lead to Analogy on the one hand f ° y;^[. 
 and to complete Enumeration on the other. In the remainder vergence. 
 of the present chapter I shaU follow out the latter with its 
 affiliated types of inference, and return in the following 
 chapter with the discussion of Analogy to the central lihe of 
 concrete inference which will take us to the end of our subject. 
 
 a. It is unnecessary to repeat the analysis of the Enumera- Complete 
 tive process which was given in Book I. It is sufficient if tion™^"^^ 
 
56 Enumeration and Mathematics [Bookii 
 
 as false we bear in mind that complete Enumeration is the establish- 
 * ®* • ment of the universal as a numerical totality or aggregate of 
 homogeneous parts, and therefore necessarily depresses the 
 pervading nature or identity of the universal into a denomina- 
 tion, and its differences into units. By an extreme of abstraction 
 all connection between the parts, beyond the fact that they 
 are units in an aggregate, is done away with, so far the nu- 
 merical point of view prevails and the universal takes on the 
 uniform attributes and modes of synthesis which belong to 
 a numerical totality as such. It has been said by Mr. Ruskin ^ 
 that two and two do not in fact necessarily make four, but 
 more often make five. So of course they often may and do, 
 but not by the process of enumeration, nor by calculation, 
 which is a mere abridgment of enumeration. Nearly all 
 fallacies and paradoxes depend upon a confusion of categories. 
 It is well to be reminded by a man of genius that there are 
 other spheres of knowledge besides calculation ; but it would 
 be wrong to take the paradox for a truth, and to impute to 
 the system of number what is a simple omission of our own. 
 Calculation is quite equal to the task of equating 2 + 2 with 5, 
 if it is allowed to indicate the generation of an additional unit 
 somewhere among the 2 and 2. 
 
 Complete Enumeration has been operative as a false ideal 
 both in the doctrine of Induction and in the doctrine of the 
 syllogism. Incomplete Enumeration naturally suggests an 
 extension of itself up to Complete Enumeration. It is readily 
 seen indeed that in dealing inductively with the ordinary 
 objects of perception completeness of the process can never 
 be attained, because the universal nature of an object is not 
 comparable with nor reducible to an enumeration of indi- 
 viduals. Therefore such enumeration must fall into the Infinite 
 series. And it is no less plain that if we interpret the univer- 
 sality of the syllogistic major premise in Barbara as depending 
 on a complete enumeration, the inference is at once reduced 
 to a petitib principii by the direct affirmation of the conclusion 
 in the major premise. Yet though both these shortcomings 
 are obvious, still the mere aggregation of instances always 
 
 * I quote from memory, merely for the sake of illustration. I have 
 no serious quarrel with the statement. 
 
ghap. II] Computation 57 
 
 tends to obtrude itself as a feature of certainty in Induction ; 
 and syllogistic reasoning always tends to assume the shape 
 in which mere extension, i.e. mere identity of individual units, 
 is the bond of union between the predicated attributes. 
 Instances of this tendency are to be found in the diagrammatic 
 representations of inferences whether by circles included 
 within larger circles, or by straight lines of varying thickness,^ 
 in the quantification of the predicate, in De Morgan's numeri- 
 cally definite syllogism, and in the logical calculus. All of these 
 treatments are founded on a view of reasoning which diverges 
 from concrete determination by attributes, but stops short 
 — except in the case of the numerically definite syllogism, 
 which is simply calculation — of arithmetical inference by true 
 numerical relations. All of these processes work Well up to 
 a certain point, being, technically, examples of quasi-sub- 
 sumption — ^subsumption introduced into a sphere in which 
 its concreteness is lost. AU of them, finally, are cases of the 
 tendency, so fatal in popular science, to accentuate at the 
 expense of everything else any aspect of any content which 
 affords the slightest prospect of reduction to a mechanical, 
 i. e. to a calculative procedure. For calculation goes by 
 fixed rules and according to regular series, and is in that sense ^ 
 an easy process, whereas concrete enquiry into actual and 
 material conditions or connections is inventive and creative 
 — the very travail of the mind. 
 
 The real ground on which number of instances may be a 
 source of certainty in Induction wUl appear when we treat 
 of that process in its scientific aspect. No doubt the influence 
 of Complete Enumeration as an ideal has operated in part 
 through association with the Calculus of Probabilities. This 
 calculus however is not the true warrant of Induction, and indeed 
 
 ^ See Sir William Hamilton's Lectures on Logic, vol. ii, Appendix. 
 
 ^ I am not so sUly as to maintain that abstruse calculation is easy in 
 the ordinary sense of the word. But I take it that its difficulties, though 
 insuperable to untrained minds, are not of the same order as those 
 presented by original investigation of actual conditions, in which the 
 intellect is thrown entirely on its own guidance, and can gain but little 
 aid from general rules. And it is not merely the logician but also the 
 physicist who may complain of calculation from assumptions being 
 substituted for investigation into them. 
 
58 Enumeration and Mathematics [Bookii 
 
 in the case of an infinite series, which for the above-mentioned 
 reason must always be the ultimate nature of mere enumera- 
 tion of instances, the calculus can have no application. 
 Enu- ^. But Complete Enumeration in its strict and proper sense 
 
 as^Sith^ 1^^^^ ^P ^^ Arithmetical Computation, and in due course to 
 metical the generalised or symbolic forms of computation which are 
 tion^" ^ foimded upon arithmetic. The judgment which corresponds 
 to this form of argument is, as we saw in Book I,^ the equation ; 
 a type of judgment in which the predominance of the whole 
 as determining the parts relatively to itself is no longer 
 visible, conformably to the fact that we have left the field 
 of subsumption, and are now dealing with combinations of 
 connections devoid of subsumptive character. The nature of 
 inference, which is common to such combinations and to sub- 
 sumptive reasoning, has been explained in general terms in 
 discussing the Essence of Inference, and will be more par- 
 ticularly examined when we have looked carefully at the type 
 of Inference now before us. 
 
 In addition to what was said in the last chapter on the 
 nature of Calculation, some more special remarks may be 
 added here. Though Calculation may take the most varied 
 forms, yet it must always depend in the last resort on the 
 conception of a whole which is the sum of its parts. Enu- 
 meration is the synthesis of this sum out of, or its analysis 
 into, the homogeneous parts or vmits themselves, through 
 the correlative and all but identical processes of addition 
 and subtraction. It is represented by such an equation as 
 3 = I -f I + I. The changes of sides and signs in an equa- 
 tion exhibit the true relation of addition and subtraction. 
 Multiplication and division are similarly correlative, and repre- 
 sent synthesis or analysis not by help of the ordinary unit, but 
 by help of an artificial unit. The equation loo = lo x lo 
 represents multiplication and division alike, being simply 
 an analysis or synthesis by means of a compound unit. 
 Thus multiplication and division are more powerful than 
 addition and subtraction, but less widely applicable, because 
 the compound unit must be uniform. If you have ninety 
 fives, the numerical system gives you the total in a moment 
 * Bk, I, chap. iv. 
 
Chap. II] Developments of Calculation 59 
 
 as 450 ; but if you have such a succession of figures as 4, 5, 3, 
 7, 9, you have no identical compound unit, and must therefore 
 proceed by the simple one, i. e. by addition. 
 
 In multipljdng and dividing powers by help of their indices, 
 the procedure (which governs I presume the use of logarithms) 
 reverts to the form of addition and subtraction, that is, to 
 the apparent enumeration of simple units instead of compound 
 units. Thus the relation of 8 to 32 comes to be represented 
 not by the ratio i : 4 (eight taken once compared with eight 
 taken four times), but by the difference between 2* and 2^. 
 Multiplication proper was the construction of a quantity out 
 of or its analysis into an identical compound unit repeated 
 so many times. Involution is the construction of a quantity 
 out of, or its analysis into, a simple enumeration of the employ- 
 ments of a certain compound unit in multiplication by itself ; 
 that is to say in repetition of itself, or of a quantity generated 
 by repetition of itself (the given compound unit), its own 
 number of times. It is plain that as each step enumerated 
 is a multiplication, or an employment of a factor in multi- 
 plication,^ in order to multiply or unmultiply (divide) one 
 power by another we do not miiltiply or divide index by 
 index, but simply count on or count off the number of acts 
 of multiplication designated by one of the indices. Thus in 
 dividing 2* by 2^ we do not take 2^ as the result, but 2^ — the 
 difference of the two indices. In dropping from 2® to 2^ we 
 have counted off three multiplications by 2, and have thus 
 reduced 64 successively to 32, 16, and 8. So far we are 
 dealing with simple enumeration applied to a complex process. 
 
 It is possible of course to trace the same development 
 further, and did the author's knowledge admit of his attempt- 
 ing the task, an interesting scheme of continuity in calcula- 
 tive processes might be obtained. When we come to powers 
 of powers and roots of powers we are dealing with com- 
 plex enumeration applied to steps consisting of complex 
 
 * To say ' each step is a multiplication ' would prima facie mean that 
 4 should = 2} instead of 2^ But yet it is not wholly false, for of course 
 the difference between, say, 2' and 2' consists of two acts of multiplication 
 by two, not of only one. In short, multiplication involves two factors, 
 and would not be represented by enumerating only one to start with. 
 In every further step the previous result is one factor in the process. 
 
6o Enumeration and Mathematics [Bookii 
 
 processes. If the index of 2^ is divided by the, index of 2^, 
 
 the result 2^ is obviously the cube root of 2^ ; and if the 
 
 index of 2® is multiplied by the index of 2^, the product 2^* 
 
 is obviously the cube of 2^. Here we are constructing by 
 
 multiplication (complex enumeration) a quantity (18), the 
 
 compound units 6 and 3 employed in the multiplication being 
 
 themselves representative of simple enumerations of repeated 
 
 processes of multiplication (complex enumeration). 
 
 Simple enumeration may of course itself be represented as 
 
 the chronicle of a process, i.e. as consisting of units equal in 
 
 number to the number of times the process has been repeated. 
 
 Only in it, in arithmetical progression, the process, though 
 
 applied to its own results, does not obtain the power of creating 
 
 a progressive difference. 
 
 Calcula- y- AH arithmetical calculation, and therefore in the last 
 
 tion com- resort all calculation whatever, may thus be reduced, I 
 
 pared . . . . , 
 
 with ar- imagme, to enumeration, or, m some form, to enumeration 
 
 gument. ^f enumerations. And thus the entire method rests on the 
 conception of the whole which is the sum of its parts — the 
 universal whose differences, though distinguishable, are taken 
 as equal and homogeneous. From the nature of this universal, 
 in which the whole does not present itself as a concrete 
 system, it is almost futile to enquire into the types and shapes 
 which it assumes in inference. Is an Equation correlative 
 to Judgment or to explicit inference ? Is a combination of 
 Equations necessary to explicit calculation, as a combination 
 of Judgments is necessary to explicit Inference ? 
 
 The equation, it must be remembered, is a comparison of 
 numerable relations in the abstract, and therefore corresponds 
 not to any form of Singular or Perceptive Judgment, which 
 a,re correlative to the simple Judgments of Enumeration, 
 but only to a universal Judgment, and more especially to 
 the pure Hypothetical. This is enough to show that the 
 Equation is essentially of a sjmthetic or inferential character. 
 And there is also a special reason why this character is more 
 emphatically marked in an Equation than in a generic or 
 h57pothetical judgment. Every judgment — ^using the expres- 
 sion in the narrower sense in which it excludes equation — ^is 
 liable if driven home to be accused of a fallacy a dicto secundum 
 
Chap. II] Equation and Judgment 6i 
 
 qttid ad dictum simpliciter, for the concrete significance of the 
 subject dwarfs and renders trivial the conditions under which 
 alone the attribute can really attach, and some at least of 
 these conditions are habitually omitted, or, if we prefer to 
 say so, presupposed. But in the equation the whole content 
 is homogeneous, and no one part can dwarf any other. We 
 may not say that 99,999 = 100,000. We must put in the 
 condition, however trivial in real life, represented by + i on 
 the left of this equation, or — i on the right. Therefore 
 every equation, even the simplest, is not only hypothetical, 
 but it is hypothetical on the basis of an explicit intellectual 
 process or synthesis of differences. There is in this sphere 
 no such thing as massing facts together, and leaving you to 
 choose how you infer, or whether you really and conscientiously 
 infer at all. To simply equate the whole with itself as a whole, 
 as true Judgment, dealing with differences of attributes, 
 may appear to do, must give tautology, and so nonsense, in 
 Equation. Being debarred from even the appearance of such 
 judgments as ' All Exogens are Dicotyledons ', the equation 
 must always have on the one side or on the other an explicit 
 sjnithesis of differences. It is therefore in itself a step nearer 
 to explicit inference than the hypothetical judgment. 
 
 The Equation then exhibits an inferential connection more 
 clearly than an ordinary hypothetical judgment. In respect 
 however of not being a categorical assertion it is on the 
 same level with that judgment, and only qualifies reality in 
 virtue of the real element which underlies its hypothesis ; i. e. 
 pure arithmetical computation qualifies reality in as far as it 
 expresses the properties of the system of number. 7 + 5 = 12 
 means If five is added to seven we get twelve, and is 
 categorical in as far as it involves the assertion, ' The system 
 of number is such that " if five is added to seven ", &c.' 
 And as all prerogatives of a subject are absent (as is also 
 the case with pure hypothetical judgments) no difference is 
 more especially referred to Reality than the others. All are 
 referred indirectly (i.e. through the system of number), and 
 without priority. 
 
 The combination of equations bears the same relation to 
 the single equation as the combination of judgments in 
 
62 
 
 Enumeration and Mathematics [Bookii 
 
 Applica- 
 tions of 
 calcula- 
 tion. 
 
 Substitu 
 tive In- 
 ference. 
 
 explicit inference to the single judgment. In each case it is 
 impossible to draw the line between the single act and the 
 combination. An equation may be taken as involving any 
 number of equational steps, just as a judgment may be taken 
 as involving any number of intermediate judgments. In 
 short, an equation, like a judgment, is the form of conclusion 
 as well as the form of premise, and in ultimate analysis 
 always partakes of both characters. But for this very reason 
 there is no difference of principle between the single form 
 and the combination, and it is sufficient in discussing infer- 
 ence to treat of the latter which has the advantage of being 
 explicit. It may here be pointed out that as the equation 
 is non-subsumptive, so the varieties and peculiarities of 
 syllogistic figure disappear in the combination of equations. 
 In every equated term or expression the whole is present in 
 its entirety, and no form of it has any such peculiarity as 
 we understand by the Universal, Particular, or Individual, 
 — the subjects and predicates of the syllogism. This in- 
 difference corresponds to the nature of the numerical whole 
 and renders arrangement and, apparently, number, of terms, 
 in calculation a mere matter of practical convenience. But 
 in every system of equations, if bona fide treated as a single 
 inference, the three terms may be detected. Our insight 
 develops along the chain of equation, and does not simply 
 drop one term out and replace it by another. 
 
 ii. Lotze has treated of equational inference, i. e. of calcu- 
 lation, under the titles of substitutive and proportional infer- 
 ence, and of inference from the constitutive equation. I will 
 comment briefly on the first of these forms at present, and 
 will return to the others when something has been said of 
 the matter to which they apply. 
 
 a. The point of substitutive inference — which is described 
 as a species of syllogism and as possessed of a major premise 
 — consists in substituting in the conclusion for the middle 
 term M the developed content of M as assigned in the major 
 premise, under the operation of a condition s representing 
 the peculiar modification attaching to the minor term S. 
 The argument is thus written in S5mibolic form ^ — 
 ^ Lotze, Logik, E. Tr., sect. 109. 
 
Chap. II] Equatioual Identification 63 
 
 Major Premise M = a + hx + cx^... 
 
 Minor Premise S = s M. 
 
 Conclusion S = s (a; + 6a' + cx^. ..). 
 
 This argument, in which a, b, c &c. represent any marks 
 within a concept, becomes efficient, as Lotze observes, only 
 when reducible to quantitative terms, because in other cases 
 the particular change effected by s in a or & is simply taken 
 from experience and is not really drawn from the form of 
 the argument, which might therefore just as well have been 
 thrown into an ordinary syllogism. But on the other hand 
 it is worth observing that if, in constructing such an inference, 
 we remain within the sphere of the quantitative universal, 
 then the relation of subsumption and the prerogative of the 
 major premise necessarily disappear. We have then simply 
 two equational connections, related to an identical whole, 
 and therefore capable of giving rise to a further connection. 
 But M is not in that case generic, nor is S specific, nor is the 
 connection of S with s {a + hx Sec.) known through their con- 
 junction in and subordination to a concrete individuality M. 
 M is no doubt here the assigned meeting-point of the relations, 
 a form of the quantitative universal which pervades the 
 equational connection before us, but S is no more a case of 
 M than M of S. And indeed, having once been led to 
 observe the connection of S with its development s {a &c.), 
 we no longer judge this true on the mere ground of con- 
 jimction in M, but on the ground of a systematic necessity 
 revealed through M. S or s M, if it is or has a true quanti- 
 tative relation to M, cannot be bona fide a case under M, an 
 element in a concrete individuality or case of a generic nature 
 M, and with this relation the whole idea of subsumption 
 vanishes. 
 
 And the favourite and catching phrase ' substitution ' must 
 be similarly treated. Substitution is a consequence and not 
 a principle of inferential relation. It arises from the identity 
 of the whole with itself in all its forms, the discernment of 
 which identity is the task of calculation. We may infer, to 
 take a very elementary example, from 24 = 12 x 2, and 8 = -3- , 
 that 8 = -^3--. We here ' substitute ' 12 X 2 for 24, because 
 we possess the connection which tells us that the former is a 
 
64 Enumeration and Mathematics [Book 11 
 
 synthesis identical with the whole 24. To ' substitute ' is 
 simply to treat a whole as identical with itself. 
 
 This ' substitutive ' inference then, in its mathematical 
 shape, has no syllogistic character, no major premise, and 
 no real dependence on a principle of substitution. It might 
 fairly be spoken of as an inference by equ'ational identifica- 
 tion. It must include, so far as I can see, the entire range of 
 strictly arithmetical computation, whether in algebraical or 
 in cirithmetical form, as contrasted with computation applied 
 to geometry, mechanics, and physics. It establishes a ratio, 
 for, logically at least, ratio is a genus of which equality is a 
 species, but it does not ostensibly compare ratios, and there- 
 fore does not explicitly challenge problems in concurrent 
 but heterogeneous series. But we must remember that any 
 calculation which does not merely develop the properties of 
 number depends for its meaning on some differences of real 
 aspect correlative to the differences of numerical aspect. 
 ' The shelf-space M of this shelf = the shelf-space required by 
 thirty octavos.' * I can have shelf-space which = 100 M, .". I 
 can have shelf-space which = the space needed by 100 x 30 
 octavos.' Here no doubt we are dealing with homogeneous 
 quantity — feet and inches — all through ; but the wholes 
 which are compared are differently motived, and these 
 differences of motive — books compared with shelves, and one 
 shelf with a library — are what give the inference its point. 
 The next step is that these differences of motive affect the 
 actual denominations of the units themselves. We come to 
 deal in short not with simple equality — identity of number 
 of the same units — but with equality of ratios, i. e. with 
 identity of the ratio between the several quantities of a set, 
 with that between the several quantities of another set or 
 other sets. The unit of enumeration, in this case, must not 
 be identical. 
 Connec- /3. We must now break off somewhat abruptly to consider 
 tionsin the apprehension of Connections in space and time, which 
 and Time, must be treated for our present purpose as an mdependent 
 root of knowledge, and must be investigated before we can 
 proceed further with the analysis of calculation. Primarily 
 no doubt the apprehension of these connections is an offshoot 
 
Chap. II] Construction 65 
 
 of the rudimentary judgment, which as we saw in Book I ^ 
 must construct its world of Things largely under the influence 
 of growing spatial and temporal discrimination. But starting 
 as we have done in explicit inference with the developed 
 concrete perception of the world of things, we have no choice 
 but to assume also the developed abstract perception of 
 relations in space and time. We reason from these relations 
 or connections before we have subjected their elements to 
 accurate enumeration or measurement, and it is the nature 
 or non-numerical inferences from such relations that I now 
 propose to consider.^ ' A is to the right of B, B is to the right 
 of C, .'. A is to the right of C ; ' ' A is prior to B in time, and 
 B to C, therefore A to C In such inferences as these, 
 Mr. Bradley has told us, we first construct, and then perceive. 
 I have expressed at length in another work, and briefly in 
 the preceding chapter, my objections to employing the term 
 construction as if it were a self-explaining account of an 
 intellectual process. But I have conceded that when restricted 
 to the sense of intellectual construction, neither imaginative 
 nor physical, it affords an apt description of the. peculiar 
 work of inferential apprehension in the field of space, time, 
 and motion.* At all events we must, I think, agree with 
 Mr. Bradley that in examples like those just given there is 
 no bona fide major premise, and therefore no syllogism. The 
 form ' A is to right of B, B to right of C, .-.A to right of C ' is 
 so obviously the natural shape of the inference thus expressed, 
 that we may be surprised at being reminded that, qua syllo- 
 gism, it has the defect of four terms. To fulfil the syllogistic 
 requirements we must set down as a major premise ' What 
 is to the right of B is to the right of C ', or even ' What is to 
 the right of B is to the right of that which B is to the right 
 of. In the latter case the entire content of the argument 
 recurs in the minor premise ' A is to the right of B and B to 
 the right of C '. Plainly this minor premise would carry the 
 conclusion without a major. 
 
 It was the author's experience, when engaged in teaching 
 
 * Bk. I, chap. ii. 
 
 * See Bradley's Principles of Logic, p. 225 ff., which on this point 
 I have followed very closely. * See p. 33 above, note a. 
 
 1337-2 F 
 
66 Enumeration and Mathematics fBooKii 
 
 elementary logic, that pupils had an invincible tendency to 
 construct ' syllogisms ' in one of these two types, the former 
 of which is defective as a syllogism, and the latter unreal and 
 ineffectual. In using the former, ' A to right of B, B to right 
 of C, therefore &c.,' their instinct was just, so far as the 
 argument to be expressed was not truly subsumptive. An 
 extension of this just practice to subsumptive inference 
 in which it becomes erroneous was no doubt the cause of 
 Dr. Thomas Brown's remarkable view as described by Mill in 
 an interesting passage.^ The complementary error, to which 
 also pupils are prone, is, in constructing a syllogism, to sur- 
 render the whole task of articulating the steps of the argument 
 by simply putting as the major premise some syllogistic canon, 
 in analogical argument some principle of analogy, or in 
 'constructive ' argument such a general principle of construction 
 as ' Whatever is to the right of B is to the right of that which 
 B is to the right of. It thus becomes necessary to mass the 
 whole content of the particular inference in hand within the 
 minor premise. Wherever a syllogistic canon is taken as the 
 ultimate major premise of inference, this error is committed. 
 The error consists in taking out the active form of the inference 
 — the intellectual function which the syllogistic or constructive 
 arrangement expresses — and making this a mere portion of 
 the content from which the inference is drawn. In drawing the 
 inference the intellectual function is inevitably active, and the 
 principle expressed in the major is no justification of the 
 activity of this function, but merely a content on which it 
 operates as it would on any other content, so that the explicit 
 major really adds nothing to the argument.^ This case, of 
 subsumption under the principle of subsumption, needs itself 
 to be subsumed under the same principle or another, and 
 so on ad infinitum. Take ' A mark of a mark is a mark of 
 the thing marked, growth is a mark of organic nature which 
 is a mark of life, .*, growth is a mark of life'. Here we have an 
 act of subsumption under a principle of subsumption, which 
 
 ^ Brown thought the major premise always superfluous. See Mill's 
 Logic, i, p. 225, sixth edition. 
 
 - See Bradley's Principles of Logic, p. 475 ; Hegel, Wiss. der Logik, 
 ii, p. 151 ; and the Author's Knowledge and Reality, p. 275. 
 
Chap. II] Added Determinants 67 
 
 act itself falls outside the principle itself and needs justifica- 
 tion in a prior syllogism, if the minor premise and conclusion 
 needed justification in this. 
 
 On the other hand, subsumption does not allow the subject 
 to be merely treated as a point of attachment, as is the case 
 with abstract series in space or in time. If we tried to infer 
 thus in concrete matter we should get something like Jevons' 
 Added Determinants, which is an excellent example of infer- 
 ence that is almost necessarily fallacious, owing to the dispro- 
 portioned effect of the same added determinant on two concrete 
 conceptions. ' A child is a human being, A. B. is a big child, 
 .*. A. B. is a big human being ; ' ' Pericles rules Athens, 
 Aspasia rules Pericles, .-. Aspasia rules Athens.' The concrete 
 subject in subsumption takes up the determinants into itself 
 and transforms them in a way which we cannot predict. 
 A woman's rule over her lover is not in pari materia with a 
 statesman's rule over a commonwealth, and a big child may 
 be a very small human being. We must not try to read off 
 conclusions from series in subsumptive matter as we can in 
 space, time or number. Construction or abstract connection, 
 on the other hand, deals with relations which bear on each 
 other with systematic necessity, and which are not affected, 
 or are assumed to be affected only within known limits, by 
 the idios3mcrasies of the points of attaclmient. In ' A to 
 right ' &c. we take A to be a point or body in space ; if not, 
 the inference is unmeaning. Therefore in this sphere no pre- 
 mise has a prerogative, and the reciprocal modification of 
 relations is constructed in the argument and not presupposed 
 in the nature of the Subject. This characteristic of ' con- 
 struction ' applies to number, space and time, and to the 
 mechanics of abstract matter. 
 
 The apprehension of relations in time needs no separate 
 treatment in logic from that of relations in space. Apart from 
 measurement, connections in time are not capable of any great 
 complexity, seeing that they contain nothing that corresponds 
 to a curve or angle in space. Mere succession is the relation 
 of one set of changes to a permanent subject ; but in this there 
 is implicit from the first the idea of duration, which involves 
 the elementary comparison by the permanent subject of two 
 
 F2 
 
68 Enumeration and Mathematics [Book ii 
 
 distinguishable sets of changes, each of which is prima facie 
 the measure of the other. There is no science of time in the 
 sense in which geometry is the science of space. From this 
 point of view it has been said that time is one degree more 
 ideal than space; i.e. its essential character of successiveness 
 falls outside the actual contact of events with sensation and 
 exists for the most part in the ideal medium of memory. It is 
 true however that the present has duration, and does not 
 exclude succession. But in thus possessing duration, in spite 
 of the fugitive character of actual sensation, the present of 
 course displays an ideal nature which makes it continuous 
 with temporal succession, a succession which pervades even 
 the present itself. 
 
 The intelligence in bringing order into the feelings begins 
 by apprehending space or time and constructing its perceived 
 world in these forms. By developing them, however, into 
 scientific characteristics of this material world, it further pro- 
 ceeds to idealise them into laws and proportions, and thus to 
 take away their immediate and perceived character. The first 
 step in this idealisation is the conception of absolute, standard, 
 or uniform space and time, a conception which guides the 
 process of measurement, but which is strictly speaking, in its 
 common-sense form, an abstraction to which no real thing nor 
 process corresponds. Constancy of ratio throughout the per- 
 ceptible world is, as we saw,^ all that measurement can give 
 us, and is what we really mean to assume. Uniform space 
 or time, as embodied in a single series and not in a com- 
 parison, is a contradiction in terms. 
 Calcula- y. The apprehension of connections — even of explicitly 
 *\°^dTo" rnediate connections — in space and time does not necessarily 
 Geometri- involve the enumeration of parts with a view to precise 
 soning^ measurement. Such apprehension begins, as we saw in Book I,^ 
 with the perceptions indicated by ' Here ' and ' There ', ' right ' 
 and ' left ', ' nearer ' and * further ', ' now ' and ' then ', 
 ' future ' and ' past '. 
 
 But all these expressions involve a continuous series, and 
 such a series is the beginning of measurement. The spatial 
 elements however, the straight line, angle and arc, are not 
 ' Bk, I, chap. iv. ^ See Bk. I, chap. i. 
 
Chap. II] Puvc Geometrical Reasoning 69 
 
 constructed by measurement but are given spatial relations, 
 although the discovery of their properties cannot be effected 
 apart from the comparison of quantities. I am not prepared 
 to say that the identification of corresponding geometrical 
 relations might not (in spite of the etymology of the word 
 ' geometry ') be prior to intentional quantitative comparison. 
 Vertical angles, or right angles, or the triangles into which 
 a rectangle is divided by the diagonal,^ might be seen to be 
 the same, before numerical comparison was applied to sides, 
 angular distances, and areas. 
 
 Apart however from definite history, nothing can tell us 
 when an implicit character becomes explicit. It is certain that 
 all developed consciousness of spatial and temporal connection 
 must operate through quantitative comparison. 
 
 Geometrical and strictly mechanical reasoning is the endow- 
 m.ent of the quantitative universal with control over the com- 
 bination of homogeneous parts in space, or in space and time 
 together. In this type of reasoning, though essentially ' con- 
 structive ', we are often reminded of subsumption by the 
 peculiar working of the quasi-generic judgment. 
 
 The square and the cube are elementary and striking in- 
 stances of the power of enumeration, i.e. of arithmetical ideas, 
 to represent or to describe generically a purely geometrical 
 relation. The ' square ' of a number is not a square surface, 
 nor does it, so far as I can see, display in itself the difference 
 between the superficial and the linear unit. But such a num- 
 ber, or rather such a numerical relation, does indicate definite 
 combinations of parts by which a square surface may be recog- 
 nised or constructed, and therefore the numerical relation may 
 for many purposes be regarded as equivalent to the surface. 
 The purely homogeneous universal, qua homogeneous, already 
 at this stage fails to grasp the nature of the content as such, 
 whose structure is to be represented by the differences of the 
 
 ^ In elementary schools it is now the practice to familiarise young 
 children with such relations as this, e.g. by folding square pieces of 
 paper, first along a line dividing them into equal rectangles, and then 
 along the diagonal, thus exhibiting the equality of a right-angled 
 triangle to a rectangle of the same height and half the base, both being 
 halves of the same square. This is an equation and so a measurement, 
 but rudimentary in as far as unanalysed. 
 
70 Enumeration and Mathematics [Book ii 
 
 universal, but succeeds in a way unknown outside mathematics 
 in presenting an adequate key to this nature. 
 
 I presume that the marvellous processes by which curves 
 of all types have been subjected to the dominion of theequation 
 must ultimately be regarded by logic in the same light as the 
 relation of the square upon a line to the square of a number. 
 These processes do not, as I understand, exhaust the nature of 
 the curves, but they exhaust a combination of directions and 
 distances, referred to an assumed point, which can be given 
 any required degree of accuracy in representing the curves. 
 Hence, though numerical relations have not in themselves the 
 aesthetic or mechanical attributes of the particular curves 
 which correspond to them, yet the nature of space permits 
 a curve to be adequately and unerringly constructed by putting 
 together homogeneous parts, viz. distances, in accordance with 
 these numerical relations. It is obvious therefore that by 
 experience, if not otherwise, both aesthetic and mechanical 
 attributes may come to appear as if directly legible in certain 
 numerical relations considered as controlling spatial elements. 
 In the case of curves these numerical relations or attributes 
 are expressed in constitutive equations, and form by far the 
 most striking examples of a transition from and through the 
 homogeneous to the heterogeneous. But strictly speaking all 
 the simple proportions which characterise e.g. the triangle or 
 the square are examples of the same principle. 
 
 We spoke in Book I of this whole class of truths as ' quasi- 
 generic judgments ', and insisted on the peculiar reversion 
 which they display towards the type of concrete or organic 
 totality. Never again in knowledge do we meet with such 
 simple abstract and mechanical construction so unerringly 
 analysing an individual and characteristic content. For this 
 reason we are tempted to take the constitutive equation as the 
 ideal of knowledge, and indeed exceptis excipiendis we are right 
 in doing so. But the excipienda are serious. When we pass 
 from abstractions like space, time and matter to the concrete 
 evolution of the real world, to organisms, to political societies, 
 and to human intelligences, not only is mechanical construc- 
 tion infinitely more difficult, but it is infinitely less adequate. 
 A curve after all is a line in space, though it is not a straight 
 
Chap. II] Adequacy of Construction 71 
 
 line ; so that it can be no such enormous leap to constitute a 
 curve out of spatial elements. But a plant is hardly in the 
 strict sense a phenomenon in space at all, and although a 
 mechanical view of it, in a sense to be explained below, must 
 certainly be aimed at by science, yet there wUl remain in it 
 much to be understood which cannot be constructed — ^not a part 
 of its actions, but the whole result. 
 
 If the constitutive equation is the type of quasi-generic 
 judgment, it follows that Inference from the constitutive equa- 
 tion is the type of quasi-subsumptive inference. Such inference 
 has two aspects. On the one hand it is pure calculation or 
 combination of connections, like any mediate equation which 
 has no meaning beyond the numerical system. It combines 
 with a proportion between two changing quantities some parti- 
 cular values of these quantities, and follows out the modifica- 
 tions which result from this combination. This process is in 
 itself, though more complex, yet not a whit more subsumptive 
 or less purely calculative than to equate 2 a with 3^^;, and 
 supplying any number as the value of a to fill in the number 
 demanded by the proportion as the value of x. In such an ex- 
 pression a and x are merely generalised numbers, or numerical 
 relations, or, if we hke, names for a problem. There is no 
 true major premise, but in its place there is the generalised 
 description of an identical numerical whole in the two cases 
 of being constructed with a factor 2 and with a factor 3, and 
 the inference consists in exhibiting the construction of any 
 such whole on the basis of these factors respectively. 
 
 If a and x represent distances in space defined by some 
 further relations (e. g. perpendicular to each other or the like), 
 and the whole expression has the effect of characterising a 
 definite figure in space, then we have the germ of what I have 
 called quasi-subsumption. The inference is still constructive 
 in the narrow sense ; it proceeds by enumeration of indifferent 
 parts as in the case first considered. But it-combines with this 
 aspect another and a different one. It exhibits a particular 
 portion of a particular curve in the light of a characteristic 
 modification of a generic type. The curve may be closed or 
 open, quick or slow, symmetrical or unsymmetrical. And these 
 attributes, although they result from the construction, are not 
 
72 Induction and Reasoning [Bookii 
 
 given within the construction. The spatial nature of the type 
 of curve in question is the quasi-generic content through which 
 the subsumption is rnade. It is not pure subsumption ; for the 
 construction would suffice in theory to draw out the particular 
 curve before us and discover its properties, without ever giving 
 it a generic name or observing that we are analysing the pro- 
 perties of something like a natural kind. And in fact, I pre- 
 sume, this is the usual order of procedure. Observations are 
 obtained, upon which as data the curve is constructed, and its 
 general nature is found only by means of this construction. 
 But on the other hand, the mere fact that we know how to 
 pass from an equational combination of numbers to a spatial 
 figure shows that we are proceeding on a principle involved in 
 the characteristic nature of such figures. The scheme of the 
 argument is — 
 
 A spatial figure constructed on such proportions has such 
 and such an outline ; 
 
 This is a spatial figure constructed on this case of the above 
 proportions ; 
 
 , • . This has this particular outline. 
 
 The element of subsumption consists in the impossibility of 
 passing from the ratio, which is only a generalised relation of 
 numbers, to the markedly individual figure in space, except 
 by identifying the subject in which the numerical relation and 
 the characteristic curve-properties are conjoined as the nature 
 of space, or, more closely, of a curve in space. 
 
 It only remains to mention that when we take in the unit 
 of time, and thereby are able to represent motion as a length, 
 and when we further erect the abstractions force and mass as 
 correlative points of view from which motion is regarded as 
 affecting bodies, we have all the organa of what may be called 
 pure mechanism, or abstract constructive science — a complex 
 and elaborate system, founded ultimately on the combination 
 of three abstractions, space, time, and number. This abstract 
 mode of consideration is true in so far as it applies to the 
 characteristics of real things, but its application is obviously 
 limited. The human body, for instance, is of course a case 
 in which the geometrical and mechanical laws of space and 
 motion have reality, but to a large part of its activity these 
 
Chap. II] Abstract constructive science 73 
 
 laws in their purely abstract form have nothing to say. I 
 
 proceed to discuss how and in what sense mechanism, and 
 
 mediately, even pure mechanism, has a wider application. 
 
 8. Lotze has spoken of inference from proportion as a limit Calcula- 
 
 of knowledge, and as assuming a type which from his descrip- pj^caWe 
 
 tion appears to be subsumptive, although he does not give it to Dis- 
 .1 . parates. 
 
 this name. t^ 
 
 (i) I am unable to see that we have in proportion either tion. 
 subsumptive inference or a limit of knowledge, so long as the Homo- 
 four terms of the proportion are either of the nature of abstract g^Jieous 
 number, or are in pari materia, i.e. of the same denomination 
 with one another. Numbers by themselves, it may be said, 
 prove nothing, and computation in the abstract is not inference. 
 But it seems obvious that the properties of the numerical 
 system as such are worth establishing for their own sake. 
 2:4::3:A;.'.A; = 6is not a worthless iype of inference, 
 although the example is one which has no interest. It depends 
 on a relation within the numerical system, and is in itself, apart 
 from its elementary character, as well worth establishing as any 
 other consequence of an isolated abstract relation. 
 
 Or again, if we want to make a picture-frame of the same 
 proportions with one that we have, but of different size, then 
 all the numbers represent lengths, and we have, say, i6in* : 
 241"- : : X : y ; x — 32-1^ • ; .'. y = 48. In this example, how- 
 ever, the limit of which Lotze speaks is just beginning to make 
 itself felt. All the numbers do no doubt in one sense stand for 
 lengths in space ; but they are lengths peculiarly related, in 
 a way which falls outside the statement of proportion. In the 
 object to he constructed — this is the very reason for which we 
 compare them — the one spatial length is to be at right angles 
 to the other ; or, in popular language, they are respectively 
 length and breadth. Thus 16 and 24, and their correlatives 
 X and y, are in one sense of one denomination, but in another 
 sense of different denominations ; and it is because they are 
 of different denominations — or dimensions — ^that we have an 
 interest in comparing them. Here moreover, as in geometrical 
 reasoning, we come upon a trace of subsumption, because the 
 essential identity which is the foundation of the inference con- 
 sists in the nature of an object which has length and breadth. 
 
74 Induction and Reasoning [Book ii 
 
 under which generic nature, as characterised by a certain ratio, 
 
 we subsume a specific case of the same nature and of the same 
 
 ratio. The meeting-point of the relations is a concrete and 
 
 not an abstract, and this is the differentia of subsumption. 
 
 It would be easy to fill up many gradations of the appearance 
 
 of heterogeneity in the terms of a proportion. First, the two 
 
 sets compared cease to be measurable by any identical unit — 
 
 whereas in the last examples both sides of the proportion are 
 
 measiu"able as distances in space. Such are the proportions of 
 
 times to distances and to areas, or of force to distance or to 
 
 mass. And secondly, the several terms, either in one set or in 
 
 both, cease to be strictly measurable by identical units. While 
 
 this is the case with one side only, some sort of proportion may 
 
 be supposed to exist, especially as the other side may present 
 
 variations of a quantitative character, though not exhaustible 
 
 by repetition of an identical unit. But when neither side 
 
 presents a true ratio, i. e. when on neither side are the several 
 
 terms measurable by an identical unit, then proportion is gone, 
 
 and we are referred back or across to Analogy or Subsumption. 
 
 a and a (2) Leaving the intermediate portion of these gradations for 
 
 the reader to fill up, I pass at once to a class of proportions 
 
 which prevail in a certain sense throughout the entire world 
 
 of knowledge. I speak of related series of contents which might 
 
 appropriately be designated * a and a ' series. The examples 
 
 which spring at once into the mind are the perceptions or 
 
 sensations of light and sound, with their respective physical 
 
 stimuli. It is true that in the connection of such series as 
 
 these we come upon a ' limit of knowledge ' ; but it admits of 
 
 question how far even in the most favourable instances of 
 
 them we can be said to have proportional inference. -"^ Perhaps 
 
 ' I suppose that ' irrational ' in mathematical language designates 
 a relation which cannot be expressed as a ratio, viz. as a relation between 
 two numbers. It would seem then that ' incommensurable ratios ' must 
 be a contradiction in terms. The convenience of the expression in 
 mathematics would not necessarily be interfered with by its self-contra- 
 dictory character. Many conceptions which involve a more or less 
 latent contradiction are employed in special sciences — quantitative 
 infinity,^ or involuntary contracts, are well-known instances. It is 
 interesting to notice that the reason of one science may be the unreason 
 of another. Hegel complains that mathematicians call everything 
 
 " See i. 163. 
 
 series 
 
Chap. II] Applications of Proportion 75 
 
 the relation of angle to arc, which Lotze gives as an example, 
 is about the extreme instance of true quantitative proportion 
 which, although quantitative, includes heterogeneous matter. 
 
 When we look at the relation of musical sound to stimulus 
 we find an ascertained parallelism between changes in the 
 rapidity of periodic vibrations that reach the ear, and changes 
 in pitch of the musical note which they generate in conscious- 
 ness. And further, the changes in pitch are a continuous 
 variation of a pervading quality and therefore are quantitative ; 
 and these are commonly measured by certain intervals of 
 change taken to be equal in the sense of sharing certain attri- 
 butes and capacities which remain the same for corresponding 
 intervals in all parts of the scale. If we attempt to make out 
 a proportional statement of these relations we may get some 
 such result as a vibrations in second : 2 a vibrations in second : : 
 note a : its octave a^ ; a relation which admits of the quasi- 
 subsumptive inference a = i6| .'. a = a certain note x, and 
 oj a certain note y. 
 
 But this inference is by no means purely mathematical or 
 quantitative. 
 
 First, we must notice the presupposed limitations, which do 
 not exist in any purely mechanical or purely geometrical law. 
 The vibrations must affect a hearing ear, and to affect a hearing 
 ear they must be within certain limitations both of rapidity 
 and amplitude, which from a mathematical point of view are 
 wholly arbitrary. 
 
 Secondly, we must observe that not only, as in true cases 
 
 of proportion such as that between the angle and the arc, are 
 
 the two sets of terms incommensurable with one another, but 
 
 also it is very doubtful whether the two terms represented by 
 
 a and a^ can be strictly called commensurable. In a sense nd 
 
 doubt the tones of the scale are units and serve as measures. 
 
 But if we ask which note is ' twice ' another, we are perplexed 
 
 between the octave, which corresponds to twice the stimulus 
 
 of the octave below, and the note, whatever it may be, which 
 
 irrational in which reason begins to intrude — i. e. in which systematic 
 heterogeneity begins to appear, e. g. in the relation between straight line 
 and curve. Ratio is the reason of mathematics, and other systematic 
 relations may be irrational in this sphere ; just as ratio may be an 
 irrational relation outside mathematics, e. g. in political science. 
 
76 Induction and Reasoning [Book 11 
 
 is next above the lowest audible note. For two of any identical 
 unit ought to be twice one. But just as the zero of the common 
 thermometer is not a zero of heat/ so there is no sense in 
 making the lowest pitch, or the point where pitch passes into 
 separate sounds, a zero of pitch from which all its grades can 
 be constructed by mere multiplication or superimposition. We 
 may say, if we like, that the quantity is intensive, i. e. that the 
 grades by which the greater is separated from the lesser 
 amount do not persist in a distinguishable form beside or 
 within the greater amount when it is attained. This, however, 
 is only to say in other words that we are passing beyond a true 
 quantitative relation. All true measurable quantity is exten- 
 sive. In as far as it is merely intensive it is unanalysed, not 
 referred to parts, and so not quantitative. Here we are be- 
 tween the two ; we have degrees which are not parts, and of 
 which the whole is in no strict sense a multiple, but which not 
 only exhibit an advance in themselves but correspond to parts 
 of which their whole is a true multiple. 
 
 Then, thirdly, we are confronted here with something like 
 a genuine subsumption. The correspondence of 33 vibration 
 per second to a note x rests on a concrete relation, which we 
 find but cannot construct, between an impact on the living 
 person through the ear and a reaction in the soul of that person. 
 It is by subsumption under this characteristic individuality 
 that we justify the conjunction, not otherwise necessary, of 
 periodic vibration and musical sound. 
 
 It should be noticed, too, as bearing on the concreteness 
 of the operation which we are now considering, that loudness 
 is a quantitative attribute of musical sound, and corresponds 
 to a distinct feature of the sonorous vibrations, viz. to their 
 amplitude, which I presume must on the whole diminish with 
 increasing pitch. This ratio, and other analysable character- 
 istics, fall within the same series of contents as that to which 
 the correspondence between pitch and rapidity applies. We 
 are thus in such a case far from being able to obtain a simple 
 proportion between contents as wholes. 
 
 ^ The idea of an absolute zero of heat does not matter for the present 
 purpose, which is merely to illustrate the nature of a series which is not 
 in a true ratio. See Mill's Logic, i, pp. 441 and 446. 
 
Chap. II] Proportion and Analogy yy 
 
 When we come to the colour-sensations, the individuaUty or 
 disparateness of the a terms increases, and the quantitative 
 relation, still traceable in sound, heat or pressure, becomes 
 much more obscure if it does not disappear. Not to speak 
 of the dark heat rays and the dark chemical rays, which mark 
 differences in the action of the ether corresponding to no saltus 
 in the ratio of vibrations, the transitions from colour to colour 
 defy all attempt at quantitative expression. No one could 
 mean anything by saying that central violet is twice or three 
 times or five times central red, except in so far as colours may 
 be characterised by an intensity of illumination which is a 
 different thing from the peculiarity of their hue. It is needless 
 to go into detaU on this head. It is plain that while the 
 variations in the mechanical stimulus, the a series, are still 
 strictly numerable, the terms of the a series are altogether 
 ceasing to present commensurable and therefore numerable 
 differences in respect of their distinctive individuality, although 
 various numerable differences may be traceable within their 
 content. Then proportion in the strict sense wholly ceases to 
 apply, because there is a ratio on one side only, and not on the 
 other ; and there cannot be equality of ratios unless we have 
 two sets of matters with a ratio between the members of 
 each set. 
 
 Nevertheless, there is in the colour series a uniform relation 
 of a proportional character. ' Wave-length x : wave-length y : : 
 violet : red ' means not that red is such and such a multiple of 
 violet, but yet that in a series in which wave-length x gives 
 violet we can be sure that wave-length y will give red. And 
 though these colours are not producible as multiples of one 
 another, yet they are identifiable, on the assumption of corre- 
 spondence to stimuli, by the process of colour-equation. Given 
 the means for producing true spectral red, a problematic red 
 colour can be equated with it, and the difference between the 
 two stated in terms of the stimulus. 
 
 e. We have here, it might be said, passed from Proportion Propor- 
 to Analogy, which abandoning its original meaning of propor- j ' ^^^^ 
 tion has come to signify an inexact comparison of relations. Hypo- 
 But Analogy in the logical sense is not really an inexact form judg- 
 of proportion, but depends on other than quantitative con- ment. 
 
78 Induction and Reasoning [Book 11 
 
 siderations, as we shall see in the next chapter. And though 
 we are now passing out of the region where equality of ratios 
 would grasp and penetrate the whole essence of the subject- 
 matter, yet there is no need to leave behind us either precision 
 in the designation of relations, or such numerical attributes as 
 accompany though without exhausting the individuality of 
 contents. For these reasons it is better not to consider that 
 we are here returning to Analogy, but rather that we are 
 approaching, from the side of exact science, the hypothetical 
 judgment, which forms the meeting-point between the concrete 
 and abstract forms of inference. And the h5^othetical 
 judgment, especially when retaining a partially quantitative 
 content, represents what may be called the wider or the 
 philosophical sense in which mechanism prevails throughout 
 the knowable world. In many regions it is not much that this 
 view of things gives us ; but it is always something. 
 
 It is needless to pursue this hypothetical judgment through 
 all the gradations in which it embodies the idea of proportion 
 throughout the sciences. Everywhere we have in the back- 
 ground the strictly numerable relations of space, time and 
 mass. The exhibition of connected groups of contents as a and 
 a series, in both of which the terms are as nearly as possible 
 commensurable, is the ideal of natural science, or of physical 
 science in the strict sense. How far in detail chemistry or 
 biology may be reducible in this sense — for there is no other 
 sense in which they can be — to molecular physics, is a question 
 of fact and practice. At present it must often seem as if 
 instead of a and a series we had rather a and x series, i. e. corre- 
 spondences in which even the more quantitative series has hardly 
 a true ratio between its terms, while the less quantitative 
 series has no ratio at all. I have in my mind such correspon- 
 dences as those between changes of temperatiu*e and allotropic 
 phenomena in chemical agents, or again between changes of 
 temperature and degrees of irritability in organic beings. But 
 the changes of temperature themselves, considered as an 
 a series, have behind them as a true a series their mechanical 
 equivalents in the wa}? of mass and motion (footpounds), and 
 thus the whole phenomena, even those of allotropism, have 
 ultimately a true correspondence with a genuine a series. Such 
 
Chap. II] Wofk and Coftsciousness 79 
 
 a correspondence would form the content of a hypothetical 
 judgment, under which quasi-subsumptive inference would be 
 possible. 
 
 (. It is under this modification of ' a and a series ' that we Con- 
 ought to consiuer such a question as the relation of the physical scious- 
 changes in the human organism to the activities of conscious- Conserva- 
 ness. I am not now dealing with the sheer question of fact, ^^^^^ 
 whether in the human or other organism, considered as a 
 machine, the production of work can be experimentally proved 
 to be limited by the supply of mechanical energy. We know 
 too well from daily experience that the output of work has 
 gradations and a limit — a limit related at any rate inter alia 
 to the supply of food. That this limit is prescribed by con- 
 ditions precisely analogous to those which are embodied in the 
 working of every machine, viz. by the constancy of energy, 
 seems to be the natural assumption so long as no other principle 
 of gradation and of limit is convincingly demonstrated. 
 
 But we now come upon a second difficulty. We assume that 
 molecular change and muscular contractions in the organism 
 must be taken as theoretically subject to the constancy of 
 energy, i. e. that life or the soul so far as operative in or through 
 the organism cannot create energy out of nothing.^ These 
 changes and contractions either are, or are reducible to, 
 mechanical equivalents in motion and mass, and between them 
 and the supply of energy a true a and a proportion might, if 
 our knowledge permitted, be established. 
 
 But between either these organic changes or the expenditure 
 of energy, on the one hand, and the states of consciousness 
 which sometimes attend these changes on the other, no possible 
 proportion could hold good. Here we have then a pair of series 
 a and x (organic changes and consciousness) on the basis of 
 a pair a and a (expenditure of energy and organic changes). 
 
 ' I cannot think that Wundt, Logik, ii, p. 507, really means to deny 
 this, though his expressions are bewildering; ' Hier (in the spiritual 
 development) gilt vielmehr (as against the law of constancy of energy) 
 ein Gesetz unbegrenzter Neuschopfung geistiger Energie.' To judge 
 from the Physiologische Psych, ii. pp. 461-3, he thinks that ' Geist ' is 
 operative throughout nature, and its ' creation of energy ' must be 
 a question merely of new forms of action. But I cannot thoroughly 
 understand his view. 
 
8o Induction and Reasoning [Bookii 
 
 It does not matter for our purpose here whether consciousness 
 is independent work performed by the organism, or is an un- 
 accountable attendant upon such work which is not represented 
 in its cost, or lastly, a consequence, or ' effect ' if we like, of 
 certain peculiar organic work, represented in the mechanical 
 cost of such work, and inseparable from such work except by 
 an utterly unmotived abstraction. In all of these cases we 
 have, whether directly or through organic activities known to 
 accompany consciousness, what may be called an a and a rela- 
 tion, or more truly an a and x relatioii mediated through a, 
 between mechanical work and consciousness. But on the side 
 of consciousness of course no ratio can be established, and 
 therefore there is no proportion. We cannot safely say that 
 to learn twenty" lines of Virgil demands twice the expenditure 
 of work that is needed to learn ten. We cannot say that to 
 write the same letter requires the same exertion on one day 
 and on another. We must however be on guard here. Inter- 
 ruption, a different state of memory, obstacles in the content, 
 impair the reliability of what might seem a unit of mental work. 
 But mere weariness of the organism which may lengthen the 
 time taken and the apparent exertion demanded, seems only 
 to affect the proportional and not the absolute work needed. 
 What we have under such circumstances is merely a case of 
 a weak machine doing slowly what a strong one does at one 
 blow. The weak machine may however be destroyed by 
 application to work too heavy for it, and in this sense even 
 an identical unit of work has not always the same total effect. 
 If a unit cannot be obtained for the a; or a series, what can 
 our would-be proportion do for us ? It enables us to say 
 generally, though not precisely, that amount of even intellec- 
 tual activity varies as expenditure of mechanical energy and 
 is limited by the sources from which that energy is drawn ; 
 and further, to say precisely, though only as a hypothetical 
 judgment of which the condition can never be entirely fulfilled, 
 that if we could equate two amounts of intellectual activity, 
 or if we could have the same intellectual activity repeated under 
 the same conditions, we should find it had absorbed or had 
 been accompanied by the same amount of mechanical work. 
 There is, that is to say, a formal and constant correspondence 
 
Chap. II] The Thinking Being 8i 
 
 between amount of mechanical energy and amount of intel- 
 lectual work ; but mechanical equivalence is so subordinate 
 an aspect of such work that this constant relation tells us 
 nothing by way of calculation, and only embodies in an abstract 
 principle what we knew before — ^if he does not eat, neither can 
 he think. 
 
 It may be objected that intellectual activity apart from 
 molecular change, which latter is not intellectual, absorbs no 
 work at all. But when any one can show us thought apart 
 from an organism it will be time enough to speak of thought 
 as an activity not dependent upon organic changes. Prima 
 facie the complex molecular changes which accompany thought 
 have thought for their natural outcome and consequence, and 
 owe their high mechanical cost to this characteristic. That no 
 mechanical expenditure goes directly to thought, but aU goes 
 to molecular change which is in some cases accompanied by 
 thought, is only what we should naturally expect supposing 
 thought to be conditioned by the activity of a physical organ- 
 ism. In any other case, i.e. supposing a contingent of energy 
 to disappear into the thought-process and be unaccounted for 
 in the balance-sheet of the body, we should have a propor- 
 tionate amount of thought unaccompanied by material change, . 
 which is unknown in our entire experience and contrary to the 
 whole analogy of that experience. All that we can say is that 
 the thinking being, as we know him, is thus and thus con- 
 ditioned. We cannot safely separate in theory what can never, 
 to our experience, be separated in fact. 
 
 iii. Mechanism in the widest or ultimate sense is thus com- The Me- 
 patible with the disappearance of the ratio in both of the ^g^^^^j 
 corresponding series. The principle of ' mechanism ' is by this Know- 
 curtailment reduced to the law of Sufficient Reason, and simply ^^^^^' 
 expresses the point of view from which the scientific under- 
 standing necessarily and inevitably regards the world. This 
 point of view is not a t5n:anny to be avoided, but a claim which 
 must be satisfied. The Understanding is a necessary moment 
 in the Reason. Instead of precise proportion, enabling us to 
 construct or to predict by a formal process, we have in 
 mechanical determination thus understood a conception which 
 confronts us with a material problem. A man's character 
 
 1337-2 G 
 
82 Induction and Reasoning [Bookii 
 
 deteriorates, or the prosperity of a nation decays. The con- 
 ception of mechanism or of sufficient reason entitles us to treat 
 these phenomena as problems demanding explanation. They 
 must not be miraculous, i. e. not isolated, ' cut off with an axe ' 
 from the system of knowledge. We express this demand by 
 saying that every change — or more generally, every modifica- 
 tion — has its reason. It is only our tendency to illustrate the 
 universal by the plural that makes us state the principle as 
 if it necessarily applied to a number of examples in which the 
 same ground has the same consequence. What we really mean 
 is that every content is a consequent, and that every conse- 
 quent has a ground. That the connection of ground and 
 consequent is necessary, and therefore if the one is repeated 
 without modifying circumstances then the other is repeated 
 without modifying circumstances, is involved in the point of 
 view from which we speak of ground and consequent at all. 
 But what we primarily mean is objectivity, not uniformity. 
 
 Some uniformity, however, is for us a corollary from objec- 
 tivity. The ultimate fact of knowledge, on which the objective 
 relation of ground and consequent depends, is the existence of 
 systematic connections. Now a system is a whole, a universal, 
 an identity in difference. From the very beginning this is 
 what we meant by something objective, something by which 
 intelligence could agree with itself in the world of meanings. 
 But such a system or identity, however heterogeneous the 
 parts that enter into it, of course pervades all these parts as 
 a common character. As we saw in the last chapter, if a, b, c 
 are mere particulars, there is no bridge from the one to the 
 other. A connecting quahty there must be, although it need 
 by no means take the shape of an immediate and simple 
 quality. Thus in highly complicated matters we go back again 
 to an earlier function of knowledge, and substitute equational 
 comparison for exact enumeration. But the comparison is not 
 here the ground of inference ; the contents have the partly 
 quantitative relation, which admits of such comparison, as a 
 consequence of their systematic connection, but the grounds 
 of inference lie in the systematic connection itself. Let the 
 a series be the phases of the artistic individuality of a painter, 
 and let the a series be a chronologically arranged series of 
 
Chap. II] Abstract Hypothesis 83 
 
 pictures in which these phases display their effects. In such 
 series we shall always have, among other processes of judgment 
 and inference, a comparison by way of equation applied to 
 pervading quaUties as between phase and phase, and between 
 picture and picture. No one would doubt that Turner's water- 
 colour picture of Durham painted in 1836 has more of certain 
 striking qualities commonly associated with Turner's art than 
 that painted in 1802. But of course there would be no sense 
 in saying that the one is twice or three times as ' Turneresque ' 
 as the other. 
 
 In series Uke these we have subsumption or abstract hypo- 
 thesis — which latter is the bridge from mechanical construction 
 to concrete systematic inference — according to the nature 
 of the subject-matter. In tracing the phases of an artist's 
 genius we have properly subsumption, the unity which operates 
 being concrete and self-contained. But yet as regarded in the 
 light of causal ideas the phase of mind may be distinguished 
 from the picture produced, and the one regarded as the cause 
 or ground from which, on the latent basis of a real individuality, 
 the other necessarily issues. From this relative point of view 
 the connection would be expressed by abstract hypothesis, 
 ' If a.^, then ag.' In this aspect everything in the universe may 
 be referred to conditions outside itself, and nothing is free, 
 complete, or self-contained. For to regard things thus is 
 simply a phase or moment of knowledge, the phase which 
 consists in determining every x in terms of some correlated y. 
 Cause and condition, reason and ground, are only species of the 
 generic idea which presides over thought of this type. But in 
 ground we have as we saw ^ a conception in which the correlated 
 terms tend to fall together, and to pass from being parts related 
 within a system to being the system itself. The whole con- 
 ception which we are discussing — the conception of ' sufficient 
 reason ' — ^is simply a coroUary of or aspect in the ultimate 
 nature of the universal, which is in other words the ultimate 
 nature of thought itself. We have constantly reiterated that 
 every universal is an identity in difference ; and it is only the 
 converse of this to say that every difference has a distinct and 
 assignable place among the differences of a universal. 
 ^ Cp. Book I, chap. vi. 
 G2 
 
84 Induction and Reasoning [Book 11 
 
 The statement of the principle of sufficient reason which 
 was laid down above, ' There is no difference ^ without its 
 reason,' may be illustrated by the formula in which Lotze ^ 
 embodies it, A + B = C. This formula is intended to mean 
 that a real subject A can only pass into a specific phase C 
 under an assignable condition B. The ' proof ' or analysis of 
 the principle must be reserved for a later chapter. Here 
 I am only dealing with its import. And we see its import 
 reduced to the most abstract type when we are in a stage 
 beyond proportion and yet have not returned to true sub- 
 sumption, i.e. when we are dealing with the pure hypothetical 
 judgment. For we have at this stage a de facto correspondence 
 of which the ultimate ground is more or less latent, between 
 the terms a and a, h and /3, and so forth. What then do we 
 mean by correspondence ? We could not say that a and a 
 correspond if a and a were respectively isolated occurrences of 
 their kind. For what could possibly justify us in picking them 
 out of the myriad complications of reality and attaching them 
 together to the exclusion of other events and relations ? 
 Correspondence involves the recognition of a universal which 
 fixes the relations of the terms that correspond. If the series 
 a, h, c is to correspot?d to the series a, /3, y, then both series, 
 simply in order to the possibility of selecting them, must be 
 capable of being regarded as a^, Uj^, a^ and a„, a^, ay If in a 
 combination of musical sounds a slight harshness a is raised 
 to a discord h, then the consequent feeling of pleasurable excite- 
 ment a passes into a feeling of pain /3. In virtue of being phases 
 of the same combination the two sounds may be represented 
 as a^ and a^ respectively ; and the two phases of emotion, in 
 virtue at any rate of relation to the same series of sounds, may 
 be represented by a„ and a^ respectively. But neither sounds 
 nor feelings, of course, are terms between which a ratio sub- 
 sists. What we can infer is, by a process which is half-sub- 
 sumption and half -hypothetical judgment, * In a pair of series 
 where the sound a^ causes the feeling a„, the sound a^ will 
 
 ^ p. 82, above. It is commonly worded ' there is no change ', Sec, but 
 I have attempted to show in Book I, chap, i, f hat change is simply a case 
 of difierence and needs no separate logical treatment. 
 
 ^ Logik, sect. 63. 
 
Chap. II] The Understanding 85 
 
 cause the feeling a/3.' When we develope any such doctrine 
 as that the source of pain is intermittent irritation of sense, 
 of which musical discord is a species, we pass into subsumption 
 of the higher kind, which has absorbed into itself what can be 
 done by mechanical construction. 
 
 The point of view which we have been considering — ^that 
 of reflection and relativity — is the point of view which has 
 been distinguished by Kant and Hegel as the standpoint of 
 the understanding. It is not separable in kind from the 
 mode of consideration which the same thinkers have desig- 
 nated by the term Reason. Nor is it an intelligible conten- 
 tion, even if favoured by the language of Kant in dealing 
 with practical philosophy, that Reason could be actual and 
 operative otherwise than as completing and containing the 
 understanding. That the understanding must have its rights 
 is one of the cardinal principles of Hegel, which Lotze has 
 but laboriously and ingeniously illustrated in his analysis of 
 the pervading mechanical aspect of the world. The real 
 prophet of the understanding, however, was Schopenhauer. 
 His treatment of the principle of sufficient reason as at once 
 the fundamental axiom of human science and the innate source 
 of its illusions, forms an ultimate and irreversible criticism 
 on the aspect of intelligence which consists, to sum up its 
 nature in a popular but not inaccurate phrase, in explaining 
 ever5^hing by something else — a process which taken by 
 itself is necessarily unending and unsatisfying. 
 
 In returning from the consideration of abstract necessary 
 relations to that of concrete real totalities, we must remark 
 that ideally speaking every concrete real totality can be 
 anal5^ed into a complex of abstract necessary relations. 
 Were this not so, as it is Wundt's and Lotze's great achieve- 
 ment to have shown in detail, teleology itself would vanish. 
 For adaptation disappears if the end can dispense with means, 
 and a universe which had no necessary connections between 
 its parts could have no definite or significant structure as a 
 whole. In the remainder of the present Book I shall attempt 
 to put these relations in a clearer light. 
 
CHAPTER III 
 
 Analogy 
 
 We now take up the thread from the end of sect, i of 
 the last chapter, and returning into the track of concrete 
 inference, we have to ask ourselves how we go forward in 
 inference from a simple enumerative Induction when we do 
 not accept the task of completing the enumeration. In this 
 case we no longer count the examples, but we weigh them. 
 We turn the focus of attention upon the concrete content 
 which as subject of both premises, as a real thing or things, 
 formed the middle term of Induction, and endeavour to deepen 
 it by observation, and to define its relations by analysis. 
 The first effect of this procedure is to transform the content 
 in question from a subject into a predicate, as no longer a 
 qualification tacitly presupposed of reality, but as an attribute 
 explicitly referred to it and under process of definition and 
 extension. 
 Analogy I- As regards the relation between Analogy and Enumera- 
 andEnu- ^j^g Induction, we have to remember that Induction only 
 
 rnpr3.tivp 
 
 Indue- . gave us a problem or suggestion ; and consequently we cau- 
 tion. j^Q^ arrange the two types of inference in a simple conca- 
 tenation by taking the Inductive conclusion as the analogical 
 premise. Rather we have in Analogy to go back upon the 
 suggestive process of Induction, and repeat it with the 
 requisite difference. Suppose that the Inductive Inference or 
 grounded conjecture has been — 
 
 The poor people ah c d are pauperised x ; 
 
 The poor people abed are constantly cared for by charitable 
 
 persons y ; 
 .-. Being cared for by charitable persons y may have to do 
 
 with their being pauperised a:. 
 If now we desire, as we ought, further to examine this 
 suggestion on the basis of the direct experience which gene- 
 rated it, we shall still make this experience — ^the cases a, h, c, d 
 
Chap. Ill] From Induction to A nalogy 87 
 
 — the middle term or ground of inference, but we shall divert 
 our attention from the number of the examples to their nature, 
 and shall therefore put their nature as an attribute in the 
 place of a predicate common to both judgments. Thus we 
 obtain an argument having a form akin to that of the Aris- 
 totelian second figure. And the premises are now no longer 
 conjunctive individual judgments, but are passing into generic 
 judgments. 
 
 In the pauperised type x, what strikes us on further ex- 
 amining the cases is the loss of independence (A as 
 common content oi a b c d) ; 
 In the charitably-cared-for type y, what strikes us on 
 further examining the cases is the loss of independence 
 (A as common content oi a b c d) ; 
 .'. The type y has a fundamental feature A akin to the type 
 
 X and the two are thus closely coherent. 
 We are apt to think that in analogy we must conclude 
 from old instances to new instances. But analogy is essen- 
 tially an argument about the significance of a type, or of 
 what in botany are called characters. Of course however this 
 inference, like all others, has the aspect of discovery as well 
 as the aspect of proof. The deeper theoretical need is to find 
 the link and limit of connection between the characters x and 
 y sometimes observed in conjunction, i. e. to prove the one 
 of the other. But the reality of the distinction between x and 
 y which gives interest to the inference makes it practically 
 certain that in some examples we shall be first struck by y 
 and in some first by x, and that we shall often need to make 
 the circuit through the identical nature A before we can even 
 detect or have ground to believe in the remaining character 
 X or y. This is the aspect of discovery. Proof overcomes 
 logical disconnection, discovery overcomes apparent presented 
 disconnection. Thus our account of Analogy can really satisfy 
 the popular idea that inference is, here as in Induction, from 
 particulars to particulars. 
 
 I subjoin one or two simple examples, in order to illustrate 
 the connection of proof and discovery, and the working of the 
 process. 
 Enumerative Induction {or observation in single instance). 
 
88 Analogy [Bookii 
 
 Almost all animals have some power of self-movement j 
 Almost all animals have some degree of sentience ; 
 .*. Sentience may be intimately connected with self-move- 
 ment. 
 Analogical Enquiry. 
 
 Self -moving creatures are creatures in need of special nourish- 
 ment and protection {qua living creatures) ; 
 Sentient creatures are in need of special nourishment and 
 
 protection {qua living creatures) ; 
 .*, Sentience is connected (by the requirements of animal 
 
 life) with self-movement. 
 I may give another instance which shows the transition 
 from Induction to Analogy just not made. Newton guessed -^ 
 that a diamond was combustible, because of its high refractive 
 index relatively to its density, a feature which he had observed 
 in many combustible bodies. 
 Enumerative Induction. 
 Oil, Canada balsam, &c. are combustible ; 
 Oil, Canada balsam, &c. have a high refractive index 
 
 relatively to density ; 
 .'.High refractive index may be connected with com- 
 bustibility. 
 In the case of the diamond the combustibility had not 
 been observed, so that when applied to it the conclusion was 
 a prediction or discovery. But the essential import of the 
 conclusion would have been just the same if no new case 
 had been in question. 
 The next step would have been to say — 
 ' Combustibility has to do with such and such attributes 
 
 of oil, Canada balsam, &c. 
 High refractive index has to do with these same attributes. 
 .•. High refractive index is fundamentally connected with 
 
 combustibility.' 
 But this step, which would have constituted an analogical 
 inference, has not, as I understand from the passage in Mill, 
 been taken. 
 
 ' See Mill's Logic, ii, p. 88. I write merely on the faith of the place 
 in Mill. The instances by which I illustrate Newton's guess are there- 
 fore of my own invention. 
 
Chap. Ill] The Fivst SuggesUon 89 
 
 We may now look at an instance drawn from the relation 
 of natural kinds. 
 Enumerative Induction. 
 The exotic Pelargonia have a peculiar herring-bone structure 
 
 in the petals j 
 The exotic Pelargonia have the same kind of seed-vessels 
 
 as our wild geraniums ; 
 .*. In flowers with the peculiar seed-vessels of our wild 
 geraniums it is worth while to look for the herring-bone 
 structure in the petals. 
 Analogy. 
 The herring-bone structure is conjoined in the Pelargonia 
 
 with the characters of Geranieae ; 
 The flowers with such seed-vessels as our wild geraniums 
 
 have the characters of Geranieae ; 
 .'. That these flowers, e.g. our wild geraniums, should 
 have the peculiar herring-bone structure ^ is exceedingly 
 probable. 
 Botanical classification might almost be said to rest wholly 
 on analogy. The above guess, like a thousand and one such 
 guesses which every field botanist is continually making, 
 is verified in fact. The eye that can detect the dominant 
 habit of. a natural genus or order in an unfamiliar species is 
 constantly inferring in analogical form, on the ground of 
 generic identity, to hundreds of details, which as a rule 
 confirm its diagnosis on more minute inspection. And the 
 term diagnosis, logically applicable, but not customarily 
 applied, to botanical science, reminds us of another great 
 province of knowledge in which analogical inference is our 
 guide and counsellor. As in the normal so in the abnormal 
 activities — ^the diseases — of the organic world, it is analogy 
 that is the chief clue to what is taking place and to what we 
 must anticipate. Diagnosis is to symptoms what classification 
 is to characters. And finally we may here mention the class 
 of examples to which we shall shortly return as throwing the 
 
 ^ As a matter of fact, all the Geranieae which I have examined possess 
 this structure. I might have mentioned this verification immediately 
 after the Induction ; but this would really take us into mere enumera- 
 tion of instances. It is the coherence with the properties of a natural 
 kind that alone gives any help towards a general conclusion. 
 
90 Analogy [Bookii 
 
 strongest light upon the true rationale of analogy, although 
 or because they tend ultimately to pass beyond its province. 
 I mean our judgment of the actual use or even of the inten- 
 tional object of mechanical adaptations of every kind, whether 
 in nature or in the work of man. Thus we may infer by 
 Analogy, 
 
 Cutting-tools have edges, and places for handles ; 
 These flints have edges and places for handles ; 
 ,-. These flints are cutting tools. 
 
 Here we go at once to analogy, without passing through 
 
 the observation of conjunctions as a first suggestion. It is 
 
 not simply from seeing handles and edges conjoined in knives. 
 
 or chisels that we know a cutting-tool must have a handle 
 
 and an edge. We know this from extraneous considerations, 
 
 especially from the texture and use of the human hand. 
 
 But nevertheless we might never have discussed the coherence 
 
 of these attributes if we had never seen them in conjunction ; 
 
 and further, in the new instance of the flints, we have had 
 
 to go through a process of observation which told us that 
 
 here too there were both edges and handles or places for 
 
 handles. Thus the present example illustrates at once the 
 
 true nature of analogy, and the ground and degree of its 
 
 dependence on Induction. The observation ' Flint tools have 
 
 edges, flint tools have handles ', does not linger in the stage 
 
 of induction, simply because we are not dependent on the 
 
 nature of flint tools to tell us the connection in use between 
 
 a handle and an edge. We leap at once to this notion of 
 
 cutting-tools, and compare the flints with them in respect of 
 
 the conjoined attributes which we try to deepen and define. 
 
