* 
 
 f\ 
 
 / 
 
 
 \
 
 i
 
 SEMICENTENNIAL PUBLICATIONS 
 
 OF THE 
 
 UNIVERSITY OE CALIFORNIA 
 
 1868-1918
 
 UNIVERSITY OF CALIFORNIA PUBLICATIONS 
 
 PHILOSOPHY 
 
 VOLUME :i 
 
 -5$ \"52 
 
 UNIVERSITY OF CALIFORNIA PRESS 
 
 BERKELEY 
 
 1918
 
 FOOTNOTES 
 
 TO 
 
 FORMAL LOGIC 
 
 BY 
 
 CHARLES H. RIEBER
 
 71 
 
 1\4 
 
 CONTBNTS 
 
 PAI 
 
 Preface •' 
 
 CHAPTEB I 
 Modern [ndictment or Formal Logic 8 
 
 CHAPTEB II 
 Apprehension, Question and Assertion 34 
 
 CHAPTEB III 
 The [mport <>k Judgment i' 1 
 
 CHAPTEB IV 
 Negation and the [npinite Judgment 68 
 
 CHAPTEB V 
 Nature of Inference 81 
 
 CHAPTEB VI 
 
 I MMKDIATK I NFERENCE L03 
 
 CHAPTEB VII 
 
 The Case A.gainst the Syllogism 122 
 
 CHAPTEB VII] 
 
 Novki.tv and Identity in [NFERENCE 1-17
 
 PREFACE 
 
 The psychologist, on the one hand, and the metaphysician 
 and the epistemologist, on the other, have crowded our presenl 
 
 \j day discussions in the Meld of pure Logic into a \rvy narrow and 
 
 ^ uncomfortable position. No sooner does the Logician raise the 
 
 \J question as to the origin and nature of the thinking process, 
 
 than the psychologist warns him thai he is trespassing in fields 
 not his. Especially is this true when we venture to discuss such 
 ^ questions as the process whereby judgmenl develops into infer- 
 
 v eiice or is depressed into conception. This we are told is not 
 
 logic, but genetic psychology. On the other hand, when the 
 1^ logician raises the question as to the nature of knowledge in gen- 
 
 eral, he is again rebuked for passing into the domain of meta- 
 physics, epistemology or ontology. It has been said that if the 
 £ logician should accept these restrictions which his neighbors have 
 
 ^ imposed upon his field, there would be little Left of logic, exec] it 
 S-J a mere collection of misleading formulae coupled with a little ele- 
 mentary grammar. 
 
 I think the situation is not quite so desperate as this, and I 
 hope in some small measure in these studies to justify the present 
 tendency to widen the field of logic. When we attempt to define 
 the nature and scope of logic, or of any other of the philosophical 
 sciences, we find our inquiries passing by imperceptible steps 
 from one field to another until presently each subject in turn 
 claims to be the whole of philosophy. I believe it to be a mis- 
 take to divorce logic — even for educational purposes — from the 
 other philosophical sciences. I do not see how it is possible to 
 answer the questions that are more than ever today besetting 
 logical doctrine until we have first settled some of the funda- 
 mental problems of philosophy. Formal Logic is again on trial 
 
 [ 5 J
 
 C FOOTNOTES TO FOBMAL LOOK 
 
 for its life. In recent years, at least four* important volun 
 have been entirely devoted to this modern indictment of tradi- 
 tional logic. Having now for some fifteen years been charged 
 with the responsibility of teaching Formal Logic, and to more 
 than half a thousand students each year, I feel morally neces- 
 sitated, as one of the humblest of the disciples of Aristotle, to 
 give some justification for the faith that is in me. 
 
 In the introductory pages of his Formal Logic, Professor 
 Schiller remarks, in a somewhat disheartened mood, "it is not 
 unlikely that this whole revolt will come to nothing and that 
 Logic will continue to be taught on the traditional lines." He 
 takes comfort, however, in the belief that the failure of the 
 reform movement will not be due to any intrinsic error or weak- 
 ness in the movement itself, but to the fact that the prestige of 
 tradition is so overwhelming, the force of habit so insidious. 
 Dr. Mercier in the preface to his New Logic also expresses gloomy 
 misgivings as to the fate of his volume. He says "by the time 
 the New Logic has stood two thousand years ... no doubt it 
 will have had all the guts taken out of it." I think, however, 
 that no serious attempt will be made to disembowel his book. Dr. 
 Mercier has been disappointed, so he says, that none of the older 
 writers, Bosanquet, for instance, have replied to his criticisms. 
 It seems more likely therefore, that his volume will be allowed 
 to dry up with its entrails in it and become an interesting object 
 for antiquarian research in the generations to come. 
 
 I have chosen the title Footnotes to Formal Logic for these 
 studies, rather than the more pretentious title Logical Theory, or 
 Principles of Logic, in order that I might convey my own con- 
 sciousness of their incompleteness and shortcomings. But, while 
 the collection of essays is by the title confessed to be fragmentary, 
 I hope I have made plain a thread of continuity running through 
 them all. I have not attempted to present a brief for Formal 
 
 * Schiller, F. C. S., Formal Logic, London, Macmillan, 1912; Sidgwick, 
 A., Elementary Logic, Cambridge, University Press, 1914; Dewey, John, 
 Essays in Experimental Logic, Chicago, University of Chicago Press, 1916; 
 Mercier, Charles, A Neic Logic, Chicago, Open Court, 1912.
 
 /'A'/./- M I. ~ 
 
 Logic that is withoul qualification; for I have at times said some 
 severe things aboul the ancienl system. Bowever, I think on t h<- 
 whole my efforts will be regarded as ;i defense of the Traditional 
 Logic, and to thai I shall not object. For, to use a very ap1 
 phrase of Dr. Mercier, it' I have to choose between the New Logic 
 and the <>M Logic, I should "plump for" the Latter.
 
 ( HAPTER I 
 THE MODERN INDICTMENT OF FORMAL LOGIC 
 
 The new theories of thought all make a common criticism 
 upon the old idealistic Formal Logic. Whether we call these 
 modern theories of knowledge pragmatic, realistic or empirical, 
 matters little for our present purpose. They all agree in saying 
 that the conceptual, a priori logic has never undertaken to set 
 forth the conditions out of which actual thought has arisen ; nor 
 has it defined the principles that estimate the success of thought 's 
 accomplishments. It has no theory of the whenci and the 
 whither of thought. "What we have to reckon with." Professor 
 Dewey writes, "is not the problem of How can I think uber- 
 haupt? but How shall I think right here and now? not what is 
 the test of thought at large, but what validates and confirms this 
 thought." 1 
 
 I wish to submit at once, and it will be one of the central con- 
 tentions of these studies that it is unfair to the formal logician, 
 even of the old orthodox type, to say that he is unwilling to take 
 notice of the concrete facts, that he has a contempt for the parti- 
 culars, that the universals are more precious to him than the 
 particular cases to which they apply. Only a hasty and reckless 
 idealist affirms any such doctrine. An essential part of thought 
 is always engaged in the effort to reach final truths — propositions 
 that are not merely finally true in the sense of being a complete 
 and adequate adjustment to an immediate situation, but truths 
 that are certain and universally valid. Even the most zealous 
 defender of the modern "flowing philosophy" admits the exist- 
 ence of this logic uberhaupt, albeit, he insists that it is a useless 
 
 i Studies in Logical Theory (University of Chicago Press, 190?»), p. ?•. 
 
 [8 1
 
 THE MODERN INDICTMENT OF FOBM M. LOGIC '.< 
 
 pursuit. Another pari of thought, which regards itself just ;is 
 essential, attempts to arrive at practical truth; it is concerned 
 with the reconstruction of the "immediate situation." Now. 
 Experimental Logic asserts its competency to pass judgmenl not 
 
 only upon its own pragmatic process, hut also upon tin- episte- 
 tnological aspirations of the Heal Logic. And it is to this basic 
 doctrine of tin- new school that the old school registers its earnesl 
 
 caveat. 
 
 The idealism represented in these pages is of a very old- 
 fashioned type. It essays to defend even so abstract an idealist 
 as Plato against the assaults of the modern realist. 2 It has often 
 been said that the logic of Platonism, or any absolute idealism, 
 drives one either to pun' intellcctualism or to pure mysticism. 
 But even Plato did not put the whole emphasis in his thinking 
 on the theory of knowledge. Philosophy was for him, to he sure. 
 primarily a discipline of the mind; but it was a discipline which 
 ended always in the service of action; it was the propaedeutic 
 for character. Thought was quite as pragmatic for Plato as it is 
 for any of the modern voluntarists, only it was pragmatic, I 
 should say, in a thoroughly defensible sense. The mind's essential 
 nature is exhibited in its everlasting aspiration after truth. But 
 perfect insight, genuine wisdom, has as its essential characteristic 
 the inevitable necessity of expressing itself. The knowledge thai 
 the mind wins must flow out into character. Man's complete life 
 consists not only in thinking perfect thoughts, working them out 
 like nuggets of gold, hut also in coining them into action. Plato 
 insisted always that Logic is the absolutely indispensable pre- 
 requisite of Ethics, and. conversely, that Ethics was the inevitable 
 outcome of Logic. 
 
 2 In these Btudies I shall often speak of Lnstrumentalism, realism, and 
 pragmatism as if they were identical doctrines. I am, of course, fully 
 aware of the several points of vital difference which have been insist'. I 
 upon by various members of the two schools. But for the purpose of the 
 
 contrast with idealism we may neglect these differences and deal with their 
 
 central agreement. Both realism and Lnstrumentalism declare that think 
 Lng is instrumental or reconstructive and not constructive, as idealism 
 always professes. They hold that thought finds real brute existences in 
 
 the world of presented tact — structures that are not created but discovered.
 
 2 FOOTNOTES TO FOBMAL LOOK 
 
 Logic in the fullest sense of the word is therefore the source, 
 but not the final goal of the Platonic philosophy, or of any serious 
 idealism. Insight is not for its own sake but for the sake of action. 
 Knowledge turns not inward upon itself, but outward upon con- 
 duet. It is practical ; it is pragmatic. According to the sublime 
 Platonic formula of life (even in its most modern interpretation 
 by Caird, Royce, Howison and others), knowledge is virtue, not, 
 knowledge is knowledge. Plato would have agreed entirely with 
 a modern up-to-date metaphorical epigram; "knowledge that 
 turns inward upon itself creates a current so hot that it burns 
 out the fuse." 
 
 Knowledge begins with surprise and ends in the rational dis- 
 sipation of surprise ; it is original, underived, reminiscent. This 
 is the basic doctrine of Plato's philosophy which has been echoed 
 and reechoed through twenty-three centuries of idealism. But 
 now we must bear in mind that it is not pure wonder, just un- 
 alloyed surprise, but rather a troubled wonder that is the source 
 of knowledge. We are not and cannot be just the passive happy 
 spectators of a stream of fugitive impressions flitting across the 
 stage of consciousness. The presentations from the sense world 
 come as competing alternatives. This it is very important to 
 remember in considering any conceptual logic. The Platonic con- 
 ception of wonder has lent itself to poetic imagination and strik- 
 ing rhetoric, but it is a misunderstanding of it that makes it syn- 
 onomous with pure reverie, mystic contemplation. Consciousness 
 is not merely passive, it is essentially active. All waking con- 
 sciousness is one continuous affirmation, an affirmation which, 
 to be sure, always expresses itself in a disjunctive judgment, 
 as we shall see later. Now Plato insisted — at times with almost 
 indignant emphasis — that sense presentations are incapable of 
 thickening up into any final meaning, or validity of their own. 
 Objects of sense perception are always particulars. And no 
 accumulation of particulars by sheer juxtaposition or association 
 cjin yield true knowledge. An aggregate of particulars is just
 
 TEE MODEBN INDICTMENT OF FORMAL LOGIC 11 
 
 another particular. Knowledge presupposes universals. There 
 is, therefore, a world of ideas above this world of fleeting sense 
 perception. And the mere beginner in the study of Platonic 
 philosophy knows thai the ideas are entities, genuine objects of 
 
 knowledge, and thai they must never be taken as slates of con- 
 sciousness merely. 
 
 The New Logic cancels the distinction between origin and 
 validity, between what we discover aboul a particular fad through 
 an analysis of its present content, and what we learn aboul it by 
 an historical study of the em id it inns of its birth and development. 
 Professor Dewey 3 says of the orthodox Logician: **Ile deals with 
 the question of the eternal nature of thought and its eternal 
 validity in relation to an eternal reality. He is concerned, no1 
 with genesis, but with value, not with a historic cycle, but with 
 absolute distinctions and relations"; and again: "We have no 
 choice save either to conceive of thinking as a response to a specific 
 stimulus, or else to regard it as something 'in itself.' having 
 just in and of itself certain traits, elements, and laws. If we 
 give up the last view, we must take the former." 
 
 It is an engaging and important question which instrumental 
 Logic asks, How does empirical science come by its general 
 principles, and particularly how does il prove them .' Bu1 the 
 idealistic Logic has always insisted that this is not the same as 
 the determination of the principles of knowledge. If the New 
 Logic intends merely to assert that we never reach a conclusion 
 unless we have already come by it through experience, lm idealist 
 will take exception. There is a deep truth in the assertion that 
 we believe first and prove afterward or not at all. We do not 
 know because we have reasoned but we reason because we know. 
 Kant was very explicit on this point. He says, "Logic, on the 
 contrary, being the general propaedeutic of every use of the 
 understanding and of the reason, can not meddle with the 
 sciences, and anticipate their matter, and is therefore only a 
 
 3 Studies in Logical Theory, p. 14.
 
 12 FOOTNOTES TO FOEMAL LOCK 
 
 universal Art of Reason, the art of making any branch of knowl- 
 edge accord with the form of the understanding. Only so far 
 can it be called an organon, one which serves not for the < nlarge- 
 iiniit, but only for the criticism and correction of our knowl- 
 edge.'* 1 
 
 I need only refer to a significant fact that has been pointed 
 out frequently, namely, that several different meanings — some of 
 them quite diametrically opposed — have been given to the term 
 'practical" as applied to judgment. Even the pragmatists who 
 may now be said to have appropriated to themselves The "'trade 
 mark" of the term practical, seem to differ widely in their 
 definition of it. In Kant "s distinction between theoretical and 
 practical reason, the theoretical reason is always practical, or 
 pragmatic, although certainly not in the sense in which the word 
 is employed in some of the recent theories of judgment. When 
 the pragmatist declares that all judgments are practical, does 
 he mean to assert that the object of the judgment is created in 
 the act of judging '. The question as to precisely what the 
 expression "creates its own object" may mean — -the question 
 upon the answer to which depend so many vital issues in Logic- 
 will be considered more fully in a later chapter in <!ealing with 
 the postulated objectivity in thought. I wish only to say, in 
 passing, that this creative activity is the essence of all the 
 alleged theoretical judgments in any type of idealism, even the 
 most ancient. The primary object of the Critiqui of tin Pure 
 H< ason was to show that thought does actually create its object ; 
 or, the least we may say, is that it assists in its creation, in so 
 far as it supplies the form that matter must take in knowledge. 
 Any Logic that regards all judgments as practical labors 
 under this inherent difficulty. How can any concrete, particular 
 instance of knowing hope, at one and the same time, to creati a 
 valuable object and to know its creation as valuable. I am 
 restating, I know, a very familiar and old criticism of prag- 
 
 i Introduction to Logic; translate,! by T. H. Abbott (London, Long- 
 mans, 1885), p. :'».
 
 THE MODERN INDICTMENT OF FORMAL LOGIt V6 
 
 matism when I say thai value cannol be regarded as the hidden 
 worth within a situation, which aeeds only to be broughl to Light, 
 or evaluated. Value is not the self-determined issue of facts. 
 Value proceeds from the activity which relates particular to 
 
 universal, fact to law. The world of value is beyond the world 
 
 of fact in the same sense that the straight line is beyond the curve 
 which it determines. 
 
 Pragmatic Logicians arc over-filled with the spirit of natural 
 science. This they say, begins with practical definitions and 
 follows practical methods to practical conclusions. Natural 
 science has come to have such an enormous place in the common 
 life, as well as in the academic world, that we can readily 
 how the New Logic has come by its over-weaning sense of the 
 importance and certainty of the scientific method. The enthu- 
 siastic devotees of natural science easily win the approbation 
 of the fickle public, when they contrast the definite advance 
 which the so-called pragmatic sciences have made, with the eon- 
 fusion and dispute which we seem still to find in the world of 
 speculative Logic. The experimental logician insists that the 
 difficulty with all the philosophical sciences — and not less so 
 with Louie than with any of the others — is that they are all 
 destitute of either accurate, initial definitions or certain methods, 
 for the solution of their problems. The analysis and the evalua- 
 tion of judgments of practice without external points of orienta- 
 tion would he as difficult as the determination of a system of 
 conies without the axes of reference. The conditions of asser- 
 tion are manifold— sometimes operating singly, hut for the most 
 part combined in amazing complexity. 
 
 It is the task of practical thought ( upon this point the idealist 
 agrees entirely with the pragmatist) to determine in what meas- 
 ure each of the antecedents enters into the joint effect. The 
 difficulty in accomplishing this task is the same as the difficulty 
 that we meet elsewhere in the inductive sciences, for example, in 
 the application of Mill's Method of Agreement. There the plur-
 
 < 
 
 li FOOTNOTES TO FORMAL LOCH 
 
 ality of causes renders the causal determination uncertain. And 
 as in the world of outer natural sciences we find plurality of 
 causes and intermixture of effects so in the world of inner 
 natural science we discover each phenomenon to be the meeting- 
 point of converging strands of conditions coming out of the past 
 and diverging strands of effects going out into the future. They 
 are like the knots in a net into which and from which various 
 cords run. All of this is a most interesting study in Psychology 
 but it is not Logic. However cleverly phenomenena may be 
 explained as the cross-section of the evolutional series, that is, 
 as the meeting-point of forces, there still remains to be explained 
 the essential identity or form of the whole. 
 
 II 
 
 Every act of thought is in the first instance an immediate 
 presence, but it is also embedded in a continuum. This con- 
 tinuum, in its entirety, is reality. It includes the present think- 
 ing, and it is or may be the object of that present thinking. We 
 have illustrated here the axiom of higher mathematics that the 
 part can be put into a one to one correspondence with the whole 
 of which it is a genuine part. On this point I should differ from 
 Professor Dewey in the central thesis of his system that "think- 
 ing is set in a continuum which is not an object of thought.** 
 On the view which I am presenting it is evident that the term 
 reality is not so ' ' particularly treacherous. ' ' as Professor Dewey 
 thinks. There is no contradiction in its two uses — as a term of 
 indefinite reference and as a term of discriminate reference. 
 The part of the continuum which is out of sight and is, there- 
 fore, not an object of thought is in the instrumental view, never- 
 theless, always suggested by the present thinking. Now the dif- 
 ference between the idealistic and the instrumental theory of 
 judgment hinges upon the meaning of the word suggest. The 
 instrumentalist says that this suggested aspect of the continuum 
 
 5 Expt rimental Logic, p. 10.
 
 THE MODERN INDICTMENT OF FOBMAL LOGIC 15 
 
 is n ever a pari of i h«- (jinn; the idealisl insist s thai the sug 
 gested fact is already in a profound sense ;i presenl fact, other- 
 wise it would qo1 be even suggested] [idealism provides, withoul 
 contradiction, for both the discrete and ili<' continuous jis|><<-t of 
 the whole within which present thinking is set. Bradley and 
 his followers, in making reality the ultimate subjed in judg- 
 tneiit have kepi in mind these two uses of the word. 6 
 
 Moreover, I can no1 think it wholly just to tin- traditional 
 theories of knowledge to say with Professor Dewey thai they 
 were concerned entirely with the "question of the eternal nature 
 of thoughl and its eternal validity in relation to an eternal 
 reality — that they were engaged, not with the genesis hut with 
 value, not with a historic cycle, but with absolute distinctions 
 and relations." 7 The old pre-Darwinian metaphysics did not 
 ignore the question of genesis, but it saw that all historical ques- 
 tions are at last dependent upon questions of value, upon abso- 
 lute distinctions. Even Plato recognized the fact that Truth 
 and falsity were organically related to practical life, to action, 
 to the very needs in concrete experience upon which the logic 
 of pragmatism lays such emphasis. And it is not attributing to 
 Plato doctrines that are not his, to say, in the terminology of 
 the new theory, thai he did not teach that truth and falsity should 
 be wholly divorced from the particular activities that we perform 
 at a specific need. Put he would reply to the pragmatists 
 today in the spirit of Ins reply to the sophists, "The construc- 
 tions of these specific activities are not true unless they conform 
 not only to the intra-temporal is but to the supra-temporal 
 ought." 
 