 Logical 2, The logical nature of analogy may be analysed as follows. 
 
 o^ana^-"^ i. As a formal syllogism in the second figure, having an 
 
 logy. affirmative conclusion, the analogical argument has the fallacy 
 
 Undistri- of Undistributed middle. We need not indeed trouble our- 
 
 middlein selves at this stage with questions of distribution involving 
 
 fig- 2. the extension of the judgment. Nevertheless a fault in the 
 
 extensional relations of an argument infallibly indicates 
 
 something which is prima facie a fault in its connection of 
 
 content. In the present case the fault is this — that what is 
 
 materially the ground of Knowledge, the content which 
 
Chap. Ill] No MajoT Premise 91 
 
 underlies and links together the two matters which demand 
 explanation, is, qua predicate or characteristic, in its wrong 
 place, the place of a consequent. Now according to the 
 ordinary interpretation of the judgment, of which we have 
 frequently spoken and which holds good for our present 
 level,^ the same consequent may have any number of inde- 
 pendent grounds. There is therefore no formal necessity 
 whatever for the two grounds or antecedents which in this 
 case possess the same consequent to have any connection with 
 each other beyond the fact that they do possess it. 
 
 But on the same ordinary interpretation of the judgment 
 if we deny the formal consequent of either of the grounds 
 while affirming it of the other, we can then deny that the 
 two grounds in question are connected through the universal 
 suggested in the premises before us. Thus the negative 
 argument escapes the formal defect which attaches to the 
 affirmative. About any further or other connection that 
 they may or may not have the denial tells us nothing, and 
 therefore it is really a denial not of all or any connection, but 
 of a particular connection through a particular middle term. 
 The customary omission in the conclusion to specify the 
 excluded connection is a fallacy a dido secundum quid ad 
 dictum simpliciter. It may be said that the denial takes 
 on the absoluteness of the assertion on which it rests. ' Every 
 Tory is a good man ; He is not a good man ; .-. He is not 
 a Tory.' If the major is true without reserve the conclusion 
 is true without reserve, and in logic we are to suppose our 
 premises true. But still we must consider what the judgment 
 means, i.e. what it really is. And no judgment is absolutely 
 meant. The conclusion does not really represent the inference 
 as a concrete thought unless we repeat in the conclusion, ' He 
 is not a Tory, so far as his not being a good man prevents his 
 being one.' This refinement has no exclusive relation to 
 analogical argument or to fig. 2, for the negative argument 
 falls into fig. i as readily as into fig. 2, the ground and con- 
 sequent in negation being reciprocal. In order to give the 
 criticism a peculiar relation to analogy we must say, ' He is 
 
 ' For the judgment is not purged of irrelevancy till it has passed 
 through scientific induction. 
 
92 Analogy [Bookii 
 
 not a Tory, so far as the peculiar way in which he is not 
 a good man prevents his being one.' This positive way is 
 variable. 
 
 Except then for the purpose of negative inference, which 
 is not purely analogical, the form of analogical argument in 
 fig. 2 is at variance with its matter, and represents no infer- 
 ential necessity at all. Inferential necessity is either sub- 
 sumptive or constructive. In order to obtain subsumptive 
 necessity one of the premises would have to be converted 
 and become a major premise. And this conversion would 
 have to be material, not merely formal ; for a formal con- 
 version of an affirmative generic judgment would destroy its 
 generic character and make it incapable of standing as a major 
 premise. The Analogical inference as it stands shares with 
 enumerative Induction the peculiarity of being a subsumptive 
 inference without a major premise — an argument from a 
 concrete content without the assertion that this content is 
 absolutely dominant for the purpose of the argument. Again, 
 in order to obtain constructive or abstract necessity the 
 relations of the contents must be reduced into abstract and 
 mechanical relations akin to the universals embodied in the 
 pure hypothetical judgment or in the equation. The formal 
 defect of analogy as it stands is expressed by the ' probably ' 
 inserted in the conclusion, which indicates a coherence under 
 conditions not precisely known. 
 Real ii. Seeing that the form of analogical argument is prima 
 
 Analogi- Z*^^*^ inconclusive, on what does its value really depend ? It 
 calArgu- represents, we said, the phase of thought in which we no 
 longer count but weigh the examples. It might be said 
 therefore that analogy is a material and not a formal infer- 
 ence. This is so far true that the value of analogy depends 
 not on a formal conjunction of attributes in a subject, but 
 on the material governing power or essentiality of a predicate. 
 Everything turns on the ' importance ' of the character which 
 forms the common predicate, and this ' importance ' is closely 
 bound up with completeness of definition. I will return 
 directly to the question of the importance of characters ; 
 but it is necessary first to point out that an inference without 
 assignable form is no inference at aU, and that therefore it is 
 
Chap. Ill] Logical ' Importance ' 93 
 
 not correct to say that analogy is a material and not a formal 
 inference. Every inference has a form, in the sense of a 
 definite relation between the differences of the universal which 
 the inference exhibits. I do not however mean to say that 
 such a form can be laid down antecedently for every inference. 
 It is this relation, as we have seen, which varies with the 
 nature of the universal, and which by its variations dictates 
 the main types both of judgment and of inference. We need 
 not here take refuge in the form of complete subsumption 
 through the conversion of one judgment. When that is 
 possible — and no doubt analogy is on the road to it — we are 
 already beyond analogy. But the form of analogical argu- 
 ment is to be found in the neglected aspect of the ordinary 
 judgment, its strong implication of a value in the predicate. 
 If all judgments were taken as reciprocal, analogy would be 
 ipso facto an argument from ground to consequent, besides 
 being as it is now from consequent to ground. ' Two grounds 
 that have the same consequent ought to cohere,' is the form 
 as it stands. ' Two grounds that have the same consequent 
 are consequents of the same ground, therefore must cohere,' 
 is the implied form, or, as we said above, the matter of the 
 inference. This form might be identified with fig. 3, and so 
 take us back to Enumerative Induction. But the content 
 being changed from instances into their defined nature, we 
 are rather taken forward into the hypothetical judgment as 
 used in constructive inference, or to complete subsumption 
 in fig. I. With reciprocal judgments the syllogistic form 
 becomes indifferent ; and the premises of analogy are im- 
 plicitly reciprocal.-'^ That their reciprocity is implicit and not 
 explicit is in accordance with the nature of analogy, which is 
 as we have agreed only a method of problematic conclusion, 
 not a method of absolute and precise determination. 
 ^ The explicit form is A is B ; The implicit form is B is A ; 
 C is B ; B is C ; 
 
 .-. Cis A. .-. Cis A. 
 
 But the implicit form deals not with mere instances as in Induction, 
 but with that B which was found to be essential in A and C. Therefore 
 the whole implied argument is — 
 
 If B, then A (which is also a sign of B) ; 
 
 If B, then C (which is also a sign of B) ; 
 .'. If C, then B and therefore A. 
 
94 Analogy [Bookii 
 
 I now return to the question of the material ' importance ' 
 of characters, the attribute on which the implicit form of 
 analogical inference depends. It is possible, and is verified 
 in daily experience, that a character or group of characters 
 from which the remaining properties of an object cannot at 
 present be derived by mechanical analysis may either amount 
 for inferential purposes to a ground, or at least may serve 
 as an unerring index of the qualities of the object. Such 
 a character or group of characters, and I may add such a 
 symptom or group of symptoms, has logical ' importance '. 
 
 I will commit myself at once to the opinion that this im- 
 portance rests in every case on a presumption drawn from 
 what I may call morphology, or from teleology ; these two 
 ideas being regarded as secondary and primary forms of the 
 same conception. In all objects or institutions made for 
 a purpose by man, at least while their nature corresponds 
 to the intention embodied in their structure, there is true 
 teleology. In all organisms, parts of organisms, objects or 
 structures that live a life or have in any way a being that is 
 to our eyes individual and distinctive, there is morphology or 
 de facto teleology. I am aware that a de facto teleology is 
 a contradiction in terms. Purpose implies more than actual 
 result. But as a description of a result in language borrowed 
 from a result of another class — from human operation — the 
 phrase though contradictory may pass ; and it is in this 
 sense alone that I employ it. If there is a peculiar principle 
 underneath this ambiguous class of results, it is at least not, 
 within our knowledge, a principle of intentional adaptation by 
 a foreseeing consciousness. But I repeat that every universal, 
 every persistent identity in difference, just because it is 
 a synthesis of differences in a universal, may be regarded 
 as a concentration of means in a distinguishable result. How 
 far such a view is ' subjective ' or in what sense it renders 
 a real aspect of the nature of things is a question to which 
 I shall return. 
 
 It is on this characteristic of all universals that anticipation 
 by analogy rests. Where we have a constitutive equation, 
 i. e. an absolute rule for the synthesis of the differences, we 
 can construct without teleology and without analogy. If, 
 
Chap. Ill] Analogy and Teleology 95 
 
 again, according to Bacon's dream, science could arrive at 
 ' forms ' or underlying qualities, capable of doing the work 
 of constitutive equations for every natural attribute and 
 every natural object, then in presence of such a form we should 
 not need analog5^ Or where complete concrete subsumption 
 prevails, where we have actual conscious teleology, e.g. in the 
 philosophical analysis of laws, institutions, opinions, logical 
 activities, we should never need analogy but for the all- 
 important fact that all these contents are determined by 
 growth and history in a way of which those who make and 
 use them are not aware, and which they cannot control. 
 Hence all such matters have an organic and almost a mechan- 
 ical side, and can be treated by comparative science — analogy, 
 as well as by philosophy — analysis. No actual law or institu- 
 tion or idea has its form exclusively determined by its explicit 
 purpose. All of them are loaded with inherited matter which 
 may in part be an incumbrance, but in large' part serves 
 purposes wider and not less essential than the purpose which 
 consciousness is able to recognise. And in human affairs 
 there is a bridge between the unconscious and the conscious 
 function ; for the latent purpose — which as latent is not a 
 purpose at all — is actually one side of the explicit purpose 
 and is continually emerging into explicit consciousness, so 
 that the de facto operation of human energy in one stage 
 characterises the explicit purpose of that stage itself and 
 enters into the explicit purpose of the next. Thus philosophy 
 can deal with even latent or unconscious significance partly 
 as an aspect and partly as a condition precedent of conscious 
 significance. The history of religion or of any achievement 
 of man's intelligence is inexhaustible in illustrations of this 
 principle. Precise knowledge, however, whether affirmative 
 or negative, whether constructive or subsumptive, excludes 
 anticipation by analogy, for analogy is a stage on the road 
 to precise knowledge.^ This condition satisfies the popular 
 requirement ^ that in Analogy we must know neither necessary 
 connection nor necessary exclusion. 
 
 To explain the connection of Analogy with Teleology, I will 
 at once take the strongest class of examples. 
 
 * Compare however p. 217, supra. - Mill's Logic, ii, p. 88. 
 
g6 Analogy [Bookii 
 
 We are on the border between analogy and a higher form 
 of inference when we argue from a presumed genuine teleology 
 to the conjunction of qualities in the content that it governs. 
 We are so far already outside analogy that the argument must 
 consist largely of judgments upon actual mechanical adapta- 
 tions, the de facto use of which is a matter of precise know- 
 ledge and not of presumption. We are not wholly outside 
 analogy, because the de facto nature of these adaptations is 
 not enough, in the case supposed, to carry our conclusion, 
 which needs the actual and intentional purpose. This, in 
 inferences of the type supposed, can only rest upon pre- 
 sumption. If we find, near a known seat of stone-age inhabi- 
 tants, some flints of peculiar shape and make, it is a mere 
 judgment on a matter of fact to say whether they are adapted 
 for use as knives or as hatchets ; but to say what they were 
 meant for, and so actually used for, and therefore whether 
 we may expect to find near them chips of wood or bones of 
 animals, is a question for analogical inference based on the 
 nature of the country, on the known or supposed habits of 
 the people, and on any convergent indications in the adapta- 
 tions of the flint tools themselves. Any character in such 
 a connected group of characters, that gives the key to the 
 pervading purpose of the whole content under examination, 
 is an ' important ' character. ' Importance ' is relation to the 
 purpose or pervading nature, the ' import ', of any system. 
 If both quahties to whose coherence we conclude are directly 
 derivable from the presumed purpose, then we are so far 
 beyond analogy, but the element of presumption which con- 
 sists in ascribing true intention or purpose is still analogical. 
 If one or both of the qualities to whose coherence we conclude 
 are not derivable from the pervading purpose, then we are 
 more completely or quite completely in the region of analogy, 
 and the inference wiU simply be that identity of purpose 
 is probably both a ground and also a consequent of uniform 
 structure. 
 
 In the former case, both properties being derivable, we 
 have :-^ 
 
 The flint knives are adapted for cutting wood ; 
 
 Cut logs and chips are connected with cutting wood ; 
 
Chap. Ill] Knowu and Unknown Connections 97 
 
 .'. Cut logs and chips ^ will probably be found near the 
 knives (i.e. if the adaptation which we observe in the 
 knives is a true index of the use for which they were 
 really made, and to which — a further presumption — they 
 were actually put. 
 Or again : — 
 A telescope with the eye-piece at one side of the tube is 
 
 probably a reflector ; 
 Lord Rosse's telescope is a reflector ; 
 .". Lord Rosse's telescope probably has the eye-piece at 
 
 one side of the tube. 
 In the latter case we have, one or both properties being 
 not directly derivable from the presumed purpose, — 
 A. clock with a watch-movement is a carriage-clock ; 
 A clock with plate-glass sides is a carriage-clock. 
 .-. A clock with plate-glass sides is probably a clock with 
 
 a watch-movement. 
 There are pendulum clocks with plate-glass sides, so the 
 analogy is not made out. There is a reason why a clock with 
 a watch-movement should be a carriage clock, viz. that it 
 is a mechanism which the motion of the carriage will not 
 disturb. But there is no reason that I know of for the second 
 premise, which rests on mere custom and turns out to be a 
 precarious basis of argument. 
 Or again : — 
 
 A horseshoe-stand is a common shape of French micro- 
 scope-stands ; 
 A very simple stage is common in French microscope- 
 stands ; 
 .•. With a very simple stage one may expect a horseshoe- 
 stand. 
 The horseshoe shape is not the best for securing steadiness, 
 so that there is no direct connection between the two pro- 
 perties of which the conclusion alleges the conjunction, and 
 the pmrpose indicated by the name microscope-stand. And 
 I have purposely introduced a limitation referring to the 
 character of the conditions imder which the purpose is carried 
 
 ^ I omit, merely for brevity, to say anything about the possibility of 
 the chips &c. having been renioved. 
 1337-2 H 
 
gS Analogy [Bookii 
 
 out, ' French microscope-stand,' in order to illustrate the 
 boundary-line between genuine conscious teleology and mere 
 characteristic individuality. Probably in this example the 
 two join hands ; French makers must have, or have had, an 
 idea that the horseshoe shape and the simple stage best secured 
 the purposes of the microscope. 
 
 The former set of examples, with both properties derivable 
 from the purpose, illustrate the general type of analogical 
 inference affecting attributes connected with self-preservation 
 in the organic world — chief or fundamental attributes. The 
 latter, with one property or neither derivable, gives the general 
 type of analogical inference affecting attributes which are not 
 vital, but which have in heredity or otherwise their own degree 
 of constancy. But these examples, though illustrative of 
 organic relations, are by their connection with conscious 
 teleology upon a higher level than those relations. 
 
 A further class of inferences, to which the last example 
 prepared a transition, is intermediate between conscious and 
 merely organic teleology. I allude to the enormous class 
 of daily inferences relating to time or locahty of origin or 
 to authorship, in the case of literary, artistic, or mechanical 
 productions. Obviously the conception of the presumed 
 period, place, or person, as significant of peculiar charac- 
 teristics, may itself be the presumed ground of inference in 
 virtue of which the coherence of certain properties is analo- 
 gically expected ; or the individual characteristics stated 
 explicitly may be the ground, and the name may be inferred 
 by analogy. Supposing a single conjunction (Inductive in 
 its nature) to have furnished the suggestion ' This design 
 which is beautiful is by A. B,' ^ then analogical enquiry will 
 infer in the form ' The beauty of this design is drawn from 
 nature yet original and full of thought ; A. B.'s designs are 
 drawn from nature yet original and full of thought ; .*. The 
 beauty of this design is probably the beauty of one of A. B.'s 
 designs.' The reader can construct further variations of this 
 very common type of argument for himself. 
 
 The common analogical inferences which run throughout 
 our treatment of organic and even of inorganic nature rest 
 
 ^ In the form : ' This design is beautiful. This design is by A. B.' 
 
Chap. Ill] ' De facto ' telcologv 99 
 
 practically on the existence of natural kinds, that is to say, 
 on morphology or on de facto teleology. I may explain the 
 distinction of degree which I attach to the two expressions 
 by reference to the general conception of self-maintenance or 
 self-preservation. Where self -maintenance means simply any 
 reaction of a distinguishable agent against or upon an influence 
 approaching it from without, -I should speak of the distinguish- 
 able individuality of that agent as morphological, i. e. as con- 
 sisting simply of a formal or recognisable self whose unity is 
 charged with no especial interest. Where on the contrary there 
 is a self maintained or preserved which exhibits the attributes 
 of life, or, however partially, of consciousness, I should say 
 that the facts, and not our own choice, demand that we should 
 apply the paradoxical idea of an actual purpose, or de facto 
 teleology. It is obvious that the conception is one varying in 
 degree and not limited by any despotic necessity to the range 
 of the organic world. After all, it is a plain fact that elements 
 combine in processes ; and the moment we single out part 
 of a process as a result '^ we introduce the conception of de 
 facto co-operation on the part of means towards an end. 
 Every distinguishable persistent content may thus formally 
 be regarded as an end, without, of course, any implication 
 whatever of an aim pre-existing in a foreseeing consciousness. 
 That from a purely mechanical or analytic point of view such 
 constituent relations are absolutely indifferent to the whole 
 which they co-operate in constituting is a necessary conse- 
 quence of regarding such relations in their isolation. But 
 without the further aspect supplied by an interest in the whole 
 as such, not merely ethical and aesthetic judgment, but 
 scientific judgment itself, loses all power of discrimination, 
 and therefore all objectivity. Even to name, as we saw in 
 the Introduction, is to select and to identify. 
 
 Analogy then rests on the ' importance ' or significance of 
 attributes, an idea well illustrated by systems of true conscious 
 
 * This singling out a part as the ' end ' is essential to teleology, but 
 must ultimately be determined by the nature of the ' whole '. Thus 
 teleology strictly speaking is a partial conception, and less ultimate 
 than the idea of the whole. See e.g. McTaggart's Commentary on 
 Hegel's Logic, sect. 255. I hope to deal more fully with this point in 
 a forthcoming work. 
 
 H2 
 
100 Analogy [Bookii 
 
 teleology which happen to be but partially known to us, 
 but really dominant throughout the various grades of actual 
 self-maintenance and individuality presented by the organic 
 and inorganic world. Analogy is never demonstration. A 
 thorough mechanical nexus and a subordination to a conscious 
 purpose in an intelligent being or rational system both pro 
 tanto exclude it. 
 No ratio iii. The obvious truth that ceteris paribus the predicate 
 ties to° ^ ^^^^ more meaning has a deeper grasp of the import of the 
 Differ- reality which it qualifies, and so is the safer ground of inference 
 ^ ^^^' respecting that reality, has introduced the fatal fascination 
 of the ratio into the doctrine of analogy. I quote from Mill ^ 
 a complete account of the idea so generated : ' Since the value 
 of an analogical argument inferring one resemblance from other 
 resemblances without any antecedent evidence of a connection 
 between them depends on the extent of ascertained resem- 
 blance, compared first with the amount of ascertained difference 
 and next with the extent of the unexplored region of unascer- 
 tained properties ; it follows that where the resemblance is 
 very great, the ascertained difference very small, and our 
 knowledge of the subject-matter tolerably extensive, the 
 argument from analogy may approach in strength very 
 near to a valid induction. If, after much observation of B, 
 we find that it agrees with A in nine out of ten of its known 
 properties, we may conclude with a probability of nine to 
 one that it will possess any given derivative property of A. 
 If we discover, for example, an unknown animal or plant, 
 resembling closely some known one in the greater number 
 of the properties we observe in it, but differing in some few, 
 we may reasonably expect to find in the unobserved re- 
 mainder of its properties a general agreement with those of 
 the former ; but also a difference corresponding propor- 
 tionately to the amount of observed diversity.' 
 
 This passage gives us the valuable suggestion of negative 
 analogy, to which I shall return below. But as to the idea 
 of ratio, we must be faithful to our principle that in analogy 
 the examples — or the properties, it matters not which — are 
 to be weighed and not to be counted. Mill's idea is in fact 
 ' Mill's Logic, ii, p. 90. 
 
Chap. Ill] Number of Resemblances loi 
 
 that by counting the properties you weigh the examples. 
 And every one must be struck by the verisimilitude of the 
 view which the above passage propounds. But on pressing 
 the matter home we see that at least the form which it gives 
 to the right idea of insisting on the depth of the common 
 predicate is a wholly unreal form, and takes us into the wrong 
 track. There is no ratio without a unit ; and, to begin with, 
 a * resemblance ' (a point of identity) is not as such a content 
 that can be employed as a unit. It is impossible to say what 
 is a point of identity and what amounts to many such points. 
 Identity is systematic through and through, and its ' points ' 
 derive their value from their relation to a system. It is im- 
 possible to break up such a system into numerable parts and 
 points without prejudging the very question — the question 
 of their respective values as index-qualities — ^which the 
 enumeration is supposed to be a straightforward method of 
 solving. 
 
 It is worth while to illustrate this point. Suppose that 
 we are asked to compare two given plants of different species 
 in order to determine their botanical affinity on analogical 
 evidence — on the evidence of observed resemblances or points 
 of identity matched against observed differences. In order 
 to meet the retort that affinity in botany is what we like to 
 make it, by the arbitrary value which we attach to the charac- 
 ters, I will assign to affinity the definite meaning of relation- 
 ship by descent as indicated through the accepted natural 
 classification. Thus the actual fact to be discovered by 
 analogy, put at its lowest value, is how the plants in question 
 are classified in the accepted natural classification, and put 
 at its highest value is how the two are related by descent. 
 Let one of these two given plants be a shrub six feet high, 
 with branches and stalked leaves, with its inflorescence in 
 branching masses, without any ' bract ' or small leaf at the 
 base of each mass, with white flowers, with nearly black fruit, 
 and when young having its leaves covered with silky hairs. 
 Let the other plant be herbaceous, six inches high, not 
 branched, with no stalks to its leaves, its flowers in heads 
 which do not branch, but which have four conspicuous 
 yellowish ' bracts ' at the base ; the flowers are purple, the 
 
102 Analogy [Bookii 
 
 fruit red, and the leaves have only a few hairs on them. Add 
 to these differences that the general look and habit of the plants 
 are very different. Now set against the above differences 
 such points of identity as number of parts of the flower, 
 structure of the flower (polypetalous with inferior ovary and 
 epigynous stamens and petals), the structure of the fruit, 
 the partly identical growth of the head of flowers (an ' umbel ' 
 in the small plant, and a ' cyme ' in the large one), and certain 
 peculiarities of the leaf surface, such hairs as there are being 
 closely appressed, and the nerves having a peculiar prominence. 
 Perhaps it is rather easier to make out a long list of identities 
 between the two plants than to make out a long list of differ- 
 ences. But we might really lengthen either list to infinity 
 by subdividing in detail characters which have been mentioned 
 in the abstract. I have little doubt however that in micro- 
 scopic structure of petals, pollen-grains, &c. there would be 
 some striking identities, hardly compensated by differences. 
 Still we can see at once that no ratio between number of 
 identities and number of differences can be constructed 
 which will tell us anything — the number on each side is 
 almost purely arbitrary. The value or importance is what 
 we have to consider. 
 
 In what does the value of characters consist as a basis of 
 natural classification or as a proof of common descent ? 
 Largely no doubt in their connection with the number and 
 general arrangement of parts. Evolution only accounts for 
 essential changes and their consequences, and though it 
 may modify the number of parts and their arrangement, at 
 first superficially and in course of generations more pro- 
 foundly, yet an older general arrangement survives long 
 beneath the modification and can as a rule be traced there.-^ 
 The arrangement of those four or five whorls of leaves on a 
 shortened stalk, which we call the flower, is thus one dominant 
 feature in the analogical estimate of a plant's affinities. Its 
 inferential value is the same whether we call it one point of 
 
 ' See Darwin's beautiful verification of the modifications of the 
 orchid-blossom by following the spiral vessels which indicate the position 
 of the original petals in the modified corolla ; Fertilisation of Orchids, 
 p. 289 ff. Homology is an analogical conception in the logical sense. 
 
Chap. Ill] Enumeration and Knowledge 103 
 
 identity, or five, or twenty. It will be observed that in 
 considering a plant in the light of evolution we have a com- 
 bination of the higher and lower forms of teleology, related 
 negatively to each other. Just as in the example employed 
 above of the ' French microscope-stand ', we have here 
 within the basis of analogy both a definite purpose suggesting 
 definite means, and the mere tendency of individual or racial 
 characteristics to perpetuate themselves. The local manu- 
 facturers' custom is gradually modified towards the better 
 mechanical adaptation, as the organism is gradually modified 
 towards the better mechanical adaptation. At any moment 
 a manufacture or an organism is a compound of recent useful 
 change, and of survival, some of which survival is obsolete, 
 and some, the major part probably, has never ceased to be 
 useful. 
 
 Thus, in the establishment of common descent, there is a 
 special value in what recent evolutionary modification is likely 
 to have spared This would include both underlying arrange- 
 ments which evolution would take very long to touch, and 
 trifling details which it would have no reason for touching. 
 
 The account which I 'gave of the differences between the 
 plants in question is the account of a common observer ; the 
 account of their identities is the account of a botanist. This, 
 it may be said, is enough to vitiate the argument against a 
 ratio, for of course knowledge and judgment are to be used 
 in making the enumerations. But the idea of enumeration 
 gives us no right to employ botanical knowledge. It is only 
 the idea of a presumption resting negatively or positively on 
 teleology that enables knowledge to operate in assigning value 
 to index-characters. Thus in judging of the plants in question 
 we have to distinguish the element of heredity, or self-main- 
 tenance in the lower sense including the deeper and also the 
 more trivial survivals, from self-preservation in the higher 
 sense (though even here not involving conscious intention) in 
 "the set of recent differentiations introduced by evolution. 
 Even thus we omit much that is most interesting and impor- 
 tant. Evolution can for example assimilate plants of different 
 origin as well as differentiate plants of the same descent, and 
 we ought properly to show that any identities on which we 
 
104 Analogy [Bookti 
 
 rely cannot have been initiated by such assimilation.^ We have 
 so far anticipated this demand by requiring the identities to 
 refer to matters with which evolution is not likely to ha\'e 
 recently interfered. 
 
 The plants of which I ha\'e been speaking are Cornus 
 sanguinea, common dogwood, and Cornus suecica, the Swedish 
 or dwarf cornel. They are in fact species of the same genus. 
 But the four yellowish bracts round the flower-heads of the 
 dwarf cornel have the appearance of petals and form a striking 
 superficial difference between the two plants, not to mention 
 the enormous disparity in size. And now, possessing the 
 names of the two plants, and having thus opened to us what 
 is known of their local distribution, we can confirm our ana- 
 logical estimate based on passive self-preservation or heredity, 
 by a presumption drawn from the coherence of the modifica- 
 tions which that estimate ascribes to active self-preservation, 
 i.e. to evolution since the divergence of the species. The 
 smaller plant is sub-Alpine and Arctic ; the larger belongs to 
 southern England and to temperate climates. This fact 
 suggests that the smaller plant, whether driven northwards 
 by a change of climate, or simply maintaining a portion of its 
 old habitat, has been dwarfed or has not grown larger, and has 
 compensated for its smallness by the brilliant simulated flower. 
 Its distinctive leaf-growth and flower-growth may be summed 
 up as a dwarfed or at least as a miniature growth, stalks and 
 branchings having disappeared or not appeared. How the con- 
 trast between the inconspicuous small dark purple flower of the 
 small plant and the larger white flower of the large plant is to 
 be explained I am unable to suggest. But it is hard to sup- 
 pose that the petal-like bracts of the small plant are not in some 
 way a compensation for the inconspicuousness of its flower. 
 Concur- iv. Before reducing this example to regular form it is y/orth 
 rent Ana- -^YYile to remark that, by assuming the two plants to be given 
 Negative ^^ to Compare, we presuppose the work of enumerative induc- 
 Confirma- tion to be done to our hand. And in fact, where a subject- 
 matter falls under an existing science, we are already in general 
 
 ' Such identities are called in biological language ' homoplastic ', as 
 opposed to ' homogenetic '. The daisy, for example, is a head of flowers 
 that mimics the appearance of a single flower. 
 
Chap, iiij Comparison in Special Science 105 
 
 beyond the stage of Enumerative Induction, though it may 
 of course operate in particular unfamiliar instances. But 
 speaking generally, the abstract ideas which guide Comparison 
 are active in every special science as precepts filled with 
 a content capable of guiding elementary observations. We 
 approach an element, or a plant, or a part of speech, just as 
 the state approaches a taxpayer, with a schedule in which the 
 heads of our requirements are already jotted down, forming an 
 abstract analysis of the predicates with which, in the class of 
 cases in question, we are concerned. But if, supposing our- 
 selves unfurnished with such a schedule, we construct a 
 conjunctive Induction for the case before us, it would run in 
 some such fashion as this : — 
 These two plants ^ have similar berries ; 
 These two plants have similar leaf-nerves ; 
 .-. The conjunction of similar leaf -nerves and similar berries 
 
 may not be an accident.^ 
 Then the Analogical argument would fall into some such 
 shape cis — 
 
 Having similar berries is conjoined in these plants with a 
 pervading identity of underlying (and so long inherited) 
 structure ; 
 Having similar leaf -nerves is conjoined in these plants, 
 
 &c., &c. ; 
 .'. Having these similar berries is connected by an under- 
 lying (and so long inherited) structure with having these 
 leaf -nerves. 
 And, as we saw, two further analogies would confirm 
 this :— 
 
 The resemblance in the berries is conjoined in these plants 
 
 with trivial identities of structure (e.g. closely appressed 
 
 hairs on the leaves) not likely to be modified by evolution ; 
 
 The resemblance in the leaf -nerves is conjoined in these 
 
 plants with trivial identities, &c., &c. ; 
 
 ' ' Plant ' here = species. This equivalence itself rests on analogical 
 argument, which however is presupposed in any highly developed 
 language, though not for all classes of objects. See above on Individual 
 Judgment, and Lotze, Logik,^ect. 14, on ' first universais '. 
 
 ^ In strict form, ' Similar leaf -nerves perhaps are (involve) similar 
 berries.' 
 
io6 Analogy ibookii 
 
 .•- These attributes are connected with each other by attri- 
 butes probably hereditary. 
 And contra-positively, giving affirmative content to the 
 negations, but leaving them their negative value in inference : — 
 What is not identical in the fruit-growth (e.g. the clustering 
 and the isolation of the fruit) is not a property likely to 
 be remotely hereditary (because obviously modified by 
 alteration of length of the stalks, i.e, by dwarfing) ; 
 What is not identical in the flower-growth (e.g. the presence 
 and absence of the four white bracts) is not a property 
 likely to be remotely hereditary (because obviously related 
 to the inconspicuous flower, i.e. to dwarfing) ; 
 .•. What is not identical in the flower -growth of these plants 
 is united with what is not identical in the fruit-structure 
 as parts in a set of properties not likely to be remotely 
 hereditary. 
 The true relation of these arguments to each other would be 
 that they should form a single analogical inference, in which 
 each positive premise and the positive conclusion should be 
 materially defined and limited by the corresponding negative 
 judgment. When this reciprocal adjustment was completed, 
 we should have analysed each of the plants into two related 
 systems, in respect of one of which sjrstems the two plants 
 would coincide, and in respect of the other of which they 
 would differ. The one system would point to the construction 
 of a common ancestor ; the other would point to the evolu- 
 tional history of the species since their divergence. As their 
 boundaries would precisel}^ fit each other we should, in arguing 
 on the basis of either, be supported by the defining influence 
 of the other ; that is to say, every judgment A is B would be 
 supported by its converses Not-A is not-B, and Not-B is not-A. 
 But though such negative relation of positive contents is 
 valuable in analogy as elsewhere, yet to be fully effective it 
 presupposes great accuracy and exhaustiveness of analysis, 
 which is not usually to be obtained where analogy flourishes, 
 and which, if obtained, takes us beyond analogy. By its 
 negative aspect such inference leans over to Scientific Induc- 
 tion, whilfe by its appeal to the coherent nature of a system 
 it tends to pass into definite or philosophical subsumption. 
 
Chap. Ill] InducHofi and Suhsumption 107 
 
 V. Analogy, like Enumerative Induction, is a critical point Diver- 
 from which two tracks of knowledge diverge. In assigning the dencieTVn 
 coherence of attributes within a system we cannot but be con- analogy, 
 fronted with negative relations, which are the conditions of all 
 precise determination and of all causal or necessary inference. 
 This feature of deepening analogical consideration points 
 forward to scientific induction — the analysis of the teleological 
 whole, or, a fortiori, of the unformed datum of perception, into 
 its definite and necessary constituent relations. The goal of 
 this path is the abstract Hypothetical judgment which forms, 
 as we have seen, the point of transition between inference by 
 combination of abstract relations and inference through the 
 nature of concrete subjects. 
 
 On the other hand, if we continue to regard the concrete 
 subject from the point of view of its totality, which has begun 
 to dawn upon us in analogical inference, our principle of 
 inference tends to assume the shape of a concrete whole, under- 
 stood as a synthesis of abstract relations. Such a subject 
 combines within itself, in perfect equilibrium, the two aspects 
 of the universal which have occupied us throughout — the 
 aspect of concrete reality and that of abstract interconnection. 
 Inference bcised upon contents of this nature may take the 
 shape of the complete subsumptive syllogism in fig. i, or, 
 when more adequately expressed, of inference under a dis- 
 junction, or finally of the explicitly teleological inference 
 respecting beauty or goodness. 
 
 It is plain that to employ in inference such a subject notion 
 as I have just indicated presupposes a detailed mastery of 
 the abstract relations which enter into it, and therefore pre- 
 supposes the advance, which was above described as a diver- 
 gence taking the direction of the hypothetical judgment. The 
 subject can be known as an embodied purpose only by inference 
 based on its necessary constituent relations. Why then should 
 we regard the abstract h5^othetical judgment as belonging to 
 a track that diverges from the direct high-road of concrete 
 knowledge ? The reason is simply that in the formation and 
 combination of Hypothetical judgments we sacrifice reality for 
 the sake of necessity, and lose an element which was present 
 in Analogy. In other words, the Hypothetical judgment with 
 
io8 Analogy [Bookii 
 
 the combining inference that belongs to it is itself an apex 
 or climax of one whole tendency of knowledge — of the mechan- 
 ical view of the world which considers necessity apart from 
 reality, and to which disease is as orderly a sequence as health. 
 This is the view of the eye of purely physical science, which 
 in a catastrophe that should extinguish life on the surface of 
 the globe might see ' no more disorder than in the sabbatical 
 peace of a summer sea '} This aspect of knowledge has been 
 sufficiently analysed and discussed in oiu: treatment of mathe- 
 matical inference which is its purest form. My excuse for 
 constantly recurring to it must be that a thorough understand- 
 ing of its range and consequences is the primary condition of . 
 any clear thinking on the subject of the reign of law, which, 
 as thus isolated, is absolutely indifferent to the purposes and 
 interests that give reality its relation to mankind. The appar- 
 ently self-dependent completeness of this analytic view of the 
 universe gives it a right to an independent development, 
 although this right of independence which it claims may also 
 be regarded as a limitation to which it submits. Science, pro- 
 fessing to be purely physical, has, as we have partly seen and 
 shall more fully see, in our own day at least occupied itself 
 with ideas which fall outside the categories of abstract neces- 
 sity. And this was hardly avoidable ; for we have seen over 
 and over again that necessity must rest upon reality, and that 
 therefore the self-completeness of the mechanical view of 
 things is in this ultimate instance merely apparent. 
 
 ^ Professor Huxley in Contemp. Review, Feb. 1887. For a further 
 consideration of this point of view, see chap, vii, below. 
 
CHAPTER IV 
 
 Scientific Induction by Analysis 
 
 The moment we begin to demand precise definition of rela- 
 tions and to attempt analysis, we are, as the development of 
 analogy proved to us, face to face with inference from negations. 
 
 I. I will now speak shortly of the nature of this inference, and Negative 
 will then attempt to explain its function in inductive analysis. ^°^^^" 
 
 -^ ence. 
 i. All inference depends on the relation of differences within its gene- 
 
 a universal ; and negative inference, in its fundamental nature, ^^^ nature 
 does not deviate from this principle. It may be laid down at ditions. 
 once that the ideal of negative inference is to be looked for in 
 Inference under Disjunction, as the ideal of negative Judg- 
 ment is to be looked for in negation under Disjunction. Our 
 discussion on the connection between bare negation and signi- 
 ficant negation will have prepared us for this conception. 
 
 But negative inference in this sense is not a peculiar or 
 separable form of reasoning. Negation and Affirmation in 
 disjunctive or precise thinking are respectively double-edged ; 
 and though this character which thought acquires from being 
 imbued with negation is pre-eminently distinctive of thought 
 that has reached the stage in question, yet it does not admit 
 of being ascribed to negation as contrasted in the abstract 
 with affirmation. It is for this reason that in treating of 
 calculation and of geometrical reasoning it has been unneces- 
 sary to devote special attention to negative inference. Nega- 
 tion appears no doubt in mathematical principles and theorems, 
 e.g. in the definition of parallel straight lines, or in the theorem 
 that if two circles cut one another they shall not have the same 
 centre. But as a general rule — I will not venture to say univer- 
 sally — it is easy to substitute for a negative expression of this 
 kind a definite though not thoroughly particularised positive 
 expression, which possibility goes to show that the negative 
 expression was adopted rather for some rhetorical convenience 
 — e.g. for brevity — than because a positive expression was 
 unattainable. Often, as in the second of the above examples, 
 
no Scientific Induction by Analysis [Bookii 
 
 the negative form of a conclusion arises from the employment 
 of an indirect proof. And an indirect proof can only operate 
 under a disjunction. True, in the present example the dis- 
 junction seems to be merely formal, — i. e. to consist simply in 
 a positive judgment and bare negation; 'have the same 
 centre,' ' have not the same centre.' But ' have not the same 
 centre ' in case of circles means ' have different centres ', the 
 relations of which are easily seen in general from the content 
 of the indirect proof itself. In mathematical or pure mechan- 
 ical reasoning there is no room for anything approximating to 
 bare negation — the excluding motive must be definitely 
 demonstrable, and contains the idea, though not necessarily 
 the particulars, of an assignable quantitative difference between 
 the excluding and the excluded content.^ Incommensurable 
 quantities are, so far as incommensurable, not quantities at all. 
 Throughout this region of inference therefore negation and 
 affirmation have as a rule their ideal complementary position, 
 and no ground is given for a special and separate treatment 
 of negative inference. For this same reason, however, where 
 and in as far as negative inference formally occurs within this 
 sphere, it formally falls outside the character required of com- 
 bining inference, and must be technically referred, not indeed 
 to subsumption, but to a special genus which also includes 
 any negative reasoning that may arise within the limits proper 
 to subsumption. 
 
 But when we turn from calculation with precise scales of 
 difference to the traditional form of the subsumptive syllogism, 
 the inherent paradox of negative inference immediately stands 
 in our path. The syllogistic rules undoubtedly contemplate 
 inference from bare negation, and also, so far as they are 
 concerned, inference that has bare negation for its con- 
 clusion. But all inference, we have been insisting, lests on 
 an identical nature or a pervading universal, which prescribes 
 a relation, whether definite or indefinite, between its differ- 
 ences. How can a universal prescribe a relation between 
 itself and a content which falls wholly outside it, and is 
 absolutely disparate and alien to its nature ? 
 
 * So that we need not say ' is ' or ' is not ', but ' differ by a yard ', ' the 
 same to a yard '. 
 
Chap. IV] The Negative Syllogism iii 
 
 We were met by this difficulty in the discussion of the 
 negatively infinite judgment, and of the ultimate indemon- 
 strability of the negative as such. Where there is absolutely 
 no connection it is impossible for denial to be intelligible ; and 
 what is not intelligible cannot convey a truth. . Denials which 
 though frivolous seem true have some shade of assignable 
 meaning beneath them.^ Therefore the only true meaning of 
 an inference in Celarent is e. g. — 
 
 To be a man excludes being a monkey (in virtue of a certain 
 universal nature which inclttding both assigns an intelligible 
 difference between the two) ; 
 
 Socrates is a man ; 
 
 .*. Socrates is not a monkey. 
 
 But the ordinary graphical representations of the extensive 
 syllogism slur over this difference, and leave us to suppose that 
 fiom an idter absence of connection together with an assignable 
 connection we can infer an absence of connection, which is to 
 introduce the infinite judgment into inference It is worth 
 pointing out, however, that even the true reasoning in Celarent, 
 considered as starting with its conclusion as a suggestion to 
 be proved,^ begins with something nearer a bare denial, and 
 ends with an intelligibly motived exclusion. ' Socrates is not 
 a monkey ; ' ' Socrates having the nature of a man, cannot be 
 a monkey.' 
 
 Thus in syllogistic negative inference we find (i) the errone- 
 ous idea that negation is utter disconnection, and that negation 
 in this sense, bare negation, can be intelligibly asserted and 
 inferred. And we have (2) the true idea that negation in order 
 to be significant must fall within a controlling identity, 
 although its ultimate shape is indemonstrable, and qua inde- 
 monstrable or irrational falls into a genus by itself, and outside 
 both subsumption and construction. And as a testimony to 
 the inevitable power of formalism in any symbolic scheme of 
 inference, we may point out (3) that the accepted syllogistic 
 
 ^ For examples, see Book I, chap. vii. 
 
 " I am confident that this is as a rule the most instructive point of 
 view from which to analyse inference, corresponding best to the vital 
 process of thought. The essential question is, what difference is there 
 in the conclusion as a judgment, before and after, or in and out of the 
 inference. 
 
112 Scientific Induction by Analysis [Bookii 
 
 rule that there can be no inference from two negative premises 
 
 is really an offshoot of the idea of bare negation. 
 
 No con- ii. If we have two bare negations or mere disconnections 
 
 fromtwo — negatively infinite judgments — nothing follows, because 
 
 negatives, nothing is said. And as two negations will always present the 
 
 external appearance of two mere disconnections, and will be 
 
 ambiguous in interpretation, concealing their positive aspect, 
 
 it is well to maintain this rule in a symbolic scheme of inference. 
 
 Once at least in every inference, the rule says, you must show 
 
 your hand, and develope your universal in terms of its positive 
 
 content. Then, with one positive relation of content before 
 
 us, we shall not be far out, it is implied, in interpreting the 
 
 denial which is subjoined to it. 
 
 Nevertheless, it must be maintained that the negative 
 syllogism acquires scientific value just in the degree in which 
 this rule is disregarded and in which the syllogism is conse- 
 quently informal. If negative inference has any value it is 
 the establishment of exact and self-consistent boundaries 
 between the species of any genus, or the modifications of any 
 principle. 
 
 The rule that two negatives give no conclusion has been 
 impeached by good authorities -^ in respect of the third figure — 
 the figure which we followed in our account of Enumerative 
 Induction. This figure is obviously adapted for the expression 
 of a positive instance, or of an exception — of an instance which 
 comes under the condition of a rule but of which the consequent 
 annexed by the rule to its condition does not hold good.^ Why 
 should it not also express a true negative instance, i. e. a negation 
 which does not conflict with but corroborates the rule by 
 coming neither under the condition nor undei the consequent ? 
 In insisting on such a principle as ' Whatever gravitates is 
 matter ' we may often find ourselves relying on such instances 
 as ' Light is not matter ; Light does not gravitate ; .• . Some- 
 thing which is not matter does not gravitate ', or vice versa, 
 
 * Lotze, Logic, sect. 89 ; Bradley, Principles of Logic, p. 254, quoting 
 Jevons. 
 
 ^ Or in case of a reciprocal judgment, also vice versa. Even in a rule 
 which is not reciprocal, a great extension of the consequent beyond the 
 condition is always suspicious. 
 
Chap. IV] Limiting Systems 113 
 
 making in favour ot the contra-positive converse either of 
 ' Whatever gravitates is matter •' or of its reciprocal ' Whatever 
 is matter gravitates '. 
 
 It has been objected against this case of a conclusion from 
 two negations that either the argument has four terms or one 
 of the premises is affirmative. If the two premises are mere 
 denials, then neither of them can furnish the negative predicate 
 required to be subject of the conclusion. For this subject 
 must be a positive content merely determined in one aspect 
 by a negation. A bare negation cannot be subject in any 
 judgment. If on the contrary in one premise such a positive 
 content negatively determined is the predicate, and the fallacy 
 of four terms is thus avoided, then that premise is affirmative 
 in form and the conclusion is not drawn from two negatives. 
 
 This objection is not only sound in form, but has substantial 
 justification. It is well known that to attach the negative 
 closely to the predicated content has a tendency to transform 
 the idea so negated from an excluded content into a positive 
 opposite. A form like * not-moral ' cannot maintain itself in 
 living thought. It must advance to ^ immoral ' or fall back 
 to ' what is not moral '. And if we admit that in the third 
 syllogistic figure the same judgment can be both affirmative 
 and negative — for accepting the above case of inference 
 amounts to accepting this — it is hard to say why the sam,e 
 double character should not be adopted, and conclusions from 
 two negatives introduced, in the remaining figures as well. 
 In the second figure we should be tempted actually to take an 
 affirmative conclusion from two negative premises ; but as the 
 ambiguous term is here the middle term, and not the subject 
 of the conclusion, we cannot do this without treating both 
 premises as affirmative (to secure an identical middle) and 
 thereby reducing our conclusion to a problematic judgment,^ 
 thus. 
 
 Good workmen do not complain of their tools ; 
 My pupils do not complain of their tools ; 
 .•. My pupils are probably good workmen. 
 
 ' Both premises must be tafen in the same way, though both may 
 be taken as either negative or affirmative. It is' only the contrast of 
 exclusion with assertion that can give a certain result in the figure. 
 
 1337-2 I 
 
114 Scientific Induction by Analysis [Bookii 
 
 Or again, 
 
 Not good workmen are not satisfied with their tools ; 
 
 Not-my-pupils are not satisfied with their tools ; 
 
 .'. Not-my-pupils are probably not good workmen. 
 Our treatment of analogy would also be illustrated by the 
 case in which Not-A and Not-B join in a positive C. But as 
 both premises would then be formally affirmative, the case 
 does not come under the present head. 
 
 It is impossible to deny that arguments like the above may 
 have material weight. Their value rests on the possibility of 
 gathering up the phenomena just bordering on a system we 
 are investigating into a system of their own, a, ^, y, limiting 
 and limited by the former A, B, C at every point. We nearly 
 achieved this — crudely of course — in our comparison of Cornus 
 sanguinea and Cornus suecica. We then obtained two systems, 
 A, B, C and a, /3, y, such that A, B, C were respectively not-a, 
 not-/3, and not-y, while a, jS, and y were respectively not-A, 
 not-B, and not-C. B and /3, the two dominant or middle terms, 
 stood, it will be remembered, for ' inherited from before diver- 
 gence of the species ' and ' modified by recent evolution ' 
 respectively ; and the object was to attach all the peculiarities 
 of the two plants systematically to one or other of these con- 
 ceptions. Obviously in such a case it depends merely on our 
 point of view whether we take as premises ' Not-A and Not-C 
 are Not-B ', or * a and y are Not-B ', or ' Not-A and Not-C 
 are /3 ', which are the various forms suggested above. 
 In the same way it might be argued in fig. i that 
 
 No mere animal has language; 
 
 A deaf mute is no mere animal ; 
 
 .'.A deaf mute has language. 
 Horrible as these arguments must appear to any one conversant 
 with syllogistic rules, I do not see how they are to be kept out 
 if the argument from two negations in fig. 3 is admitted. 
 
 There is however an indispensable condition on which alone 
 any value can be ascribed to these inferences. This is that 
 the negation of a content should in all cases be merely an 
 aspect of a positive content ^ which is really in question, and 
 
 ^ There is a puzzling inconsistency in this identification, because the 
 treatment of ' man is not-mortal ' as an affirmative judgment, which 
 
Chap. IV] Scheme of Negative Instance 
 
 115 
 
 this we know to be the case in all significant negation, although 
 not reckoned upon in the technical rules of the syllogism. 
 Moreover, we have seen, that we are not bound to omit in the 
 conclusion of inference any relevant matter given in the pre- 
 mises. But if not, we can in any case secure the positive 
 significance of the denial of a content by supplying in the 
 conclusion the middle term of which it is denied. Thus in one 
 of the above examples we may conclude ' Light is something 
 which does not gravitate, and is not material '. 
 
 iii. We have now obtained the logical formulation of the The 
 Negative Instance. Like the Exception, it begins in Enu- instance 
 merative Induction, and is capable of development through 
 Analogy. I shall assume throughout my examination of its 
 working, in order to avoid uninstructive complications, that 
 the rule or law suggested by Enumerative Induction, of which 
 the negative instance is confirmatory, has come to begin with 
 from affirmative instances, and is expressed in an affirmative 
 judgment. Then we may formulate the cases supplied by 
 mere Enumerative Induction, with their sequels in Analogy, 
 as follows : — 
 
 Affirmative Instance Exception Negative Instance 
 
 suggesting against confirming 
 
 the prima facie rule that B is probably C. 
 
 AisC; 
 AisB; 
 .*. B is or may be C. 
 
 Cis X y zR^ ; 
 
 B is AT y ^^ R' ; 
 
 .'. B is for good 
 
 reasons likely to be C. 
 
 A is not C ; 
 
 AisB ; 
 
 .". B may not be C. 
 
 C is not X y zW 
 
 i. e. is Xi yi z^ Ri==) ; 
 Bis X y zBl; 
 .'. B is not exactly C. 
 
 a is not C ; 
 a is not B ; 
 .•. Not-B may 
 Not-C. 
 
 be 
 
 Not-C is Xi j'j Zi Rf 
 Not-B is Xi yi z^ R,' 
 .-.Not-B is Not-C 
 i.e. CisB). 
 
 Symbolic 
 scheme of 
 Instances. 
 
 Enumer- 
 ative In- 
 duction. 
 
 Analogy. 
 
 I have regarded as making ' not-mortal ' a positive or significant content, 
 was historically, as reference to a class ' not-mortal ', the origin of the 
 ' infinite judgment ' which is the very type of bare negation. The inter- 
 pretation employed in the text regards ' not-mortal ' not as a fictitious 
 class but as a positive attribute excluding mortality. 
 
 * Analysis of A. 
 
 * The analysis of a, which is not-A, i. e. not x y z R. 
 
 12 
 
ii6 Scientific Induction by Analysis [Bookii 
 
 Example 
 of In- 
 stances. 
 
 Enumer- 
 ative In- 
 duction. 
 
 Analogy. 
 
 Affirmative Instance * Exception* Negative Instance 
 
 suggesting against confirming 
 
 the flower-structure in these two plants probably 
 is characteristic of a common descent shown 
 also in the leaf-structure. 
 
 In these two plants 
 there is similar leaf- 
 structure ; 
 
 In these two plants 
 there is similar flower- 
 structure ; 
 
 .•. The flower-struc- 
 ture may be an ele- 
 ment in an inherited 
 group of qualities to 
 which the leaf-struc- 
 ture also belongs (or, 
 in brief, may be at 
 bottom one with the 
 leaf-structure). 
 
 The leaf-structure 
 in these two plants can 
 be connected with a 
 whole set of identical 
 generic properties ; 
 
 The flower-structure 
 in these two plants in- 
 cludes a whole set of 
 identical generic pro- 
 perties ; 
 
 .•. The flower-struc- 
 ture in these two 
 plants probably is cha- 
 racteristic of a com- 
 mon descent shown 
 also in the leaf-struc- 
 ture. 
 
 In these two plants 
 there is not wholly 
 identical leaf-struc- 
 ture ; 
 
 In these two plants 
 there is wholly identi- 
 cal flower-structure ; 
 
 .•. Flower-structure 
 seems not to be gene- 
 rically connected with 
 leaf-structure. 
 
 Leaves have not the 
 same stalk-arrange- 
 ment (i.e. are sessile in 
 one case and stalked in 
 the other) ; 
 
 Flowers have the 
 same stalk - arrange- 
 ment in both plants 
 (i.e. are stalked in 
 both) ; 
 
 .•. Flower-structure 
 does not follow varia- 
 tions of leaf-structure 
 (in these two plants, 
 i.e. species). 
 
 In some aspects of 
 these two plants there 
 is a difierence, e. g. of 
 leaf-stalk ; 
 
 In some aspects of 
 these two plants there 
 is a difference, e. g. of 
 flower-stalk (umbels 
 V. cymes) ; 
 
 .•. The difference of 
 leaf-stalk may be con- 
 nected through those 
 aspects of the two 
 plants) with the dif- 
 ference of flower- 
 stalk. 
 
 The difference of 
 leaf-stalk belongs to 
 a connected set of as- 
 pects ^ of these two 
 plants not concerned 
 with their remote 
 hereditary properties; 
 
 The difference of 
 flower-stalk belongs 
 to a connected set of 
 aspects ^ of these two 
 plants not concerned 
 with their remote 
 hereditary properties; 
 
 .•. The difference of 
 leaf -stalk is connected 
 with the difference of 
 flower-stalk by a rela- 
 tion not concerned 
 with their remote 
 hereditary properties. 
 
 * The Exception of course cannot be made successful if the Negative 
 Instance is to be so. I have therefore treated the Exception as a mis- 
 taken interpretation of the facts which the Negative Instance interprets 
 rightly. * Viz., the recent dwarfing of one plant. 
 
Chap, ivi Systematic Necessity 117 
 
 2. The object of Scientific Induction is, given a suggested Scientific 
 coherence, ' B may be (probably is) C,* which has become ^jo^^ 
 through analogy a hypothesis in germ represented by an 
 ' importance ' attached to the mediating content x y z K, to 
 bring such a coherence into the form of one or many pure 
 Hypothetical judgments. The outward and visible side of this. 
 process is to modify the rule, i. e. the contents B and C with 
 their connecting content x y z K, so that there shall be no 
 exceptions ' B is not quite C ', and that the two contrapositive 
 converses ' Not-C is not-B ' and ' Not-B is not-C ' ^ shall be 
 true when filled up with positive contents precisely excluding 
 B and C respectively. The inward and intellectual side of the 
 process however simply consists in grasping a necessary relation 
 based upon some fundamental reality. This essential activity 
 of the scientific spirit can only be characterised beforehand in 
 respect of its most general attributes, which are embodied in 
 the external process to be described as Scientific Induction. 
 We can affirm from the known nature of the logical universal 
 that it must be purified by exceptions and finally limited by 
 negations. But as all data presented to us are thoroughly 
 concrete, it foUows that there is an endless possibility of erro- 
 neous abstraction and construction in all adjustment of contents 
 to one another, so that the outward and visible side of induc- 
 tion, though knowable in respect of certain essential phases, 
 can never assume the character of a mechanical method or 
 royal road to knowledge. In the same way the ultimate 
 necessity of the law or principle at which we arrive can be 
 guaranteed by no general considerations. It depends in 
 general, we know, on the systematic necessity of the negations, 
 which, representing its relation to the reality within which it 
 falls, hedge it in on every side and exhibit it as no longer itself, 
 but as transformed, whenever and in as far as their limits are 
 passed. But the specific necessity of individual truths cannot 
 be assigned by any general theory of science. 
 
 i. Induction then in its most general sense consists in satis- Induction 
 tying the principle of suflEicient reason by an analysis of j^fe^ 
 
 ence. 
 ^ The contrapositive converse of C is B, which affirmative judgment, 
 and therefore its contrapositive converse, must be true if B is C is to be 
 a pure or reciprocal judgment. 
 
ii8 Scientific Induction by Analysis [Bookii 
 
 experience, directed to revealing the true coherence of differ- 
 ences within universals. But as soon as this is stated, a 
 difficulty arises in distinguishing Induction from Inference as 
 such, which has precisely the same object. And this difficulty 
 has, historically speaking, prevented the range of Induction 
 from being consistently defined. As in Jevons' theory of 
 Induction, the most recent and, so far as I know, the most 
 thorough and appreciative account of the operation, so in 
 Mill's famous analysis of the four methods of experimental 
 enquiry, we are dealing with processes essentially deductive. 
 On the other hand, if we try to confine ourselves to what has 
 been termed ' Inference from particulars to particulars ' we 
 cannot meet the requirements of Scientific Induction. The 
 name Scientific Induction is indeed something of a contra- 
 diction in terms. Induction is meant to mean the treatment 
 of instances. In this meaning the idea of enumeration and 
 even of the calculus of chances is confused with the idea of 
 an analysis of observations — a confusion all the harder to 
 disentangle, because number of observations does as a rule 
 assist analysis and contribute to eliminating error. Scientific 
 analysis as such, however, does not deal with instances, but 
 only with contents. When we speak of a scientific treatment 
 of instances, we mean a precise determination and skilful 
 resolution of their content. 
 
 Therefore the distinction between Induction and other forms 
 of Inference, erroneously described as the distinction between 
 Induction and Deduction, is chiefly a distinction of aspects, 
 largely based on a confused idea of Induction, but yet in some 
 degree justified. I have just spoken of the confused idea in 
 virtue of which Induction is regarded as a treatment of in- 
 stances pure and simple. I need only add that a semi-numerical 
 content may often have to be added to an inductive analysis 
 of causes, where our knowledge of conditions falls short. 
 Here we really fall back on number, on ratio of instances to 
 instances. If a self-fertilised flower is fertilised 90 times in 
 100 cases, and an insect-fertilised flower only 20 times in 100 
 cases, then the number of cases strengthens the unlikelihood 
 of any exceptional variety and relevancy of unknown con- 
 ditions, and we take self-fertilisation to be the more effective 
 
Chap. IV] Ifiductton afid Discovery 119 
 
 process, because there are fewer unknown conditions which 
 stop it, or more which assist it. This helps the confusion which 
 regards Induction in contrast to Deduction as an affair of 
 number of instances. 
 
 Again, Induction does not exclude Deductive processes. All 
 Induction whatever is guided by principles ; and Induction 
 as considered in Jevons' theory essentially consists in processes 
 of mediate Inference, which he explicitly calls Deduction, and 
 which operate by deriving data deductively from hypothetical 
 premises. And usage bears him out. The verification of 
 hypothesis has been considered from Bacon downward as an 
 integral part of scientific induction. And nothing can be more 
 deductive than the connection of a hypothesis with the con- 
 sequences by which it is verified. 
 
 But the distinction, as one of aspects, is justified. It is 
 nearly akin to, but not identical with, the distinction between 
 discovery and proof. This distinction indeed we refused to 
 recognise, because what is not proved is not really discovered. 
 Nor does Induction coincide with discovery. For discovery 
 may include as in mathematical science construction and proof, 
 which no one would call inductive.^ 
 
 But in a deeper form an analogous distinction to that meant 
 to be drawn between discovery and proof does hold good 
 between Induction and Deduction. We may take Induction 
 as Inference viewed from the side of the differences. Deduction 
 as Inference viewed from the side of the universal. In Induc- 
 tion far excellence the Real presents itself in concrete and more 
 or less isolated data, in virtue of which the universal nature, 
 or the system of further differences charged with the universal 
 nature, is referred to reality. In Deduction par excellence the 
 Real presents itself as qualified by an intelligible system — 
 e. g. by mathematical attributes ; and further differences are 
 referred to reality as constructed by and out of this system. 
 It may be doubted whether Newton's discovery of Gravitation 
 was Inductive or Deductive. That in process it was largely 
 
 * There may be and indeed must be true induction in mathematical 
 matter in so far as instances suggest underlying laws. The case of 
 gravitation, to be discussed below, illustrates the degree in which this is 
 possible. 
 
120 Scientific Induction by Analysis [Bookii 
 
 deductive there is of course no doubt. The popular story 
 however, about the falling apple,^ would indicate, if true, an 
 inductive aspect — that of a problem set by concrete data, and 
 resolved by analysis and hypothesis. But we must not suppose 
 Newton's mind to have been as empty of mathematical general- 
 isations as our own. He probably brought a systematised 
 qualification of Reality, drawn from elements in the researches 
 of previous mathematicians, to meet the facts that demanded 
 explanation. In this example the aspects of Induction and of 
 Deduction are about equally balanced, and we see the whole 
 principle involved in the distinction together with its merely 
 transitory importance. The relation of the universal to its. 
 differences is not affected by the order in which they have 
 presented themselves to us as qualifications of Reality. But 
 it is this order alone which furnishes the differentia of 
 Induction. 
 
 Regarded as relations within a system, i.e. in the Ught of the 
 principle of Sufficient Reason, all inductive explanations point 
 beyond themselves. They demand in the first instance the 
 explicit statement of the system from which their necessity 
 is derived, and thus they appeal as we have seen from the 
 pure Hypothetical judgment to the Notional or Disjunctive 
 judgment. But the underlying real systems themselves are 
 in various degrees limited and incomplete, and in virtue of 
 their finite nature, as we have seen to be the case with space 
 and time, demand explanations which go further and further 
 afield in accounting for the boundaries which persistently 
 present themselves. The task of explanation imposed upon 
 the mind by the principle of sufficient reason is therefore an 
 endless task. The principle of sufficient reason, as Schopen- 
 hauer says, is not like a cab which you can send away when 
 it has brought you to your destination. Nothing is isolated, 
 but as the connections which debar isolation reach to infinity, 
 nothing is complete, nor has what it requires in order to justify 
 its existence. This is the standpoint of relativity, which 
 applies in a degree to all known matters. How far we can 
 escape from this standpoint, which has been called the stand- 
 
 * For comments on this and for an excellent criticism on popular 
 notions of Induction, see De Morgan's Budget of Paradoxes, pp. 49, 81. 
 
Chap. IV] Limits of account of Induction 121 
 
 point of the Understanding, and which as thus stated is merely 
 an abstraction of our own minds, will appear when we return 
 to more concrete forms of thought. 
 
 Two observations may be made about the account here to be 
 given of Scientific Induction. I shall not speak in it especially 
 of Causation. I have attempted to show in Book I ^ 
 that cause is a merely popular idea, indicating one or another 
 ill-defined grade in the process of inductive explanation. The 
 only distinctive pecuharity of Cause contrasted with Reason 
 is that it refers to operation in time. I believe that all which 
 has value in this idea will be elucidated by our account of 
 inductive explanation, taken together with the analysis of the 
 idea of Cause to which I have referred. 
 
 And I do not propose to give any account of inductive 
 disproof. Disproof is for the theory of Inference only a form 
 of correction or modification. If at any point we are unable 
 to perform the processes necessary to correction, then we, have 
 pro tanto a disproof — if e.g. we fail in accommodating a sug^ 
 gested rule to actual exceptions, or actual exceptions to a 
 suggested rule. But for theory such a failure is not a positive 
 phenomenon. We must suppose that there is a trUe rule, 
 which, if we could but hit upon it, would cOver the facts and 
 appear as a correction of our disproved rule. The failure to 
 light upon a hypothetical rule fulfilling these conditions is 
 a mere delay in making the required correction, of which 
 theory need take no account. Bacon's complaint that the 
 ' axioma distinctione aliqua frivola salvatur ' is, but for 
 ' frivola ' which is its sting, an account of the sole and inevit- 
 able process of knowledge. 
 
 In order to exhibit distinctly the variations which impede 
 a clear definition of Induction, I propose to speak separately 
 of Induction as perceptive analysis and of Induction as 
 inferential explanation. These two varieties, together with 
 Analogical Inference and Enumerative Induction, are all con- 
 fused together in the popular idea of Induction as opposed to 
 Deduction.^ 
 
 ^ Chap. vi. 
 
 " Compare Mill, ii. 25 ff. He tries to separate Hypothesis from Induc- 
 tion, but really includes, thpugh he denies doing so, much Hypothesis 
 
122 Scientific Induction by Analysis [bookii 
 
 Induction ii. Induction in the narrowest sense is perceptive analysis, 
 tfve^ana?* a. We Suppose ourselves to have obtained from any source 
 lysis. whatever, all such sources being ultimately reducible to 
 Symbolic analogy, the problematic judgment that the attribute or 
 sion of occurrence B in virtue of a nature a b c R, has probably 
 the pro- 2i necessary coherence with the attribute or event C. This 
 is so far only a presumption arising from the value for cognition 
 which we have been led to attach to the nature a b c R — 
 a value depending, in aU the higher and truer applications 
 of analogy, on the ultimate identity of human purposes and 
 necessities,^ and in the lower walks of inference on the identifi- 
 cation of self-maintenance or self-preservation with some such 
 idea as that of purpose. I follow Lotze in employing an 
 expression of the type a b c K in which a, b, c may be taken 
 to stand respectively for definite attributes or relations and 
 R for the residual nature of the concrete whole before us, con- 
 sidered as only contributing its normal support to the opera- 
 tions oi a b c and not as actively interfering to modify them. 
 It is worth mentioning that Mill's account of the Experimental 
 methods, otherwise at least suggestive, is rendered terribly 
 perplexing by his use of corresponding letters A and a to 
 indicate from the first the several antecedents and consequents 
 underlying concrete phenomena. The result is that his first 
 statement of every problem presupposes in symbolic form its 
 explicit solution. When the phenomenon can be resolved into 
 antecedents ABC and consequents a b c the work is already 
 done. Mill, no doubt, does not mean to have determined by 
 his expression the fact that a particular element A of the 
 given content is from the first known to correspond to another 
 particular element a. He intends A and a to ])e empty forms, 
 indicating the problem which our analysis has to solve. But 
 the correspondences of the symbolic letters are undoubtedly 
 misleading. 
 
 in Induction. His test seems to be that where you have a vera causa you 
 have Induction, not Hypothesis. But he admits that in Induction the 
 vera causa maynot be known to be present in the case under investigation. 
 ' The process of learning a foreign language, and ultimately of 
 understanding language at all, is an excellent example of this. We are 
 guided throughout by the assumption that identical aims and feelings 
 underlie the different systems of expression. 
 
Chap. IV] Limit of Isolation 123 
 
 I mention this question partly because it illustrates our 
 present task. The problem is just to break up B into a /3 y R, 
 so that we can say of each element in turn, ' If a R, then a R ; 
 and if a R, then a R.' In each case we must understand all 
 the elements which we are not observing to fall back into the 
 mass of R. This neglect of the other elements is capable of 
 two interpretations. Either the other elements may be taken 
 to retain their normal relation to the a under investigation, 
 and are not especially and abnormally operative upon it under 
 the conditions of the observation, or they are actually inopera- 
 tive and might be removed. This latter interpretation can 
 never be justified without special proof, which must address 
 itself to a definite analysed R. For every conjunction of condi- 
 tions whatever is an R, i.e. an inexhaustible concrete, even 
 in the most precise experiment, and all that can ever be done 
 in the way of isolation is to exclude some portion x of the 
 whole concrete R, by substituting for it an element y which has 
 the effect of turning R into R^. We have then excluded x, 
 but not R as such, i.e. we can only exclude R in as far as we 
 can analyse it. 
 
 And to end the subject of symbolic expression, I may point 
 out that for simplicity's sake I shall not consider the whole 
 analogical suggestion ' B is probably connected with C, both 
 being conjoined with a 6 c R ', but shall confine myself to one 
 member at a time, as we should have to do in a practical 
 investigation, e.g. to ' B is conjoined with, and probably 
 coheres with, « & c R '. This is not an inadequate treatment. 
 It would be easy to add C as a character to ab c'R, indicating 
 that their conjunction must be taken subject to unknown 
 conditions ; and in any case the investigation of B in relation 
 to fl S c R is certain if pursued to the end to lay open the track 
 of coherence between ab c'R and C. The defect of symbolic 
 modes of expression in these higher forms of reasoning is that 
 not only are all elements of the content most variously inter- 
 connected, and far from being on the same level in value, but 
 also every element of the content is undergoing transformation 
 from the beginning to the end of the whole process. Therefore, 
 as Mill no doubt really intended, corresponding symbols like 
 a and a represent a pair of series or a pair of continuous 
 
124 Scientific Induction by Analysis [Bookii 
 
 devielopments within the inference rather than a pair of fixed 
 contents. 
 Estab- ^3. I will begin by analysing at some length an example of 
 
 ^^f cTd"* perceptive analysis conducted chiefly through observation as 
 ary Hy- Opposed to experiment — though experiment was at times 
 cS Tud supplied — and in respect of its content just on the borderland 
 ment. between analogy and scientific induction. 
 
 It might be suggested without doing violence to facts that 
 the Linnaean classification in botany corresponds on the whole 
 to the stage of enumerative or conjunctive Induction ; the 
 mere natural classification to Analogical Inference ; and 
 the analysis of plant-structure and evolution in the light of 
 the Darwinian hypothesis to scientific induction — to percep- 
 tive induction where we deal with the visible adaptations of 
 particular species, and to generaHsing or reflective induction 
 when we lay down universal conditions as controlling the 
 evolution of the organic world. 
 
 Let us suppose that Analogy, the habit of ascribing what 
 I have ventured to call de facto purposes to adaptations in the 
 organic world, has made it probable to us on inspecting the 
 flower of the Bee Ophrys that it (B) is adapted for self- 
 fertilisation {a b c R). 
 
 Here the expression ' adapted for ', in consonance with the 
 notion of de facto purpose, refers not merely to the mechanical 
 adjustment of a contrivance, but to the fact of that contrivance 
 actually achieving in normal use the purpose which it suggests. 
 A case in which we cannot make out this additional element 
 of meaning will be mentioned below, and in it the purpose will 
 not rank as established by Induction. 
 
 I should observe, too, that the element C which we usually 
 spoke of in analogy and which we mean to omit here for the sake 
 of brevity may in the present example be identified with any 
 peculiarity the conjunction of which with the general appear- 
 ance B might have first attracted our attention to the flower B. 
 Of course my analysis is only rough and tjrpical. I select 
 two or three prominent characters out of a whole apparatus 
 of converging contrivances. 
 
 The object is now to analyse the flower B in the light of 
 a b cK. We may attempt this roughly as follows : — 
 
Chap. IV] Fertilisation of Bee Ophrys 125 
 
 (a) Caudicles (stalks of pollen-masses) are of the right 
 length to (a) reach the stigma. 
 
 (/3) Anther-cells open of themselves, and {b) let the pollen- 
 masses fall to the level of the stigma. 
 
 (y) Hanging poUen-masses oscillate in the wind till (c) they 
 strike the stigma. 
 
 R in this example has the significance that the remaining 
 parts of the flower and plant are necessary to give the process 
 its value, and to make it possible for the contrivance to operate, 
 by nom"ishing and mechanically supporting the flower. But 
 all this is involved in the nature of a plant, and therefore 
 assuming a, /3, y to be in a living plant, and that, of course, 
 the right plant, R need not be further considered in the analysis 
 at present ; i.e. until it in some way interferes with the possi- 
 bility or reality of the action we are investigating. 
 