 Professor Schiller asks the logician of the old school a simple 
 question which he rightly says cannot be shirked: "When he 
 asserts what seems to him a truth does he take any steps to ascer- 
 
 c Bosanquet says: "The subject in every judgment of Perception is 
 some given spot or point in sensuous contact with the percipient aelf. Bui 
 as all reality is continuous, the subject is not merely this given spot or 
 point." Logic (ed. 2; Oxford, Clarendon Press, it'll i. T. 78. 
 
 " Logical Theory, p. 14.
 
 16 FOOTNOTES TO FORMAL LOGIC 
 
 tain whether or not it is 'objective, 1 and whether other men 
 (all or any) agree with him? If he does, what are they and 
 what is their logical value? If he does not, why should not his 
 claim be treated as a random one?" 8 But now this is precisely 
 the question which a score of critics have been asking the prag- 
 matist for the last two decades. In an essay on "Pragmatism 
 and the a priori" printed in 1905, I said: 
 
 A judgment must be more than a mere effort to reconstruct the situa- 
 tion in which we find ourselves from moment to moment ; so much is, of 
 course, the first condition it must fulfil. But in addition to being a suc- 
 cessful present response, it must be true. This requires that it not only 
 conform to a passing is, but to a permanent ought. Each judgment of mine 
 is, in one aspect, my response to a present situation. But before I am 
 entitled to call it true, I must know why the response has been what it is; 
 that is, I must be able to say that another than myself would have responded 
 to the situation in precisely the same way. 
 
 Experimental Logic tells us that we must take all of our 
 problems, logical, ethical, and even religious, to experience for 
 solution. We must let the particular concrete facts of sense 
 experience tell their story. But the result is, as I have tried to 
 point out, experience has in the end no necessary story to tell. 
 Did not Hume prove that once for all? If we follow the realist 
 far enough, as he lets facts recite their tale of explanation, he 
 invariably brings us back to the point from which he set out. 
 He displays a remarkable combination of true insight, with what 
 seem inexcusable lapses from reason in his empirical explana- 
 tions. These modern apostles of the "flowing philosophy,'" are 
 standing upon a platform from under which all support has been 
 taken. The pragmatist proceeds with his empirical test for truth 
 paying no heed to the constant protest of the idealist against 
 the circular reasoning that is involved in any attempt to make 
 experience self-explanatory. To the idealist's question, How 
 do you explain the contradiction in experience? he replies 
 naively, "There are no contradictions." Of course no contradie- 
 
 s Mind, a. s. XVI II (1909), 402.
 
 THE MODERN INDICTMENT OF FORMAL LOGIC 17 
 
 tion will ever be discovered in experience if he tesl experience 
 by itself. 
 
 The difference between the idealistic and the pragmatic inter- 
 pretation of experience is to be found in the way in which each 
 of the two schools reads off the relationship between external 
 and internal meaning. For the idealisl the whole problem of 
 knowledge reduces itself to the question, How are primary or 
 interna] meanings of ideas related to their secondary or appar- 
 ently external meanings? For the realist, the pragmatist, and 
 in fact for every type of positivist, the question is, How are the 
 brute facts of the primary objective reality related to the second- 
 ary apparently internal meanings which we call ideas.' If experi- 
 ence be taken in a wide sense as synonomous witli the entire con- 
 tent of consciousness, and thus made to cover both the active 
 as well as the passive aspects of thought, then of course the 
 idealist would agree with the empiricist that the laws of thought, 
 as well as the laws of existence come from experience. 
 
 Ill 
 
 The critics of Formal Logic have failed, I venture to think, 
 to distinguish between the thought form and the language form 
 in which that thought form expresses itself. The two are not 
 the same; and Formal Logic deals with form in the first, not 
 the second sense. Professor Sidgwick says, "Preoccupied as 
 Logic has chosen to be with forms of statement, it cannot wholly 
 desert the idea that the meaning of a statement is something that 
 belongs to its form, instead of the form being a more or less 
 successful attempt on the part of a speaker to express a mean- 
 ing."'' Not all teachers of Formal Logic, I am sure, would agree 
 with this statement. The translation of the literary or rhetorical 
 forms of statements into the logical form of thought, is the 
 work of the grammarian and the philologist. We admit that the 
 
 8 EU mt ntary Logic, p. !<>»>.
 
 18 FOOTNOTES TO FORMAL LOGIC 
 
 grammatical form is often highly ambiguous, and that it is a more 
 or less successful attempt on the part of the speaker to express 
 a meaning — it is a thought form. But the thought forms are 
 not ambiguous, although they have manifold meanings. It is 
 the work of the formal logician to explicate the various impli- 
 cations, or manifold meanings. 
 
 It is a significant fact that in its indictment of the Tradi- 
 tional Logic the New Logic does not condemn formal reasoning 
 in toto. Sidgwick says: "We do occasionally reason about the 
 extensive relation of two accepted classes to each other by means 
 of the relation of each of them to a third class, and for that pur- 
 pose we may put letters like X, Y, and Z, in place of the terms 
 and so test the validity of a syllogism apart from the truth of 
 its premises and conclusion." (Elementary Logic, p. 164). 
 Now the defenders of Formal Logic may well regard this as a 
 concession of the greatest importance. If there can be found 
 a single instance where the form of thought does not have to wait 
 upon the matter, controversy is at an end and the formal logicians 
 have won the debate. This is all that Formal Logic has ever 
 contended for, and we do not here avail ourselves of the prin- 
 ciples that the exception proves the rule in the narrower sense 
 of that axiom. These instances, where it is admitted that we 
 reason formally, are abstractions from the concrete situations, 
 and if the form can be divested of its matter in a single instance 
 there is nothing to prevent our applying the principle univers- 
 ally. 
 
 Formal Logic, today, has set for itself the task of determining 
 all indefinable concepts and all indemonstrable propositions. The 
 several contributors to the volume on Logic in the Encyclopedia 
 of Philosophical Sciences are quite in agreement on this point. 
 We must bear in mind, however, that the modern process of 
 logical definition consists in pursuing a concept back to some 
 prior indefinable concept. And we must always remark that, 
 when we are dealing with a class of inter-related concepts, it is
 
 TTlEMODEBh INDICTMENT OF FORMAL LOGU 19 
 
 often immaterial which of the group are taken as the indefinable 
 prerequisites of the others. In like manner the present-day 
 Formal Logic regards the process of demonstration as the reduc- 
 tion of all propositions to the least number of indemonstrable 
 propositions. And here, too, in considering any collection of 
 propositions constituting a real group it is immaterial to the 
 structure of the group which is placed in the position of the 
 indemonstrable proposition, and which are its derivatives. 10 
 
 IV 
 
 Of the four authors who in recent years have led the attack 
 on Formal Logic, Dr. Mercier is the most vehement in his 
 denunciations of the traditional system. He thinks it a serious 
 indictment that among the foremost writers on the subject, since 
 the time of Aristotle, no two are agreed on what the subject mat- 
 ter is. what its limits are, or even whether it is a science or an 
 art. He insists that it is neither logical nor useful to write upon 
 a subject without first determining the nature of tin; suhject 
 matter. But this 1 think is not a serious indictment. Many 
 investigators are doing most logical and most useful work in 
 Dr. Mercier 's own special province of insanity, and yet we may 
 say of these workers, as Dr. Mercier says of the formal logicians, 
 that no two writers on the subject since the time of Pine! have 
 agreed as to precisely who should be included in the class, insane. 
 
 In his attack upon the Traditional Logic, Dr. Mercier has 
 said that the system which he has propounded is so different 
 from all previous expositions as to warrant the title, .1 A-//' 
 Logic which he has given to his book. But in the opening pages 
 of the volume we find him giving an account of the nature of the 
 reasoning process almost identical with thai which Aristotle gave 
 
 io Cf. Croce, Encyclopedia of Philosophical Scu nces, I. L86. "It depends 
 on us whether any particular axiom be taken as a theorem and any par- 
 ticular theorem as an axiom, according to the order which we adopt in our 
 
 deductions. ' '
 
 20 FOOTNOTES TO FOBMAL LOCK: 
 
 in the Prior Analytics. Dr. Mercier maintains that there an- 
 three processes of reasoning — induction, deduction and analogy. 
 Now, however much logicians through the centuries may have 
 differed from Aristotle in their own personal opinions of the 
 nature of the reasoning process, they have all admitted that we 
 owe to him the tripartite division of the reasoning process into 
 analogy, deduction and induction. Although Dr. Mercier has 
 condemned in very emphatic language the whole of Traditional 
 Logic, yet when he comes to his own account of the three types of 
 reasoning he says, when writing about deduction: "The Logic 
 expounded in that book is the Logic of Inference ; of Consistency ; 
 of Proof and Disproof ; of Form. L^seless in the discovery of 
 Fact ; ignoring the truth or falsity of the matter of which it 
 treats ; its value is in testing Consistency ; in argument, in ex- 
 plicating, convincing, refuting. This is the field of Traditional 
 Logic." 11 We thus observe that while denying the uselessness of 
 the Traditional Logic in the discovery of facts, Dr. Mercier 
 nevertheless accords to it a wide field of usefulness in other 
 directions. 
 
 Dr. Mercier criticizes the logicians of the old school because 
 they employ a nomenclature that is often inappropriate and 
 ambiguous. He discovers, in the words describing the classifica- 
 tion of propositions as real and verbal, a clear misnomer in the 
 term, verbal; "for all propositions," he says, "are expressed in 
 words, and are therefore verbal. Here therefore at the very 
 outset of our logical studies, we meet with a striking instance, 
 the first of very many, of the inaccuracy, looseness, and ambigu- 
 ity with which words, the material of their craft, are used by 
 logicians." 12 But I submit that we should none of us write 
 much upon the subject of Logic or upon any other subject, if 
 we waited until words said exactly what they mean, or meant 
 exactly what they said. It is interesting to observe, also, that 
 
 11 New Logic, p. 11. 
 
 12 Op. cit., p. 17.
 
 THE MODEBN INDICTMENT OF FOBMAL LOGH 21 
 
 the classification which Dr. Mercier suggests, instead of the 
 one ordinarily found in textbooks, is itself aol free from ambigu- 
 ity of the very kind which he criticises. We are all of us ;it the 
 
 mercy of vocabulary. 
 
 The idealists join the empiricists in deploring the imperfec- 
 tion of language as a means of conveying thought about first 
 principles. It is nol a new discovery that Language is inadequate 
 to speculative thought. Nor does it require elaborate proof to 
 show that Language was created for the utilitarian purpose of 
 communication in the world of appearances. The idealist, there- 
 fore, describes his conceptions of final reality very unsatisfac- 
 torily by means of a vocabulary which has had its origiu in tie- 
 world of relative reality. All who believe in the world of things 
 that abide, must therefore express themselves imperfectly by 
 myth, parable or metaphor. Plato, Christ and Buddha often 
 deplored the defects of language in their attempt to teach tie- 
 glad tidings of salvation through the sense of the universal. The 
 scientist and the pragmatic thinker in general, who traffic in 
 things seen, are not so handicapped by the short comings of 
 language as are those who are concerned with the unseen. We 
 make many allowances for the scientist when he expresses him- 
 self in halting ways by means of our imperfect instrument of 
 language, which does not keep pace, in its revisions, with the 
 revisions of knowledge. We understand the astronomer when 
 he says, "Tomorrow when the sun rises I shall make some obser- 
 vations." We do not rebuke him for the inaccuracy and expect 
 him to say, "Tomorrow when the earth revolves and causes the 
 sun to appear to rise, etc." The idealist bespeaks a like patience 
 and tolerance from his hearers when he attempts to describe the 
 still more distant realities by means of illustrations from the 
 world of sense. He is fully aware that his metaphors are faulty, 
 defective, and inconclusive.
 
 22 FOOTNOTES TO FORMAL LOGIC 
 
 V 
 
 The genetic theory of judgment, upon which pragmatism rests 
 its entire logic, is stated most clearly and concisely by Mr. 
 Schiller : 
 
 I cannot but conceive the reason as being, like the rest of our equip- 
 ment, a weapon in the struggle for existence, and a means of achieving 
 adaptation. It must follow that the practical use, which has developed it, 
 must have stamped itself upon its inmost structure, even if it has not 
 moulded it out of prerational instincts. In short, a reason which has not 
 practical value for the purposes of life is a monstrosity, a morbid aberra- 
 tion or failure of adaptation, which natural selection must sooner or later 
 wipe away. is 
 
 In the present essay I wish to reaffirm the central criticism 
 that idealism has made upon the logic of pragmatism ever since 
 its birth — in its present reincarnation — in Professor James' lec- 
 ture on "Philosophical Conception and Practical Results," be- 
 fore the Philosophical Union of the University of California in 
 1808. I shall attempt to show, as I have maintained elsewhere 14 
 that thought is not merely an instrument in the struggle for 
 existence, not simply one of the devices with which nature has 
 equipped us to secure a more comfortable adaptation to our en- 
 vironment. I shall contend that aside from being a useful instru- 
 ment in the struggle for existence — its secondary and derived 
 function — it has the more important primary office merely to be 
 true. It has been asserted often in the history of Logic that 
 thought has an external meaning, through which it refers to 
 an end beyond itself, and an internal meaning which constitutes 
 an end in itself. It is one function of judgment to be useful, 
 that is, to reach out beyond itself. But its other and more funda- 
 mental function — a function without which that other function 
 is meaningless — is just to be true, to be self -consistent. 
 
 Some pragmatists have hestitated to commit themselves to the 
 doctrine that all judgments are practical. Such leaders, how- 
 
 13 Humanism : Philosophical essays (London, Macmillan, 1903), p. 7. 
 
 14 << Pragmatism and the a priori/'' Present series, I (1904), pp. 72-91.
 
 TEE MODEMN INDIi lMl\ T OF FOBMAL LOGIC 23 
 
 ever, as Schiller, Sidgwick and Mercier have unhesitatingly 
 declared, qo1 only, thai all truth works, bu1 also thai all thai 
 works is true. Bu1 Professor Dewey seems always to leave his 
 readers in doubl as to precisely whal view lie holds. In his very 
 latesl utterances In- lias again failed to make his position clear. 
 In an article entitled, "An Alleged New Discovery in Logic" 
 Mr. I). S. Robinson criticises Professor Dewey's Experimental 
 
 Logic and remarks 1 ' that he is in donht whether Professor Dewey 
 would say that all judgments are practical. In his rejoinder 
 Professor Dewey admits "There is danger of a serious ambiguity 
 in discussing practical judgments as a distinctive type and also 
 intimating that in some sense all judgments may he practical." 
 lint when Professor Dewey "intimates" (not asserts), that 
 "some" (not all) judgments "may he" (not are) practical, I, 
 too, find myself in donht. I am still old-fashioned enough in my 
 idealistic convictions to think that the pragmatist can not avoid 
 committing himself to at least one assertion that is not prac- 
 tical — or at any rate not practical in the same sense as the 
 others — namely, this very judgment that all judgments are prac- 
 tical. And it is not mere quibbling to say that the judgmenl 
 that all judgments are practical, is not itself a practical judg- 
 ment. It is another way of saying that the judgments of utility 
 are in one dimension of thought and the judgments that pro- 
 nounce upon the members of the series of useful judgments are 
 in a different dimension of thought. 
 
 Empirical Logic" 1 has always declared that all definition 
 presupposes a psychological treatment of mental states; and 
 
 is Jour, philos. ami psych., XIV. 225, April 26, 1017. 
 
 is There is an important sense in which every theory <>t' judgment is 
 empirical. When I say that a judgment, or anything else, is empirical, 
 one implication always is that it might have been otherwise. And in our 
 theory that judgment is just such a selection from competing alternatives 
 presented to the mind, this constitutes one of the earliest ami most basic 
 
 characteristics of the judging consciousness. Wherever we tiinl the possi- 
 bility of error, we are dealing with empirical facts. Ami there i^ this 
 paradox about facts: to lie real facts they must po-scss the inherent possi- 
 bility of being different, ami hence not facts.
 
 24 FOOTNOTES TO FOL'MAL LOGIC 
 
 idealists have always admitted that a study of psychic facts as 
 they are immediately presented to consciousness is indispensable 
 to any doctrine of truth. But they .insist that this is not the 
 sufficient condition of truth; the apperceiving or unifying of 
 the sense-presented facts is performed by the self-active prin- 
 ciple of mind. If there is value to our individual experiences, as 
 they come to us strung along in time, and if it is unnecessary 
 to make this temporal validity rest back upon a validity that is 
 not in time, all talk about a world of absolute truth and perfec- 
 tion is meaningless. If Experimental Logic is self-sufficing, then 
 there is no Logic uberhaupt. 
 
 Experimental Logic would explain my present thought by 
 locating it between an a priori situation out of which it emerged 
 and a subsequent situation into which it flows. Idealistic Logic 
 maintains that the three situations — past, present and future — 
 even when thus casually connected in the chronological series 
 are not self-explanatory. There is exhibited in Instrumental 
 Logic, we hold, the ancient fallacy of failure to distinguish 
 between psychological cause and logical ground. 
 
 The logical coherence in our judgments, according to Experi- 
 mental Logic, is our interest in the situation in which we find 
 ourselves, when called upon to judge. We are constrained to 
 reconstruct that part of the world with which we are in imme- 
 diate contact. The union of the subject and predicate in judg- 
 ment is the outer expression of this purpose or interest. This is 
 certainly true as a psychological account of the judging process. 
 But having said that interest or purpose is the cause of the inter- 
 connection of ideas, we still have on our hands the more serious 
 problem of finding the ground of the present purpose. This, 
 as the idealist has often insisted, is not self-explanatory for cause 
 and ground are not identical. It is one thing to say that we 
 judge because we have a need, an interest, or a purpose ; but an 
 entirely different thing to discover the ground of this need. How 
 may I know that this present purpose to reconstruct reality is a
 
 TEE MODERN INDICTMENT OF FOBMAL LOGIi 25 
 
 true purpose? Only when I have lai<l hold of a higher and ulti- 
 mate purpose, namely, a criterion of this specific purpose. In 
 short, I fail to see how purposes are capahle of self-evaluation. 
 
 Experimental Logic while emphasizing effects of action as 
 tests of validity, docs not furnish a criterion by means of which 
 we may distinguish good from bad effects. Every judgmenl 
 reconstructs reality, and thereby helps to continue the present 
 order, say the defenders of the new theory of knowledge. We 
 pronounce the judgmenl true if it contributes to the existing 
 order, and false if it does not. lint now. in order that we may 
 distinguish a good effect from a had one. we need sonic criterion 
 extrinsic to the situation to tell us why it is besl to have the 
 present system perpetuated. In every experimental logic, truth 
 means objectivity, and its criterion is utility. But in the prac- 
 tical world there are different kinds of utility. If the useful is 
 the true, we ought likewise to have grades of truth, and be able 
 to speak of the true, the truer and the truest. This is. indeed, 
 precisely what the pragmatist does say — a doctrine open to 
 criticism, to say the least. Moreover, even if we admitted the 
 possibility of gradations in truth (for the logic of realism insists 
 that this is by no means manifestly absurd), the pragmatic test 
 furnishes no criterion for distinguishing between the different 
 kinds of truth. But it is evident that it is not mere utility, but 
 utility of the right kind, that is needed to establish the objectivity 
 in judgment. 17 
 
 In every judgment, according to the pragmatic theory of 
 knowledge, something new is added to the system of cognitions 
 already in the possession of the one who judges. The test of 
 
 17 Cf. Windelband, Ency. Philos. Set., 1, 24. "And here we come 
 
 on a double aspect of all logical laws: on the one hand they are rules for 
 the empirical consciousness, according to which all thinking which has truth 
 for its aim should be carried on; on the other they have their inner and 
 independent significance and being, quite independent of the actual hap- 
 pening of ideational processes, which are or are not in accordance with 
 them. We may call the latter their value-in-themselves, the former <• 
 value-for-us. ' '
 
 26 FOOTNOTES TO FORMAL LOGIC 
 
 the rationality of this new element is its compatibility with the 
 old. If it works it is pronounced true, and is given its appropriate 
 place in the established order. If it does not fit in with the old 
 it is rejected as false. But this definition of truth is more adroit 
 than accurate. Is not the pragmatist all the while begging the 
 whole question? Does he not presuppose the truth or rationality 
 of the old, namely, this thought system which he possesses at 
 the moment of judgment? His criterion of inner consistency 
 works very well, if we grant him enough rationality to start the 
 process. The instrumentalist, I should say. borrows just enough 
 of the idealistic insight to set his scheme in motion and then dis- 
 avows the debt. The idealist has ever insisted that this determin- 
 ation of the primal rationality can never be achieved by a poste- 
 riori methods. That which is workable is not, for that reason 
 alone, true. A new fact may fit in with the old. and yet may 
 not know itself to be error, because it does not know the system 
 into which it has been accepted, is false. 
 
 I cannot think that the total meaning of an idea is to be 
 found by searching only forward from the idea to its conse- 
 quences, as Professor James teaches, nor yet by looking both 
 forward and back as Professor Dewey and his disciples insist. 
 The deepest truth about thought is found in an entirely different 
 dimension. It lies in a world that is logically prior to the postu- 
 lates of either of these forms of pragmatism. Thought is con- 
 structive as well as reconstructive. It is not merely an instru- 
 ment in the struggle for existence, but is itself legislatively 
 sovereign over the process of evolution within which it manifests 
 itself as an instrument. Not what an idea has come out of, nor 
 what it is just now seen to be, nor what it is going to do here- 
 after, but what it eternally is, must furnish us with our deepest 
 insight into the nature of thought.
 
 THE MODEBN INDICTMENT OF FORMAL LOGIt 27 
 
 VI 
 
 The agnostic realism a1 the heart of every form of pragmatic 
 
 logic is not easy to refute. It lias descended directly from the 
 agnosticism of the Gritiqut of Pun Reason. The only way to 
 dissolve this realism is to make use of Kant's own discovery, and 
 pursue his logic to the legil [mate conclusion of its own movement. 
 Kant pointed out the path thai must be pursued in order to 
 explain the inherent contradictions in the realistic conception 
 of causality. He demonstrated, it would seem for all time, thai 
 the principle of efficient caauality cannot belong to reality, hut 
 that it is the mind's contribution to experience. Eowever, he 
 failed to see that for this very reason there can be no genuine 
 datum in knowledge. If the facts of experience are really giv< n, 
 if they are thrown at the mind from the world of things in 
 themselves*— then this transcendent reality possesses the princi- 
 ple of efficient causality. This, however, Kant's own doctrine 
 explicitly denies. His insight enables us to see what he him- 
 self seems never to have been fully aware of, that if the things- 
 in-themselves have not in them the principle of efficient causality 
 they are incapable of giving anything to mind. Things-in-them- 
 selves can not contribute causally to the content of knowledge. 
 
 The fundamental point at issue between Plato and Aristotle 
 on the import of judgment has been perpetuated, in philosophical 
 discussions, to the present day. The idealists say with Plato 
 that necessary truth is that from which every purely material 
 external or given element has been cancelled. The only truth is 
 formal truth. The later-day pragmatic or instrumental logicians 
 have insisted that truth as thus defined would be relegated to 
 the world of mathematical abstraction, to the realm of "bloodless 
 categories." Plato provided for a more vital connection between 
 the universal and the particular, the abstract and the concrete 
 than appears on the surface. Aristotle's attack on Plato on 
 this subject was not entirely defensible. And no serious idealism
 
 28 FOOTNOTES TO FORMAL LOCK 
 
 at the present time imposes this requirement on knowledge. Plato 
 did not demand that the given, the concrete, the particular ele- 
 ment in knowledge should vanish entirely. Now it is obviously 
 a question as to the precise meaning of the given. The given 
 may he so defined that it can be kept as a constituent element of 
 the highest knowledge. A datum which is just hurled at a passive 
 mind would, of course, contaminate knowledge and forever reduce 
 it to relativity and incertitude. In perfect knowledge there can 
 be no Streng-gegebenes, nothing genuinely novel or totally differ- 
 ent. But the logic of naive realism declares that such a Streng- 
 gegebenes is an inexplicable and irreducible element of the know- 
 ing process. Absolute knowledge, it declares, is forever impos- 
 sible; such opinions or beliefs as we have, we arrive at by a 
 posteriori methods entirely. The logic of naive realism and the 
 Instrumental Logic declare that we are not at all concerned with 
 the ultimate beginning of thought. In fact, thought cannot be 
 traced back to its source. It cannot see itself start; it must 
 simply accept itself as fact. But now it can be pointed out, even 
 to the proverbial plain man on the street, that there can be no 
 arriving at knowledge or anything else without starting. There 
 must be a beginning somewhere, an initial point of departure 
 which is itself underived. 
 
 VII 
 
 Empirical Logic has always dealt extensively with the word 
 fact. All knowledge, it says, must have its foundation deep down 
 in the world of concrete fact. To this we may reply : In order 
 to realize itself, thought must, to be sure, pass through fact. 
 This Plato never denied, and the student in the philosophy of 
 Kant learns, almost in his first lesson that the a priori forms of 
 thought are empty and without meaning, until they have received 
 their material filling. Thought does not see itself start. But we 
 are not warranted in saying that because it does not see itself 
 start, it arrives without starting. Of course, men reasoned accen-
 
 THE MODERN INDICTMENT OF FOBM IL LOGIC 29 
 
 rately before they knew the reason for their accuraie reasoning. 
 They followed oui premises to their coiielusion, or traced enn- 
 elusions back in their grounds, guided by principles of correct 
 thinking before those principles were noticed or understood. 
 Aristotle was preceded by many centuries of exact thinking. It 
 was not li is primary purpose to make men rational — that, for 
 the most p;irt, they already were. lie was interested to show 
 men. by critical analysis, in whal their existing rationality con- 
 sisted. 
 
 Thought does firsl become aware of its own movement as it 
 passes through fact — as it issues out of one situation to go over 
 into another. But this is not the last step in its self-realization. 
 It is an unjustified arrest of thought's activity not to allow it 
 to pass through fact and, returning to itself, to discover the 
 undt rived laws of its movement. Thought does find itself by the 
 \\ ay of fact, but when its activity is unhindered it passes to the 
 higher level where it sees that itself furnishes the prior condition 
 of the discovery of itself in the facts. To think actually, we must 
 indeed think about something; this something, the object matter 
 of thought, whatever it may be, must in the first instance be sup- 
 plied through the medium of the senses. Thought itself does not 
 become an object of thought until after, it has been called into 
 exercise by objects presented from without. But while the mate- 
 rial or external element varies with every successive act of 
 thought, the formal or internal element remains the same in all; 
 thus the necessary law, or form, binding on the thinker in every 
 instance, is distinguished from the contingent objects, about 
 which he thinks on this or that occasion. Obviously the words 
 matt rial, exti mail, and obj<<f are not here employed in any naive 
 sense. In a later chapter, when we come to discuss more in 
 detail the nature of the objective element in thought we shall 
 define the object entirely in terms of the expected self-trans- 
 cendence of the subject. 
 
 The new pragmatic Logic and the modern realistic meta-
 
 30 FOOTNOTES TO FORMAL LOOK' 
 
 physics underlying it — so their devotees frankly confess — 
 acknowledge important contributions which they claim modern 
 natural science makes to their doctrine. There has been a very 
 prevalent tendency in the thinking of the last quarter of a cen- 
 tury, to abandon or to ignore almost entirely what through all 
 the ages has been considered the highest concern of the human 
 mind, namely, the search for first principles, logically prior to the 
 causal series and its validating ground in time and space. This 
 tendency to abandon all attempts to orient our temporal experi- 
 ences — our dynamic lives — by resting them back upon a static 
 encircling reality is undoubtedly due to the enormous place that 
 the method of natural science has come to occupy in the higher 
 intellectual life of our time. The vast and comparatively sudden 
 development in the biological sciences under the guidance of the 
 master principle of evolution has filled many minds with an over- 
 powering sense of the importance, the certainty and the useful- 
 ness of this principle in other fields. But there are yet many 
 unshaken idealists, 1 s who still believe that Kant's first question, 
 "What can I know and how do I know it?" has to be raised and 
 answered, too, in a final and affirmative fashion, before the 
 scientist has valid possession of his method even within the field 
 where alone it is applicable. The validity of the scientific method, 
 lies entirely in its application to its proper object, namely, the 
 facts of sensible experience both inner and outer. But it does 
 not follow that, because science can give no certitude in the real 
 world beyond sense, there is no method of certainty possible in 
 that super-sensible world. Metaphysics is absolutely indispens- 
 able to the existence of Logic or of any other science. 
 
 The theory of judgment that is offered in these pages demands 
 an objective system which the judgment itself confesses must lie 
 beyond its primary activity. But this postulated objectivity in 
 
 i s E.g., Windelband says: "Modern Metaphysic, with its attempts to 
 piece itself together out of borrowings from the sciences, is far more con- 
 temptible than the old Ontology which, starting from the realm of validity, 
 had at any rate the courage to attempt the deduction of the interconnection 
 of the universe as an articulated whole." Ency. Philos. Set., I, 65.
 
 THE MODERN INDICTMENT OF FORMAL LOCK' 31 
 
 judgment, as I shall try to show later, is not inconsistent with a 
 monistic theory of the universe; it is even compatible with the 
 most nai've subjective idealism. However, it provides for a relax- 
 ing of a too-rigid monistic ontology. When we declare thai the 
 subject awaits its object, and then define that object as no other 
 than this expected self-transcending, synthetic achievement of 
 the subject, we avoid the contradictions of an epistemological 
 dualism on the one hand, and an ontological monism on the Other. 
 Both for knowledge and for existence the idea and its object 
 are — to use Bradley's very apt expression — "'coupled apart." 
 
 The New Logic is distinguished from all the older idealistic 
 systems by its refusal to accept the distinction between ground 
 in fad and (/round in thought. As has now frequently been 
 pointed out, pragmatic Logic dispenses entirely with ontology in 
 the historic sense of the word, and therefore, identities the causi 
 of the existence of serial facts — in their serial manifestation — 
 and the (/round of our thinking them serially. We hold that this 
 distinction is vital and that, while there is a practical viewpoint 
 from which it may be ignored, it cannot be totally cancelled. This 
 is one of the first and most persistent criticisms that various 
 idealists have made upon the instrumental theory of judgment. 
 
 The genetic theories of judgment are all compelled to admit 
 that the ground of belief is finally an unsolved problem. Psy- 
 chology seems to have discovered that chronologically we believe 
 things first and afterwards demonstrate them. Thinking as dis- 
 tinguished from believing is retrospective rather than prospec- 
 tive; il is demonstration rather than inference. Now it is not 
 only Psychology that confesses itself baffled with this puzzling 
 question of the reason for our beliefs, but Logic also finds the 
 ground of knowledge in a sense inexplicable. As I have already 
 said, knowledge is a postulate of logic; it is a fact that must be 
 assumed before logic itself can come into existence. If Logic 
 is "thinking about thought," then this thought is obviously taken 
 for granted when the thinking about it begins.
 
 32 FOOTNOTES TO FORMAL LOGIC 
 
 Professor Dewey has often admitted, 19 by implication at any 
 rate, that he has not remained true to the Hegelian idealism of 
 his earlier writings. And yet many of his later utterances seem 
 to me as entirely opposed to the naive associationism of the earlier 
 empiricists, Locke, Mill, and Bain, as is any idealism. And there 
 are also serious divergencies from the even more radical empi- 
 ricism of the later pragmatists, Schiller, Sedgwick and Mercier. 
 For Professor Dewey 's ideas taken by themselves are entirely dis- 
 crete facts. They are continuous only when embedded in the 
 specific situation out of which they arise and into which they 
 descend. And yet I must repeat that I fail to see how the ' ' situa- 
 tion" with all its "brute" objectivity can ever provide for the 
 continuity that is necessary for "knowing things together." 
 
 I wish to offer a homely illustration of an illusion of continuity 
 in the optical world analogous to the essential discontinuity that 
 lurks in the instrumental theory of thought. Each of the various 
 moments of a motion picture as they are flashed on the screen 
 might be described in terms of what precedes and what follows 
 it. "We say we watch the scene being enacted, we follow the plot 
 and we think we see explanatory continuity there. But if an 
 imaginary being, living in that screen w r orld — totally unaware of 
 the projecting power of the stereopticon — were asked to give an 
 account of what really does happen, he would say precisely what 
 Hume said about the world that we actually see. No causal con- 
 tinuity is found on the screen. One picture appears and then 
 disappears and another totally disconnected from the preceding 
 one takes its place. The clever makers of the motion pictures, 
 taking advantage of actual discontinuity, can feign all kinds of 
 continuity by piecing together parts of films taken miles and 
 days apart. The only truly explanatory continuity is found when 
 
 19 Cf. Studies in Logical Theory, p. 36. "There is no such thing as either 
 coincidence or coherence in terms of the elements or meanings contained in 
 any couple or pair of ideas taken by itself. It is only when they are co-factors 
 in a situation or function which includes more than either the "coincident" 
 or the "coherent" and more than the arithmetical sum of the two, that 
 thought 's activity can be evoked. ' '
 
 THE MODEBN INDICTMENT OF FOBMAL LOGIC 
 
 we read our way hack at each insiatii to and through the proj. 
 ing power of the stereopticon itself. So. too, must the rtates of 
 consciousness that appear chronologically in the instrumental 
 theory of judgment be translated into a thoughl process that 
 transcends time and of which that outer evolution is hut the 
 projection. 
 
 A less concrete, ami therefore in some ways a more satisfac- 
 tory illustration may he taken from geometry to show the essen- 
 tial discontinuity in the stream of consciousness. The points of 
 ;i parabola, for example, take their places serial im in obedience 
 to the requirements of fads external to themselves. Each point 
 obeys the law of keeping equidistant from a fixed straight line 
 and a fixed point; as a particular fact in the series, it is inde- 
 pendent of the points that lie next to it. An external spectator 
 might imagine that the points arranged themselves in this orderly 
 fashion by a kind of reciprocal reference to each other. Each 
 point, it might be thought, could find its place in the series by 
 taking its bearings from its predecessor and passing the angular 
 reading on to its successor. But the curve has no such intrinsic 
 principle for its spatial determination ; it is the result of the indi- 
 vidual compliance of each point with entirely external conditions. 
 The straight line, however, can and does define itself as a quantity 
 in extension by precisely such an intrinsic principle. One has a 
 practical illustration of this in watching a company of soldiers 
 "fall into line."
 
 CHAPTER II 
 APPREHENSION. QUESTION AND ASSERTION 
 
 I 
 
 It has frequently been maintained that Logic is not concerned 
 with the question as to the structure of the idea, or how many 
 ideas may be grasped in a single pulsation of consciousness, or 
 any other of the many questions in which one idea is involved. 
 The unit of Logic, we are told, is the judgment, and every judg- 
 ment contains at least two ideas. Bradley and his disciples have 
 rightly rejected the view that judgment is the comparison of two 
 ideas. However, there is a sense in which Ave may say that two 
 ideas are involved in every judgment. The ultimate molecule of 
 knowledge, to use a chemical metaphor, is always diatomic. Con- 
 scious judgment is the idea that I have an idea. To have, or to 
 entertain an idea is to refer it to reality ; but this reference of the 
 idea to reality implies at least one other idea which might have 
 been referred to reality instead. If we had only one idea we 
 should never, I think, distinguish between it and reality and we 
 should never talk of referring it to reality. 
 
 Obviously, these questions which lie in the borderland of 
 controversy between Logic and Psychology can never be settled 
 until we know precisely what we are to understand by one idea. 
 If we mean by an idea a state of consciousness so immediate and 
 withal so simple and single in its structure as to exclude all 
 internal multiplicity, then Logic can have nothing to do with 
 it, and perhaps not Psychology, since the existence of a mental 
 state described by Jevons and the earlier logicians and psycholo- 
 gists as simple apprehension, has justly been called in question. 
 That may always be regarded as one idea which includes within 
 
 [34]
 
 APPREHENSION, QUESTION AND ASSERTION 35 
 
 Its synthetic grasp all the secondary ideas which a purposive will 
 cares i<> make in it. It is the purpose to hold the multiplicity as 
 a single objed of attention thai makes i1 one idea. The only true 
 individual is a will-object. From the point of view of the act of 
 synthetic attention the idea is one, bul it is nol on thai accounl 
 simple. For this reason the expression simple apprehension is 
 a misnomer. Apprehension may be of multiple content. For tin- 
 purpose of the present discussion we need not go further into this 
 controversy. 
 
 It should be pointed out, however, thai the expressions, mental 
 states, state of consciousness, idea, image, are all of them ambig- 
 uous, and this ambiguity when carried over into the Logical debate 
 becomes the source of hopeless confusion, and the "cause of all 
 our woes. *' No word in Logic has caused more confusion than the 
 word irfxi. Even in ordinary usage it has been taken to stand 
 for both a universal and a particular content of consciousne ss It 
 would be better to regard the idea as one aspect of the concept. 
 My concept of a tree may be analyzed into three moments: 1 
 the existence of an image in the mind which mighl be called my 
 idea of the tree, (2) the aggregate of inner qualities, I :! I the ex- 
 ternal reference or signihYai Bradley, as is well known has 
 
 characterized these three moments as (1) the that, (2) the what, 
 and (3) the meaning of the idea. Logicians and psychologists still 
 use the word idea instead of concept, which is freer from ambig- 
 uity. The concept is not exhaustively understood when it is 
 treated psychologically only; it is more than just a simple psychic 
 act. The word idea in its more limited use does stand for such a 
 focus of analytic attention, lint no idea is mere idea ; the cogni- 
 tive function, that is. the relation to something beyond itself, 
 which it means, is necessary to the very being of the idea. And 
 yet, self-contradictory as it may appear, we must say that when 
 we have an idea of an object that objed is already an essential 
 part of the idea. For Logic, the idea, or mental state is a oiu 
 enwrapping a many. It is a content contemplated from a mul-
 
 36 FOOTNOTES TO FOBMAL LOGIC 
 
 tiple, that is, a dual viewpoint. From one of these points of view 
 the idea or concept is a plurality ; in its outward relation to the 
 rest of the universe it is many. But when it faces the thinker, it 
 is one ; its former plurality has now become the object of a single 
 act of attention. 
 
 Some psychologists have analyzed thought out into a serial 
 arrangement of its acts in which we find the concept placed 
 between the judgment and abstraction. The judgment depends 
 upon the concept and the concept in turn depends upon the pro- 
 cess of abstraction. No serious objection can be made to this 
 serial arrangement if we do not construe the relationship of 
 dependence as a uni-directional function. The structure of the 
 concept and the judgment are different only for Psychology, for 
 Logic they are identical. When I say the sky is Hue there is pre- 
 cisely the same thought of the relation in the act involved as when 
 I say the blue sky. The difference lies in the fact that the concept 
 is pure receptivity while the judgment meets the datum with a 
 reaction in the form of an acceptance or a rejection. 1 The judg- 
 ment discovers the concept as an isolated state of consciousness, 
 atrophied or bereft of the support of reason. It rehabilitates it 
 by connecting it again with its reasons. There is, therefore, 
 partial justification for regarding the concept as prior to the 
 judgment. But on the other hand the concept in the first instance 
 was constituted by an act of judgment or abstraction, and so 
 there is truth in the remark that judgment both precedes and 
 follows the concept. Again we must observe here the distinction 
 between idea and concept. The idea is always particular ; it is 
 composed of sensuous elements and is static. The concept is uni- 
 
 1 Croce seems to discredit unduly such an analysis of the content of 
 consciousness. He remarks : ' ' This division concept, judgment and con- 
 clusion involves the assumption that three different moments can be dis- 
 tinguished within what is really a single and unanalysable act of thought. 
 As a matter of fact, no one will ever succeed in thinking a concept, a real 
 concept or a judgment which is not at the same time a conclusion, being 
 connected in a system with other conceptions and judgments. " It is 
 doubtless true as Croce says that no one will ever think a concept by itself, 
 but it is not impossible to think the concept in its coordinated position 
 within the whole of a specific content. Ertcy. Philos. Sci., I, 202.
 
 APPREHENSION, Ql E8TI0N AND ASSERTION* 
 
 versa] ; it is the power or capacity of a perception to mean some- 
 thing — to stand for something external to itself. The idea is the 
 psychical image that comes and goes. The concepl is the signi- 
 fication or the fixed content. 
 