 The very important relation of y to c in the above analysis 
 assumes the operation of an external cause, and requires a 
 confirmation without which the whole analysis is futile ; for 
 as the pollen masses when liberated do not fall on the stigma, 
 but only hang like a pendulum on the level of the stigma, it is 
 incumbent on us to show how they can be and are brought 
 in contact with it. There is a further interest at this point 
 in afiirming or denying the action of insects, which are usually 
 necessary to cross -fertihsation, but the need for whose inter- 
 vention would impair the certainty which is the purpose of 
 self -fertilisation. Here we have recourse to the negative 
 instance which, here as usual, contains an element of experi- 
 ment. For the essence of the negative instance is to obtain 
 a positive content equivalent ad hoc to an exclusion, and this 
 can only be done by a disjunctive limitation of possibihties, 
 and an exact ascertainment of the reahty within the possi- 
 bilities so hmited. The limitation of possibilities consists, not 
 in removing all R, which is impossible, but in securing an R 
 analysed and beUeved to be passive ; and artificial combina- 
 tions give the best chance of obtaining this condition. And 
 the exact ascertainment of reaUty consists in observing a 
 positive or negative condition, or both, whose nature we can 
 exhaustively analyse. Here again artificial production gives 
 the best chance. To test the connection of y (movement by 
 
126 Scientific Induction by Analysis [Bookii 
 
 wiiid) with c (contact vvdth stigma) Mr. Darwin put a spike of 
 Bee Ophrys in water in a room. Thus he secured an R, 
 residuary conditions, which he could ensure to be passive 
 (absence of touching by animals or by any unknown cause of 
 motion), and having thus limited the possibilities he was able to 
 observe with certainty and with a high degree of exclusiveness 
 the absence of wind, not-y, which resulted in absence of contact, 
 not-c, the pollen-masses continuing to hang freely in front of 
 the stigma. Thus he obtained the confirmatory or true nega- 
 tive instance ' not-y is not c ', which is the contrapositive 
 converse of ' c is y ', i.e. ' contact arises from wind.' We have 
 here left the ground of formal logic,^ in which ' not-y is not c, ' 
 could only rest on the knowledge that ' c is y '. In the process 
 now considered ' c is y ' actually rests on the knowledge that 
 ' not-y is not c '. The corroborative power of the negative 
 instance in induction depends on the fact that it has a positive 
 content within the same ultimate system as c and y, and, 
 within that system, related by way of definite negation to 
 them. Thus the negative instance is capable of independent 
 agreement with the positive case. * Not-y is not c' = ' Free 
 caudicles without wind give no contact '. 
 
 But it will be said that we have gone too fast. We read 
 the ' free caudicles in a room give no contact ' as ' not-y is 
 not c '. But it was probably also ' Not-G (no insects) is not c ', 
 ' where no insects, there no contact,' i.e. in searching R we 
 have found a not-G, an absence of a condition, which, it is 
 suggested, may not be, as R was meant to be, indifferent. 
 We may treat this as a positive suggestion from analogy, 
 ' G is probably c ; ' for in the absence of such a positive sugges- 
 tion we should have no more cause to note the absence of 
 insects G from the experimental R than to note the absence 
 of direct sunlight L or extreme changes of temperature T, 
 But there is plenty of analogy for insects fertilising plants ; 
 so ' G is probably c ' demands attention. 
 
 Mr. Darwin provided against this suggestion by exposing 
 some of the flowers under a net, which excluded insects but 
 admitted wind. In the cases so treated contact was effected. 
 
 ^ See i. 305-7. What is true of the double negation is true of the con- 
 trapositive converse which implies double negation. 
 
Chap. IV] A SuggcsHon and Exception 127 
 
 We may read this off as an exception in the form ' not-G is c * 
 against the suggested rule ' G is (probably) c', or * insects 
 (probably) produce the contact ', and as at the same time 
 a positive instance in favour of the suggested rule ' y is c ', 
 ' wind makes contact '. This double-edged character, proper 
 to a negated content at this stage, is justified by the experi- 
 ment above-mentioned which might be read off as ' R y not-G 
 is c ' ; R standing for the mass of conditions presumed to be 
 indifferent, not-G for the exclusion of insects, y for the presence 
 of wind, and c for contact. 
 
 y. And this connection y is c (wind acting on the pendent Estab- 
 poUen-masses produces contact with the stigma) has been ^^ -R^ci- 
 defined and confirmed — i.e. re-inferred in a precise form procal 
 through the tv/o conjunctions claiming to be connections, thetical 
 R-not-y is not c (pendent pollinia without wind ^ do not touch Judg- 
 the stigma) and R y-not-G is c, i.e. pendent pollinia with wind 
 and without insects^ do touch the stigma. From not-y is not c 
 (R being disregarded as the common basis) we infer c is y, i.e. 
 
 * contact comes from wind ', the reciprocal of ' wind produces 
 contact '. And by ' y-not-G is c ' we confirm this reciprocal 
 ' contact comes from wind ' by overthrowing the suggestion 
 that G may be the operative agent in c, and consequently that 
 either wind or insects may be concerned in the contact. 
 
 It is true, however, that we have not obtained, against 
 
 * G may be c', the more fatal exception ' G is not c ' (in presence 
 of insects no contact is effected) ; the exception which we 
 obtained is strictly an exception against the reciprocal of this, 
 viz. against c is G or contact comes from insects, i.e. against 
 the suggestion that insects are the only agency in producing 
 contact. Thus we have not strictly proved, as against insect 
 agency the only suggested alternative, that wind is the exclusive 
 agency in the self-fertilisation of this flower, for when wind 
 was excluded, insects were probably (in the room) excluded 
 with it. In fact the y with which we began included G, and 
 
 * Experiment of the flower in a room. 
 
 * Experiment of flowers under a net in the open air. This experiment 
 goes far to give the pure judgment ' only y is c ', which no ordinary 
 Judgment-form will express for Logic, except the clumsy equivalent 
 
 All c is 7 '. I have written it ' 7-not-G is c '. 
 
128 Scientific Induction by Analysis [Bookii 
 
 was really ' wind-or-insects ', and it is of this y that the 
 reciprocal ' c is y ' was proved by the experiment not-y is not-c. 
 But we subsequently make it probable that this y ought to 
 mean wind only, by making it certain that it may mean wind 
 only. This shows the transformation which a content under- 
 goes in course of an inductive inference. 
 
 And for the kind of matter with which we are deahng this 
 conclusion is perhaps sufficient. We are studying the use of 
 an adaptation, which use any normal agency suitable to it will 
 suffice to establish. We could not hope to prove that no insect, 
 or that no human hand, has ever fertilised a Bee Ophrys by 
 pushing the pendent pollen-masses. When we know that the 
 wind can do it, and does it without other aid, and that wind 
 is a common occurrence, and that in the absence of wind 
 (though in the absence of other things at the same time) the 
 adaptation fails, then we are justified in saying that here we 
 have the only agency which is normal enough to account for 
 the growth of a contrivance adapted to it. Logically, these 
 considerations are represented by the claim of every judg- 
 ment to become reciprocal, which formal claim has different 
 values and interpretations in different kinds of matter. Here, 
 for instance, we might make our judgment truly reciprocal — 
 and purely truistic — by transforming the content of y into 
 simply ' a sufficient cause of motion '. This would suffice for 
 a mechanical construction of our problem, but not for an 
 organic explanation of it. An organic adaptation demands 
 for its explanation a definite regular agency to which it is 
 adapted ; it need not exclude agencies of diverse origin ; but 
 it is pretty certain to shape itself on some one well-defined 
 type of operation. Thus in -speaking of agencies to which 
 evolution has adapted structures, the claim of any actual and 
 normal agency to be the exclusive agency is prima facie very 
 strong. To make it absolute we should proceed by analysing 
 c as we have analysed B itself, and showing that y, wind 
 agency, a.s ^ v (, is the only agency corresponding to c as x y z. 
 But this I at all events am unable to do, further than by 
 pointing out that ' normal ' and ' general ' in y correspond to 
 ' gradual growth ' and ' need of a reliable agent ' in the con- 
 trivances concerned in c. 
 
Chap. IV] Exclusive Agency 129 
 
 Thus far we are left with B as a /3 y R is « & c R or S. The 
 flower of the Bee Ophrys as having flexible caudicles of the 
 right length and self-opening anther cells, and considered as 
 acted upon by wind, is adapted for self-fertilisation by the 
 poUinia falling to the level of the stigma and oscillating till 
 they touch it. 
 
 8. In formal logic the affirmation of one attribute can have Conver- 
 no influence on the affirmation of another about the same General- 
 subject unless an explicit contrariety between the two af&rma- isation. 
 tions is within our knowledge. In short, difference does not 
 justify negation. To say that a flower is self-fertilised does 
 not formally warrant us in denying that it is cross-fertilised. 
 But in science every content claims to be treated as a system, 
 and every attribute must either quarrel with any other attri- 
 bute suggested of the same subject, or must make peace with 
 it on definite terms. Therefore the inductive conclusion B is S, 
 ' The Bee Ophrys is self-fertilising,' which we have thus 
 obtained, contains in its claim for reciprocity, i. e. for pre- 
 dominance or essentiality on the part of the attribute, a further 
 suggestion to which in material or actual knowledge we are 
 bound to pay attention. We cannot indeed expect to show 
 that every self- fertilised plant is a Bee Ophrys ; i.e. we cannot 
 reduce self-fertilisation to mean solely the adaptations of the 
 flower in question, nor can we extend our idea of the flower 
 in question to include all adaptations that in any plant might 
 ensure self -fertilisation. The attribute ' self-fertilisation ' is 
 not sufficiently concrete and specific to be identified in this 
 way with the nature of a particular species of plant. But 
 though we cannot reduce self-fertilisation as such to mean 
 simply and solely the fertilising contrivances of Ophrys apifera, 
 we are confronted by the reciprocal tendency of judgment with, 
 another problem which Darwin, with his usual exhaustiveness 
 of apprehension, has frankly stated and discussed. We saw 
 that B is S, or, to prepare for our present enquiry, B is 6 S, 
 i.e. The flower in question is characterised by its own peculiar 
 contrivances for self-fertilisation. Can we convert this judg- 
 ment materially ? Can we say ' Self-fertilisation S, not cross- 
 fertilisation F, is the characteristic of this species ', or in 
 hypothetical form, ' If S pure and simple, then B ? ' This 
 
 1337-2 K 
 
130 Scientific Induction [bookii 
 
 suggestion might be embodied with more formal correctness 
 in double negation or in contra-position, as ' B is not not-S ', 
 or, ' If any not-S, then not-B,' and the question would thus 
 arise whether F (cross-fertilization) was not-S in the sense of 
 being incompatible with S in B. But Simple Conversion 
 without limitation (formally impossible) expresses the guiding 
 idea more effectually, in demanding that an essential attribute 
 of a subject shall be the sole attribute in the relation to which 
 it belongs. Here however this suggested reciprocal is not true. 
 The contrivances which have their meaning in subserving 
 cross-fertilisation, the viscid discs, sinking caudicles, and 
 elastic threads tying up the pollen-masses, are present in the 
 Bee Ophrys without the least trace of becoming aborted, and 
 therefore a strong analogical inference holds, to show that 
 B being d eJ'isY, and so is not-S in as far as not-S is identified 
 with F ; in other words, that S, and not-S in the sense of F, 
 are not contrary or incompatible in B, and so if we like that F 
 is in this case not to count as not-S, or else that B is both S 
 and not-S, to which, if not-S only means different from S, 
 there is no objection. 
 
 A certain methodical gain is drawn from affirming this con- 
 junction of S and not-S, although unintelligible to formal logic. 
 Having failed in Conversion, we are driven to Generalisation. 
 For though S and F form no logical contradiction, but are 
 prima facie quite compatible with one another, yet ultimately 
 and from the point of view of a harmonious theory there is 
 a contradiction until we reconcile them. Difference without 
 a reason, — i.e. difference in the same relation, or difference 
 of means ^ to the same end qua the same, — is a contradiction. 
 We express this problem justly by saying, ' The flower B is 
 self-fertilised S, and apparently may also be cross-fertilised 
 Not-S.' We are here in need of a further suggestion by which 
 to generalise S and not-S into one conception. This sugges- 
 tion cannot be mechanically obtained, but must be drawn by 
 analogy from our general knowledge of the organic world. 
 Combining what Darwin says in the place under discussion 
 
 ' Apart from the insufficient amount of the one means, which therefore 
 may need supplementing by another. If the one means is as easy to 
 provide as the other, this reason falls away. 
 
Chap. IV] Difference and Antagonism 131 
 
 with his views in other works, we might give this suggestion 
 the form, ' IS (heaUhy preservation of the species) demands 
 some F (cross-fertilisation) at least ; ' under which we may 
 infer by analogy from ' B has besides S some F (not-S) ' that 
 ' B the special adaptations of the Bee Ophrys have for their 
 all-embracing and determining nature the tendency to 2 the 
 healthy self-preservation of the species, including both S and 
 not-S '. 
 
 Beyond analogy, in this final inference, we cannot go, for 
 cross-fertilisation is not, according to the passage upon which 
 I rely, affirmed of Reality as a datum in the content of Ophrys 
 apifera, but is itself only inferred from analogy ; and therefore 
 the general conclusion, though a suggestive concurrence of 
 analogies, cannot be considered as a truth resting upon 
 scientific induction. The operation of the contrivances by 
 which the self-fertilisation of this flower is secured may on the 
 other hand be regarded as made good by precise perceptive 
 analysis at every point. 
 
 In establishing this positive attribute of self-fertilisation 
 considered as significant of a de facto purpose, we have about 
 reached the limits of perceptive analysis. In establishing the 
 probability of cross-fertilisation we have in, one sense gone 
 beyond the limits of perceptive analysis into the region of 
 hypothesis, if in another sense we have retrograded into mere 
 analogy. Such a hypothesis as we have just recommended by 
 analogy, if drawn out into a variety of precise details and 
 supported by their precise verification as real data, would be 
 the essence of reflective, mediate, or generalising Induction. 
 We must however bear in mind that hypothesis was present 
 in a germinal form throughout perceptive analysis, throughout 
 analogy, and even throughout enumerative induction, where 
 it was represented by the content of a common name ; so 
 that there is no saltus between these phases of inference. The 
 fascination which attaches to the researches of the great 
 masters lies just in their power of absorbing, by exhaustive 
 analysis, the mass of perceived data into intelligible con- 
 ceptions. 
 
 iii. In order to estimate the logical character — the position Logical 
 in the evolution of thought — of such a process as this wliich ^^^^^'^t^'" 
 
 J<2 
 
132 Scientific Induction [Book ii 
 
 ofPercep- I have attempted to describe, three special points must be 
 
 ductioti l^riefly treated. These are, a. What is the essence of the 
 
 inferential process concerned ? ^. What is the purpose of the 
 
 symbolic representation of it by letters ? y. What part in it 
 
 is played by number of instances ? 
 
 ^^'^ a. Ordinary mediate inference, either subsumptive or con- 
 
 essence as -^ ^ 
 
 Inference, structive, may be detected m every step of the process which 
 we have examined, as in any complex judgment of perception. 
 As we analyse, for example, the flower into its parts, and its 
 parts into mechanical adaptations, we obtain the material for 
 a three-term inference by which the adaptations in their 
 mechanical aspect would be formally brought home to the 
 flower. Or again, the contra-positive conversions and the 
 ideal reciprocity of the judgment, to which we have so freely 
 appealed, may be held to require explicit proof through syllo- 
 gistic or disjunctive argument based on abstract principles. 
 The mediate inference thus involved is of two kinds. 
 
 With regard to the mediate inference involved in every 
 complex judgment of perception, and therefore in every precise 
 one — this is really present in the Induction of which we are 
 speaking, and may sometimes need to be explicitly drawn out 
 in order to correct the results of an overhasty perceptive 
 analysis. Especially this is the case when we are employing 
 experimental apparatus which embodies whole chains of 
 reasoning and concentrates on a single datum a multitude of 
 precisely determined conditions. The observer e.g. with a 
 microscope must always bear in mind what it is that his 
 instrument does in virtue of the principles of its own construc- 
 tion, and in many classes of observations is liable to be thrown 
 back on constructive optical inference, in order to determine 
 the interpretation of the appearance presented to him, — 
 whether it means a true line or an interference-line, whether 
 an elevation or a depression, whether absence of structure or 
 complete transparency of structure (in which latter case the 
 use of polarised light will sometimes detect the illusion). Such 
 mediate inference as this is really and genuinely present in the 
 processes we have been considering, being concerned with 
 material principles relevant to the special subject of the infer- 
 ences. But yet such mediate inference does not belong to the 
 
Chap. IV] Mediate Inference in Induction 133 
 
 differentia of Induction, but is shared by all Inference what- 
 ever, being inherent in the nature of Judgment. 
 
 On the other hand, it appears to me that mediate inference 
 from abstract principles of knowledge, such as principles of 
 disjunction, of causation, or of sufficient reason, is not a 
 genuine element of scientific Induction at all, although it may 
 be the duty of the logician to point out a relation between 
 inductive inference and such principles as these. The active 
 form of thought, to which these principles belong, loses, as we 
 have seen,^ its active nature if it is made a mere content 
 within an inference. The relation, for example, of the judg- 
 ment that embodies a ' negative ' instance to the affirmative 
 judgment which it corroborates is a case of the active form of 
 negation engaged in acquiring a definite content within a 
 certain complex system. We should gain nothing in such 
 a case by erecting an argument to the effect that What is not 
 A is not-A. The problem is, given the forms A and not-A, 
 the positive and its limit, to bring these two forms into material 
 agreement in respect of the matter to be organised. 
 
 To reject abstract argument from principles of knowledge is 
 however a different thing from the omission to exhibit the 
 material of inference as permeated and articulated by the 
 active forms of thought. Such an omission I hold to be 
 unjustifiable. I have argued elsewhere that Mr. Bradley goes 
 too far in holding that an inference qua inference is not bound 
 to exhibit its principle or rationale. 
 
 The essence of induction in this, the perceptive stage — and 
 beyond this stage it more and more transcends mere induction 
 — is in the peculiar parallelism between the positive connec- 
 tion which suggests, the negative connection which defines in 
 corroborating and corroborates in defining, and the ' excep- 
 tional ' connection which modifies either itself or the affirma- 
 tive connection. I have explained ^ why I do not take account 
 of the sustained exception which overthrows. The logical 
 peculiarity of the process is in the positive and consequently 
 independent value of the negations, which are established 
 without being derived from the affiirmations, but operate on 
 the latter through the formal interdependence of negation and 
 
 ' Cp. chapter i of the present Book. - p. ii6, above. 
 
134 Scientific Induction ibookii 
 
 affirmation. The process is of course not mechanical. Mechan- 
 ical Induction is an idle dream. • The reciprocal adjustment of 
 the negations and affirmations consists in the revelation of 
 intelligible systematic ideas which are thus inferred to be true 
 of reality. 
 Theoreti- /3. The symbolic representation of these processes by letters 
 
 cal pur- j^^g^y seem to have an external affinity with the processes of 
 
 pose of -^ . . -^ ^ 
 
 represen- equational logic. But the two systems are to be regarded in 
 
 *^,*^ b" j^y precisely opposite aspects. In the above discussion not-a and 
 
 not-a have been employed to designate contents which are 
 
 positive, but have, towards a and a respectively, a boundary 
 
 or negative side. The only object of such designations was to 
 
 emphasise, for theoretical purposes, the negative relations 
 
 subsisting between certain inter-connected positive contents. 
 
 But for practical use the events or attributes in question must 
 
 be taken in their concrete form, upon which everything turns. 
 
 By manipulating them in the shape of abstract symbols no 
 
 progress can be made in the task of Induction, which is a 
 
 problem of material suggestion and adjustment. * Just where ' 
 
 and ' just in so far as % fails to be a it fails to be « ' ; this is the 
 
 meaning of the inductive ' not-a is not a '. And no handling 
 
 of symbols ^ can express or can warrant this ' just ' and ' in 
 
 so far as ' which are the whole essence of the process. What 
 
 warrants these expressions of definite relation is and can be 
 
 nothing less than a ground or real system containing parts 
 
 which negatively determine each other. It is the business of 
 
 Induction in the form of perceptive analysis to initiate the 
 
 disentanglement and reciprocal determination of elements 
 
 within such systems, in the light of ideas — germinal hypotheses 
 
 —suggested by analogy. Analogy, in fact, does not cease to 
 
 operate in Induction. Induction is Analogy fortified by 
 
 negative and precise determination. 
 
 Part y. Induction, we saw, is popularly identified with proof by 
 
 number instances, and owes its recognition as a distinct method of 
 
 of in- inference to this identification. 
 
 stances. 
 
 ^ Of course this remark does not extend to true calculation, which 
 has been independently treated and does not fall within induction. The 
 two processes have some common ground in statistics, as will appear 
 from 7 below. 
 
Chap, ivj Obsevvcd Ratios 135 
 
 (i) But scientific induction does not depend on or in any in per- 
 way deal with instances as such, i.e. particular occurrences ^^P*Y° 
 or observations with reference to their particularity — their proper, 
 rumber or recurrence. Here we have an antinomy, to which 
 at the present stage we need only draw attention, as it has 
 really been solved by the distinction between Enumerative 
 Induction and the subsequent diverging phases of the Induc- 
 tive process. All that scientific Induction demands is a con- 
 tent referred to reahty ; in how many observations or cases 
 or occurrences the content is presented is a matter of entire 
 indifference to science. If, to put an extreme supposition, the 
 entire content, positive and negative, employed in the above 
 analysis of the Bee Ophrys, could be observable in a single 
 flower, that single flower would, subject to one reservation to 
 be mentioned presently, form a sufficient ground for all the 
 conclusions that were then drawn. What characters can be 
 and what cannot be united in a single or continuous observation 
 is a question of the nature of the object concerned, and not 
 of logical theory. The same flower cannot be both fertilised, 
 and ultimately not fertilised at all. It can be both fertilised 
 (later) and not-fertilised (up to a certain point of time). Or 
 it can be both self-fertilised, and not-self-fertilised in the 
 specific sense of being cross-fertilised. The first of these three 
 comparisons requires two ' instances ' ; the two latter need 
 only require one apiece, or indeed one between them. And 
 then is an ' instance ' a plant or a flower ? If a plant, one 
 instance would probably do all we should demand. 
 
 (2) There is, however, one case to be distinguished to which Known 
 
 the above remarks do not apply. The self-fertilisation of the ^^^^ts of 
 
 ^^ -^ unknown 
 
 Bee Ophrys, Darwin says, is markedly ' successful '. The Bee condi- 
 Ophrys, which is self-fertilised, in many dozens of plants had *^°^^' 
 a capsule (seed-vessel) for every flower.^ The Fly Ophrys, 
 cross-fertUised by insects, had only seven capsules in forty- 
 nine flowers. This ife again ' a is a ',_' not-a tends to be not a.' 
 And here number of instances is essential to the result, because 
 we are dealing with the operation of conditions not fully known. 
 This throws us back at once into enumeration of instances, 
 statistical methods, or even the statement of chances. We 
 ' Exceptis excipiendis — deformed flowers. 
 
136 Scientific Induction [Book 11 
 
 proceed by the comparison of hypotheses explanatory of 
 observed ratios, as we saw in discussing the statement of 
 chances. If, to use an extreme illustration, we could say ' Fly 
 Ophrys is exclusively insect-fertilised ', and ' the observed 
 plants of Fly Ophrys are in a place inaccessible to insects ', 
 then we should not need a single instance to fortify the con- 
 clusion that all these plants must remain unfertilised. But 
 as we do not know with precision what conditions are opera- 
 tive, and to what degree, in securing or hindering the approach 
 of the right insects to the flower at the right moment, we are 
 reduced to enumerating observed instances in order to obtain 
 an actual ratio between successes and failures, upon which 
 we may base an estimate of the nature of the cause or causes, 
 whether in the flower or outside it, which would probably have 
 produced the observed ratio of successes to failures. We have 
 as data, say, forty-eight cases and forty-eight successes in 
 self-fertilisation, compared with forty-eight cases and only six 
 successes in cross-fertUisation by insects. We have to conjec- 
 ture or construct the kind or type of causes which are most 
 likely to have produced these two observed series. 
 
 Supposing indeed that we take into account all unknown 
 conditions whatever, no question can be raised, for it is a rnere 
 transcription of the series to say that the one flower is less 
 adapted to the conditions which have acted on it, than the 
 other to the conditions which have acted on it. And supposing 
 that Darwin excluded interfering causes in counting both his 
 sets of instances, as he did in one, there is no more to be said. 
 The self-fertilised plant meets the unknown conditions wholly 
 and the other does not. In order to compare probabilities we 
 must have a suggestion as to some special kinds of causes that 
 normally operate with an assigned frequency,^ and for the 
 
 ' We must in short take by way of hypothesis some ' natural cycle', 
 or what comes to the same thing, some cycle external to that observed, 
 otherwise there are no two ratios to compare in respect of each observed 
 series. See Book I, chap. viii. We might indeed compare the proba- 
 bilities that each series proceeded from a supposed cause, and from 
 chance (unknown independent conditions) respectively, but this would 
 be, where we know some of the conditions operative, to forfeit the use 
 of knowledge which we possess. If we wished to reckon the probability 
 of either series occurring by chance, I suppose we should have to take 
 (Jaute de mieux) the chances of failure and success as even for each flower.. 
 
Chap. IV] Normal and Abnormal Conditions 137 
 
 sake of illustration I will assume that obvious accidents have 
 not been excluded. As every adaptation has its limits bej'ond 
 which conditions become abnormal to it, i.e. are accidents, 
 I am able by this means to suggest the idea that the two kinds 
 of flower may be equally well adapted to normal conditions, 
 but that in the observed series of cases the Fly Ophrys may 
 have been the victim of a set of disasters which destroyed the 
 flowers inspected, by causes lying outside the limits of adapta- 
 tion of either flower. Abortion of the flower or destruction 
 by insects before maturity may easily prevent seeding in one 
 flower out of four. Now of course in the first place it is an 
 impossible assumption that Darwin would not have noticed 
 any extraordinary prevalence of abnormal interfering causes 
 confined to the flowers of the Fly Ophrys. In order to obtain 
 a useful * not-a is not a ' the two negative contents must 
 diverge from the positive a and a only in a-ness and a-ness. 
 They must be, as we have insisted, within the same real system ; 
 i. e. the R of general conditions must be the same in both, or 
 in the same relation to both.^ 
 
 But in the second place, making this false assumption for 
 the sake of illustrating our point, we will suggest that one 
 flower in four of the Fly Ophrys is on the average destroyed by 
 accidents which no adaptation could avert. And then it be- 
 comes not impossible that in a given series of forty-eight 
 inspected flowers, these accidents have been heaped together 
 by unknown causes ; and that the flowers, though adapted 
 to a// normal conditions, — i.e. as successfully adapted as those 
 of the Bee Ophrys, — were nevertheless in forty-two cases out 
 of a given forty-eight hindered from being fertilised by a series 
 of extraordinary accidents. We have then to compare, as 
 regards the Fly Ophrys, the hypotheses of maladaptation to 
 normal conditions, such as to cause failure in forty-two cases 
 out of forty-eight, and of perfect adaptation to normal con- 
 ditions, hindered of its effect by abnormal conditions in forty- 
 two cases out of forty-eight. The possibility of making this 
 
 ^ It is not indeed fair to say that in order to a just comparison the Fly 
 Ophrys must have its insects as the other must have its wind, because 
 the question is whether the Fly Ophrys was wise to rely on so capricious 
 an agency as that of insects. But there must be no extraordinary 
 influence known to be keeping the insects from it. 
 
138 Scientific Induction [Book ii 
 
 comparison by calculation depends on our being able to assign 
 an average ratio of operation to the abnormal causes. Taking 
 them to produce on an average established by general observa- 
 tion one failure to be fertilised in every four flowers, and 
 excluding probabilities derived from the non-appearance of 
 extraordinary hindrances in the instances of the Bee Ophrys, 
 we have to determine the probability that in forty-eight inde- 
 pendent flowers, with three favourable chances and only one 
 unfavourable for each flower, we should obtain a set (in any 
 order) of forty-two failures and only six successes. I presume 
 that this problem is the same as to estimate the chances of 
 drawing a black ball exactly forty-two times in forty-eight 
 out of a box containing only four balls, being three white balls 
 and one black ball. These chances would be expressed I 
 suppose by (|)^ x (5)*^ — the chances of six successes in drawing 
 a white ball on assigned occasions — multiplied by the com- 
 binations of forty-eight things taken six together, in order to 
 add together the number of independent ways in which six 
 successes and forty-two failures can be realised. 
 
 This probability, which must be very low, owing to the 
 enormous number of failures required, with the low chance 
 ^ for each, has to be compared with the high probability with 
 which the assumption that, normally, insects only visit one 
 flower in eight, and that therefore the flowers are maladapted 
 to seven sets of conditions in eight, would give as a consequence 
 the ratio of forty-two failures in forty-eight flowers. This 
 would I suppose be the same as the chance that out of a box 
 containing seven black balls and one white, forty-two black 
 balls should be drawn in forty-eight trials. The combinations 
 remain the same as in the former case, and the factor supplied 
 by the fractions expressing the chances would be {\f x (|)*^, 
 involving a high power, the forty-second, of the very favourable 
 chance |. The comparison of these probabilities would be 
 our warrant for deciding, on the assumptions which we have 
 made, that Fly Ophrys is much worse adapted to normal con- 
 ditions than the Bee Ophrys. In fact, our conclusion is much 
 more certain than on these assumptions, for it is certain that 
 any violent interfering cause which destroyed one flower in 
 four would have been noticed and excluded by any such 
 
Chap. IV] Share of Estimated Reality 139 
 
 observer as Darwin. But in as far as we rely on the exclusion 
 we are ceasing to rely on number and are going back to analysis 
 of content. The exclusion, however, in such varied and un- 
 certain conditions is probably imperfect, and therefore, in our 
 actual inference, I take it that w^e eke out our reliance on 
 Darwin's accuracy of comparison by a reliance on the pro- 
 bability of a normal feature in the conditions (viz. a degree of 
 unsuitability to the flower) as against the very low probability 
 of a variety of accidental conditions which Darwin did not 
 exclude. We shall illustrate this particular application of the 
 inference from number of instances directly. 
 
 The above case may serve as a type of all Inductive pro- 
 cesses in which number of instances, as number, plays an 
 essential part. Their essence consists in selecting as most 
 probable that cause or class of causes which would produce, 
 as an alternative bearing the largest proportion to the sum 
 of possible alternatives, the ratio actually observed among 
 the phenomena. Apart from the assumption of any parti- 
 cular cause, every additional instance enormously increases 
 the improbability of every single definite succession by making 
 every such succession one among an immensely increased 
 number of possible alternative successions (or conjunctions). 
 If therefore any cause can be alleged or supposed, which 
 would give that particular definite succession which exists 
 in reality as sole alternative or as one of a comparatively 
 small number of alternatives, the principle of impartial 
 ignorance urges us to decide for that cause as giving to the 
 actual observed succession the nearest approach to its actual 
 position as real — i. e. the largest share of estimated reality. 
 Or if two or more causes are suggested, from which each 
 component event of the actual observed succession can be 
 derived as one out of different numbers of alternatives 
 respectively (e. g. as one out of three alternatives in one case 
 and as one out of twenty alternatives in another), then we 
 compare the probability of these two causes just on the same 
 principle as that on which we compare the probability of a 
 single imputed cause and that of the total absence of any 
 single cause at all, forming a case in which the actual succession 
 must be attributed to a succession of what we call accidents. 
 
140 Scientific Induction [Book ii 
 
 A particular class of accidents however, such as that assumed 
 above as destroying one flower in four before maturity, is 
 of course a class of causes, and may be defined and treated 
 for purposes of calculation as ' a cause '. 
 
 Number of instances thus operates by increasing the im- 
 probability per se of every particular conjunction or succession 
 of phenomena, and therefore increasing the probability of 
 any cause which can be proved capable of producing the given 
 conjunction or succession as one out of fewer alternatives 
 than the number derivable from any other suggested cause 
 or from the whole series of instances treated as accidental. 
 Probability is estimated by counting, on the basis of impartial 
 ignorance ; hence the opposition between enumeration of 
 instances and analysis of content. 
 
 The case of so-called elimination of irregularities by accu- 
 mulation of instances may readily be exhibited as an appli- 
 cation of the above principle. A class of causes, or common 
 element in a variety of active conditions, is for our present 
 purpose a cause or ground. If, on the accumulation of 
 instances, there appears in the observed succession or con- 
 junction any feature, e. g. of recurrence in certain cycles, or 
 a fortiori of persistence in a single character, which can 
 be hypothetically referred to any common element in the 
 wholly unknown conditions ; then the accumulation of 
 instances progressively increases the relative probability of 
 causation by this common element, by progressively de- 
 creasing the probabiUty of every conceivable sequence, in- 
 cluding the one observed, if considered as the result of accident, 
 i. e. of independent causes.^ In other words, it becomes more 
 and more probable that, the unknown irregularities not- 
 withstanding, the unknown conditions include a common 
 element, however composed, relative to the persistent feature 
 of the observed conjunction or succession, and uninterfered 
 with by the unknown irregularities of the unknown conditions. 
 Material considerations of content, suggesting an approxima- 
 tion to exhaustiveness in the enumeration of kinds of instances 
 and consequently of kinds of conditions, are almost invariably 
 
 * See below, p. 170, on Kirchoff's proof of the presence of iron in the 
 sun. 
 
Chap. IV I Artificial Observation 141 
 
 present to reinforce in some degree the argument from sheer 
 probabihty. 
 
 iv. Experiment is observation under artificial conditions. Observa- 
 What is artificial bears to a certain extent the impress of !^°" ^"*^ 
 
 t-xpen- 
 
 human intelligence, and is, to this extent, abstract and ment. 
 idealised. Human action, in virtue of the human thought 
 which directs it, is definite and selective. And ' artificial ' 
 means produced or arranged by human action. The differ- 
 ence between observation and experiment therefore is in the 
 degree of definiteness and ideal selection which is present in 
 the material conditions of the latter process. 
 
 a. It is obvious that natural conditions would serve the Natural 
 purposes of enquiry as well as artificial conditions on the nient"" 
 assumption that they were exhaustively known. And if 
 exhaustive knowledge of natural conditions were in no case 
 possible, observation could not exist as a scientific process. 
 But it must be noticed that in giving effect to the knowledge 
 which guides it, observation itself tends to take on the 
 character of experiment. The transition between the two 
 processes is therefore gradual. Experiment would usually be 
 considered to begin where we pass from intentional selection 
 of our standpoint and from the use of contrivances auxiliary 
 to perception, to actual analytic interference with the object 
 under observation. Before the line is reached, however, 
 observation passes into something which may properly be 
 called ' natural experiment '. I quote an excellent passage 
 from Jevons ^ in illustration of this point. 
 
 ' It may readily be seen that we pass upwards by insen- 
 sible gradations from pure observation to determinate ex- 
 periment. When the earliest astronomers simply noticed the 
 ordinary motions of the sun, moon, and planets, upon the 
 face of the starry heavens, they were pure observers. But 
 astronomers now select precise times and places for important 
 observations of stellar parallax, or the transits of planets. 
 They make the earth's orbit the basis of a well-arranged 
 natural experiment, as it were, and take well-considered 
 advantage of motions which they cannot control. Meteorology 
 might seem to be a science of pure observation, because we 
 ' Principles of Science, pp. 400- 1 . 
 
142 Scientific Induction 1 book 11 
 
 cannot possibly govern the changes of weather which we record. 
 Nevertheless we may ascend mountains or rise in balloons, 
 like Gay-Lussac and Glaisher, and may thus so vary the points 
 of observation as to render our procedure experimental. We 
 are wholly unable either to produce or prevent earth-currents 
 of electricity, but when we construct long lines of telegraph, 
 we gather such strong currents during periods of disturbance 
 as to render them capable of easy observation.' 
 Observa- ^. There is a further point connected with this transition 
 accurate^ which calls for remark. We habitually speak of telescopic, 
 instru- microscopic, or even of spectroscopic observation. Con- 
 sidering what an enormous artificial interference the instru- 
 ments thus employed exert upon the image of the object to 
 be observed, it may seem strange that we call the result an 
 observation and not an experiment. The instinct which 
 guides our use of language is however just, at least so far 
 as concerns the ordinary applications of telescope and micro- 
 scope as magnifying instruments. An apparatus which merely 
 brings the object nearer our perception is far excellence an 
 observing instrument. In the compound microscope the image 
 is variously transformed, and often goes through some degree 
 of chromatic dispersion, in transitu, but as it is reconstituted 
 liefore reaching the eye, these transformations do not amount 
 to experiment. This question turns on the employment of 
 interference not merely to make an object accessible to us, 
 but to analyse its content. Thus the moment we modify the 
 object under observation itself, e. g. by applying heat, elec- 
 tricity, or chemical reagents on the stage of the microscope, we 
 say that we are experimenting. When we use spectroscopic 
 devices to observe the real prominences of the sun, without 
 waiting for a total eclipse, we are really analysing the solar 
 image, though not the sun, but strong analogy from the 
 general use of optical instruments makes us still say that 
 we are observing. In actually compounding coloured lights 
 with a colour-box for the purpose of equation, however, there 
 is no doubt that we are experimenting. The fact is then 
 that experiment is not merely observation under artificial or 
 determinate conditions, but observation under determinate 
 conditions which constitute an integral part of the image or 
 
Chap. IV] Phascs of Condition and Result 143 
 
 product to he observed. Thus common dissection is not experi- 
 ment, though it introduces conditions in the way of separation 
 and demarcation as definite as anything can be ; but vivi- 
 section is experiment, because the determinate conditions 
 it produces enter as factors into the action of the organism 
 observed. 
 
 y. Returning for the sake of brevity to the symbols which Experi- 
 we used before, we may say that the function of experiment pressed ' 
 is to exhibit both a and not-a as determinate cases of j3, y, 8, ^^ logical 
 &c. which form the ultimate analysis of R so far as R is ' 
 relevant to a. The cases of /3 y 8, &c. obviously may include 
 zero values of any one or more of these factors, and apart 
 from a special hypothesis to be tested — or rather if the 
 hjrpothesis to be tested is merely that ^3 y 8 are concerned in 
 a — all possible combinations of values of the three or more 
 series must be tried, a moreover is certain to be continuous, 
 and to admit of variation within itself ; for no phenomenon 
 is utterly atomic. But in order to secure a distinct corre- 
 spondence between phases of condition and of effect, it is well 
 to treat every appreciable phase a, within the general a, in 
 turn, as a bounded by not-a, so as to identify its condition a, 
 viz. a phase of /j y 8, with absolute precision, as being on both 
 sides bounded by not-a, viz. other positive phases of /3 y 8 
 excluding that which is a. The goal to be attained, if the 
 experimental conditions admit of it, is a reciprocal Hypo- 
 thetical judgment ; consisting of an affirmative hypothetical 
 judgment in the form, ' If a (a determinate phase, or series 
 of phases, of /3 y 8), then a,' supported by its simply corrobora- 
 tive equivalent, ' If not-a,^ then not-a ' (viz. determinate 
 phases of ^ y 8 excluding the phases a), and by its recipro- 
 cally corroborative equivalent, ' If not-a, then not-a.' 
 
 Can this reciprocal, equivalent to 'li a then a ', be justified 
 
 by experiment, which can at best take the shape, ' in order 
 
 to remove a you must remove a,' and not ' by removing a 
 
 you remove a * ? It can be thus justified on the assumption 
 
 ^ Not-a under experimental conditions is of course itself positive and 
 exclusive of a. If there are different not-a's, as is quite possible at first 
 sight, they determine different a's. E.g. aerial impulses too slow to be 
 heard as musical sound, and discord, are two not-a's as against a's in 
 musical sound. 
 
144 Scientific Induction tbook it 
 
 that a considered as a phase of /3 y 8 is an ultimate anatysis 
 of R. For in this case all possible combinations of the 
 ultimate components of R have been exhausted, and we can 
 lay down throughout them all the demarcation between a and 
 noi-a. But if we take R in its primary meaning, of which we 
 cannot stop short without special justification — ^viz. as the 
 entire system of the universe — this assumption can never be 
 true except in virtue of a consistent abstraction by which it is 
 taken as true. 
 
 Such an abstraction is the source of mathematical neces- 
 sity. I will not say that in mathematical construction we 
 are secure from the irruption of any conditions beyond those 
 which we have put there, because we may be guilty of omission 
 or oversight on mathematical ground, and the fact that 
 discoveries can be made in mathematics seems to show that 
 such omission constitutes the gradually receding limit of the 
 science. But it may safely be said that in mathematical 
 construction we are secure against any conditions which do 
 not fall within the definite general t5^e of those which we have 
 put there. 
 
 Apart from such an abstraction, the assumption that we 
 have a perfect analysis of R is always erroneous, and the 
 postulate that we must express a and not-a in terms of the 
 ultimate analysis of R is theoretically incapable of being 
 fulfilled. The approximate or presumptive fulfilment of the 
 postulate depends chiefly on our general systematic knowledge 
 of the course of things, which enables us, as we think, to draw 
 a line between R^ the whole irrelevant residuum, Rg the real 
 basis of both a and the positive not-a which make up the 
 phenomenon prima facie in question, and therefore as such 
 irrelevant to the distinction between a and not-a, and Rg the 
 limited number of precise positive conditions on the combina- 
 tion of which, incj;uding their reciprocal interference, the precise 
 distinction between a and not-a depends. R3 is finally reduced 
 to the general a. It is obvious that R^ has its roots in R^, 
 and Ro in R^, so that the distinction between these remainders 
 cannot be pressed far except on the ground of specific know- 
 ledge. Gravity for example belongs to R, in relation to an 
 acoustical experiment which I purpose to describe presently. 
 
Chap. IV] Is ResiduuM irrelevant ? 145 
 
 No doubt gravity is essential to this experiment in the same 
 sense in which it is essential to all that takes place on the 
 surface of the globe. But the variations of grayity within their 
 actual limits do not affect the experiment appreciably or at 
 all. Thus general systematic knowledge operates through con- 
 fining the immediate problem to R3 or at most to Rg and Kg, by 
 setting down Rj as for this purpose not-R, viz. not a residuum 
 within the problem, but one outside it. R of the problem 
 (viz. R2 and R3) is related to not-R of the problem (viz. RJ 
 just as a is related to not-a in the immediate experiment. 
 
 And secondarily, in as far as R^ is not materially known, 
 but is an unknown residuum, a presumption of its irrelevancy 
 may be supported by the number of instances in which R 
 (as R^ and R3 )is a sufficient R for the experiment, i.e. presents 
 a and not-a as required. This confirmation of the line drawn 
 between the R of the problem and the not-R of the problem 
 is precisely the same in kind as the confirmation by number 
 of instances of a material difference in the adaptation of two 
 plants to their environment, worked out above, p. 135. Every 
 successful trial to generate a and not-a on the basis of the 
 R of the problem alone, increases the difference between the 
 probability of the result on the hypothesis that it is due to 
 the known factors included in the R of the problem, whose 
 certainty of existence is assumed,^ and the probabiUty that 
 the successive occurrences of a and not-a are due to inde- 
 pendent causes, some of which must therefore fall outside the 
 persistent conditions which make up Rg and Rg. 
 
 If, on the other hand, we confine ourselves to the R of 
 the problem in its most limited sense, viz. to R3 analysed as 
 /3, y, 8, then the assumption that we have in /3, y, 8 an ulti- 
 mate analysis of R can only be questioned on the ground of 
 a further analysis suggested or presumed. The possibility 
 of a positive suggestion needs no explanation ; it would arise 
 from conjunctive induction and pass through analogy in the 
 ordinary way, having the form * 8 is probably cpmplex, 
 consisting of A, //, y ', and would be tested by further experiment 
 in the ordinary way, some part of such experiment probably 
 
 * Because if we fail to produce them all, we do not expect o, nor count 
 the case as a trial. 
 
 1337-2 L 
 
146 Scientific Induction [Book 11 
 
 coinciding with passing /3 y 8 through their possible variations. 
 This experiment would however then be extended by taking 
 account of the variations and zero values oikyiv and including 
 or excluding these, as the result might require, in the analysis 
 of a and not-a. A presumption of further analysis very com- 
 monly arises when no positive suggestion is forthcoming. We 
 have a strong presumption e.g. from the history of chemistry 
 and from the nature of ordinary substances that we shall not 
 constantly be lighting upon new elements ; and therefore we 
 do not assume an unfamiliar substance to be an element — 
 i. e. we presume that further analysis is possible — even though 
 we should fail to analyse it at the first attempt. 
 
 After using the above example, however, I must guard 
 myself against the idea that ' analysis ' is for this logical pur- 
 pose to be understood in a sense borrowed from chemistry. 
 Logical analysis is the understanding of any whole in reference 
 to its constituent parts or factors, and chemical analysis is 
 only the understanding of a chemical whole as chemical. It 
 is a trite observation, but perhaps necessary to be repeated 
 here, that the analysis of an organism, if it is not its analysis 
 as an organism, may destroy rather than display its inmost 
 nature. If h is an organic element, and A, ju, v are its chemical 
 constituents, then our first business in ' analysing ' is to 
 ascertain whether we want these constituents A, /x, v, which 
 are, strictly speaking, constituents not of h but of by (8 as a 
 merely chemical substance), or whether we want other con- 
 stituents 0, 73-, r, which if we can we may then further construe 
 into forms of combined chemical action X ix v {o), k ijl v {-n), 
 \ fjL V {t). In speaking of organic characteristics as capable of 
 analysis, I have in mind such questions as the precise degree, 
 direction and mode of transmission in which irritability in 
 plants sets up reflex action ; or how far certain movements 
 are reflex and how far purely mechanical — e. g. in the case 
 of circumnutation.^ The description of analysis needed in 
 
 ^ I have not the smallest desire to deny that the joint action oi \ n v 
 as chemical agents may make up, and, for all I care, initiate the action of 
 5 as organic. The question of abiogenesis is an open one for Logic. 
 I am only pointing out that, combined as 5, the constituents A, fi, v, 
 acquire organic attributes o, ir, t, which are capable of having their 
 nature precisely determined by experiment. 
 
Chap. IV] Logical Analysis 147 
 
 each particular case must of course be determined by the 
 natme of a, and the consequent nature of parts or factors with 
 reference to which it is to be understood. 
 
 8. A very simple and beautiful example of the progressive Experi- 
 rcciprocal definition by experiment of a — a and not-a — not-a ^^^^ ^^^ 
 is to be found in the weU-knOwn verification of the connection Sireu 
 between rapidity of periodic vibrations and musical pitch, as ^°^ ^'^^ 
 given by help of Helmholtz's Siren. The reader would do 
 well to study the account and figure of this instrument in 
 Helmholtz's Popular Lectures.^ In the light of the account 
 which has just been given of the logical purpose of experiment 
 we may roughly analyse this arrangement as follows : — 
 
 Rj, or the not-R of the problem, may be typified by the 
 action of gravity, which pervades all matter, but the varia- 
 tions of which within their actual limits are indifferent to the 
 phenomena now in question. 
 
 The R of the problem, consisting of Ro and R;,, witliin 
 which a — a and not-a — not-a are to be sought for, is in general 
 terms the musical sound produced by the machine, and its 
 conditions, including the machine. Of these we may take as 
 K, (extending, as we knew it must, continuously into RJ the 
 air in the room, the hearing ear, and the machine itself, as 
 operative in the production of a physical effect which together 
 with a hearing ear results in musical sound. Rg is relevant 
 as the proximate basis of the phenomenon itself, and as such, 
 regarded by contrast to R^ or not R, is itself an a defined 
 by a not-a and connected with an a. But prima facie and 
 outside the experiment itself, Ro does not demand much 
 analysis. The air in the room or some conductor of sound 
 must act as a medium between the machine and the ear — 
 sound cannot pass through a vacuum ; — the ear must not be 
 outrageously abnormal — this is included in a reasonable inter- 
 pretation of * hearing ear ; ' — and of course there must be no 
 other source of sound undistinguished from the machine itself. 
 And as R3, the unanalysed whole which is the phenomenon, 
 we must take the action of the machine as already somewhat 
 idealised by analysis, i.e. in respect of its quantitatively 
 specified effect upon the air in generating aerial impulses with 
 ' Engl. Trausl., published by Longmans &. Co., Series I, p. 57 li. 
 
 L2 
 
148 Scientific Induction [Book 11 
 
 a measurable rapidity of succession restricted to certain limits, 
 and in one series, or in two simultaneous series, at pleasure. 
 a, the musical sound,^ is most conveniently considered as 
 included in R3, but as also distinguished by anticipation and 
 confronted with the gradually narrowing R's and their analyses 
 as the problem to which they are all directed. Ultimately, 
 however, a itself will of course be reacted upon by analysis, 
 and will be found to include distinct elements both in kind 
 and in degree. 
 
 If we omit, for the sake of brevity, to speak of the charac- 
 teristics of quality and loudness in musical sound (and these 
 are in fact not especially illustrated by the Siren), we find 
 that R3 is immediately reducible to a very simple relation, 
 the relation of comparative rapidity of succession between 
 series of puffs of air, which series differ in no other assignable 
 respect. R3 is, in other words, assumed ad hoc to be exhaus- 
 tively analysed. Confining our attention, to begin with, to 
 the case of a single series (and not two sounding at once) we 
 become aware first of a constant relation between any given 
 rapidity and the pitch of the note which is heard while that 
 rapidity is maintained, and secondly of a relation of quasi- 
 proportion, sufficiently explained above,^ according to which 
 rapidity is to rapidity in a definite numerical ratio, while pitch 
 is to pitch in a definite recognisable relation, measurable by 
 intervals but not made by summation of intervals. First, 
 then, every particular rapidity is to us as an a, deviations 
 from which on either side are to it as not-a, corresponding to 
 an a deviations from which on either side are to it as noi-a. 
 But as each and every deviation from a brings a * proportional ' 
 deviation from a with it, every such not-a is to some corre- 
 sponding not'a as an a to an a; and we have therefore the most 
 perfect case of negative relation between positive contents. 
 But, secondly, when the quasi-proportional character of the 
 two series attracts attention (which it did from the earliest 
 times, as a fact demanding explanation, owing to the relation 
 
 * ' What musical sound ? ' the reader may ask. I reply, in fact some 
 musical sound in particular, but as a problem musical sound in general. 
 It is impossible to particularise the sound you have heard, except as 
 a result of advancing analysis, ■ See p. 74, above. 
 
Chap. IV] Deviations as cases of Law 149 
 
 of the length of strings to the notes which they sound) it 
 becomes an essential element in the relation which constitutes 
 R3, and presents itself as a further determination of the mere 
 principle ' rapidity has a constant connection with pitch ', 
 which forms the first simple a — a. We thus obtain the 
 suggestion of a law, and the verification of this suggested law 
 becomes the object of the experimental process. A law is 
 treated just like any content a. The object is to show that a 
 the realisation of the condition is attended by a the realisation 
 of the consequent, and that r\ot-a, any deviation from the 
 consequent (ultimately perhaps a variation of the consequent), 
 is preceded or attended by a deviation from or variation of 
 the condition. Thus as always our goal is in the Hypothetical 
 judgment, ' If 0, then a,' with its reciprocal, ' If a, then a.' 
 
 It is further worth while to mention how the experiment 
 in question obtains minute measurable variations of a and a 
 at pleasure. If rapidity corresponds to pitch in a certain 
 proportion, then two rapidities in the right proportion corre- 
 spond to a definite harmony. Deviations from a harmony 
 are recognisable by a trained ear with extreme minuteness. 
 Helmholtz's Siren will sound two sets of impulses, of con- 
 trollable rapidity, together ; and in the first place by adjust- 
 ing the two precisely to the proportion required by the law, 
 it verifies the law a — a in a compound case. But then by a 
 contrivance for very delicately, and measurably, altering the 
 rapidity of one of the series, a slight or considerable discord 
 can be produced at pleasure. If we were interpreting a — a 
 as '1:2 gives note and octave ', this result reads as a con- 
 firmatory content, 'not a — noi-a,' i.e. ' deviation from i : 2 
 gives deviation from note : octave.' But of course, as before, 
 this not-a is a case of a, rapidity corresponding to pitch, 
 though not to two notes, one an octave above the other 
 because the sets of impulses are not as 2 : i in rapidity. 
 
 But here, with the Siren alone, we are pretty much at an 
 end of our analysis. That R3 is not merely a law of rapidity 
 in succession, but a complex theorem concerning shapes of 
 vibrations and their decomposition into pure pendulum 
 oscillations, related to the quality of a and to discordant 
 beats in a (if a includes two notes sounding together), does 
 
150 Scientific Induction [Book it 
 
 not appear from the above experiment. It would perhaps 
 not have been suspected but for the obvious fact that an 
 air wave must have some shape, on the one hand, and that 
 pitch is not the only element in sound, on the other. 
 
 The point of the above illustration consists especially in 
 displaying the various senses of not-a, and the various stages 
 of its adjustment to a. Rj is not-a in one sense, R^ in 
 another, and in a relative and shifting manner portions of 
 R3 are not-a also. The same applies throughout to not-o. 
 Induction consists in separating the R's and in establishing 
 those variations of a which appear, against any fixed starting- 
 point, as relative not-fl's (and the same with a). 
 
 I may conclude this chapter by calling attention again to 
 what I have insisted on in another work,^ as the claim of 
 an experimental apparatus to be considered in the light of 
 a reasoning machine. It must be gi'anted that in any logical 
 engine whatever we have to make the conclusion, i. e. to read 
 it of¥ as a conclusion, and if we are to do this we may read 
 off the connection of imperfect ratio and false harmony from 
 the Siren as distinctly as we can read a combination of letters 
 from Jevons' logical machine. In the operations of nature, 
 causes have their consequences ; but the causes are not 
 precisely known, and the consequences are therefore not 
 consequents. In experimental instruments we find the 
 attempt made to generate actual consequences which shall 
 also be consequents, as arising from conditions precisely 
 known in respect of the mode and degree of their combination. 
 Any instrument which does this may be called a reasoning 
 machine, whether it deals with combinations and eliminations 
 of letters as logical symbols, or with the same relations of 
 actual number, or of any definite motions with their effects. 
 The value of the connections thus demonstrated is of various 
 degrees ; but a complex experimental apparatus has the 
 advantage in the synthetic variety of the contents which it 
 exhibits as relevant to each other, if the logical machine 
 has the advantage in the abstract generality of its formal 
 conclusions. 
 
 ^ Knowledge and Reality, p. 327 ff. Cp. Jevons, Principles of Science, 
 p, 282 ff. 
 
CHAPTER V 
 
 Scientific Induction (continued). 
 
 I. Hypothesis is a name that may be applied to any Hypo- 
 conception by which the mind estabhshes relations between Postulate 
 data of testimony, of perception, or of sense, so long as that 
 conception is one among alternative possibilities, and is not 
 referred to reality as a fact. 
 
 i. From Aristotle onward, indeed, logicians have been Hypo- 
 anxious to consider a hypothesis as the suggestion of a real V^^^^^ 
 agent — a thing or occurrence in a thing — related to the data side Pos- 
 as ' cause ' to ' effect ' ; and to distinguish such a suggested *"'^*^^' 
 ' agent ' from a mere suggested ' reading ' of the phenomena 
 — a principle, law, or definition. Of course there is a primary 
 difference between a material agent and an ideal law or 
 principle, but the distinction is not ultimate in theory and 
 appears to be, for this reason, incapable of being sustained 
 in scientific practice. A ' working hypothesis ' — and most of 
 the great unifying conceptions of modern science are working 
 hypotheses — is the suggestion of a real agent taken as equiva- 
 lent to the suggestion of a mere law or principle. It is 
 worth while for the sake of clearness to look at the distinction 
 between law and real agent in a form recently given to it by 
 Lotze, viz. as the distinction between Postulate and Hypothesis . 
 
 In the account to which I refer ^ the name of Postulate is 
 given to the conditions which are absolutely and essentially 
 involved in a given set of appearances, and apart from which 
 ' the content of the observation with which we are dealing 
 would contradict the laws of our thought '. These conditions, 
 it must be observed, need not be abstract, except in the sense 
 of being definite and precise. They might therefore, I infer, 
 exhaust or define the nature of a real agent, in so far as a real 
 agent is capable of being determinately known. But it is 
 plain that as a rule they will not suffice to do so. The concrete 
 ' Lotze, Logik, sect. 273. 
 
152 Scientific Induction [Bookii 
 
 nature of a material thing will contain much that is indifferent 
 to the conditions precisely involved in any determinate effect. 
 
 By hypothesis, therefore, in this same accotmt, is meant 
 a conjecture which specifies the natural agents taken to be 
 at work in a phenomenon and to be the means of fulfilling 
 the postulate involved in it, in the case under investigation. 
 In other cases, it is implied, the same postulate might be 
 satisfied by means of other agents. And, it should be added, 
 by Q. fiction is meant the reference of an effect to a cause or 
 principle which we know to be incapable of producing it, but 
 from the real effects of which it only differs by an error which 
 is capable of being determinately assigned. Omitting the 
 case of a confessed fiction, and including a fiction, not con- 
 fessed to be such, under the title of a hypothesis, we may 
 throw the remainder of our discussion into the form of 
 an enquiry into the distinction between Hypothesis and 
 Postulate. 
 
 The Postulate sets an abstract problem which Hypothesis 
 has to solve in the concrete. The distinction prima facie 
 coincides with that upon which Mill lays stress in his treat- 
 ment of hypothesis, between a quantitative law of action, 
 and the thing which acts according to that law. But it 
 would certainly seem that every hypothesis in order to be 
 established must be passed over into the content of the 
 postulate, in the sense that, without the matter suggested in 
 the hypothesis, no less than without that suggested in the 
 Postulate, ' the content of the observations with which we 
 are dealing would contradict the laws of our thought.' For 
 this is ultimately the ground on which we affirm of Reahty 
 everj^hing that we do so af&rm. When the postulate is 
 sho^\^l to contain the hypothesis, by a concrete proof that 
 the suggested thing or fact is necessary to prevent self- 
 contradiction in our thought, then we have a hypothesis 
 with a vera causa (see ii. below). When the hypothesis is 
 moulded into the postulate, not or not exclusively by proof 
 of the concrete supposition, but in a great degree by atten- 
 uating its content into a ' law of action ', then we have a 
 ' working hj^othesis ', i. e. materially an abstract postulate, 
 but formally a supposition of a real agent. Such a hypo- 
 
Chap. V] Law and Agent 153 
 
 thesis is a fiction which may or may not be a confessed fiction. 
 In Mill's notes on Whewell ^ we see the process of attenuation 
 at work, reducing hypotheses to fictions which are confessed 
 by Mill and not confessed by Whewell. Modem science seems 
 to the outsider more and more tending to substitute explana- 
 tion by laws of action for causation by unknown real agents. 
 But, in theory, a determinate agent may be involved in the 
 postulate just as much as an abstract law, supposing that the 
 agent is operative in the content in modes sufficiently many- 
 sided to assign it a determinate nature. For logic, law and 
 agent are ahke conceptions by which thought constitutes the 
 content into an organised whole ; both may be ' within ' the 
 content, if we include in the content what is needed to con- 
 stitute it rightly ; neither can be within the content if we 
 separate it, by an unrciil and indeed impossible distinction, 
 from the work of thought in determining it. Every object 
 of perception is such a conception, by which data of sense are 
 determined in a way necessary to make them intelligible. 
 
 The real distinction which Lotze should have d^a^^•n is 
 not between the law of action and the concrete real agent, 
 but between the concrete real agent as known to be necessary 
 for the explanation of the observations, and such an agent 
 as not so known, but arbitrarily imagined, or identified vith 
 something known from other sources. If we assume a thing 
 thus arbitrarily, or on the ground of extraneous kno\\iedge, 
 then (considering the thing in the latter case apart from the 
 extraneous knowledge on the ground of which it is assumed) 
 we have the relation ' If a, then a ', but not the reciprocal 
 ' li a, then a ' ; i.e. in other cases other agents than a might 
 satisfy the same postulate, or minimum of conditions, involved 
 in a. But this unnecessary element in a h\^othesis cannot 
 of course be acquiesced in. The supposed real agent must 
 either be elevated into the content of a postulate, or depressed 
 into that of a fiction. Obviously, however, before deciding 
 
 ^ Mill's Logic, i, p. 335, and ii, p. 24 ; e.g. ' Can an agency undulate ? 
 Can there be alternate motion backwards and forwards of the particles 
 of an agency ? ' MiU is maintaining in effect that \MieweU's view of the 
 imponderable agents reduces them to laws of action. He is distinguish- 
 ing an agency from an agent (the ether). And compare ClifiFord on 
 Causation, Lectures, &c., vol. i, p. 153. 
 
154 Scientific Induction [Book u 
 
 that the latter course is the only one open to us, we must 
 concentrate all available knowledge upon the supposed real 
 agent in order to test its right to become a postulate. One 
 science e.g. may need one aspect of it, and another another. 
 Hypo- ii. Thus to meet the difficulty that many characteristics 
 
 with Vf ra ^^ ^ thing assumed hypothetic ally to account for certain data 
 Causa. are likely to fall outside what those data demand and justify, 
 it is usual to require of a hypothesis that a the supposed 
 agent shall be a vera causa. This can ultimately have but 
 one meaning. It must come to this, that a, though containing 
 elements which are superfluous for the explanation of the data 
 from which we happen to have started, yet contains no elements 
 which are not necessary to the explanation of some data or 
 other. It is commonly said that a vera causa is one inde-^ 
 pendently known to exist, or accessible to direct perception. 
 Of course we do not restrict our conviction of reality to 
 matters accessible to direct perception — the centre of the 
 earth, the inside of a block of marble, the other side of the 
 moon, are cases in point. And if we did attempt this restric- 
 tion, what is direct perception ? All perception is inferential, 
 and proceeds by furnishing conceptions which bring data of 
 sense into intelligible relation. And if we require that the 
 cause shall be independently known to exist, this is a mere 
 question of the range of observations which it is to explain. 
 A vera causa then is a thing, or occurrence in a thing, whose 
 reality we are thoroughly convinced of from the necessity of 
 reconciling observed data,^ and there is no reason in the 
 nature of things why a single science or a single range of 
 reality should not suffice to produce such conviction. 'Direct 
 perception ' is a mere popular phrase without logical meaning. 
 The question is siniply whether our data are determinate 
 enough to guide us to the nature of a real thing as explaining 
 them. What is really demanded in the vera causa is probably 
 
 ' Tlie most thorough and simple way of classifying matters known 
 from testimony or history is to include them under the head of concep- 
 tions which are necessary to determine observed data, the observed 
 data being the books, speech, &c.. which bring the facts to our individual 
 notice. As to ranking agents under the head of conceptions, I may say- 
 that this is not roducing agents to mere conceptions. As known and 
 established to us, they are conceptions, though they may be more. 
 
Chap. V] ColUgation of Facts 155 
 
 independent evidence of the thing's reality, with an eye to 
 the doctrine of chances. A single coherent set of errors may 
 vitiate a whole coherent system of appearances, but the 
 chances against errors in independent sets of observations are 
 the same as the rapidly increasing chances against coincidences 
 of independent events.^ This is a parody (as the doctrine of 
 chances is always a formal parody of some material truth) 
 of the operation of multiform data in moulding a concrete 
 hypothesis, which will be illustrated directly. 
 
 Thus in a ' working hypothesis ' we have postulate and 
 hypothesis tending to identification by attenuation " of the 
 hypothesis, in a hypothesis with vera causa we obtain the 
 same result by extension of the postulate to cover the alleged 
 cause and turn it into a vera causa. 
 
 2. In an ultimate sense, there is no knowledge without Phases of 
 Hypothesis. thesis. 
 
 i. 'All science may be rightly described as progressive Rudi- 
 " colligation of facts " through superinduction of conceptions ' ^ ^y^^P 
 if it is understood that, though such conceptions are present thesis. 
 in the real facts and are not mere additions out of our heads, 
 yet in the progress of our knowledge such colligation does not 
 operate upon the real facts themselves, but only on the facts 
 as imperfectly understood by us. Thus the whole course of 
 the present work has been an attempt to trace the progressive 
 determination of feelings, or nf facts imperfectly understood, 
 by conceptions which may be regarded as hypotheses in course 
 of development and proof. The continued identity of an 
 individual, for example, which is the soul of the individual 
 judgment, may be regarded as a conception or hypothesis 
 which is superinduced (though without conscious reflection) 
 upon the successive appearances which we observe, and 
 ' colligates ' these facts. And as we have seen in speaking 
 
 ' If the chance of error in one set of data is |, the chance of indepen- 
 dent error in two sets (of the same but independent liability to error) is 
 5-, in three ^, and so on. 
 
 - A working hypothesis often, and perhaps usually, partakes of the 
 character of a fiction, being in fact suggested as a vera causa, and subse- 
 quently attenuated till it is clearly not a vera causa, though retaining 
 its original claim to be so. 
 
 ■■' Green, Philosophical Works, ii, p. 288. 
 
156 Scientific Induction [Book 11 
 
 of Induction, hypothesis in a genuine sense, as a conscious 
 activity, begins to operate where the individual judgment 
 begins to be employed in explaining the conjunction of 
 attributes, in conjunctive or enumerative Induction. From 
 this point, at which Hypothesis is represented by the content 
 of a generic or specific name, we have watched its development 
 through analogy and through scientific analysis, till in the 
 experiment of the Siren we found ourselves testing by deter- 
 minate perceptive comparison a relation which can only be 
 completely explained by a complex mathematical theorem.^ 
 Mediate ii. Procedure by Hypothesis proper is mediate. 
 
 Hypo- j^ jg clear from what has been said that we must assent 
 
 thesis. 
 
 Hypo- in substance to the view of Jevons and Sigwart which is in 
 thetical the main that of Whewell "^ and De Morgan,^ so far as it asserts 
 Indue- the essential identity of Induction with procedure by Hypo- 
 *^°"- thesis. And indeed Mill himself might almost be reckoned 
 
 on this side. He shows* triumphantly that the Method of 
 Difference will test the premises of a Deduction, and the fact 
 that the ' instances ' on which it operates are in that case 
 obtained by Deduction, he sets down as of no consequence, 
 i.e. as not interfering with its Inductive character. But it 
 is not so clear that this method, which unquestionably will 
 test the consequences of a precise deduction and therefore 
 the truth of its premises, will perform any other function 
 that could be called Inductive. Mill's objection^ against 
 Whewell's hypothetical method, on the ground of insufficient 
 provision for excluding unproved or unproveable elements of 
 hypothesis, is an objection which arises from the impossible 
 demand for merely negative and exhaustive determination. 
 It is very probable that Whewell makes too little of the necessity 
 for showing or for its being possible to show that nothing hut 
 a could produce a ; but what Wliewell seems to have rightly 
 felt is that this is after all in its essence a material and positive 
 question, depending on the degree and mode -of connection 
 between a and a, and being for logic the same as the question 
 
 ^ The theory of wave-propagation, which explains among other 
 things the discordant beats produced by sonorous impulses which have 
 not certain definite ratios oi rapidity. 
 
 - See Mill's Logic, ii. 24. ' Budget of Paradoxes, p. 49. 
 
 * Logic, ii. 12. ^ See Mill's Logic, ii, p. 24. 
 
Chap. V] Fufiction of Hypothesis 157 
 
 whether a as such produces a. The possibility of proof or 
 disproof, which is claimed as essential to the * legitimacy ' 
 of a hypothesis, must be a material or real possibility, and 
 reduces itself to specific presumptions that proof may be had, 
 which are in themselves grades of proof. But while accepting 
 the general view to which I have alluded of the importance 
 of hypothesis in Inductive Inference, I am unable to agree 
 with some important results which have been held to follow 
 upon such a view. 
 
 /S. I shall begin by endeavouring to lay the true doctrine Example 
 
 very briefly before the reader, in the sense in which I mider- pf fusion 
 
 . between 
 stand it and m which it seems to me to follow from our previous hypo- 
 discussions. It will then be necessary to speak of the relation *^^^^^ 
 between Induction in the scientific sense and the work of 
 generalisation which is popularly ascribed to it, and I shall 
 conclude the present chapter with some observations on the 
 above-mentioned misapprehensions, and on the true relation 
 of Induction to Inference as such. 
 
 The purpose of the example which I propose to analyse is 
 to exhibit the mediate identification of a hypothetical cause, 
 at first sight somewhat remote, with a given effect. I inten- 
 tionally select an instance in which the identification is not 
 quite perfect, in order to display the full nature of the difficulty 
 to be overcome. 
 
 As a datum to be explained, we will take the curious fact, 
 long known to scholars, that the Greek god Apollo, especially 
 the Apollo of the Troad, is associated with the mouse, both 
 in his appellation Smintheus and in recorded usages — ^there 
 were sacred mice and figures of mice in his temple, and so 
 forth.i 
 
 The conjunction of aspects which excites surprise in this 
 fact is the association of an insignificant animal with the 
 worship and the temples of a comparatively pure religion. 
 A large choice of analogies lies open to us, any one of which 
 might furnish some sort of mediation between these two 
 extremes, and of these that which is at first sight the most 
 
 ^ My example and my arguments are all drawn Ironi j\Ir. Lang's 
 Custom and Myth, j^. 103 ft'. My purpose however only permits the 
 most meagre reproduction of some points out of this interesting study. 
 
158 Scientific Induction [Book ii 
 
 remote may perhaps on a consideration of all the phenomena 
 be considered the most hopeful. 
 
 It seems that in the Peruvian religion we find this same 
 conjunction of aspects, the association of insignificant animals 
 with the worship and the temples of a comparatively pure 
 creed. And in that instance, it further appears, we have a 
 definite and complete mediation or explanation of the two 
 terms or ' extremes '. Before the establishment of Sun- 
 worship by the Incas as the creed of the state, the Indians of 
 the various tribes worshipped tribal animal gods, including 
 all sorts of insignificant animals, the Indians of each tribe 
 believing themselves to be descended from some one of these 
 animals. ' After the establishment of the purer religion, the 
 Incas had the good policy to collect all the tribal animal gods 
 into their temples in and round Cuzco, in which the two 
 leading gods were the Master of Life, and the Sun.' This 
 toleration of an older and cruder in subordination to a purer 
 faith is a very common phenomenon, as Mr. Lang truly 
 observes, in religious evolution. And he cites an example of 
 a festival described by Theocritus which still continues in 
 a Catholic country. 
 
 Here then we have a content the whole of which is given 
 (I assume) in perception or in the proximate interpretation of 
 perception, viz. in history. Analogy or Induction would not 
 commonly be held to apply within the limits of this content ; 
 but nevertheless in as far as within the single ' instance ' or 
 range of reality — which is really the life of a whole nation — 
 a principle is detected by our thought, there is operative what 
 constitutes the essence of inductive as of all other inference. 
 But no details have to be referred to reality solely on the 
 strength of the principle, because it happens that they are all 
 warranted by testimony.^ 
 
 Now if the content which perplexed us in Greek religious 
 history fell bona fide within the lines of the content thus 
 warranted and interpreted in Peruvian religion, no inference 
 
 ' It is probable, and appears I think from j\Ir. Lang's account, tliat 
 the interpretation even of the known succession in Peru into an intelli- 
 gible evolution would involve, as almost every interpretation does, 
 some remodelling and supplementation of details. So far we have 
 inference in the popular sense. 
 
Chap. V] Suggestion of a Hypothesis 159 
 
 would be necessary, or rather, the purely lorinal inference 
 which recognised the identification would suffice to include the 
 Greek problem under the same solution as that which supplies 
 itself for the Peruvian problem. But the very slight and 
 superficial abstraction which is all that we have thus far 
 formulated of the Greek problem can warrant no such material 
 identification — so far as we have yet stated the point, ahnost 
 any hypothesis might explain it ; the misunderstanding of 
 a name, or the caprice of a priest or king. Wliat we must now 
 do is to look in the Greek problem for the facts and relations 
 of which we have seen the significance in the Peruvian problem. 
 But as historical data such facts and relations are wanting ; 
 and here we have the essential difference between Induction 
 by analysis of Perception, and Induction by mediate Hypo- 
 thesis. Our hypothesis is prima facie a conjectural matter of 
 fact falling wholly outside the content which has to be ex- 
 plained. The view winch I wish to illustrate is that our proof 
 of the hypothesis must ultimately depend upon the charac- 
 teristic positive connection between the hypothesis and its 
 consequences. This connection is as we have seen elucidated 
 and purged of irrelevancy by the establishment of limiting 
 negations, but is not otherwise dependent on the disproof of an 
 indefinite number of alternative hypotheses, and is no more 
 restricted to mere probability than is the determination of any 
 perceiveddataby any conception which makes them intelligible.^ 
 We have before us, as a datum of fact, a surprising con- 
 junction between Apollo and the mouse, especially in Apollo's 
 temple. We have as a suggested fact which might explain 
 this conjunction, a previous state of Greek or neighbouring 
 tribes in which they worshipped animals such as the mouse, 
 together with a religious evolution in which the earlier cult 
 survived by the side of the later and purer worship. According 
 to the ordinary process of Induction as inverse Deduction, 
 
 ' Contrast with this the mechanical views of Jevoiis, Principles of 
 Science, p. 152, and Sigwart, Logik, ii, p. 357. Jevons thinks that no 
 proof by Imperfect Induction (Induction falling short of complete 
 enumeration) can be more than probable. Sigwart thinks that a hypo- 
 thesis is refuted by refuting its consequences, but not proved by estab- 
 lishing them, though it grows in probability as its consequences agree 
 with the facts. 
 
i6o Scientific Induction [Bookii 
 
 we proceed to ' deduce the consequences which might be 
 inferred from the hypothesis '. 
 