 Berkeley and the other oominalists were plainly right in their 
 criticism of Locke's doctrine of abstrad ideas. Locke described 
 the process of abstraction as an affirmative act of mind. Thought, 
 on this view, selected the common characteristics in several 
 objects, and tied them up in a separate bundle with an existence 
 and meaning of its own. But it is more accurate to speak of 
 abstraction as the result of negative thought. The abstract or 
 general we get, not by attending to what is like in several objects, 
 but in neglecting what is unlike. A great deal of the difficulty 
 that hangs about this subject would be removed if we observed 
 the distinction between having and possessing an idea. It is one 
 thing merely to have an idea and quite a different thing to have 
 it as your own — to possess it — that is. to have it in relation to 
 other ideas. It is the old familiar distinction between cognition 
 and recognition. 
 
 II 
 
 The object of description must be an objed in relation. Unre- 
 lated objects are, as Hegel lightly said, indescribable; they can- 
 not even be named. The attributes in terms of which 1 describe 
 any objed immediately presented to consciousness, are all of them 
 expressions of the relations of the presented objed to objects not 
 now present — that are elsewhere in space and time. Descriptive 
 judgment must, therefore, always be conceptual or representa- 
 tive. If there were only one objed in existence we should not 
 need a name for it. although we might need a word to distinguish 
 between the existence and the non-ex ist ence of this single object. 
 Naming is an act that belongs to the world of exposition and com- 
 munication. We attach labels or names to objects only for the 
 purpose of distinguishing them from other objects.
 
 38 FOOTNOTES TO FORMAL LOGIC 
 
 But prior to our knowledge of the object as described, we 
 know the object as merely apprehended. There is, to be sure, 
 serious objection to saying that we know the object in this first 
 simple awareness. The word know is full of all sorts of ambigui- 
 ties and it is one of the purposes of these studies to isolate some 
 of its meanings. When we say that we know the object, in both 
 common and technical usage, we mean that we are not only aware 
 of it, but that we are aware of it in its describable relations. 
 Knowing is a relating activity. But it is quite impossible to find 
 a word that will perform any less ambiguously the self-contra- 
 dictory task of connoting the absence of connotation. However, 
 there can be no doubt about the fact. 
 
 The expression, immediate consciousness which is often em- 
 ployed to describe this primitive datum of knowledge, stands for 
 a mental state that is already well along toward the stage of 
 description by means of relations. The word consciousness itself, 
 etymologically at any rate, connotes a togetherness. But it is 
 very important to distinguish between internal and external 
 relatedness. "We shall insist that this first direct awareness brings 
 to us knowledge of isolated concrete wholes, within which we see, 
 or appreciate, or know qualities in relation. 
 
 It must be repeatedly emphasized that the state of mind that 
 has now so often in Logic and Psychology been called simple 
 apprehension is one of just pure acceptance or acknowledgment. 
 It is a psychic experience in which there is no distinction between 
 our apprehending the object and the object which is apprehended. 
 Psychologists and logicians have been pretty much of one mind on 
 this point, but there has been little agreement upon a word to set 
 forth the mental state itself. Hobhouse has described the general 
 characteristics of immediate consciousness of a fact by the word 
 assertion ; this has somewhat released the fact so known from 
 being related to other facts. But the word assertion has now too 
 often been employed as a synonym for affirmation to warrant 
 its being transferred to this primitive awareness or pure recep-
 
 APPREHENSION, Ql E8TI0N AND ASSERTION 39 
 
 tivity. And doubtless the same objection could be made to the 
 term acceptana ; the latter, however, is freer from the notion of 
 activity, or decision. The expression "assertion of the object' 
 already suggests that thoughl lias gone out to meet the object 
 with question, criticism, and decision. I think the word acknowl- 
 edgi is the most satisfactory fortius primitive state of conscious- 
 ness. In letter writing we distinguish between acknowledging and 
 answering a letter. So when the mind receives its facts it may 
 just acknowledge them, it need not go further and reply t<> them. 
 
 Every fact is, indeed, related to other facts in the real world, 
 but I need not know this in order 1o proclaim my acceptance of 
 one of the related facts as an isolated thing. 1 can take it at its 
 face value; I can bow my acceptance or acknowledgment of it. 
 When I merely contemplate the w^\ rose, that is, when I appre- 
 hend it simply, I acknowledgi something immediately present, 
 and nothing more. I am aware of the wd color, hul am not aware 
 of the relation of the red color to anything else. When I say, the 
 lice in my garden is tall, I am undoubtedly describing the objed 
 by means of its relation to other objects. I am also (pate truly, 
 although not so obviously, describing the tree through iis rela- 
 tions when 1 say the tree is green. But such description is sub- 
 sequent to mere apprehension, and is always in the interest of 
 communication. The descriptive judgment functions socially. 
 
 The apprehended content cannot contain the relation of the 
 object apprehended to any other object. It merely envisages its 
 own system of inner relations. In looking at a net from a dis- 
 tance, I can be aware of 1 he knots wit bout thinking of the threads 
 that run from knot to knot. 1 can gaze at the star. Sinus, con- 
 template, accept. <uhnowledgi it without consciously relating it 
 to other stars. I Jut as soon as I wish to describe — that is. com- 
 
 2 The critical analysis of the thinking process had revealed even to the 
 Greek logicians the two factors of apprehension and assertion in every 
 judgment. They distinguish clearly between Kardtffcm ami oi-,KaTaOf<ns. 
 These two aspects of the judging consciousness arc also recognized, it seems 
 to me. in the distinction between urtheilen and beurtheilen, which several 
 hum iern \\ liters ha \ e proposed.
 
 40 FOOTNOTES TO FOBMAL LOGIC 
 
 municate to my fellows — what I have thus apprehended, I must 
 betake myself to the discovery of the relation of Sirius to other 
 heavenly bodies. Every description of an object, of course, pro- 
 ceeds always by means of relations ; but the object so described 
 was undoubtedly already present as an unrelated fact. It was 
 once merely acknowledged. To accept or acknowledge the fact 
 is one thing, to describe it another. 
 
 Now it is not until we arrive at the stage of description that 
 we may properly speak of the psychical process as judgment. The 
 mental state which I have here called acceptance, or acknowledg- 
 ment, has often been described as inchoate judgment, or sensory 
 judgment. There can be no serious objection to such an account 
 of this primitive stage of acknowledgment provided we keep in 
 mind the real difference between it and true judgment. At the 
 second stage Ave have the possibility of error. In simple appre- 
 hension, or acknowledgment, there is no question of truth or 
 falsity, and hence no possibility of error. The object presents 
 itself and we accept it without comment. Moreover, the object 
 of an unquestioned simple apprehension — -an acknowledgment 
 without comment — is always unalloyed fact, that is, fact present 
 and unembarrassed by attachment to any fact not present. We 
 can make no mistake in such an acknowledgment or acceptance. 
 It is only when we comment upon the acknowledged fact, when 
 we venture out along the relations of the present fact to other 
 facts not now present that error arises. But then we are no longer 
 merely apprehending the object we are making a judgment about 
 it. 3 We must distinguish therefore between assertion without 
 comment or risk, that is, just acceptance or acknowledgment, and 
 assertion with the risk that accompanies the necessity of selecting 
 from competing alternatives. The latter is true decision, it is 
 
 s I cannot therefore agree entirely with Bosanquet that ' ' being dis- 
 tinctly aware of reality is another name for judgment." (Essentials of 
 Logic, p. 40). If we should make use of the well-known distinction between 
 clear and distinct knowledge, of Descartes and Leibnitz, in which distinct- 
 ness points inward and clearness outward, we might say that being clearly 
 aware of reality is another name for judgment, and being distinctly aware 
 of reality is another name for the simple apprehension as I view it.
 
 J/77,'/- EEN8I0N, Ql E8TI0N AND A88EB1 ION 4 1 
 
 affirmation or denial. As Hegel has Baid, to asserl thai a earn; 
 is passing the house is not a judgmenl unless we are in doubl 
 whether h is a carriage or a cart. 
 
 Ii has been doubted, and with reason, whether we can ever 
 entertain a significant simple apprehension withoul decision. It 
 must be admitted, thai as occurrences in a continuous psycho- 
 logical process, apprehension of fad and decision concerning it 
 are inseparably connected. They are, aevertheless, Logically dis- 
 tinguishable. In our normal adult life any Longitudinal section 
 of consciousness would reveal a highly complex mental state. We 
 should never find in such cross-sections of the stream of conscious- 
 ness, at first apprehension and then judgment. Both would 
 appear in each and every cross-section. And we can take thought 
 about any one of the elements in the complex content only by 
 abstracting from the real organic process itself. The two acts, 
 apprehension and judgment, though theoretically separable are 
 joined in one concrete state of consciousness. We do not first 
 find apprehension, and then decision and then action. All normal 
 waking consciousness is one continuous affirmation, and, within 
 this persistent judgment, simple apprehension is seen to be a 
 distinguishable, though not a separate element. Moreover, it 
 must not be supposed that the two aspects, apprehension and 
 judgment, merge by imperceptible gradations one into the other. 
 We have already sen, the true differentia, simple apprehension 
 is naive in its attitude toward the apprehended fact, judgment 
 comes with the discovery that the observe, 1 fad mighl have been 
 different. 
 
 Midway between immediate awareness — the primary datum 
 of knowledge — and the full-blown judgment, there is found the 
 impersonal judgment. This type of judgment has caused much 
 trouble, but only to those logicians who se1 up arbitrary and 
 impassable harriers between the different compartments of mind. 
 There is no especial difficulty in understanding the impersonal 
 on the view that regards all waking consciousness as an organic
 
 42 FOOTNOTES TO FORMAL LOGIC 
 
 whole, and that thinks of the concept, the judgment and the 
 syllogism as the varying degrees of explicitness in which this 
 whole expresses itself. Much of the controversy in the history 
 of Logic ahout impersonals would have been entirely removed 
 if the distinction between the judgment and the proposition had 
 always been distinctly recognized. 4 
 
 Now there can be little objection to the assumption — and 
 obviously it must forever be an assumption — that the earliest 
 states of consciousness in the development of the individual mind, 
 are of this undifferentiated character. In childhood, and per- 
 haps in the animal consciousness, we find simple awareness the 
 sole content. There is more difficulty in the view that we may 
 again relapse into this level of simple awareness, from our later 
 normal adult consciousness, in which we are cognizant of the 
 distinction between subject and object, the self and the non-self. 
 Bradley is certain that, both prior to and subsequent to the stage 
 of consciousness in which there is a distinction between subject 
 and object, there is a stage in which we are not thus aware of 
 the distinction between what is known and the knower thereof. 
 We are quite justified, it would seem, in our inference as to 
 animal intelligence from our own human experience of the stream 
 of ideas, or reverie. 
 
 It is in one sense wrong to call simple apprehension the 
 primary operation of the mind. In describing simple apprehen- 
 sion as the primary datum of knowledge I have pointed out that 
 the terms, earlier and later, are out of place in any account of 
 the relation of judgment to simple apprehension. Every imme- 
 diate apprehension is simultaneous with a judgment and every 
 judgment with an apprehension. 
 
 There is a point of importance that must now be noted. We 
 
 * I think, for example, that Couturat, who is otherwise very mindful 
 of this distinction, has ignored its importance in his discussion of the 
 impersonal proposition. He says: "It rains is an indeterminate and incom- 
 plete judgment. This example shows us at the same time that there are 
 judgments without terms, without subject or attribute." Ency. Philos. Sci., 
 I, 139.
 
 APPREHENSION, Ql ESTlOh AND ASSERTION 43 
 
 have seen bow judgment transcends simple apprehension by 
 biquiring into the outer fortunes of the apprehended fad and 
 discovering its external relations. As merely apprehended the 
 fact was unequivocal; it was an immediate feeling, a knowing 
 
 and being in one. But now the discovery of the relations of the 
 apprehended fact to its fellow facts in the objective order is the 
 discovery, also, that each of these relations might have been 
 different. Thoughl has thus transcended the unambiguous simple 
 
 acknowledgment of fact. Bu1 in passing to this higher stage of 
 decision, or judgment, that is. the stage of selection from among 
 possible relations, the original simple apprehension does nol dis- 
 appear; it remains continuously in view as the foundation of the 
 later selective knowledge. Immediate awareness is not a stage 
 that appears and then disappears. 
 
 Ill 
 
 It will not be out of place to pursue this analysis a step 
 further. Can we not discover a stage in the complex contenl of 
 consciousness prior to apprehension ? Do we not first hav( the 
 fact in the experience of one moment and then in a subsequent 
 moment apprehend it? Such a distinction has been made. It 
 has been held that to be in consciousness and /// hi appreJa nded 
 are not identical stages, that mere presence in consciousness 
 does not imply even in the faintest degree the suhject-object 
 relation, while in apprehension the relation of consciousness to 
 the presented fact has for the first time become explicit. But, 
 in my opinion, this is a refinement of distinction that cannot he 
 defended. To be in consciousness and to be apprehended as being 
 in consciousness are identical facts, and both postulate the sub- 
 ject-object relation. The content of simple apprehension is non- 
 relational hut this does not exclude internal variety in the 
 content itself. This immediate awareness unrelated in itself 
 but yet embosoming distinctions is. I believe, what Bradley lias 
 continually spoken of as "feeling."
 
 44 FOOTNOTES TO FORMAL LOGIC 
 
 It has been urged as an objection to every such analysis of 
 the logical content of consciousness that it hopelessly confuses the 
 psychological with the logical point of view. Logic, it is said, 
 demands real distinctions — definite lines of demarcation. But 
 I see no reason for contending that logical consciousness is any 
 more definite in its entire content than is psychological conscious- 
 ness. We do not go wide of the mark when we say that the 
 logical apprehensions, like the psychological sensations shade by 
 imperceptible gradations from explicit to implicit and vice versa. 
 The content of sensation has its focal point of greatest clearness 
 from which it fades away to a zero point of indefinitness ; also, 
 we apprehend, or comprehend, or know by means of the concept . 
 the judgment, or the syllogism in varying degrees of explicitness 
 of the content. 
 
 We must insist again that this immediate experience does 
 not represent a stage in the psychical development which is at 
 one time present and necessary and later disappears. When the 
 discrimination between the self and the non-self has arisen and 
 we find the relational type of consciousness, this primary aware- 
 ness must still be a felt aspect of the whole content. As Bradley 
 has said, ' ' all that is thus removed is the mereness of immediacy. 
 The one point which I wish to repeat with especial emphasis is 
 that it is an error to suppose that our conscious contact with 
 the world of objects starts with judgment. Reality has been 
 presented to mind in its first simple awareness — the object has 
 been accepted as a constituent datum of knowledge. The expres- 
 sion "a mere suggestion" hints at this stage of simple appre- 
 hension where fact has been accepted without affirming it. 
 
 It would, perhaps, be a more precise account of the primitive 
 datum of knowledge to call it an inner movement of analytic 
 attention confined entirely to an immediately presented fact. 
 But we should guard against the mistake of thinking that in 
 this earliest stage of consciousness any act of classification is 
 involved, for this would imply a comparison with other facts not
 
 APPREHENSION, QUESTION AND ASSERTIOh 45 
 
 now present. \W must also distinguish between the judgmenl 
 to which we have passed in proceeding outwardly to a classifica- 
 tion of the given fad with other not-given facts, and the ground 
 of this judgment. Theoretically ;it Least, we may say thai the 
 ground varies from the zero point of complete indifference, or 
 iinmotived assertion, to complete conviction, or internal self- 
 sufficing sat is fact ion. lint now, this stage of apprehension, which 
 we are attempting to fix. is at a level below the zero of sheer 
 doubt. The doubl is always a decision not to decide. Apprehen- 
 sion, however, has not even this characteristic, for here we have 
 just the self-revelation of the inner content of the datum, and 
 ahout that there is no doubt . 
 
 It will be seen that this account of the relation between appre- 
 hension and judgment is in close agreemenl with Wundt *s theory 
 that all judgmenl in the last analysis involves an act of will. 
 Professor Adamson has challenged this view, asserting that judg- 
 menl requires no reference to reality beyond the '"sensible press- 
 ure," that it is just the belief in the existence of the objects 
 from which the sense perception issues. Judgment, he says, 
 "requires in addition to the belied" that something exists, no con- 
 sideration as to whether the belief itself be true." Tins. I think, 
 is a doctrine that is opposed to fact. In our account every judg 
 ment calls for a decision as to the validity of the fact. In this 
 state of consciousness that Professor Adamson has described as 
 already the beginning of judgment, we have only analytic atten- 
 tion to the pressure from the sense-presented fact, not analytic 
 judgment.
 
 CHAPTER III 
 
 THE IMPORT OF JUDGMENT 
 
 I 
 
 The various questions about the nature of judgment — the 
 relation of subject to predicate, of percept to concept, of analysis 
 to synthesis, of form to matter — all presuppose that the word is 
 has one well-defined meaning. But the problem of the copula is 
 beset with world-old difficulties. Russell, who is always tem- 
 perate in his statements, has said, "Is is terribly ambiguous," 1 
 and has pointed out five quite different meanings. And 
 DeMorgan before him, with his eagle's eye for paradoxes and 
 ambiguities remarked : ' ' The complete attempt to deal with the 
 term is would give the grand cyclopedia, and its yearly supple- 
 ment would be the history of the human race for the time." 2 
 
 It will not be necessary for our present purpose to go far into 
 the subtleties of these modern discussions of the meanings of is. 
 It should be pointed out, however, that these ambiguities are not 
 new discoveries. Aristotle was fully aware of the unavoidable 
 ambiguity in any word that is made to serve as connecting link 
 between subject and predicate in judgment. Following his 
 teacher, he spoke most often of the relation between the world 
 of concrete things and the world of ideas, which is expressed in 
 the judgment, as one of participation. And for twenty-three 
 centuries, from Aristotle to Bradley, the expression "participate 
 in" has been condemned for its metaphorical vagueness and 
 ambiguity. The important thing to be borne in mind is that at 
 heart it is always the same relation, whether we say that a thing 
 
 i Princijyles of Mathematics (Cambridge, University Press, 1903), I, p. 64. 
 2 Formal Logic (London, Taylor, 1847), p. 49. 
 
 [46]
 
 THE IMPOST OF .1 r i><, \i i:\ I 47 
 
 is a copy of the idea, or that it participates in it, or that it is 
 the idea. And the essential characteristic of this relation 
 between subject and predicate in judgment is thai ii is non- 
 temporal. This fact, namely, that the relation is not in time, 
 while the relata arc, will receive fuller elucidation in the sequel. 
 It is for the reason that the time elemenl is both in and around 
 the judgmenl that some part of the verb to b< has always been 
 preferred to express the relation between suhjeel and predicate. 
 As has so often been pointed out, if there were no reason why 
 the verb to be should be used as the sign of predication it would 
 be difficult to explain its presence in so many languages. 
 
 Among the many meanings of is, its existent ial import should. 
 of course, be considered first. T he cop "l« j" tlip pro position . 
 S is P, in the first instance, stands for the fact that in every 
 judgment there is undeniably present to consciousness a some- 
 thing. However widely they may differ in other ways all theories 
 of predication arc agreed upon this point. We are not now inter- 
 ested in the question whether this affirmation of presence is of 
 something present to consciousness or in consciousness, that is, 
 whether it is to be regarded as a datum or ideatum. TJje "pre- 
 sence" characteristic of is must be taken as original — it is not 
 derived from or constituted out of relations between the presented 
 object itself and another object. It has no temporal origin. The 
 present which is asserted iii the judgmenl is not a somewhat 
 coming after a priori past. Nor is it to be defined as the imagin- 
 ary line of demarcation between the past and the future. The 
 present is not that which comes after something past, but the 
 past is something which came before the present, /sstands 
 always as the reminder that knowledge is won by the extension 
 of the present. 
 
 Tt is no disparagement of the underived validity of the pr< s< ni 
 to show, as may be shown, thai we have not achieved knowledge 
 until we have thus expanded the present into its relation with 
 things other than itself. If thought were confined strictly to
 
 48 FOOTNOTES TO FORMAL LOGIC 
 
 the present it would not know it, and we should never be impelled 
 to judge. In judgment the present yields to the internal con- 
 straint to transcend itself. But the apprehension of the present 
 and the effort, in judgment, to pass beyond the present must 
 not be confused. They are different acts. The present as imme- 
 diately apprehended is singular — it is a this unrelated to any 
 that. But as a this it is the unification of its own unique attri- 
 butes; as apprehended fact it owes no allegiance to its other. 
 But knoivledge of this as distinguished from its apprehension 
 does require an insight into the relations of the this to the that. 
 The system of Hegel differs from other idealistic philosophies 
 on the question of the time factor in judgment. Hegel discredits 
 immediate consciousness, declaring that the conception of immed- 
 iacy breaks down under the strain of its own inherent self- 
 contradiction. I can apprehend an object presented to conscious- 
 ness in one act and in a second act of thought I can be aware of 
 the first state, but not as immediately present. I cannot think 
 that I think, I can only think that I thought. But this does not 
 seem to me to be a valid objection to immediacy of consciousness. 
 It is true that we can never communicate descriptively the present 
 state of consciousness without judging and thereby causing the 
 present to slip away from itself into the past. The second act. 
 indeed, is not immediate in the same sense as the first act. "When 
 I say "I think that I thought," the "I thought" which is the 
 object of "I think" is, indeed, other than that which thinks it, 
 but otherness is here unjustifiably construed as equivalent to 
 past. The Hegelian recourse to memory is unnecessary. Intro- 
 spection, I think, will also discover that memory plays no such 
 part, as Hegel thought. When we examine the thought that has 
 this possession of an immediate content, we do not find in it any 
 act of remembering, as this doctrine declares. The mind seems 
 truly to be noting something which is present to it then and 
 there. "What I feel" says Bradley, "that surely I may still 
 feel though I also at the same time make it into an object before
 
 TEE IMPOST OF JUDGMENT 49 
 
 in.'." None of the various words thai are compounded with self — 
 self-consciousness, self-contemplation, self-reproach, etc. — sug- 
 gests a combination of the present with remembered aspects of 
 itself. Subject and object are both in the same present time. 
 This is illustrated in the humorous poem the first line of which 
 runs •"Says I to myself, says I." 
 
 It is true that the complex content of immediate consciousness 
 may experience one aspect of itself to be more vividly present 
 than another. But these remote or less vivid aspects are not 
 therefore to be relegated to the past. Differences in the "felt 
 immediacy" are like the differences in the marginal vision of the 
 eye. They are all present in varying degrees of definiteness. 
 I can not, obviously turn the whole content of consciousness into 
 an object at once. A part of the self must be held in reserve, 
 so to speak, to be the experiencing subject of the part that has 
 taken its place as object to be experienced. And the line of 
 cleavage within the whole content may differ for different pur- 
 poses. Also the sameness of the parts does not exclude differ- 
 ences. In the line "Says I to myself, says I," the person speak- 
 ing and the person addressed are the same and yet obviously 
 different, for the better self is addressing the evil self. 
 
 It is important in discussing the meaning of is to distinguish 
 between being and existence. Every conceivable thing, every 
 object of thought has its being, but not all have existence. The 
 minimu m requisite of being is the quality of number. Anything 
 that can be thought of as having membership in the number 
 series has the quality of being. But things have existence only 
 if they ■"stand out" in systems of special inter-relationship. We 
 may deny the exist ena of anything only if we are able to save 
 its being. Contradictory as it may seem we must say that what 
 does not exist must still bt something. The assertion "S is no1 ' 
 is on the one side either entirely false, or, on the other, more than 
 idle — just empty breath. If S were just nothing at all, il would 
 be meaningless to say "S is not." Being is the general attribute
 
 50 FOOTNOTES TO FORMAL LOCK 
 
 that belongs to anything that can stand as subject of a proposi- 
 tion. This truth was expressed in an earlier paragraph in the 
 statement that in every judgment there is unmistakably present 
 to thought a something. The judgment "S is P," means to assert 
 that reality has the characteristic, S-P. s 
 
 II 
 
 In considering the nature of the concept or idea we saw that it 
 is difficult to discover any difference in kind among the cognitive 
 states of consciousness, from simplest concept to the most com- 
 plex judgment. That the concept seems to shade by imperceptible 
 gradations into the judgment was recognized by Aristotle and 
 before him. And in the modern discussions we find writers who, 
 having defined the concept and the judgment in static terms, 
 in independence of each other, are much embarrassed by the 
 discovery of forms of thought that refuse to be classed as either. 
 There are forms which have already burst the conceptual shell 
 and yet are classed as concepts ; and, on the other side, there are 
 forms which are classed as judgments that are lacking in the 
 essentials of judgment. The recognition of this distinction led 
 Bain to call the verbal proposition the "notion in the guise of a 
 proposition." 
 
 Nevertheless, when one describes thinking as a movement 
 from the particulars of concrete sense experience to conceptual 
 universals, he disregards a most important aspect of the knowing 
 process. In its analytic attention thought makes distinctions (or 
 we should say, heightens distinctions already vaguely present), 
 and these distinctions when synthesized form the generals. But 
 this is only one-half of the process. These abstractions which 
 
 s Plato long ago pointed out the paradoxical fact that when you call 
 a thing a non-entity, a mere illusion, you do not thereby get rid of it. 
 There is a deep metaphysical significance in the remarks of the colored man 
 passing by a church yard at night : "I don 't believe in ghosts nohow, 
 but I hope they never find it out, it might make them mad to think a fellow 
 didn't believe in them."
 
 TEE IMPOST OF JJJBGMEh I 51 
 
 lie at the end of the movement in this direction axe qoI kept in 
 cold storage, bu1 are thrown back again upon the concrete 
 instances from which they arose. And in this return movement 
 the concepts, or universals, always put a new meaning into the 
 concrete instances. Nevertheless, in this reciprocating movement, 
 thought is not acknowledging its inadequacy to reality. This 
 is not a make-shift, or compromise, confessing thought's incom- 
 petence; it is an exhibition of the highest type of control of 
 reality. A transverse cross-section, so to speak, of the movement 
 would reveal the seeming contradictions of idleness and falsi- 
 fication. Any moment of the process would exhibit tautology, or 
 novelty, when detached from its setting in the whole. But a 
 longitudinal section would reveal the true nature of the process 
 in its totality, where the tautology, in the light of the anticipated 
 novelty, is not to be condemned as idle; and the novelty, resting 
 hack on the identity, rescues the judgment from the charge of 
 falsity. 
 
 As bearing upon our search for the essence of judgment we 
 may revert to the significant distinction that has often been made 
 between knowing and understanding. It is alleged that we are 
 here dealing with thought processes that are sufficiently differem 
 to require two different words. Understanding is a later and 
 and higher phase of thinking. We have understanding when we 
 appreciate or evaluate knowledge, when we know that we know, 
 and why we know. Although the distinction between the two 
 kinds of knowledge has frequently been pointed out, there lias 
 not been offered, it seems to me, a convincing account of their 
 relation. Bearing in mind that these words represent stages in 
 the development of knowledge, and therefore have something 
 in common, the question at issue in the relation between the two 
 types of knowing is What precisely have they in common .' Are 
 they different in kind or are they, as has been remarked, an 
 earlier and a later stage in what is essentially a simple process 
 That there are these two kinds of mental activities is evidenced
 
 52 FOOTNOTES TO FORMAL LOGIC 
 
 by the fact that most languages have two different words to 
 represent them: scire and cognoscere, in Latin; kcnnen and 
 wissen in German; savoir and connaitre in French, stand for 
 these two kinds of knowing. In English, in addition to the words 
 knowing and understanding, we have several aspects of the same 
 distinction expressed in the phrases, "knowledge of acquaint- 
 ance" and "knowledge about." 
 
 It will be well to examine more closely the difference that is 
 here intended. We need to discover, if possible, the point at 
 which there is a change in kind as we pass from the lowest form 
 of sensory judgment to the highest type of reflective judgment. 
 Knowledge of things by acquaintance is not far removed from 
 Hegel's unrelated immediacy; it is just simple apprehension 
 or existential awareness. But now all w T ho have ever attempted 
 to describe and explain this simplest form of knowledge have 
 admitted the difficulty in giving it any. logically independent 
 standing. It seems to have no existence apart from the higher 
 knowledge, the knowledge of truth. Even Russell, while claim- 
 ing logical independence for the knowledge of acquaintance, 
 says: "It would be rash to assume that human beings ever, in 
 fact, have acquaintance with things without at the same time 
 knowing some truth about them." All that we seem justified in 
 saying is that we find these two distinguishable, but not separable 
 stages in the natural course of thought — first immediate aware- 
 ness, then being aware of the awareness. I can think, and then I 
 can think or recognize that that is one of my thoughts. The sec- 
 ond, or complex stage is the stage of description, definition, evalu- 
 ation. But already in the first or simple stage there are implicit 
 these characteristics which on the reflective level have become 
 explicit. 
 
 This distinction between the two types of knowing we have 
 in Professor James' familiar illustration of the difference 
 between cognition and recognition. A bird flutters against my 
 window pane, and I acknowledge the event in its first stage of
 
 THE IMPOST OF JUDGMENT 
 
 immediate awareness with "Hello, thing-a-bob. " Ami in the 
 second stage lit' evaluation I say, "Ah, robin." lint even here, 
 is the difference more than relative? Is the transition from one 
 pulsation of consciousness to the other marked by any difference 
 
 in kind? The first judgmenl is in the form of 8 is /' in which 
 there is already ;i partial definition which the second judgmenl 
 # is I' only makes more explicit. 
 
 Some writers suppose thai there are in the thoughl process, 
 more than the two stages we have just considered. Adamson 
 says: "The real order is sensation and sensory judgment, con- 
 ception, memory and memorial judgment, experience and experi- 
 ential judgment, inference, inferential judgment, inferential 
 conception."' I5ut the more stages one marks out in the process 
 the more does one emphasize the fad that consciousness is a 
 single continuous affirmation in which there is nothing at the 
 end of the process which was not also present at the beginning. 
 In other words, there is no distinction between beginning and 
 end. We may read off the story of our analysis in either direc- 
 tion, thus revealing the true nature of thoughl as the exhibition 
 of a whole through its genuinely simultaneous differences.' 
 Temporal arrangement in the proposition is an entirely different 
 thing from l ogical coherenc y, in the judgment. The relation 
 between the parts of a logical whole is unique, it is altogether 
 different from sequence of time and from contiguity of space. 
 Logical coherence has been confounded with sequence in time 
 
 4 Encyclopedia Britain* /<•</. XVI, 8S0. 
 
 sCf. Bradley, in Mind, n. s., XVII (inns,, 170. "The content of the 
 judgment is one thing ami its psychical duration is another thing, and in 
 principle we have seen that the duration is irrelevant. But en tl ther 
 
 hand every judgmenl is a psychical event ami has therefore duration. 
 Wholly to deny this aspect seems a fundamental error.'' 
 
 ,; < T. Bosanquet, Essentials of Logic (London, Macmillan, L895), p. 7:;. 
 "The separate existence of the spoken or written word, produces an illusion 
 which has governed the greater part of logical theory so far as concerns 
 the separation between concept ami judgment, i.e., between entertaining 
 ideas and affirming them in reality. In our waking life, all thought is 
 judgment, every idea is referred to reality, and in being so referred, is 
 ultimately affirmed of reality."
 
 54 FOOTNOTES TO FORMAL LOGIC 
 
 and with contiguity in space, because in speech and in writing 
 we do produce mental and physical symbols subject to time and 
 space. 11 But it should be remarked that it is not sufficient 
 to say that in most modern and highly developed languages, the 
 subject, predicate and copula in the proposition are separate 
 words, while in the ancient and undeveloped languages they are 
 welded together in a single form. Some explanation of the 
 phenomenon should be offered. If "I am loved" is equivalent 
 to amor, it would be interesting and important to know what 
 principle of evolution has produced the former differentiated 
 expression. Is it entirely a phenomenon in the growth of 
 language, or is it vitally connected with certain stages in the 
 movement of the judging process itself ? 
 
 No judgment can ever become so complex as to escape 
 embracement in a single idea. But the related parts of this 
 enwholing idea are not themselves just ideas in relation. Judg- 
 ment is not merely the affirmation or denial of a relation between 
 the two ideas. This has been pointed out so frequently in recent 
 discussions that I need only refer to it in passing. When I 
 assert that an automobile is going down the street. I do not mean 
 that my idea of an automobile is traveling down my idea of a 
 street. What I mean to affirm is that the objective world does 
 have in it a complex of related facts which I characterize as 
 automobile-going-down-The-street. But, as I have already in- 
 sisted, the object to which the idea refers its content is in no 
 wise alien to that idea. Every idealistic theory of judgment 
 must of course hold that this object is just the self-transa n<lin</ 
 character of tin idea. What I wish to emphasize is the fact that 
 the ideas between which the relation exists are not the same in 
 kind as the idea within which the relation is embedded. A dis- 
 persive category operates in the former instance and a synthetic 
 category in the latter.
 
 THE IMPOST OF JUDGMENT 
 
 III 
 
 Among the disputed problems lying on the borderline of 
 Psychology and Logic is the question, which we have already 
 noted, of the difference between perception and the perceptive 
 judgment. Bradley and others have insisted upon the impor- 
 tance of distinguishing between these two mental states. We 
 have already discussed one aspect of this subject. In pure per- 
 ception there is a direct reference to an object, which is a datum 
 in the etymological sense of the word. The objed is something 
 given to the subjed ive activity independenl of thai activity. The 
 perceptive judgment, however, is an inner ideational process 
 proceeding from the spontaneous activity of the subject, in 
 response to or as a reaction upon the perception, 'flic difference 
 lies in the essential distinction between activity and passivity. 
 The ultimate object in every assertion or eiiunciative act of con- 
 sciousness is an individual. In the perceptive judgment this 
 objective is given to thought directly, and implies the existence 
 of two things only, namely, that object and the mind that thinks 
 it. But in the cognitive or reflective judgment the objed — again 
 an individual — is given indirectly. In the reflective judgment 
 the object is only vicariously present in the concept, to which 
 concepl other like objects have already been given and to which 
 future objects may in turn be presented. The transition from 
 perception to perceptive judgmenl is made in the interest of com- 
 munication. 
 
 The proposition as the outward expression of the inward Ead 
 of judgmenl is primarily an instrument of intercourse — its func- 
 tion is purely social. 1 It begins with an undifferentiated whole 
 in the position of subject, and concludes with this same whole 
 
 i Windelband has laid greal stress on the social character of knowing. 
 "Perceiving ami knowing," lie says, "as empirical functions arc entirely 
 
 social in their nature. They arc integral parts of the common mental In 
 fur the lonely strivings after truth of the individual arc a late product of 
 civilization which is ahvays runted in seme historical community of knowl- 
 edge and tends to discharge itself into it again." i •. I'i !os. v .. I, <>17.
 
 56 FOOTNOTES TO FOEMAL LOGIC 
 
 differentiated into members, one of which takes its place in the 
 position of predicate. The analysis of this undifferentiated 
 whole is what the speaker accomplishes, when by means of a 
 descriptive, elucidative, or demonstrative judgment, he under- 
 takes to instruct his hearers — when as we say he communicates 
 information. Now the logician who stresses the non-temporal 
 character of judgment finds it difficult to account for these differ- 
 ent meanings that are found at the two significant dates in the 
 life history of the subject, namely, its meaning before and its 
 meaning after the differentiation. The judgment is thus seen to 
 be neither exclusively temporal nor non-temporal. It may be 
 both without contradiction. 
 
 The failure to recognize this fact, namely, that the judgment 
 claims to be both temporal and non-temporal has thrown the 
 new theories into hopeless confusion. The judgment is not in 
 time, but the judging is. The judgment in the speaker's mind, 
 prior to his determination to express its meaning — to tell his 
 hearers something — is not in time. But the judging, which 
 unfolds itself outwardly in the proposition is in time. The 
 empirical theories of judgment have with right insisted that 
 there is a sense in which the judgment, or more accurately the 
 judging process must be regarded as in time. But this temporal 
 expression of itself is just the standing reminder of the irra- 
 tionality of sense, or the ill-adaptation of conception to percep- 
 tion. If thought were entirely adequate to the task of communi- 
 cation, it would not adopt this apparently self-contradictory 
 device for its outward expression. But the a-priorist has also 
 rightly insisted that the judgment (not the judging) is non- 
 temporal. It has no parts that may be arranged seriatim like 
 the parts of a sentence. The relation between subject and 
 predicate is not a relation between successive mental states, but 
 is itself a unitary progressive state. 
 
 Professor Schiller says "We have steadily kept in view the 
 fact that Judgment is the primary act of thought and that the
 
 THE IMPOST OF Jl DGMENT 57 
 
 attempl of formal Logic to analyse' ii into something more 
 elementary is a fictitious procedure, which can I"' justified only 
 by its convenience and success. 8 Now many who are distinctly 
 not pragmatists would agree entirely with Professor Schiller 
 thai judgmenl is the primary ad of thought, and that only by 
 abstraction can we arrive at anything more elementary. Also 
 in the majority of the ordinary textbooks, when- the firsl chap- 
 ters treat of tm-nis ami ideas, the authors are careful to point 
 
 out that such discussions belong properly to philology, ami to 
 psychology. Even Jevons who is so outspokenly an associa- 
 tionist in his view as to the nature of the thinking process says: 
 "The continued study of Louie convinces me that this doctrine 
 of terms is really a composite and for the most part extra-logical 
 body of doctrine.'' 
 
 It is true, as Aristotle remarked, and as since then so many 
 logicians have repeated, a word has no reality in Living Language, 
 and the idea no reality in Living thought. We must not regard 
 the proposition as a synthesis of words, nor the judgment as a 
 synthesis of ideas. And yet, when once the act of judging lias 
 been performed a retrospective analysis discovers ideas to be 
 different, hut not separati aspects of the judgment. 
 
 The data of knowledge appear to come in a stream of isolated 
 sense-presented facts, which the mind is called upon to weld 
 together into wholes of ever increasing complexity. The 
 sequence in the mental states seems to he first the idea A. then 
 the idea />'. and Lastly the judgmenl .1 in relation to B. Some of 
 the older empiricists were hold enough — even in the face of 
 the insurmountable difficulty at the third stage — to say that such 
 a process of crystallization by tin- external accumulation of id - 
 is the tine explanation of the thinking process, lint the impossi- 
 bility of ever achieving any real continuity in this process of 
 knowing things together, led the later associationists to substi- 
 
 - Formal Logic, p. 92. 
 
 » Studies in Deductivi Logic, p. 1.
 
 .18 
 
 FOOTNOTES TO FOIIMAL LOGIC 
 
 tute analysis for synthesis as the central function of thought. On 
 this view the most elemental judgment — or if we an- not pre- 
 pared to call this primary state a judgment — the most primitive 
 datum of knowledge is an undifferentiated feeling or sensation. 
 Judgment then, is not a combination of two ideas into one, but is 
 the separation of this primary undifferentiated feeling into its 
 two correlated aspects. But this analytic process is also embar- 
 rassed by at least three unmanageable difficulties: (1) What 
 precisely is the original feeling, (2) what is the principle of 
 differentiation and how does it operate, and (3) what are the 
 two facts or aspects to which the division leads? 
 
 The ancient dilemma of ignava ratio which conceals the 
 fallacy of incomplete disjunction has been perpetuated in the 
 modern attack upon the validity of judgment. Predication is 
 discredited today in almost the identical language of the 
 Sophists. Either our predicate is contained in the subject or it is 
 not. If it is not, we have no right to say that the subject is the 
 predicate, and the judgment is false; if the predicate is already 
 in the subject, the judgment is idle. Now I submit that this 
 argument is cogent only in the sphere of quantity where the term 
 "contained in" has application in an intransitive relation only. 
 In the quantitative world an object cannot be both inside and 
 outside of a class. But the relation between subject and predi- 
 cate in judgment depends upon a totally different conception of 
 a class. The two alternative positions in which the predicate is 
 placed in the ancient dilemma — inside or outside the subject — 
 do not exhaust the possibilities. With a different conception of 
 the relation of a term to its class the predicate may be both inside 
 and outside of the subject; there is both novelty and identity 
 in judgment — stability and risk. This very important subject 
 of novelty and identity in judgment I propose to discuss farther 
 in a special chapter.
 