 In drawing consequences from a hypothetical state of facts 
 we have to apply that state of facts to the reality on the basis 
 of which it is supposed, and to examine in detail the results 
 of the combination. This analysis of the content of the 
 hypothesis is not a contrivance of demonstration, but an 
 inevitable necessity of knowledge. In working out, for example, 
 the hypothesis now before us, we must take into account the 
 customs relating to marriage and to names which belong to 
 that phase of savage life which we are conjecturally imputing 
 to the Greek race in the past. Among savages named after 
 tribal animals which they worship and bear as name or emblem, 
 and from which they trace their descent, the members of one 
 family do not intermarry with people bearing the same name 
 or emblem, and the children of every marriage take the 
 mother's name or emblem (totem). These names consequently 
 tend to become scattered throughout a large region, and are 
 associated with the well-known phenomenon, for which in very 
 early society there are obvious grounds, of counting kinship 
 through the mother and not through the father. On the 
 other hand, when this state of society passes away, as in 
 European nations it has passed away, it is plain that a powerful 
 family will crush out the names of the other families in a 
 district, and form a local tribe called by an animal name. 
 From this hypothesis thus analysed, if applied to ' mouse 
 families ', there follow primarily four results, which briefly 
 stated amount to this : — 
 
 (i) There would be places named from mice, and mice will 
 be held sacred in those places. This was so in the Troad. 
 
 (2) The mouse-name would be given locally to the god who 
 superseded the mouse. This was so in the places called after 
 the mouse. 
 
 (3) The figure of the mouse would be associated with the 
 god in his temple, and used as a badge or local mark in places 
 where the mouse had been venerated. The former usage was 
 found, and the latter was not uncommon, in Greece. 
 
 (4) Stories would be told in the district in question to explain 
 the worship of the mouse. This was so in the Troad. 
 
Chap. V] Results of Hypothests i6i 
 
 I do not say that these four points, thus baldly stated, 
 carry us very far. But in so far as they support the hypothesis 
 at all, they do so not merely as an arrangement of coincidences 
 due more probably, in a calculable degree, to a single cause 
 than to independent unknown causes ; but, like an arrange- 
 ment of results which some person has the power and a strong 
 motive to produce, they support the conjectural cause by the 
 material connection of the data with it, or a material extension 
 of the data towards including it. One of the above points for 
 example is the appearance of the figure of a mouse as a badge 
 or city emblem in Greece. This, when referred to an actual 
 race of men exceedingly conservative in its customs, is a point, 
 though a trifling one, actually in common between hypothesis 
 and data. The badge or crest of a city is not the same thing 
 as the totem of a family, but the connection of parts of cities 
 with local tribes is too well made out in Greece and elsewhere 
 to give us pause. And the veneration of an animal by the 
 people of a city in ways strikingly analogous to totem worship 
 is made out in the case of Egyptian cities. Of course this 
 point may be otherwise explained than by the suggested 
 hypothesis, and so may all the others ; but they all, as referred 
 to the life of a race, demand some explanation, and the only 
 difficulty is to model that explanation rightly. It is this idea, 
 that of moulding a hypothesis, that should be substituted for 
 the idea of gauging its probability as something attaching to 
 its definite and irrevocable form. To meet paradox by paradox, 
 rather than admit that a hypothesis can only be established 
 by the refutation of infinite others ^ and the non-refutation 
 of itself, I would maintain that of every set of data some positive 
 hypothesis (viz. that ' something or other ' conditions these 
 data) is within our knowledge demonstrably true, and that the 
 problem of induction by the inverse method or by hypothesis 
 is merely to further determine this ' something or other '. In 
 this work of definition, as we have abundantly seen, negation 
 is all-important ; but it must be motived and relevant nega- 
 
 ' This is the root of the idea that no results of hypothetical Induction 
 can be certain. The idea is ridiculous when it is once seen that hypo- 
 thetical Induction is identical in principle with common perception and 
 with all Inference whatever. 
 
 1337-2 , M 
 
i62 Scientific Induction [Bookh 
 
 tion, * not this, because that, which has a determinate relation 
 to this.' 
 
 I should weary the reader by further discussion of the 
 mouse hypothesis, which moreover space forbids me to treat 
 in its interesting details. But I must point out that by con- 
 sidering the peculiar marriage customs (e.g. maternal kinship), 
 sacrificial and festival rites, and animistic beliefs, which are 
 traceable throughout Greek life, and which are characteristic 
 of the primitive phase that forms the content of our hypothesis, 
 we can remodel hypothesis and data once more, and this time 
 into a really intimate approximation to each other. Hypo- 
 thesis and data approach amalgamation in the conception of 
 a finely gifted race still bearing in its prime the traces of a 
 natural though characteristic evolution out of a savage past. 
 We might almost claim that a savage phase of life is a vera 
 causa, apart from the proof of our special hypothesis,^ not 
 only in the Peruvian but in the Greek race. Is not the concep- 
 tion of a past and natural evolution, in the case of any race 
 of men which we may be considering, a conception ' apart from 
 which the content of the observation with which we are dealing 
 would contradict the laws of our thought ' ? But if so, then, 
 according to the distinction accepted above, the conception, 
 although that of a real agent or event, is a postulate and not 
 a mere hypothesis, and therefore is the conception of a vera 
 causa ; and the work of induction is, as said above, to assign 
 to the postulate in detail its actual content or law of action. 
 
 Other hypotheses, independent of that which the author 
 advocates, are carefully dealt with in the chapter from which 
 I have been quoting. And I think that any one who considers 
 the matter in the light of this or any equally genuine piece of 
 research must feel that just in so far as the adverse hypotheses 
 are independent, their refutation, although a sine qua non of 
 the establishment of the hypothesis advocated, can never 
 genuinely contribute to that establishment. In other words, 
 theirefutation of other hypotheses is a genuine assistance to 
 one hypothesis only when it elicits positive content which goes 
 to model this latter hypothesis. 
 
 Before leaving this subject I must refer back to the dis- 
 ' Every hypothesis when proved is a hypothesis with vera causa. 
 
Chap. V] Moulding the Hypothesis 163 
 
 cussion of Book I ^ on cause and ground, and must explain 
 that the content of a hypothesis may correspond, according 
 to the degree of its purity or relevance, to any member of 
 the series there described ; to cause, to effect, to antecedent, 
 consequent, or ground. The reason for treating an example 
 in which the popular sense of cause is dominant was simply 
 that the equally popular sense of hypothesis, from which the 
 theoretical difficulty of its use arises, corresponds to the 
 popular sense of cause (or effect). The more scientific type 
 of hypothesis approaches more nearly prima facie to the 
 nature of a postulate or ground — of a principle included in 
 the facts, or of a systematic reality which they constitute. 
 And hypotheses which are, to begin with, of this type do 
 not present the great apparent difficulty of passing by sheer 
 inference from isolated data to actual things and facts not 
 included in them. As we have seen, a hypothesis which to 
 begin with is not of this type, necessarily tends, in course of 
 demonstration, to approximate to it ; just as, in the case 
 which we tried to analyse, certain isolated data and isolated 
 suggestions about the Greek race tended to coalesce into a 
 systematic conception of that race as developing in a normal 
 fashion under the natural influences and conditions which 
 appear to be common to mankind. 
 
 3. It is unquestionably the case, that a process or result Generali- 
 which may be termed Generalisation is somehow connected ^^ti°"- 
 with Induction. The only question is how to state the con- 
 nection. 
 
 i. I trust that the popular idea according to which Indue- ' From 
 tion is a process from what happens often to what happens ^f "ex ° 
 always, from particulars to the totality of particulars, has ploded. 
 been set in its true light by the whole scheme of our account 
 of Induction. The conception, to which unhappily Professor 
 Jevons adhered, of Perfect and Imperfect Induction as corre- 
 sponding to complete and incomplete enumeration is hope- 
 lessly fallacious. It cannot, I think, be necessary to pursue 
 this error at the present stage. 
 
 ii. There is a sense in which all abstraction, i.e. all becoming By mere 
 conscious of the determination of sensuous data by explicit nation. 
 
 ' Chap. vi. 
 M2 
 
164 Scientific Induction [Book ii 
 
 conceptions, operates as Generalisation. Such generalisation 
 is embodied in the hypothetical judgment, which of course is 
 not hypothetical qua judgment and is in no sense a hypothesis, 
 but is an affirmation, based upon a reality illustrated bj^ 
 a hypothesis. The explicit conditions forming a determinate 
 case which, as the antecedent in the hypothetical judgment, 
 illustrate or qualify Reality, take the consequent with them 
 wherever they go, and in this sense the judgment is general, 
 absolute, or universal. Supposing the judgment to be abso- 
 lutely true — and formally we can suppose nothing else of 
 a judgment which we make, though of natural phenomena no 
 judgments are absolutely true — it is absolutely universal. 
 Varieties of detail may fall within, it, but they do not affect it. 
 Against such unessential variations, and against mere number 
 of examples in time and space, the explicit antecedent appears 
 as general, and in selecting and defining it a work of generalisa- 
 tion has practically been accomplished. There is no advance 
 from known to unknown in the strict sense of the case we are 
 now considering. There is no advance from known to unknown 
 in saying that a pair of parallel straight lines which you may 
 intend to draw to-morrow will never meet. If the ' intent and 
 purpose ' of the antecedent ' hath full relation ' to the example 
 to be adduced, there is prima facie no inference, no extension, 
 no advance, in affirming the consequent true of that example. 
 
 A still stronger and a far more important case of such 
 generalisation by mere determination is afforded by mediate or 
 inverse induction through hypothesis. A hypothesis is a hypo- 
 thesis because it is not to begin with present in the data, and 
 has to be brought there by mediation. But to supply matter 
 for modelling a conception which is not furnished by mere 
 direct interpretation of sense, i.e. by perception or by testi- 
 mony, a set of data must have wide range and be capable of 
 a high degree of systematic inter-relation. Thus e.g. in an 
 anthropological hypothesis about the past of the Hellenic race 
 a considerable portion of the history of Europe is ultimately 
 involved, and the data bearing on it are inter-related and 
 elucidated. 
 
 In this sense a hypothesis or mediately obtained deter- 
 mination of observations by a conception superinduced upon 
 
Chap. V] Kiiids of Generalisation 165 
 
 them, is likely to involve as a result an elucidation and articu- 
 lation of a wide range of reality. Sparta and Athens, Crete 
 and the Troad, Sicily and Magna Graecia, all fall within the 
 region of reality which through determination of our knowledge 
 about it by the anthropological hypothesis in question would 
 acquire for us a certain set of highly important common 
 properties and relations. Here the generalisation results from 
 the range of the explicit system, and not from the mere 
 abstract precision of a hypothetical antecedent . What we are 
 systematising is a realit5^ and the judgment which expresses 
 our conclusion may indeed, like all precise judgments, be 
 thrown into hypothetical form, but its content makes it really 
 categorical. In it therefore we have two kinds of generalisa- 
 tion, one depending on the range of the system which we have 
 constituted, the other on the hypothetical abstractness which 
 makes even this concrete system a case, within the lines of 
 which systems differing from it in other relations may con- 
 ceivably fall. 
 
 iii. The generalisation that falls within the limits of strictly Material 
 scientific Induction is confined to what has just been described °o„i(."i' 
 as Generalisation by mere determination. It is not generalisa- Generali- 
 tion in the sense of an advance from the known to the un- 
 known. Obviously there can in no case be such an advance 
 except in the sense that the unknown becomes known. And 
 this advance is made in the determination itself ; the case, 
 when determined, is known, and is generalised in so far only 
 as it is known. Water is composed of oxygen and hydrogen 
 in certain proportions. There is no further generalisation in 
 applying this to water such as we have analysed ; and if there 
 could be a doubt whether a certain liquid was in that sense 
 ' water ', the judgment gained by previous analysis would not 
 prima facie determine it. The hypothetical character of this 
 judgment is an automatic apparatus for excluding material 
 generalisation. In thcextreme instance of such exclusion the 
 antecedent ' water ' is little more than a name, to which 
 ' composed of oxygen ' &c. supplies the content. Then if 
 ' composed of oxygen ' &c. is not true in a particular case, 
 that case ipso facto falls outside the hypothetical judgment. 
 Or in a less extreme instance, ' water ' may indicate certain 
 
i66 Scientific Induction [Bookii 
 
 visible or other properties which are synthetically related in 
 the judgment to the chemical composition. But here again 
 the least variation in those index-properties may formally 
 throw the case in which it occurs outside the hypothetical 
 judgment. 
 
 This is all very well so long as we interpret the hypothetical 
 judgment to be strictly hypothetical abstract or necessary. 
 But the account given in Book I of the Universal Judgment 
 in its sub-forms of Corporate and Generic Judgment reminds 
 us that we have a Categorical element to deal with in the 
 characteristic nature which binds things together into ideal 
 or actual totalities, and we have to face the possibility that 
 the nature of these totalities may conflict with the content 
 of hypothetical judgments in which they are set down as 
 antecedents. Every universal is an identity in difference, and 
 the identification of the conditions by which inductive enquiry 
 has determined a content is not, as we assumed just now, 
 a purely formal activity, but is, like every judgment, a syn- 
 thetic and material operation. Reliance on the accuracy of 
 our analysis will lead us back to a Lockeian formalism, if 
 we neglect the identification of the data analysed. * Man is 
 rational, because if a creature turns out not to be rational, 
 it is not what we called a man,' is an argument which, unless 
 specifically justified, has no more content than A is A because 
 we called it A. If no distinct elements are fixed within the 
 synthesis, the synthesis itself is destroyed. But on the other 
 hand, if we affirm our analysis directly of a generic content 
 which is categorically taken and includes a system of differ- 
 ences, it is clear that we are pledging ourselves to a material 
 generalisation. Does ' water ' for example, in the judgment 
 above cited, include steam and ice ? Apart from specific 
 chemical knowledge, I do not see how we could predict that 
 it would do so. And if we say ' water ' for chemical science 
 is matter of a certain composition, whether in a liquid, solid 
 or vaporous state, then we have got back to the nominalist 
 judgment criticised above ; ' « is xy because what is not xy 
 is not called a.' 
 
 I do not mean to say that the above considerations are of 
 serious importance in precise scientific induction, in which the 
 
Chap. V] Material Truth 167 
 
 definition of the data as elements in a synthetic relation is 
 always a primary problem. But either in popular applications 
 of science — the most fertile of all sources of fallacy — or in 
 provinces of knowledge which are largely dealt with by analogy, 
 it is essential to bear in mind that the identification of the 
 datum, which has been analysed or determined by a concep- 
 tion, with either the popular import or the analogical generic 
 content of that datum, is always a matter involving a material 
 synthesis and not a mere formal recognition. Where indeed 
 the precise determinate conditions of a phenomenon are 
 explicitly recognisable, there the identification of the pheno- 
 menon is a formal act, and the hypothetical judgment applies 
 ipso facto. But where, as is constantly the case in practice, 
 and, owing to the nature of a universal, always in theory, the 
 conditions are not unambiguously recognisable, but only either 
 a part of them, or a case of them, or an index-mark of them 
 can be discovered, then we must form a synthetic judg- 
 ment of identification or distinction, based on the general 
 principles which we have seen to govern argument by 
 analogy, viz. on the reality of a system of recognisable types 
 and purposes. 
 
 Apart from such a material assumption the truth of principles 
 derived from Scientific Induction itself would be practically 
 though not theoretically destroyed.^ A system of unapparent 
 deviations in the properties of natural objects, such as to 
 defy classification, might be such as to destroy the applicability, 
 while not interfering with the formal truth, of hypothetical 
 judgments. In our earlier discussions on the hypothetical and 
 categorical aspect of judgments, it was conceded that the pure 
 hypothetical judgment does not allege the existence of the 
 elements which it explicitly puts in relation. But it is also 
 clear that no ordinary result of Induction ought to be taken 
 bond fide as a judgment of this type. A judgment which cannot 
 be denied but which has no range of real application has only 
 abstract and not concrete truth. If all our knowledge were 
 of this character, as qua mere determination it conceivably 
 might be, it would have no hold upon reality. 
 
 ^ i.e. would be destroyed for concrete and real theory, but not for 
 abstract and formaltheory. 
 
i68 Scientific Induction [Bookii 
 
 So long indeed as the variations of natural objects observed 
 a continuous and mutually coherent progression, we should 
 only have a state of things not unlike the system of animated 
 nature, which would be in some respects favourable to know- 
 ledge by the clearness with which it would mark the course 
 of evolution, and might not be incompatible with human life. 
 But it is easy of course to imagine varieties in fundamental 
 properties of substances not indicated by external appearance, 
 which though following strictly from natural antecedents, and 
 not in any way miraculous, would yet be incompatible with 
 such a degree of knowledge as is necessary to maintain human 
 life on the surface of the globe. No analysis of water would 
 help us, however true under the conditions under which it was 
 made, if something which we could not distinguish from water 
 except by renewed chemical analysis were liable to arise out 
 of water by a concealed process of causation, and were endowed 
 with the properties of sulphuric acid. No formal principle 
 will meet this conceivable difficulty. Many distinctions all- 
 important for human life are only learnt by degrees or are 
 only drawn with imperfect success — e.g. between pure water 
 or milk and the same liquids when contaminated with sewage- 
 poison. We can only say that i/we are to live on the surface 
 of the globe the results of scientific induction must not only 
 have formal or hypothetical truth, but must also have that 
 degree and proportion of categorical application which is 
 necessary to enable us to adapt ourselves to the environment. 
 This degree of categorical application, of which mere deter- 
 mination, except in the case of an extended system of reality 
 like the Hellenic race, or Europe, or the British Constitution, 
 or the Solar System, can tell us nothing whatever, measures 
 the work of recognition or of generalisation which is over and 
 above the work of generalisation by mere determination. 
 When I say ' Water is composed of Oxygen and Hydrogen ', 
 I must mean by water, not necessarily all, but some large 
 proportion of what I commonly take to be water. If not, 
 my judgment, however true in the abstract, fails to grasp 
 reality in the concrete. 
 
 The ideal of knowledge, no doubt, is not in this analogical 
 generalisation, but in the second and larger kind of generali- 
 
Chap. V] InducHoft and Chance 169 
 
 sation by mere determination, viz. in the progressive reduction 
 of reality to a single system or to comprehensive single 
 systems. It must be remembered, too, that the synthetic 
 nature of every universal or identity is double-edged. If all 
 sets of conditions have to be recognised and interpreted as 
 universals, all sets of conditions should be fixed and determined 
 in the inductive analysis as universals — i.e. with the full pre- 
 vision that differences, variations, extreme cases, will arise 
 within them. Nevertheless, it seldom happens even in geo- 
 metry that a principle when fiist established is established 
 in its full content and application. Inductive analysis can 
 never make full provision for the application to fresh cases of 
 a principle which it discovers, except in as far as it discloses 
 the nature of a comprehensive individual system of Reality 
 within which other individuals fall. 
 
 4. Our results as regards Induction are then as follows. General 
 
 i. Our view of Induction as an inverse process differs essen- j^d^ °. 
 tially from that of Jevons by its dependence on material and tion. 
 positive connections, which are only defined by negation. In- Di^er- 
 verse procedure by hypothesis is for him essentially a matter jevons, 
 of probability, and depends on the exclusion of alternative 
 hypothesis simply qua alternatives, i.e. ultimately on the 
 statement of chances ^ or the number of cases out of all con- 
 ceivable cases which are in favour of the result in question 
 upon the hypothesis proposed. This view essentially depends 
 upon the false conception of . generalisation which has been 
 frequently alluded to, and according to which the ideal of In- 
 duction is perfect Induction, i.e. the summation of an infinite 
 series. As we have seen,^ the statement of chances admits of 
 valuable and extended application where we are dealing with 
 classes of unknown conditions, i.e. conditions known to us 
 simply as furnishing such and such numbers of ' equal alter- 
 natives ' ; and in astronomical and other exact science it is 
 justified by the splendid success of its results. I will venture 
 however to point out, in respect of one example adduced by 
 Jevons, that other considerations seem to have contributed 
 
 ^ Sigwart seems to waver between this view, and the true view of 
 proof by content. Logik, ii, pp. 428 ff. E. Tr. ii. 308. 
 » p. 135, supra. 
 
170 Scientific Induction [Book 11 
 
 to the inference beyond those which fairly aiise out of the 
 statement of chances. Kirchoff' s proof of the presence of iron 
 in the sun ^ depends upon the exclusion of the alternative that 
 the 60 dark lines of the solar spectrum coincide hy chance with 
 the 60 bright lines of the incandescent vapour of iron. The 
 probability of a chance coincidence being (from the distance 
 between the lines on the spectrum) about \ for each line, the 
 probability in favour of a chance coincidence for all 60 lines 
 is about {\)^, i.e. less than one in a trillion. ' But on the other 
 hypothesis,' Jevons continues, ' that iron exists in the Sun, 
 it is highly probable that such coincidences would be observed.' 
 Here the proof seems to appeal to some of the considerations 
 which belong to the positive connection between given content 
 and hypothesis, or to material generalisation, or to both. 
 Why should ' the other hypothesis ' be ' that iron exists in 
 the Sun ' ? The answer must be, I should suppose, either that 
 the 60 bright lines have a connection with the nature of iron, 
 as a characteristic or exclusive differentia, which would dispense 
 with the proof by calculation — or that though there is no 
 exclusive connection between the nature of iron and the pro- 
 duction of 60 bright lines, yet in fact no known substance but 
 iron produces such lines, and it is very improbable on general 
 grounds that a substance unknown to us but sharing this 
 property with iron is present in the Sun.^ The former of 
 these considerations would belong to the nature of true 
 Inductive determination, the latter group to the postulates 
 of material generalisation. The real function of number 
 and ratio in Induction has been sufficiently illustrated 
 above. 
 Ultimate ii. After the discussion on p. 117 above of the connection 
 
 nature of between Induction and other inference, I need only sum up 
 Indue- , T J i.- • 
 
 tion. the view which I have taken m a very few words, induction is 
 
 ' Jevons, Principles of Science, p. 245. 
 
 ' The fraction (j)" represents, I suppose, the chance of 60 coincident 
 cases all produced by independent causes ; but ought we not also to 
 consider the probability not merely of one unknown cause producing 
 all the cases, and that cause being iron, but that of all the possible 
 alternatives in which 2, 3 and so on up to 58 inclusive, of the coincident 
 cases, are produced by a single unknown cause, and the remainder in 
 each alternative by accident ? 
 
Chap. V J What do cousequeuces prove? 171 
 
 not a species of inference, as calculation, geometrical reasoning, 
 analogy and subsumption, are species of inference. It has 
 not, that is to say, for its differentia any peculiar nature 
 in the universal which carries the conclusion. It is conse- 
 quently, like Comparison or Recognition, like Observation or 
 Experiment, a transient and external characteristic of in- 
 ference. An Inductive proof, when completed, may be a 
 geometrical construction or an arithmetical calculation, an 
 articulate subsumption or a morphological analogy. Its 
 Inductive character belongs exclusively to the process of 
 discovery, and depends on the relation between the elements 
 of the content and the qualification of reality from which the 
 process of cognition starts. Inferential connection is one, 
 and is necessary and invariable ; but the points at which 
 a single and coherent system may be in contact with the real 
 world as known to an individual cognitive subject are infinitely 
 various. From these points, whatever they may be, the 
 cognitive subject has to build up the single and coherent 
 system, which he then refers to reality. When these points 
 are isolated perceptions, occurrences or qualities, then the 
 task of building up the system which they necessitate is called 
 Induction. 
 
 Inductive proof rests, like all Inference, on systematic and 
 necessary connection of content. How many observations, 
 what experiments, how many and how favourable conjunctions 
 of phenomena, may be needed to disclose the connection to 
 us, is, as Aristotle implied in the Posterior Analytics,* theoreti- 
 cally indifferent. The observations do not give us the connec- 
 tion, but we judge the connection on the basis of the system 
 demanded b}^ the observations, and this systematic or reasoned 
 judgment is the essence of the proof. 
 
 Is a principle then proved by the number and variety of 
 its verified consequences ? It gains nothing from any repetition 
 of identical consequences once established to be fact ; but 
 variety of consequences may be said to prove it by displaying 
 its nature as actual and modelling it into concrete identity 
 with themselves. I incline to think that the truth upon this 
 
 ' Anal, post., p. 90, a. 24 ; cp. p. %j, b. 39 ; and see the author's 
 Knowledge and Reality, p. 285: 
 
172 Scientific Induction by Analysis [Book 11 
 
 point is best stated through the paradox proposed above. ^ 
 Every fact, every sense-perception, every datum of testimony, 
 absolutely and irrevocably proves something and necessitates 
 the assumption of some agent or principle. Repetition of the 
 same datum, qua the same (i.e. assuming that it was completely 
 and correctly observed at first, which is never true), can add 
 nothing to what it proves. But every further datum which 
 can be connected with the first goes to develop the content 
 of that agent or principle which both the data prove. If 
 therefore we speak of the mere proof that something or other 
 beyond the datum, must be assumed, one datum is as good as 
 a host to prove this, and the proof of it is absolute at first ;. 
 and to allege variety and range of data as contributory to this 
 proof is to fall once more into the fallacy of generalisation 
 from number of instances. What is proved once does not need 
 to be proved again. Every datum proves irrefragably the 
 reality of the system to which it belongs, whatever that may be. 
 But this representation of the matter, though it leads up to 
 the truth, is in itself a paradox without real import. A proof 
 which proves the reality merely of something or other is a 
 proof of nothing at all. But if we speak of the proof of a deter- 
 minate agent or principle or real system, then both range and 
 variety of data are essential to the proof, and the proof of the 
 whole is not absolute at once, and therefore the proof of any 
 part, as a part in that whole, is not absolute at once. For the proof 
 depends upon the intelligibility with which the hypothesis — 
 to use the terms explained above — is adjusted to or included 
 in the postulate ;■ that is to say, with which the alleged real 
 system is identified with the real something demanded by all 
 the data taken together. And from the nature of knowledge 
 as a system the necessity of this synthetic connection can only 
 be evident in an extended range of applications ; and hence 
 it is — not from number of consequences, but from the varied 
 determinations which are indispensable to define any universal 
 in its inter-connected differences, that range and variety of 
 data are contributory to the proof of a hypothesis.^ Thus we 
 
 ' p. 161. 
 
 ' I am omitting, to avoid confusion, the consideration of repeated 
 observation as eliminating accidental errors, which depends on the 
 
Chap, vj What Constitutes Induction 173 
 
 may say, if we like, that variety and range of data contribute 
 nothing to the proof of a hypothesis, but only aid in its 
 definition.* But we must then bear in mind that the proof 
 to which range does not contribute, and which each isolated 
 datum effects absolutely and ultimately, is a proof of some- 
 thing in general, but of nothing in particular. 
 
 Induction, then, is the reference to reality of a system on 
 the ground of particular differences within it by which reality 
 is taken as qualified ; and may involve, in the constitution 
 of the system for knowledge and in its identification with 
 those differences, any process known to Logic. It is essentially 
 an advance from the Individual or concrete Generic judgment 
 to the pure hypothetical, or to its higher form, the Disjunctive 
 judgment. When we are able to start from a reality qualified 
 to us by pure hypothetical or by disjunctive judgments, then 
 we can go at once from the differences as in the universal to the 
 relations of other differences, and we can refer these differences 
 to reality on the basis of the universal itself which is accepted 
 as real. We do not in this case employ species of inference 
 unknown to Induction ; but the process in which we employ 
 them has not the peculiar relation to given Reality, e.g. the 
 gradual emergence of negative determination, which con- 
 stitutes Induction. 
 
 principle of chances illustrated above. Accidental errors are errors 
 arising from a variety of unknown causes. Repeated observation dis- 
 tinguishes series such as are likely to be due to a single cause, from 
 series likely to be due to unknown causes. 
 
 ' It is a good way of stating how far a hypothesis is proved to ask 
 ourselves what we should have to disbelieve if we disbelieved it. The 
 more it is efficient as an interpretation of the data, eliciting and depend- 
 ing on their individualities, the more difficult it is to disbelieve it without 
 disbelieving the data, or at least without disbelieving a certain reading 
 and colouring of them which ex hypothesi is included in their verification. 
 The proof that ' nothing else can explain them so well ' is really depen- 
 dent on this reading and colouring of them expanding into the detail of 
 the hypothesis, not on the detached destruction of competing hypo- 
 theses. And then of course the wider the range of the data, the more 
 difficult it is in turn to disbelieve them, without disbelieving the whole 
 of the rest of our experience. There can be no doubt I think in principle 
 that true conclusions — data as deduced — support their premises. 
 
174 On Defective Formulation [Bookii 
 
 ON DEFECTIVE FORMULATION OF THE INDUCTIVE 
 PRINCIPLE 
 
 Inference iii. A point which I have touched upon above, relating 
 tition^^^ to the basis of Induction, has recently been brought into 
 prominence by the attitude of M. Bergson, with the imitation 
 and repetition theorists whom he appears to follow,^ to the 
 creative and constructive activity of the intellect. I cite 
 a typical passage {Evolution Creatrice, p. 218) : ' L'intelligence 
 a pour fonction essentiel de lier le meme au meme, et il n'y 
 a entierement adaptable aux cadres de l'intelligence que les 
 faits qui se repetent.' 
 ' Same a. Such a statement is in the sharpest possible conflict with 
 
 cause, ^Y\Q, view of intellectual activity which to many of us seems 
 effect.' natural and obvious. But when we refer to the most accredited 
 expositions of the logical theory of Induction, which attempts 
 to deal with the characteristic working of the scientific intelli- 
 gence in the advancement of natural knowledge, we find them 
 dominated by ideas which appear to justify M. Bergson 's posi- ' 
 tion. What I wish to attempt is a brief reconsideration of the 
 exact meaning and function of these ideas in Inductive Logic. 
 The basis of Induction is usually stated in some such 
 formula as ' Same cause, same effect '. It is unnecessary for 
 our present purpose to raise the questions connected with the 
 converse formula, ' Same effect, same cause.' It is enough to 
 understand the simplest truism of Identity, that a thing does 
 what it is its nature to do under given conditions,'^ and cannot 
 do otherwise except by some change in the conditions ; from 
 which it follows, that if, in an alleged causal nexus, the alleged 
 effect is sometimes absent while the alleged cause is present, 
 ceteris paribus, it is impossible that the alleged cause should be 
 the real cause of the effect in question. The principle is sound, 
 beyond any doubt, as far as it goes. It is, in fact, nothing 
 more than can be read off from the law of non-contradiction, 
 as formulated, for example, by Plato. The same thing cannot 
 behave differently to the same thing in the same relation. If 
 
 * Cp. Tarde, Les Lois de I'lmitation, p. 15. ' II n'y a de science . . , 
 que des quantites et des accroissements, ou, en termes plus generaux, 
 des similitudes et des repetitions phenomenales.' 
 
 '• Cf. Mr. Joseph's Introduction to Logic, chap. xix. 
 
 I 
 
Chap. V] Mere Elimination ? 175 
 
 it seems to do so (Plato's condition ' at the same time ' is 
 superfluous), you can infer that there is a difference in the 
 supposed agent. The same, so far as it is concerned (i. e. if no 
 condition is altered) produces the same ; what produces some- 
 thing different, out of itself, is not the same. If this much is 
 not to be assumed, we cannot treat anything as having an 
 assignable nature. Truth ceases to have a meaning. Any- 
 thing might behave anyhow. 
 
 Now it is from this law or truism that, according to current 
 logical theory, the fundamental Inductive test of causal con- 
 nection is derived. The Inductive process is thus regarded 
 as one of elimination.^ You have before you, it is assumed, 
 one or more suggested connections of cause and effect, and 
 you labour to eliminate from among them all alleged causes 
 that are present in the absence of effects with which they 
 claim to be connected. Such elimination leaves, it is pre- 
 sumed, a surviving statement which approaches more and 
 more closely to a true, i. e. an invariable, causal connection. 
 The principle is simply that which M. Bergson refers to ; 
 What is the same, does the same ; if the same product is not 
 there, the same agent is not there. The same produces the 
 same. And yet, if this were all, we should have a difficulty 
 in denying M. Bergson's doctrine which I began by stating. 
 It would then seem to be the case that the essential work of 
 the intellect lies in binding the same to the same, and that 
 the true type of the logical universal — ^the essence of cogni- 
 tion — is, as M. Bergson says, the relation of an abstract 
 statement to examples which repeat its tenor wholly without 
 variation. That water boils at sea level at 212° Fahr. would 
 be such a generality ; and according to the number of instances 
 in which people boiling their kettles at or near sea level '' found 
 
 * The rules of elimination which depend on the further principle, 
 'Same effect, same cause ' (i.e. on the exclusion of plurality of causes), 
 rest merely on a more precise consideration of the ideal of identity, which 
 it is not necessary to take account of in order to understand the point at 
 issue in this discussion. See Joseph, chap. xxii. 
 
 ** I am satisfied to take a case in which strictly accurate repetition is 
 all but impossible, because it illustrates the real fact, which is that the 
 interest of the generality lies in the differences which it binds together. 
 A strict repetition could have no interest at all. 
 
176 On Defective Formulation [Book ii 
 
 the water to be about 212°, would be its rank and power as 
 a piece of knowledge. 
 This a f3. But why should we deny M. Bergson's doctrine ? Per- 
 
 jq" °' haps it may be the truth. As a prima facie answer to this 
 suggestion, we need only refer to such a criticism of tau- 
 tology as- we find, for example, in Mr. Bradley's Principles of 
 Logics 
 
 M. Bergson's doctrine is logically bound to deny not only 
 the advance from one truth or connection of fact to another, 
 but the possibility of apprehending or of uttering any signi- 
 ficant truth at all. It may appear that this criticism is 
 exaggerated, because the doctrine explicitly treats (so far as 
 I am aware) as outside the principle of the intelligence, only 
 the difference between the corresponding terms of one nexus 
 and those of another nexus, and not the difference between the 
 terms themselves — alleged cause and alleged effect — which are 
 constituents of a single nexus. But there is no escape by this 
 road. If tautology is the principle of the intelligence, the 
 connection of any two distinct terms, say, as cause and effect, 
 stands on the same ground as the connection between two 
 different connections. With tautological identity as the 
 principle of intelligence, all systematic coherence, between 
 term and term, equally as between judgment and judgment, 
 inevitably vanishes. 
 
 But in fact there is (i) some misinterpretation involved in 
 setting up the principle ' Same produces same ' as the dominant 
 principle of scientific Induction and as governing the nature 
 of the generalisation which is the aim of that process ; 
 although 
 
 (ii) I admit and maintain that the current logical statement 
 of the theory of Induction lays itself open to this misinterpre- 
 tation. The view which I have taken above ^ indicates, I 
 believe, the right theoretical direction, with its consequence 
 as regards the place of elimination of erroneous hypotheses in 
 drawing Inductive conclusions. But I hope that the point 
 will be made clearer by a few additional remarks. 
 Its mean- (i) When you postulate as the basis of Inductive Inference, 
 '"S- the principle ' Same cause, same effect ', you do not mean that 
 
 " e.g. p. 29. ^ p. 164. 
 
chai'. V] A Stereotyped Nexus 177 
 
 the effect is the same as the cause. ** They must be ditferent, 
 if the relation of cause and effect is to be worth establishing. 
 You do mean (a) that assuming the truth of an alleged causal 
 nexus A — B, it only applies in cases which are absolute 
 repetitions of it, i.e. where you have exactly the same A as 
 before without any variation ; and (/rJ) that in examining the 
 truth of an alleged causal nexus A — B, your rule must be that 
 if you find a case in which, ceteris paribus, B is different 
 (0 or B,) and A is unvaried, your alleged causal nexus A — B is 
 disproved. For if it were true, the same cause would be 
 producing, ceteris paribus, two different effects, which is impos- 
 sible. (If A is plural, or rather, various, and B singular, this 
 is not literally a case excluded by the formula ' Same cause, 
 &c.', which is strictly taken silent about it, i.e. about plurality 
 of causes, and no negative inference follows, unless we are 
 making what usually counts as an additional postulate ' Same 
 effect, same cause '). 
 
 What you mean by ' Same produces same ', then, is an 
 assertion that the cause, in a nexus guaranteed by this principle, 
 is unvarying compared with itself, and the effect unvarying 
 compared with itseU. You imply no comparison between 
 cause and effect. 
 
 And your principle makes no suggestion towards the 
 estimation of any possible cause and effect allied to or devel- 
 oped out of those forming the nexus whose truth we assume 
 to be accepted. According to a proper interpretation of the 
 word ' same ' some such expansion would be permissible, 
 passing from a — b to a — /3 and from a — li to A — B. But 
 what makes it impossible is the demand for a methodic rule. 
 Plainly there cannot be a general rule that will tell how much 
 variation in your cause and effect, each from each, will be 
 justified under the principle ' Same cause, same effect '. And 
 therefore, if you want a rule, you must take one which justifies 
 no variation at all, and makes your ' generalisation ' cover 
 nothing but sheer repetitions, and degrades your procedure 
 
 '^ In a remote sense some such meaning might be assigned to the true 
 Inductive principle which I desire to see established, and it may be that 
 some hint of this possibility prevents the formula under discussion from 
 seeming as naked as it really is. Its strict meaning can only be that 
 stated in the text. 
 
 1337-2 N 
 
178 On Defective Formulation [Book ii 
 
 in connecting the same with the same into one which admits 
 of no novelty or true inference. 
 
 But the two types of connection thus disregarded, that of 
 cause and effect, and that of any generalisation and its more 
 advanced but kindred form, really contain the very life and 
 mainspring of Inductive thought. How the suggestion of the 
 effect B issues from the fact of the cause A ; or how the more 
 complex and advanced a (def) — b (xyz) came to be substituted 
 for the cruder A — B ; this is where the real work of the scientific 
 intelligence lies. This is the work of invention or discovery, 
 of which the imitation and repetition theorists, whom M. Berg- 
 son appears to me to follow, have never succeeded in giving 
 any serious account. ** It is the process by which isolated 
 observations are built up into a science, through an assignment 
 of conditions which is always becoming more systematically 
 complete on the one hand, and more relevantly precise on 
 the other. Examples of such an inventive pursuit of a universal 
 relation would be the rise of the science of acoustics out of the 
 old observation that the pitch of musical notes has a ratio 
 comparable with that of the lengths of the stretched strings 
 which produce them ; or the development and limitation of 
 the conception of equi-potentiality as applied to organic 
 growth in recent embryology. Here we have the plain fact, 
 that it is the essential character of intelligence to bind different 
 to different in binding same to same ; and that it is for the 
 former character that the latter is valuable, and, indeed, it is 
 through the former only that the latter can exist. But the 
 sameness here in question is not the sameness of M. Bergson's 
 doctrine or of the formal Inductive test. We can see this from 
 the nature of its aim. The universality or generality, which is 
 the goal of such a process, is not the relation of the terms of an 
 abstract judgment, term for term, each to each, to the terms 
 of repeated cases which fall under it. It is the relation of the 
 different terms of a judgment to each other, or of an organised 
 system of conditions, representing a certain range of experience 
 (e. g. our experience of musical sound or of embryonic growth), 
 to the several connected factors or conditions, whether constant 
 or varying, which it embodies and explains. Its universality 
 * Cf. especially Bergson, !l£volution, p. 177. 
 
Chap. V] The Maiuspring of Knowledge 179 
 
 is not measured by millions of repeated instances, but by depth 
 and complexity of insight into a sub-system of the world. 
 
 (ii) The logical theory of Induction gives but scanty atten- True 
 tion to this work of the universal in suggesting and pursuing ^Pi^it of 
 new connections, because, for good logical reasons, that is, tion. 
 because of the individuality of truth, it cannot be reduced, 
 like the eliminative test, to something like a formal rule. 
 Nevertheless, this work is the true spirit and mainspring of 
 the inductive advance of knowledge"; and to disregard it, while 
 insisting on an eliminative test, is an error analogous to 
 demanding a general criterion of truth. But truth has no 
 criterion except the fuller truth. And the real interest of 
 logical theory in the advance of knowledge is to note how, by 
 the analysis and purification of its conditions, a perception 
 passes into an organised system of understanding. 
 
 The existing connections or universals with which the mind 
 is stored, act as clues among the new experiences which con- 
 front us, selecting those that are kindred or complementary, 
 and inventing new systematic ideas after the manner of what 
 have been called proportional systems, and by means of relative 
 suggestion.* That is to say, that an existing connection of 
 thought, when confronted with new matter, is able to reproduce 
 itself in a new form which is at once appropriate to the new 
 matter, and continuous with the connection as previously 
 thought. This is not a question of reproducing objects of 
 thought which have previously been connected in the mind. 
 It is a question of continuing some elements of such a con- 
 nection into new forms of nexus, because the connection 
 between the new objects has a real kinship with the connection 
 between the old, although differentiated by the nature of the 
 new objects themselves, and made, as a connection, something 
 new, and not a repetition of what it was before, like the 
 
 * Cp. Stout, Anal. Psych., ii, p. 80. I note that Professor Stout here 
 observes that relative suggestion ' would not of itself enable (the dis- 
 coverer) to fix in exact detail the special variations '. In the case he is 
 dealing with, calculation was necessary. In our instance from embry- 
 ology, observation is necessary. But it seems to me that the question 
 what calculation ? what observation ? is answered by the governing 
 idea in both cases, and the relevant conclusions are selected by it, and 
 it is it that they develop. 
 
 N2 
 
i8o Oil Defective Formulation [Book ii 
 
 continuation of a varying curve from the datum of a given 
 fragment of it.* Such a continuation is plainly not a repetition, 
 and I think that in view of the current theory of Inductive 
 generalisation, the notion of repetition as a condition of 
 knowledge is not meant to apply to such an inventive con- 
 struction as that of which I am speaking. 
 
 Let us look at an example. In recent embryological dis- 
 cussions,'' covering the old ground of preformation and 
 epigenesis, we read of experiments which prima facie suggest 
 two precisely opposite causal connections. 
 
 Half an ovum, we are told, in certain cases will produce 
 only half an embryo ; but in other cases the half ovum may 
 develop into a perfect embryo. The former fact suggests 
 a complete preformation of the organism, each part of it 
 in a fixed part of the ovum ; the latter suggests that the ovum 
 has a structure of which ' every part may become anything '. 
 It is of great logical interest to look at the course which these 
 two alleged types of connection have imposed upon Inductive 
 research. Sheer prelocalised preformation is an idea, it would 
 seem, that the experiments undertaken to confirm it immedi- 
 ately destroy. And if a universal nexus had no power of 
 developing into novelty, this check would have been check- 
 mate, and the idea would have been dead. But a universal 
 can take on new shapes as demanded by new matter ; and 
 though, as it seems, the ' mosaic theory ' (of the independent 
 preformation of parts) must be abandoned in its rigid shape, 
 yet the most various experiments on the tissues of organisms 
 in later stages have shown that some of these are necessary 
 to the development of some organs, and that therefore some- 
 thing essential to special development (perhaps ' organ-forming 
 substances ') is preformed, though not necessarily pre-localised. 
 The logical interest is, that the idea of preformation, defeated 
 in its primary and rigid shape, has been able to act as a clue 
 to new experiments in a different region, such as to confirm 
 it when restated in a more subtle and flexible form. 
 
 So with the idea that every part of the ovum has the capacity 
 
 * Cp. Bradley's Principles of Logic, p. 281 fit. 
 
 '' My example is drawn from Driesch's Gifford Lectures and Jenkin- 
 son's Experimental Embryology. 
 
Chap. V] Ifidnctive Invention i8i 
 
 of becoming a whole. It is easily seen that this capacity is 
 limited, and is sooner or later lost ; but the idea of the kind 
 of causation at work modifies itself according to the limitations 
 which are discovered, and seems to suggest new lines of 
 research which promise to account both for the capacit}^ and 
 for its limitation and arrest. And the logical interest is, that 
 by means of this suggestion, that of ' organ-forming sub- 
 stances ' and their distribution, it appears as if the two 
 universals in question, ' preformation ' and ' epigenesis ', 
 might coalesce in an idea different from either, but satisfying 
 the requirements of both. 
 
 Of course I am offering no opinion upon the value of these 
 investigations. I only adduce them as striking examples of the 
 ordinary course of a universal in its Inductive development. 
 What works throughout is a continuity through differences ; 
 and its value is in the differences it connects. This is through- 
 out the essence of creation and invention, which permeates 
 the whole of life, and so everyday a process as the use of 
 language is a striking example of it. No one ever used the 
 same word twice in precisely the same sense ; in ' finding the 
 right word ' there is always a creative effort. 
 
 Now the general rules of Inductive elimination, based on 
 ' Same produces same ', are simply the minimum negative 
 criterion of truth, and can do by themselves no Inductive work 
 a^ all. To rely on them alone is to reduce Induction to trial 
 and error.* 
 
 y. Thus, I do not think it is true to say that ' Same cause, The True 
 same effect,' is the basal principle of Induction ; and if this is Principle, 
 so, there ceases to be any ground for maintaining that it is the 
 essential function of the intelligence to connect the same with 
 the same. The true principle I should rather state in some 
 
 * It is a subtlety that in fact the underlying positive nature of 
 negation often asserts itself, and the ' just-not a gives just-not b ' affords 
 a positive extension of the nature of a and b respectively, which may be 
 theoretically valuable, see above, p. 1 34. Thus in Driesch's Tubularia 
 experiment, it is now alleged, the capacities of different cells are just 
 not equal, as they just belong to different elements of the body. And 
 this suggests that differentiation is present in a certain degree — a posi- 
 tive correction and extension of Driesch's conclusion. Driesch, Gifford 
 Lectures, i.p. 128, and J enkinson, Experimental Embryology, p. 292 n. 
 
i82 On Defective Formulation [Book ii 
 
 such form as that every universal nexus tends to continue 
 itself inventively in new matter. It is true that to guide this 
 process we can have no general criterion, because, as we have 
 said already, the only criterion of truth is the fuller truth — the 
 science at a more developed stage. And, therefore, there can 
 be no rules for it, and it tends to drop out of logical theory. 
 But none the less, it is this process to which the whole positive 
 construction or invention of our inductive knowledge is due ; 
 while the principle ' Same produces same ' can only eliminate 
 what, having been suggested, is found on further trial not to 
 produce the minimum characteristic of a real nexus. We have 
 seen, indeed," how a good experiment may sometimes reveal 
 a correlation of serial variations, which is in itself a positive 
 expansion of the suggested nexus. But this is only incidental 
 to the strict process of Inductive Elimination. 
 
 The neglect of the positive continuity between differences 
 as the inventive factor in Induction appears to me to show 
 itself in the doctrine that Inductive progress consists strictly 
 in mere elimination of the unfit, ^ in reducing the number of 
 nexuses that can claim the position of the true invariable 
 law. This doctrine seems to me to subordinate the more 
 important process and element of proof, because it can have 
 no abstract criterion, to the less important, which is nothing 
 but an abstract criterion. But if the aim of logic is not to 
 give rules of practice, but to understand the nature of know- 
 ledge, this ground of subordination is invalid, and it remains 
 true that the mainspring of inductive advance in natural 
 knowledge, as of knowledge in general, is the power of ideas 
 to make experience coherent, and that therefore the demand 
 of continuity between term and term or between nexus and 
 nexus — of a positive explanatory character attaching to the 
 nexus — is a fundamental requirement of inductive science, 
 which is in fact merely an elementary stage of knowledge, 
 Develop- and shares all its positive characters.'' 
 
 ing the . jYiQ modification outlined above in the idea of Inductive 
 
 rsexus. 
 
 * P. 175 and p. 181 footnote. 
 
 '' See Bradley's criticism of one form of Disjunctive reasoning, Princi- 
 ples of Logic, p. 515, and above, p. 156. 
 
 ' But see Mr. Joseph's example from the discontinuity between 
 
Chap. V] Getting the full Conditions 183 
 
 universality or generalisation follows from this conception. 
 The value of an Inductive conclusion, as of any piece of 
 knowledge, lies in the amount of reality which it enables us 
 to grasp, and this is very slightly tested by the number of 
 cases in which the nexus is repeated in fact. And if the idea 
 of identical repetition could be realised (which it cannot, for 
 every so-called repetition is differenced by a new context) the 
 frequency of recurrence would have no connection with 
 universality at all. 
 
 What is here advocated as the true view .of Inductive 
 advance has been suggested by Green's treatment of logical 
 theory,* and has in some degree been embodied in the present 
 work, at the point ^ where it dealt with true Inductive general- 
 isation as consisting in the range of differing data and con- 
 ditions welded into a system by any investigation, as contrasted 
 with the number of recurrent cases which may fall under 
 a single abstract statement ; and there is a definite logical 
 necessity for making the former type of universal the goal 
 to which the latter is a halfway house or less. For, as Plato '^ 
 pointed out and as Mr. Bradley ^ has recently emphasised, 
 statements of fact (implicit statements of nexus), but slightly 
 hedged with conditions, must always be at the mercy of 
 unexpressed factors for their truth or falsehood. They 
 tumble backwards and forwards between ' is ' and ' is not ' ; 
 Plato's famous expression, which Mr. Bradley's argument in 
 the passage just referred to strictly and precisely justifies. 
 The remedy, as Mr. Bradley says, is to get the conditions into 
 the subject ; and this means either an explicit or an implicit 
 reference to a complete system.® 
 
 physical cause and psychical effect, p. 453. I believe, however, that 
 more could be done than is usually done to remove this discontinuity, 
 though of course there can be no resolution of the ultimate difference 
 of kind. But I suggest that a consideration of the way in which 
 elements of brain-excitement reinforce and modify each other, would 
 have made impossible the defects, say, of Kant's ethical doctrine. An 
 idea unsupported by outlets of activity could not be a powerful idea, and 
 therefore not one ethically fitted to be paramount. 
 
 * Works, ii, pp. 288-90. ^ Above, pp. 164 and 169. 
 « Rep., p. 479, c. ^ Mind, No. 72, p. 499. 
 
 * See above, i, p. 245, for judgments which imply, though they do 
 not expressly include, a relevant scientific system. 
 
184 On Defective Formulation [Book ii 
 
 The normal and natural working of intelligence, then, is 
 creative and constructive, tending towards the concrete and to 
 continuity within differences. The universality which is its 
 mainspring is in itself a nisus to the concrete. This operative 
 continuity is not represented by the linkage of the same to the 
 same. Its law — the law of intelligence — is not the law of 
 Identity, unless the law of Identity is construed in a way that 
 takes it deep into the postulates of organic systematisation.* 
 And phenomena which should merely repeat themselves would 
 present an absolute barrier to the central nexus of the intellect. 
 Mere repetition, in fact, if it were possible, would be incom- 
 patible with understanding. 
 
 I am, therefore, still confident that the restriction of Induc- 
 tive proof to the disqualification of competing hypotheses is 
 a fundamental error of principle.^ What really works in the 
 proof is the same as what works in the discovery, the power, 
 that is, of an idea to harmonise experience. No doubt the 
 hypothesis which best satisfies this condition would also be the 
 least likely to fall a victim to the rule of elimination. But yet, 
 theoretically speaking, if accepted for this latter reason, it is 
 accepted, so it seems to me, for the wrong reason, and its value 
 as knowledge is not genuinely apprehended. But this point 
 is only incidental to my discussion, and I will not pursue it here. 
 
 * See below, ii, pp. 210-1 1. 
 
 ^ I am afraid that here I lind myself in opposition to Mr. Joseph, 
 whose Logic I greatly admire. And I must add that I cannot at all 
 follow Mr. Lindsay's comment on the above remarks (The Philosophy 
 of Bergson, p. 27,0), 'When we say, this is like A, and .*. its effect will 
 be like B, we are applying a result of that insight [viz. the insight that 
 A causes B] and we are concerned with A' only in so far as it resembles 
 A. This implies that A' repeats A, for its difference with A must for 
 our purpose be ignored.' Mr. Lindsay has no doubt considered the 
 relation of this statement to the conception of inference as a develop- 
 ment of universals into their differences. But I really cannot under- 
 stand it. Let A be a given depth of corolla-tube, seen to condition B, 
 the length of an insect's proboscis. In applying this insight to A', in 
 whicli the depth is different, how can we ignore the difference? Or 
 would Mr. Lindsay contend that no universals can be developed into 
 definite new applications except in quantitative law ? But this would 
 svirely be an extraordinary thesis. All non-mathematical inference, 
 except perhaps pure subsumption, would be abandoned. For nature 
 of universals see especially Bradley's Logic 281 ff. For further instances 
 Stout Anal. Psych. 1. c, or above iSo; cp. also p. 192. 
 
CHAPTER VI 
 
 Concrete Systematic Inference 
 
 A PURE hypothetical judgment, the outcome of scientific 
 Induction or the embodiment of abstract relations in com- 
 bination, expresses a synthetic connection based upon an 
 underlying real system. Analogical inference, from which 
 scientific Induction was a divergence, depended rather upon 
 an estimate, usually inadequate, of such real systems in their 
 concrete import. Now if, as a result of a highly exhaustive 
 Scientific Induction taken together with an Analogical reason- 
 ing, we are able to recombine the abstract relations which the 
 former has disclosed one by one, into a single totality which 
 has an obvious significance, then this totality or system is the 
 real determinate ground of each separate relational judg- 
 ment that enters into our conception of it, and belongs, at 
 the same time, to the concrete or categorical type of knowledge. 
 For the ground which warrants a hypothetical judgment is in 
 the last resort always a real system, and moreover the content 
 of every judgment is understood ^ to have such Reality as it is 
 capable of. 
 
 I. Therefore, in dealing with totalities which are thus Philoso- 
 thoroughly concrete and thoroughly rational, we are able to ? L\^ 
 advance from the figure of analogy * A and C are B, there- tion. 
 fore A is probably C ', to the first figure of the Aristotelian 
 syllogism, ' A is B, B is C, therefore A is C 
 
 In spite of all that has been written about and against the 
 syllogism, I can find no more simple and natural expression 
 than this for the reasoned judgment which embodies a real 
 necessity. Thus applied, the syllogism is subsumptive in so 
 far as it appeals to unity of relations within a concrete subject, 
 but has abandoned the differentia of subsumption proper, in 
 so far as the definite form taken by the result of the appeal 
 depends on intelligible coherence and not on mysterious con- 
 
 ' See Bk. I, chap, ii, on Categorical and Hypothetical Judgment. 
 
1 86 Concrete Systematic Inference [Book ii 
 
 junction. It is essential to such arguments that the teleological 
 or quasi-teleological unity of the subject, which in analogy 
 was conjectural and obscure, should be absolute and explicit. 
 It is only this absoluteness that can warrant the position of 
 the middle term as subject in one premise, i.e as a qualification 
 which prescribes the precise content affirmed of it in the 
 predication. It is only this explicitness that can justify by 
 a specific^ necessity the determinate relations which the unity 
 of the subject imposes on the two extremes. The conditions 
 thus demanded can only be fulfilled in subjects the nature of 
 which is known as a definitely organised system. We saw 
 indeed, in the earlier discussions of Book I,^ that such a system 
 cannot avoid presenting quantitative relations between its 
 parts, in as far as its pervading unity contains within itself 
 differences of a common quality. But in a true concrete 
 individuality such quantitative relations are secondary, result- 
 ing from the nature of the system but not exhausting it, and 
 therefore the system, although definitely intelligible, cannot 
 be ' constructed ' by geometrical or numerical combination. 
 Such combinations may however enter into it in various degrees. 
 Judgments which deal with these concrete individualities are 
 at once individual and universal, and have been analysed in 
 Book I as a combination of these characters."^ 
 
 Fluid though the distinctions between types of inference 
 necessarily are, it will be convenient to distinguish the im- 
 portant class of inferences now before us by an unmistake- 
 able differentia, at the risk of unduly limiting their province. 
 This differentia is the ascription of real teleology to the content 
 analysed. And by real teleology I mean the embodiment or 
 operation of a conscious purpose entertained by a human 
 intelligence. All other teleological inferences, such as those 
 depending upon the de facto teleology (quasi-teleology) of the 
 organic world are most conveniently relegated to the category 
 of analogy. 
 
 The lowest case of real teleology is closely akin to that 
 
 ' See Bk. II, chap, i, on specific necessity of Judgments. 
 ' See Bk. I, chap. iii. 
 
 * See on the Corporate Judgment and the Individual Generic Judg- 
 ment, above, Bk. I, chap. v. 
 
Chap. VI] Alt individual System 187 
 
 which was the highest case of analogy. A tool, instrument, 
 or machine, of which we know the use intended by the maker, 
 furnishes this lowest case of real teleology, while any object 
 of the same class the use of which we could only conjecture, 
 furnished the highest case of quasi-teleology or analogy. It 
 was in part from the example of an instrument contrived by 
 human intelligence that Plato introduced the conception of 
 function or final cause into philosophy ; ^ and the ultimate 
 meaning of ' organism ' is a system of tools or instruments. 
 The term ' mechanical ' in its modern philosophical accepta- 
 tion abstracts from one-half of the import of ' machine ' ; for 
 though we are accustomed to think of mechanical determination 
 as a resultant of any de facto combination of forces, yet we 
 are not accustomed to think of a machine except as a com- 
 bination of forces for a purpose consciously entertained. 
 
 At first sight, then, we have in the tool, instrument or 
 machine with known purpose, an adequate example of the 
 type of knowledge before us. ' A screw that is meant to turn 
 one way only must have its head cut so as to give the screw- 
 driver no purchase when turning the other way ; a coffin- 
 screw is a screw meant to turn one way only ; therefore a 
 coffin-screw is one which has its head cut,' &c., &c. Or again : 
 ' A locomotive engine meant to drag a weight « at a velocity 
 b must have boiler-space x and cylinder-stroke between the 
 limits z and z^ ; a locomotive which is to work in the New- 
 castle coal traffic must drag a weight a, &c., &c. ; therefore 
 a locomotive which is to work this traffic must be constructed 
 as above determined.' 
 
 It will strike the reader however on looking at such examples 
 as these that the premises are very closely allied to hypothetical 
 judgments, and are much more ' constructive ' than ' sub- 
 sumptive '. It is true that in the analysis of a machine the 
 inference does rest on the system oi the mechanical combination, 
 
 ' Republic, end of Bk. I : Speirafw rw kni rovro ipfaaOivri. The 
 examples alleged by Plato in this important passage are of very different 
 values, and are well worth careful attention. The well-known descrip- 
 tion of the function of a thing as o ai' ^ fiovu (Kfivw -noiri tis -q aptara 
 leans to de facto teleology, and would not of course protect an object 
 from a function alien to its nature but relative to human purpose. Such 
 a function could justify no analogy. 
 
1 88 Concrete Systematic Inference [Book ii 
 
 and that this system with all the details dependent on it 
 can, in a machine that works well, be deduced from the intel- 
 lectual purpose which the constructor proposed to himself to 
 realise in that mechanical combination. So far, as reading 
 the significance of the parts in the coherent whole without 
 which they would lose it, the inference is subsumptive. On 
 the other hand, all tools or machines are liable to initial or 
 acquired mal-adaptation. Their de facto function or actual 
 result may diverge from their intended function. And when 
 this comes to pass, their existence as mechanical combinations 
 is not thereby terminated. A clock that has a hopelessly 
 variable rate may not, philosophically speaking, be rightly 
 called a clock (being absolutely useless to indicate time), but 
 it remains a real mechanical combination in which co-operating 
 parts produce a necessary result. In other words, though 
 a machine embodies a purpose, yet it only embodies it in a 
 mechanical form, dependent, that is, on the right adjustment 
 of a mechanical combination, and therefore on the continuance 
 of that right adjustment. Therefore in every such inference 
 there might be substituted for the statement of purpose 
 a statement of the mechanical system in which the purpose 
 is supposed to be realised ; and as the purpose is only present 
 in the actual system of adjustment, and not as an intellectual 
 idea, such an analysis would be in one sense adequate to 
 the nature of the object analysed. Such inference might 
 fairly be treated as employing merely hypothetical judgment 
 and constructive combination, taking no account of any 
 significant unity in the content of inference, or of any special 
 relation between it and the real world. The system would, 
 by such a transformation, have forfeited its individuality and 
 have become a mere necessary sequence of relations upon 
 relations in the abstract world of force and mass, instead of 
 an actual whole in the unique structure which we call reality. 
 It must be noted however that the limitation or abstraction 
 which is needed to make such an account intelligible, has 
 by the change supposed become merely arbitrary. Qua 
 mechanical result, every cinder that dropped from the fire- 
 box and every cloud of vapour blown from the funnel 
 would have as good a right to be described and deduced 
 
Chap. VI] Purposc ill Mechauical Form 189 
 
 from the mechanical combination which makes up the loco- 
 motive, as would the capacity of the engine in the way of 
 traction. 
 
 ' But the purpose may be hypothetically inserted into the 
 inference, as indeed was done above.' We may state a purpose 
 or any other content hypothetically, if we indicate that by 
 intentional abstraction we are doing so. I only say that, 
 apart from any mark of forcible abstraction from reality, 
 a judgment or inference that deals with a system having unity 
 in a purpose presupposes the reality of that system because 
 its content is adequate to reality, while a judgment which 
 merely draws the necessary consequences of a determinate 
 combination of forces, without reference to any purpose to 
 which that combination is directed, is essentially hypothetical, 
 for the particular combination has no pre-eminent individuality 
 or raison d'etre ; and essentially imperfect, because in the 
 absence of a raison d'etre there is nothing to guide the selection 
 of aspects or of consequences. In this sense the hypothetical, 
 the arbitrary, and the merely mechanical coincide. 
 
 In the distinction between a machine which serves a purpose, 
 and a machine which does not, we have in a nut-shell the 
 question of categories. Both are actual mechanical combina- 
 tions producing results, and neither has in it one whit more 
 life or intellect than the other. But it is perfectly clear that 
 our understanding of the useful one is incomplete if by pre- 
 serving our ignorance of its purpose we remain on the same 
 level of apprehension with reference to it which is the highest 
 we can possibly attain with reference to the other. And it 
 is absurd to say that the category so implied is an accidental 
 aspect and does not represent a fact. It is true however that 
 this category of purpose does not exist within a mechanical 
 system in its proper or intellectual form, and that therefore 
 the system can be regarded by a natural abstraction as on 
 a level with a purposeless combination, and may by internal 
 or external changes at any moment become such. This 
 hypothetical aspect of a combination of forces, in virtue of 
 which it produces its resultant according to fixed necessities 
 and in complete indifference to any purpose, is the purely 
 ' mechanical ' relation of a machine, and if exclusively pressed 
 
1 90 
 
 Concrete Systematic Inference [Book ii 
 
 Logical 
 Content. 
 Real 
 System. 
 
 home destroys as we saw all possibility of regarding it as an 
 individual thing having its unity in a function. 
 
 Beginning with the mechanical contrivances of which we 
 have been speaking, there extend upwards in a series which 
 forms the content of philosophy the phases and embodiments 
 of man's intelligence and conscious will. All of these, the 
 individual will with its complement in the moral order of 
 society, the product of fine art, and the religious or philo- 
 sophical system, are totalities which combine an explicit 
 intellectual unity with determinate interdependence of parts. 
 The statement of the general character of these embodiments 
 of mind may serve as an example of the argument we are 
 considering. ' The mind is a unity of reciprocally determinate 
 but not reciprocally exclusive parts. A feeling is an element 
 in the mind ; therefore a feeling enters into a unity of recipro- 
 cally determinate but not reciprocally exclusive parts.' Or 
 again : * The British Constitution is in its main features 
 determined by the thoroughgoing application of ordinary law ; 
 the position of the prime minister is a function of the British 
 Constitution ; therefore the position of the prime minister 
 is in its main features determined by the thoroughgoing ap- 
 plication of the ordinary law.' Or, finally : ' The general will 
 is expressed in the moral order of society ; the individual 
 will finds its freedom in the general will ; therefore the 
 individual will finds its freedom in the moral order of society.' 
 
 When we consider the logical nature of such arguments as 
 these, we notice two obvious characteristics of the content, 
 and one, resulting from them, of the form. 
 
 i. In respect of their logical content they are at once 
 categorical and hypothetical, a. The systems which form the 
 content of such reasoned judgments as these are naturally 
 taken as real systems in virtue of their individuality. It is 
 of course not impossible to construct a political or religious 
 system on paper the consequences of which are laid down in 
 hypothetical judgments and inferences from them, which in 
 form might be identical with such judgments as are here 
 employed. The content of such judgments has an indeter- 
 minate place in reality so far as it has a meaning or objective 
 reference, and depends on determinate reality so far as it 
 
 I 
 
Chap. VI] TeUological Contents 191 
 
 proceeds to affirm actual consequences. But the content of 
 a judgment which deals with an individual system is taken 
 as real in our world unless the contrary is indicated ; and even 
 in hypothetical judgments that depend on the nature of the 
 human mind, the real ground which would have to be made 
 explicit in order ultimately to justify the consequences drawn 
 is the intelligible and concrete system of that mind itself. 
 Prima facie, therefore, we are dealing in these arguments 
 with categorical judgments about reality, which explicitly 
 postulate the real grounds that in the hypothetical judgment 
 were latent. 
 
 / ft. The nexus of the inferences in question is not, as in Apodeic- 
 Analogical Reasoning and in Enumerative Induction, devoid qyg^ce 
 of strict apodeictic sequence. The systems of which we have 
 been speaking, although they need not be capable of mechani- 
 cal, numerical or geometrical construction, — which however, 
 as in the case of a machine, may play their part in the analysis 
 of the concrete whole, — are nevertheless invested with hypo- 
 thetical or apodeictic necessity in two forms ; in the relation 
 of their parts one to another within the systems themselves 
 as wholes, and in their own ultimate relation as parts to the 
 unique system of reality as a whole. 
 
 Of these the former is for our logical purpose the more 
 important. Within such a whole as the normal order of 
 civilised society, regarded as the expression of the general 
 will, it is obvious that there are parts united by necessary 
 relations dependent on the nature of that whole and capable 
 of being expressed in hypothetical judgments if we abstract 
 from the explicit assumption of the whole itself. We may 
 say, for example, ' If a right, then a duty.' The justification 
 of this statement would be given by the affirmation, as a 
 real ground, of the moral purpose involved in the moral order, 
 which purpose exhibits itself as right or duty according to 
 the attitude which the individual will may assume towards 
 it. Such an inference as this does not cease to be necessary 
 when its ground, in this case the moral purpose and moral 
 order, is affirmed to be real. The basis of the synthetic transi- 
 tion is here as everywhere the nature of an identity or universal, 
 and that the universal is affirmed to be fact makes no dif- 
 
192 Concrete Systematic Inference [Book ii 
 
 ference to its apodeictic force. What in particular that 
 apodeictic force may be, how it should come to pass that one 
 thing can necessitate another, depends, as I have said before, 
 on the ultimate fact of the nature of knowledge. What we 
 have more particularly to observe at this point is the coarseness 
 of the illusion that systematic necessity can only exist in 
 spatial and numerical perception. Given the relation of man's 
 intelligent will to an actual moral order, the relation of right 
 and duty is .as plain a consequence as, given the nature of 
 space, the equality of vertical angles. And apart from a given 
 reality, there is in either case nothing, from which nothing 
 can follow. 
 
 Hence we arrive at the second aspect in which individual 
 systems, though real, are nevertheless hypothetical. They 
 are each and all of them, for us, hypothetical upon the whole 
 given reality within which they exist. When we speak of a 
 thing as real, we imply that it is complete and self-existent ; 
 for if it is not, its reality includes a condition beyond the 
 content which we have included in the thing, and it therefore, 
 as we have formulated it, not including the conditions essential 
 to its own reality, is falsely asserted to be real. 
 
 Here we have the aspect of relativity which prevails 
 throughout our knowledge, which is increasingly overcome by 
 the work of intelligence in as far as it connects the actual 
 and intellectual world into an organised whole, but is never 
 thoroughly done away. 
 
 Logical ii. As regards the form of these inferences, it follows from 
 °'^"^*. what has been said that the only value of the syllogistic 
 
 in fig I. arrangement is to exhibit the structure of the reasoned judg- 
 ment, which itself contains or displays the articulated universal. 
 No question arises as to which premise we know first, and 
 so which supports the other. The prior or previous phase 
 of the inference is not the proof of detached premises, but 
 the entire thought in a less precisely articulated form. If 
 we are urged to say whether we know the major, the minor 
 or the conclusion first, the only true answer is that, in their 
 full import, we know them all simultaneously. As detached 
 fragments of experience we may know any one of them first. 
 And as each element of the universal when rightly under- 
 
Chap. VI] A Real Necessity 193 
 
 stood involves the others in their full determinateness, there 
 can be no real difference in kind of import between major 
 and minor premises, and no reason for preferring one order 
 of the terms to another. The order will in fact be subjec- 
 tive, depending upon the qualification of reality which we 
 take as starting-point, whether in time — if our inference has 
 the accidental aspect of a progress in time — or because of 
 its individual nature. The real purpose is the dominant 
 essence of the universal, but the real purpose may be taken 
 as conveyed by the general idea of the system in question 
 as a whole, represented by its name, or as involved in the 
 analytic scheme of its parts, or as concentrated into some 
 special application by which some one part does the work 
 of the whole. And thus any one of these elements of the 
 universal may stand as the middle term in reasoning, i.e. as 
 the ground or universal par excellence. Hence there is no 
 use in considering the syllogistic rules at the point we have 
 now reached. They belong to calculative and in some degree 
 to analogical argument ; but the postulate on which they 
 rest, of the absence of reciprocal determination between the 
 elements of inference, does not hold good of a coherent 
 system when thoroughly known. We have thus arrived at 
 a goal analogous to that attained by the theories of Quanti- 
 fication and of Equation in judgment, at a perfect reciprocal 
 identity between the elements of the reasoned judgment, so 
 that any one of the terms may occupy any place in the argu- 
 ment. But we have attained it, as we hope, without sacri- 
 ficing difference to identity, and thereby destroying the identity 
 itself. The equational form, though it symbolises correctly 
 certain results of the reasoned judgment (the conjunctions 
 which this judgment in fact involves), yet crushes into shape- 
 lessness its true living texture, and, as a simple sign of the 
 deformation, forbids all growth and reconstruction within the 
 inference itself, which reconstruction nevertheless, as we have 
 seen and shall further see, cannot be avoided. 
 