 I III: IMPOST OF -II DGMENT 59 
 
 h will not be necessary for the general purpose of this inquiry 
 into tin- nature of judgmenl to u r< " into any detailed consideral ion 
 of the perennial question ;is to whether the class rl< w of predica- 
 tion is Logically fundamental. I shall discuss the <-l;iss view of 
 predication and the subjed of tin- relation of extension to inten- 
 sion in considering tin- validity of the syllogism. I must, how- 
 ever, point out ;it this time what seems to be a very prevalenl 
 mistake in the more recent criticisms of the class view. Windel- 
 band says : 
 
 As far back as Aristotle, Logic has given way to the temptation of 
 regarding the subject thus conceived as falling within the sphere of the 
 predicate as the type of all judgment, ami subordination or subsumption 
 as tin 1 prevailing meaning of the copula. This is an error in principle of 
 tlic scholastic logic, "Gold is a metal," is indeed a real subordination; but 
 "Gold is yellow" never means in living thought that gold ought to be 
 subsumed under yellow, which would be obviously uonsensi — and certainly 
 iint always that gold is to be reckoned among yellow bodies, but rather that 
 gold has the property of yellowness. Subsumption may be thought of as a 
 side issue, but it is not the precise meaning of the judgment. 10 
 
 Windelband has failed, in my opinion, to state the precise 
 grounds of the distinction between a "side issue"' and a ■■pre- 
 cise meaning." If these two expressions are to be taken as 
 synonymous with ■'essential" and "accidental," then by defini- 
 tion the side issue or accidental characteristic of judgment 
 cannot be regarded as the prevailing meaning of the copula. Bu1 
 if the side issue is always an essential side issue, thai is. if 
 it is a real property in the scholastic sense, we may for certain 
 purposes consider it the precise meaning and relegate the former 
 precise meaning to the position of side issue. If the judgment 
 has various meanings, all equally present, by what criterion shall 
 we decide lietweeu the primary ami the secondary meaning — the 
 precise meaning ami the side issue. How much we mean when 
 
 H>Ency. Philos. Set., I, 37.
 
 CO FOOTNOTES TO FORMAL LOOK 
 
 we say "all men are mortal," how we reach these meanings, and 
 how we rank them in importance, is the basic question in Logic. 
 
 This distinction between the main issue and the side issue, 
 the bona fide meanings and tbe spurious meanings has been car- 
 ried into the distinction between the problematic and the apo- 
 deictic judgments. Professor Sidgwick has said: "No propo- 
 sition can, after all, be more than true; that no piling up of 
 adverbs like 'certainly' or 'necessarily' will intimidate the actual 
 facts." 11 But the modal adverbs, I submit, have no intention to 
 "intimidate the facts"; they apply to the thought about the 
 facts, not to the facts themselves. The attempt to dispense with 
 modality in propositions rests back upon the denial of the 
 scholastic distinctions between rationes cogsnoscendi and rationes 
 esscndi. The reasons for knowing, or perhaps we should say 
 the reasons for belief, may vary from the zero of pure doubt 
 to entire conviction. The reason* for being exhibit no such 
 gradations. It is, indeed, a contradiction in terms to speak of 
 reasons for being. But there are, and must be, reasons for 
 knowing, and when knowledge searches for its reasons it epitom- 
 izes these supporting or inferential judgments in modal adverbs. 
 The necessity in apodeictic judgments depends upon scientific 
 or demonstrative evidence, while the necessity in assertoric judg- 
 ments depends solely upon enumeration or observation. 
 
 The act of comparison which our theory regards as the pri- 
 mary function of judgment is not so simple a process as on the 
 surface it appears to be. Comparison involves cross-reference of 
 one object to another, that is, each object submits to being 
 assessed by a principle which is inherent in the other object. 
 Bosa nquet thinks that comparison is not necessary to every judg- 
 ment. Comparison he holds can not be expressed with complete 
 convenience in a single judgment. Now it is true that the com- 
 paring act is not evident in the judgment in its simple form ; 
 but when the entire content of the judgment becomes explicit 
 
 Ji Eh mi ntary Logic, p. 71.
 
 THE IMPOST OF JUDGMEN1 61 
 
 and it is made fully aware of its reasons, then comparison is seen 
 always to Lie a1 its heart. 
 
 More is needed for an ac1 of judgmenl than jnsi the juxta- 
 position of sub j eel and predicate in consciousness. Comparison 
 
 means more than simple association. The association theory of 
 
 thoughl is incapable of bridging the gap between the two facts. 
 taken simply as facts in relation. Thought must betake itself 
 to the circumambient universal at each step. However, the 
 universal which is thus operative in each particular stats of 
 
 consciousness is not always manifest. As Bosanquet lias said: 
 
 Its operation is extended throughout a series of the fugitive psychical 
 facta in- ideas, ami althougb in logical thinking its operation is conscious, 
 
 i.e., selects ami modifies within the contenl of these ideas, yet it is not in 
 
 it-.elf necessarily a conscious activity. It acts in consciousness, but need 
 not lie conscious of its own principle of action. i'-' 
 
 V 
 
 The teaching of ordinary Logic, that every proposition is a 
 sentence but not every sentence is a proposition, is not entirely 
 free from criticism. It is alleged that only the declarative sen- 
 tences are true propositions. Bui every sentence has a mean- 
 ing, even the imperative, optative, and exclamatory sentences: 
 though these, to he sure, cannot be said to be either true or false, 
 in the form in which we find them expressed. The old familiar 
 definition of a sentence — that it is an expression of thought in 
 words — tells a hidden truth about those forms which are com- 
 monly not admitted to the rank of real propositions. A thoughl 
 is always implied in every command, wish, or exclamation. A 
 complete analysis of the states of consciousness corresponding 
 to the various so-called sentences would reveal both a cognitive 
 and an emotional aspect in each. In the indicative mood the 
 cognitive characteristic is overt and the emotional characteristic 
 is implied. In the other moods the emotional aspect is expressed 
 
 i- Logic, II. ti.
 
 62 FOOTNOTES TO FORMAL LO(,l< 
 
 and the judgment, or assertion, or cognitive characteristic is 
 
 implied. The exclamation "fire," the command, "avaunt," the 
 
 wish "a horse! my kingdom for a horse," each implies an 
 
 assertion which is not expressed. Instrumental Logic is quite 
 
 right in maintaining that for the purposes of complete definition 
 
 and in our practical lives we should take into account these 
 
 implications. But it is wrong, in my opinion, to assert that 
 
 it is impossible to detach the cognitive factor for exclusive 
 
 study. 
 
 A state of consciousness may be simple and unequivocal while 
 
 its outward expression may be duplex, that is to say, one judg- 
 ment may require for its expression two propositions. And on 
 the other hand there may be a multiple content in mind — two 
 or more judgments — with only one proposition to represent 
 them. Illustrations of the former we find in the rhetorical 
 devices for securing em]masis through tautology, repetition or 
 elaboration. "The last rose of summer is gone. It is fled," 
 are two sentences or propositions, but one judgment. "All the 
 planets except Venus and Mercury are outside the earth's orbit," 
 "None but the brave deserve the fair," are duplex propositions. 
 Each is in form a single sentence containing two assertions. The 
 name exponible which was given by the older logicians to these 
 propositions with multiple meanings was etymologically some- 
 what unfortunate. Any of the more modern words plurative, 
 duplex or portmanteau propositions is to be preferred. A care- 
 ful analysis of these portmanteau propositions, particularly the 
 exclusive propositions, which are either omitted or given only 
 slight consideration in most discussions of the import of proposi- 
 tions will throw light upon the nature of judgment and of infer- 
 ence. In the exclusive proposition "None but the brave deserve 
 the fair," we have the interesting situation of two judgments 
 and two propositions telescoped into one sentence. It is likewise 
 interesting as an illustration of an attempt on the part of the 
 speaker to recognize the existential import of propositions but
 
 THE IMPORT OF JUDGMENT 63 
 
 to provide, in the form of the assertion, !'<>r a aon-committa] atti- 
 tude toward the question of the existence of the Bubject. 
 
 It is often said thai the educational value of elementary 
 Formal Logic consists chiefly in the exercise of paraphrasing 
 poetical or rhetorical assertions into the type-forms of proposi- 
 tions, with the leasl possible sacrifice of meaning. I do not think 
 this is true. The translation of propositions from their rhetorical 
 to their logical form is a Literary occupation. This is a task that 
 properly belongs to the grammarian and the philologist, not to 
 the logician as such. This is ;m interesting and important work, 
 hut it is no more the special business of Logic than the transla- 
 tion of a foreign Language would he. The translations of propo- 
 sitions should he distinguished from their transformations. Tin- 
 task of the logician begins after the student of language has 
 translated the poetic or rhetorical form into the type-proposi- 
 tions. He has the task, then, of transforming the standardized 
 proposition into its various implications. Logic is the scu nci 
 of inference, not the <irt of translation. Given an unequivocal 
 type-form it is the business of the logician to classify all the 
 other propositions that deal with the same subject and predicate 
 as true, false or doubtful. And this involves an intellectual 
 discipline of great interest and value. The recent successful 
 developments of Symbolic Logic exhibil more truly the proper 
 scope of Logic, than does Genetic or Instrumental Logic. I 
 repeal the criticism so often made, that the latter is not Logic 
 hut Psychology. 
 
 An excellent i 1 1 ust ration of the failure to distinguish between 
 Grammar and Logic is found in Dr. Mercier's treatment of 
 propositions. lie writes : 
 
 For logical purposes, the tnosl important distinction between different 
 propositions is thai between the Incomplete and the Complete. This is a 
 distinction new to Logic, bul it is one of the greatest importance. An 
 incomplete proposition is, as its title implies, a proposition of which an 
 element is missing. Every proposition expresses a relation; and, as we shall 
 find further on, a relation consists of three elements— two related terms,
 
 64 FOOTNOTES TO FOBMAL LOCK 
 
 and the ratio which expresses the relation between them. Any one of these 
 elements may be missing. ... In the proposition "A is B," the term A 
 may be missing; but we can keep the proposition in form until the missing 
 element can be supplied, and at the same time introduce a reminder that 
 the term is missing, and needs to be supplied, by putting in place of the 
 missing term the relative ' ' what. ' ' By this means we obtain the incom- 
 plete proposition, "What is B. " Similarly, if B is missing, we can throw 
 the incomplete proposition into the form, "A is what?" These are mani- 
 festly questions, and should be characterized as cpiestions by the addition 
 of the interrogation sign ; and we then get the incomplete propositions, 
 ' ' What is B ? " " A is what ? ' ' which at once preserve the form of the 
 proposition, and remind us that the proposition is incomplete and clamors 
 for completion. 1 :: 
 
 Here it seems to me, Dr. Mercier has disregarded the vital 
 distinction between a question and a proposition. He is quite 
 right in asserting that all propositions are preceded by questions 
 of some sort. The question may, indeed, be most vague and 
 amount merely to a psychological restlessness, but this question 
 is one thing, and the assertion that follows upon it quite another. 
 If instead of writing these so-called propositions as a question, 
 for instance, "What is B?" he had written it as an assertion, 
 "Somewhat is B," he would have been closer to the facts as we 
 find them in the mind. These so-called incomplete propositions 
 correspond not to incomplete but to indefinite judgments. It is 
 not true that there is no subject but that the nature of the asser- 
 tion is such that we are not able or not concerned to specify it. 
 The whole meaning of the judgment has gone over into the 
 predicate, and in the subject position we have a that without a 
 what. This, I believe, is the true account of the impersonal 
 propositions. 
 
 is New Logic, p. 30.
 
 THE IMPORT OF JUDGMEN1 65 
 
 VI 
 
 Every judgmenl claims to be true; if it did not, it would 
 forfeil its righl to be called a judgment. This claim to be true, 
 means that the mind that judges distinguishes between idea and 
 object, in recognizing that il might have an idea which is nut in 
 agreemenl with the object. Here, again, it is necessary 1<» dis- 
 tinguish between a judging consciousness ami one that merely 
 apprehends. The difference between the two is that one con- 
 fesses the possibility of error, while the oilier knows nothing 
 of the distinction between truth and falsity. There is an <-ssmi- 
 tial difference between the simple apprehension "This is A," 
 
 ami the judgment, "This is J." The judgmenl is never rely 
 
 the awareness of something present. It asserts qualities thai 
 are derived from relations which transcend the present. And 
 in this reference to facts not present there is the risk and the 
 possibility of error winch differentiates the judgmenl from the 
 apprehension. 14 
 
 Error is the most perplexing subject in the whole field of 
 Philosophy. Why does it exist? Or is there perhaps no such 
 thing as error, as the sophists alleged? Plato felt called upon 
 to devote an entire dialogue to the refutation of the sophist's 
 view and after twenty-three centuries the new realists find it 
 their most embarrassing problem. There would truly never be 
 any error, we should never make mistakes in judging, if we 
 never took any risk in the predicate, if we always said "A is A," 
 and never attempted to predicate of A something other than its 
 
 H On this point sit Sidgwick, Elementary Logic, p. 1!><>. "This risk, 
 then, is always present when we make a predicative statement, however 
 carefully worded the statement may be. There is no way of escaping it. 
 
 short Of Ceasing to make any predications at all. It is the price we pa\ 
 the power either of generalising or of describing a Subject; it is a defect 
 that belongs to a quality." 1 should agree entirely with this account of 
 
 the essential risk in judgment, but should differ as to its interpretation. In 
 
 the chapter on "Novelty and Identity in Inference" I have tried to show- 
 that the risk in judgment is not destructive of a stability t'.,at is just as 
 essential as the risk.
 
 66 FOOTNOTES TO FOEMAL LOCK 
 
 bare identical self, something genuinely different from it. But 
 we do take the risk and must take it. And it is the business 
 of critical philosophy to ask for the reason why we take the 
 risk and what is the success of our venture. We see at once, 
 that the modern query, "How can one mind contain both the 
 possibility of knowledge and the liability to error!" is identical 
 with Kant's fundamental problem, "How are synthetic judg- 
 ments a priori possible ?" and this in turn is the same as Plato's 
 question, "How can we affirm of a subject a non-identical 
 predicate ? ' ' 
 
 It is very easy to state the difficulties about error, but far 
 from easy to remove them. The Law of Excluded Middle 
 declares that reality and non-reality exhaust the entire universe. 
 Now from the purely subjective point of view, that is, before we 
 attempt to classify any of the facts of universe, this law is com- 
 pelling. A thing is either real or it is not real ; we cannot accept 
 anything between these two. When, however, we begin the 
 process of classifying subjective and objective facts, on this 
 principle, we get along very well until we come to the group of 
 negative conceptions among which error is found. These stub- 
 bornly refuse to go into either of the two aforesaid classes. 
 Error, for instance, refuses to be classed as either reality or 
 non-reality. It insists upon having a third place made for it. 
 for which as we have just seen, Logic at the outset makes no 
 provision. There is truth in the remark that error is the occu- 
 pation by an actuality of a place which does not exist. 
 
 Thus does thought discover a most interesting dilemma about 
 thought. It can compel truth to reveal its own intrinsic false- 
 hood. Also it can extract from error the confession of its essen- 
 tial reality and necessity. To put it otherwise, in the manner 
 of Bradley, an appearance which is, must fall somewhere. But 
 error, because of its intrinsic negativity cannot belong to reality, 
 and again, it cannot belong to appearance, because that, with all 
 its contents, cannot fall outside the Absolute. An appearance
 
 THE IMPOST OF .11 DG Ml \ I 67 
 
 entirely outside of Reality is aaught. The essential character- 
 istic of falsehood, error, fiction, is thai an actuality Bhould claim 
 to be something other than itself. Many of the popular wit- 
 ticisms are based on this fundamental paradox. For example, 
 the definition of a liar as one who tells the truth aboul something 
 thai never happened. It will be observed thai I have differed 
 from Bradley as to the place of error in judgment. He con- 
 tends 15 that we can not. while making a judgmenl entertain the 
 possibility of its error. One can not judge ami doubl a1 the 
 same lime. I have insisted thai one does not judge unless one 
 dues feel 1 he aeliial constraint of a doubt. 
 
 i i Mind, d. s. XVII (1908), L54.
 
 CHAPTER IV 
 NEGATION AND THE INFINITE JUDGMENT 
 
 I 
 
 There are four possible ways in which we may regard the 
 relation between the affirmative and the negative judgment. We 
 may hold that : ( 1 ) each is an independent and final form of 
 thought's functioning — original, underived and self-directing; 
 (2) negation comes after affirmation and is the result of a 
 thwarted affirmation; (3) affirmation follows negation and is 
 what we find left over after negation has destroyed certain 
 possibilities; (4) affirmation and negation are correlated aspects 
 of a more fundamental form of thought. 
 
 The first is the view of common sense and need hardly be 
 discussed, although it is the innocent presupposition of some 
 systems of Logic. It has been included in this fourfold classi- 
 fication for the sake of formal completeness. The second view, 
 which makes negation subordinate to affirmation, has had many 
 advocates, notably Sigwart and Erdman. The third doctrine, 
 omiiis determinatio est negatio has had able defenders from 
 Spinoza to Venn. Although this controversy concerning the 
 logical priority is many centuries old. the supporters of the 
 second and the third views are still quite equally divided, which 
 suggests that each side has hold of one aspect of a multiple truth. 
 The fourth position maintains that neither affirmation nor nega- 
 tion is logically prior, and that while each necessarily involves 
 the other, both are dependent upon a more central form of 
 thought. This view makes possible, it seems to me, a genuine 
 reconciliation of the divergent claims of (2) and (3). 
 
 Sigwart ? s view that every negation presupposes an affirm- 
 ation, has been characterized as "monstrous" by Bosanquet. 
 
 [68]
 
 \li. Alios AND THE INFINITE JUDGMENT 69 
 
 However, we musl admil this is a true and accurate description 
 of a stage in the complex whole of the judging process. Thai 
 reality is a system of inter-related fads is a postulate of every 
 judgment. This affirmation of an orderly whole which is tin- 
 logical presupposition of every specific judgment, always takes 
 the form of a disjunctive judgment. Il is an assertion to the 
 effect that reality offers alternative possibilities to the judging 
 consciousness. "S is either /' or non-P." Bosanquet 1 and 
 Bradley- are doubtless right, however, in saying that ihis postu- 
 late can not properly be called an affirmative judgment. Judg- 
 ment implies belief and we can hardly be said to have judged 
 and ''believed" when the mind is poised between tin- balanced 
 teems of a disjunction. 
 
 This postulate, or disjunctive affirmation, which precedes 
 the negation is not the same in kind as the affirmation which 
 comes after the negation. They differ as suggestion differs from 
 assertion. It is true that in the Life history of the judging 
 process negation does occur between two affirmative states. Bu1 
 the one is an ideal construction and the other an affirmation of 
 fact. The prior disjunctive judgmenl is a crucial instance, 
 and has the same structure as a genuine hypothesis in science. 
 It is strictly non-committal. It has been said that the suggestion 
 in the disjunctive judgment is the same as the assertion that 
 remains after the selective process of negation. This is the only 
 view that lends support to Sigwart's doctrine, bu1 this is clearly 
 untenable. We can not say, as Sigwart's view would have us 
 say. thai negation is the rejection of an actual judgment. The 
 acceptance of the hare presentation of the choice between alter- 
 native possibilities is not a judgment. 
 
 Bosanquet says, "Every significant negation, S is not P can 
 be analysed as S is X which excludes P." Bui now we may 
 properly ask "At what stage 1ms the exclusion taken place?" 
 
 i Logic, I, 321. 
 
 ^Principles of Logic (London, Paul, L883), p. tin.
 
 7U FOOTNOTES TO FORMAL LOGIC 
 
 If there is no necessity for putting the verb is and excludes in 
 the same tense, we may consider the exclusion to have been per- 
 formed first and thereafter the discovery made that the inclu- 
 sion of ^i in X had been affected thereby. The complex judg- 
 ment would then read as follows: A (B having been excluded) 
 is found to be X. This obviously would be a return to Venn's 
 Theory of Judgment. Again we might stress the inclusion and 
 say: A (in being A') has excluded B. The vital question is 
 whether the exclusion is before, after or simultaneous with the 
 inclusion ? The logical analysis of the content of consciousness 
 does give support to the view that the only meaning of any 
 affirmation of a proposition is found in what it denies. Actuali- 
 ties can not be asserted, they arise spontaneously out of, or by 
 the side of, the destroyed possibilities. The actualities we seem 
 to get by the way of pure affirmation are always pseudo-actuali- 
 ties ; they have never more than a hypothetical existence. And 
 yet on the other hand, the psychological analysis always finds 
 negation at a point farther from reality than affirmation. 
 
 The logical negative does in fact always contradict, but in 
 contradicting never affirms the reality of that which has been 
 denied. The dichotomy which is at the bottom of every nega- 
 tion, begins with existential reality, but in breaking up the 
 whole into parts it is powerless to keep in each part the full 
 measure of the reality of the whole." The assertion that "S is 
 not P" is the same as the denial that S is P, and both are equi- 
 valent to "S is P is false." And in no one of these three 
 equivalent statements has thought passed beyond P into non-P. 
 No assertion is made about the reality or the non-reality of P. 
 Bradley has maintained that negation can not in any way be 
 derived from affirmation, nor affirmation from negation, and yet 
 he thinks it wrong to consider them coordinate species of a 
 higher form. But although he is unwilling to accord to either 
 the prior position in Logic, in Psychology he places negation 
 
 s Cf. Bradley, Principles of Logic, p. 118.
 
 NEGATION AND THE INFINITE JUDGMENT 71 
 
 after affirmation. Since negation presupposes a positive ground, 
 he says, "'it stands at a differenl Level of reflection." And this 
 again is in accord with the view expressed earlier. No difficulty 
 is found when we observe the distinction between the Logical and 
 the psychological aspects of judgment. 
 
 When Bradley says "Nothing in the world can be denied 
 except on the strength of positive knowledge," he is after all 
 admitting the main contention of those who hold thai negation is 
 a thwarted affirmation. It is true, as has already been shown, 
 thai tlie prior affirmation which lie concedes does not refer the 
 
 ideal COntenl to reality with the same claim to truth ;is the 
 later affirmation, namely, that which selects from among the 
 presented alternatives. The first is a sinit/<si<<l affirmation while 
 the second is an <issirl<</ affirmation. lint Sigwarl himself 
 recognizes the essential difference between these two forms of 
 affirmation when he says. "The primitive judgmenl should not 
 he called affirmative at all ; it would he better denoted as positive. 
 The simple statement A is B is an affirmation only when opposed 
 to the negative judgment." In view of this explicit statemenl 
 1 do not see why Bradley finds Sigwart's doctrine so "obviously 
 absurd." 
 
 There is a prevalent tendency, especially in the elementary 
 texthooks of Logic, to define affirmation and negation in terms 
 of approval and disapproval. This is not precisely accurate, fur 
 there is also an aspect of approval latent in every negation. We 
 accept negation as true or false, and thus approve or dis- 
 approve 4 It is impossible in thought to draw a line between 
 affirmation and approval. We do not first affirm, and then, after 
 having contemplated the object of our affirmation, pass to a 
 second act of approval. Approval and affirmation are simul- 
 taneous. In discussing the relation between apprehension and 
 judgment, we saw reason to distinguish between mere acknowl- 
 
 M >n this point sec Sigwart, Logic; translated by Dendy (ed. 2; London, 
 Macmfflan, 1895), I, 381.
 
 72 FOOTNOTES TO FOEMAL LOGIC 
 
 edgment of a content without critical reaction, and true judg- 
 ment or acceptance through criticism. But this we held was a 
 theoretical distinction entirely. In living thought there is a 
 simultaneity in the midst of the succession. 
 
 II 
 
 The infinite judgment has been much discredited. Since it 
 attaches no positive and definite characteristic to the subject, 
 it has been condemned as idle, practically worthless, and even 
 illogical. Honesty is non-blue, for instance, is meaningless, 
 because the negative term includes all possible predicates other 
 than blue and does not even so much as insist upon the existence 
 of the predicate. It is the farthest limit of indifference. This 
 doctrine of the essential irrationality and futility of the infinite 
 judgment is very old. By some it has been traced back beyond 
 Plato to Anaximander. But I must point out at once, as bear- 
 Plato to Anaximander. But I must point out at once, as bear- 
 ing upon a later defense of the infinite judgment, that the aireipov 
 of Anaximander was a positive infinite, and by him regarded 
 as the source or original of all things. Modern writers think 
 they find justification for the contempt which they heap 
 upon the infinite judgment in Aristotle's own treatment of 
 the subject. But we may doubt whether Aristotle would have 
 approved of this later-day entire condemnation of the infinite 
 judgment. This problem first presented itself to Aristotle in 
 his discussion of terms. He saw as plainly as any one since his 
 time that there is a paradox about the negative term. It must 
 be defined as a term which implies the total absence of a 
 quality. Technically speaking it connotes the absence of conno- 
 tation. It is the self-contradictory attempt to make something 
 out of nothing. 5 
 
 •"• Bosanquet has stated the dilemma with admirable clearness: "The 
 Negative Judgment presents at first sight a paradoxical aspect. We are 
 bound to take it, qua judgment, as playing some part in knowledge, and
 
 NEGATION AND THE INFINITE Jl DG HE \ / 1 
 
 It is alleged to be ;i self-contradiction to say thai a term may 
 connote just the absence of a quality. It is not strictly speak- 
 ing true, we are told, as is often supposed by the opponents 
 hare denial, that no term can be purely negative. Bui now ii 
 depends entirely on what we mean by.a purely negative term. 
 The class of privative terms, which logic has been compelled to 
 recognize from the first, is a genuine class; and the definition of 
 this class of terms must be greatly strained to allow even a 
 modicum of positive quality in a privative term, in the ordinary 
 interpretation of the word positive. A positive character of an 
 entirely differenl sort it does possess. The negative term denotes 
 an object which in the first place I neks the qualities denied by the 
 negative term hut has other qualities in terms of which thai 
 very lack is defined. Every negative must have a positive basis. 
 A sheer naught can not be the ground of a denial. Non-P will 
 always signify what an object will be, which mighl be /', but is 
 not. But granted that these so-called privative terms do have 
 a genuine positive connotation, even if slight, there seem to be, 
 nevertheless, other terms which have no purpose other than to 
 deny. An alien, even within a Limited universe of discourse, is 
 defined entirely in terms of what he is not. A bachelor connotes 
 an unmarried man, ami bachelors (as bachelors) have nothing 
 in common save that they are not married. Such terms are 
 positive as to denotation, but negative as to connotation. Bu1 
 even these terms can. I believe, be brought under our general 
 rule. The positive term as understood by common sense and 
 ordinary logic is positive directly and definitely, the negative 
 term is positive indirectly and indefinitely, bu1 none the less 
 genuinely. In a later chapter on immediate inference I shall 
 
 as at any rate capable of contributing Borne factor to the ideal fabric of 
 
 reality. But it assumes the external shape of ignorance, or at least of 
 
 failure, and the paradox consists of this— that in negation the work of 
 positive knowledge appears to be performed by ignorance. The contradic- 
 tion arises, as we have seen ether contradictions arise, from the adoption by 
 thought of a shape which at best expresses it but partially, and the reten- 
 tion of that shape when the aspect which it did express has come to 
 
 be dwarfed by ether aspects of knowledge." Logic, I. 293.
 
 74 FOOTNOTES TO FOBMAL LOGIC 
 
 advance a new interpretation of the ancient rule for distribu- 
 tion based upon this distinction which I think answers the much 
 debated question as to the validity of inversion. 
 
 We here encounter the same problem that confronts one 
 wherever one has to do with the "relational way" of thinking. 
 We begin with what appears a mere couple, a two in relation. 
 But the "endless fission" breaks out and we discover that no 
 relation is purely diadic. Relations are always within as well as 
 between; and while they are explicitly diadic they are implicitly 
 triadic. In earlier paragraphs we saw this to be true of the 
 relation between form and matter, denotation and connotation, 
 intension and extension. They are all correlatives having inde- 
 pendent variability within some larger whole. Now this con- 
 ception of the essential triadic character of every relation pro- 
 vides an explanation, I believe, for the class of bare denials 
 which the relation of affirmation to denial requires. Every 
 object denotes a this or a that, and connotes thisness and that- 
 ness. Now when a this goes beyond itself for its connotation 
 and accepts thatness for its meaning, we have — stated most 
 abstractly — a pure negation, a bare denial. And such abstract 
 statement of the problem I venture to think is not a mental 
 "fiction." We have thus properly provided for the outstand- 
 ing "rare" cases where the mind halts between denial and 
 affirmation. 
 
 All of this suggests, as Windelband and Kant before him, 
 have held, that there is a third kind of quality between affirma- 
 tion and negation, and in a sense coordinate with them. Where 
 there is no sufficient positive ground for a direct assertion the 
 mind is satisfied with probable, indirect or negative grounds. 
 But, furthermore, it should be pointed out that every indictment 
 of the infinite judgment, which begins, as most criticisms do, 
 with a condemnation of the negative term, is an illogical pro- 
 cedure, for terms are not the prior units out of which the judg- 
 ment is constructed. The judgment is itself the unit of thought
 
 NEGATION AND THE I\ II \ 1 1 I. Jl /». Ml. \T 75 
 
 and the negative term is derived by abstraction, or dismember- 
 ment of a prior infinite, or Limitative judgment. We do not find 
 the non-S'a and the non-P "s lying about ready made and then 
 proceed to affirmations or denials aboul them. These negaiive 
 terms are the by-products of the reverse process. We firsl 
 observe thai P cannot be attributed to 8 and State this fa el ill 
 the negative judgmenl "8 is not /'." Whereupon the query 
 arises, if /'can not be attributed to x. what can be? In answer 
 to this question, non-P is created and the response is embodied 
 in the pseudo-affirmative judgmenl "S is non-P." The nega- 
 tive judgment {t 8 is non-P" affirms something indefinite. There 
 is, therefore, abundant reason to assert with Lotze thai the true 
 meaning of this latter judgmenl is never available for practical 
 purposes until it is restored to the negative which was it source. 
 But now it should be observed that the negative term non-P 
 is not truly indefinite in the sense of being wholly undefined or 
 unbounded. In the technical Language of the schoolman, it is 
 always distributed. And if it is genuinely distributed we do 
 have some knowledge that extends over the entire class or else 
 the ancient doctrine of < 1 ist libution falls to the ground. To say 
 that noti-1' is distributed is to declare emphatically that it is 
 not entirely impossible to hold together the large and apparently 
 chaotic group of objects comprised in non-P. The fact of dis- 
 tribution declares that there is at bottom an essential homo- 
 geneity in the group, and this guarantees the accuracy of all 
 the transformations in which the negative term is employed 
 in the various immediate inferences. Obversion, or infinita- 
 tion, is for this reason a valid inference. I think no defender of 
 the infinite judgment has ever claimed that non-P can exist as 
 an independent concept. We can not, it is true, conceive such 
 a class of objects, that is. we can form no mental picture of it. 
 It is, therefore, unintelligible, bu1 not on that account unthink- 
 able. We can employ it both in the theoretical and in practical 
 thought processes. The symbolic logician makes rigorous use
 
 7(5 FOOTNOTES TO FORMAL LOGIC 
 
 of it in his theoretical thinking, and the empirical scientist 
 applies it continually in his search for causal connections. The 
 scientist narrows the field in any inquiry by destroying, one by 
 one, the possihilities of his multiple hypothesis. And, as I have 
 already insisted, each destruction of a possibility is a positive 
 advance towards his goal. 
 
 It is quite true that the mind is rarely ever satisfied to remain 
 in the stage of bare denial. But it is precisely these exceptional 
 cases where it does halt at bare denial, however rare they may 
 be, that logic must take into account. We may ask two questions 
 here: (1) Should we at any time be unable to pass through 
 bare denial to denial with affirmation, have we made no logical 
 advance whatever? (2) If the infinite judgment is illogical 
 and impractical, how can we explain its persistence in thought 
 and language? I shall attempt to show that it is no answer 
 to these questions to say with Hegel that the infinite judgment 
 is "idiotic." 
 
 The history of Logic has repeatedly taken cognizance of this 
 dilemma about negation, and yet, in my opinion, there is no 
 real warrant for the disparagement of the infinite judgment. 
 The modern critics provide the answer to their criticisms in 
 the emphasis that they place upon the difference between the 
 assertion of impossibility and the denial of necessity. Absence 
 of a reason for assertion, it is justly held, does not mean the 
 presence of a reason for denial. To have no opinion against, is 
 not the same as to have an opinion for. It is possible, is not a 
 legitimate inference from we do not know it to be impossible. 
 There is some justification for the view that there is no middle 
 ground between affirmation and denial — that there is no such 
 thing as suspended affirmation. But now whatever position we 
 take on logical the problems here in question, it is nevertheless 
 an undeniable psychological fact that the mind may put itself 
 in three different — even if not correlated — attitudes towards any 
 suggestion. It may not only accept or reject, it may also doubt.
 
 NEGATION AND THE INFINITE Jl DGMEN1 77 
 
 At an election the counter records the "ayes" and "noes"' and 
 also the "no1 voting." And in Psychology we are told ofte'n 
 of the indifferenl zone thai lies between the extremes in sensa 
 
 tion. It is an answer not to the point to sav thai the state of 
 consciousness called indecision is decision qo1 to decide. The 
 question is. Why do we require Oor Psychology and practical 
 
 life a threefold division and for Lo^ic a twofold division .' 
 
 We see. therefore, thai a careful examination of these con- 
 siderations which seem to militate againsl the infinite judgmenl 
 shows thai they are unfounded. In the firsl place it can be 
 shown that the infinite judgment, in the process of delimiting 
 any universe of discourse, if not the whole objective system, has 
 made a distinct forward movement. And this step does not have 
 to l)e retraced, that is to say, a second infinite judgment in the 
 next stage of division proceeds from where the firsl left oil'. It 
 is not like the process of throwing a die where each throw is 
 no nearer certainty than the one before it. The infinite judg- 
 ment is no logical treadmill. In theory it is true, as Plato and 
 after him Kant said, that the infinite judgment subtracts one 
 from the infinite uumber of possibilities, and leaves remaining an 
 infinite number. But in practice, the application of successive 
 infinite judgments does very rapidly reduce the total sphere. 
 Only half a dozen steps are needed in the Tree of Porphyry 
 to pass from a sum/mum <j< mis to a very definite injlnui sjxeies. 
 A practical illustration of the rapidity with which the successive 
 infinite judgments will narrow a field of inquiry is found in 
 the familiar parlor game of "twenty questions." Here one 
 person undertakes to perform the apparently impossible feat 
 of telling what another is thinking about by asking him twenty 
 questions to be answered only by yes or no. This is often 
 accomplished with surprising swiftness. 
 
 All the so-called )i<</utir< results in the experimental work 
 of scientific laboratories may be expressed in each instance in 
 the form of an infinite judgment; and these negative results are
 
 78 FOOTNOTES TO FORMAL LOGIC 
 
 surely not without value. The scientist assumes that the object 
 of his search will be found in a certain field, but after laborious 
 investigation discovers that he has set up a false hypothesis, and 
 must seek elsewhere for the cause of the phenomenon under 
 investigation. He registers this fact in the infinite judgment, 
 "S is non-P." And he intends that the judgment shall be 
 genuinely affirmative, for he knows that the phenomenon must 
 have a cause. The clearing of the field by the destruction of 
 false hypothesis is not idle. The scientist never hesitates to 
 publish his "failures to find" for the guidance of fellow workers 
 in the same field. A negative Baedecker (if one dared to print 
 such a guide book) which told tourists where not to go, might 
 be more useful than the positive form. It would permit of real 
 discoveries by the independent seeker. 
 
 Ill 
 
 The symbolic logicians have pointed out the significant fact, 
 that the term P is no more indefinite than the term non-P. Why 
 should we think that the objects that compose the class P are 
 any more homogeneous than those of the class non-P? The 
 belief that one of these classes is small and homogeneous and 
 the other large and heterogeneous is an idea that is thrust in 
 from without. Granted that the members of the class non-P 
 have nothing in common save the absence of S, this does not 
 make them a less coherent group than the class P. Non-P is, 
 indeed, the contradictory or negative of P, but in Formal Logic 
 either of the two terms which stand in the relation of contra- 
 dictories may be taken as the positive and the other as the nega- 
 tive. For example, a powerful social, political or religious move- 
 ment often grows from small beginnings when its adherents were 
 described by some negative word. The Anti-Saloon party in some 
 prohibition communities is overwhelmingly large, positive and 
 coherent. The fundamental fact with which Formal Logic is con- 
 cerned is that the two classes P and non-P are mutually exclusive 
 and together comprise the whole universe of thinkable entities.
 
 NEGATION AND THE INFINITE JUDGMENT 79 
 
 Symbolic logicians have also said that Kanl's threefold 
 
 classification of propositions into positive, negative and infinite 
 has no theoretic defense; it depends entirely upon practical 
 differences of meaning. The three forms "3 is /'." "S is not 
 /'." and S is non-l' have their origin not in any strid doctrine 
 of negation, hut in the practical convention of something less 
 than complete oegation, namely, opposition. In all those judg- 
 ments in which the predicate is regarded as an attribute, it is 
 for practical purposes quite sufficient to use opposites, thai is. 
 terms which mutually exclude each other, as do contradictories, 
 but winch do not lordlier include the entire universe of think- 
 able objects. The class of infinite judgments is a concession to 
 contrary oegation, and to the attributive view of predication. 
 And this view, as I have already tried to show, is merely a nee - 
 sary stage on the way to the class view of Symbolic Logic. 
 
 It has often been maintained that the assertion of a mere 
 distinction, that is, an assertion of differences in degree is no 
 assertion. This is only partly tine. The common definition of 
 negative or contradictory terms, that they are two terms that 
 are mutually exclusive and that together exhaust the entire 
 universe of thinkable things, needs some qualification. They are 
 totally different, the definition says, that is, different in kind. 
 Now this distinction between differences in degree and differ- 
 ences in kind is one which Logic has always regarded as of the 
 deepest significance. But what, we may ask, is the criterion 
 of this distinction between the differences in degree and tin- 
 differences in kind? Entities which are different in kind must 
 after all have something in common. They must belong to the 
 same universe of thought somewhere, otherwise they would have 
 ceased to be two and would have become oothing. The Hegelian 
 criticism of the Aristotelian Law of Contradiction is just. 
 Where there is a distinction there must be at least one principle 
 of unification. Only one thing can both be and not be, namely. 
 nothing.
 
 80 FOOTNOTES TO FORMAL LOCK 
 
 While A and non-A are different in kind, yet it is evident 
 that that which differentiates one of these conceptions from the 
 other is not an intrinsic principle. There is nothing in the 
 nature of the two conceptions which can tell us where the one 
 ends and the other begins. The principle of this division is 
 always extrinsic, that is, it lies in the purpose of the thinker. 
 Every dichotomous division is made in the interest of an external 
 need. Without such an extrinsic point of departure we should 
 pass from A to non-A by imperceptible gradations within the 
 same qualitative sphere. However far apart we place A and 
 non-A, they will have something in common, otherwise they 
 could not be thought together. The same norm that defines A 
 will also define non-A.
 
 CHAPTEE V 
 
 The N \n re of I nference 
 
 I 
 
 The dictionaries have found it accessary to give a score or 
 more of synonyms to cover the many uses <>t' the word infen nc< 
 by philosophers and Laymen. 1 
 
 Logicians have not been so much concerned with the ambiguity 
 in the word, as with the contradictions thai seem to lie a1 the 
 heart of the process of inference itself. Aristotle, very early 
 in Ins thinking about the fundamental problems of Logie. dis- 
 covered the paradox in all judgment. No term it seems, can 
 be truly predicated of another term: it can only be predicated 
 of itself. The only true propositions are the identical propositions. 
 You can not truthfully affirm thai ".1 is />'." but only that 
 "A is A." This dilemma arises then, in saying "A is /;.'" you 
 predicate what the object A is not, and yon therefore speak 
 falsely; but on the oilier hand, if you say "A is .1." you indeed 
 predicate what it is, but yon say nothing and the judgment is 
 idle. So thought vibrates between the extremes of tautology 
 and falsity; apparently with no possibility of a resting place 
 between the two. 
 
 Now while the modern logicians profess to be seriously dis- 
 turbed by this ancient dilemma they define inferena in ways 
 
 'Sonic of tlic dictionary synonyms of inference are: analysis, anti- 
 cipation, argument, argumentation, assay, assent, assumption, conclusion, 
 conjecture, conviction, corollary, criterion, decision, deduction, demonstra- 
 tion, dilemma, discovery, elench, enthymeme, examination, experiment, 
 
 experimentation, finding, forecast, ^ene'-alization, guess, hypothesis, illa- 
 tion, induction, inquiry, investigation, judgment, lemma, moral, persua- 
 sion, porism, prediction, prevision, presumption, probation, prognostica- 
 tion, proof, ratiocination, reasoning, research, ^it'tiiiLT. surmise, test, 
 
 theorem, verdict. 
 