 As a particular case of the inapplicability of the syllo- 
 gistic rules to the inferences now before us, it may be men- 
 tioned that we have here nothing to do with inference from 
 negative premises. We must take the negative form to have 
 
 1337-2 o 
 
194 Concrete Systematic Inference [Bookii 
 
 done its work and obtained positive significance, in the process 
 which we have watched of constituting such a system as that 
 which we are now considering. We are now considering these 
 systems as real grounds, and so with reference to what falls 
 within them, and not with reference to what falls outside 
 them. For to what falls outside the system itself, unless with 
 reference to a further system including that ' outside ', the 
 system can ex hypothesi only be related in the way of bare 
 negation that has no import and is no judgment. In analysing 
 the completion of a type of knowledge it is vain to raise a 
 question which would take us back to the beginning of the 
 course we have traversed. But as a determining agency within 
 a real system, and as invested by that function with positive 
 import, negation reappears in disjunctive reasoning. 
 Disjunc- 2. The nature of disjunction and its imperfect forms have 
 Disiun^- ^^^" discussed under the head of the disjunctive judgment, 
 tive Rea- and it only remains here to recapitulate the inferential nature 
 soning. ^j ^j^.^ ^j^^ most complete and explicit form of the universal. 
 Inference under a disjunction is usually represented thus : 
 * A is either B or C, A is not B .-. A is C ; ' or, ' A is B .♦. A is 
 not C Yet such an inference has no meaning except in the 
 case of a disjunction of ignorance or a disjunction referred to 
 a point of time. The categorical minor premise adds nothing 
 whatever in the way of content to the disjunctive major 
 premise. It only has meaning as resolving a doubt or as 
 affirming one member of an alternative to be true in a given 
 point of time. This defect could not be removed by specifying 
 in the minor the ground on which that one member of the 
 alternative is affirmed, for this ground cannot really fall out- 
 side the content of the disjunction and its specification can 
 only throw a doubt on the categorical natm-e (in the narrower 
 sense) of the minor premise itself. ' The signal is either 
 danger or safety ; it is red and so danger .-. not safety.' Ob- 
 viously here, if we can conclude from ' red ' to ' danger ' in 
 the minor premise, this relation must fall within the knowledge 
 which constitutes the major ; and moreover, by introducing 
 a specific grotmd of assertion it exposes the minor to a charge 
 of being hypothetical. 
 We saw in treating of the disjunctive judgment that the 
 
Chap. VI] No Negative Inference 195 
 
 disjunction of ignorance and the disjunction referred to time 
 are not cases fundamentally distinct from the true disjunction 
 of knowledge, being justified, in as far as they are justified, 
 by the same type of knowledge which forms the basis and 
 content of disjunction proper. Only, being limited by an 
 accidental condition (the speaker's knowledge, or an arbitrary 
 point of time), they lend themselves to an appearance of 
 progressive inference through supplementation by a perceptive 
 or narrative judgment, which applies them under a limiting 
 condition without expressing that condition. In the true dis- 
 junction, which expresses the organisation of a system as 
 such, the reference to an arbitrary condition falls away, and 
 although the judgment is capable of inferential application 
 under specified conditions, whether of time or of other kinds, 
 yet this application is not essential to its import, and is 
 not demanded by its form. 
 
 We are thus driven to the paradoxical conclusion that the 
 essence of disjunctive argument is included \\dthin the dis- 
 junctive ' major premise ' ; in other words, that this judgment 
 is in fact not a mere premise but at once a categorical judg- 
 ment and a complete systematic inference, in which the 
 content of a real system, thoroughly understood, is developed 
 in its reciprocal positive and negative bearings. The imiversal, 
 or pervading identity, is developed in it as a system of a's 
 and ' just not a's V such that in virtue of every ' not a ' the 
 system is positively determined to a certain definite a, and 
 in virtue of every a the system is negatively determined to 
 a certain definite not-a (which is b). Our ideal of inferential 
 knowledge does not go beyond an individual system of this 
 kind, of which every part is mediated in its turn by all the other 
 parts and assigned by them its appropriate place in the whole, 
 whose pervading nature is present in every part and prescribes 
 the arrangement and content of all. Such a system contains 
 its own applications, for the material conditions under which 
 it developes its nature are given within it. The mere realisa- 
 tion of one alternative member as fact or as a point in time, 
 e. g. in present perception, has in relation to such disjunc- 
 tive knowledge the aspect of a case brought under it by an 
 ^ See account of Scientific Induction, chap, iv, above. 
 02 
 
196 Concrete Systematic Inference [Book 11 
 
 unknown condition, and so implies a defect in the disjunctive 
 knowledge itself. For if there is no such defect, then per- 
 ception or testimony can add nothing to the necessary reality 
 embodied in the disjunction. A watch is either going or not 
 going ; and I do not need observation or testimony to tell me 
 that at any time when the mainspring is broken it is not going. 
 ' But your disjunctive knowledge will not teU you beforehand 
 or apart from observation whether the mainspring is broken.' 
 I reply, ' Oh yes it will, up to the limits to which it extends' 
 It will tell me the signs of breaking, the risks of breaking, 
 the limit of breaking-strain ; and therefore, supposing my 
 knowledge of the world were disjunctively complete, it would 
 tell me exactly when and how often the mainspring has been 
 or will be broken. That it does not practically tell me this is 
 not owing to the defectiveness of disjunctive knowledge but 
 to my not possessing it. Therefore, as in aU the affairs of life, 
 I have to supplement scientific knowledge from testimony 
 and unorganised observation, i. e. observation of what occurs 
 under conditions not precisely known. But this observation, 
 qua unorganised, adds nothing to knowledge, though in fact 
 every content that is distinctly observed has necessarily some 
 organisation, and leaves the disjunctive judgment a little 
 richer than before. But as mere abstract position or afl&rmation 
 of a case fuUy known before, it adds in theory no element 
 whatever to our disjunctive knowledge of a real system. 
 
 Therefore the disjunctive judgment must be taken to 
 correspond not to the major premise of the syllogism, but 
 to the whole syllogism. The syllogism must tell us, for 
 instance, that the human will, being an activity of the human 
 intelligence, sets its purposes before it in the form of definite 
 ideas. The disjunction would in this case perhaps tell us that 
 the human animal asserts himself practically either through 
 the intelligence as will or through the sensuous instincts as 
 appetite ; or again, that he asserts himself through the in- 
 telligence either practically as wiU or theoretically as know- 
 ledge. Here we obviously have the whole content of the 
 syllogistic ' reasoned judgment ' but in a more elaborate and 
 more thoroughly articulate form. It is clear that the whole 
 conclusion, in so far as it is a conclusion that grasps scientific 
 
Chap. VI] Conjuftctton and Disjunction 197 
 
 truth as the definition of a real system, falls within this 
 disjunctive judgment. The application of it in a special his- 
 torical case can be of no importance, unless the new example 
 suggests new matter for the definition of the term involved ; 
 in which case the content of the example must be taken up 
 into the disjunctive judgment. 
 
 I need hardly remark that it need not be an objection 
 against a disjunction of this class that the determinations of 
 the system do not exclude one another in time. The essential 
 point is to know how the system in question, e.g. the mind, is 
 organised into parts which as such exclude one another. I am 
 not prepared or concerned to deny that will and appetite may 
 coexist in a mixed state of mind, or even that appetite may be 
 included in will ; but in as far as the mind merely has appetite, 
 it does not will, and in as far as the mind distinctly wills, it 
 has not mere appetite. The disjunction would only be false 
 if appetite and wiU were essentially identical parts of the 
 mental system, and not, so far as the mind enters wholly into 
 either, reciprocally exclusive.^ 
 
 ' Then mere differents are disjunctively opposed ? ' Yes, 
 if the conditions are precisely assigned under which the real 
 subject becomes capable of the one and incapable of the other. 
 A ' conjunction ' or conjunctive judgment about a single sub- 
 ject differs from a disjunction merely by the non-assignment 
 of the precise relations under which the various determina- 
 tions attach. Thus it is, as Plato showed, that knowledge 
 can solve the apparent contradictions of the perceptive 
 judgment. ' A is both great and small.' Knowledge dis- 
 tinguishes cases and explains, ' A is compared either with x 
 and then is great or with y and then is small.' ^ 
 
 The inferential principle of Disjunction is nothing more 
 than the principle of all inference in its most explicit form. 
 Every matter capable of being known consists in a common 
 nature including within it and constituted by parts or differ- 
 ences, which are related to one another at first sight negatively 
 
 ^ Appetite, when it enters into will, must surrender its character as 
 mere appetite, not merely by the addition of something else, but by 
 taking on a new character in itself. 
 
 " See Plato, Republic, p. 524. 
 
198 Concrete Systematic Inference [Book 11 
 
 qua excluding one another, but further, through this very 
 negation, are related positively because by their negative 
 relation they positively determine one another. Every such 
 matter when explicitly stated in articulate form, is known 
 as a disjunctive judgment. And this is the nature of the 
 ultimate judgment by which the individual consciousness 
 sustains its real world. The simplest cases of these reasoned 
 judgments are to be found in the spatial perception, in which 
 the determining differences take the shape of parts external 
 to each other and so negatively related, but nevertheless by 
 their position determining one another, and so through their 
 negative relation positively related. But the most perfect 
 cases are those intellectual creations that are the objects of 
 philosophical science, in which the whole system not merely 
 appears by its common nature in parts which remain external 
 to each other, but tends to throw itself in its entirety into 
 each of these differences, passing by an organic necessity from 
 one difference to another. Here, in short, the differences are 
 not merely parts which remain outside one another, not 
 merely phases which succeed one another, but moments which 
 succeed one another so that the earlier are retained in the 
 later through a progressive development, and yet the distinc- 
 tive character of each moment is not weakened. Such, for 
 example, is the relation of the conceptions which by their 
 development constitute the history of philosophy. 
 
 It is usual to treat of classification as one special form, 
 among others, of logical thought. I am unable to regard it in 
 this light. It appears to me to be merely an external conse- 
 quence, reappearing in every kind of universal, of the- relation 
 between universal and differences. The nearest approach 
 to pure classification is therefore' to be found in superficial 
 arrangements destined merely to facilitate reference, in the 
 dictionary, the index, the Linnaean system. After this come 
 the natural or morphological systems of botany and zoology, 
 in which the universal appears though not explicitly, yet 
 effectively, through analogy. While in mathematical concep- 
 tions as in the true systematic disjunction we have classification 
 relegated to its proper place, as a corollary of the com- 
 prehensive application of explanatoiy theory. 
 
Chap. VI] Will and Purpose 199 
 
 3. By introducing into logic the real or conscious teleology The judg- 
 of the human intelligence, we have rendered unavoidable vaiue? 
 some consideration of the judgment of value, which rests upon 
 the correspondence of a real system and the purpose for which 
 it exists. This judgment obviously presupposes two condi- 
 tions ; i. our knowledge of the purpose for which a system 
 exists, and ii. our knowledge of the degree in which the system 
 fulfils that purpose. 
 
 i. The former condition demands a real teleology ; * that Real 
 is, a conscious purpose for which the system is intentionally iogy°" 
 recognised or maintained by the human will. We cannot 
 here enter upon the questions, belonging to ethical science, 
 which arise with reference to the objective justification of 
 man's recognition of a purpose in the non-intellectual world. 
 Indeed we cannot avoid extending such questions in some 
 degree to the world of man's own voHtion by admitting that 
 e. g. the systems of law and government which appear prima 
 facie to be made and maintained by man with a view to a 
 purpose which he consciously sets before him, have nevertheless 
 an element of growth or development which goes beyond the 
 knowledge or intention of any single individuals at any time 
 concerned in framing them. The works of mind, in short, 
 are something more, as the works of nature are something 
 less, than the intentional achievements of any individual will, 
 and therefore our estimate of their value is in many respects 
 analogous to that recognition of a purpose which we apply so 
 faUibly to natural objects. We may however — for we must — 
 assume on the whole that the persistent purposes of mankind 
 are represented within our own intelligence, and that therefore 
 in our estimate of law and morality, of art and rehgion, of 
 political and social institutions, there is at any rate some firm 
 foimdation of real teleology. 
 
 ii. The second condition demands mediation. We have to Media- 
 ascertain whether a wHole fulfils its purpose by comparing the *^°"* 
 
 * See above, p. 99 note, on the defect of the conception of teleology, with 
 the removal of which, however, it ceases to be teleology. The standard 
 of value should rather be expressed as Individuality, and the condition, 
 which many would insist on, that value involves a feeling mind, is 
 satisfied by the consideration that a feeling mind is necessary to indi- 
 viduality. 
 
200 Concrete Systematic Inference [Bookii 
 
 operation of its mechanism with the idea which is intended 
 to be its essence. This mediation was involved in the philo- 
 sophical syllogism, in so far as the purpose of the whole was 
 taken to be its essence or unity. But after analysing, in the 
 disjunction, the matter of the universal into a system of 
 reciprocally determined parts and moments, we have forced 
 upon us the question whether the totality of these parts or 
 moments corresponds in detail to the purpose with which we 
 credit it. Such correspondence is what we understand by good- 
 ness or value. We may say for instance of a given social system 
 that under it the people are either aristocrats who are not the 
 best and do not rule, or a proletariate who pay no honour to 
 those above them and who cannot be ruled. And this contra- 
 diction between the effect of the S5^tem as realised in its parts, 
 and its recognised purpose, entitles us to say that it is a bad 
 system ; in the form ' a being either ^not x or ^not z is not A.' 
 Extra-logical as this judgment of value may seem to be, 
 it is really implied in the constitution of knowledge from the 
 point at which quasi-teleology begins, and with it the con- 
 ception of ' a thing ' takes its rise.^ I shall have to return to 
 this subject in the last chapter when I come to speak of the 
 ultimate nature of dialectical or logical necessity to which 
 the term aesthetic has sometimes been applied. 
 The main 4. Inference was first defined on p. i as the ' mediate 
 of In- reference of an ideal content to Reality ', and further explained 
 ference. on p. 3 as ' the indirect reference to reality of differences within 
 a universal, by means of the exhibition of this universal in 
 differences directly referred to reahty '. And we have gone 
 throughout on the principle that the species of inference are 
 determined by the species of universal which occur in the 
 realm of knowledge. Having attempted to analyse these 
 species, and to point out their ailfinities and their distinctions, 
 we have not much more to say about the nature of inference. 
 
 But it may be useful by way of recapitulation to read off 
 from the somewhat tedious treatment to which we have 
 subjected the phases of inference a few answers to the vexed 
 questions which concern it. 
 
 * See note on previous page. If we replace the conception of teleo- 
 logy by that of individuality, the judgment of value wUl appear, as it 
 ought, inherently logical, in the sense of Plato's aXridua and ovaia. 
 
Chap. VI] No Schedules of reasoning 201 
 
 i. Is the syllogism a complete antecedent scheme, pre- 
 scribing the shape and outcome of every possible inference ? 
 ii. Is there any fundamental set of conditions to which all 
 Inference must conform, and further, iii. what relation does 
 the syllogism bear to such a set of cotiditions ? 
 
 i. There is no such thing as an antecedent scheme pre- No ante- 
 scribing, so to speak, a set of schedules in one or other of scheme of 
 which every argument can be written out merely by filling Inference, 
 up the blanks. The form of knowledge is an active and 
 constructive principle, to the workings of which no abstract 
 type antecedently prescribed can be adequate. Not merely 
 is Logic incapable of passing judgment on actual truth, but 
 it is incapable of prescribing beforehand the type of relations 
 which an inferential totality may impose upon its parts. 
 Granting that where we are dealingwith imperfect subsumption, 
 with the relations of attributes conjoined in individual subjects 
 according to unknown groimds, the syllogism is able to antici- 
 pate the very indefinite form of combination that can result, 
 yet we should not dream of claiming for it this capacity of 
 prediction in the region of calculation, of mechanical or 
 geometrical construction, or of philosophical subsumption. It 
 is true that as regards the last-named process we found a 
 t5^e of reasoning which appeared to represent it adequately 
 in the syllogism in Barbara. But the reader must have 
 observed in the examples which were given, if judged by the 
 standard of formal logic, that irritating inaccuracy of form 
 which is known to teachers in the first attempts of pupils to 
 construct a precise syllogism. In our examples and in their 
 efforts this inaccuracy is due to the same cause ; to the difficulty 
 of moulding the vital and constructive action of thought into 
 shapes prescribed by an artificial scheme, which does not 
 precisely correspond to any single type of intellectual action. 
 The violent transformations by which formal logic attains 
 this end are not perhaps an undesirable scholastic exercise ; 
 for they unquestionably drag into hght, though only as a 
 meagre and skeleton framework, a certain ultimate community 
 of type in all inferential operations. In so far as the difficulties 
 of pupils arise from inability to transform or translate their 
 intellectual operations ai all, any exercise which demands such 
 
202 Concrete Systematic Inference [Bookii 
 
 transformation is perhaps better than none. But in the 
 analysis of operations that constitute highly determinate 
 individual totalities the difficulty of conforming absolutely to 
 the scheme of the traditional syllogism rises into something 
 like impossibility, because the parts within such a totaUty 
 do not lie side by side like units in a ' class ', but have peculiar 
 and distinct relations, imposed, each upon each, by their 
 individual place within the whole. 
 
 Thus we cannot preserve, or can only by a tour de force 
 succeed in preserving, the identical correlations of terms 
 demanded by the rules of formal logic. In our example ' the 
 mind is a unity of determinate and not exclusive parts ' ; 
 we could not go on to affirm ' a feeling is the mind ', according 
 to the good old t5^e ' Socrates is a man ', and so we could not 
 conclude that ' a feeling is a unity ', &c. But we were obliged 
 to say either that a feeling is a reaction of the mind, or that 
 a feeling is an element in and is a part of the mind, and could 
 only conclude that a feehng is a factor or element in such a 
 unity. And the other examples given in the same context, 
 which preserve more appearance of correct formulation, are 
 in reality no less charged with individual and diverse relations. 
 The mere fact that the syllogism naturally leads on to tne 
 complete disjunctive judgment is the most striking proof 
 of this. I may say at this point that to treat ^ the dis- 
 junctive judgment in systematic Logic as a form of thought 
 needing completion by Induction, Analogy and Subsump- 
 tive Syllogism, seems to me to be a hopelessly erratic 
 selection of phases out of the progress of the individual 
 mind. This progress includes no doubt even in very early 
 stages those imperfect shapes of disjunction which I have 
 called the disjunctions of ignorance ; and these disjunc- 
 tions are expanded into systematic knowledge by the pro- 
 gress of determining thought in its various forms. But 
 to make the complete disjunction prior to the imperfect 
 forms of syllogism involves a retrogression from complete 
 systematic knowledge of a real ground to the knowledge of 
 the operation of this ground in individual cases and in 
 a latent form. 
 
 * As Lotze does, Logik, sect. 97 £f. 
 
Chap. VI] Terms and Data 203 
 
 ii. If we ask the more reasonable question, not whether Condition 
 a form can be laid down beforehand for every possible in- g^^e 
 ference such that the inference can be drawn by merely 
 putting terms into the blank spaces of one or another of certain 
 prescribed schedules, hut whether in the common nature of 
 thought a system of conditions can be discovered which in 
 one way or another is conformed to by every act of inference, 
 on this head I think that an affirmative answer may be- 
 gathered from our previous discussions. 
 
 {a) Inference must have three terms and no more. 
 
 The explanations given in chap, i of the present Book 
 appear to me to justify this assertion. They consist in a 
 sharp distinction between terms and data — ^the number of 
 data being accidental, whUe the number of terms or moments 
 depends on the essential nature of the universal ; and in the 
 restriction of Inference proper to mediate Inference. We 
 admit however that the function of thought from elementary 
 reproduction upwards is essentially one, and we more especially 
 contend that every judgment, in so far as it is explicitly 
 S5mthetic, that is to say in so far as it affirms one definite 
 content to be a consequence of another definite content, is an 
 activity only separated from Inference by the degree of 
 distinctness with which its parts are analysed. Every such 
 judgment, and therefore ultimately every judgment, can by 
 further reflection be expressed as a three -term inference, and 
 this is especially the case with what we called the true Imme- 
 diate Inferences, Comparison, Abstraction, and the rest. 
 
 (&) An explicit Inference is a conclusion from two premises 
 and no more, which assert relations between differences qua 
 belonging to a single universal. Assuming therefore that the 
 propositions which express the premises are not to be disguised 
 purposely or through negligence, but are bona fide to express 
 the judgments employed in reasoning, the two premises must 
 have an identical term in common. And 
 
 (c) that this identical term must be universal follows neces- 
 sarily from the theory of inference which has been developed, 
 and follows also from the fact that this one term is able to 
 stand in both premises. For a universal is that which without 
 prejudice to its identity persists through or contains in itself 
 
204 
 
 Concrete Systematic Inference Ibookii 
 
 Relation 
 of Syllo- 
 gism to 
 these 
 condi- 
 tions. 
 
 The tra- 
 ditional 
 Syllo- 
 gism. 
 
 different relations. The simplest example may be found in 
 what we termed the ' Inductive ' Syllogism, in which, if we 
 take the middle term as the meaning of a proper name, we 
 argue that Socrates is both good and a Greek, therefore a 
 Greek may be good. Here Socrates, although ex hyfothesi an 
 individual, is universal at least in virtue of the double relation 
 to good and Greek — i.e. of the synthesis, in the ' middle 
 term ', of these differences. The universal or identity, however, 
 need not, as in this case, be a ' subject ', although it will be 
 found ultimately to imply a subject. The identical point in 
 space, in which two lines meet in a spatial construction, is 
 the synthesis of two relations in space, but is not, only implies, 
 space itself as a whole containing these relations. 
 
 And {d) I do not see how we can escape from saying that 
 not only one premise, hut both premises must he universal. The 
 only apparent exception would be the case in which one 
 premise is negative ; about which it might be urged that the 
 common term does not stand in two relations, but in one and 
 none, i.e. in one only. If this were so, however, the negative 
 premise would be a bare denial, would be no judgment, and 
 could give rise to no conclusion. I do not see how a conclu- 
 sion can arise without a synthesis of two positive relations. 
 
 If then {e) negation means bare denial, it results that there 
 can be no negative premise. But as bare denial is not a case 
 of genuine judgment we must interpret negation to mean 
 significant denial only, and in this sense we must lay it down 
 that hoth premises may he negative.'^ 
 
 iii. If now, in order to define our attitude towards the con- 
 troverted questions which centre in the doctrine of syllogism, 
 we enquire ; In wliat relation does syllogism stand to the type 
 of inference determined by the conditions just enumerated ? 
 we shall obtain the following results. 
 
 We must distinguish the traditional syllogism with its 
 apparatus of rules and its distinctions of quality and quantity 
 from the syllogism as treated in the present work. 
 
 a. The traditional syllogism is a hybrid between what we 
 have called analogical inference and what we have called 
 inference or induction by complete enumeration. It would 
 ^ See chap, iv, above. 
 
Chap. VI] The Syllogism as a hybrid 205 
 
 therefore {a) exclude many forms of inference which perfectly 
 conform to the above conditions, and also some which have been 
 included in our account of the syllogism. Not only would it 
 exclude ' calculation ' and what has been called ' construction ' 
 in the mechanical or geometrical sense ; but it would find no 
 place for Induction or Analogy or even for philosophical sub- 
 sumption as above described. Induction would be excluded 
 by the conjunctive premise consisting in a number of indivi- 
 dual judgments ; Analogy by the material weight and stress 
 thrown upon the definition of the predicate, which the 
 ordinary half-numerical syllogism has no power of indicating ; 
 and philosophical subsumption by the genesis within it of 
 new relations, not prescribed by any major premise. The 
 traditional syllogism, in short, fails to recognise the S5mthetic 
 activity of thought. 
 
 (J) The form of universality relied on by the traditional 
 syllogism is vicious, except for pxnrposes of calculation, which 
 it does not attempt. It is true that its express form of totality 
 ' All A are B ' does not really cover what we understand to 
 be its import ; but its rul6s and transformations are derived 
 from this express form, and exclude such vital and genuine 
 processes as for example modal conversion. The fact that we 
 interpret the numerical totaUty into true synthetic connection 
 only shows that the inadequacy of this form of universal is 
 actually recognised. 
 
 (c) There is no justification for the traditional pre-eminence 
 assigned to one premise as the ' major ' ; a pre-eminence which 
 depends on the vicious quantitative form of the universal, 
 and carries with it the petitio principii which has been irre- 
 sistibly demonstrated to be present in the traditional syllogism. 
 
 {d) There is no justification for the distinction between uni- 
 versal and particular premises, except in as far as by a reserva- 
 tion depending on unknown conditions one premise may 
 become merely probable. 
 
 {e) The true ' reduction ' or transformation of arguments in 
 figs. 2 and 3 into fig. 1 can only be effected by a material trans- 
 formation of their content into the content demanded by fig. i 
 through the processes of analogy and scientific induction. Reduc- 
 tion without transformation of content is a grammatical tour 
 
2o6 Concrete Systematic Inference [Bookii 
 
 de force which illustrates no principle except that a simple 
 
 inference can be awkwardly expressed. 
 
 The syl- ^. When we come however to make the comparison between 
 
 reasoned^ ^^^ general conditions of inference and the syllogism as 
 
 judgment, described in the present work, our results are somewhat 
 
 different. Syllogism as we have described it is a subsumptive 
 
 reasoned judgment depending upon the unity of differences 
 
 within an individual subject, and making the intelligible 
 
 ground of this imity explicit in various degrees, according 
 
 to which the unity displays itself as a conjunction or as 
 
 a coherence. 
 
 The syllogism as thus understood is {a) co-extensive with 
 subsumption, and exclusive only of calculation and construction. 
 The differences between the syllogistic figures in the sense in 
 which we have retained them depend on the degree in which 
 the Reality that stands as subject to the reasoned judgment 
 is already qualified by antecedent judgment as a concrete unity 
 or individual system. In the Inductive Syllogism the Subject 
 is as nearly as possible a particular, a mere name or designative 
 reference ; in the Analogical Syllogism it is a particular as 
 known under a universal characteristic, an individual ; in the 
 Syllogism of Philosophical Subsumption it is an individual 
 thoroughly known as a universal in its particular differences, 
 and so a concrete system. 
 
 (b) The difference between the syllogism thus understood, and 
 the abstract combinations of arithmetical or geometrical reasoning, 
 lies merely in the correlative imperfections of the two pro- 
 cesses. The syllogism begins with the perception of unanalysed 
 individual unity, which it is unable to bring to bear as a deter- 
 minate relation upon the attributes conjoined within it, and 
 thus rests in the mere fact of their conjunction. Calculation 
 and construction begin with the perception of a specific 
 determinate unity by which relations affect and generate each 
 other, without making clear at the outset within what concrete 
 system, and subject to what ultimate conditions, these deter- 
 minate combinations (e.g. in space) are effected. The two sets 
 of Inferences ultimately involve the same elements, 
 
 And therefore (c) if the determinate ground is made clear 
 within a subsumption, or the individual subject is made clear 
 
Chap, vij Syllogtsm and Calculation 207 
 
 which includes a combination of relations, the two types of 
 inference fall theoretically together, and either may be classed 
 as the perfect form of the other. But, as we have seen, this 
 identification would remain formal and not wholly bona fide, 
 because of the comparatively indifferent and unconstraining 
 character of the abstract totalities within which geometrical 
 or arithmetical reasoning is carried on. It is true, on the other 
 hand, that the syllogism as we have treated it has no repug- 
 nance to the genesis of constructive relations within the unity 
 that is expressed in the inference. 
 
 Here we see the true interdependence of the classificatory 
 ideal of knowledge with the ideal which takes the shape of 
 explanatory theory. The former is teleological, categorical, 
 and concrete ; the latter is mechanical, hypothetical, and 
 abstract. It is only by a combination of the two — ^which are 
 not ultimately separable — that a real and coherent world can 
 sustain itself in the judgment which is knowledge. 
 
CHAPTER VII 
 
 The Relation of Knowledge to its Postulates 
 
 The for- I. It is usual to devote some discussion in a logical treatise 
 Sta^s^of ^^ *^^ principles or axioms on which the possibility of know- 
 know- ledge is supposed to rest. Adhering as I do to the conviction 
 ^ ^^' that ' The truth is the whole ', I cannot be expected to attempt 
 a justification of any abstract principles as points of attach- 
 ment antecedently furnished upon which the truth of know- 
 ledge could be supposed to depend. But as postulates, as 
 general characteristics of known Reality, which it is convenient 
 to state in an abstract form in any systematic treatment of 
 knowledge, because they are inwoven in the whole texture 
 of the real world, some of these axioms call for comment 
 both on their actual import and on their alleged necessity. 
 
 It is convenient to distinguish the abstract principles or 
 postulates which are thus found to be involved in the nature of 
 knowledge, as i. Formal, 2. Material Postulates. This distinc- 
 tion must not be understood to mean that some are drawn 
 from the nature of intelligence exclusively, while others are 
 merely drawn from the content furnished by perceptive ex- 
 perience. It would be more correct to say that those which we 
 call formal are drawn from the character of experience merely 
 as experience, existing no doubt solely for inteUigence, but for 
 that very reason not separable in its source or nature from 
 any other source or nature which could be described as intelli- 
 gence pure and simple. Whereas those which we call material 
 are drawn from the actual significance which we ascribe to 
 the content of experience as developed in a concrete system, 
 and being ultimately coincident with the conclusions of 
 philosophy and of science must necessarily vary with the 
 progress of these constructions. And it is obvious that the 
 formal principles are in fact continuous with and grow into 
 the material principles, the two kinds of axioms bearing at 
 bottom the same relation to one another that exists between 
 
Chap. VII] AxiOMS US PostuluteS 209 
 
 the judgment that there is a system, and the judgment that 
 the system is of such and such a nature. The former, of course, 
 impHes the rudiments of the latter, as the latter includes the 
 import of the former. Accordingly the distinction between 
 the two classes of principles will correspond to the distinction 
 between abstract and concrete science ; ^ between explanatory 
 theory and classification ; between the law of sufficient reason 
 and the conception of a teleological whole. 
 
 I call these principles by the name of Postulates, because 
 when presented to us as abstract reflective ideas they operate 
 as guides to knowledge ^ which lead to their own subsequent 
 substantiation in a concrete form. As reflective conceptions, 
 then, they are postulates, i.e. principles which we use because 
 we need them. But they only come to be reflective ideas 
 because on analysis of experience they are found to be active 
 factors in it from the first, factors which acquire their content 
 fari passu with experience itself, of which they merely express 
 the animating principle of growth. They cannot therefore be 
 taken in a definite form as hypotheses or axioms antecedent 
 to experience. Experience may be said to begin with the 
 certainty that ' there is somewhat ' ; and the postulates of 
 knowledge do but express in abstract form the progressive 
 definition of this ' somewhat '. 
 
 Among formal postulates of knowledge it will be sufficient 
 very briefly to examine the four most notable ; the Law of 
 Identity, the Law of Contradiction, the Law of Excluded 
 Middle, and the Law of Sufficient Reason. As a sub-form 
 of the latter the Law of Causation demands no separate 
 treatment. 
 
 Each of these laws may be interpreted in more ways than 
 one, according to the degree in which we may acquiesce in its 
 mere abstract form, or attempt to penetrate its further mean- 
 ing. But at any rate with a view to anything like a separation 
 between intelligence and experience, as such a separation is 
 
 * This is in strictness almost equivalent to the distinction between 
 physical science and philosophy. But of course evolutionary science 
 with the conceptions of ' higher ' and ' lower ' does not fall within 
 physical science as thus defined. 
 
 * See the account of reflective ideas as guides to knowledge in com- 
 parison, &c., ii, chap. i. 
 
 1337-2 P 
 
210 Relation of Knowledge to its Postulates [Bookii 
 
 The Law 
 of Iden- 
 tity. 
 
 Tauto- 
 logy. 
 
 Symbol 
 of Con- 
 crete 
 Identity. 
 
 Unity of 
 Reality. 
 
 purely fictitious, there is nothing to be gained by cutting 
 down the content of these principles to a minimum, in the hope 
 of restricting their reference to thought as opposed to things. 
 
 i. The Law of Identity must be taken to signify at least 
 that it is possible to make judgments that have a meaning 
 and are true. 
 
 a. In the bare form ' A is A ', however, a form which is 
 not drawn directly from Aristotle or from Plato, the law does 
 not prima facie possess this significance, and therefore indeed 
 not any. If it means that A is A and no more, or is mere 
 A, then it is aggressively untrue, for it denies the synthesis 
 of differences which alone can make a judgment. If, again, 
 the law is taken as a mere symbol of the pervading unity of 
 the logical subject, and not as intended to exclude all differ- 
 ences from entering into it, then it is an inadequate symbol, 
 erring by omission though not by exclusion. In an absolute 
 tautology which excludes or omits difference, identity itself 
 disappears and the judgment vanishes with it.^ 
 
 Therefore, /3. we can only assign a meaning to the law 
 ' A is A ' if we take the repeated A to be not a specification 
 of the identical content, but an abstract symbol of its identity. 
 The law will then mean that, in spite of or in virtue of the 
 differences expressed in a judgment, the content of judgment 
 is a real identity, that is to say, has a pervading unity. It says 
 that there is such a thing as identity in difference, or in other 
 words, there is such a thing as genuine affirmation — S5mthesis 
 of differences referred to reahty — which yet is true, that is 
 to say, does not interfere with (but in fact is indispensable to) 
 identity. 
 
 And, y. we are only expanding what is implied in the allega- 
 tion of real identity if we say that the law ' A is A ' ultimately 
 asserts the thorough-going unity of Reahty. A significant 
 judgment, symbolised by ' A is A ', lays down for itself no 
 reservation beyond that which its own content may dictate, 
 
 * It is desirable to remark upon this peculiarity of the formal ' Laws of 
 Thought ' as represented in symbolic letters, because the error to which 
 it tends is characteristic of false doctrines of identity and dijfference. 
 Locke defines Identity by saying, ' When the ideas — ^vary not at all,' 
 and the notion of negation in formal logic is also that of ' mere ' or ' bare ' 
 negation. Cf. Euler's circles. 
 
Chap. VII] Contradiction and Excluded Middle 211 
 
 and claims therefore to be true without any reserve. Its 
 simple affirmation leaves no room for any discontinuity in the 
 real world, such that on one side of it the judgment may be 
 true, and on the other false. If there were such a discontinuity, 
 the judgment, such is the claim of the categorical affirmation — 
 and aU affirmation qua affirmation is at least categorical — 
 would have taken note of it within its content, and would in 
 that respect affirm imder a reservation. But once true, always 
 true. All reservations necessary to truth are included in the 
 content. Reality, therefore, is one throughout. Relation to 
 time, for example, is not mvolved in the fact of affirmation, 
 but only, if at all, in conditions belonging to the content 
 affirmed which depend upon facts in time.^ Affirmation as 
 such is unconditional, that is to say, is not limited by con- 
 ditions outside its own content, and so if true, is true without 
 reserve. There is not one Reahty of which it is true and 
 another of which it is false. Reality is what it is, and if it 
 turns out not to be what we thought, then we thought amiss, 
 i.e. judged falsely. 
 
 ii. The Law of Contradiction is but the complement of the Law of 
 Law of Identity. It supphes something without which the Law ^j""*^^* 
 of Identity is not logically complete nor distinctly intelligible. 
 But yet, by the fact of conferring distinctness, it is an addition. 
 
 This Law also, a. in its barest statement ' A is not both A Truism or 
 and not-A ', if understood to deny that A can be B, is either ^ ^^' 
 unmeaning or aggressively false. Considered as the principle 
 of the negative infinite judgment A is not mere B, it corresponds 
 as the form of bare negation, to A is mere A as the form of 
 bare affirmation. In this form it is simply inadequate or 
 unmeaning, and equivalent to ' A is at least A '. But taken 
 as the exaggerated abstraction of negative judgment in the 
 sense ' No A can be any not-A ', i.e. ' No A can be B at all ', 
 it corresponds to the more open interpretation of the Law of 
 Identity as ' A is at least A ', and is equivalent to the more 
 aggressive interpretation of that law as ' A is mere A '.^ For 
 
 ^ See i, chap, v, on Time in the singular judgment. 
 
 * The corresponding meanings of the Law of Identity and the Law of 
 Contradiction, judged by the latitude employed in interpretation, are 
 not their equivalent meanings. The more exaggerated denial is equiva- 
 
 P2 
 
212 Relation of Knowledge to its Postulates [BookIi 
 
 it then denies that any B (not only that mere B) can be united 
 
 in a judgment with A. This is simply a reiteration in negative 
 
 form that A is mere A and no more. 
 
 A genuine But if, /3. we take the Law of Contradiction in the obvious 
 
 law of sense that a statement and its denial cannot both be true, 
 
 thought. 
 
 it bears witness to the fact that a judgment may be truly 
 
 denied, i. e. that a judgment may be false, and therefore that 
 there may be truth in a negation.^ It has been observed above ^ 
 that, apart from the traditional distinction of quantity, the 
 difference between the Logical contrary and the Logical con- 
 tradictory, i. e. between the principle of contradiction and the 
 principle of excluded middle, disappears. But because they 
 retain a meaning for vital thought although not for formal 
 logic, even in the absence of quantitative distinctions, we will 
 distinguish the two aspects of negation treated of by these 
 two principles, and will speak first only of falsehood established 
 by truth, and not of truth established by falsehood. Though 
 really, if our instance of contrariety ^ is * A is B ' and ' A is 
 not B ', we have before us both falsehood established by truth, 
 and truth established by falsehood. 
 A law of y- If we do not press hard on the implications of the Law 
 Reality. Qf Identity, it may be said that the significance of the Law of 
 Contradiction carries us one step further. But it is doubtful 
 if truth can exist apart from the conception of falsehood, and 
 
 lent to the more tautological assertiou, and the more pregnant or 
 significant assertion to the denial of mere identity. Thus 
 
 ' A is mere A ' corresponds to ' A is not mere B '. 
 
 
 
 # \ 
 
 i^r. 
 
 ' A is at least A ' corresponds to ' A is never any B '. 
 
 ^ According to the traditional rule, a statement may be so denied that 
 both judgment and denial are false. But obviously in such a case some 
 denial is true, though the one made is not. To say that a judgment is 
 false is to say that it is truly denied. 
 
 ^ See above, on negation, p. 295 fif. 
 
 * I have pointed out before the inconvenient accident that the Law 
 of Contradiction applies to Contraries only, while Contradictories or 
 Logical Contradiction come under the Law of Excluded Middle. 
 
Chap. VII] Determinate Negation 213 
 
 therefore it is better to say that the Law of Contradiction 
 simply confirms and reiterates that assumption of the unity 
 of reality which the Law of Identity involved. Reality, the 
 Law of Contradiction asserts, is a consistent unity ; which is 
 merely to say over again that it is a unity. You cannot, that 
 is to say, play fast and loose with reality. What is true at 
 all, as the Law of Identity said, is true throughout Reality ; 
 but more than that, every such truth is double-edged, and 
 carries with it throughout Reality consequences by which it 
 affects and limits matters that are prima facie outside itself. 
 To infer from ' A is B ' that ' A is not not-B ' means at bottom 
 that A is determined by B in respect of C or D. 
 
 iii. The law of excluded middle, expressed by Aristotle as Law of 
 ' Between the assertions of a logical contradiction there is no ^f(|^/|"g ^*^ 
 middle ', i.e. no third alternative, applies of course to all strict 
 denial, for all strict denial is a logical contradiction of the 
 judgment denied. 
 
 a. In its symbolic form ' A is either B or not-B ' it lays down ATmism. 
 the ultimate formal schema of negation as the absolute alterna- 
 tive. Literally interpreted according to this symbolic form it 
 has corresponding defects to those of the previous laws when 
 interpreted in the same way. That is to say, all that it abso- 
 lutely lays down is the form of bare negation which is per se 
 not enough to constitute a judgment, because it involves the 
 truth of the infinite judgment ; but which in relation to any- 
 thing further, for example to the intelligible antithesis ' A is 
 either B or C ', is only the affirmation of a possibility, and the 
 hypothetical definition of a relation. To invest a positive 
 contrary C with the logical character of a contradictory not-B, 
 is the work of determinate knowledge. 
 
 l3. Interpreted in the plain sense, e.g. as by Aristotle, the a law of 
 law of P-xcluded Middle means that the significant negation Thought, 
 of any judgment is an absolute alternative to it, viz. that not 
 only the judgment and its negative' cannot both be true, but 
 one or other must be true, and if true, we may faiiiy add, 
 must be significant. This means that falsehood can establish 
 truth, or that negation can involve afhrmative consequences. 
 In this sense the postulate in question is the essential principle 
 of disjunction, which is an absolute alternative between two 
 
214 J^elation of Knowledge to its Postulates [Book ii 
 
 or more positive and significant members. Therefore genuine 
 disjunction has not the form ' A is either B or not-B ', but 
 has the form ' A is either B or C ', which invests the positive 
 assertion, in virtue of which C is taken to deny B as its con- 
 trary, with the absolute exclusiveness that only belongs of 
 right to the bare form of denial, which has for its essence to 
 express the contradictory. In other words, the old account of 
 the contrary, that it denies, and also asserts something more 
 beyond the denial, must also be true of any significant con- 
 tradictory. 
 A law of y. The principle of Excluded Middle, then, ultimately affirms 
 Reality. ^|^^^ Reality is not merely one and self-consistent, but is 
 a system of reciprocally determinate parts. In affirming that 
 a significant or genuine judgment is possible, such that within 
 it a negation ^ shall carry a determinate and explicit positive 
 consequence — not merely, as the law of contradiction affirms, 
 that a truth may carry with it definite negative consequences — 
 the law of Excluded Middle fixes upon that reality which is 
 constructed and maintained by judgment the character of 
 a self-determining whole. For a nothing can only be invested 
 with the character of a something by being a precisely limited 
 nothing that implies a positive nature in the limiting and 
 sustaining something, such that in affirming the nothing we 
 are not affirming an absolute nothingness, but are covertly 
 alleging a positive something which is or is involved in the 
 nothingness of something in particular. From the mere and 
 entire non-existence of mechanical cohesion, i.e. of any such 
 thing as mechanically coherent substances, nothing strictly 
 speaking could be inferred. The idea would be the content of 
 a bare denial, and unintelligible. But from the failure of 
 mechanical cohesion in the axle of a locomotive running at 
 sixty miles an hour under precisely known conditions, all other 
 substances retaining their mechanical properties, the most 
 precise and detailed results could be predicted and must 
 
 ' According to the bare scheme of Excluded Middle, the significant 
 negation must be a negation of the negation ; for though the falsehood 
 of the affirmation involves the truth of the negation, 3-et in the phase 
 to which such a scheme belongs we are hardly warranted in affirming 
 that a negation as such has positive significance. This use of double 
 negation is a factor in identifying contrary with contradictory opposition. 
 
Chap. VII] Nccessify and Reality 215 
 
 follow. This is a simple instance of the difference between 
 the negation which has meaning and consequences, and that 
 which has none. 
 
 iv. The law of Sufficient Reason, with its sub-form the law Law of 
 of Causation, is a corollary from that aspect of reality which R^^gon"^* 
 the negative laws of thought have brought to our notice, and of 
 Reality being a system of reciprocally determining parts, tion^^' 
 every part or feature of reality may be regarded as a conse- 
 quent to which some other part or parts, or ultimately the 
 whole, stands as ground. Every consequent, so this law 
 tells us, has a ground from which it necessarily follows. 
 Necessity indeed means nothing but the inevitableness of the 
 consequent when the ground is given. ^ 
 
 In plain English, the Law of Sufficient Reason represents 
 the demand of intelligence for the explanation of everything 
 by something else. And it is plain that in the case of anything 
 but the absolute whole this demand must go on to infinity, 
 for outside any given content there is always something which 
 can be regarded relatively to that content as something else. 
 We have sufficiently criticised the operation of this law, the 
 law of natural science as such, in the construction of the 
 would-be totalities of abstract time and space, and it is not 
 necessary to repeat the proof that this aspect of experience, 
 taken per se, generates and must generate the infinite series. 
 For it rests on the relations of parts in abstraction from the 
 whole, or in other words, without the element of totality. 
 
 One point must be noticed here. Schopenhauer rightly 
 maintains that absolute necessity is a contradictio in adjecto, 
 because all necessity is ex hypothesi conditional. We have 
 therefore not spoken of an absolute necessity but only of a 
 real necessity, namely a necessity rooted in a ground which 
 is a fact. We ought not to feel as if in this substitution the 
 world had lost something of its rational coherence. Absolute 
 necessity was a false ideal, and produced a fallacious preference 
 
 ^ See the admirable section 49 in Schopenhauer's treatise on the ' Satz 
 vom Grunde '. His attempt, however, to show (sect. 50) that the law 
 of ground and consequent in cognition does not entail an infinite series, 
 although in causality or in space this is entailed, cannot be called success- 
 ful. It depends on his distinction between Causality and Sufficient 
 Reason. 
 
2i6 Relation of Knowledge to its Postulates [BookII 
 
 The 
 
 material 
 postu- 
 lates of 
 Know- 
 lodge. 
 
 of necessity to reality. For a part, necessity is a higher point 
 of view than mere perceptive reality, because necessity involves 
 relation to the whole, whereas perceptive reality, being isolated, 
 is only formal ^ or potential reality. But for the whole, reality 
 is a higher point of view than necessity, for reality is its self- 
 dependence as a whole, while necessity would at once depress 
 it into a part. 
 
 The above are the principal ' Laws of Thought '. We class 
 them not as principles of intelligence apart from experience, 
 but as principles of science or of rational experience as such, 
 discoverable by analysis in every minutest portion of its 
 texture, and capable of being regarded by a very easy abstrac- 
 tion as essential to its existence as contrasted with its special 
 significance. They may therefore be ranked together as the 
 formal postulates of knowledge, or as the formal aspect of 
 the principle of Uniformity, in contrast with those which are 
 not prima facie necessary to the existence of experience, or 
 involved, at all events equally, in all reality as such ; and 
 which may therefore be considered under the head of material 
 postulates of knowledge. The reciprocal implication of the 
 formal and material postulates in one another, of a teleological 
 significance in a self-consistent system, is plainly a matter of 
 degree, and our task is to analyse the mode in which it does 
 exist, not to predict how it must exist. 
 
 2. To emphasise the transition from the formal to the 
 material postulates of experience, I make use of the follow- 
 ing sentence from a distinguished writer : ^ — 
 
 ' It is conceivable that man and his works and all the higher 
 forms of animal life should be utterly destroyed ; that moun- 
 tain-regions should be converted into ocean depths ; the floors 
 
 * i. e. it has the contact with feeling which is the form of all contact 
 with reality, but it falls short in content and is a mere fragment which 
 has something, we do not yet know what in particular, of reality in it. 
 
 " I quote and comment upon this passage purely because it is a strik- 
 ing illustration of my point. I have not the least intention of imputing 
 to its eminent author (Professor Huxley in Contemp. Review for 
 February, 1887) that he in fact undervalues those activities, the annihi- 
 lation of which, according to this passage, would make no breach in 
 the order of science. I cannot but think, on the other hand, that any 
 logical theory with which such a statement were compatible would be 
 gravely defective. 
 
Chap. VII] Laws of Nature 217 
 
 of oceans raised into mountains ; and the earth become 
 a scene of horror which even the lurid fancy of the writer of 
 the Apocalj^se would fail to portray. And yet, to the eye 
 of science, there would be no more disorder here than in the 
 sabbatical peace of a summer sea.' 
 
 Translated into simpler language, this sentence means that 
 if all these things happened, they would happen without a 
 miracle ; or in logical phrase, they would be capable of explan- 
 ation according to the law of sufficient reason. And this is 
 undoubtedly a truth that we must lay to heart. Our choice, 
 being what we are, lies between the experience intelligible 
 according to the formal laws, or none at aU. A ' suspension 
 of the laws of nature ', a ' supernatural interposition ' or 
 ' interference ', is perhaps the one and only matter that if 
 alleged as a fact can be denied on the sole evidence of the 
 abstract ' laws of thought '. Against any phenomenon, any 
 occurrence, however extraordinary, these laws, apart from 
 more concrete experience, have no foothold and no purchase. 
 But the allegation that something is known and yet not 
 knowable, nay more known as not knowable and in respect 
 of the pecuUar essence which makes it not knowable — this, 
 if we would retain our sanity, we must refuse to entertain as 
 conceivable. And if supernatural means anything but this, 
 any causation handled by superior knowledge and power 
 within the unity of Reality, then for logic it is natural and we 
 must treat it as we treat aU natural phenomena. We deny no 
 occurrence on the strength of formal laws ; we only denj' 
 a theory about the occurrence. Formal laws do not care 
 how extraordinary a phenomenon may be ; anything may 
 have happened or may happen ; the only question is whether 
 it did, or will. 
 
 Much xmclear thinking and much false sentiment might 
 have been avoided if the mechanical aspect of nature had 
 been recognised ^ long since as Professor Huxley states it. 
 Nature, as a mechanical system, is not teleological. Disease 
 and deformity are as natural, as orderly, as much according 
 to law, as health and beauty. It is idle verbiage to enlarge 
 
 ' e.g. by Charles Kingsley and teachers of liis school wlio preach 
 concurrence with and conformity to the ' laws of nature '. 
 
2i8 Relation of Knowledge to its Postulates [Book ii 
 
 upon a contrast between law and lawlessness in the natural 
 world, considered as a natural or formally knowable system. 
 The only lawlessness is in the supposed supernatural within 
 the natural. Nothing that happens can escape from the 
 principle of suiBcient reason, and therefore nothing that 
 happens is without an aspect of law. 
 
 But these considerations, though true, are not the whole 
 truth. We unquestionably expect something more of the 
 world than a capability of being known according to the law 
 of sufficient reason. It is the nature and the warrant of these 
 expectations that I now desire briefly to examine. 
 The main- i. I do not think that it can be doubted that we expect an 
 ofT^e^ indefinitely prolonged — ^not necessarily everlasting — continu- 
 ance of such conditions of the earth's surface as are compatible 
 with human life. It would not be justifiable to derive this 
 expectation from the formal postulate considered above on 
 any such ground as the necessity of a human intelligence to 
 the existence — as we understand existence — of the actual 
 woild. This merely logical necessity might at worst be satisfied 
 by an appeal to our ignorance ; for how can we know that the 
 human intelligence is the only intelligence, in the system of 
 things ? But in any case we are now compelled to accept as 
 fact a state of the globe prior to the existence of the human 
 race, or even of organic life, and if we find no insuperable 
 difficulty of form in this view of the past, why should there be 
 any in a corresponding belief as regards the future ? 
 
 It may be said, again, that our whole state of knowledge, 
 and the absence of urgent warning from our scientific look- 
 out men, justifies a disbelief in any imminent disaster or trans- 
 formation of the earth's surface. Now it is my contention 
 in the present chapter that the postulates of which we are 
 speaking simply sum up the pith and essence of our know- 
 ledge, and I have no reason to doubt that the actual state of 
 scientific prediction is a large element in the practical certainty 
 with which we regard the future of our globe. Unmotived 
 possibilities rightly go for nothing, and it is the case, I suppose, 
 that there are not at present above the scientific horizon any 
 seriously motived possibilities of a speedy end to man's 
 existence. 
 
Chap. VII] Eschatology 219 
 
 But I cannot think that this exhausts the question. It 
 appears to me that the real root of our conviction is ethical, 
 and ultimately depends upon our confidence in the relation 
 of our purposes to the scheme of the universe. Such an ethical 
 conviction is not a ttov otw outside our knowledge, but is the 
 very core of almost all that knowledge on which our distinc- 
 tively human life essentially depends. The purposes of the 
 civilised world form the real teleology " on which our organised 
 knowledge of society and of all human achievement is based, 
 and it is on the conviction, inwoven in this knowledge, of the 
 reality of these purposes in their essential content, that our 
 faith in the future seems to me to be founded, and under 
 present conditions of knowledge to be rightly founded. 
 
 It may be said, with an appeal to eschatology, that such 
 a faith is not even a ' quod semper, quod uhique ', &c., and that 
 a speedy end to man's existence on earth has in fact frequently 
 been expected by large bodies of human beings. On this sug- 
 gestion two observations are to be made. In the first place, 
 it would be interesting, both logically and psychologically, to 
 know the exact effect of such a belief on the practical postulates 
 of civilised life in those who hold it — to know, in short, the 
 degree of reality with which, as a working belief, it has ever 
 been held. To some extent the doctrine has been specially 
 directed to meet the dangers which it tended to cause, by 
 inculcation of the duty of diligence in business and of orderly 
 conduct as the best preparation for the end. And then in the 
 second place, as this adaptation of the doctrine shows, the 
 conception of an ethical continuity of purpose is satisfied by 
 the idea in question, although not necessarily under the form 
 of a continued terrestrial existence.^ 
 
 ^ See notes, pp. 99, 199, above. The argument would be sounder 
 in form, but not very substantially different, if we substituted ' indivi- 
 duality ' for ' real teleology ' ; the general principle is that our criticised 
 desires though not our given desires have evidential value, where 
 ' criticised ' means divested of self-contradiction. But anything more 
 than the briefest indication of this problem does not belong to Logic. 
 
 ' Under this head, of a satisfaction for our ethical demand otherwise 
 than in the form of our continued existence, may be classed in great 
 part the curious psychological fact of the slight practical effect produced 
 by prospective death even on men whose lives are by any cause gravely 
 imperilled. I ascribe this, though in part only, to our prospective 
 
220 Relation of Knowledge to its Postulates [Book it 
 
 If the question were pushed home, and we were asked to 
 translate our ethical postulate into terms of time and degree, 
 we could only, I think, fall back on conceptions akin to the 
 /jio9 TeKeios of Aristotle, i.e. on the conception of a duration 
 and environment of life adequate to the accomplishment of 
 some worthy purpose. And what catastrophes befalling the 
 human race are compatible with the purposes of the world 
 we cannot presume to guess. ^ It would be hard to believe, 
 for example, in the likelihood of a catastrophe which should 
 overwhelm a progressive civilisation like that of modern Europe 
 and its colonies, so that the history of the world would have 
 to be begun anew, without any influence at any time arising, 
 by rediscovery of remains, from the prior civilisation. 
 
 ' But we may be mistaken in our postulate.' Certainly we 
 
 may be mistaken, as in our present knowledge, so in the 
 
 sum and substance of our present knowledge. But unmotived 
 
 satisfaction in the maintenance of our essential activities and purposes 
 by others after our death ; and I do not think that this satisfaction would 
 exist in view of a prospective extinction of the race. Again, the truth 
 that a belief in some continuance is necessary to a)iy action, and that 
 some action is necessary to any continuance, is merely the minimum 
 grade of the postulate we are discussing. 
 
 ' The writer is aware of a strong prejudice in his own mind that 
 a disastrous earthquake in London is an exceedingly improbable occur- 
 rence. Not, of course, that volcanic agencies can act otherwise than 
 they must, but that such a degree of inconstancy as to tempt an enor- 
 mous heavily built city to be erected, and then to turn and rend it, 
 would seem malicious on the part of Nature. The prejudice is only 
 mentioned as a psychological curiosity, and is not defended for a moment. 
 The writer believes it to be a blundering application of an ultimatelj' 
 genuine principle.'' 
 
 * I am aware that this note has been adversely criticised, and I admit, 
 as I admitted in it, that the actual belief expressed in it is probably 
 indefensible. Yet I do not cancel it, because it calls atteiiticn to a 
 technical point which seems to me fundamental, and which I doubt if 
 my critics have observed. It is this, that as inference from particular 
 to particular is impossible, and you must always make the circuit 
 through the universal nature of the system on whose manifestations 
 you are arguing (see above, pp. 22, 1 39), it is necessary to accept a heavj' 
 responsibility when the whole nature of that system is concerned, and 
 if you cherish a general view about it, and allow this view to affect your 
 inference, it is illogical not to formulate and defend your view. If you 
 believe that the world-system is wholly indifferent to the interests of 
 civilisation, you shoulder just as heavy a logical responsibility as if you 
 believe the opposite. And you are bound to exhibit your view. 
 
Chap, vii] The minimum of Knowledge 221 
 
 possibilities of error must go for nothing ; and in departing 
 from the positive import of the knowledge which at present 
 we possess, we abandon concrete reality for more or less 
 abstract imagination. In this first material interpretation 
 which we have been putting upon the law of the Uniformity 
 of Nature, we have simply been analysing a condition which 
 is essential to the maintenance of human life as reality now 
 presents it to us, viz. the prospect of continuance. If the 
 constancy of content which this prospect demands were ever 
 to become doubtful with good reason, the doubt would ex 
 hypothesi show itself in our knowledge on positive grounds ; 
 but tni then we must accept this constancy not indeed as an 
 ultimate certainty, but as a leading characteristic of our 
 actual world. 
 
 ii. But the imifoimity of nature as materially understood The re- 
 goes at least one step further than to postulate the maintenance values 
 of human life on the earth's surface. It also postulates the 
 reality of those purposes and achievements which make man 
 what he is. 
 
 It is possible to fancy not merely a state of the earth in 
 which the life of the human animal should be physically 
 impossible, but a state in which though life were possible 
 and actual, yet the apparent caprices of nature, however 
 formally rational, should prohibit all advance in knowledge 
 and civilisation. What degree of ambiguity in the appearance 
 of natural bodies, in spite of an actual constancy of their 
 properties, might make knowledge impossible, is a question 
 which there is no sense in asking, as we have no measure by 
 which to estimate the answer. Many ambiguities have been 
 resolved by knowledge ; but the operations of the intellect 
 unquestionably demand not only the theoretical constancy of 
 properties, but some degree of limitation in their variety. 
 Exhaustiveness is, in short, though not theoretically deducible 
 from the law of Sufficient Reason, a largely and increasingly 
 essential element of knowledge. What would it help us that 
 the specific gravity of gold is constant, if elements imdis- 
 tinguishable from gold by other ordinary tests, but differing 
 in specific gravity, were continually to present themselves in. 
 our operations upon Nature ? And although infinitesimal 
 
222 Relation of Knowledge to its Postulates [Book ii 
 
 variation is a predominant law of the organic world, yet 
 knowledge is at least greatly facilitated by the existence of 
 marked points of transition between species and species/ and 
 it is plain that a succession of animals differing by variations 
 of minute and equal value would not be compatible with our 
 present modes of natural knowledge, although in geometrical 
 matter the intelligence has displayed the power of theoretically 
 grasping an absolutely continuous evolution. 
 
 It might be said indeed that we were alleging above that 
 * If there is to be human life there must be human life ', and 
 are alleging now ' If there is to be knowledge there must be 
 knowledge ', truisms which amount to nothing. So far as 
 content goes, this may, by abstraction, be true. A mere 
 analysis of content is eo ipso hypothetical. But the content 
 which we are analysing is, moreover, affirmed of our real 
 world as an integral element of the significance of that world, 
 which significance is primarily ethical. 
 
 And this significance for which I am contending is not an 
 a priori postulate or axiom, from wliich any specific know- 
 ledge could be derived apart from experience. If I am asked 
 ' What is the material uniformity ? How do you limit it ? 
 What does it imply ? ' I can only answer by pointing to 
 the progressive content of knowledge itself. The postulate 
 of Uniformity is ultimately that there is such uniformity -as 
 our knowledge in detail reveals to us. Do I beheve that mass 
 and energy are constant, that gravity operates in the region 
 of the fixed stars, that any of the heavenly bodies have an- 
 imated inhabitants, or that the elements are ultimately reducible 
 to a single form of matter ? None of these, I should have to 
 reply, are questions of an ultimate logical postulate. Our 
 convictions upon all of them must be determined by the state 
 of our knowledge and by our estimate of its tendencies. From 
 an ethical postulate we can deduce nothing but the empty 
 form of a logical principle, the form that ' what is involved in 
 ethical * reality is real ' ; the material details must come from 
 science only. 
 
 ^ Owing, no doubt, to the extinction of intermediate forms. 
 * In any new work dealing with these points I should not make use 
 of the term ' ethical ', which now seems to me an individualistic term, 
 
Chap. VII] Meaning of ' a priori ' 223 
 
 The three degrees then which may conveniently be distin- Three 
 guished in the interpretation of the Law of Uniformity oi'v^tei-ptQ- 
 Nature or of the Unity of Reality, considered as the postulate Unifor- 
 of knowledge, may be assigned as follows. E^^y °* 
 
 (i) ReaUty is a mechanical system through and through, j^gality 
 This postulate is expressed in the so-called ' laws of thought ' is mecha- 
 which find their most explicit form in the * Law of Suf&cient ^^^ ' 
 Reason ', or principle of Relativity. 
 
 (2) Reality as a mechanical system is adapted to the Reality is 
 evolution and maintenance of life, i. e. is at least quasi-teleo- i^ologicaL 
 logical. This is a first approximation to what is practically 
 assumed as the material Uniformity of Nature. 
 
 (3) Reality as a mechanical system is further adapted to, Reality is 
 or includes as elements within its unity, the substantive [^^j^^^^^j^ 
 purposes of human intelligence, i. e. is really teleological. 
 
 It is possible, by intellectual abstraction, to dissociate the 
 first of these aspects from the others, as the import of ' mechani- 
 cal ' can be dissociated ^ from the import of * machine '. It 
 is not possible to dissociate either quasi-teleology or real 
 teleology from a mechanically-conditioned system. The nature 
 of a system can only be real in as far as the parts or differences 
 that enter into it have a real mode of activity. Miracle 
 destroys teleology, for it destroys the relation of part to whole. 
 And activity or variation of activity, that has no ground in 
 the one Reality, is miracle. 
 
 3. It seems desirable to conclude the present work by The 
 bringing to a point the views that have been implied through- ^l^^^^g^^f 
 out it upon the ultimate nature of intellectual necessity, and Necessity. 
 upon the sense in which such necessity can be predicated of 
 any elements within knowledge. 
 
 i. It would be a tedious task to analyse at length the 
 
 applicable to an attitude right and characteristic for a finite being 
 within a whole, but neither to the whole, nor to the position of the finite 
 being completely considered. I should substitute some such expression 
 as ' the conception of absolute reality '. ' Human ' is an instance, not 
 an ultimate. But obviously the problem goes beyond Logic. 
 
 ^ This concession must be read subject to the reservations of p. 99. 
 This dissociation is not possible in an ultimate sense. But of course 
 dissociation from any particular teleological scheme is abundantly 
 possible, and that is the point of material importance. 
 
224 Rdation of Knowledge to its Postulates [Book ii 
 
 A priori components of Mill's discussions ^ relating to the basis of 
 necessity necessary truth. But nothing could, in my judgment, be more 
 diation. conducive to a thorough mastery of the question than a 
 careful study of the chapters referred to in Mill's Logic in 
 the light of some plain distinctions, which, in default of a 
 better guide, I will here endeavour to lay down. By Mill 
 himself, together with the writers whom he quotes, nearly 
 every position of importance in the controversy is assumed 
 in its turn, and the argument is a strange mixture of penetrat- 
 ing sagacity with unphilosophical confusion. 
 Mediate a. Necessity, as we have abundantly convinced ourselves,^ 
 nature of involves mediation or inference. No isolated judgment qua 
 forgotten, isolated can have necessity. Every necessary truth must, in 
 so far as it is necessary, present itself as the conclusion from 
 an antecedent. In the idle controversy whether axioms are 
 known a priori or ' from experience ' this aspect of necessity 
 is forgotten on both sides. 
 ' From (i) If ^ priori necessity is taken as inherent within the 
 
 some- four corners of the axiom itself, the very nature of necessity 
 prior,' is contradicted, and the only meaning which I presume the 
 phrase a priori can ever have had is stubbornly denied to 
 it.^ 'A priori ' (e/c irpoTepajv) says in so many words that the 
 knowledge to which this term applies is 'from something 
 prior to it ', i. e. is derivative, inferred and mediate. The 
 metaphor involved in ' prior ' no doubt created for Aristotle 
 a problem about the series of premises, which, it would seem, 
 must come to an end somewhere in an ultimate premise ; 
 a problem which could only be solved, as Aristotle, I imagine, 
 was really quite aware, by making the series ultimately return 
 into itself, and lose its successive character by transformation 
 into an organised system.* But this difficulty about the 
 
 ^ Mill's Logic, Bk. II, chaps, v and vi. 
 
 * Cp. especially above, i. 134. 
 
 * I am quite unable, for the reasons assigned in the text, to subscribe 
 to the views as to a priori knowledge which are stated in sections 355-6 
 of Lotze's Logik. In placing the test of ' self-evidence ' in an immediate 
 recognition without any process of proof, he appears to me to surrender 
 altogether the rational character of knowledge. His subsequent ex- 
 planation, sect. 358, seems to me exactly parallel to Whewell's practical 
 retractation respecting the law of atomic weights. See below, p. 227. 
 
 * See p. 269 below. 
 
Chap. VII] Vicious Intuitional Belief 225 
 
 ultimate premise of a series, even if unsolved, does not justify 
 the neglect of the plain logical differentia imposed by the 
 term a priori upon all that claims to be known a priori,^ viz. 
 that it shall be inferred from knowledge, whatever this may 
 be, other than itself. 
 
 (2) If, on the other hand, by those who object to the ' a Indis- 
 priori ' origin oi knowledge, supposed to be alleged as not associa- 
 experiential, an appeal is made to any form of indissoluble tion. 
 association, originating no doubt in constant experiential 
 conjunction, but operaiing finally through a sheer psycho- 
 logical inability to disjoin the parts which insist on present- 
 ing themselves together in the mental picture, here if any- 
 where we have the vicious doctrine of a priori knowledge in 
 its most outrageous form. For, it must be remembered, 
 the past is past ; the psychological history of our conviction 
 cannot come into court when we wish to demonstrate the 
 conviction to be true or false. It is of no use to say, ' I have 
 seen it so often that I cannot help believing it true.' One 
 might almost as well say, ' I have said it so often that I cannot 
 help believing it true.' The question is not how often you have 
 seen it, but what you now know that you saw, and under 
 what precise conditions. If nothing in the content of the 
 experience, as it now is in the mind, goes to exclude error 
 or to carry conviction,^ then we believe it simply because we 
 find it in the mind, which is just the description of vicious or 
 intuitional a priori belief.^ 
 
 ^ Prantl, Geschichte der Logik, vol. iv, p. 78, quotes from Albertus de 
 Saxonia, a.d. 1390, as the oldest authority for the dualistic use of ' a 
 priori ' : ' Demonstratio quaedam est procedens ex causis ad effectum, 
 et yocatur demonstratio a priori et demonstratio propter quid et potis- 
 sima ; . . . . alia est demonstratio procedens ab effectibus ad causas, et 
 talis vocatur demonstratio a posteriori et demonstratio quia (that) et 
 demonstratio non potissima.' Nothing could be more sharply opposed 
 to ' immediate ' knowledge. 
 
 ^ The distinct relations to the percipient, which make us sure that our 
 recollection is not a fancy, are what perform this office in an actof 'simple' 
 memory. In fact, no act of memory is absolutely simple, as indeed no 
 intellectual act of any kind is. The truth of our recollection is inferred 
 from content, not accepted because of mere psychical indissolubility. 
 
 * In the discussion alluded to in the text, Mill is on the whole the 
 champion of organised knowledge and inferential necessity against 
 unreasoned conviction and mere indissoluble association. But he 
 
 1337-2 Q 
 
226 Relation of Knowledge to its Postulates [Book ii 
 
 Organised ^. The distinction on which the relation of necessity to 
 organised Experience really turns is the distinction between organised 
 experi- and unorganised experience. The former can give necessity ; 
 the latter cannot give knowledge. To maintain with Whewell 
 that there is a necessity which does not depend on experience 
 is to concede Mill's contention that necessity is a psychological 
 illusion. If there is no organisation of experience into a system, 
 the latter view is obviously the truth ; but with the necessity 
 which Mill rejects there must in that case also be thrown 
 overboard the knowledge which he maintains. If there is 
 organisation of experience, then the necessity which attends 
 complete conception, although nothingirrational, supernatural, 
 or immutable, is more than a psychological illusion. It 
 simply means that given this and that, being the conditions 
 imposed by our knowledge of the matter in hand, then the 
 other must follow because of the relation between them. 
 
 This distinction may be, I think, pretty thoroughly eluci- 
 dated with reference to Whewell's treatment ^ of the prin- 
 ciple, in his time quite a recent discovery, that chemical 
 combination takes place between elements in certain con- 
 stant definite proportions only. Whewell was able to per- 
 suade himself that this law, when once understood by a mind 
 with adequate scientific resources, could not but be accepted 
 as a law whose falsity was inconceivable. Of course such an 
 assertion, made by a writer suspected of a belief in intuitional 
 
 wavers in his position, ( i ) by refusing to maintain against Whewell that 
 a justifiable necessity can be generated by experience, and confining 
 himself to the contention that an illusory show of necessity can be so 
 generated — this means that the experience of which he is thinking is 
 the mere repetition of sense-perception and not a determinate system 
 of science ; and (2) by the constant appeal to the profusion of experi- 
 mental evidence in favour of geometrical axioms, and in particular to the 
 mental picture of parallel straight lines as the instrument, by a constant 
 repetition of experiment, of generating the certainty that they are 
 incapable of meeting. Here we lose sight of the principle which owes 
 so much to Mill's advocacy, that one good experiment will establish 
 a law. Sir J. Herschel as quoted by Mill wavers in precisely the same 
 way, appealing now to iteration of experience, and now to systematic 
 knowledge. Spencer seems to hold the view characterised in the text, 
 not interpreting his test by conception into logical proof and therefore 
 leaving us to suppose that it consists in psychical conjunction. 
 
 ' Fully adduced and discussed in Mill's chapters above referred to. 
 
Chap, vii] lutuUion and Conception 227 
 
 or something like innate and unreasoned convictions of 
 necessity, about a principle ' the discoverer of which was still 
 living ', was open to the ridicule with which Mill assailed it. 
 But the interest lies in the explanations which Whewell sub- 
 sequently offered, and which make the course of his mind 
 in the matter tolerably clear. In order to perceive necessity 
 in such a case, you must, he says in effect, understand the 
 terms, you must conceive all the elements of the problem 
 distinctly, and you must be furnished with a degree of scien- 
 tific knowledge which not eyery man of science possesses. 
 The ' intuition ' of the truth, he says, ' may be a rare and 
 difficult attainment.' 
 
 There can hardly be two opinions as to what all this means. 
 Conception as thus understood is simply systematic know- 
 ledge, and the reason why you cannot conceive the law false 
 is that you have attained a thoroughly mediate insight that 
 the system of science requires it to be true ; i.e. that if it 
 were taken not to be true your system of reality would be 
 shattered and overthrown. This necessity is read into the 
 terms of the principle in question, the interpretation of which 
 has been insensibly enlarged, and without careful analysis 
 there is great likelihood that the principle will seem to possess 
 a necessity involving no relation to anything outside itself. 
 In the particular case in question it may be — ^though the 
 suggestion is hazardous — ^that a confusion was operative in 
 Whewell's mind between a very abstract principle which is 
 involved in the place held by quantity in the real world, and 
 the peculiar law discovered by Dalton as the law of atomic 
 weights. All quantity is definite, and every combination is 
 a combination of definite quantities. Nor can there be any 
 doubt that every mixture has different properties according 
 to the relative quantities of the things mixed together. Wine 
 and water will mix in any quantities, but the mixtures will 
 not all be the same. I venture to write down these platitudes, 
 as Mill, in maintaining that the occurrence which Whewell 
 called inconceivable really represents the general rule, almost 
 seems to forget that every mixture is a mixture of definite 
 quantities, and that a change in the proportion will make 
 a difference in the mixture. No doubt this comparatively 
 
 Q2 
 
228 Relation of Knowledge to its Postulates [Book it 
 
 formal principle is a long way from the law which Dalton 
 discovered, viz. that the peculiar combination known as 
 chemical combination would not take place at all except 
 between definite proportions of the elements. But yet, 
 assuming the constancy of the resultant combinations, e.g. 
 that there is only one kind of water and not two or more kinds, 
 and also the limitation of their number, i.e. that there is not 
 in nature a series of compounds containing the same elements 
 as water but in slightly different proportions — and I should 
 have imagined that the truth or untruth of these two sug- 
 gestions must have been notorious to chemists before Dalton 's 
 time — ^then presupposing all this it does seem to an outsider 
 as if the law of combination in definite and constant propor- 
 tions ^ ^^'as pretty much rendered necessary by the mere 
 nature of quantity. At all events, without being so rash as 
 to infer from the operations of my own mind to those of 
 Wliewell's, I maj' suggest that some such process as the 
 above, which is obviously a mediate inference from matters 
 of fact combined with a formal principle about quantity, 
 constantly follows upon the discovery of a law. We are apt 
 then tacitly to presuppose the matters of fact, and to identify 
 the new law with the formal principle which it interprets. 
 This, I venture to think, is the key to the general character 
 of the process which Whewell's mind must have passed through 
 in the case before us, with the result of his mistaking mediate 
 for immediate necessity.^ In any case, his reason for believing 
 Dalton 's law plainly was, as he says in so many words, that 
 he thought he saw the whole order of nature to be involved 
 in it. If the intuition of an a priori necessity excludes media- 
 tion or inference, then this logical process was not the intuition 
 of an a priori necessity. 
 
 * The theory of atoms goes further than this in form. But I under- 
 stand Mill and Whewell to be speaking of the law only in as far as it 
 refers to definite proportions. 
 
 ^ It is said that men always begin by denying a new truth, and then 
 say that they knew it before. This is simply that the material interpre- 
 tation or development of an accepted abstract principle is at first strange 
 to them and they resist it ; but when they have imderstood it, they 
 pass it over into the old formal principle, identify the two, and become 
 unconscious that they have made any advance, 
 
Chap. VII] Conception and Imagination 229 
 
 In as far then as Conception means this complete insight, 
 its necessity is clearly the sole test of truth, being simply 
 identical with the necessity of knowledge. Mill's polemic 
 against the test by mere Conception is largely justified by the 
 ignorant use that was made of this test, as if it were immediate 
 and operated by mere inspection. In this polemic Mill shows 
 himself alive to the true source of experiential necessity, 
 although he rejects the term necessity except in reference to 
 mathematical reasoning. Thus, strangely enough, Mill re- 
 introduces into knowledge the distinction between necessary 
 and not-necessary truth, which the experiential school might 
 be expected to deny. And his account of the distinction is 
 on the whole sound, referring it simply to the difference 
 between the complete knowledge of the conditions, which is 
 possible in mathematics,^ and the partial knowledge of the 
 conditions which alone is possible in ordinary physical investi- 
 gation. It would be better, however, either to abolish the 
 term necessary altogether, or to extend it to all scientific 
 knowledge as such. 
 
 Mere imagination, on the other hand, as Mill rightly contends, 
 though inclined to extend the contention erroneously to con- 
 ception, has nothing to do with truth or knowledge either way. 
 Allegations are not more likely to be true because we can 
 imagine their content, nor less likely because we cannot. 
 
 It follows from the above considerations — 
 
 (i) That every judgment is tiecessary ^ and mediate in as far 
 as it is known ; and that no judgment has necessity or precision 
 (which depends on the explicitness of the mediating conditions) 
 if taken apart from the totality of knowledge ; 
 
 and (2) That the content of every judgment, as well as its 
 truth or necessity, is correlative to the one ultimate judgment, 
 i. e. to the whole system of knowledge ; and that therefore 
 while we do well to maintain that the body of knowledge has 
 certain indispensable functions, we nevertheless commit an 
 error of principle if we deny that the identity of these functions 
 is like other identities compatible with variation. 
 
 * The view of mathematical conceptions as hypothetical does not 
 concern us here. See Bk. I, chap. iv. 
 
 ^ See also chap, i of this book, on the specific necessity of judgment. 
 
230 Relation of Knowledge to its Postulates [Book ii 
 
 Rehabili- 
 tation of 
 formal 
 distinc- 
 tions. 
 
 Thus for instance knowledge, or reality as known, must 
 have such a function of relativity as that which we express 
 by the law of causation. But to suppose that the shape in 
 which that function happens to be familiar to us, involving 
 perhaps homogeneity of cause and effect, is necessarily an 
 ultimate shape, is one of the most mischievous results of the 
 fallacy of an isolated necessity. I do not think that there 
 can be any doubt that even the conceptions of the straight 
 line or of three-dimensional space are modified in their content 
 by the explicit distinctions needed to save them from being 
 confounded with arcs of great circles on a sphere surface or 
 with space of more or less than three dimensions. Unques- 
 tionably the new conceptions, however unreal, make them- 
 selves felt as restricting the absoluteness of the old ones. 
 Every judgment is relative to the whole of knowledge, and 
 no judgment entirely escapes modification as this whole is 
 modified. 
 
 ii. In order to illustrate the true import and value of such 
 conceptions as that of a priori truth or of necessary knowledge, 
 I will venture to give a brief sketch of the process, tending to 
 repeat itself in history, by which such distinctions are most 
 thoroughly apprehended, and which, if only in the individual 
 mind, is perhaps necessary to their apprehension. 
 
 \Vhen, in an epoch of genuine enquiry, a student first opens 
 his eyes, so to speak, in the philosophical world, he finds 
 himself confronted by a multitude of traditional distinctions, 
 some of which claim to be fundamental lines of demarcation. 
 Impressed with the ruling idea of all great epochs or earnest 
 intelligences, that of the unity of reality, he assumes a pro- 
 testant attitude towards these distinctions, which appear to 
 him incompatible with the demands of his genius or of his 
 time. His iconoclastic zeal is inflamed by the justification 
 which it finds in the obviously meaningless and mechanical 
 rigidity of the tradition which it attacks, a tradition that has 
 come to be in many respects a real offence against the primary 
 postulates of intelligence. And turning from his contem- 
 poraries to the great masters of thought whom they profess 
 to interpret, he finds in them also the phrases and ideas which 
 he has learnt to regard as the symbols of an unmeaning super- 
 
Chap. VII] Distinctions reassert themselves 231 
 
 stition. And therefore, finding no help in man, such a pro- 
 testant reformer in philosophy will proceed to reconstruct his 
 world on the basis of that aspect of it in which its unity has 
 been revealed to him ; that is to say, in the case of logic, 
 probably on the basis of sensation, of observation, of particulars, 
 of inductive experience. 
 
 But when with labour and pains some progress has been 
 made in this reconstruction, then for the reformer or for his 
 successors there arises a further stage. The duty now falls 
 upon them of maintaining the essential distinctions of thought, 
 between perceptive comparison and geometrical demonstration, 
 between empirical laws and laws of nature, between induc- 
 tion by simple enumeration and the constructive processes of 
 methodic science. When these antitheses are fully developed, 
 then the time has come for a rediscovery of the meaning of Plato 
 and Aristotle. The language which science is compelled to hold 
 reveals itself as coincident with that of the teacher who first 
 explained in what science consists. The distinction between 
 the province of self-contradictory opinion ^ and the province 
 of coherent knowledge recovers for science the meaning which 
 it had all but lost for scholarship. When it becomes un- 
 avoidable to erect, within the whole of ' experience ', which 
 has been passionately proclaimed to be coextensive with 
 knowledge, the included wholes of ' empirical ' observation 
 and mere fact, as opposed to deductive certainty and mathe- 
 matical necessity, then it is understood how such distinctions 
 as these when originally made were distinctions within the 
 knowable world, and were not incompatible with the unity 
 of experience. No geometrician, I imagine, would accept the 
 statement that the ratio of the diameter to the circumference 
 of a circle, so far as ascertained, is ascertained by observation, 
 because this would mean that it was found by direct measure- 
 ment. But, in denying this ' empirical ' origin of the cognition 
 in question, he would not suppose that he was alleging its 
 
 ^ De Morgan's Budget of Paradoxes is little else than the self-defence 
 of science against opinion. The failure to distinguish relations, which 
 in the world of opinion makes difference into contradiction, is well illus- 
 trated by one of De Morgan's cases, an argument against the rotation 
 of the earth which asks ' How can a man go 200 yards to any place if 
 the moving superficies of the earth do carry it from him ? ' p. 78. 
 
232 Relation of Knowledge to its Postulates [Book ii 
 
 independence of our acquired knowledge concerning space 
 and spatial relations. He would explain, I suppose, that no 
 doubt the calculation in question was based upon spatial 
 relations that could only come into the human intelligence 
 through its being aware of a spatial world (however this its 
 spatial perception is attained), but that nevertheless the 
 conclusion is reached by a process of reasoning or calculation, 
 and is not an observation in the sense in which it is an observa- 
 tion that there are ten volumes in the shelf at my right hand. 
 And by extending the same reasonable interpretation to Plato 
 and Aristotle which we extend to ourselves, remembering, 
 that is, that all contentions are relative to certain purposes 
 and proceed on certain assumptions, it becomes possible to 
 recover something like their natural meaning. 
 
 The development of Logic in England from Bacon to Mill 
 and Jevons is a good illustration of the process which I have 
 attempted to describe. And on a still larger scale, extending 
 to every side of life, I make no doubt that the Renaissance 
 itself, and also the new Renaissance of Winckelmann, Schiller 
 and Goethe, were examples of a similar phenomenon. Ancient 
 systems of thought or of religion can in fact only be interpreted 
 in as far as their interpreters feel the necessities which were 
 pressing upon their authors. And thus the individual mind, 
 in as far as its ideas develope from a root of genuine interest in 
 reality, tends to pursue an analogous course. If a great master 
 of thought could come on earth again after some centuries, 
 he would seldom find his true followers among those who have 
 never deviated from the straitest sect of his exponents. 
 
 Thus a cynic might say that the history of philosophy is 
 a process in which the meaning of Plato and Aristotle is 
 periodically forgotten by their disciples and rediscovered by 
 their antagonists ; who then, perhaps, become their disciples, 
 and so the cycle recommences. And the observation would 
 be just except in so far as it impUes that in each rediscovery 
 no advance is made on the meaning as understood before. 
 The cycles of philosophy repeat themselves, but not with 
 identical content. The Encyclopaedia Britannica is a very 
 different thing from the Encyclopaedia of existing knowledge 
 as sketched in Plato's Republic. 
 
Chap, vu] Logical Meaning of ' A esthetic ' 233 
 
 iii. It has been suggested by a great writer ^ — and the ' Aesthe- 
 suggestion falls in with many current ideas about philosophy ^1^^!^*^^'' 
 — that the necessity or propriety on the strength of which 
 sjmthetic connections are derived from or combined into an 
 including unity, ultimately the unity of the world, may be 
 rightly described as ' aesthetic '. This conception contains 
 elements of very unequal value, and I suspect that the element 
 for the sake of which it is recommended is one for the sake of 
 which it ought to be rejected. 
 
 It does not matter, or ought not to matter, whether we speak 
 of self-evidence, propriety, or necessity. They all attempt to 
 express the same fact, that in knowledge, that is in judgment, 
 we are not free, but are under a constraint exercised upon us by 
 the content of knowledge itself, such that some judgments 
 have to be accepted and others to be rejected. But if we ex- 
 press this fact by the term necessity, then in virtue of the 
 explanations which have been given above we exclude, and 
 rightly exclude, an interpretation which the terms self -evidence 
 and propriety admit if they do not compel, that is to say, 
 an intuitional interpretation. 
 
 'Aesthetic necessity,' then, would either mean something 
 which we might accept as a fact, though we should pronounce 
 its appellation unduly limited, or else would be a contra- 
 diction in terms. I will consider the latter alternative first. 
 
 a. An aesthetic judgment, like a moral judgment, is in in one 
 everyday life, at any rate, not expHcitly mediated. It is ^^"^^'^^ 
 the peculiarity of the aesthetic product, or of the aesthetic diction, 
 aspect of any object, that cilthough coherent and rational, 
 having passed through the medium of mind, yet nevertheless, 
 qua aesthetically operative, it is not discursively analysed. 
 Although in aesthetic judgment discursive analysis must play 
 its part, yet such analysis is not the essence of aesthetic 
 appreciation, but is on the contrary that which aesthetic 
 appreciation has in common with scientific understanding, 
 and is the mere organon of careful perception, by which the 
 aesthetic product is constructed and brought to notice in the 
 mind. A work of art, or any object regarded as beautiful, 
 makes an appeal to feeling ; which, as such an appeal, must 
 
 ' Lotze, Logik, sects. 364-5. 
 
234 Relation of Knowledge to its Postulates [Book ii 
 
 be immediate, although the feeHng to which it appeals is 
 moralised or spiritualised, and consequently there is on both 
 sides, in the work of art and in the spectator, a rational content. 
 This, though it appeals to feeling in an immediate form, is of 
 course capable of being analysed in mediate form. But yet, 
 as the work of art is the outcome of a spiritual mood of feeling 
 in the artist, so it appeals to such a mood in the spectator. 
 It was not constructed by combination of abstract relations, 
 and though its fabric must be coherent and charged with intelli- 
 gence, yet no mere intellectual reconstruction of such a fabric 
 can reproduce the spiritual mood which is the essence of the 
 work of art. This, if expressed in an abstract or inferential 
 form, may retain a value for philosophy, but loses the dif- 
 ferentia of fine art. Therefore, as necessity involves explicit 
 mediation, and aesthetic judgment in the strictest sense 
 excludes explicit mediation, to speak of aesthetic necessity 
 is a contradictio in adjecto. It is this immediate or intuitional 
 self -evidence, this appreciation hy feeling, which, as I suspect, 
 the suggestion before us intended to identify with logical 
 coherence or necessity. If recommended in this sense, the 
 suggestion must I think be absolutely rejected. Necessity 
 only attaches to a judgment in as far as that judgment involves 
 the whole of knowledge. Unreasoned necessity is irrational 
 belief. 
 Ill /3. If, on the other hand, aesthetic necessity merely meant 
 
 sense a ^^^^ synthetic coherence of parts which every aesthetic whole 
 type of shares with all universals whatever, then though we should 
 
 10£flC3,l 
 
 necessity, admit the description to be true, and in one respect striking, 
 yet we should have to add that it really did no more than 
 refer us to one instance, and that an imperfect one, of the 
 general relation to be described. An aesthetic whole is, so 
 to speak, a universal made easy. In it the individual unity 
 which belongs to everything real is not left to be toilsomely 
 unravelled by reflection, but is presented in a shape capable 
 of at once appealing as a unity to sense-perception or to 
 imagination. Hence the discursive analysis which is instru- 
 mental in the apprehension of a work of art, however subtle 
 in its ultimate refinements, is ex hypothesi in great part 
 evident and unavoidable. In this sense and to this extent 
 
Chap. VII] Analysts of Work of Art 235 
 
 the rational coherence in which all knowledge consists is 
 strikingly illustrated, not by the aesthetic judgment itself, 
 but by the analysis which accompanies the apprehension of 
 a work of art in so far as this apprehension is of the same 
 nature with the apprehension of any perceived object or 
 complex of relations whatsoever. For this reason it is not 
 uncommon to take a work of art as an example of the com- 
 pulsion by which the nature of a whole controls its parts, 
 simply because this control, which is the essence of individuality, 
 lends itself readily to analysis in a work that is pervaded 
 by an especially harmonious unity.^ But precisely the same 
 is the case with geometrical conceptions, and for precisely 
 the same reason geometrical necessity, which is not only 
 rational but also essentially mediate, is often taken as the type 
 of logical necessity. 
 
 Of these two classes of examples the geometrical con- 
 ception is the more perfect in one respect and the aesthetic 
 in another. The aesthetic object is an imperfect type of 
 necessity because its nature is not exhaustible by reasoned 
 judgment, but consists in being such as to produce a certain 
 spiritual mood. As this mood involves and is accompanied 
 by some degree of reflective apprehension directed to the 
 coherence of parts in the artistic whole, which coherence is 
 necessary, there is apt to be a confusion between the feeling 
 and its concomitant insight which leads to an erroneous 
 notion of immediate necessity. And it may be added that 
 in trained artistic perception there is an immediate reaction 
 of repugnance or acceptance, analogous to the every-day 
 moral judgment, which is right and accountable in its place, 
 
 ^ The famous simile of the statue in the beginning of the fourth book 
 of Plato's Republic will occur to every one. This simile, occurring at 
 a critical point in an important work, is perhaps responsible for a current 
 idea that the Logic and Ethics of Plato and Aristotle were ' aesthetic ' 
 or ' artistic '. But the fact is that Plato and Aristotle dealt almost 
 exclusively with the general principles which underlie all individuality 
 and function, and illustrated these from fine art, from industrial art, 
 and from science, almost indifferently. They possessed indeed no 
 specific term for fine art, and though they gave a just weight to the idea 
 of beauty, yet nothing in their theories was aesthetic if that means 
 sentimental or unreasoned. If anything, they were too systematic and 
 intellectual. 
 
236 Relation of Knowledge to its Postulates [Book 11 
 
 but is the worst possible elucidation of logical necessity, with 
 which the form of feeling is wholly incompatible. The geo- 
 metrical object is not open to this censure. Its nature is to 
 be capable of systematic construction through and through. 
 And the pervading nature in virtue of which the universal 
 determines its differences, the root of logical necessity, is no- 
 where more explicitly formulated and applied than in geometry. 
 
 As to individuality, however, the matter is reversed. A 
 work of art, though not an embodiment of real teleology, — 
 for it has not a purpose conceived as a definite reflective 
 idea, — has nevertheless the content or nature of real teleo- 
 logy, being thoroughly penetrated with reason ^ in the form 
 of feeling. It is therefore individual in a special sense, as 
 an outward and visible form thoroughly identified with an 
 idea that pervades it, so that the work of art is distinctly 
 relative to human intelligence, though it has no separable 
 purpose embodied in abstract human thought. Thus a work 
 of art is an exceptionally effective instance of an individual 
 whole. In geometrical objects the pervading unity is of the 
 most various kinds, and sometimes, taking the imperfect form 
 of a progression to infinity, appears to be incapable of con- 
 stituting a whole complete in itself. Even space seems 
 powerless to limit itself, and therefore its parts seem rather 
 to lie indifferently behind one another than to constitute 
 a totality in which each has its peculiar place and function. 
 In this sense no doubt the peculiar and specific necessity 
 imposed upon parts by the whole which they constitute is 
 better illustrated by the aesthetic than by the geometrical 
 whole. 
 
 Yet the wholes of real teleology, the moral order, for ex- 
 ample, as exhibited in a moral person filling his place in a 
 community, illustrate the nature of rational necessity better 
 than either the aesthetic or the geometrical system. The 
 identification of necessity with the idea of an intuitional or 
 isolated self-evidence is the rock to be avoided. 
 
 * Mr. Matthew Arnold's phrase ' criticism of hfe ', appUed to poetry, 
 explains what is meant by saying that art contains reason. That the 
 reason must be in the form of feeling this term ' criticism ' appears to 
 ignore. 
 
Chap. VIII Specific Necessity 237 
 
 Necessity, then, is a character attaching to parts or differ- 
 ences interrelated within wholes, universals, or identities. If 
 there were any totality such that it could not be set over 
 against something else as a part or difference within a further 
 system, such a totality could not be known under an aspect 
 of necessity. The universe, however we may conceive of it as 
 including subordinate systems, must ultimately be incapable, 
 ex hypothesi, of entering as an element into a system including 
 more than it. Strictly speaking, therefore, its relation to 
 knowledge must be one of reality, not of necessity. But also, 
 strictly speaking, it is a reality which we have no power to 
 question or to explain, because all our questioning or explana- 
 tion falls within it. There can be no meaning in talking about 
 what might be the case if the universe were other than it is, or 
 about what has been the case to make the universe what it is. 
 
 But except in the case of this unique and imaginary refer- 
 ence of that which is assumed to be the absolute whole to 
 something outside itself, every judgment is the synthesis of 
 differences, in a whole or identity expressed or understood, 
 and is therefore at the same time the analysis of that identity. 
 It makes no difference to the ultimate or actual import of 
 a judgment whether as a process in time it took its rise from 
 the synthesis of two data, or from the analysis of one. In 
 every judgment there are differences within an identity. In 
 every judgment therefore there is affirmed a necessity based 
 on a reality. The necessity itself may have for its content 
 a further redity, or may remain an abstraction which can 
 onlj'' be set down as descriptive 01 illustrative of reality. 
 The latter is the case with the more extreme forms of the 
 hypothetical judgment. 
 
 The various forms of universal which are the source of 
 necessity and constitute the content of judgments, the com- 
 parative value of these forms for knowledge, and the affinities 
 between them, are the object-matter of Logical Science. 
 And because our intelligence creates and sustains our real 
 world by a continuous judgment which embraces these forms, 
 in their concrete connection, within the unity of its system, 
 it is further true that Logical Science is the analysis, not 
 indeed of individual real objects, but of the intellectual struc- 
 
238 Relation of Knowledge to its Postulates [Book 11 
 
 ture of reality as a whole. In speaking of the intellectual 
 structure of reality, it seems to be suggested that reality is 
 modified by knowledge and is dependent upon mind. How 
 far and in what sense this is the case I have attempted to 
 explain in some additional chapters dealing with current 
 contentions of to-day. 
 Genetic 4- In more than one passage of the first edition of this 
 iheory ^ork I referred to considerations bearing on the limits of a 
 
 and Ne- ° 
 
 cessity. Genetic theory of Logic. The development of systematic 
 
 thought as it reveals its inherent nature in response to stimuli 
 
 largely conditioned by its own advance, and according to its 
 
 own necessity, appeared to me to be the true type of genetic 
 
 analysis. ''^ It seemed to me fuither that a sharp distinction 
 
 must be drawn '^ between varied forms and degrees in which 
 
 the conditions of knowledge might be fulfilled in various 
 
 environments, and any attempt at evolutionary explanation 
 
 of its ultimate principles, such as the law of non-contradiction. 
 
 On the other hand I was careful to point out " that even such 
 
 leading principles — the necessary functions, as I proposed to 
 
 call them, of the rational mind — were not to be considered 
 
 as formal propositions, given and self-evident each within its 
 
 own four corners, and irresponsive to alterations in the general 
 
 body of knowledge. I regarded them as roughly ^ comparable 
 
 with the main functions of an animal organism, which may be 
 
 fulfilled in all sorts of shapes and degrees, but must be fulfilled 
 
 if life is to reside in it. 
 
 There must, I urged, for example, be a function in the body 
 of knowledge corresponding to what we know as the law of 
 Causation. But in what precise shape it is to be asserted has 
 been and is still a matter of controversy, which will no doubt 
 continue to lean in different directions from time to time 
 according to the requirements of the matter to be dealt with. 
 
 I propose here to return to the above question, which 
 has been the subject of much recent discussion, and has 
 lately met with a substantive treatment in a treatise on 
 Genetic Logic. 
 
 " Vol. i, p. 2. •> Ibid. pp. 7-8. = Vol. ii, p. 229. 
 
 ^ Roughly, because for life the environment is the surface of the earth , 
 For mind it is the universe. 
 
Chap. VII] Reasofi Creative 239 
 
 i. There is, however, one general difficulty which may be dealt Reason 
 with in advance. ' What matter ? ' it may be replied to me. Adapta- 
 ' According to current views, and your own in particular, all tion. 
 genesis is only revelation, and there is no true creation de 
 novo. " Tout est donne." Suppose that reason is only an 
 evolutionary adaptation, selected by the environment from 
 variations of thinking, for you at least that makes its nature 
 none the less its own. However moulded, it had to be as it 
 has turned out. What difference can the particular process 
 make ? What logical interest can you have in combating 
 a view which professes to trace the genesis of the logical 
 reason as an adaptation due to natural selection ? ' Now in 
 a sense I am prepared not to admit but to contend that 
 everything is modelled by the environment — the whole — which 
 means, in the end, by something like natural selection. But 
 within this wide principle there are distinctions which must 
 be taken. Above all, we must distinguish systematic con- 
 trivance — the conscious working of a principle of totality 
 and non-contradiction — from trial and error. The conscious 
 endeavour towards non-contradiction and totality is no doubt 
 a powerful instrument towards survival through natural 
 selection, but it is also a great deal more. It is within itself 
 a power of construction and of judgment, by its own law and 
 necessity, in its own right. This power is what we call reason 
 and intelligence ; it is characteristically self-contained and 
 self-complete ; and has its own necessity, which is systematic, 
 and not the mere success de facto that comes through trial 
 and error, the pure and simple form of moulding by natural 
 selection. 
 
 How reason is truly creative I have briefly discussed above, 
 and hope to consider more at large in another work. Briefly, 
 I should urge that reason alone means creativeness, the con- 
 tinuity of the bona fide old with the bona fide new, and that 
 there is nothing in the universe that is strictly creative except 
 reasonable ^ and logical process — such for instance as we 
 observe in every original work of art. That every such element 
 is new and unparalleled is a quahty secured to it according 
 
 ^ See above, p. 182. 
 
240 Limits of a Genetic Theory of Logic [Book ii 
 
 to the degree of its individuality, which is one thing with its 
 logical perfection. To repeat or be repeated means imperfect 
 individuality — a failure, pro tanto, to hold one's own as an 
 element in the whole. But I must not here digress further in 
 this direction. 
 
 Reason, then, however it manifests itself in answer to 
 demands of an environment, has its own necessity and does 
 its own selection in virtue of its own constructive principle. 
 It is the nature of this necessity, and the organisation which 
 embodies it, that we investigate in Logic, and from the stand- 
 point of which, so far as the system has been apprehended, 
 we can judge and understand its partial incarnations in the 
 course of evolution. This distinction between rational neces- 
 sity and de facto survival will be further insisted on in the 
 sequel. 
 Imitation ii. I understand it to be the claim of the recent Genetic 
 S^^^ tion t^^o^'y o^ Logic to explain the rise and growth of the charac- 
 teristic organisation of thought which we portray in logical 
 science, by a process of Imitation through which thought- 
 variations are suggested, together with one of Selection, 
 through which only certain of these are permitted to survive 
 owing to their fitness for social and practical needs. Granted 
 these factors, it is held, the nature of logical thought can be 
 accounted for by them and out of them. 
 
 My contention is, on the other hand, that Imitation is merely 
 a later and partial aspect within the character of relevant 
 response which belongs to the principle of non-contradiction 
 developing in its world of Identity and Diversity of experience, 
 which is to it as the world of organic being is to the principle 
 of Life."^ And further, that Selection is something which 
 Thought does for itself — as in the relation of any theory to 
 the experience it unifies — and from its own standpoint. A 
 Genetic theory, therefore, I contend, may exhibit the de facto 
 evolution of the thought system and thought principle under 
 historical influences ; but it can never derive from other 
 factors that systematic necessity of reason, rooted in the 
 principle of non-contradiction, in virtue of which it pronounces 
 some judgments to be true and others to be false. 
 ' But see p. 238 above as to the different environments of the two. 
 
Chap. VII] Similarity versus Identity 241 
 
 iii. Imitation is a partial case of relevant response, which Meaning 
 depends on a recognition of Identity in Difference, a. I can °ion"^* ^ 
 not agree with the view that this distinction is verbal, e.g. 
 in its application to biology. It is easy to show that a working imitation 
 whole cannot be represented in terms of similarities between gpo^g^^' 
 its members. And for the same reason the nature of the mem- 
 bers themselves must in a great measure be omitted from such 
 a representation. The Linnean classification, or the ciurrent 
 ' natural ' classification in botany, may be taken as a repre- 
 sentation according to resemblances, though I should not 
 admit that any scientific classification is so intended. But a 
 region of the world, as a whole of competing and co-operating 
 members, according to the light thrown by the principle of 
 evolution, can never be represented in such a form as this. 
 It can never bring together the things which have most to 
 do with each other : competing species of plants, co-operative 
 plants and animals, the soil, the climate, and their effect 
 on the hving things. Of course all this can be added in foot- 
 notes, as it were, to classification by resemblances ; but it 
 cannot be represented in the structure of the classification 
 itself. It would be like trjdng to explain a locomotive by 
 arranging its parts in classes according as they ressmble each 
 other. The reason of the impossibihty is that the parts or 
 members have their connection through their differences ; 
 and in a classification by resemblances, these, though they 
 have their weight as differences, have no weight as instruments 
 of identity. This whole subject is treated by Green,* and 
 I think is too little understood. I should strongly suspect 
 that the reform of logic in this sense in the great Idealist 
 days promoted, or at least was akin to, the transition from 
 Linnaeus to Darwin. 
 
 /3. Imitation (I summarise in my own language) is alleged Why held 
 to be a vera causa, it shows, is psychical, genetic, you can see causa^? 
 it at work ; the operation of a universal (that is, an identity in 
 difference) is an assumption, shadowy, almost, I think, a priori, 
 mystic, antiquated, invisible. I assume, it is urged, publicity, 
 the common awareness of a situation in which more than one 
 person is concerned, which ought to be explained. 
 
 * See p. 183 above. 
 1337-2 R 
 
242 Limits of a Genetic Theory of Logic [book ii 
 
 Now I cannot see any ground for all this in the facts. Imi- 
 tation no doubt is a fact, and plays an important part in 
 furnishing the self with material. I quite recognise the value 
 of the work which has been done on this subject. But surely 
 response and reaction, indices of communication through a 
 common nature, are much wider and more primary facts, 
 extending over the whole world, physical and psychical. The 
 adapted response is earlier — is it not ? — than consciousness ; 
 and the process of its passing under the control of intelligence 
 and being emancipated from trial and error, is fairly well 
 understood, though still doubtful in some details. But the 
 adapted response, as controlled by intelligence, just means 
 a consciousness of the situation based on an inference which 
 pro tanto dispenses with the test of material action ; an inference 
 based on perception is substituted for a certain number of 
 errors, as when a man sees at a glance how to open a gate, 
 which a dog will paw at till it comes open. There seems to 
 me no assumption in this ; it is a plain statement of fact, 
 and of fact more general and fundamental than imitation, and 
 requiring no more assumption. 
 
 With responses adapted by intelligence on the part of two 
 
 or more agents you have ' publicity ' or ' the situation '. 
 
 What you want, to account for this, is not imitation, but the 
 
 power of consciousness to combine perceptions and see their 
 
 results — in short, the unity of consciousness. As I understand, 
 
 it is urged that this must not be assumed but can be and 
 
 ought to be genetically accounted for. This I will speak of 
 
 when I come to comment on the meaning of the term ' genetic '. 
 
 My present point is merely that imitation is the secondary, 
 
 less general, and less completely stated fact, and that the 
 
 assumption of it, while involving, as much as a response does, 
 
 the cissumption of the unity of consciousness, is in no special 
 
 way a help towards explaining the apprehension of a situation 
 
 as a whole. 
 
 False y.. The treatihent of facts introduced by this theory seems 
 
 tfou^of ^° "^^ precarious all round. Particularly is this the case with 
 
 Imitator the separation of the imitator and the inventor. I am con* 
 
 ventor winced that a really critical study of any branch of history 
 
 would demonstrate the crudeness of this antithesis when 
 
Chap. VII] Is Truth explained ? 243 
 
 offered as a matter of principle. The advance of the human 
 mind, independently, so far as can be judged, of individual 
 original genius, is one of the most striking phenomena of 
 history, and one is inclined to add that the deepest transforma- 
 tions are those which have taken place in this way. It is an 
 old and true saying that man must advance or recede ; to 
 stand still is impossible for him. That is to say, the application 
 of tradition to life is in itself a generator of inventions ; it is 
 impossible even to borrow ideas without drawing conclusions . 
 which the lender never drew. And it is well known how rarely, 
 if ever at all, an invention can be assigned to a single mind. 
 The history of art is very instructive on this point, e. g. the 
 education of a Turner.* 
 
 iv. The second question (p. 240, on evolution of Thought), Truth or 
 seems to amount to this : Does a genetic account of thinking belief ? 
 explain by what character judgments are true, or only under 
 what influence we have come in fact to hold (often wrongly) 
 certain judgments to be true ? And what bearing has either 
 alternative on the theory of selective thinking ? 
 
 a. I will say at once that I see no meaning in a genetic Limits of 
 account of knowledge, except as a history of opinion ; but account. 
 I admit that this involves a history of mental organisation. 
 A simple illustration will do as well as an ambitious one. 
 We constantly make such judgments as this : ' A. B. is a 
 moderate Evangelical ; he was brought up as an extreme one, 
 in a family and circle whose views were extreme, but his 
 work and intercourse with varieties of people have made him 
 much more temperate.' Here we have the true place of a 
 selective theory of thinking, so far as I understand it, in a 
 nutshell. A. B. inherited a platform, an organised mental 
 constitution and logical or qu£isi-logical system ; i. e. he 
 acquired it by adaptation to his parents' and teachers' views, 
 or imitated them. Starting from this, he developed his later 
 position through varied forms of social selection acting on 
 his idccLS, involving accommodation to practical needs ; and 
 he now has a mental content and organisation at once fairly 
 
 '■ See, in Mr. Finberg's book, the drawing copied by Turner in boyhood 
 from an engraving, set side by side with the engraving from which it 
 was copied. 
 
 R2 
 
244 Limits of a Genetic Theory of Logic [Book ii 
 
 harmonious with the circle in which at present he moves, 
 and determined as a whole by the platform which he inherited. 
 I do not doubt for a moment that a history of all of us and of 
 the human race could be written in terms analogous to these 
 with a great deal of truth. And it would not omit the facts 
 of mental organisation. The metaphysician, the psychologist, 
 the biologist, mathematician, and also the EngUshman, French- 
 man and German, would all prove to possess, yes, and to have 
 acquired and developed, certain favourite categories, certain 
 forms of logical or quasi-logical bias, and predispositions to 
 accept explanations of certain appropriate types. 
 
 In such a historical enquiry some theory of selective thinking 
 might have, so far as I see, very interesting applications. It 
 would show by what needs and under what direction of 
 attention the minds of nations and individuals had grown 
 into certain structures, and had acquired certain logical pre- 
 dispositions. 
 
 But even here it would be necessary either to expand very 
 largely the sense in which, or to lunit very strictly the extent 
 to which, we affirmed action to be the instrument of selection. 
 If action meant aU change of consciousness directed to an end, 
 then, in referring the course of cognition and mental organisa- 
 tion to the needs of action, we should be making cognition 
 itself the standard of cognition,'' and saying that it learns to 
 act as it does act primarily by seeking its own ends and 
 secondarily by taking account of a certain contact with 
 material action. Then we might fearlessly say that ' action ' 
 
 ^ Mr. Stout in his Manual of Psychology seems to me to agree on the 
 whole with me, never blinking the relative importance of the cognitive 
 system as compared with external action, nor the liability of social 
 endorsement to be erroneous. But in one place he seems for a moment, 
 as I venture to think, to slur the distinction on which I am here insisting. 
 On p. 547 he insists that because belief is a condition of activity, there- 
 fore activity must be a condition of belief. And this remark he extends 
 to theoretical activity, though, indeed, as referring it to the provisional 
 acceptance of working hypotheses, he gives it a very restricted and 
 innocent application. But the point I wish to urge is this. In a ' prac- 
 tical ' activity the end is assumed to be given, and it is not a cognitive 
 end ; therefore in this case there is some tendency to adopt beliefs 
 which purely cognitive processes might not confirm ; i. e. there is 
 a possibility of a real non-cognitive influence on cognition. But in a 
 theoretical activity, unless a preconceived opinion is to be supported 
 
Chap. VII] Meaning of ^Action' 245 
 
 is the sole test and instrument of selective thinking. How 
 ' action ' operates, would be the further question, to which 
 Logic would be the answer. 
 
 If, on the other hand, action were taken in the sense of the 
 production of change in the external world, we should return 
 quite a different answer. We should say that the influence 
 of practical needs was a diminishing factor as the content 
 of systematic knowledge increased.* We should point out 
 that when thought has become complex, action on the external 
 world is to it as sensation is to science, a condition which is 
 little more than negative ; something, disagreement with 
 which demands more or less modification of the discrepant 
 thought, but any given agreement with which carries us but 
 a very little way towards truth. We should further urge 
 that the much talked of ' social endorsement ', as applied to 
 systematic ideas, has no existence. This is a very important 
 point in its practical bearing. Social endorsement does apply 
 roughly to habits of action. But to cognitive ideas, to the 
 actual content of inventions, and to theories, as such, it has 
 no application, only touching them in one or two points out 
 of thousands ; and to suppose otherwise is a very mischievous 
 superstition.^ It is a transference of the ideal postulate 
 of reason, that all valid judgment is valid for all intelligence, 
 to the de facto social consciousness, to which it applies only 
 in grades so contingent and varying as to be of no selec- 
 tive value whatever. The leading ideas of society, so far as 
 they can be conjectured from their expression, are always in 
 
 (which is an aberration from the theoretical consciousness), the end to 
 be obtained is not given, but is itself a conclusion to be constructed. It 
 therefore involves ipso facto a modification of the beliefs ancillary to 
 it, and the dangerous primacy of action over reason is not confirmed bj- 
 this instance. 
 
 * Mr. Stout in his Manual seems to me perfectly clear on this point ; 
 and to be wholly free from the ambiguity whether thought is made true 
 by being socially and practically selected, which I find in others. 
 
 '' I hope I shall not annoy a friend who conversed with me in the 
 U.S.A., in 1892, if I make use of his observation to me : ' Sir, the people 
 of these States have endorsed the philosophy of Mr. Herbert Spencer. ' 
 The example seemed too apposite to be neglected, as showing the 
 laxity with which a rough coincidence in one or two points is construed 
 as an ' endorsement '. 
 
246 Limits of a Genetic Theory of Logic fBooKii 
 
 arrear of the truth known to experts, and more especially 
 
 are discrepant with its own habits of action, which do 
 
 represent in a rough and unorganised form the external 
 
 needs of life.* 
 
 The exclusive importance attached to action on the external 
 
 world, and to social endorsement, even as influences on the 
 
 history of opinion, is, I hold, a mere paradox, unsupported 
 
 by facts. The subordination of the vast cognitive systems 
 
 and interests of mankind {which have, it must be remembered, 
 
 their own relations, dictated by cognitive needs, with the 
 
 ' external world ' or sense-perception) to the test of action in 
 
 the narrower sense of material external change, I believe to 
 
 be simply an elementary blunder. If, on the other hand, we 
 
 are only asked to call these interests and systems ' practical ', 
 
 as Aristotle carefully pointed out that they are, in virtue of 
 
 their inherent conativeness, we are asserting, I take it, the 
 
 contradictory of Pragmatism,^ but are returning to obvious 
 
 truths.'' 
 
 The ft- And when we raise the whole question of Pragmatism, 
 
 Making of j g ^g j understand, not ' How do we come to think something ? ' 
 Truth. r 1 • 1. 
 
 but ' What tests or makes its truth ? the idea of selection by 
 
 social endorsement, or by success in producing change in 
 
 the external world, loses all claim to consideration, except as 
 
 involving agreement with sense perception, which is provided 
 
 by cognitive activities in a much more adequate form. As 
 
 we have seen, nearly the whole of cognition is simply untouched 
 
 by action on the external world. In such action itself the 
 
 outward change effected is but a minor part, from which, as 
 
 we know, e. g. in all ethical considerations, it is impossible 
 
 with certainty to understand a man's mind ; and when 
 
 ^ e. g. T. H. Green usually agreed with J. S. Mill on questions of public 
 policy, though on all theoretical matters their minds were diametrically 
 opposed. This is possible, just because theoretical ideas, even of social 
 matters, have so very little of their content in contact with practice. 
 
 '' Because Pragmatism says, as I understand, that the only ends of 
 action are those which consist in change wrought upon the external 
 world, and that, to these, cognition is a means. For me, cognition, as 
 a harmony in our experience, has the character of an end of action, 
 though not the whole end. But external change is never an end. 
 
 *■ See Stewart, Notes on Aristotle's Ethics, 1098, a 3, and citation from 
 the Politics. 
 
Chap. VII] Selection makes Truth ? 247 
 
 we come to the great cognitive systems the prerogative of 
 such action vanishes altogether. Indeed, there is but one 
 criterion of truth, and that is, a fuller systematic cognition of 
 the content whose truth is in question. No history of opinion, 
 no formation of a platform, no idiosyncrasies of mental 
 organisation, can come into court when the question of truth is 
 raised. Then we have to do with nothing but the systematic 
 necessity of knowledge and the fact that fuller cognition can 
 compel every false judgment to expose itself as flat self- 
 contradiction. 
 
 Now the advocates of Genetic Logic seem to me to mean 
 that selection by social and practical needs not merely accounts 
 for our holding opinions, but also constitutes their truth or 
 falsehood. If so, then, as the problem opens out, we have the 
 whole of Pragmatism on our hands, and are, as I hold, beyond 
 the limits of legitimate genetic explanation. Grant, e.g. for 
 the sake of argument, that the unity of consciousness first 
 appeared in practical action in the narrower sense given above 
 (as it must have done if there was a time when consciousness 
 was entirely ' practical ' in its aim), or that it is motor in its 
 nature, or that it appears in some sort of general sensory 
 process. All that is interesting in the history of opinion, but 
 has no bearing on the logical value of such unity. This is 
 only to be discovered by an analysis of the part played by it 
 in the organisation of experience so as to avoid self-anni- 
 hilation by self-contradiction. It is an old story ; granting 
 (what is not true) that we need not play the game, yet if we 
 sit down to it we must observe the rules. If we are asked, 
 Why must we ? there is no answer but to show by analysis 
 in any given case that in trying to evade them we are dis- 
 guisedly throwing up our hand. I can imagine its being replied, 
 ' But you say that A.B.'s rules and platform are got by his 
 history and education ; then surely his truth is so too.' The 
 answer is that his rules and platform are an imperfect apprecia- 
 tion of the rules and platform, and cannot stand against 
 another, in him or outside him, which more nearly approaches 
 them, and therefore is able to exhibit his as self-contradictory. 
 His knowledge, or rather opinion, qua his, may be compared 
 to his body, a de facto structure, accounted for by accident 
 
248 Limits of a Genetic Theory of Logic [Book ii 
 
 and selection as well as nutrition and correlation. But his 
 knowledge qua knowledge may be compared with the work 
 his body is now capable of as a machine — a test to which his 
 genesis has nothing whatever to say. Truth is the most 
 organised organisation of reality in the medium of judgment ; 
 our history may excuse our failures in it, but cannot make 
 them successes. 
 
 Views like this suggest to some thinkers the idea of ' the 
 mind, for no reason, and by no regular processes, making 
 its truth what it will ' ; or of ' the essential mysticism of a 
 priori formahsm which prevailed before the rise of the genetic 
 point of view '. 
 
 This again is an old story. The very error with which I am 
 charged appears to me to be merely in the mind of my anta- 
 gonist. The whole antagonism of principle between classical 
 and modern logic ; the whole conception of a modern develop- 
 ment of the genetic point of view, considered as any- 
 thing which affects the nature and criterion of truth ; the 
 whole idea of ' thought in itself ' as opposed to the nature of 
 the real in cognition — all this appears to me to be the 
 merest mare's nest. The truth of anything is for me 
 simply its fullest nature so far as expressible in judgment, 
 organised, as the fullest nature must be, so as to avoid 
 diminution by the contradiction of its parts. What I deny is, 
 not that thought is the expression of organised reality, but 
 that the organisation of reality is confined to the production 
 of material change in things. The nature of things is both 
 general and special, and besides its more general and formal 
 characteristics, there are all sorts of grades and variations 
 as we push deeper and deeper into the heart of complex 
 individuality. These, as found by analysis, form respectively 
 the more abstract and more concrete elements of Logic. 
 But obviously all of them contain and confirm the general 
 nature of truth. 
 
 Why should not the universal ' be a mental experience 
 which has for its physical counterpart the synergy of adapted 
 action ' ? To me the answer seems simple — because there 
 is very little thought, proportionately speaking, to which 
 there is any adapted action, in the sense of external material 
 
Chap. VII] The Efids of Action 249 
 
 change, to correspond. I have said that I think that unity very 
 likely first showed itself in adapted action. But no thought, 
 probably, ever had its content exhausted in the adaptation 
 of external action ; no thought of a cultured mind can ever 
 be so exhausted to-day, even in the most practical of activities ; 
 and a very great part of life, a part which even economically 
 and industrially is an immense and commanding interest in 
 the world, has no end in external adapted action at all, but 
 on the contrary uses and transforms such action by making 
 it its means. A great scientific laboratory, for example, has 
 not its imity in a material operation to be produced ; its 
 actions have their unity in a cognition to be attained. The 
 same point is very strikingly shown in the enornious material 
 activities of a Wagner or Handel festival ; whose whole 
 practical business has for its determining purpose the produc- 
 tion of a harmony in minds, of the same general (not specific) 
 nature as a cognitive state. The harmony is the end ; the 
 ' action ' is the means. 
 
 The formation of new reality, as a bona fide addition to the 
 universe of what was not in it before, seems to me a contra- 
 diction in terms. But the discovery of reality new to us, 
 and the adaptation of intelligence to it, is surely a fact which 
 no one has ever denied. And what we call the discovery of 
 reality, the coming to take part in it, as for example by 
 education a finite mind must at some moment begin to — 
 accepting its burden as part of the experience we have to 
 work out^ — all this is not simply a finding of something pre- 
 existent. It is an element, an appearance, of the tension by 
 which something maintains itself in ultimate reality ; an 
 element or appearance without which the self-maintenance 
 could not be complete. There are not two worlds, an original 
 which pre-exists, and a copy which we make according to our 
 discoveries of the first. When we discover, we neither add 
 to the universe nor repeat it. We simply play our part, 
 which as we are finite, has a beginning and an ending, in its 
 self-maintenance. 
 
 Now if this distinction would satisfy the genetic point of 
 view, I think we might come to terms. But if that view 
 means a that new reality is created in the sense of being 
 
250 Limits of a Genetic Theory of Logic [Bookii 
 
 actually added to the universe by no continuous self-main- 
 tenance or logical process, and not created in the sense of being 
 discovered as above explained, by entering into its act of 
 continuous self -creation, and ^ that action on the external 
 world, and social selection, are the determinants and criteria 
 of truth, then I am afraid there can be no reconciliation 
 between us.^ 
 
 * See Bradley Mind 79, 323 if. where he urges that 'My act never is 
 creative ' (p. 329). I take it that he does not deny that the universe, 
 as a life, maintains itself in some degree through my act. He only 
 denies, I gather, that my act brings something new into the nature of 
 the universe as a whole. 
 
CHAPTER VIII 
 
 The above Theory of Judgment in relation to 
 ' Absolutism ' 
 
 I, A theory of Judgment must be criticised on its own Our 
 
 merits. Still, it would point to some defect in such a theory, Theory 
 
 ^ . . -' preju- 
 
 if , without the strongest possible reason, it should tie us down diced ? 
 
 ah initio to an ulterior metaphysical doctrine. 
 
 Judgment, we may say, should be an instrument of asserting 
 whatever we want to assert. If it trammels us in our beliefs, 
 we must surely be interpreting it wrong. 
 
 Therefore I understand it to be an attack on the theory of 
 Judgment which, having originated elsewhere, is in the main 
 adopted in this work, when we are told by distinguished 
 writers ^ that it by itself ^ makes necessary the doctrine of 
 Absolutism. The attack is primarily indeed addressed to 
 reveal the slightness of the foundation of the latter doctrine ; 
 but I take it that its suggestion is double-edged, and might be 
 briefly rendered thus : ' Your logical theory is a caprice which 
 is enough by itself to force 3'ou to Absolutism, and will not 
 let you say what you mean. Your Absolutism is a meta- 
 physical doctrine founded on little or nothing beyond this 
 logical caprice.' My aim in this chapter, as befits a logical 
 treatise, is to combat the first of these two suggestions. But 
 so far as the ' by itself ' is concerned, this cannot be done with- 
 out reference to the positive grounds which force the theory 
 of Judgment to define itself in favour of Absolutism. And 
 therefore to indicate the reasons for the latter doctrine, though 
 strictly belonging to metaphysics, also becomes relevant here. 
 
 The criticism runs thus : If every judgment in ultimate 
 analysis qualifies an existing reality by an abstract universal, 
 
 '^ Mr. Russell, Philosophy of Leibniz, p. 15, and Principles of 
 Mathematics, p. 448 ; Professor Stout, Aristotelian Proceedings, 1902-3, 
 p. 7 ; Professor A. E. Taylor, ibid., 1908-9, pp. 202-5. 
 
 ^ These words, ' by itself,' indicate a principal feature of the criticism 
 in the sense in which I desire to repel it. 
 
252 Judgment in Relation to ^Absolutism' [Book 11 
 
 it is impossible to arrive at a pliiralitj^ of individuals which 
 can be ultimate subjects of predication, because no combination 
 of abstract universals can confer the uniqueness * which alone 
 distinguishes an individual. There can therefore be but one 
 ultimate Individual to which all predicates must belong ; and 
 this doctrine is Absolutism. 
 
 On this basis there are two charges against our theory of 
 Judgment, First, that its consequent, the doctrine of Abso- 
 lutism, is false, and therefore the antecedent, the theory of 
 Judgment, must be false also. That is, there are many ultimate 
 subjects of predicates, and a theory which involves the denial 
 of this must fail. 
 
 Secondly, in any case the theory of Judgment binds us 
 from the beginning to a certain metaphysical view, which is 
 an unfair and improper use to make of a logical caprice, or, let 
 us say, of a logical analj^sis of the mere form of assertion. 
 No finite J- The Set of facts Upon which the former charge is supported, 
 real self- begins, as I understand, with the necessity of recognising real 
 pluralities of terms in logic and in mathematics. From this 
 fact, as I read the argument,^ is inferred, what is not included 
 in it as a fact, the existence of a plurality of substances of 
 which, on the strength of an appeal to our private experience, 
 the self is taken to be the principal example. And the exis- 
 tence of such true substances is also independently affirmed. 
 By substance is meant something which can only be a subject 
 and never a predicate, and which is a uniquely individual 
 existent, so far independent that as a part or element it is 
 no less individually real than the whole, while the whole is 
 no less individually real than the parts. ° 
 
 Now the doctrine of a single Individual Reality rests on 
 the demonstration that no finite individuals are self-complete 
 and self-contained, and that therefore none such can be self- 
 existing substances, or irreducible subjects of predication.'' 
 
 '^ See Professor Stout, loc. cit. 
 
 '' Taylor, loc. cit. It is very noticeable that this fact is not taken as 
 itself including the existence of a plurality of substances ; so that prima 
 facie it is a proof that you can quite successfully work with a plurality 
 of terms which have no claim to be substances. " Ibid., pp. 208-9. 
 
 '^ Cf. Bradley in Mind, 74, p. 160, which I saw first after this passage 
 was written. 
 
Chap. VIII] Degrees of Substantiality 253 
 
 I suppose that every discussion of substance to-day must 
 start from the position which Lotze has made familiar ; "■ 
 that to call anything a substance must indicate its mode of 
 behaviour, and not an occult somewhat presumed to be in- 
 herent in it. From such a point of departure we come at 
 once to the position that substantiality, like individuality, 
 is a matter of degree. No finite real is wholly independent and 
 self-existent ; none, that is to say, when taken as a subject, 
 can be concerned in judgments which are completely true 
 either regarding its predicates or regarding its relations with 
 other subjects.'' If this is so — and even the argument 
 which I am disputing admits and maintains it *= — there is no 
 finite real which is in the full sense a substance. No judgment 
 in which such a real stands as subject or term can ultimately 
 be true ; the connections alleged about it must either be too 
 much or too little. 
 
 I must explain that to deny the self-existence of any fjnite 
 real, is not to assert that Reality could be complete without 
 it. Nothing is self -existent, but nothing is non-contributory. 
 
 ii. The above argmnent is merely carried into detail in the Degrees 
 doctrine of degrees of individuality. Tliis, if we start from vijuality. 
 Lotze 's position, is indisputable ; and is over and over agahi 
 asserted both by implication and in so many words in the 
 argument under discussion . ^ There are terms, we saw it admit, 
 which are not substances ; and when we come to substances, 
 it is granted that the finite self has less individuality than the 
 social whole, which nevertheless most people would not admit 
 to be a spiritual substance at all.^ And in fact, no finite 
 individucil is self-contained, self -consistent, or self-dependent ; 
 all finite individuals differ in their degrees of these charac- 
 teristics. This seems to me to be one of the truths which 
 are accepted without being believed. I do not think that it is 
 
 "■ Metaphysics, Eng. Trans., p. 76. ^ See i. 206 flf. above. 
 
 <= Taylor, loc. cit., and Stout, Ar. Proc, p. 21 ; and cp. Bradley, 
 Appearance and Reality, in the arguments against Pluralism, pp. 141 -3 
 and 607. 
 
 ^ e.g. p. 211, 'we might draw a distinction here between individual 
 substances of higher and lower orders.' 
 
 ® I cannot reconcile this with the requirement that the element is to 
 be as real as the whole, and vice versa, ibid,, p. 208. 
 
254 J lodgment in Relation to ' Absolutism ' [Book ii 
 
 or can be seriously disputed on philosophical grounds. All 
 the distinctions which philosophy takes account of between 
 higher and lower grades of life and experience come back to 
 this. Any logical or metaphysical system is enough to show 
 how the positive value of the law of non-contradiction 
 embodies itself in such gradations ; and the argument of 
 Mr. Bradley's Appearance and Reality is, as I understand it, 
 the same in principle throughout. Yet if this principle were 
 not only accepted but believed there would surely be at once 
 an end of pluralism and of the multitude of self-existent 
 substances. If all finite subjects have in various degrees their 
 reality outside them, it is idle to speak of any of them as 
 substances in the sense before us. As a striking example of 
 gradation, we may note how the series of individuals passes 
 downwards into cases where individuality, and with it reality, 
 touch a minimum, and fade into the extremes of self-contra- 
 diction and self-ahenation, as in various grades of the animal 
 mind, or in the terms, such as point or atom, for which it is 
 not claimed that they are substances. Confront an upholder 
 of selves as self-existent substances with a brood of new- 
 hatched chickens, and ask him whether these are individual 
 substances or not. They are certainly unique by their relation 
 to presentation ; but this, as we shall see, is a feature actually 
 opposed to true individuality. If, further, they are in be- 
 haviour and capacities true individual substances, or if they 
 are not, the answer is equally fatal to the substance-theory. 
 In the former case an enormous difference of degree is admitted 
 within the series, so great as to destroy the value of the 
 self-existence claimed for its members ; in the latter case 
 a distinction of kind is admitted between grades of spiritual 
 beings which cannot be other than arbitrary. 
 Experi- iii. The appeal to our experience of ourselves is of all 
 self^fatal things the most fatal to a doctrine of self-existent substances, 
 to doc- The evidence is so abounding that it is hard to know where 
 sub- ^^ begin. Perhaps it is enough to say that no doctrine of 
 
 stances, a monadic self, in the sense of a self which is single and sub- 
 stantial, has ever been able to deal with the self as it actually 
 exists ; * Plato's least of all, as he constantly admits and 
 * Cf. Appearance and Reality, p. 86 ff. 
 
Chap. VIII] The mouadic soul impossible 255 
 
 maintains. What we miss in him, what would have taken him 
 fairly beyond the doctrine of the monadic soul, which hampers 
 him as he himself points out,* is the conclusion which lies so 
 near him, that the terrestrial course of the soul is the soul's 
 opportunity for self-perfection, and that when struggling with 
 multiplicity it has not fallen, but is for the first time (as com- 
 pared with its self-existent purity) in the way to rise. The 
 logic of his system in fact demands this point of view, and it 
 might be said to be implicit in his doctrine of the earthly 
 life ; ^ but I cannot say that he has anywhere to my knowledge 
 expressed it. Some kind of unification at some stage of being, 
 no doubt we v/ith Plato assume as inevitable. But what 
 kind of unification, and at what stage of being, whether or 
 not within the limits of an individuality that can be called 
 ours — ^this is altogether a different question. Nothing in our 
 experience seems to warrant or even to suggest it, while our 
 moments of fullest life seem most distinctly to deny it. That 
 our self, or will, or mind, at its best, is not the self or will or 
 mind of a unique individual, bounded, so to speak, by our 
 normal circumference, is the one definite point on which 
 spiritual experience seems unambiguous. "^ And in the relation 
 of the individual to society, described as before referred to, 
 we have this admitted ; and, as its consequence, that no 
 individual which has a foreign environment can act in a way 
 purely self -expressive. What kind of individuality is that, 
 which cannot express itself in its acts ? It is to me quite 
 astonishing that an appeal in favour of a doctrine of inde- 
 pendent substances should be made on the ground of our 
 experience of ourselves. What all great masters of life have 
 felt this to reveal has been a seeking on the part of the self 
 for its own reality, which carries it into something beyond. 
 And social experience, like that of art, is absolutely conclusive 
 on this point. 
 
 iv. But a logical objection is raised against an apparent Difficulty 
 subject being in any sense a ' predicate '^ bdnS'S 
 
 * Rep., ix. end and x. 6ii C. dicate. 
 
 '' As the need and value of the Fall is in Christianity. 
 
 ° See Bradley's Ethical Studies, p. 288. 
 
 •^ It is noticeable that Mr. Bradley, in the Principles of Logic, spoke 
 of judgments about non-temporal subjects as a class of singular 
 
256 Judgment in Relation to 'Absolutism ' [Book ii 
 
 Class Pre- It is urged that to predicate an individual subject of the 
 ica ion. ^jijgQjy^g j^g^g ^]^g self-contradictory result that the Absolute 
 is included, so to speak, in that individual as a class of one ; 
 in other words, is identified with that individual. 
 
 Now the connection of Subject and Predicate in judgment 
 has essentially nothing to do with the inclusion of the subject S 
 in a class P. Judgments which are so construed * mean some- 
 thing else, and are in no case the equivalent of assertions of 
 class inclusion. And the importance of this is, that though 
 in some cases class inclusion is inferrible from (in no case 
 equivalent to) them, yet, following the straight line of what 
 judgment really means, not only do we never at all deal with 
 class as such, but when we come to the point where Logic 
 deals with the universal in its true form, we leave the pre- 
 conception of class behind us for good and all. From the 
 point where the development of the judgment branches into 
 the assertion of differences within individuals (the Singular 
 judgment with proper name for subject ^) on the one hand, 
 and the abstract nexus of different contents (the ' hypothetical ' 
 judgment) on the other, the predicate has nothing more to do 
 with class significance. The meaning which has really underlahi 
 all its forms, the holding differences together within a whole 
 of identity, becomes sole and unmistakable. 
 
 The real significance of the Individual Judgment is revealed 
 when it has developed into the Disjunctive judgment, in 
 which you have a significant individual subject-system set 
 out in the subordinate actual forms which it takes under 
 
 judgments in which the true categorical, undiscoverable elsewhere, might 
 conceivably be found. He gave as an example among others, ' The 
 soul is a substance.' (Principles of Logic, c. 2, s. 7, 41, 81). I should 
 suppose that the criticism of Appearance and Reality is hostile to the 
 claims of these judgments to express metaphysical truth, although 
 they might still be recognised as forming a separate class in Logic. 
 
 * Bradley's Logic, pp. 162-8. 
 
 ^ It may be said ' But you can treat this as a class judgment ', as in 
 the old type ' Socrates is mortal '. The fact is, you can play almost 
 any trick with the forms of proposition, because they have so much 
 in common. But what such a judgment form really challenges us to do, 
 is to develope the content of Socrates as an individual whole containing 
 connected differences. And so the predicates should be regarded as 
 elements entering into him, just as his acts are. 
 
Chap. VIII] Individual as Predicate 257 
 
 different conditions. ' When the Absolute tumbles into the 
 water it becomes a fish ; ' so in asserting itself under this or 
 that condition of its own imposing it becomes Mr. Smith or 
 Mr. Jones. Why not ? No true relation of membership 
 within a concrete universal can be expressed in a class- 
 predication, or in any judgment to which such a predication 
 is equivalent. And no judgment, strictly speaking, expresses 
 by its form a class-predication at all. 
 
 V. It is said' that a predicate is always universal (meaning Imper- 
 abstract universal), and that therefore an individual can ^^^^^1"*^' 
 never be a predicate, even of the Absolute. can be 
 
 First, it should be remembered that the individual is the ^ionai 
 highest and only true form of the universal, and if a member Predi- 
 of a system, has in it the nature of the whole to which it 
 belongs. It can, therefore, as has just been pointed out, be 
 a predicate of that whole, if the conditions under which it • 
 becomes so are specified. 
 
 Secondly ; no doubt a wholly self-complete and self-con- 
 tained individual could not be a predicate of any other in- 
 dividual. No conditions could be assigned under which it 
 would be so. They would be two perfect worlds, and there 
 could not be two perfect worlds either side by side or in any 
 dependence on each other.* 
 
 But we are free from all difficulty on that head, for it is 
 amply clear and confessed that our individuals are finite and 
 imperfect. They are, as we saw,^ members within a whole 
 on which they are dependent for their very self-hood and self- 
 identity. Such individuals can certainly be predicates, in the 
 sense in which members of a whole are conditionally predicable 
 of the whole. The nature of an organism, starting as an equi- 
 potential whole, may express itself, in elements conditioned by 
 being at one end of the body, as a head, in those conditioned 
 by being at the other end, as a tail, or according to other 
 conditions as eye or gills. Of course these organs are predicates 
 of the organism as a whole, subject to the conditions which 
 have differentiated them. 
 
 But there is something more. Individuals which like all 
 
 finite individuals fall short of true Individuality are, as we 
 
 * Appearance and Reality, chap, xx end. '' Above, 254-5. 
 
 1337-2 S 
 
258 Judgment in Relation to ' Absolutism ' [Book ii 
 
 have seen, not, as they stand, terms in true judgments.^ They 
 have no power to resist reduction when considered in the 
 light of the demands of reaHty ; and are in ultimate analysis 
 connections of content within the real individual to which 
 they belong.^ And this becomes important in the present 
 case ; for though no one doubts that the self has a degree of 
 individuality, yet its real character consists not in individuality 
 but in a claim to it, which may or may not, so far as a first 
 appearance can show, be realisable consistently with the exist- 
 ing form and arrangement of the self. That the latter is the 
 case in a considerable degree, i.e. that the self, in order to 
 become anything like a true individual, must be very greatly 
 transformed from what we are aware of it as being, I hold to 
 be an obvious truth, guaranteed by aU experience and by 
 every serious religious creed and philosophical belief." 
 
 I repeat and summarise ; a member in a whole can be 
 predicated, under a condition, of that whole which is his 
 subject."^ And further, an imperfect individual is according 
 to the degree of his imperfection a subject whose connection 
 with his predicates can only be expressed in judgments which 
 are untrue ; and to bring his nature into harmony with the 
 truth of the whole it must be transmuted and rearranged so 
 that it can be expressed as a true connection within the 
 content of the whole. It is plain from the argument before 
 us that this is so. The kind of individual with which we are 
 dealing is unable to express his own nature in his own be- 
 haviour. He is, in Spinoza's language, very largely ' passive ' ; 
 the acts ascribed to him are not his own. And therefore 
 judgments in which he appears as a subject are not true. 
 
 Take as an extreme case the minds of animals, of which 
 we spoke aboye. Are they not best treated, most adequately 
 
 * See Mind, 74, loc. cit., and above p. 254. 
 •^ See Principles of Logic, p. 93. 
 
 ° It seems to me clear that Plato, even if he holds the soul to be eternal, 
 does not think the same of the self. 
 
 * Professor Stout, Ar. Proc, loc. cit., p. 21, seems to me to take an 
 example" of part and part for a relation of whole and part. The roof 
 or pillar holds in each the nature of the cathedral, though not so directly 
 that of each other. Certainly each of these is predicable, condition- 
 ally, of the cathedral, as an eye is of the organism. 
 
Chap. VIII] The Theory of Judgment not biassed 259 
 
 treated, as streams or eddies of mind in which some temporary 
 combination, some minor aspect or centre within the universe 
 demands transitory expression, in cases where the needs and 
 conditions do not exist which give rise to an apparently 
 individual subject ? No one, who has loved a dog, can doubt 
 that its mind has a value of the same kind, if remotely 
 the same, as his own.* No one, on the other hand, can well 
 suppose that it has the distinctness and organisation of content 
 which we should expect of anything that is to have a permanent 
 place of its own as a separate member of the system of reality. 
 Surely the solution must be of the general type Which conceives 
 this partial mind as contributing a character, some intensi- 
 fication of loyalty and affection, to some greater existence,'' 
 but not claiming in itself to be a unique differentiation of 
 the real. 
 
 vi. So far then it seems clear that there are plenty of good Absolu- 
 grounds, akin to but not dependent on the theory of judgment Q^Tts^^*^ 
 in question, for presuming that there is ultimately but one own sub- 
 true individual Real, of which all contents that can be affirmed founds 
 in judgments are ultimately predicates. In fact it would 
 almost appear that this is not denied.*^ And if so we have 
 only to establish, in answer to the second charge, that our 
 theory of judgment lets one say, for ordinary purposes, 
 what one likes about ' individuals ' as subjects of judgments, 
 and about other pluralities of terms. 
 
 2. And passing here to the second charge (p. 252), we recall Freedom 
 that this is a point which has been greatly misapprehended, ment on 
 
 i. For all current purposes of logical utterance — and we have this 
 seen that the criticism itself is at a level which concerns no- 
 thing more, nothing really ultimate — it is the doctrine of a sole 
 self-existent subject which has first given complete freedom to 
 the judgment. For, in view of it, the traditional theory of a 
 
 * Cp. Bradley, Mind, 72, 508. 
 
 *" Compare the well-known and attractive doctrine of the final 
 annihilation of the wicked only, which in its modern form consists in 
 conceiving an individual participation in eternity as something which 
 is not for every mind, but perhaps for some. 
 
 "= Professor Stout, loc. cit., seems to me to affirm a plurality of 
 ultimate subjects, but to admit that they are not ultimately self- 
 existent. 
 
 S2 
 
26o Judgment in Relation to ^Absolutism ' [Book n 
 
 Gram- proposition divided into S and P becomes a mere superstition.^ 
 ™p*re- ^^ permits the judgment to be formulated as any complex 
 jected. of terms and relations, any arrangement of a plurality of 
 apparent subjects, as well as of a substantive and adjective 
 standing in the regular scheme as grammatical subject and 
 predicate. Ultimately all this can make no difference ; for 
 the one part of the judgment is not judged of the other ; the 
 whole complex, grammatical S P and all, is predicated of the 
 ultimate Reality. Thus one shape of judgment is as good as 
 another, except that the most natural and convenient is the 
 best. No one has resisted more strenuously the folly of forcing 
 every assertion into the S P schema than believers in the sole 
 Real. One may use the form of the common subject, as the 
 present writer has urged, ^ to express the condition or limitation 
 under which the ultimate Real accepts the predicated content. 
 But this is not what the common S P schema takes itself to 
 mean, and is not intended for a defence of it. 
 
 Thus I infer that no objection lies against the doctrine 
 
 of a sole ultimate subject from any tendency to interfere 
 
 with the freedom of the judgment-form, which this doctrine, 
 
 more than any other, has tended to establish. 
 
 Indi- ii. But there is a last intensification of this objection to 
 
 deraandr ^^^^ with. It is contended that whatever may be the fact as 
 
 Designa- to what we commonly call subordinate individuals, whethei 
 
 mistake ^" reality they are genuine subjects or not, our theory does 
 
 not leave the question open, but cuts away ab initio all 
 
 possibility of distinguishing them as individuals. For it 
 
 restricts us to universal predicates, and universal predicates 
 
 can never, by any complication of them, distinguish and define 
 
 individual subjects. This can be done, and can only be done, 
 
 by contact with immediate experience.'' This is to say, that 
 
 Individuality rests upon designation, to which a predicate 
 
 can never be equivalent, for it never confines us to a * this ' ; 
 
 and therefore an individual can never be defined bypredicates. 
 
 And I reply at once that Individuality cannot possibly rest 
 
 on designation ; and that what does so rest is not Individuality 
 
 " See Principles of Logic, p. 23, and above, i, p. y6. 
 
 ^ See above, i. 3, 75-7. 
 
 " Stout, Ar. Proc, loc. cit., 19-24 ; cp. Bradley, Mind, 72. 500. 
 
Chap. VIII] The Individual Definable 261 
 
 but Particularism ; '^ the very sign of negation and imper- 
 fection, which, wherever it applies, is the proof pro tanto of 
 the absence of Individuality. But yet the point is in a sense 
 perfectly sound. Our individuals, so far as imperfect, do 
 depend on designation for the recognition of their uniqueness. 
 And this is a conclusive proof that they are not and cannot 
 be genuine individuals. I cannot understand why Professor 
 Stout calls them ultimate when, as it seems to me, he explicitly 
 admits that they are not.*" For designation just excludes self- 
 containedness and self-completion, and that uniqueness which 
 comes of filling a definite place in an ordered whole. ° It is 
 tending, I note, to become a commonplace that the indivi- 
 dual can only be designated and cannot be defined. But in 
 truth, ultimately, the distinction should be reversed. A true 
 individual cannot be designated, but it alone, and nothing 
 else, can be defined. Designation means pointing as with 
 the finger ; miite identification ah extra ; but the true 
 
 * Bradley, Principles of Logic, 76-7 ; Mind, 72, loc. cit., and 74. 167-8. 
 
 *> Ar. Proc, loc. cit., p. 21. I cannot think that the argument of 
 p. 23 successfully impeaches Mr. Bradley's criticism of the analytic judg- 
 ment of sense. 
 
 ° No doubt (Mind, loc. cit.) it is impossible to recover, on the level of 
 ideas, the uniqueness belonging to mere designation, the mute and 
 negative ' this not that '. Objections may always be raised such as 
 Mr. Bradley raises in the passage referred to. You cannot specify 
 a partial and imperfect individual by conditions which ensure that he 
 is unique in the universe. But this is not because he is individual, but 
 because he is imperfectly individual. And so far as an experience 
 possesses individuality — so far as it has a complete and self-contained 
 nature, positive and real, — so far it has uniqueness because it includes 
 the conditions which protect it against repetition by assigning its place 
 in the universe. That these conditions cannot be complete when the 
 individual itself is partial and imperfect is only natural. But for all 
 that, in principle, uniqueness depends on completeness of explicit 
 conditions and not on designation, and thus we are intensifying and not 
 enfeebling it as we tend to complete the organisation of experience 
 through ideas. If a perfect individuality is not to be experienced in 
 the form of discursive thought, that is nothing surprising, and in no 
 way suggests that it may not be approachable through that form. . As 
 we have seen throughout, individuality varies pari passu with degree^. 
 of being and reality. It is altogether perverse to find in it the character 
 of the datum of mere contact, as of the undefinable. See Green, Prol., 
 sect. 194 and author's notice of G. E. Moore's Principia Ethica ; Mind, 
 xii. 259. 
 
262 Judgment in Relation to ' Absolutism ' [Book 11 
 
 individual, and any real so far as individual, identifies itself 
 not mutely but explicitly, and not ah extra, or negatively,* 
 but intrinsically, by what it has in itself. If about any element 
 you are able to urge that so far as we know there might be 
 another just the same, that is a sufficient proof that the first is 
 not genuinely individual. If it were, it would contain, in its 
 completeness, the reason why there could be no other beside 
 it. Uniqueness by designation, by mute contact with our 
 experience, is, we might say perhaps, formal.^ Uniqueness by 
 adequacy of content and absence of need or room for repetition 
 we might call material. In dealing with the imperfect elements 
 which meet us in our experience we have need of both ; but 
 nevertheless the predominance of the one or of the other 
 practically measures the whole distance, within our world, 
 between the poles of the unreal which is merely given, and the 
 real which is coherent and self- complete. 
 Doctrine iii. We have sufficiently seen then I hope, that [a) the 
 of uiti- theory of the sole ultimate subject does not stand by itself, 
 ' Subject ' as a logical caprice, in necessitating the theory of the Absolute, 
 philo^ but is the consequence of a comprehensive and well-supported 
 sophical philosophical attitude, and (6) that it does not, as a matter 
 fre^e!^^ of expression, forbid our common so-called individuals any 
 completeness that could be ascribed to them ; but that they 
 fall short only because they are incapable of receiving more, 
 and, in the higher forms of judgment are denied only a means 
 of distinction (the ' this '), which could not possibly be service- 
 able in establishing their individuality. 
 
 * i. e. by a mute discrimination against others. 
 
 ^ See i, 106 and 207 above on the relation of the Demonstrative to 
 the Universal Judgment. 
 
CHAPTER IX 
 
 Truth and Coherence 
 
 I. It seems worth while, for the reasons assigned in the Dis- 
 Preface, to restate at this point the general attitude of the ^^Q^j.f_ °^ 
 present work to the theory of truth, spon- 
 
 The main current doctrines on this matter have been con- j^'^ory 
 veniently designated in recent discussion as the theory of 
 Coherence and the theory of Correspondence respectively. I 
 should hardly have thought it necessary to explain that I 
 cannot for my own part conceive how the doctrine of Corres- 
 pondence can be adopted as a serious theory, were it not that 
 in an elaborate criticism * of the first edition of this work it 
 has been urged that I have myself adopted it.^ 
 
 The genetic theorists have discovered the failure of the 
 correspondence theory, and beheving some of us to be old- 
 fashioned, they attribute it to us and then attack it. But we 
 think, or at least, I think, that no logician really of the first 
 rank ever held it, and that our critics are belated in awaking 
 to its impossibility. However, whether the misconception 
 is my fault or my critic's, it will be well to make a short re- 
 statement of my view towards the close of so voluminous 
 a work. The details of the criticism will all, I think, settle 
 themselves if the radical misconception is explained. But I 
 
 * Cf. 'Bosanquet's Theory of Judgment.' Miss Thompson, Chicago 
 Decennial Publications, 1903. I may note that for myself I entirely 
 disclaim the epithet ' epistemological ' which Professor Dewey frequently 
 employs in his introductory essay. For I understand it to imply a 
 theory of cognition in which truth and reaUty are treated as external 
 to one another, in fact, some form of the correspondence theory. He 
 is indeed discussing Lotze and not any writer with whose views I am 
 in agreement. But I am not sure how far his criticism is meant to 
 stretch, and it is better to guard oneself. 
 
 *" Under all the circumstances, this supposition recalls to me a vulgar 
 story current in my youth, of a doctor who, finding himself unequal to 
 treating the patient's actual ailment, proposed to inoculate him with 
 a quite different malady, ' for,' he said, ' I'm death on that.' 
 
264 Truth and Coherence [Book 11 
 
 shall further take occasion to express my own interpretation of 
 
 the present position in the philosophical world, with reference 
 
 to logical theory, which offers certain highly suggestive 
 
 antitheses. 
 
 An Ex- i. I will say at once that there is just one expression in 
 
 wWch°" my book which in my opinion may have given some sort 
 
 might be of colour to what I must call my critic's fundamental error. 
 
 jjj ' It is the phrase in which I stated the relation of Reality, 
 
 as the subject to be defined, to thought as the process of 
 
 defining it. I said : * ' It is an essential of the act of judgment 
 
 that it always refers to a Reality which goes beyond and is 
 
 independent of the act itself.' Such an expression, taken by 
 
 itself, or in a treatise framed on wholly different lines from 
 
 the present one, would not have been inconsistent with a 
 
 conception of reality as an existent world external to our 
 
 thinking, in resemblance or dissimilarity to which lay the 
 
 truth or falsehood of our ideas. But in criticising a work 
 
 which takes for its watchword the saying that ' The truth 
 
 is the whole ', offering this as the solution of the difficulty 
 
 that a world outside thought cannot be laid hold of by thought, 
 
 it does seem to me a gratuitous misconception. And further, 
 
 I think it is one which not only every paragraph of general 
 
 theory, but still more the whole progress and structure of the 
 
 book disowns. The mere structure of the treatise is enough 
 
 to explain the expression. 
 
 Reality is independent of the Judgment in two senses. 
 There is, of course, an ultimate Reality ; a higher experience 
 than ours ; we must postulate that if we do not mean to accept 
 e.g. all individuals' worlds of experience as separate and 
 unconnected. When I speak of this Reality as independent 
 of our act of judgment, as it is in an enormous proportion, 
 I do not mean to exclude the truth that our judgment, in an 
 infinitesimal degree, contributes to sustain it, and forms an 
 element in its life. In this limited sense the two forms of 
 Reality are interdependent. But their interdependence is not 
 correspondence, and their independence is not that of original 
 and copy. 
 This Reality then shows itself in our world of experience 
 
 * i, 97' 
 
Chap. IX] ' Veritas norma sui ' 265 
 
 in a way which is independent of our act of judgment in a 
 second sense. For our immediate experience, our feeling, our 
 possession of a contact with a world, has individuality in a 
 mode which as a mode of experience * our judgment cannot 
 confer or originate, but can only attempt to restore by a 
 secondary process, when its unity is transcended. The contact 
 in feeling has existence and quality together, and primarily is 
 satisfactory and self-contained, though carrying a sense of 
 diversity which challenges analysis in judgment, but is as such 
 independent of interpretation through judgment. 
 
 We construct our world as an interpretation which attempts 
 to restore the unity which the real has lost by our making 
 its diversity explicit. This construction is our intellectual 
 world. It is a form of reality, possessing some of its characters ; 
 and there are other forms, higher and lower. But none of 
 them can be a world external to our thought and yet acting 
 as its standard. The thing is a contradiction in terms, not 
 because of the metaphor of externality, but because of the 
 vital autonomy of the thought system. 
 
 If we ask, how we know our interpretation to be true or 
 false, to possess or not to possess the character of reality, 
 so far as its discursive form allows, the answer comes from the 
 principle of non-contradiction, which is only another form 
 of words for the principle that the Truth is the whole. This 
 could easily be shown at length.'' The important point is that 
 the principle of non-contradiction is positive and constructive ; 
 its force cannot be evaded by a logical quietism, by sajdng 
 nothing. For you cannot get away from the world ; if you 
 try to say nothing you are in contradiction with a mass of 
 experience ; not with a presumed external world, but with 
 what enters into your own being ; and you leave it in contradic- 
 tion with itself. 
 
 ii. Our doctrine of truth is therefore wholly immanent. The 
 
 There is no external standard, and, of course, no possibility f^itenon 
 
 ' ' ... imma- 
 
 of applying it if there were one. The criterion " identifies itself nent. 
 
 * For its content is modifiable. See below, p. 297. 
 
 ** I hope to go over this ground in much greater detail in a forthcoming 
 work of a more metaphysical character. 
 
 " We have been warned that a criterion is properly a label, extraneous 
 to the character which it indicates. But any such criterion in highly 
 
266 Truth and Coherence [Bookii 
 
 absolutely with that imposed by the doctrine of coherence.* 
 And the structure and nisus of the treatise is a simple embodi- 
 ment of this principle. It is a progressive interpretation of 
 the ' this ' ; the contact with reality in which we possess 
 both existence and quality. It is an advance from one form 
 of individuality to another ; from individuality which has 
 never gone beyond itself to individuality which has experienced 
 contradiction and is being approximately restored as an 
 explicit system of non-contradictory content. It is a product 
 of the interest and purpose to explain all that you can ; to 
 push the explanation further and further in response to the 
 demand for removal of contradiction in the relative whole 
 of experience at every stage. This interest and purpose is 
 the clue pursued by the effort of judgment from beginning 
 to end. It is the special and distinctive cognitive interest. 
 And a treatise like the present endeavours to trace in its 
 genesis the system developed by the action of this interest 
 which is of course inclusive of all more special stimuli and 
 occasions. The whole interpretation, as referred to the 
 individuality that appears solid, but therefore only implicit, 
 in the ' this ', possesses the character of reality, viz. indivi- 
 duality ; not perfectly, but in the degree in which the form 
 of finite thought can achieve it.^ We know this by the- fact 
 that this character, the character of a systematic whole, is 
 the condition of our possessing a world of experience at aU. 
 If we let a contradiction stand, we possess so much the less 
 of reality. Something cancels something, and we are the 
 poorer and dissatisfied. 
 
 Truth its iii. Immanence is the absolute Condition of a theory of truth. 
 
 own test, j^ jg ^Yiis, that makes the fundamental contrast between the 
 coherence and the correspondence theory. As I said at 
 
 organised matters is a bad, i. e. highly fallible criterion. And it is well 
 to insist that in such matters the only sound criterion is the character 
 itself or some important element of it. 
 
 * See the author's Knowledge and Reality, p. 331 (publ. 1885), 
 for a criticism of the simile of the foundations of knowledge. This 
 criticism is always decisive of a writer's attitude to the correspondence 
 theory. Cf. Bradley, Mind, 71. 335. 
 
 '' Need I say that errors in the personal thought-process are expected 
 and admitted ? 
 
Chap. IX] De facto Correspondence 267 
 
 starting, truth is individual.^ This is only another formof words 
 for the principle of non-contradiction, the principle that the 
 truth is the whole, and the doctrine that coherence is the test 
 of truth and reality. Truth is then its own criterion. That 
 is to say, it can only be tested by the more of itself. Your 
 completest system at the moment cannot be further tested. 
 You can only test it further when you are in a position to make 
 it more complete. Then what interferes with its greater 
 completeness must go. 
 
 Is it necessary to say a word about comprehensiveness ? 
 Sometimes we are told that our criterion is mere formal con- 
 sistency. This can mean nothing but that the critic has not 
 thought the matter out to the bitter end. By coherence or 
 consistency we mean the consistency, so far as attainable, 
 of the whole body of experience with itself. Nothing less 
 would satisfy the law of individuality or the necessity of 
 non-contradiction. But in this interpretation of consistency 
 comprehensiveness is obviously included. 
 
 iv. One word more about correspondence. If an identical Not all 
 principle operates in different worlds, e.g. in the experiences gpo^jjence 
 
 of different spiritual beings, the products aie likely to corre- means 
 
 copying 
 spond. And I notice a tendency ^ to aid the process of mocu- 
 
 lating us with the malady which is not ours, by insisting on 
 
 this obvious truth. If the fundamental principle of reality 
 
 is operative in the sphere of finite thought, of course this 
 
 sphere will show a character that possesses certain common 
 
 features with those of other spheres or of the ultimate real. 
 
 But if correspondence,*' i.e. identity in certain characters of 
 
 two or more systems, must result, that is no argimient that 
 
 correspondence is the criterion for either system. If two men 
 
 add up a sum right and therefore the same, that does not 
 
 mean that the sums are right because they are the same, or 
 
 that one man has copied from the other. Of course, there is 
 
 a reality which is more than an individual's thought. There 
 
 is, at least, the thought of other individuals. And undoubtedly 
 
 these will correspond, i.e. will show a structure identical in 
 
 * i, p. 3 above. 
 
 ^ See even Joachim in The Nature of Truth, p. 174. 
 
 •^ On the nature of correspondence, see Essentials, p. 18. 
 
268 
 
 Truth and Coherence 
 
 [Book II 
 
 The 
 
 Logical 
 World 
 to-day. 
 
 ' Life, 
 ' Prac- 
 tice,' 
 ' Feeling, 
 
 The mis- 
 concep- 
 tion 
 which 
 governs 
 the move- 
 ment. 
 
 principle but different in details. But that is nothing against 
 the character of both being immanently determined. 
 
 I shall return in a later section to the question in what sense 
 the coherence theory fails. 
 
 2. I will now venture to state what I believe to be the 
 cause and tendency of the peculiar logical movement of 
 to-day. 
 
 i. It is plain that the last half century has brought to 
 philosophy in general a great revival of interest. This re- 
 ' vival has coincided with a marked increase of the tendency, 
 traceable in European thought ever since Rousseau, to empha- 
 sise the philosophical value of feeling, of practice and actioii 
 in the plainest meaning of the woids, and of what has come 
 to be called, in an almost technical sense, ' life ' and ' living '. 
 The movement has conceived itself as a sort of democratic 
 revolution in the things of the mind,* and is obviously con- 
 nected with the change of affairs in society and politics. A 
 supposed aristocracy of intellectualist principles is to be 
 dethroned. Truth is to become more vital, more accessible, 
 its touchstone more obvious and more easily applied. Life, 
 one may say, is to be substituted for thought as the central 
 object and impulse of philosophy. 
 
 All this has had and is having the usual effect of revolu- 
 tionary demands in philosophy.^ The new theorists are insist- 
 ing on something which was really vital in the older tradition, 
 and the result of their movement will probably be a certain 
 alteration of balance and emphasis in the formulation of that 
 tradition. One can hardly suppose that a movement so 
 widespread and so popular will bring with it no elements 
 of gain at all. If it brought nothing but its adherents' interest 
 in philosophy it would already have brought a good deal." 
 
 ii. But the movement itself, I am sure, is conducted under 
 a misapprehension. It has hold of something very partial 
 
 * Cp. the author's Philosophical Theory of the State, ed. 2, Introd. 
 Nietzsche represents perhaps the ' Saviour of Society ' who attends 
 upon some democratic mbvements. 
 
 '' Cf. the analysis p. 231 ff. above, of the relation of epochs of em- 
 piricism to the traditional distinctions of Logic. 
 
 " As will appear, I believe this to be far the greater part of the gain 
 it will bring. 
 
\ 
 
 Chap. IX] Place of Genetic Logic 269 
 
 and consequently sees, and, as I have pointed out, further 
 produces by its assiimptions, a fundamental opposition where 
 there is really nothing but a part unduly contrasted with 
 its whole. 
 
 Let us particularise. Genetic Logic, the treatment of 
 thought as a system or at least an aggregate of adaptations 
 evolved in response to the needs of practice, has in principle 
 adopted and popularised the coherence theory of truth. This 
 doctrine, being as we have seen a doctrine of immanence, is 
 essential to all vital philosophy and logic, and, to the best 
 of my belief, no other has in fact been held by any leader of 
 European thought from Plato downwards.* But by re- 
 stricting the coherence which is to be the standard to the 
 coherence of adaptation with external action, at first (as no 
 one can doubt) in the purely normal and everyday usage 
 of the latter term, it has on the one hand voiced a popular 
 demand, but on the other has precluded a real understanding 
 by itself of its own philosophical position. And so it strongly 
 tends, as we saw, to assume that in the older philosophy, 
 which it feels to be in some way its antithesis, the view opposed 
 in principle to its own, that of correspondence to an external 
 standard, must be the prevailing one. And it conducts its 
 controversy on this basis, reinforcing its attitude by utilising 
 another popular demand, that for actual individual endeavour 
 and modification of things, which it is unable to unite (the 
 great and ultimate test of a philosophy) with the belief in 
 a perfect and timeless real. And the completer form of its 
 own logical view, the coherence theory of truth, it is apt to 
 stigmatise as a mere formal consistency.'' 
 
 * See, for example, my remark on Aristotle, p. 224 above. I know 
 that this has been adversely criticised, but I believe that when we 
 consider the full meaning of apprehension by vovs as the sort of insight 
 which comes, for instance, by induction, my view will be seen to hold 
 good. Cp. for example, Burnet's Ethics of Aristotle, pp. xxxvii and 
 xlii. I may say in general that I should have guarded myself much 
 more emphatically against the correspondence theory if I had ever 
 imagined that it could by any mischance be imputed to me. 
 
 *> As I suggested above, the controversy is thrown completely askew 
 if you take Lotze as typical of philosophical Logic. The whole state- 
 ment of the issue, as based upon the contrast of thought in general 
 with reality in general (Dewey in Introductory Essays to Chicago 
 
270 Truth and Coherence [Book 11 
 
 Fallacies i"- Thus in a very able statement '^ of the contrasted 
 of Gene- positions of genetic and the older philosophical Logic, I seem 
 ' to myself to find three connected misconceptions at the very 
 basis of the whole representation. 
 
 First, there is Dualism. Thought is from the beginning 
 conceived in contrast to its occasions. It is taken as reflective, 
 as what arises now and again when we set ourselves consciously 
 to ' think '. That is to say, this is the limitation of the thought 
 with which the writer deals. Something called Constitutive 
 thought is mentioned in contrast with it ; but whether this is 
 simply the working thought by which we carry on unreflective 
 life, or some theoretical construction of a creative force in 
 the universe it seems impossible to tell. What is clear is this 
 much, that not merely the limitation of thought as a distinc- 
 tive form of reality which operates through ideas, but the 
 special limitation of ' pale reflective thought ' as against 
 ' active endeavour ', or of ' abstract description ' as against 
 ' living appreciation ' are accepted as formulations for the 
 object of the new conception of Logic. ^ ' Thought arises in 
 response to its own occasion.' Then, by removing only the 
 definiteness of the occasion, which ought to be retained, and 
 retaining the dualism of nature between constructive and 
 discursive thought, which ought to be removed, an ant-ithesis 
 is created against philosophical logic which assigns to it as 
 its characteristic problem the relation of thought in general 
 to reality in general, as the epistemological issue out of which 
 its whole treatment springs." And an apparent corroboration 
 of this attitude is found by giving a predom.inant place to an 
 analysis of Lotze's position. 
 
 University Decennial Publications, 1903) appears to me thus utterly 
 falsified. If we want to deal with a master of philosophical Logic why 
 not select Hegel or Plato or even Green ? That is, if one was not going 
 to take the obvious course of considering Mr. Bradley's whole position 
 with regard to Thought and Reality. * Dewey, 1. c. 
 
 •* This takes us back to the conception of thought as decaying sense, 
 which, whether right or wrong, is sharply opposed to the conception of 
 it in the masters of Idealism. I should explain that Idealism, in the 
 sense in which I use it for the philosophy, say, of Hegel, is the antithesis 
 of what is commonly called Rationalism. But I know of no other 
 name that would carry the reference. 
 
 " Dewey, p. 6, and cp. Green, Prolegomena to Ethics, p. 27. 
 
Chap. IX] Logic and Epistemology 271 
 
 This idea of the situation — I say it mainly to make my 
 own conviction clear — seems to me wholly and utterly false. 
 The relation — ^the nature of the antithesis — is in my view 
 altogether different from this. 
 
 In Logic as I understand it, attempting to follow out at 
 a long interval the practice of the masters, there is no episte- 
 mology in the sense supposed,* no treatment of thought in 
 itself as opposed to reality in general, no question of a bridge . 
 from the one to other. In analysing the thought-world it holds 
 itself to be analysing the structure of reality, the detailed 
 and articulated responses by which the living body' of experi- 
 ence exhibits its endeavour to approximate as a system of 
 ideas to a non-contradictory whole. Of course all these phases 
 could be construed as responses to the environment. But 
 the environment for thought is not the sphere of external 
 action but the universe of experience. The occasions which 
 evoke responses of thought within specific limitations are 
 merely a fragment of this total environment. The genetic 
 theory, so it seems to me, has merely insisted on an arbitrarily 
 limited fragment of the genuine logical theory. 
 
 From this, therefore, it is separated in degree rather than 
 in kind, by a further error involved in its naive Dualism ; 
 an error for which I can find no better name than Occasionalism. 
 Thought, we are told, is always within the limits of a specific 
 occasion, a specific purpose. It is charged against what is 
 treated as general logical theory ^ that it disregards these 
 limits, or only regards them as throwing light on the terms 
 on which thought transacts its business with reality. ' But 
 in the end all this is incidental. In the end the one problem 
 holds. How do the specifications of thought as such hold 
 good of reality as such ? In fine, logic is supposed to grow 
 out of the epistemological problem, and to lead up to its 
 solution.' *= 
 
 * The explanation i, p. 3 above, was intended to guard me against 
 the appearance of dealing with ' epistemology ' or ' a theory of cogni- 
 tion ', by which I mean an examination of the nature of knowledge as 
 something apart from the reality which is then taken as its external 
 standard. 
 
 ^ It should be remembered that this is not accepted as a just title 
 for philosophical logic. *= Dewey, p. 6. 
 
272 Truth and Coherence [Book 11 
 
 All this, as I see the situation, is the same old half-truth 
 turned into a complete delusion. There is no discussion of a 
 relation of thought in itself to reality at large. No question 
 arising out of it determines the course of logical investigation. 
 But it is perfectly true that thought (in a way, as we shall 
 see, comparable to life, about which the same error is made) 
 has in all its specific responses and adaptations the universe 
 implicitly before it. Its adaptations, like those of an organ 
 in an organism, are controlled throughout by a system of 
 functions which is a response to something continuous in the 
 nature of the environment — as in life, to the conditions of 
 organic existence on our earth's surface ; so in knowledge, 
 to the condition of belonging to a universe. Occasionalism, 
 the insistence on response to specific occasions as the condition 
 of thought,thus misses its underlying and continuous character, 
 as the active form of totality ; the nature by which all experi- 
 ence strives of itself towards the whole. Thought is essentially 
 the nisus of experience as a world to completion of its world. 
 The intervals of conscious reflection are merely one of its 
 forms of advance, and are not, in their paleness and meagre- 
 ness, characteristic of thought, which is essentially organic 
 concrete and constructive. In its Occasionalism again the 
 genetic theory is saying something so far true, but fragmentary, 
 and is again taking it as the basis of an antithesis which has 
 no existence, except as a relation of a partial to a more 
 comprehensive view. 
 
 And lastly. Dualism and Occasionalism take shape in 
 Adapt ationism. This is more than a recognition — which would 
 be justified — that all thought may be regarded as a response 
 or adaptation to surroundings. It consists {a) in neglect of the 
 character of thought as a system of functions adapted to the 
 removal of contradiction throughout experience and having 
 •always this complete systematic function operative in con- 
 trolling specific responses or adaptations ; And (6) in the 
 suggestion that, considering the complete explanation of 
 evolutionary growths to be only possible through regarding 
 them as adaptations to their environments, each to each, 
 the antithesis of origin and value ought to be treated as 
 superseded, and psychology, for instance, should become in 
 
Chap. IX] Meaning of Natural Selection 273 
 
 its aspect of a historical science a serviceable instrument in 
 logical valuation. 
 
 a. As to the former of these points, it is now I think Thought 
 recognised that to consider a living organism as a mere box f "^^'^of' 
 of patent * contrivances, a collection of adaptations to parti- devices, 
 cular situations of environment, is to consider it inadequately. 
 
 Every adaptation is built on a system, and the system is 
 determined by essential functions, which may be regarded 
 if we like as a great general adaptation. But these functions, 
 as a system, it must be borne in mind, constitute a large 
 proportion of the environment for every specific adaptation. 
 In every adaptation life is there as a whole, and has the whole 
 nature of the environment in view, not as a general abstraction, 
 but as a concrete whole that enters into every specific situation. 
 So with thought. It is, if we like, all developed as responses ; 
 but it is inadequately considered if it is considered as a box 
 of tricks. Thought never really forgets the universe. There 
 is always more in it than its occasion brings, or rather, it 
 makes its occasion more than it is. 
 
 b. And the idea that evolutionary explanation has disposed Value not 
 of the antithesis between genesis and value seems to me more ^epen- 
 
 ° dent on 
 
 particularly to mvert the real relation. It is true of course history. 
 that natural history is much interested in natural selection ; 
 but the decisive point for logical theory is that natural selec- 
 tion is not in the smallest degree interested in natural history. 
 One may fancy oneself pleading before the court of natural 
 selection. ' Only give me time, and I can explain everything ! 
 The fact is, I was not adapted to to-day's environment, but 
 only to yesterday's. That is why I am not equal to the situation.' 
 But the court, I take it, replies, ' My dear sir, in the court 
 of history that would be interesting, but in this court it is 
 wholly irrelevant. We must ask you to deal with the situation 
 of to-day, or — .' It is being equal to the whole situation that 
 is the criterion for Logic as for Morals. Past adaptations can 
 justify no theory of to-day. Have we or have we not a system 
 
 * The Mendelian theory is not quite this. But even its way ol re- 
 garding an organism, as, if I grasp the idea rightly, a group of more or 
 less independent factors, seems difficult to accept without further 
 explanation. 
 
 1337-2 T 
 
274 Truth and Coherence [Bookii 
 
 which gives the possible maximum of non-contradiction, in 
 the construction which it puts upon the fullest conceivable 
 experience ? This is our standard for the present, and in it, 
 for the past. And Professor Dewey says what seems to me 
 equivalent to accepting this standard ' The historical point 
 of view explains the sequence ; the normative follows the 
 sequence to its conclusion, and then turns back and judges 
 each historical step by viewing it in reference to its own 
 outcome.' * Yes, but the sanction lies surely not with the 
 history of adaptation, which shows a certain stage to be 
 de facto the outcome ; but with the court of natural selection, 
 which applies the test of adequate or inadequate adaptation, 
 that is, of power or impotence to deal with contradictions, 
 taking the whole body of experience together as constituting 
 the concrete situation. This is the test, the test of coherence 
 and non-contradiction, which philosophical Logic accepts ; 
 the immanent test of the presence of the character of Reality 
 within the thought-form as one of the many branches or 
 appearances of the real. 
 Psy- iv. Psychology, from anthropology upwards, beginning with 
 
 chology ^ natural history conditioned by quite other environments, 
 into leads gradually up to a situation in which, as the proper 
 ^S^^' character of mind emerges, the logical test by present adequacy 
 of working supersedes the historical explanation by past 
 adequacj^ of work in a less complete environment. 'Working ' ; 
 that is the apparent watchword, the name accepted on both 
 hands for the test which might bring the two theories together. 
 But to cover the problem of philosophical Logic it must take 
 the environment as the widest conceivable experience, and 
 must recognise the fact and right of cognitive interest.* 
 
 When once the ultimate criterion is accepted, with the 
 extension of the supposed new view to its natural boun- 
 daries, that is from practical working to dealing adequately 
 with experience, I cannot understand how the relation of 
 Psychology to Logic should present a difficulty. I have 
 observed above that the epistemological attitude which the 
 
 " Chicago Publications, p. i6. 
 
 '' The true t3^e of the relation of Psychology to Logic is in the relation 
 of associated contents — impure universals — to pure logical connections. 
 
Chap. IX] Limitations of recent views 275 
 
 new theory is attempting to force upon the old is nowhere, 
 so far as I know, accepted byit.^ And in fact the historical 
 method, the explanation of past phases in the Ught of their 
 environment, was not derived by philosophy from the historical 
 or evolutionary sciences, but rather by them from it.'' It is 
 a notable characteristic of Plato, and could hardly have been 
 more prominent than it is in Hegel's Phenomenology and in 
 his Philosophy of Mind. It is unfortunate that there is really 
 no word free from irrelevant suggestions for what we mean by 
 Idealism when we apply it to the philosophy of Plato or of 
 Hegel. But taking ' Objective Idealism ' as a more or less 
 accepted equivalent, we may say that the history and estimate 
 of thought-adaptation in relation to the environment has 
 always been the peculiar pride and province of objective 
 idealism. Only, the actual test of truth, of the character of 
 reality in the thought-form, was by it always kept separate 
 from the historical estimate of imperfect forms, the justifi- 
 cation of which had shown itself, as we may say, doubly 
 relative. ° 
 
 V. This then, is one part of the logical situation as I feel Summary 
 obliged to conceive it. It is well to vindicate for Logic the ^^^^^^^^^ 
 sphere of Life and practice as against an imaginary heaven attitude, 
 of ideas — to which however no master of thought has relegated 
 it. It is well to bring the development of thought together 
 with the conception of adapted response, and to apply to it the 
 general idea of natural selection. It is well to vindicate for the 
 individual mind a living share in the self-maintenance of Reality 
 as against the idea which Plato repudiated of a statue-like 
 immoveable system . All these are attitudes of special emphasis 
 due to the philosophical and semi-philosophical movement of 
 the last fifty years. But if the reforming theorist limits 
 practice to the sphere of external action, adaptation to the 
 history of de facto success apart from the principle of its deter- 
 mination, and our living concern with Reality to effecting in it 
 
 * I have explained why I think it misleading to take Lotze as a 
 specimen for criticism. 
 
 •• A remark of W. Wallace. I have not the reference. 
 
 ■^ ' Relative ' as falling short by the standard of our best experience ; 
 doubly relative, because that standard is itself not absolute. 
 
 T2 
 
276 Truth and Coherence [Book 11 
 
 ultimate change, in a time which is ultimately real, then 
 his view remains fragmentary, and he has failed to grasp the 
 inheritance which is coming within his reach. 
 Realism 3. Complementary to the view of truth which I have just 
 diacv™^ attempted to explain — the view for which thought is an 
 adaptation, and truth along with reality is bona fide in process 
 of being made — is the reassertion of Realism in the modern 
 world. Realism, indeed, however opposed to the conception 
 of a universe in actual genesis, belongs at bottom to the same 
 impulse of modernism. The very same flowing tide which 
 carries with it the demand that truth shall be a mere adaptation 
 to vital needs, brings also the antagonistic requirement that 
 truth shall lie in a relation to simple given fact. On both 
 sides we have the demand for immediacy ; here the inamediacy 
 of satisfaction, there the immediacy of apprehension. And 
 the second, as we admitted of the first,* has doubtless, even 
 from our point of view, contributions to offer. The first, we 
 hoped, would bring about a correction of the confusion of 
 Idealism with rationalism, and destroy the conception of a 
 pale and meagre thought, identified with decaying sense. The 
 latter, we hope, will undo the unhappy connection with mere 
 psychicalism or mentality ^ and bring into prominence the 
 more robust conceptions of a philosophy which admits true 
 differences of kind within the whole. 
 
 I propose to devote the following chapter to explaining 
 the attitude involved, in the theory of truth which has been 
 followed through the present work, to mental states and the 
 claims of naive realism. 
 
 But here some remarks will be in place concerning a doctrine 
 of truth which, as far as I grasp it, shares on one side only 
 the position of naive realism and simple apprehension, while 
 on another side committing itself to a special theory of existence 
 with which naive realism has directly nothing to do.'' The 
 doctrine of simple apprehension, and the true meaning of the 
 
 "■ p. 268 above. 
 
 •^ See e.g. Mr. Moore's Refutation of Idealism, cited and commented 
 on in Joachim's Nature of Truth. 
 
 "^ I think that even in their theory of existence the two have an impulse 
 in common, that of hardening into isolated existence purely relative 
 objects. 
 
Chap. IX] Mr. Russell on Relations 277 
 
 principle that knowledge makes no difference in what is known, 
 will be spoken of in the following chapter. 
 
 a. 'The world is a world of many things, with relations The world 
 which are not to be deduced from a supposed nature or scholas- °j -^"1^ 
 tic essence of the related things. In this world, whatever is 
 complex is composed of related simple things. There is no 
 identity in difference, there is identity and there is difference, 
 and complexes may have some elements identical and some 
 different, but we are no longer obliged to say of any pair of 
 objects that may be mentioned that they are both identical 
 and different.' ^ 
 
 The core of the view, as is well known, is the rejection of 
 what have been called * internal relations ', i. e, relations 
 grounded in the nature of the related terms ; and the assertion 
 of mere external relations, i. e. as I understand that there 
 is no reason why relations should be so grounded.^ The phrase 
 ' internal relations ' seems to me not quite satisfactory, as 
 suggesting relations between parts within a given term. At 
 least the view which to me appears reasonable would be better 
 expressed by some such term as ' relevant relations ', i. e. 
 relations which are connected with the properties of their 
 terms, so that any alteration of relations involves an alteration 
 of properties, and vice versa. 
 
 The following reasons for accepting a doctrine of relevant 
 relations appear to me to be unimpeached. 
 
 (i) In a large proportion of cases the relevancy of the Relations 
 relations to the properties of the related terms involves a ^^ kinds 
 community of kind. You cannot have a spatial relation be- 
 tween terms which are not in space. You cannot have a moral 
 relation between terms which are not members of a moral 
 
 * Russell, Philosophical Essays, p. 169. I do not think it is main- 
 tained on our part that relations can be deduced from the properties 
 of single terms which are in relation. I understand the point of interest 
 to be that you cannot explain one term of a complex without explaining 
 the rest. Every complex, it must be remembered, has a special quality 
 of its own, and every member of it has a quality relative to this ; see 
 
 i, PP- 139-40. 
 
 '' Op. cit., p. 161. It would be important to know if it is maintained 
 that relations cannot be so grounded, because then we could ask for 
 the author's explanation of the more obvious cases in which they appear 
 to be so. 
 
278 
 
 Truth and Coherence 
 
 [Book II 
 
 The 
 
 meaning 
 of terms 
 relative 
 to their 
 grouping. 
 
 Rela- 
 tions ex- 
 press be- 
 haviour 
 of terms 
 in groups 
 
 world. Why is it absurd to ask for the distance from London 
 Bridge to one o'clock ? Surely because the one term is in 
 space and the other in time. This is not a general argument 
 that if the relation were other the terms would be other, from 
 which any possible conclusion might follow.^ It is an analytic 
 determination of a common positive element on which both 
 property and relation depend. 
 
 (2) There is further no case in which on philosophical 
 scrutiny ^ the relevancy of relations to properties is not per- 
 ceptible. I do not say that the relation can be reduced to 
 a fact about the one object only together with a fact about 
 the other object only.'' The point of the relevancy of rela- 
 tions, as I understand it, is that each of two or more terms 
 can only be understood if all are understood, ' Father ' and 
 ' Son ' is a vulgar traditional instance. But I do not see 
 that it is not a sound one. And in every case, I think, the 
 basis of such a necessity can be shown. This or that observer 
 may not possess the knowledge or the acuteness required to 
 formulate the element which changes with the relation in 
 precise detail. But it can always be shown what sort of thing 
 must be relevant to the relation. So much so, that I cannot 
 think this to be really and totally denied of so-called exter- 
 nal relations. And I will pass on to a point of view which 
 raises this question. 
 
 (3) Relations are true of their terms. They express their 
 positions in complexes, which positions elicit their behaviour, 
 their self-maintenance in the world of things. This is really 
 the all-important argument. And I cannot believe that if 
 the doctrine of mere external relations were completely stated, 
 we should not find the same thing admitted by it, in one way 
 or another.*^ If the relations make no difference to the terms, 
 
 ^ Russell, Philosophical Essays, p. 166. 
 
 '' I have in mind Mr. Bradley's argument in Appearance and Reality, 
 ed. 2, p. 572 ff. " Russell, p. 161. 
 
 ^ As I understand the appearance of this is avoided by connecting 
 the mind with the relation straight, so to speak, and not through the 
 terms. But this seems to me simply a bold omission of a fact in the 
 complex. Does not the conception of a ' sense ' in a relation like love 
 necessarily admit this ? The term A is different according to the 
 ' sense ' of the relation of love between A and B. Or take spatial 
 
Chap. IX] Pluvalists are AhsoluHsts 279 
 
 it follows that things do not react or behave with reference 
 to the complexes to which they belong. Yet if Charles I 
 had died in his bed, he would have died in a different bodUy 
 attitude from that in which he died on the scaffold. 
 
 6. I do not understand relations to be adjectives of their Rela- 
 terms. They are not adjectives because they involve other asserted 
 terms which are as substantive as any of which we might be to be ad- 
 inclined to pronoimce them adjectives. Relations cannot be 
 reduced to qualities, nor qualities to relations. Relations 
 are just the way in which discursive thought represents the 
 unity of terms which it cannot make adjectives of one other. 
 As Mr. Bradley has said that they are a modus vivendi between 
 predicates of the same subject whose unity we cannot really 
 construe to ourselves, so it might be said they are a modus 
 Vivendi between terms in the same universe, of whose unity 
 in the imperfection of our experience, the same is true. 
 
 None of the objections which have been put forward appear 
 to me to touch these points.* 
 
 I quite understand that on the doctrine offered to us 
 Identity in Difference must go. And I quite see for myself 
 that it must go ' in the end ', that is to say, in any experience 
 for which objects are self-contained, and cease to transcend 
 themselves. What our pluralist realists ^ are grasping at 
 is therefore justly anticipated. Undoubtedly the Real is 
 self-complete and self-contained. But I insist on the words 
 ' in the end ' because it is their repudiation of them " that I 
 take to be the root of their failure. They are the extreme 
 Absolutists. They are not content to have the Absolute ' in 
 the end ', as we more modestly claim it, not meaning after a 
 lapse of time, but in so far as what are fragments for us point 
 out to us a completion beyond them. And there is surely a 
 difference of completeness in different experiences. But they 
 
 relations in the visual field. When a new object is inserted in the field, 
 every object in it becomes a member of a new pattern, and so necessarily 
 exhibits a new quality. 
 
 * Of course I am following Mr. Bradley, Appearance and Reality, 
 loc. cit., though he is not responsible for what I say. 
 
 " I do not wish to use a name that will be disliked. I merely invented 
 an appellation that seemed to be fair, for shortness' sake. 
 
 " Russell, pp. 159, 163. 
 
28o Truth and Coherence [Bookii 
 
 will have the Absolute here and now ; and to make it handy 
 and adaptable for everyday use they split it into little bits. 
 A universe of tiny Absolutes ; that is really what they offer 
 us.^ But if any of these Absolutes imply any term beyond 
 themselves their absolutism breaks down. And we have tried 
 to show that in all relations this is the case. 
 Truth c. As to error we have only to bear in mind that degree 
 
 not abso- ^^ partiality of the truth asserted must combine with a belief 
 lute. that it is the truth, the whole truth, and nothing but the truth, 
 in constituting the degree of erroneousness. And also, for 
 practical purposes and within certain limits we let imperfect 
 truth pass as absolute. A repudiation of the phrase ' in the 
 end ' denies these distinctions. But surely in denying them 
 it denies nearly all the facts of life. Presupposing these reser- 
 vations, what has been said in satire ^ is surely a plain truth, 
 which only needs complete application to make it obvious. 
 A man who accepts the view that all his judgments have only 
 partial truth is certainly pro tanto less wrong in each of them 
 than if he believed he had got in each the truth, the whole 
 truth, and nothing but the truth. But obviously, in this form 
 the principle is only a general warning, and cannot directly 
 amend the actual partiality of what a man judges as truth. For 
 this follows from determinate reasons, and in each case he 
 must judge or not judge. A purely general warning cannot 
 guide his judgment. But it can stimulate him to caution and 
 criticism, and this is an obvious excellence in his whole 
 cognitive system, which is excluded by the belief that partial 
 truth can be absolute. A man who has grasped the warning 
 that you must only believe about one-half of written history 
 is certainly pro tanto, i.e. if both have the same positive 
 knowledge, nearer historical truth than one who thinks he 
 may with safety swallow it all. And though this caution alone 
 will of course not tell a man which half to believe, yet it will 
 place his cognitive system in a much truer relation to the facts, 
 than that of a man, who, making the same judgments as the 
 other, believes them to represent absolute truth. It is the 
 
 * I suppose this is a famiUar idea in the case of the Atomists and the 
 Eleatics. See Burnet, Early Greek Philosophy, ed. 2, p. 387. 
 " Russell, p. 155. 
 
Chap. IX] Ofi what Falsehood depends 281 
 
 case no doubt, that you cannot, out of caution, half make 
 a judgment ; you must make it or not. But it is further true 
 that to make an additional judgment, ' there is a good deal 
 more to learn about ' this or that character or incident, puts 
 your positive judgments in a proportion to the facts which 
 is likely to be much more in harmony with them, than if you 
 entertained no such critical principle. 
 
 d. I believe the fact to be that the doctrine of which we are The illu- 
 speaking gains its vraisemblance and its apparent clearness, gj^pie 
 from clinging to just the region of so-called plain and simple fact, 
 fact, the illusory hardness and isolation of which — really 
 a defect of low-grade knowledge ^ — it takes for absoluteness. 
 And in this region it does seem prima facie absurd to take 
 error as partial truth. You must be, it appears, either right 
 or wrong. The fact is fixed, and you are in relation with it 
 or are not. There are no degrees of truth, and nothing which 
 is truth in the beginning and not in the end, or in the end and 
 not in the beginning. I will try to show the nature of this 
 delusion, as it seems to me, by a few words on truth of fact 
 and truth of system. 
 
 ' It is plain — that the truth or falsehood of a given judg- 
 ment depends in no way upon the person judging [it is 
 common ground that there must be a mind to judge], but 
 solely upon the facts about which he judges.' ' Thus the 
 judgment that two terms have a certain relation R is a relation 
 of the mind to the two terms and the relation R with the 
 approximate " sense " [ = direction of the relation from A to B 
 or from B to A] ; the "corresponding " complex consists of the 
 two terms related by the relation R with the same " sense ". 
 The judgment is true when there is such a complex, and false 
 when there is not. The same account, mutatis mutandis, will 
 apply to any other judgment. This gives the definition of 
 truth and falsehood.' The complex, it is to be remembered, is 
 composed of simple related things.^ 
 
 * Of course no one uses the whole of his own experience in his theories. 
 He uses what for some reason has struck him and seemed typical to him. 
 I do not think it is without precedent that men of very high attainments 
 should rely theoretically on very naive types of experience. I think 
 analogies for this are rather common. 
 
 •^ Russell, pp. 169, 173, 184; cp. Stout, Ar. Proc. 1911. 
 
282 
 
 Truth and Coherence 
 
 [Book II 
 
 be telling 
 a lie. 
 
 I wish to explain, by a comparison of judgments differently 
 related to ' the facts ', why it appears to me that, in the first 
 place, truth and falsehood depend on the judging mind in 
 another and more vital sense than is here admitted, and not 
 on the mere presence or absence of a complex of entities 
 corresponding to the judgment, and, in the second place, that 
 the facts themselves, though they are real, are not real in 
 the way here asserted, as bits of reality, immediately accessible 
 to apprehension, and corresponding each to each with the 
 terms of our commonplace judgments. 
 Stating a (i) Let US begin with Charles Reade's mediaeval physician, 
 hp^* ^f,^ff who, having a grudge against a reluctant patient, tried to 
 have him arrested, laying an information that he intended 
 to fly the country. But ' his sincere desire and honest endeavour 
 to perjure himself were baffled by a circumstance he had 
 never foreseen nor indeed thought possible. He had spoken 
 the truth. AND IN AN AFFIDAVIT'. For the patient 
 had fled. 
 
 Here the doctor told a lie, but in telling it, he spoke the 
 truth ; if, that is, we judge by correspondence with the facts. 
 One might urge that his assertion, being contrary to his belief, 
 was not a judgment at all, but a form of words intended to 
 produce action in another's. This I think is true.* But it 
 does not seem to me to destroy the point of the instance. 
 Why could a form of words, corresponding with the facts, be 
 in his mouth nothing but a lie ? Because it was contrary to 
 his belief ? But what does that mean ? Belief is not a chance 
 thing, sprung from nowhere. It means that it was contrary 
 to the system of his knowledge as determined by his whole 
 experience at the time. 
 
 (2) Take another case — ^tho so-called true conclusion from 
 one or more false premisses. Here again we have truth, if 
 judged by mere correspondence with the hard fact. For 
 example, on a local railway I know, the signals are down all 
 Sunday. A stranger imaware of this practice might infer 
 that a train is due. And it might well happen, three or four 
 times in the day, that at the moment of speaking a train was 
 in fact due. Judging by hard fact this judgment would be 
 '^ See above, i, p. 34. 
 
 Stating 
 a fact 
 may be 
 an error. 
 
Chap. IX] False ground, false judgment 283 
 
 true. But would the man be right in his judgment ? It is 
 a point on which probably his companions might wrangle 
 ^^dth him ad nauseam. He seems to have got a truth which 
 he had no business to have got. If he had known a Httle more — 
 possessed a little more truth — he would not have got it. And 
 the truth, as he possesses it, is felt to be unsatisfactory, and 
 half or more a falsehood, because its dependence is wrong : that 
 is, it is judged, as a truth, in part at least, by the system of 
 judgment with which it is connected. And more than this ; 
 it is infected, in its own nature, by the faults of this system. 
 Its logical stabihty is highly incomplete ; it would be upset 
 by a second trial ten minutes later, or by a most trifling bit 
 of additional knowledge. But logical stability — incapability 
 of being confronted with a contradictory experience — is, we 
 shall see, the very core of truth. 
 
 In the closer tissue of a science, this defect amounts more 
 obviously to actual falsehood. The ' true ' conclusion partici- 
 pates so definitely in the character of the system from which 
 it issues. Those theorists who held that agriculture is 
 especially and peculiarly a desirable industry held, in this 
 view, I suppose, what corresponded to an indubitable fact. 
 But when they deduced it from the view that wealth is not 
 genuinely produced in any other occupation, they connected 
 it with grounds which destroyed its value, and made it a 
 dangerous falsehood, by including in it an unjustified pre- 
 sumption against other forms of industry. 
 
 Strictly speaking, there is no reason for dropping the 
 premisses in stating a conclusion. And if they, being false, 
 are retained, the falsehood of the conclusion, though apart 
 from this corresponding with facts, is exhibited on the face 
 of it. Here again, it is obvious that the truth or falsehood 
 of a judgment depends not merely on correspondence to a 
 complex, but on the completeness and comprehensiveness of 
 the system with which it is connected in the mind.^ Its truth 
 is threatened, we have seen, both if it is at variance with the 
 
 '^ You may say there is nothing in this but that one judgment about 
 one complex is true, while another about a fuller complex including 
 the first is false. But what is shown is that correspondence to its 
 complex is not enough to make the first judgment true. 
 
284 Truth and Coherence [Book 11 
 
 system, and if this system fails to give true connections, 
 prima facie outside the judgment directly in question. 
 Howwe (3) Now let us take the strongest instance in favour of 
 come by non-dependence on the judging mind. This, it appears to 
 facts. me, is to be found in the current knowledge of facts currently 
 admitted, forming the stock-in-trade of daily life and con- 
 versation, and considered out of the context of science or of 
 any critical analysis.* * Charles I died on the scaffold.' 
 This judgment most people would describe pretty much in the 
 language cited at the beginning of this section. It is true, 
 they would say, because it corresponds to a complex of terms 
 and their relation, which are or were facts or things. There 
 is or was such a complex of things and such a relation between 
 them, and therefore the judgment which expresses the mind's 
 relation to it is a true judgment. What the facts are or were 
 is taken as a matter of general agreement ; it would be held 
 pedantic to ask where we get at them, how we apprehend them, 
 what precisely they are or were, what meaning the judgment 
 actually carries with it. Our intellectual outfit for everyday 
 use consists of ' facts ' postulated in this way — ^the normal 
 furniture of our mind ; what Plato called the world of opinion. 
 We take the material hurriedly from authority and tradition ; 
 or from negligent perception interpreted by authority and 
 tradition.^ We do not pursue their context. We do not fix 
 their limits or analyse their detail. Thus we let them shrink 
 and harden into isolated counters dealt with by our thought, 
 worn and defaced by rapid and careless exchange. And it 
 is of these current counters that our world of fact is constituted, 
 which we take to be self-existent, independent of our minds, 
 each fact independent of the others, related to them but 
 unaffected by their relation, complexes which are the standard 
 of truth to our judgment. If our judgment corresponds to 
 facts as presented to us in these current counters in which 
 we commonly believe, that is all we ask. 
 
 * It is such facts, I suppose, which another school would consider 
 to have received Social endorsement, and to be made true by answering 
 their purpose. 
 
 '' Could even a scholar, for instance, as a rule, exhibit a convincing 
 argument that the works ascribed to the ancient authors were really 
 written at such times and by such persons as is commonly supposed ? 
 
Chap. IX] System of mind, and of things 285 
 
 (4) Now I am not suggesting that these facts are not The facts 
 actual, and that the judgments which correspond to them are ^q^ less^ 
 not true, in a sense sufficient for their purpose. My con- than 
 tention does not tend to making less of the facts, e. g. to ^^™P^^ • 
 reducing them to mere ideas, but to making more of them, 
 i. e. to showing that as realities they cannot stop at the arbitrary 
 point we have adopted. And, no doubt, it follows that the 
 mind has had much to do with them already and must 
 have much more to do with them as they proceed. As they 
 stand, they are a selection out of reality for everyday use, 
 carelessly handed down or observed, clipped, worn, their 
 interconnection neglected. But they do well enough as a 
 standard for everyday truth, and our judgments, which we 
 take to ' correspond ' with them, do well enough as everyday 
 truth. 
 
 But, even within this world of what we conceive as corre- 
 spondence to hard fact, we do acknowledge differences of 
 truth, or, if this language is preferred, degrees of correspon- 
 dence to fact, according to the furnishing of the mind. 
 ' Charles I died on the scaffold,' we commonly assume is not 
 so true in the mouth of a child who has just learned it by 
 heart as in the mouth of a schoolboy who knows something 
 of the history and significance of the seventeenth century. 
 And in neither's mouth is it so true as in that of a historical 
 student to whom the seventeenth century is a familiar world 
 and a living interest. It is not a thing which is true or false 
 by touching or not touching.* From the first, it is an apprecia- 
 tion of elements in a system, and of their determination by 
 the system, and is a matter of degree. Our ordinary estimate 
 of truth fully admits this to be the case. 
 
 We have been urging so far that the system of the judging 
 mind is an element in truth, and also, in the last paragraph, 
 we come in sight of an inference affecting the actual things 
 or facts which are taken as the standard. 
 
 (5) I will pass to an instance which clinches both these in the full 
 
 point'- . Sp*,e' 
 
 When we come to consider the knowledge of any leading facts are 
 
 historical authority on the period of Charles I, we find two ' 
 
 ^ See Aristotle, Metaph., 1072 b 21 Bify&vwv koi vowv. 
 
286 Truth and Coherence [Bookii 
 
 remarkable things. First, quite undoubtedly, and in all 
 common usage, such a man's judgment ' Charles I died on 
 the scaffold ' is far truer than that of the child or the schoolboy 
 or the ordinary conversationalist. This shows how much 
 depends on the mental system of the judging mind. 
 
 Secondly, when at this level we begin to look for the single 
 standard of fact which we are accustomed to rely on, it is 
 not to be foimd.* At first sight, it is absorbed into the great 
 historian's knowledge. For us, something picked out of that 
 knowledge is the standard. Our ' facts ' as we used to call 
 them, now show as little bits or threads of reality, which we or 
 others for us have selected out of the huge web of the world as 
 known by such an authority as this. Of course the facts have 
 not turned into any one's mere mental system. But they seem 
 essentially continuous with mental systems. We do not mean 
 to deny that they — as much of them as is warranted on good 
 authority — are real facts. What we are saying can only 
 mean that he helps us to get at them. That is all very true ; 
 but then, when we get at them through his knowledge they 
 are much developed from what they seemed when we were 
 readily passing them from hand to hand among each other. 
 Now we see that even in their discovery they are not simple 
 or independent. They depend for being discovered and 
 warranted on an enormous constructive work of criticism, 
 starting from present experience, and continued through heaps 
 and heaps of testimony and evidence allot which is instrumental 
 to that view of facts which will give the highest degree of 
 coherence to the system so constructed.^ Yes,but ' the facts ', 
 
 * Compare with this the difficulty which the layman often has in 
 asking a question such as a scientific man can answer. To the layman 
 a point appears simple and single which to the expert is full of distinc- 
 tions and reservations. The writer once procured a meteorological 
 record of temperature with a view to its bearing on a stoppage in the 
 building trade. But he found, of course, differing readings of several 
 instruments under different conditions, and could not tell, without 
 further enquiry, which of the temperatures was important for his 
 purpose. The simple ' fact ' vanishes as you come nearer, as a headland 
 breaks up into an intricate outline of planes and edges as you approach 
 it, or if you try to read a book with a microscope. 
 
 '' Cp. The Presuppositions of Critical History : F. H. Bradley. Parker, 
 1874. 
 
Chap. IX] The real facts,-where and whut ? 287 
 
 it will be urged. All this is getting at * the facts ' ; but the 
 facts were there all the same, however hard to get at ; and 
 when got at, by whatever means, can be and are the standard 
 of truth.' Well j but we must consider the point that the facts 
 are not to be found simple of themselves, as we incline to imagine 
 in our everyday exchange of them. They are not and cannot 
 possibly be the working standard of first-grade thought. You 
 may copy them in your judgment, when the historian has 
 found them out for you. But the working standard, which 
 determines them, is not themselves, but his immense critical 
 construction. Accounts of eye-witnesses, e.g. are nothing but 
 material ; and, as a rule, very contradictory material. 
 
 The facts, then, though bits of reality, are mediated to 
 us by an immense mental construction, and are not really 
 separable from this. They are not and cannot be, as simple 
 and isolated, the first-hand standard of truth. We may select 
 certain results and make them up into a standard for a certain 
 level of truth, e. g. one good enough for examination purposes, 
 and that different for different examinations. But that is 
 simply an artificial extract. 
 
 That is one point. The facts, in history at any rate, are 
 not simply there, so that they can act as a given standard, 
 correspondence to which is truth. The primary working 
 standard is critical system, or, what is the same thing, 
 scientific investigation.* 
 
 (6) But then there is another thing. When we get our The full 
 facts, our results, what we take to be real, it is something compre-^ 
 much beyond what we were wont to take as facts. It is a hensive 
 commonplace that in the higher knowledge we are beyond ^^^ ^™^* 
 what is commonly called fact.^ We may say that our current 
 counters were fact, but they were neither the whole fact, nor 
 nothing but the fact. What is the full significance and 
 implication of the death of Charles I ? And could we seriously 
 say that a judgment about it is true in which its full significance 
 and implication is ignored, more especially as on the other 
 hand the picturesque and immediate aspect of the event is 
 
 * See, for an example of what is involved in a simple measurement, if it 
 is to be precise. Knowledge and Reality, pp. 330-1. 
 '' See e.g. Bradley's Logic, pp. 92-3. 
 
288 Truth and Coherence [Bookii 
 
 certainly not affirmed ? The facts are not ' in the end ' 
 isolated and independent. There is a stage when they seem 
 so, but you cannot arrest them at that stage. As coherence 
 with a system is the standard by which we establish facts, 
 so the part they play in a system of reality, their influence 
 and importance, which imply a further transformation, is 
 the standard by which we judge their degree of reality, and 
 therefore the degree of truthfulness of the judgments that 
 affirm them. Ultimately, these two systems are one, the 
 system of experience, a critical system which is always trans- 
 forming the facts, as we know them and rank them, towards 
 a higher logical stability. 
 
 Of course these remarks contain nothing that is new.* But 
 I hope they clearly explain my view about the relative places 
 of correspondence and coherence in the meaning of truth, 
 and about the alleged independence, both as regards mind, 
 and as regards each other, of the things or facts of the real 
 world. 
 Coher- 4- The standard of system or coherence is a standard 
 
 ence does applicable to discursive thought. It is the standard of truth, 
 not imply ,.,.,., i , i e n • i • 
 
 corre- which itself does not pretend to be the perfect or all-mclusive 
 
 spon- experience.^ 
 deuce. 
 
 A judgment is true, as I understand the term, when or m 
 
 as far as its self -maintenance as a judgment is perfect. That 
 is, in other words, when the whole system of the judgments, 
 which experience forces upon the mind which makes it, con- 
 tains less contradiction in case of its affirmation than in case 
 of its denial. Such a judgment is ' true ' because on the whole 
 it cannot be denied — not, that is, till there is a change, other 
 than its denial, in the body of experience. 
 
 * The line of the discussion is closely akin to that of Plato's discussion 
 of trueness and reality, which agree in the character of logical stability. 
 See Companion to Plato's Republic on 479 ff., 509 ff. 
 
 '' It is perhaps hardly necessary at this time of day to say that I have 
 now in principle adopted Mr. Bradley's view of the relation of thought 
 to reality, with which the ideas of my early work, Knowledge and 
 Reality, were more or less in conflict. I shall refer below to a reserva- 
 tion on this view which I still entertain, and which I think is consistent 
 with the attitude of this work. The point is merely that there is more 
 analogy between the work of thought and solid and complete reality, 
 than Mr. Bradley, treating thought as solely discursive, seems to cillow. 
 
Chap. IX] No Archetype of ' Coherence ' 289 
 
 i. Stated in this way, which appears to me to be the right Coher- 
 way, the doctrine that truth consists in the self-maintenance ^^^^^^^^ 
 of judgments, which again consists in their systematic coher- back on 
 ence, does not seem to me to fail quite in the way which has gpo^! 
 recently been imputed to it.* Judgment professes to express dence. 
 the nature of the real so far as it can be uttered in a system 
 of predicates and relations. It does not propose or suggest, 
 so far as I can see, that the real is another system of predicates 
 and relations, which that constituted by judgment pretends 
 to reproduce or to resemble. Therefore its failure is one and 
 decisive, simply consisting in the fact that it is not, like the 
 higher experience which we suppose to be the sum and sub- 
 stance of all Reality, solid and immediate as well as perfectly 
 individual and non-contradictory. It does profess to qualify 
 Reality, to tell us about the nature of Reality ; and in as far 
 as it arranges content in a non-contradictory system it does 
 so tell us and qualify Reality. It sets out the content of the 
 real in a shape of special interconnection and emphasis, the 
 definiteness and varied accentuation of which in the diverse 
 worlds of knowledge constructed from different centres, 
 obviously proffers a side of the whole without which the perfect 
 experience would in certain respects fall short of perfection. 
 In the dissociation of the perfect experience involved in 
 finiteness, this side appears alone. ^ 
 
 But, so far as thought is discmsive, it does not profess 
 to furnish any appearance of Reality but its own, and if it 
 is said to be ' about ' the ' other' of thought," that involves 
 no claim to represent the fuller experience in its own character. 
 Reality is operative in truth. The nature of the latter 's 
 self-maintenance as tested by the principle of coherence, non- 
 contradiction, or individuality, (all of them expressions for 
 the same character) leaves no doubt of that. But the claim 
 to have Reality at work in it, subject to special conditions, 
 involves no appeal to correspondence, though correspondence 
 in a sense must result.* And in my view the fallacy above 
 
 * Joachim, Nature of Truth. 
 
 ^ That is, markedly distinct in character. No side of experience is 
 ever really alone. 
 
 *^ Joachim, pp. 170-2. ^ See above, p. 267. 
 
 1337-2 U 
 
290 Truth and Coherence [book 11 
 
 signalised — a sort of fost hoc ergo propter hoc — is involved 
 in the assertion that ' current Logic, consciously or uncon- 
 sciously employs the nature of truth as correspondence, and 
 if that notion is challenged throws the burden of justification 
 on metaphysics '.* 
 
 The failure or limitation of the coherence theory of truth 
 
 lies then, I urge, simply in the fact that judgment, to which 
 
 it belongs, is an appearance of reality in relational form, doing 
 
 its best to attain individuahty in that form, which up to a 
 
 certain point it achieves,^ but which, because it is relational 
 
 and points endlessly beyond itself for completion, it can never 
 
 thoroughly attain. But it possesses, as we have suggested, 
 
 merits of its own, clearness, special interconnection, emphasis, 
 
 apart from which it is easy to divine that the ultimate Reality 
 
 would lack an element. 
 
 No ' ap- ii. Thus I suggest that the enquiry I am referring to leaves 
 
 tUnT™^ its own true track in emphasising the impossible demands 
 
 to an of perfect coherence, ° as an attribute or essential of perfect 
 
 original, ^^^^^i ; instead of adhering throughout to the position that 
 
 the perfection of truth is not within its own character, but 
 
 must lie in a reality different in kind. The importance of this 
 
 point is that in this way an imaginary perfect tjrpe of truth 
 
 and coherence is set up, by their ' approximation ' to which 
 
 actual truth and coherence are to be judged. The term 
 
 * Joachim, pp. 119-20. This suggestion seems to me quite fatal to 
 a working logic. 
 
 *" I shall return to this question, in speaking of the reservation above 
 alluded to. 
 
 " Ibid., pp. 170-2. ' A theory of truth as coherence, if it is to be 
 adequate, must be an intelligible account of the ultimate coherence in 
 -which the one significant whole is self-revealed ; and just before " any 
 partial experience", e.g. human knowledge, is "true" more or less, 
 according as it exhibits a character more or less approximating to the 
 complete coherence ' (my italics). I suggest that the ' ultimate ' or 
 ' complete coherence ' is not an intelligible expression. Coherence is 
 the substitute, possible only in a system of predicates and relations, for 
 the immediate unity, transcending mediateness, which we are compelled 
 to ascribe to a perfect Reality. I repeat that the affinity of two 
 exhibitions of a principle, or of two kindred principles, has nothing to 
 do with correspondence in this discussion, which means correspon- 
 dence of a copy with the original by which it is to be judged. The 
 application of it in other senses in this context involves the fallacy 
 of post hoc ergo propter hoc. 
 
Chap. IX] Poiut ts the immanent standard 291 
 
 approximation, I take it, involves the correspondence theory 
 to which accordingly at this point the enquiry harks back. 
 Thus we lose the immanent standard, and with it the whole 
 merit of the coherence theory. But reality in all its forms 
 and phases can defend and maintain itself according to the 
 principle of non-contradiction. It never depends for its 
 relative logical stability upon approximation or correspon- 
 dence to anything else. 
 
 iii. And further I suggest that it is a confusion to use the The 
 conception that even truth is not quite true to suggest a 1^ ^^t' • 
 recurrence to a correspondence theory.* The meaning of not truth, 
 this conception is very simple when we once have grasped 
 the point that no experience short of perfect realityis altogether 
 itself. It is in that sense, that even the truest truth, such 
 as the coherence theory of truth, is not quite true ; that is 
 to say its fullest completeness lies in something, a more perfect 
 form of experience, which is beyond itself ; and we may call 
 this, to emphasise the relation of transcendence, a truer 
 truth. 
 
 But it is not truth in the form of truth, and there can be 
 no question of truth in its own form possessing correspondence 
 or approximation to its character. Truth stands on its own 
 ground, as a fulfilment imder its own conditions of the nature 
 of reality ; and it can be tested as truth under these conditions 
 and under no others, and therefore, as we have seen, by itself 
 only and by nothing else in the imiverse. There is no meaning 
 in the suggestion that ' the coherence-notion of truth on its 
 own admission can never rise above the level of knowledge 
 which at the best attains to the truth of correspondence '. 
 
 The coherence-doctrine is a theory, and so far is only truth. 
 But coherence does not further and doubly fall short not 
 merely by being only truth, but by resting its claim to be 
 truth on imperfect correspondence. It rests its claim on the 
 
 * Joachim, p. 174. ' Since all human discursive knowledge remains 
 thought " about " an Other, any and every theory of the nature of truth 
 must itself be " about " truth as its Other ; i. e. the coherence -notion of 
 truth on its own admission can never rise above the level of knowledge 
 which at the best attains to the " truth " of correspondence. Assuming 
 that the coherence-notion of truth is sound, no theory of truth as 
 coherence can itself be completely true,' &c. 
 
 U2 
 
292 Truth and Coherence [Book ii 
 
 working of reality within it, and not on any correspondence 
 that may result from this ; and to get away anything truer 
 you would have to pass beyond truth into another form of 
 reality. This may seem a needless subtlety ; but it is impor- 
 tant to avoid the implication that truth as such is something 
 away and beyond, which the coherence-notion ought to corre- 
 spond to, but does not quite succeed. If this is admitted we 
 lose our immanent standard. 
 Our 5. One reservation, it seems to me, must be made upon the 
 
 ^m' doctrine that thought is essentially discursive and relational, 
 world. It points only to an anticipation of the fuller experience, and 
 as I am quite aware, not to an achievement of it. But it 
 appears to me suggestive, and more than that, I cannot see 
 my way out of it. 
 
 It is nothing more than the recognition that the worlds 
 we severally live in, with the spatial world of each of us, have 
 been fundamentally transformed and reconstructed by thought 
 working in and on perception and general experience. They 
 are now, as for example our spatial world with its full pro- 
 perties and qualities, worlds all different and peculiar, and 
 yet solid and individual in an appreciable degree, possessing 
 up to a point existence and quality in one. The interest is, 
 that if this is so — and I cannot open my eyes without finding 
 it so — we have created for ourselves by thought originally 
 discursive, a new immediacy, a new ' given ', a new basis 
 of feeling and object-matter of simple apprehension. Nothing 
 is more various, more relative, more progressive and personal, 
 than the so-called simple apprehension of objects which we 
 roughly postulate to be the same. For if we are to admit 
 such a thing as ' simple apprehension *, we must take it as 
 purely relative. Its object is a phase of our experience and 
 not a stratum of it.* Our worlds are all different, and yet all 
 apparently solid, and clothed in inseparable contents, which 
 nevertheless are of our own discrimination and attribution. 
 And these are not as a rule taken as predicates. They are 
 taken as belongings of the quasi-subjects or rather quasi- 
 substantive objects, although we can separate any of these 
 contents and make them into predicates. The objects of our 
 * See below, chap, x, passim. 
 
Chap. IX] Thought not wholly discursive 293 
 
 world, which are thus admitted as concrete subjects, are of 
 course affirmed in the general judgment which sustains the 
 everyday reality which we accept. But they are as I said 
 just now not naturally subjects in the sense of dividing them- 
 selves according to an S P relation. The judgment which 
 affirms them takes most naturally an impersonal or existen- 
 tial form. 
 
 When treated as subjects, they are not naturally taken 
 as subjects of their nearest habitual predicates. These have 
 qualified and clothed them, and are presupposed, not ex- 
 plicitly affirmed, in judgment. It is only in textbooks of 
 Logic that we say ' Man has two legs '. ' The grass is green * 
 and the like. All this belongs in usage to the solid starting- 
 point, not to an S P judgment proper. But these starting- 
 points, though relatively given, are really artificial, and in 
 some degree different for every mind. 
 
 These relative data or quasi-individuals are indeed the 
 so-called subjects which were to count as a plurality of things *. 
 But the interesting point about them is their relativity. 
 Thought has made them, and as may be seen in any criticism 
 of their solidity, can unmake them. And to speak more 
 obviously and without reference to abstruse speculation, we 
 can see that it is always remaking them. 
 
 This is all I desired to point out ; that a quasi-real world, 
 apparently solid and individual, is always being deposited as 
 part of the work of thought. I draw no general conclusion 
 but this, that thought which can thus deposit an apparent 
 solid individual, is not so far removed from the nature of the 
 fuller experience as an exclusive study of the discursive S P 
 judgment tends to make us suppose. This was the side of 
 thought which e. g. to Green seemed characteristic and im- 
 portant.^ I do not in the least care to enter into a verbal 
 controversy whether it is more properly called thinking or 
 something else. But that our discursive judgment itself is 
 always building up a world which its operation then presup- 
 poses — ^the world in which each of us lives, and takes it as 
 actual — ^this I do think is an important part of its character 
 and a striking analogy between it and ultimate reality. 
 
 * p. 277 above. •• e.g. Works, iii. 144-5. 
 
294 Truth and Coherence [Book ii 
 
 Does 6, One word more. This quasi-real world of our own 
 
 ^'^"^' ti ■ - i^^^^^"S ^s alwaj's passing at its edges into the discursive 
 world? S P process of science and synthetic judgment. And on this 
 No, It IS ground it may be objected to our view of coherence and cor- 
 respondence ; ' But here you have a real and immediate 
 world, actual in your experience, and your synthetic judginents 
 are about it. Does not this mean that your truth is corre- 
 spondence — ^the right representation of your relatively real 
 and solid world ? ' And I answer, ' emphatically, no.' For 
 our ' given ' solid immediate and real world, in which all these 
 characters are merely apparent, is absolutely plastic,* as in all 
 immediate judgment and every object of simple apprehension. 
 It is just as likely that it may have to yield to Science or 
 Speculation as that they may have to yield to it. Nothing in 
 the whole field is a fixture to which all other elements have to 
 correspond. Nothing is certain except the necessity that the 
 whole should be coherent. 
 
 * This is not plasticity of ultimate Reality, but may perhaps have 
 been mistaken for it. 
 
CHAPTER X 
 
 The Relation of Mental States to Judgment 
 AND TO Reality 
 
 It seems desirable, for the reason stated in the Preface, The 
 to conclude with a brief discussion of the sense in which, if ^®"*^^. 
 
 states in 
 
 at all, mental states enter into judgment and into the real question, 
 world. 
 
 By mental states or facts in this connection I mean such 
 as are taken to be concerned with judgment, and not volitions 
 or emotions, unless of course these happen to be the content 
 of judgment. 
 
 I. The view of the relation of mental states to Judgment * Doctrine 
 which has been adhered to in the present work consists of two p^eslnt 
 principal considerations, work. 
 
 First, a, that no mental states in a human consciousness are 
 mere mental states, but all contain matter that has been and 
 may be significant ; but secondly, /3, therefore, that the differ- 
 ence between mental states and ideas with a meaning lies in 
 the ' use ' of the former.. 
 
 a. In the first place, then, aU sensational or perceptual con- All sense- 
 • 1 • 1 XI X £ content 
 
 tents, at least m a human consciousness, bear the stamp oi signifi- 
 
 some symbolic relations and hold their place in the systematic ^^^^y ^V^ 
 
 judgment which affirms our world. There are no ideas which may be- 
 
 are not directly or indirectly affirmed of reality, and therefore ^°^f ^ . 
 
 a fortiori none which are not symbolic or significant. mind. 
 
 In taking this view from the beginning,^ I was strongly 
 
 influenced by a fact almost too elementary to mention, but 
 
 one which I am glad, nevertheless, to see plainly referred to in 
 
 * The view was suggested to me, of course, by Mr. Bradley's Principles 
 of Logic. But he is absolutely without responsibility for my account 
 or defence of it. I ought perhaps to refer to his footnote in Mind, N. S- 
 60. 44S-6, which indicates that he has intentionally modified the ex- 
 pression of his views on ideas since his Logic was written. 
 
 '' See vol. i, p. 69 ff., and Knowledge and Reality, p. 142 flf., on ideas 
 in fiction. 
 
296 Mental States in Relation to Judgment [Book 11 
 
 a very valuable recent argument.* It is the fact that for a 
 human consciousness at all events, there is, in the main, no 
 storehouse of mere unapplied psychical material, no sensations 
 which are unattached subjective states, nothing psychical 
 which is not stamped and figured within its own sensuous 
 being by divisions, relations, intensities, all relative to its 
 meaning as signifying some object of thought. There is in 
 the main nothing psychical analogous to a painter's colours 
 on the palette, before he uses them to represent objects. It is 
 a question for psychology whether sensational states can ever 
 escape the despotism of significance, and be a something in 
 the mind which belongs to and suggests nothing more than 
 itself.^ I believe that if they could be proved to do so, it 
 would be little more than a curiosity of research. These 
 would be, so to speak, immediate, or mere mental states, 
 because they had not attained objective determination ; 
 because they were, crudely speaking, below objective appre- 
 hension and nearer to what we might conjecture of some non- 
 human consciousness, in wliich, however, lacking the contrast 
 to the objective, they could not be distinctively ' subjective '. 
 But it follows from the point of view we are now drawing out 
 that the existence of immediacy, of mental states or psychical 
 facts, does not depend on the reality of such limiting cases '^. 
 Immediacy is a character that may be assumed by any 
 mental complex or object, however logically articulate or 
 external and independent of mind it may appear under certain 
 conditions. And no complex or object is altogether beyond 
 it. Every one has its immediate mental aspect. Thus, on 
 the one hand, there is no mental state to be applied in judg- 
 
 * Professor Stout in Mind, January 191 1. The present chapter has 
 been influenced by this very valuable article. Only, if I understand it 
 right, it says that the sensational nuances are part of an immediate 
 stratum, beyond which is the meaning to which thought is directed 
 through them. Thus you get — so it seems to me — a dualism, which I 
 wish to deny, between the shaped and nuanced sensation, and the object. 
 
 •^ As I have asserted to be exceptionally the case, i, p. 71. I 
 suppose it may be possible to have a sensation without taking it as 
 meaning anything but just itself. I do not believe it is a common 
 experience, even, say, with pain or emotion ; see below, p. 300, and cp> 
 Hoernle in Mind, 61, pp. 75-6. 
 
 <= See the other alternative specified, i. 71, above. 
 
Chap. X] Anything may become psychical 297 
 
 ment, which is not already organised as part of a significant 
 structure, an object of thought, to the nature of which, as we 
 saw, its actual sensuous detail and constitution is subdued. 
 On the other hand, there is nothing in this to prevent it from 
 becoming completely and emphatically, what it always and 
 necessarily is in some degree, a part of our psychical being, 
 a particular mental state or occurrence, one with us in feeling 
 and active in the total life of our mind. And as we are con- 
 vinced that there is nothing or almost nothing absolutely and 
 finally immediate or wholly below mediation and determination, 
 and yet immediacy is certainly a large element in the mind, 
 it follows that this, viz. psychical immediacy as one side of all 
 ideas whatever, not only may be but must be a fact. Imme- 
 diacy is not a stratum of our consciousness, but a phase which 
 all or any of its objects participate in and may totally pass 
 into. No doubt, what is an object of thought cannot in so far 
 be an immediate state of ourself, and vice versa. But it is 
 always in some degree both, and there is nothing in its being 
 an object of thought ever so determinate and elaborate to 
 prevent its falling back into an almost complete immediacy, 
 in which case it carries within it the full detail of the content 
 which it possessed as an object of thought. \Vhen we feel 
 ourselves most at one with art or nature we are also furthest 
 from being deprived of the quaUties and distinctions of the 
 content ; rather we then hve in them with the most sensitive 
 completeness. It is the objective relation — the externality of 
 the cognised object — ^which is then in abeyance so far as 
 immediacy is complete. The content has really become all 
 but a subjective state. 
 
 In a word, immediacy, or psychical existence, or being as 
 a mental state, is a condition into which the whole mental 
 content may pass, and into which it is capable of passing as 
 a whole, the marks of thought and the stamp of objective 
 relations being in no way obliterated by the transition. This 
 is the old contention that sensation is full of the ' work of 
 thought ', as e.g. notably in the perception of distance, which 
 is demonstrably not given in the peculiar sensation of the optic 
 nerve, and yet is seen in a way prima facie indistinguishable 
 from any visual sense-perception. We cannot separate 
 
298 Mental States in Relation to Judgment [Book ii 
 
 sensation from thought, and it is not sensation only that 
 can become immediate. Immediacy, as was said above, is 
 a phase and not a stratum of our experience, and mental 
 states, and existence as a mental occurrence, are the same 
 thing as immediacy. 
 The 'use' /3. Secondly then ; it follows from this consideration that 
 tents'as ^^^ practical purposes the difference between mental states, or 
 ideas; particular existent mental contents or occurrences, and ideas 
 with a meaning or universal thoughts of real objects (universal, 
 because all real objects are universal, as persistent elements 
 of reality) lies in the ' use ' of the former. I will put what I 
 mean as frankly as I know how, to assist, if possible, both 
 readers and critics rather than to guard myself. There is, we 
 have agreed, no great storehouse or constant new production 
 of psychical states or psychical material such as to be primarily 
 subjective, non-significant, mental existences or occurrences, 
 waiting for objectification through a sort of christening and 
 name-imposing process.* But, all the same, we proceed in 
 judgment as if there were. Our world of known objects, of 
 apprehension, sensation, perception, contains within it a mass 
 of psychical stuff ; and the fact that, as we have said, all this 
 is stamped and appropriated ab initio does not in the least 
 interfere with our treating it as a storehouse of such stuffs 
 and using or appropriating it over again, and modified, in 
 every new psychical production. I hear a noise in the room 
 overhead. It is perfectly significant and I know exactly what 
 it is ; it is the patent roUer-broom. But the fact that it is 
 thus appropriated in judgment does not in the least prevent 
 me from using it to think of a cab coming to the door. 'A cab 
 sounds just like that,' and this change of application of its 
 content necessarily implies the recognition in it of an immediate 
 or existential side, a treatment of it as something which is an 
 occurrence in my mind and can be used to qualify a subject 
 quite other than that which it qualified before. In this use 
 its previous structure and nuance are partly disregarded and 
 partly modified. 
 
 Is this term ' use ' a mere word ? Can we not get nearer the 
 fact which it indicates ? 
 
 * Cp. explanation, Introd., p. 17 note. 
 
Chap. X] The ' usc ' of a content 299 
 
 Mr. HoernM ^ has warned psychologists against the idea that 
 the complex of word-meaning is formed by mere association. 
 I suppose we may generalise his remark, and say that mere 
 association is not enough to develop meaning. It is different 
 to think first of one thing and then of another, and to treat 
 the one as a qualification or character of the other. No doubt 
 this is true. But we have surely learned of late that every 
 association is at bottom a pure connection of judgment, and 
 where judgment afifirms a character of a subject you certainly 
 have meaning. This seems to give us the distinction we want. 
 A content is * used ' when, in judgment, it qualifies a real 
 world ; when its nature, carrying us beyond its mental exis- 
 tence, makes us attend not to the latter, but to a quasi-inde- 
 pendent subject, ultimately a condition under which that 
 nature is true of reality. It is the work of thought as opposed 
 to feeling ; of what we know to what we are ; if only we 
 remember that thought adds no element to feeling, but merely 
 re-organises its matter. 
 
 Thus we use our stores and our fresh production of psychical 
 stuff, in their original and acquired content,*' or any part of 
 it, to qualify subjects independent of those whose stamp and 
 figure it bears ah initio within itself. And this is possible 
 because it is after all in one aspect and more or less completely 
 a psychical existent, and as such is not tied down to any 
 significant structure, although primarily appropriated by one 
 or another. 
 
 And it should be observed as a general principle of judgment "= 
 that subject quaUfies predicate no less than predicate subject ; 
 for the judgment is a brief expression of the same imity 
 which is more fully uttered in inference, where premisses 
 qualify conclusion just as conclusion qualifies premisses. This 
 explains how a psychical content may appear to become more 
 in meaning than it was as a content, when it is synthesised 
 with a relatively ^ self -existent subject. 
 
 * Mind, 61, p. 76. 
 
 ^ See vol. i, p. 69, note, with reference to Professor Stout's paper in 
 Aristotelian Proceedings, 1903. 
 
 ° See Appendix to ii, chap, i, p. 41 note'=, and vol. i, p. 69. Cp. 
 previous note. 
 
 ^ No finite subject is more than relatively self-existent. On the 
 
300 Mental States in Relation to Judgment [Book ii 
 
 The term ' use ' in short, implies the distinction between the 
 existence and the content of a mental state. When we take 
 a character out of one complex and apply it to qualify another 
 we may be said to ' use ' it. It is a case of the law of thought 
 by which the nature of an existent carries us beyond it. 
 In being ' used ' it becomes part of the clothing, so to 
 speak, of a determinate subject in the world which judgment 
 sustains ; and in becoming this it is penetrated by new 
 relations, and takes on a new stamp and new articulations 
 in response to the nature of the subject which stands 
 ready to receive it. ' The coat is rough,' * The road is 
 rough,' ' The sea is rough,' ' The man is rough.' In each 
 of these predications the common content which has become 
 one with the word — say ' unevenness ' — has taken on from its 
 subject a special nuance and articulation. But what is one 
 with the content is itself a Vciriable amount, and is affected 
 by usage and by the nuances and articulations which it is 
 in the habit of taking on. The psychical existent or immediate 
 is not a part of our mental formation but a phase of it. 
 \Vhat is acquired enters into it as much as what is given, if 
 indeed there is any sense in speaking of the given when it is 
 impossible, finally and in principle, to draw a line between 
 the given and the acquired. Any content of apprehension or 
 comprehension may become a state of our mind. 
 
 The result of our discussion amoimts to this. 
 
 AU mental states are phases into which our objective 
 apprehension under certain conditions may fall. All our 
 objective apprehension is something which is capable of taking 
 the shape of a mental state, i.e. of becoming immediate. I may 
 add as to the former point that none of the cases commonly 
 alleged as cases admittedly of mental states or states of the 
 self, e. g. the experience of pain and pleasure, are wholly free 
 from objective reference. A great part of the horror of pain 
 depends upon this ; that something seems to be devouring 
 you, or growing within you, or crushing you, or piercing you, 
 or tearing you. The mental state in virtue of its content passes 
 
 fresh determinations acquired by a content in use see Professor Stout, 
 At. Proc., 1903. And on the self-transcendence of the existent, cp. 
 Hoernl6, p. 75, who finds a difficulty in it. 
 
Chap. X] Mental States and the Real 301 
 
 into affirmation, as affirmation in virtue of its existence passes 
 over into the mental state. You cannot find a kind of ex- 
 perience which is necessarily amental state and no more; nor can 
 you find one which necessarily involves an apprehended object 
 and no less. It is a fundamental error of principle to look for 
 either. Immediacy is a phase and not a stratum of experience. 
 
 2. Having thus discussed the relation of states of the self The Real 
 to judgment, it remains to draw the consequences of this ^°\ , 
 relation in its bearing on the real world — to take a test case, by sub- 
 though not the most important case, on physical reality. traction. 
 
 The full detail of such a discussion as Mr. Prichard has 
 recently devoted to Kant's Theory of Knowledge, goes beyond 
 the purpose of a treatise on systematic Logic, I am only 
 anxious to explain the attitude to the ideal construction of 
 reaUty which underlies the present work, and for that purpose 
 I shall refer to some of Mr. Prichard's arguments. 
 
 I place in the forefront of my observations a principle, 
 which I take to be fundamental, and to which I have already 
 more than once referred. The significance of judgment and 
 knowledge as of experience in all its forms lies always on 
 ahead, and not behind ; that is to say, in attempting to discern 
 the real reality which justifies any experience you must 
 go forward from it to the more concrete and more complete, 
 and not retire upon something from which an element has been 
 withdrawn. This is the well-known principle that the truth is 
 the whole ; the same is true of the reality ; and it is in ap- 
 proximation to the whole, and not by disruption of the 
 organism of experience into two opposing sides, that truth and 
 reality corroborate one another. So far as the Realist move- 
 ment of to-day is a reaction towards naive realigm, it is a 
 contradiction of this fundamental principle — an outcome of 
 theoretical timidity and pessimism, which prefers in a difficult 
 situation to seek safety in retrogression rather than success 
 in advance. For the moment, I believe that this character 
 is uppermost in it. But it must be, of course, at this time 
 of day, naive realism with a difference ; and I hope to in- 
 dicate in passing that of necessity it carries elements within 
 it which point to a real philosophical reform. 
 
 I will briefly observe on three points in which current 
 
302 Mental States in Relation to Judgment [Book ii 
 
 Know- 
 ledge 
 involves 
 Mental 
 States. 
 
 Reality 
 lies 
 ahead, 
 not be- 
 hind. 
 
 theory seems to affect the notion of apprehension and 
 comprehension by the mind in relation to reality. 
 
 I understand it to be maintained : 
 
 a. That external objects, spatial and physical objects, are 
 not in any sense or degree states of the mind ; for in the first 
 place, there is no need that they should be so in order to be 
 known ; and in the second place, if they were so, they could 
 ex hypothesi not be known as apart from the knowing self ; 
 and it is an axiom that they are so known. And as a sub- 
 contention to remove the apparent contradiction of the main 
 doctrine, it is urged that knowledge is an activity sui generis 
 and cannot be explained. 
 
 j3. It would follow that the present writer is wrong hi 
 attaching considerable value to subjective idealism as a 
 propaedeutic ''* and a partial truth. 
 
 y. It is dangerous to say that judgment sustains the world,'' 
 and untrue to say that we relate Predicate to Subject ; that 
 inference is a process of ideal construction, or that we ideally 
 construct reality.*' 
 
 In my view, all these opinions depend on the one central 
 fallacy pointed out above, that to find the reality independent 
 of experience you must have recourse to a reality apart from 
 experience. 
 
 a. We have seen that all judgment and its elements, not 
 to mention sensation and feeling, are in certain aspects always, 
 and in certain phases completely, states of the self. 
 
 (i) But it is urged that the objects thus known or the 
 experiences thus experienced are not dependent for their 
 qualities, for elements of their real being, upon judgment, 
 sensation, and feeling ; and therefore, though all these involve 
 mental states, yet the objects known or the phases experienced 
 in them have none of their reality in these states. 
 
 I note at starting the extraordinary contention which this 
 view makes necessary, that colours, sounds, smells, tastes, and 
 sensations of touch are not qualities of things ; * and with 
 this, the attempt to show that because we know space to have 
 
 '■^ Essentials, p. 20. •* Caird, Proc. Brit. Academy, vol. I, 
 
 p. 106. *= Prichard, 242-5. 
 
 ■^ Prichard, 86-7. To be on all fours with the other cases it should 
 be what you feel in sensations of touch. 
 
Chap. X] Reality lies ahead 303 
 
 three dimensions, though we can never see it so, therefore we 
 know space as it is independent of perception. This latter 
 argument precisely illustrates the tendency which I call going 
 backward instead of forward to look for reality. To know 
 what space is involves perceptions of more than one kind, not 
 merely visual, and, on the top of that, inference, i.e. a mode 
 of conception which resolves the contradictions of perception. 
 And because the knowledge of the nature of space involves 
 the work of a percipient plus that of an intelligence, i. e. 
 because the apprehended nature of space is a reconciled 
 perception, going beyond the possibilities of actual per- 
 ception into the realm of thought, we are told that the 
 properties of Space do not involve a percipient at all.* The 
 fact is that they imply an intelligent percipient (if this needs 
 to be formulated as though a percipient could be not 
 intelligent) ; and that, just as the contradictions of perception 
 have forced us to go beyond perception to something not 
 presented in any actual perception, so the further employ- 
 ment of intelligence, in removing the contradictions of its 
 primary constructions, may force us to assume as reality 
 something which excludes the ultimate reality of any space 
 at all. You can only correct a perception by going forward 
 in the positive process of removing contradictions. You 
 destroy all positive reality if you attempt to go back by simple 
 subtraction to a point anterior to perception and say that the 
 the real is, what it is when perception is withdrawn — a pre- 
 dicate in this case involving, though not wholly given in, percep- 
 tion. We see here the abstractions to which we are driven 
 if we refuse to look for the self-existent reality in the inclusive 
 whole which the effort to think things completely forces us 
 to assume. If we turn back in search of independence gained 
 by omission, we cannot avoid committing arbitrary acts of 
 abstraction like the foregoing at every step. 
 
 (2) Now we can see the explanation of the doctrine which Truth in 
 we find ascribed to a mere assumption.^ It is held, we are can only 
 told, that the mind can only apprehend what belongs to its appre- 
 own being, and that this is a gratuitous assumption. It is, j^g^jf . 
 if taken in one sense, a false assumption, but it is, as against 
 
 * Prichard, p. 91. ^ Prichard, p. 118. 
 
304 Mental States in Relation to Judgment [Book ii 
 
 the opposite error, not at all gratuitous. It starts from the 
 obvious fact, now coming to be admitted even by realists, "* 
 that the object apprehended, say, in sense-perception or in 
 thought, forms an integral part of our mental life and emotions, 
 contributes influence to it, and derives predicates from it. 
 But so long as this obvious fact is denied by a realism which 
 so far remains naive (owing as I must believe to a very simple 
 and popular fallacy which I will point out directly), any 
 philosophy which respects the facts while bluffed into accepting 
 this denial, must necessarily say that the objects of appre- 
 hension are simply psychical states and nothing more. Sub- 
 jective Idealism is the nemesis of realism. What is wanted 
 is to go forward, amending and expanding the experience 
 which progressively approximates to giving us things as they 
 are, under the full conditions which enable them to be what 
 they are. The reality thus attained altogether transcends at 
 once our particular mental states and the thin abstractions 
 which form the realist's actual world. We need no assumption 
 that the mind can only apprehend what belongs to its own 
 being. We need only to recognise the obvious fact that what 
 it apprehends at least participates in its own nature, a fact 
 which the realist is forced to admit, both by the degree in 
 which be truncates reality when he withdraws from it what 
 he believes to belong to the mind ; ^ and by the degree in 
 which the remainder which he is forced to leave to it still 
 distinctly exhibits a living logical nature far transcending 
 what can be ascribed to a physical object as physical. 
 Thus, he tells us, * gold ' is by itself and apart from mind 
 ' a connection of universals *< — i.e. it obeys the law of the self- 
 ti"anscendence of finite experience and embodies in itself a 
 complex of conations.'' And if we refuse to recognise' this fact 
 
 * Who, so far as they admit it, are no longer naive realists. 
 
 '' Prichard, pp. 116-8. 
 
 •= (Prichard, pp. 242-4). We shall see, too, below that inferential 
 connection is to be a character of external reality per se. Unless it 
 is so, it is nonsense to speak of merely discovering connections. You 
 can only discover conjunctions of fact. Necessary connections must 
 be inferred by intelligence, unless they infer themselves. I am per- 
 fectly certain that the present so-called realism, which does not yet 
 understand whether it is naive or not, will have to hark back to an 
 
Chap. X] Fallacy of Apartness 305 
 
 in our theory of the reaHty beyond our particular mind, it 
 must compel us falsely to concentrate the real into mere states 
 of the finite centres themselves. 
 
 (3) I note the same retrogressive impulse in the idea that What ex- 
 explaining a thing means explaining it away, i. e. deriving it means^°" 
 from what is not itself.* To explain a thing, surely, is to think viz. com- 
 it in terms of the whole. A good explanation makes more, thinking 
 not less, of what it explains. It draws the outline of its full 
 individuahty — which only its relation to the whole can exhibit 
 
 — and calls attention to the law of its being. Even an aesthetic 
 product can be enhanced in value by good explanation. But 
 I fully agree that it is impossible to have a theory of cogni- 
 tion, if that means a theory of cognition apart from a theory 
 of reality, because to omit either is to omit what is essential 
 to the full individuality of the other. 
 
 (4) And now we come to the supposed axiom of independent Fallacy 
 reality, and what I take to be the fallacy on which it rests, ^epen" 
 ' Knowledge unconditionally presupposes that the reality dent of 
 known exists independently of the knowledge of it, and that ^^^^ 
 we know it as it exists in this independence.' ^ If we construe 
 
 ' independence ' as = ' being apart from ' I am quite sure that 
 this statement is false. Knowledge has no such presupposi- 
 tion. We have no such conviction. The presupposition of 
 knowledge, and our conviction, may be stated '^ in the first 
 place briefly : ' So far as we know things, we know them as 
 they are ; ' and then more precisely, ' Knowledge presupposes 
 that the system of judgments in which it consists can maintain 
 itself against any contradiction, and that the reaUty known is 
 unmodified by knowledge except in the direction of being 
 revealed as more completely itself.' Thus the axiom as first 
 stated rests on a plain fallacy a dido secundum quid ad dictum 
 simpliciter. The nature of reality is not differentially depen- 
 
 outrageous form of Hegel's extreme doctrine, that every ' thing ' is a 
 judgment and a syllogism. 
 
 * Prichard, p. 124. 
 
 ^ Prichard, p. 118. ' Independent ' seems to = ' apart from ', p. 119. 
 
 ■= A difference of opinion about the statement of essential functions of 
 knowledge is not at all a surprising thing. The functions are relative 
 to the whole, and our view of them depends on our view of it. Cp. 
 vol. ii, p. 229. 
 
 1337-2 X 
 
3o6 Mental States in Relation to Judgment [Book ii 
 
 dent on knowledge ; but it is a fallacy to go from that to the 
 statement, 'Reality is what it is apart from knowledge,' unless, 
 as seems to be partly the case,* you are relying on the contrast 
 between knowledge and other forms of experience. It is 
 a plain fallacy to say that because the difference between 
 a, b, and c is not due to x, therefore a, b, and c can be what 
 they are if x is withdrawn. 
 
 And it does not suffice to suggest that to the special nature 
 of any reality may be annexed the additional characteristic 
 of being known.* The point is that the nature common to 
 every reality — ^say, for instance, the admitted fact that it is 
 a connection of universals," involves its sharing the life and 
 characteristics of experience. If it is argued that you must go 
 to the special nature of every reality to determine whether 
 or no it is dependent on mind (or, to put it more truly, and 
 in a way that avoids subjective idealism, ' whether it partici- 
 pates in the life of experience'), the answer is that that question 
 has long been considered and the result is not doubtful. 
 The admission that the secondary qualities have special 
 natures dependent upon mind is enough by itself to break 
 down the principle that qualities of things must be inde- 
 pendent of perception.^ And if independence breaks down 
 here, it cannot be maintained with apprehension and with 
 knowledge. The nature of reals is fatal to the axiom that 
 we know things as they are apart from cognition. The essence 
 of this axiom is to look for leality in abstraction and isolation; 
 rightly to accept the thing-in-itself as being what we know it 
 to be ; but without a shadow of justification or probability to 
 assume that the being of the thing in itself is compatible 
 witli isolation instead of demanding as a condition of its exist- 
 ence the full context and interconnection of experiential life. 
 
 (5) This inclination is natural, because it promises to 
 
 * Prichard, p. 118. Of course we do not say that knowledge is the 
 only form in which Reality can appear, nor the most adequate. But 
 we do say that reality is inseparable from experience, and that is enough 
 to negative the contention that it is what it is apart from mind. The 
 only plausible case of being apart from knowledge is that in which, like 
 pain, it is plainly not apart from mind, but another kind of experience 
 takes the place of knowledge. 
 
 ^ Prichard, p. 116. * See above, p. 304. 
 
 ^ Prichard, p. 120 If., cp. 86 If. 
 
Chap, x] Apart from knowledge — minus the organ 307 
 
 common-sense a simple ultimate real, ensming facility of A simple 
 treatment and finality in apprehension. But the anticipation ^^^^ ™"sf 
 of facihty and finality in contact with the real is, I am certain, mental 
 fundamentally vicious, and any theory which is guided by °®"^S' 
 it stands ipso facto self-condemned. We have noted the 
 involuntary recognition of this truth by the modern realist.* 
 But as recognised under his dualistic assumption it becomes 
 false. It tends to ascribe a psychical character to things 
 apart from the mind. But what we want, and what an un- 
 distorted view of the presupposition of knowledge affords us, 
 is not a psychical character of things apart from the mind, 
 but a logical character of reaUty as revealed through the mind 
 — self-revelation being essential and inherent in the real, 
 whose nature apart from it is self-contradictory. 
 
 (6) And in the proposition that the real is for knowledge if lude- 
 the same that it is apart from knowledge I note an old elemen- pendent 
 tary difficulty which seems to me insuperable. How can you from, 
 separate the cognitive apprehension of an object from the different 
 operation of the organ of sense upon it ? Grant, for the sake objects 
 of argument, that if, per impossihile, you could compare a ^^^ ^^^ 
 mind's cognitive consciousness of a perceived object with appre- 
 the full report of the Hving and healthy organ of sense directed ^^"^^°"- 
 upon it but minus consciousness, you would find that the 
 bare addition of cognitive consciousness had not falsified 
 the report, and therefore that the cognition had in no way 
 modified the apprehension of the full object ; the full 
 object being the object of perception plus the modification 
 effected in its physical operation by the organ of sense. 
 Then (omitting ex hypothesi the fact that in the absence of 
 consciousness apprehension would not have taken place at 
 all) under the impossible condition which I have granted you 
 would be entitled to say that the intervention of cognitive 
 consciousness left the object — the full object — precisely as it 
 would be apart from such intervention.^ 
 
 * Professor Alexander's contention, e. g. Ar. Proc., 1908-9, that what 
 are commonly called psychical objects are physical, cannot be carried 
 through without a rapprochement between what aire commonly called 
 physical objects and the psychical. The comment of the text seems 
 to me to apply to his view, 
 
 " I omit for the sake of argument such matters as the influence of 
 
 X2 
 
3o8 Mental States in Relation to Judgment [Book ii 
 
 But this, I take it, is not by any means the case which is 
 in question when we are told that the object of knowledge 
 is for knowledge the same that it is apart from knowledge. In 
 this doctrine I presume we are comparing the object as per- 
 ceived through the organ of sense plus cognitive consciousness 
 with the same as it is when withdrawn, not merely from 
 the operation of cognitive consciousness, but from that of the 
 organ of sense as well. But that the object should be the 
 same under these two conditions, of being known after trans- 
 mission through a sense-organ, and of neither being known 
 nor transmitted through a sense-organ, is surely a physical 
 impossibility. A physical object cannot be the same when a 
 complex physical condition is superadded to it and when 
 that condition is withdrawn. And the superadding of this 
 complex physical condition is in every case inseparable from 
 the apprehension of the object; therefore it cannot conceivably 
 be the same when apprehended and apart from apprehension.* 
 
 For us this has no difficulty. We do not doubt that the 
 thing really is as it is apprehended, because its reality for 
 us is its full self-maintenance imder the completed conditions 
 of experience. But it seems to me absolutely fatal to the 
 axiom of knowledge which was criticised above. You may 
 throw overboard, as appeared to be practically done by the 
 view in question, the secondary qualities,^ but you cannot in 
 the full sense of the axiom secure even the primaries. And 
 I must insist that with the abandonment of the secondary 
 qualities the axiom is absolutely surrendered. If the real 
 world apart from knowledge has no secondary quahties, it 
 has hardly anything of what we care for. It is not recognisable 
 as our world at all. 
 
 It may be argued that the nervous disturbance, or whatever 
 the result of the sense organ's operation may be, is not the 
 
 apperception, and allow the hypothesis that cognition should bring no 
 modifying influences with it to the report of the organ of sense. 
 
 * Note that in one place the theory we are discussing makes the real 
 qualities of a thing exist independently not merely of knowledge but of 
 perception and sentience (p. 86). Thus sentience cannot be appealed 
 to as presenting the complete physical object as it is apart from 
 knowledge. The real must be apart from sentience no less than 
 from knowledge. But cp. 306 sup. and reff. '' Prichard, p. 86. 
 
Chap. X] Continuity of matter and mind 309 
 
 object of perception, and we are never so much as aware of it. 
 That is a very good argument against saying that what we 
 perceive are neural tremors and nothing more. But it is 
 wholly irrelevant to the point that a vibrating violin-string is 
 not sonorous in the absence of a hearing ear, and a candle 
 is not a source of Hght in the absence of a seeing eye. These 
 are simple physical facts ; and they suffice to overthrow the 
 doctrine that objects are the same for cognitive apprehension 
 that they are apart from it.* 
 
 In conclusion, then, the true axiom of knowledge is that we 
 can know things as they really are. And that means, that 
 we know them in their full self-maintenance. There is no axiom, 
 that Warrants us in arguing directly from the reality of full 
 experience to the reality of abstraction, and if we adopt this 
 procedure we must do it on the special ground that what we 
 exclude is ad hoc irrelevant, a contention which always leaves 
 us exposed to some degi^ee of risk. 
 
 And as to mental states, our conclusion so far is certainly 
 not that the reality which we know either must or does 
 consist solely of the mental states of particular minds. But, 
 we urge, this proposition is false only because it would identify 
 the real with a particular phase or character of mental being, 
 and wiln that, moreover, as it is in each mind taken apart. 
 Our conclusion is, therefore, that the stuff of our mental states 
 does really and truly characterise and belong to external 
 objects, although, as characterising such objects, it ceases to 
 be a mere mental state. It follows that the nature of external 
 objects is continuous with that of the stuff of mind, and is 
 physical, i.e. has variations relative to those of other objects, 
 as well as psychical. Physical or spatial objects are just as 
 we know them, and truly have the characters which our 
 knowledge (so far as it is knowledge, i. e. so far as it is consistent 
 
 * Professor Stout's doctrine as stated in Mind, 77. 12-13, seems to 
 me not to be open to this objection, because, \\hile holding that in 
 presentation we have a glimpse of matter as it really is, yet in answer 
 to the further question, ' What matter ? ' he replies, as I understand, 
 ' the matter of our body, and of other things only as affecting that,' 
 not, as I read him, the matter of other things in so far as they do not 
 affect that of our body. I should not have thought that in this latter 
 point Mr. Moore would agree with him, as implied on p. 9. 
 
310 Mental States in Relation to Judgment [Bookii 
 
 with itself and with experience) attributes to them. The stuff 
 of mental states, therefore, enters into them, and though the 
 stuff of each particular mind is only a very small contribution 
 to the real world, yet it is a contribution, and is capable, in 
 principle, of furnishing some element which no other particular 
 mind supplies. 
 
 Objects then are only not mental states of particular minds 
 
 first because they are not states of mind, but interdependent 
 
 with minds and characterised by the stuff which is also 
 
 experienced in states of mind ; and secondly because if 
 
 they were states of mind it would not be the states of 
 
 any particular mind but the states of all minds. It 
 
 follows that the destruction of a single mind with its states 
 
 neither destroys the objects apprehended by it, nor again 
 
 makes no difference to their existence. It diminishes, in 
 
 principle, their amount of reality, and presumably moreover, 
 
 in doing so, deprives them of some character which no other 
 
 mind sustains in them, and the loss of which therefore is a 
 
 genuine loss of being to the object. So far mental states of 
 
 particular minds are the material of objective reality, not 
 
 merely as themselves psychical facts, but as facts which are 
 
 necessary to the nature of real objects. 
 
 The ob- (7) The same tendency to seek truth by omission is ex- 
 
 oercep- amplified in the desire to treat perception as essentially less 
 
 tion is than judgment, and to deny it the right to use the word ' is ' ; 
 
 tiOTiaVlv setting down the expression * is for me ' as a contradiction 
 
 'forme', in terms. '^ 
 
 * The assertion that something is so and so implies that it 
 is so and so in itself whether it be perceived or not, and 
 therefore the assertion that something is so and so to us as 
 perceiving though not in itself, is a contradiction in terms.' 
 The truth about this seems to me quite simple. Everything 
 is what it is under conditions. It is itself under full, normal, 
 or typical conditions, the distinction of which from any 
 partial or transient conditions is a matter of degree — of 
 convenience for science or for common sense. We cannot 
 possibly attain a right conception of * itself ' by the with- 
 drawal of all conditions. That is the fallacy signalised above. 
 
 * Prichard, pp. 72 &., 99 S. 
 
Chap. X] Vulue of SubjecUve Idealism 311 
 
 In perception, as in any other judgment, you may fail to 
 be aware of the conditions to which your judgment is subject. 
 In that case, judging unconditionally of what is conditional, 
 you fall into error. But if you name the conditions, or indicate 
 by a phrase of relation like ' for me ' that you are aware of 
 conditions though you cannot or will not mention them, the 
 predication ' is ' becomes appropriate at once. Everything 
 is what it is under conditions, and what it is ' in itself ' is only 
 distinguished by being under conditions which you accept as 
 normal. The thing which looks pink to a colour-blind man is 
 pink to him.* The condition of its being pink is present ; 
 that of its being blue is absent, and if it were not pink under 
 the existing condition it would have to be other in itself than 
 it is. The unconditional judgment of knowledge, interpreted 
 as about the thing apart from knowledge, is false precisely 
 in the same way as the judgment of perception is apt to be, 
 An unconditional judgment must be false unless you interpret 
 it to mean ' presupposing the normal or typical conditions '. 
 
 j3. I am therefore constant in the opinion ^ that Subjective Sub- 
 Idealism is a valuable propaedeutic to philosophy and especially {d^eaiism 
 to Logic. I understand it to mean that we know nothing insists on 
 but states of our own minds. It is not actually true, but it tinuity of 
 is truth of a higher order than that of naive realism. Naive universe, 
 realism I understand to deny that qualities which depend on 
 minds can be qualities of objects ; for it is essential to it that 
 objects should be what they are apart from minds. This 
 doctrine conditions reality by the withdrawal from experience, 
 and so cuts the universe in two. Subjective Idealism is its 
 nemesis. The latter urges that the qualities of reality are 
 continuous with the psychical, and then, if and because you 
 say that reality can have no psychical qualities, it repudiates 
 the dead reality so offered, and limits the real world to what 
 is admittedly self-maintaining in the context of a vital whole. 
 
 Thus it insists on the fundamental truths of the continuity 
 of nature throughout the real, and the dependence of its being 
 in some degree on every particular mind. It is this continuity 
 and this dependence — the life and wholeness of things — which 
 appear more especially distasteful to realism, and which it 
 
 * Ibid., p. 72 note, ^ Essentials, 19 ff. 
 
312 Mental States in Relation to Judgment [Bookii 
 
 avoids by the ignava ratio of withdrawing reaUty from any 
 essential participation in the whole of sentience and intelligence. 
 Against this logical quietism — profoundly connected, I am 
 convinced, with the timidity and pessimism of the day — the 
 subjective Idealist raises an audaciously exaggerated protest. 
 Whatever the object of knowledge may ultimately be, he 
 contends, it can only attain or sustain what is worth calhng 
 reality in and through a share in the full and continuous life 
 of feeling, sensation, and intelHgence. His error is to confine 
 the life in question to the particular mind, and to reduce the 
 real world to a mere combination of its states. But this error 
 means not that he is too idealistic, but that he is not idealistic 
 enough. He accepts the false doctrine which tells us that 
 a real world independent of knowledge must be complete 
 apart from knowledge, and rightly rejects a real world so 
 defined. He cannot therefore suggest the only solution which 
 can satisfy the logical need, a real world furnishing out of 
 its self-dependent being a content to knowledge and experi- 
 ence, but of a nature continuous with theirs, and one in which 
 self-revelation is inherent. Nothing but this can satisfy the 
 logical and metaphysical postulate that truth and reality lie 
 in approximation to the whole. And this postulate, which 
 is one with the law of contradiction, lies at the root of Logic. 
 Anything ultimately atomic, or independent, or non-plastic — 
 any truth or reahty not relative in respect of its qualities to 
 its degree of participation in the whole, is irreconcilable 
 with this postulate, and with a system of Logic resting on the 
 conception of logical stability. * 
 
 It is this fundamental principle that Subjective Idealism 
 maintains, when it treats the real world, however erroneously, 
 as a mere outgrowth or complex of mental states, and as 
 dependent for its being on particular minds. It thus emphasises 
 what I may call the arduousness of reality, both of its theoreti- 
 cal conception and of its detailed apprehension. Its conception 
 demands to be maintained always on the level of the life of 
 mind ; that is, when we think of what we mean by reality 
 we have also to think of feeling, sentience, and intelligence in 
 tlieir various grades of perfection as actually involved and 
 '^ Cf. p. 288 above. 
 
Chap. X] Sustaining the world 313 
 
 operative in sustaining the real in corresponding degrees. And 
 its detailed apprehension in the same way depends for its 
 completeness, not on mere adjustment to a hard datum, but 
 on the degree in which the whole is brought to bear upon the 
 given. Therefore there can be no simple apprehension (except 
 in the arbitrary sense that we may accept a certain level of 
 insight as satisfactory ad hoc), and no such thing as a receptive 
 attitude to data. The most obvious of perceptions involves 
 the beginning of a critical process, progressive, arduous, and 
 never finally accomplished. All this is the logical lesson of 
 subjective idealism ; and therefore in spite of its failure to apply 
 its doctrine to the self-dependent real object, I welcome it 
 as a logical propaedeutic. 
 
 y. ' V/hen an idealist speaks of the judgment by which Sustain- 
 we sustain the world,* however adequate may be his explana- ^"fjf 
 tion of such language, it is apt to excite a suspicion that his structing 
 theories, if they were completely worked out, would lead to 
 the individual being regarded as his own universe and his own 
 God.' ^ 
 
 ' When it is said that our world, or the world for us, is due 
 to our activity of thinking, and so in some sense made by us, 
 all that should be meant is that our apprehending the world 
 as whatever we apprehend it to be presupposes activity on 
 our part ' — ' Nothing is implied to be made. If anything is 
 said to be made, it must be not our world, but our activity 
 of apprehending the world.' ' Again, in judgment we cannot 
 be said to relate predicate to subject. . . . We must say that 
 in judgment we recognise real elements as related or combined.' 
 ' Again, when we infer, we do not construct, ideally or other- 
 wise.' ' Ideal construction is a contradiction in terms, unless 
 it refers solely to mental imagining, in which case it is not in- 
 ference.' . . . ' — Inference would cease to be inference, if by 
 it we made and did not apprehend a necessity of connection.' " 
 * The very nature of knowing presupposes that the thing known 
 is already made, or, to speak more accurately, already exists.' '' 
 
 " Cp. e. g. vol. i, p. 84 above. 
 
 '' E. Caird, ' Idealism and the Theory of Knowledge,* Proceedings of 
 British Academy, vol. i. 
 
 " Prichard, pp. 242-5. '' Ibid., p. 235. 
 
3^4 Mental States in Relation to Judgment [Book ii 
 
 The points raised in the statements here quoted are 
 primarily metaphysical, and as such go beyond the scope of 
 this work. But they are greatly affected by a precise con- 
 sideration of what we actually do in judgment and inference, 
 and so far it seems necessary to offer som.e explanation in 
 regard to them. And if this explanation involves a word or 
 two of indication as to where we stand, in a philosophical 
 logic, with reference to the subject-matter of metaphysic, 
 perhaps at the close of a logical treatise such an indication 
 is permissible. The underlying question seems to be whether 
 in cognition we are co-operating in the self-maintenance of 
 reality, as ourselves organs within it ; or are apprehending 
 ah extra something finished and complete apart from us. 
 Of these types of view it is the former that has prevailed 
 in my treatment. I am aware that it needs careful statement, 
 and will endeavour to state it with due precision in what 
 follows. 
 
 How much then is meant and implied by saying (i) that our 
 
 judgment sustains the universe, and (2) that in judgment and 
 
 inference we make or construct reality ? * 
 
 Judg- (i) jhe expression in question was primarily employed to 
 
 volves a emphasise the idea of a total affirmative attitude to our world 
 
 world and ^g distinct from the isolated judgment or proposition as 
 
 commonly regarded m logic, qua selected and detached m 
 
 abstract thought or in language. 
 
 There were two things, as it seemed, to be insisted on, in 
 conceiving such an affirmation as the genuine iype of judgment. 
 One was the overwhelming impression, conveyed alike by 
 thought and by perception, of an affirmative and not merely 
 receptive attitude in presence of our whole connected world. 
 Everything, it seemed, had on it the stamp of meaning ; and 
 everything that had on it the stamp of meaning was ipso facto 
 affirmed as soon as our thought rested, or our eyes were 
 opened, on a whole including it. The point was not in any 
 new account of affirmation ; but that whatever we meant 
 by affirmation in the fullest sense as applied to a definite 
 judgment is true of our attitude to the world as a whole with 
 all its inter-connected detail. The example which seemed 
 
 * Cp. with citations above, i. 42. 
 
Chap. X] Ouv affirmation as a whole 315 
 
 peculiarly insistent was the field of vision. It contained, as 
 it seemed, innumerable judgments of magnitude and spatial 
 inter-relation and other properties and relations, all affirmed 
 at a stroke and so to speak as a solid whole on the simple 
 opening of one's eyes. If the experiment is made of denying 
 any one of them, any property or relation appearing within 
 the field of vision, we discover beyond a doubt that we have 
 affirmed it, seeing that we must either defend it by argument 
 or admit that we were in error. 
 
 And the second matter was the underlying wholeness and 
 imity of this enormous world of affirmation.* Everything in 
 it is affirmed, but affirmed subject to being a part in the whole, 
 and the consciousness of this reservation is essential to the 
 affirmation. Every detail is asserted as in its way true and 
 real, but only in its way, being modified by a huge co-ordinate 
 affirmation, shading off into an undefined underlying unity, 
 merely implied, but none the less affirmed.'' 
 
 This world of our affirmation, with its double aspect of 
 innumerable detail and implied unity, seemed to be the world 
 we practically lived in, and undoubtedly to be dependent 
 upon our energy and capacity not for the nature of its content, 
 but for being, so far as we had to do with it, more or less of 
 itself. This was the primary sense in which our judgment 
 could be said to sustain our world. Its point was that our 
 world was all in judgment, none of it in mere reception ; and 
 the amount of it so to speak, depended on — was coincident 
 with — the amount of our particular mind. 
 
 This is the meaning of ' sustaining our world ' with which 
 logic is concerned. It is merely an expansion of the customary 
 application of the term ' judgment ', demanded by consistency. 
 It has the strictly logical advantage of putting in a strong 
 light the unimportance of grammatical subject and predicate, 
 which can hardly be found in the judgment so described, 
 the ultimate subject being as always Reality ; and also of 
 emphasising the abstract and conditional character of the 
 detached judgments which we make explicit as fragments, 
 
 * See i. 84 above, and Essentials, p. 33 ff., and cp. Stout, Mind, 77, 
 pp. 5 and 6. 
 
 '' Cp. Essentials, loc. cit. 
 
3i6 Mental States in Relation to Judgment [Bookii 
 
 attempting to compensate for their abstractness by precision 
 of connection. 
 
 But if this meaning is challenged on metaphysical grounds, 
 and we are asked how far we, we as finite fragmentary minds, 
 can be said really to sustain the universe, we have not to 
 disown anything that we have said. We are only driven a 
 little nearer to metaphysic ; and the answer is that we sustain 
 the universe not only for ourselves, in the sense that it is 
 through our own experience, and under its limitations, that 
 we have to play our part in it, but in the more metaphysical 
 sense that supposing a given mind and its states not to be,* 
 the universe would actually be the poorer, however inappreci- 
 ably, by certain elements of its self-revelation peculiar to the 
 experience of that finite mind.^ 
 
 The former of the above views is all that strictly belongs to 
 Logic, if we are at all to distinguish Logic from Metaphysics. 
 What Logic aimed at ° was to show by what characters, 
 exhibited in the structure of cognition, the object of cognition 
 is revealed as more or less of itself and as possessing more or 
 less of reality or logical stability. 
 
 Metaphysic would have a return game to play. It would 
 show that finite minds which for Logic sustain the universe, 
 are ultimately organs moulded by it and through which it 
 sustains itself. Both points of view are true, and it is the test 
 of a philosophy to succeed in combining them."^ 
 Both (2) To say that before we know or apprehend an object it 
 
 must exist, or its making must be finished, complete and apart 
 
 * We must not say ' to perish ', or ' cease to be '. That would raise 
 the question whether such events were not mere appearance — whether 
 anything could be lost to the universe. 
 
 *• Not merely by lack of the mind as a member of the whole, as by 
 lack of an unconscious creature, but by lack of its view of the whole. 
 
 " i. 3 above. 
 
 ^ In this respect the relations of Logic and Metaphysic are not unlike 
 the relations of morality and religion. In morality, too, the ' individual ' 
 seems to sustain the weight of the world. All is on his shoulders ; he 
 acts out of himself ; all turns upon what he does next. So it does, and 
 the point of view is a true one. But if we go on to ask what the ' indi- 
 vidual ' is, and how far he is really and truly an isolated and independent 
 creature, then we get into the provinces of society and religion, which 
 modify without annihilating the purely moralist point of view. 
 
 Realists 
 
Chap. X] Pure cognittofi V. pure creation 317 
 
 from the knowing or apprehending, is a very simple and and 
 natural version of the presupposition of knowledge which we ^^tfsts 
 referred to above.* It will serve, indeed, as a first approxima- put us 
 tion to the true relation between knowledge and ' making ' °^aUty^ 
 which I hope to suggest. It assumes, I repeat, a reality given 
 as self-complete, and that apart from the apprehensive organ 
 or process. We, the knowing mind, stand outside a reality 
 which is complete without us ; without us, at least, qua cogni- 
 tive subjects. And I believe that to be consistent it would 
 be necessary to add, without us as sentient beings either. 
 
 It may ^help us to discern the true relation of the process 
 and object in question, if we first turn to the extreme opposite 
 of the above theory of apprehension, an opposite with which 
 I, quite as much as the new realists, am at war. It might be 
 expressed by saying that in knowledge we create, aijd create 
 not only truth but reality. We make it, that is, out of nothing, 
 and by means of nothing. We do not make it by the law 
 of the universe or of our minds or of the two together or of 
 anything at all, out of anything that was given. Against any 
 idea of this type the reproach would be flung — ' Then tout 
 est donne.' 
 
 This view presupposes a modifiable ultimate reality, outside 
 which, in some strange fashion, we stand, with a miraculous 
 power of adding new determinations to it in virtue of no 
 existing nature, either of it or of our own.*" It is strange and 
 suggestive that both the one-sided attitudes necessarily place 
 the mind outside the reality ; in the former case that the 
 mind may not dictate to the real ; in the latter, that the real 
 may not dictate to the mind. 
 
 Now we can discern what our attitude must be. We have 
 rejected all ideas which make truth depend on copying or 
 correspondence. But again, we hold continuity and intel- 
 ligibility to be destroyed if pure creation is possible — if, that is, 
 ultimate reality is modifiable ; if, that is, once more, the real 
 is modifiable otherwise than by its own law. 
 
 ^p. 305. 
 
 '' It does not matter, I think, whether these consequences are accepted 
 by the theorists in question or not. The test is the rejection of con- 
 tinuity. 
 
3i8 Mental States in Relation to Judgment [Book ii 
 
 For us, the universe is undoubtedly the object of apprehen- 
 sion and knowledge, prior to them and determining them. But 
 it is not an object given and complete as a whole apart from 
 apprehension and knowledge, still less, of course, from experi- 
 ence.* And the relation of apprehension to it is neither 
 copying on the one hand, nor creation on the other. These 
 are fit expressions for the working of a mind from the outside 
 upon a hard and self-complete real, or upon one unfinished 
 and incapable of self-determination respectively. But for us 
 the mind is a constituent of a living and self-determining real. 
 We might apply to its activity the term apprehension, with 
 explanations, or perhaps even the term creation, again with 
 explanations. But it will be best to look first at the nature 
 of our object, and to judge for ourselves how the relation of 
 knowledge to it should really be described. 
 Nature of (3) The object of cognition, then, is not a simple object. It 
 Co^tmU° ^^ ^^^ ^^^ given ; and it is not given as a whole. If we try to 
 tion. get at it on the assumption that it is given, we find it eluding 
 us, and extending into an infinite succession or extension of 
 particulars in space and time. And with all our trying we 
 find in the end that even these particulars are not directly 
 given. Now strictly speaking nothing but a given fact can 
 be ' apprehended '. Therefore it is clear that our universe, 
 qua object of cognition, cannot be in the strict sense ' ap- 
 prehended '. To know it as we presume it to be, that is, as 
 a whole and a system, we must * apprehend ' what is not 
 given ; and this qualification of the object at once modifies 
 the idea of apprehension. It is just as when we read in Plato 
 and Aristotle about 'imitation '. It seems simple enough at 
 first, to imitate a given object directly. But then we find that 
 one can * imitate ' a moral character with paint-brush or 
 chisel, or even, perhaps, one can imitate what is not but 
 ought to be. Such qualification of the object must expand 
 the meaning of the verb ; and so in knowledge the nature of 
 our object changes the meaning of apprehension and cognition. 
 
 * If this latter point is to be taken as admitted by the new realists, 
 it appears to me that the whole question is decided. It is impossible 
 seriously to admit into the reality of the existent universe some forms 
 of experience, and exclude others, prima facie of a completer kind. 
 
Chap. X] Can you apprehend what is not given ? 319 
 
 If you are to ' apprehend ' an object by far the greater part 
 of which has to be got at by inference, and all of which is 
 continuously transformed as apprehension proceeds, you can 
 only interpret the term apprehend in a way which has some- 
 thing to do with making. I suggest as the key to the required 
 meaning some such word as ' elicit '. Your object of knowledge 
 has in a great measure to be elicited from the given. For 
 the object is a whole, but not a given whole, and is always 
 beyond itself, and is offering more to your apprehension than 
 is already there for you to apprehend. 
 
 If we are substantially agreed on this character of the 
 object, it becomes a verbal question whether we say that we 
 construct * reality, that we relate a predicate to a subject in 
 judging, that we make an inference, or that we apprehend, 
 the given and fragmentary facts with such modifications as 
 logical necessity requires, and so again apprehend the necessity 
 with which a predicate, not given, belongs to its subject, or a 
 conclusion, ex hypothesi not given, belongs to its premises, 
 or by which one factor of reality, given per se, conditions 
 and is conditioned by another, also given only per se. In 
 the latter case it is fairly certain that some corners of the 
 given will have to be cut off through the operation of the 
 conditioning necessity. 
 
 Now strictly, I repeat, it is misleading to say ' I apprehend ' 
 anything but a fact or a given conjunction of facts. If you 
 say ' I apprehend ' the product of two numbers of five places 
 each, I think it would be held that you must be a calculating 
 
 * I have myself commented on the term ' construct ' as properly 
 expressing only the auxiliary employment of mental imagery in inference 
 (ii. 33), and there is a verbal inconsistency between that passage and 
 the earlier one which speaks of the construction of reality, i. 42. What 
 I meant to urge was that the metaphor from physical construction does 
 not really explain the construction of reality. It is the latter that is 
 the true construction, and the former derives its significance from it. 
 You only construct even physically if you follow a principle and make 
 what you meant. Mental construction is mere imagining only if you 
 slide from the relevant to the irrelevant content. But if, being in 
 possession of a mass of conflicting evidence concerning, say, a historical 
 event, you frame a conception which harmonises a great part and 
 explains the contradictions of the rest — the typical process by which 
 we learn what reality is — I hardly see what to call the process if not 
 construction. 
 
320 Mental States in Relation to Judgment [Book ii 
 
 boy. But if we like to say ' apprehend ' in the sense that 
 possessing the given and the law of its system, and operating 
 on it accordingly, we are able to apprehend it with modifications 
 which belong to it, of course we may say so. But any distinc- 
 tive implication as to the priority of the special object of 
 apprehension appears in that case to have vanished. 
 
 Thus it may be urged that all critical systems which support 
 and elucidate ' facts ' by bringing them into a coherent whole 
 — e. g. the facts of history ^ — all ' laws of nature ' and ap- 
 preciations of necessary connection, all intelligibility by which 
 the given itself is known and framed in inter-connections and 
 inter-dependences which are not and cannot be given, are 
 ultimately ' found ' in the universe and not ' made ', and so 
 are * apprehended ' and not ' constructed '. But surely tliis 
 is to go back to the naive empiricism which so much pcdns 
 and labour have been spent in transcending. If anything at 
 all has been made clear in the history of philosophy, it is 
 surely that as we get to truth, especially of the higher orders, 
 we get away from facts. It is not a contention especially of 
 philosophical idealism. It is as true for Mill and Jevons and 
 Mr. Bertrand Russell ^ as for Lotze, Greea. and Bradley, not 
 to speak of earlier philosophers. No working Logic can be 
 put together upon any other basis. 
 
 Now of course the predications in question are presupposed 
 to be true of the universe. It is their general presupposition 
 and prior object. But it, if you omit from it mind as a 
 constituent, does not furnish a given object of apprehension 
 which corresponds to them or which they can be said to copy. 
 You may say our higher knowledge is a shorthand for innumer- 
 able facts. That is, of course, extreme empiricism, and leads 
 to the denial that the universe is a whole. But this position 
 is so far sound, that if you contend that judgments to be true 
 must reproduce facts that are simply found, then our higher 
 knowledge must be mere shorthand, or false. If these higher 
 
 ^ Cp. Mr. F. H. Bradley's Presuppositions of Critical History. 
 
 ^' That is to say, so far as I can follow, all Mr. Russell's higher truths, 
 viz. those of Logic and Mathematics, are truths of implication and in 
 no way deal directly with particulars. Mr. Russell would not, I pre- 
 sume, assent to the consequences which I suggest. 
 
Chap. X] Knowledge is an activity of the Universe 321 
 
 truths are ' found ' in the universe, they are only found as the 
 statue is in the marble, that is, in such a way that the process 
 has more to do with the result than the matrix material. In 
 the controversy about the relations of knowledge and practice 
 it has become clear beyond dispute not only that practice, 
 besides making the product always finds the real, but that know- 
 ledge, besides finding the real, always modifies the given. To 
 know the truth of anything, you cJways go further afield. Even 
 if you ask, ' Is the sensation of touch A a sensation of touch ? ' 
 you mean to ask about it something further, e.g. 'Is something 
 more to be detected than I have apprehended, which will 
 be decisive that what I feel is a sensation of touch ? ' * This 
 is the beginning of construction — ideal construction — which 
 rests on. the fact that all finite reality goes beyond itself, and 
 is completer and completer in more and always more of its 
 connections. By this ideal construction it has — ^to borrow 
 a phrase from another context — its own nature progressively 
 communicated to it. 
 
 But do we ' make ' the construction ? Is it not there as a 
 whole, though unknown to us at first, and we apprehend it ? 
 Does not making exclude knowledge ? The answer has been 
 offered in the whole preceding argument, and it is for the reader 
 to judge. \^^hat seems to us is, that we certainly do not 
 create the construction, but no less certainly do not in any 
 natural sense ' apprehend 'it. It is true — conditionally true — 
 of our universe ; and in that sense, is ' there ' before we make 
 it. But it is not given before we make it, and this does not 
 apply to individuals because of fortuitous ignorance, but to 
 the whole nature of what can be given compared with what 
 can only be inferred. If we rule out of the universe the living 
 power of mind which alone can complete the given into a 
 coherent whole, a systematic construction, modifying the 
 facts wdth a view to their inter-connection, could never come 
 to be given at all. It has not only less — ^less irrelevancy — 
 but more — more relevancy — than what can be given or found, 
 and can never be adequately described as found or given. 
 A necessary connection even between two given terms is a 
 reciprocal inferential relation,^ implying a system beyond 
 
 * Cp. Nettleship, Remains, i. i8off. '' Cp. e.g. vol. ii, p. 8 above. 
 1337-2 Y 
 
322 Mental States in Relation to Judgment [Book ii 
 
 either, and not present in the apprehension of each alone or 
 of both together. 
 
 It is only by a misapprehension, as I have tried to point 
 out, that such an interpretation of knowledge seems to conflict 
 with its presupposition. Knowledge is an essential form of 
 the self-revelation of the universe ; experience as a whole 
 is the essential form. In knowledge, the universe reveals 
 itself in a special shape which reposes on its nature as a 
 whole, and is pro tanto proof against contradiction. It is, 
 like the whole wealth of life and of history, elicited from a 
 relatively given by the forming and interpreting activity of 
 mind, which in this activity is an organ of the universe itself. 
 Plainly, if you hold that to be a part of the universe disqualifies 
 knowledge from being true (because without it or prior to 
 it the universe is not completely there) you must, as I said, 
 to make knowledge capable of truth make it external and 
 additional to the universe. 
 
 But the detail which it presents in the form of cognition 
 is true of the universe, although falling within it, because the 
 universe, qua object of cognition, in its self-maintenance 
 against self-contradiction in that form shows that it must 
 take the detailed shape which it does take and no other, and to 
 know is to endow it with that form, making the given more 
 and more of itself. 
 
 And in Logic we study the character of the universe or the 
 reality with reference to the degrees of stability, which, if we 
 postulate bona fide employment, attach to the various frame- 
 works at different stages of the structure arising from its 
 self -utterance in that form. 
 
 The ' driving force of Idealism ', as I understand it, is not 
 furnished by the question how mind and reality can meet 
 in knowledge, but by the theory of logical stability, which 
 makes it plain that nothing can fulfil the conditions of self- 
 existence except by possessing the unity which belongs only 
 to mind. External objects, therefore, are fragmentary and 
 dependent. 
 
INDEX 
 
 Absolute Necessity , a contradic- 
 tion, ii. 215. 
 
 Absolutism, ii. 251 ft. 
 
 Abstract Number, i. 161. 
 
 Abstraction, i. 61 ; ii. 20 ft. 
 
 Abstraction and Necessity, i. 1 34ff. 
 
 Adaptationism, in Genetic Logic, 
 ii. 272. 
 
 Added Determinants, ii. bj. 
 
 Addition and Multiplication, ii. 58. 
 
 Addition and Multiplication of In- 
 dices, ii. 59 ff. 
 Aesthetic neces.sity' criticised, ii. 
 
 233 ff- 
 Affirmation and Negation, i. 279 ff. 
 Albertus de Saxonia, on ' a 
 
 priori ' and ' a posteriori ', ii. 
 
 225 note. 
 Alexander, Prof. S., ii. 307. 
 All, meaning of, in Judgment, i. 
 
 152. 
 AUness and Necessity, i. 211. 
 Alternative Classifications, i. 61. 
 Analogical Judgment, i. 212 ff. 
 Analogy, True and false basis of, ii. 
 
 99 ff. 
 Analytic, i. 91. 
 Annual rings in trees, i. 219. 
 dTr6(f>aats, dist. aTeprjais, i. 31 S- 
 A priori, ii. 224. 
 Aristotle, i. 9, 11, 14 note; on 
 
 pijfia 19 note, 23, 256, 281-2, 
 
 315; ii. 151, 171, 213, 246 note, 
 
 269 note, 
 Arnold, Mr. Matthew, ii. 236 note. 
 Association of ideas, ii. 14, 225. 
 Atomic weights, theory of, ii. 226. 
 Axioms, ii. 208. 
 Axioms, as Postulates, ii. 208. 
 
 Bacon, ii. 121. 
 
 Bare Denial, i. 281. 
 
 Bee Ophrys, ii. 124. 
 
 Bergson, Involution Creatrice, ii. 
 
 174 ff. 
 Bradley, ' Principles- of Logic,' i. 
 13 note, 29 note, 32 note, 33 
 
 note, 44 note, 46 note, 47 note, 
 57, 69 note, 74 note, 100 note, 
 139 note, 141 note, 142 note, 
 23s, 238, 263, 265-6, 270 note, 
 280, 305 ff., 313, 315, 324, 352, 
 361, 379 note ; ii. 37 ff., 65, 
 112, 133, 176, 184, 254, 261, 
 287 ; Mind, i. 131, 293 note; 
 ii. 183, 250, 295 ; Appearance 
 and Reality, i. 248, 293 note ; 
 ii. 15 note, 253, 278 ; Pre- 
 suppositions of Critical History, 
 ii. 286, 320. 
 
 Braid, i. 13 note. 
 
 Brown, Dr. Thomas, ii. 66. 
 
 ' Budget of Paradoxes,' De Mor- 
 gan, i. 374 ; iu 120. 
 
 Burnet, Early Greek Philosophy, 
 ii. 280 ; Ethics of Aristotle, ii. 
 269 note. 
 
 Caird, E., Proceedings of British 
 
 Academy, ii. 302, 313. 
 Calculation, ii, 29. 
 Categorical and Hypothetical, i. 
 
 87 ff., 269. 
 Categories of Sense, i. 188. 
 Causation, law of, ii. 215. 
 Cause, i. 250 ff. 
 Chances, statement of, i. 336. 
 Change and Difference, i. 131. 
 Characteristic Ratio, 1. 123. 
 Characters, ' important,' ii. 94. 
 Chicago University Decennial Pub- 
 lications, Miss Thompson, i. 43 
 
 note ; ii. ch. ix. 
 Chronological indications, i. 199. 
 Class, inclusion of subject in, ii. 
 
 256. 
 Classifications, alternative, i. 61. 
 Clifford, on Causation, i. 250; ii. 
 
 153 note. 
 Coherence Theory of Truth, i. 2 
 
 note ; ii. ch. ix. 
 Collective names, i. 54. 
 Colligation of facts, ii. 155, 
 Colour-match, i. 195. 
 
324 
 
 Index 
 
 Companion to Plato's Republic 
 (Bosanquet), i. 293 note. 
 
 Comparative Judgment, i. 108. 
 
 Comparison proper, ii. 19. 
 
 Complete Enumeration, ii. 55. 
 
 Complex Enumeration, ii. 58 ff. 
 
 Conception, test of truth, ii. 227 ff. 
 
 Concepts, i. 29. 
 
 Condition and Conditioned, i. 248. 
 
 Conditional dist. Hypothetical 
 Propositions, i. 234 note. 
 
 Conjunction and Disjunction, i. 
 
 330- 
 Consciousness and Energy, ii. 79. 
 Constitutive Equation, ii. 71. 
 Construction, ii. 33, 313, 319. 
 Continuous magnitude, i. 149. 
 Contradiction, law of, ii. 211. 
 Contraposition, i. 314. 
 Contrariety and Contradiction, i. 
 
 290 fif. 
 Conversion, i. 307. 
 Copula, i. 75. 
 Copying and Truth, i. 42 note ; ii. 
 
 ch. ix. 
 Corporate Judgment, i. 199. 
 Counting analysed; i. 146. 
 Counting mediate, i. 159. 
 ' Criticism of life,' ii. 236. 
 Cross-fertilisation, ii. 129. 
 
 Dalton, ii. 227. 
 
 Darwin, Origin of Species, i. i ; 
 Fertilisation of Orchids, ii. 102, 
 126 ff. 
 
 Day cause of Night ? i. 259. 
 
 De Morgan, ' Budget of Para- 
 doxes,' i. 374 ; ii. 120, 156, 231. 
 
 Designation, ii. 261 note. 
 
 Designative, dist. Significant, i. 
 120 note. 
 
 Determination, Generalisation by, 
 ii. 163. 
 
 Dewey, Prof., in Chicago Publica- 
 tions, ii. 270 ff. 
 
 Dicey, Prof., ' Law of the Consti- 
 tution,' ii. 18. 
 
 Difference and Change, i. 131. 
 
 Difference needs a standard, i. 118. 
 
 Discovery, ii. 8. 
 
 Discrete Magnitude, i. 149. 
 
 Discrimination, ii. 24. 
 
 Disjunction and Conjunction, i. 
 330.' 
 
 Disjunctive Judgment, i. 322. 
 
 Distinction, i. 21. 
 
 Double Negation, i. 302. 
 Driesch, Gifford Lectures, ii. 180. 
 Dualism, in Genetic Logic, ii. 270. 
 
 Ehrenberg, i. 299. 
 Elements (formative), i. 19. 
 Enumerative Judgment, i. 145-6. 
 Enumerative Induction, ii. 50. 
 Equation, ii. 31. 
 Equation, Constitutive, ii. 71. 
 Equation and Judgment, i. 191. 
 Equational logic, ii. 31. 
 Essentials of Logic (Bosanquet), i. 
 297 note, 36 1 ; ii. 267, 302, 3 1 1 , 
 
 315- 
 Exception, i. 370. 
 Excluded Middle, law of, ii. 213. 
 Exhaustive Judgment, i. 157, 212. 
 Existence of geometrical figures, 
 
 i. 181. 
 Existential meaning in Generic 
 
 Judgment, i. 223. 
 Experiment, ii. 143. 
 Extension, see Intension. 
 External Proportion, i. 128. 
 
 Figures of Syllogism, ist, ii. 185 ; 
 
 2nd, ii. 87 ; 3rd, ii. 50, 112. 
 Final Cause, in Plato, ii. 187 note. 
 Finberg's Turner, ii. 243. 
 Formative elements, i. 20. 
 
 Generalisation, kinds of, ii. 163 flf. 
 Generic Judgment, i. 210. 
 Genetic Theory of Logic, i. 2 note, 
 
 7 note ; ii. 238 ff. 
 Green, Prof. T. H., ii. 155, 241, 
 
 270. 
 Ground, i. 238 ff. 
 
 Hamilton, Sir W., ii. 57. 
 
 Hegel, i. i, 74, 163, 381 ; ii. 54, 
 
 66, 74, 85- 
 Helmholtz, Popular lectures, ii. 
 
 147. 
 Herbart, i. 141. 
 
 Herschel, Sir J., in Mill, ii. 226. 
 History and Science, i. 261. 
 Hoernle, Prof., i. 69 note; ii. 296 
 
 note, 300. 
 Huxley, Prof., ii. 108 note, 216 
 
 note. 
 Hypnotism, degrees of, i. 380. 
 Hypothesis, dist. Postulate, ii. 1 5 1 . 
 Hypothetical, i. 88 ff., 238 ff., 268. 
 
Index 
 
 325 
 
 Idea, i. 44. 
 
 Idealism, true driving force of, ii. 
 322. 
 
 Ideas, Locke on, i. 68. 
 
 Identification, i. 25 ; ii. 24. 
 
 Identity, i. 13, 25 ; Locke on, ii. 
 210 ; Law of, ii. 210. 
 
 Imagination atid Conception, ii. 
 229. 
 
 Imitation, ii. 241 ff. 
 
 Imperative, i. 100 note. 
 
 Impersonal Proposition, i. loi. 
 
 Indices, ii. 59 ff. 
 
 Individuality and Proportion, i. 
 12-5. 
 
 Individuality and Reality, i. 135. 
 
 Individuals, finite not self-existent, 
 ii. 257. 
 
 Induction, Essence of Perceptive, 
 ii. 132 ; not a species of Infer- 
 ence, ii. 171. 
 
 Inductive Syllogism, ii. 13, 50. 
 
 Inference, Nature of, ii. i, 3 ; 
 Ultimate Conditions of, ii. 203 
 If. ; Conditions of, compared 
 with Syllogism, ii. 204 ff. 
 
 Infinite Judgment, i. 281. 
 
 Infinite Series, i. 161, 185 note. 
 
 Infinity, nunierical, i. 163. 
 
 Instance, i. 370. 
 
 Intension, i. 44 ff., 57 ff., 64 note. 
 
 Intensive Equation, ii. 32. 
 
 Interjection, i. 99. 
 
 Internal Proportion, i. 128. 
 
 Interest or Purpose of Judgment, 
 i. 22 and note. 
 
 Jenkinson, Experimental Em- 
 bryology, ii. 180 note. 
 
 Jevons, i. 47, 351 ; ii. 31, 112, 118, 
 141, 150, 156, 159, 169 ff. 
 
 Joachim, H. H., Nature of Truth, 
 ii. 267 note, 289 ff. 
 
 Johnson, Prof., i. 234. 
 
 Joseph, H. W. B., Introduction to 
 Logic, ii. 174, 182, 184. 
 
 Judgment, i. 31, 67 ff., 142 note ; 
 and Equation, i. 191. 
 
 Kant, i. 93, 281, 363 ff. ; ii. 85, 183. 
 
 Keynes, J. N., Formal Logic, i. 29 
 note, 51 note, 57, 234, 244, 247 
 note, 288 note, 297 note, 355 ff. 
 
 Kind and Quality, i. 115. 
 
 Kirchoff, on Iron in the Sun, ii. 
 170. 
 
 * Knowledge and Reahty ' (Bosan- 
 quet), i. 148 note, 150 note, 153 
 note, 247 note, 274 note ; ii. 66, 
 150, 171, 266. 
 
 Lang, Custom and Myth, ii. 157 ff. 
 
 Laws, ' Formal ' laws of Thought, 
 ii. 208 ff. 
 
 Liberty, Equality, and Fraternity, 
 Sir James F. Stephen quoted, 
 i. 191. 
 
 Limitation, conversion by, i. 310. 
 
 Lindsay, A. D., Philosophy of 
 Bergson, ii. 184. 
 
 Linnaean classification, i. 9; ii. 124. 
 
 Locke, i. 68, 91 note, 171 note ; ii. 
 210 note. 
 
 Logical Stability, ii. 45, 283, 288, 
 312, 316, 322. 
 
 Lotze, Logic, i. 15 note, 17 note, 
 21 note, 29 note, 30 note, 57, 
 63, 78, 92 note, 99 note, 141 
 note, 198 note ; ii. 53, 62, 7211 
 112, 151, 202, 224,233; Meta- 
 physik,i. 13 note; Mikrokosmus, 
 
 Machinery, double import of, in 
 Logic, i. 219 ; ii. 187. 
 
 McTaggart, J. E., Commentary on 
 Hegel's Logic, ii. 99. 
 
 Major Premise, ii. 52, 64. 
 
 Material truth, ii. 167. 
 
 Mathematics, truth of, ii. 48-9. 
 
 Measurement, i. 120. 
 
 Mechanism, i. 189 ff. 
 
 Mediate enumeration, i. 159. 
 
 Mill, i. 8, 13 note, 44, 141 note, 
 265, 382 ; ii. y6, 88, 95, 100, 
 118, 121, 153, 156, 224. 
 
 Mill and Lotze, i. 141. 
 
 Miracle, ii. 217. 
 
 Mommsen, i. 11 note. 
 
 Moore, G. E., ' Refutation of 
 Idealism,' ii. 276 note ; Priu- 
 cipia Ethica, ii. 261 note. 
 
 Morphology, i. i ; as weakened 
 Teleology, ii. 94. 
 
 Mortality, i. 344. 
 
 ' Mouse ' families, hypothesis re- 
 garding, ii. 157. 
 
 MuUer, T. B., in Mind, i. 306. 
 
 Naming, i. 7, 21. 
 Necessity, a real, ii. 190. 
 Necessity amd Abstraction, i. i34ff. 
 
326 
 
 Index 
 
 Necessity and Allness, i. 211. 
 
 Necessity : see ' Absolute ', ' Aes- 
 thetic '. 
 
 Negation, i. 277 ff. 
 
 Negative Instance, ii. 115 ff. 
 
 Nettleship, R. L., i. 66 note, 69 
 note ; ii. 321. 
 
 Night cause of Day ? i. 259. 
 
 Number (see counting), i. 146. 
 
 Objectification, not presupposes 
 pure subjective states, i. 17 
 note. 
 
 OccasiouaUsm, in Genetic Logic, 
 ii. 271. 
 
 Omission, how related to Abstrac- 
 tion, i. 58 ff. 
 
 Ophrys apifera, ii. 124. 
 
 Opposition of Judgments, i. 294. 
 
 Organon (Aristotle), i. 256, 315. 
 
 Particulars to Particulars, ii. 27, 
 
 51- 
 Parts and whole, i. 93 ff. 
 Personal era, i. 199. 
 Physical Alternatives, i. 337. 
 Physiology, i. 2. 
 Plasticity, of iiltimate Reality, ii. 
 
 294. 
 Plato, i. 9 ff., 25, 30 note, 84 ; ii. 
 
 187, 197, 235 note. 
 Plurality of Causes, in Mill, i. 252. 
 Possibility, i. 367. 
 Posterior Analytics, i. 256 note ; 
 
 ii. 171 note. 
 Postulate, dist. Hypothesis, ii. 151. 
 Pragmatism, ii. 247 ff. 
 Prantl, Geschichte der Logik, ii. 
 
 225. 
 Predicate, i. yj ; (in Aristotle), i. 
 
 19. 
 Predication, i. 76. 
 Premises of Inductive Syllogism, 
 
 ii. 13. 
 Prichard, H. A., ' Kant's Theory 
 
 of Knowledge,' ii. 301 ff. 
 Privation, i. 315. 
 Proper Name, ;. 47 ; dist. Generic 
 
 Name, i. 213. 
 Proportion as Inference, ii. 7iii.; 
 
 as Individuality, i. 127. 
 Proposition, dist. Judgment, i. 74. 
 Pure Case, i. 245. 
 
 Quality and kind, i. 117 ; meaning 
 of.i. 98. 
 
 Quantity, category of, i. 193. 
 Question, i. 33, 366. 
 
 Ratio, i. 151. 
 
 Real world and my world, i. 77. 
 
 Realists, ii. 276. 
 
 Reality and Individuality, i. 139 ; 
 
 in Judgment, i. 71. 
 Recognition, ii. 22 ff. 
 Reduction, in the true sense, ii. 
 
 205. 
 Relative, i. 23. 
 pr]jjLa, i. 19. 
 pij/ua aopioTOV, i. 281. 
 Republic, Plato's, ii. 183 note, 197, 
 
 235- 
 
 Ross, G. R. T.,i. 355 ff. 
 
 Royce, Prof., World and Indi- 
 vidual, i. 163. 
 
 Russell, Hon. Bertrand, i. 164 ; 
 ii. 40 ff., 251 ff., 276 ff. 
 
 Scheme of Arguments, ii. 42 ; of 
 
 Judgments, i. 92. 
 Schopenhauer, on Euclid, i. 237 ; 
 
 Seynsgrund, 251 ff.; on the 
 
 Understanding,^ ii. 82, 215. 
 Science and History, i. 261. 
 Self -fertilisation, ii. 124. 
 ' Sense ' of a relation, ii. 28 1 . 
 Sigwart, Prof., i. 33 note, 45 note, 
 
 61-2, 140 note, 277 note, 278, 
 
 30s, 315, 363, 379 note ; ii. 20, 
 
 159, 169. 
 Singular Judgment, i. 196. 
 Srep^triy, dist. ajT6<f)a<rts , i. 315. 
 Stewart, Prof., Notes on ' Ethics ', 
 
 ii. 246. 
 Stout, Prof., i. 69 note, 114 note ; 
 
 ii. 179, 184, 244 note, 251, 296 
 
 note, 309. 
 Structure and Individuality, i. 
 
 128. 
 Subject, i. 76. 
 Subjective States, i. 38 note, 39 
 
 note. 
 Subjectivity of Space and Time, i. 
 
 186. 
 Substitutive Inference, ii. 62. 
 Subsumption, ii. 28. 
 Sufficient Reason, law of, ii. 215. 
 Supposition, ii. 11. 
 Syllogism, fig. i, ii. 185 ; fig. 2, ii. 
 
 87 ; fig. 3, ii. 50 ; traditional, 
 
 ii. 204 ; as reasoned judgment, 
 
 ii. 206. 
 
Index 
 
 327 
 
 Symbolic Ideas, i, 70. 
 Symbolic Logic, ii. 40 flf. 
 Synthetic, i. 91. 
 
 Tarde, Les Lois de I'lmitation, ii. 
 
 174. 
 Taylor, Professor, i. 165 ; Arist. 
 
 Proceedings, ii. 251 fif. 
 Tense, i. 105, 203. 
 ' Thermometer of Probability,' i. 
 
 374- 
 
 Thing, what is a, i. 129. 
 
 Thompson, Miss, i. 43 note, 
 97 note ; ii. 263 ff. 
 
 Three Terms, ii. 12. 
 
 Time, Constancy of, i. 170 ; Judg- 
 ment in, i. 79 ; in Predication, 
 i. 203 ; of Predication, i. 203 ; 
 Reality of, i. 257. 
 
 TO Kaff eKcoTTov, in Inductive Syllo- 
 gism, ii. 13. 
 
 Totems, hypothesis of, in Greece, 
 ii. 160. 
 
 Understanding, the, ii. 85. 
 Universal Judgment, i, 207 ff. 
 
 Venn, Logic of Chance, i. 344 ff. 
 
 Waitz (Aristotle's Organon), i. 
 
 315- 
 
 Whateley, on Privative and Ne- 
 gative Terms, i. 315 note. 
 
 Whewell, i. 382 ; ii. 16, 156, 224. 
 
 Whole and parts, i. 93 ff. 
 
 Word, no Greek term for a, i. 11. 
 
 Wundt, i. 56, 62, 141 ; on Con- 
 stancy of Energy, ii. 79. 
 
c/ C^ 
 
 
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