 ! 81 1
 
 82 FOOTNOTES TO FOSMAL LOGIC 
 
 that show they have for the most part ignored the paradox. 
 The conclusion in any inference, mediate or immediate, we are 
 told in varying language must be another, or a new, or a differ- 
 ent, or a fresh proposition. But we find few serious attempts 
 to define otherness, newness or difference. Again we are told 
 that inference is the "explication of implications," or the 
 "passage from one fact to another" ; it must be "more than vain 
 repetition." Or it is the "supporting of a judgment by its 
 reasons," the "discovery of necessary connections," "combining 
 of two premises so as to cause a consequent conclusion, or "draw- 
 ing a conclusion from premises. ' ' And again none of the essen- 
 tial words are clearly defined. The writers often confess that 
 they are employing the significant words of their definition in 
 "new" ways, that the meanings that they attach to them are not 
 in conformity with ordinary human usage. Hobhouse suggests 
 that there is something unusual in his use of the word "new," 
 by continually writing it with quotations. 
 
 It will be well to consider several of the typical definitions 
 of inference ; to show how they reveal in varying degrees the 
 ' ' circle in defining. ' ' Adamson says : 
 
 Inference is that mental operation which proceeds by combining two 
 premises so as to cause a consequent conclusion. Some suppose that we 
 may infer from one premise by a so-called ' ' immediate inference. ' ' But 
 one premise can only reproduce itself in another form, e.g., all men are 
 some animals; therefore some animals are men. It requires the combina- 
 tion of at least two premises to infer a conclusion different from both.- 
 
 Later we shall examine this view that rejects the immediate 
 inference. I wish at this time to point out that the expression 
 "to cause a consequent conclusion" is ambiguous, redundant, 
 and inclusive. It tells us only, at best, that an inference is an 
 inference. And this circle in defining lurks in all the other defini- 
 tions. According to Joseph : 
 
 Ency. Br! I. XVI, 879.
 
 THE NATUBE OF INFERENCE 
 
 [nference is ;i process of thoughl which, starting with one or more 
 judgements, ends with another judgemenl made accessary by the former. 
 The latter, which in relation to the judgement or judgements from which 
 
 the process starts is called conclusion, which must in comparison with 
 them lie ;i in a- judgement; to repeal in fresh words our original Btatemenl 
 
 is not inference, any more than translation is inference. For the ii 
 
 part .'i new judgement is only got by putting together two judgements, 
 and, as it were, extracting what they yield. But there are a few con 
 elusions which we appear to draw, not from any "putting together" of 
 two judgements but simply from the relation to one another by putting 
 together of the terms in one judgment. This is called immediaU infer- 
 ence. 3 
 
 Welton's definition rends: "Inference or reasoning is the 
 process by which we pass from affirming one or more propositions 
 to another different judgment which we make as the necessary 
 result of accepting the first." Also, "Conclusion states the orig 
 inal truth in a new form." 4 And again, kl Inference or reasoning 
 is the deriving of one truth from another. By this is meant 
 that the new judgment is accepted as true because, and in so 
 far as. the validity of the judgment from which it is derived is 
 accepted.""' Bosanqnet's much discussed definition is, "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."' Miss 
 Jones says, "One proposition is an inference from another, or 
 others, when the assertion of the former is justified by the latter 
 and latter is, in some respect different from the former." 7 
 Windelhand insists that "Inf< n nc< is nothing else than a way of 
 establishing judgments, and is indeed a judgment by means of 
 judgment." 8 This definition is satisfactory until we come to see 
 that the whole question at issue is just the meaning of this 
 
 s Introduction to Loan- (Oxford, Clarendon, L906), p. 209. 
 
 * Manual of Logic (London, ('live, 1891), V. 24. 
 
 ■• Ibid., I, 256. 
 
 o Logic, I, -t. 
 
 ■Jones, E. B. C, Elements of Lo^ic (Edinburgh, Clarke. 1890), \>. 139. 
 
 a Ency. Philos. Sci., 1. 27.
 
 84 FOOTNOTES TO FORMAL LOGIC 
 
 process of "establishing" judgments. Inference has very often 
 been described as the extracting from a proposition of its implied 
 meanings, or the explication of implications. But here we have 
 again a petitio, for this description presupposes the definition of 
 explication and implication. The symbolic logicians have recogn- 
 ized this inevitable circle and have for the most part frankly 
 accepted among their indefinable notions the notion of impli- 
 cation. 9 
 
 One of the commonest of all the vague words which we are 
 tempted to employ in the definition of inference is the word 
 virtually. Many writers say, that if the premise in an inference 
 only virtually contains the conclusion, then, when the conclu- 
 sion is "drawn from" or "extracted from" the premise, the 
 "new" judgment at which we arrive will be both a different 
 way of viewing and a different way of expressing the same 
 truth. As a typical illustration of an account of inference which 
 employs several of these ambiguous words I cite the following 
 from Joseph: "In all inference there must be some movement 
 of thought ; we must conclude with something not quite the same 
 as what we started with; though the obviousness of the infer- 
 ence is no ground for denying that it is inference.*" This 
 activity of thought as it passes on to a "fresh" point of view, 
 this step which it takes as it clothes itself in a "new" form, is 
 an inference. But such an account I am inclined to think does 
 not get to the center of the difficulty. It has solved the problem 
 by translating it into a new form. The vital question is, What 
 is the difference between a judgment that is actually and one 
 that is only virtually contained in tin premise? Again we may 
 ask, What have we added to the "old" when we say that thought 
 has been "active" in "stepping" to the new point of view. 1 
 
 9 e.g. Eussell says: "A definition of implication is quite impossible. 
 If p implies q, then if p is true q is true, i.e., p 's truth implies q 's truth ; 
 also if q is false p is false, i.e., g's falsehood implies p's falsehood. Thus 
 truth and falsehood give us merely new implications, not a definition of 
 implication." Principles of Mathematics, p. 14. 
 
 io Introduction to Logic, p. 217.
 
 tii E x.iti i; I-: OF is /•'/•; i; /•: NCE 
 
 When is the change qo1 a step.' It is said, thai the obviousni 
 of the step is no objection to calling it an inference. And again, 
 we have on our hands the word obvious which is quite as vague 
 as virtually, new, old or fresh. Since inference is not really a 
 transition in time, il is evident thai a conclusion will nol lose it s 
 character as inference as soon as it becomes obvious, [nference 
 involves discovery bu1 it does not cease to be inference when 
 (the discovery having been made) thought vindicates the infer- 
 ence by proof. As Bosanquet lias so well said. "Discovery with- 
 out proof is conjectun ; an elemenl of proof is needed to con- 
 stitute inference, and indeed to constitute discovery. The activ- 
 ity of inference cannot be identified with the perception of 
 something new. It is quite a normal occurrence thai the ele- 
 ments which are indirectly referred to reality should also be 
 directly referred to reality." 11 
 
 Hobhouse says: "Any assertion is 'new* (as compared with 
 some other) as long as the two contents are in any way distinct. 
 Whatever the real inseparability of the Tacts, as Long as they are 
 distinct to pass from the one to the other is to make a new- 
 assertion." 1 -' I>nt it seems to me that Hobhouse has no1 reached 
 the central issue either. To define the "new" as thai which is 
 "in any way distinct" is hardly satisfactory. We are at once 
 confronted with the difficulty of showing how two contents may 
 be regarded as distinct if they have, as he declares, a real insepa- 
 rability. In all his discussions of the nature of thinking, Hob- 
 house has quite consistently maintained that it is the primary 
 function of inference to reach "new" facts. But in the last 
 analysis, by "new" facts he means those which have not been 
 presented to the mind in any previous sense perception or act 
 of memory. But the past is connected with the present by a 
 continuous tie; therefore predication, which always passes be- 
 yond the present, can not be truly novel. Every theory of infer- 
 
 u Lof/ic, II, 8. 
 
 12 Hobhouse, Theory of Knowledgt (London, Afethuen, L896 . p. 216.
 
 86 FOOTNOTES TO F011MAL LOCK 
 
 ence must finally go back to the world-old Platonic Doctrine of 
 Recollection. Inference is the process of discovering what we 
 already logically possess but did not observe that we possessed 
 until we psychologically came upon it. 
 
 If consensus of opinion may be taken as a warrant for the 
 assertion, the modern discussions as to the nature of inference 
 have shown that it must be more than direct apprehension, or 
 immediate experience. Welton says, "Inference involves 'mental 
 process,' " and with this others, for example Joseph, agree. 
 They declare that in all inference there must be some "move- 
 ment of thought." But here again are we not begging the whole 
 question? How shall we decide when and in what way thought 
 has moved? What is to distinguish between a mental process 
 which yields an inference and that state of consciousness which 
 is not a process and which is therefore characterized as bare 
 tautology. I confess that often in these pages I have myself had 
 to resort to the expression "movement of thought." but I have 
 tried to show that these words are meaningless unless they 
 involve a reciprocating process — forward and backward, analytic 
 and synthetic. The paradox of inference does not disappear 
 when (as some writers seem to think) we attach adjectives to 
 the terms, old and new, to the inference and the inferend. We 
 are told that the conclusion of an inference must not be a men 
 repetition of the old — that there must be genuine novelty. But 
 this does not dissolve the paradox. Any tautology is bare 
 tautology and any novelty is genuine novelty. 
 
 The objection which Mill, and after him, Adamson and others 
 have raised against the immediate inferences, namely, that there 
 is in the conclusion no "new" truth, will hold also against 
 mediate inferences and even against induction. The attempt to 
 regard induction as different in kind from deduction breaks 
 down under the weight of its own inherent self-contradiction. 
 The logician who offers a theory of induction that attempts the 
 self-vindication of its own processes has on his hands this
 
 / HE \ I l i BE OF INFEBE VC1 B7 
 
 dilemma: either he tacitly presupposes the universal truths and 
 hence his method is not their sole source, or, on the other hand, 
 they remain unproved because his method is confessedly a method 
 of probability only. The syllogism, as was pointed ou1 by its 
 earliesl critics, is indeed incompetenl to supply its own premises. 
 But now. when induction steps in to furnish deduction with 
 these universal truths for its premises, it is shackled by the same 
 fetters t't-f mi which it proposes to relieve deduction, [nduction 
 is itself a process of reasoning from premises, and must obey the 
 fundamental law which governs deduction ; the conclusion is true 
 only if the premises are true. In a commendable, fraternal spirit, 
 induction would remove the "mote" from its brother's eye, dis- 
 regarding the "beam" in its own. The symbolic logicians are 
 right, in my opinion, in their criticism of induction. 13 
 
 II 
 
 The dictionaries, and many of the ordinary textbooks in 
 Logic have defined inference in terms of judgment and judg- 
 ment in terms of inference without recognizing or confessing the 
 "circle." Many attempts have been made by recent writers, to 
 establish either a temporal or a logical priority in favor of one 
 or the other. Such discussions have generally resulted in the 
 discovery that each of these functions may be taken either as 
 chronologically or logically prior to the other. In attempting 
 to distinguish between judgment and inference, we find that the 
 ambiguity between these two words has made it possible for one 
 writer to make inference prior to judgment while another makes 
 judgment prior to inference. Both judgment and inference as 
 
 13 Cf. Russell, Principle* of Matin unities, p. 11. ••What is railed induc- 
 tion appears to me to be either disguised deduction or a method of mak- 
 ing plausible guesses." Also Shearman, Scope of Formal Logic (louden, 
 1911), p. xiv. "In so far as such studies set forth methods of proof 
 the Studies are formal in character, and in so far as they refer to matters 
 
 that .are preliminary to the application of proof, they are not Logic 
 at all."
 
 88 FOOTNOTES TO FOBMAL LOGIC 
 
 conscious processes pass through various stages of development. 
 When we take inference at its early, rudimentary and uncon- 
 scious beginning, we shall find it of a lower order than judgment, 
 if at the same time judgment is taken at the highest stage of its 
 development. And on the other hand primitive judgment is 
 needed as a prerequisite for overt inference. Judgment is the 
 lower limit of inference and inference is the upper limit of judg- 
 ment ; that is to say, in judgment the given fact, the process of 
 its justification, and the product are merged into a single state- 
 ment. 
 
 Bradley has made the difference between inference and judg- 
 ment depend upon the directness or indirectness of the reference 
 of the predicate to reality. He has defined judgment as the 
 direct reference of a content to reality and inference as the 
 indirect reference of a content to reality. This is a distinction 
 that at first sight seems very clear. But we soon discover that 
 we have only postponed the difficulty and have stated the orig- 
 inal question in a new form. When we pursue our analysis into 
 the distinction between direct and indirect we seem soon to be 
 lost in another maze of bewildering perplexities. The essence 
 of Bradley's doctrine is that whenever, on the strength of what 
 we know about a this, we make an assertion about a th<it, we are 
 inferring. But as we saw in a previous chapter, there is no 
 distinct and intelligible line of separation between the this and 
 the thai. The whole theory hinges again upon the distinction 
 between the explicit and implicit which is not a distinction in 
 the form, but only in the matter of thought. However, I believe 
 the "circle" is less objectionable in Bradley's way of distinguish- 
 ing between judgment and inference than in any other. 
 
 Every judgment when called upon to exhibit its reasons 
 develops into an inference. This statement does not refer to the 
 inductive process of establishing the universal propositions that, 
 are required for deduction. We have seen that judgment begins 
 its existence when it is observed that the predicate might have
 
 THE NATUBE OF INFEBENt I 
 
 been something else. Now in order to causi the judgmenl to 
 become conscious of its reasons we have merely to hold in thoughl 
 a suggested eonl radictory predicate as a substitute for the predi- 
 cate actually found in the judgment. This actual predicate, in 
 the process of rejecting the possibli predicate, vindicates itself 
 with a because. Thus the judgmenl "N is /'" expands into the 
 following disjunctive inference: "N is either /' or non-P," bu1 
 for such and such reasons "S cannol be non-P," therefore "S is 
 /'." Moreover, this fad thai judgmenl vindicates itself by 
 enlarging into an inference is another way of stating the general 
 idealistic doctrine thai all knowledge is a system of parts so inter- 
 related thai the whole may be unravelled from whatever point 
 we begin. 
 
 As Hohhoiise and others have said, there is no psychological 
 evidence that inference is developed among the states of con- 
 sciousness later than judgment, or thai it in any way makes use 
 of the completed process of a prior judgment. As soon as the 
 object is presented to the mind ir is stimulated not only to make 
 an analysis of the fact itself hut also to compare it, to notice its 
 position in the system of facts. Prom simple apprehension, 
 through conception and judgment, to inference, the process is 
 one undivided whole. Both inference and judgmenl start with 
 something given. Each represents a particular way that the 
 mind has of reacting upon this datum. Judgmenl begins with 
 terms which it either analyses or combines. The inference begins 
 with propositions which it likewise analyses or combines. They 
 differ merely in the character of the material upon which they 
 operate, and consequently may he said to differ not at all. or to 
 differ merely in degree. In the one case the difference between 
 the datum and the conclusion is explicit and in the other h is 
 more or less implicit. Although they are inseparable aspects of 
 one mental fact, nevertheless explicit judgmenl comes into con- 
 sciousness before explicit inference. Here, again, we have an 
 illustration of that universal law in the evolution of thought,
 
 90 FOOTNOTES TO FORMAL LOGIC 
 
 namely, that we become aware of the concrete result or product 
 first, and the process or law later. 
 
 A casual examination of any instance of "I think 1 ' reveals 
 both a forward and a backward movement of thought. The one 
 movement is from premises forward to conclusion, the other from 
 conclusion back to premises or "reasons." In the former case 
 we say "M is P and S is M, hence, therefore, <>r consequently S 
 is P." This is commonly called inference. In the other we say 
 "S is P" because, for or since "M is P" and "8 is M." This 
 is proof or demonstration. In discussing the nature of analysis 
 and synthesis previously, I urged the importance of viewing 
 these two movements as inseparably correlated aspects of any 
 complete living thought. And again in the matter of the relation 
 of inference and proof, both are always found together. There 
 is never a forward movement of thought, that can know itself 
 to be a genuine forward movement, if it does not always feel 
 at its center its own latent backward movement. There is no 
 inference — no true discovery — without proof. A discovery that 
 is bereft of this validating backward movement would be pure 
 adventure (if that were possible). But now, analytic attention 
 to the thought process always finds one of these movements more 
 prominent than the other. "We might employ the word no son 
 to denote the combined forward and backward movement in its 
 logical totality. Then the word inference might stand for the 
 process of attaining a belief and proof for the process of sup- 
 porting the belief. 
 
 The real problem at issue in immediate inference is not the 
 determination of the precise limits which any judgment places 
 upon the various movements or aspects of its meaning. This is 
 transformation or what Bosanquet has called "interpretative 
 inference"; it is the determination of all the ways in which the 
 predicate may be referred directly to the subject. "Substantial 
 inference" we have when we pass from one content or relation 
 to another indirectly. It is difficult to distinguish between a
 
 ////•; NATURE OF l\ II in V< / '.'1 
 
 dired and an indlrecl reference to reality. The difference is 
 
 between what we see and what we do ao1 see, lint what we might 
 see from another point of view. And this is no1 a distinction 
 that depends upon obviousness or immediacy in their ordinary 
 meaning. Inference is a process which changes our power of 
 perceiving the object. DeMorgaii remarks thai "inference d< 
 not give us more than there was there before, bu1 it may make 
 us see more than we saw before." The perfect mind makes no 
 distinction between direct and indirect reference to reality. It 
 is not obliged to say, "The facts present are thus and thus, 
 therefore I should infer thai fads not present are thus and 
 thus. (Omniscience does not have to compare facts in order to 
 know them.) It has what might be called a unito-multiple point 
 of view, from which the difference between the direct and the 
 indirect insight disappears. It does not have to run around an 
 object to see how it looks on the other side; it sees both sides a1 
 once. 
 
 Ill 
 
 The attacks on Formal Logic invariably proceed upon a mis- 
 taken understanding of the manner in which the idealist thinks 
 of the relation between form and matter. Since Hegel, many 
 logicians have reaffirmed his doctrine of the essential correlativ- 
 ity of these two aspects of reality. We have come to sec that 
 form and matter do not exist separately, nor can they even be 
 considered entirely apart from each other. We should not think 
 of them as we think of the seal and the wax in the classic illus- 
 tration of form and matter. And yet we may speak of the form 
 of reasoning as being different from its matter, without con- 
 tradiction. In truth, while there is no final and complete sepa- 
 ration of matter from form, there is yet a difference amounting 
 to a relative distinction. Although the two are not a separated 
 twain, they are nevertheless separable. They are. in fact, inde- 
 pendent variables within their correlation. The mathematician
 
 92 FOOTNOTES TO FORMAL LOGIC 
 
 has to deal often with such binary systems of independent 
 variables. In the world of sensory facts, too, we frequently find 
 one and the same form encompassing a variety of contents at 
 different times and places, and on the other hand, the same con- 
 tent manifests itself in a variety of forms. Moreover the inde- 
 pendent variability goes so far, paradoxical as it may seem, as to 
 permit the one to pass into the other. What is form in one rela- 
 tion becomes matter in another relation. This latter truth is 
 of the greatest importance for the right understanding of the 
 theory of thought that in current discussion calls itself dynamic 
 idealism. 
 
 The serious question for Formal Logic is whether, in this 
 correlation, we can ever escape the necessity of defining each by 
 the other. There are many such circular definitions ; for 
 example, form is that which remains permanent when the matter 
 changes and matter is that which remains permanent when form 
 changes. It has often been remarked that all reasoning is in the 
 last analysis circular, that no definition can escape the indict- 
 ment of begging the question. But whatever position one may 
 take on the vexed question as to the possibility of transcending 
 reciprocal relations in definition and description, we may yet 
 maintain that thought itself does pass from thesis to antithesis 
 and thence to synthesis, although language may lag behind. The 
 third stage of genuine synthesis, that is, the synthesis that does 
 not itself in turn require an antithesis, must elude logical defini- 
 tion. Here it may be said is an instance of a judgment that has 
 no exact counterpart in the realm of propositions; vocabulary 
 has not followed thought, Now the thought which reconciles 
 the contrasting correlation of form and matter can only be 
 described by again employing the word, form. The Real Logic — 
 the contemned Logic iiberhaupt — would be concerned with this 
 form. This is what idealism has always meant by the synthesis 
 of opposites in higher unities. It has not meant, for example, 
 that good is bad, or that past is present, etc., but that these
 
 I III: SAI I ill: OF l\ FERE \< I 
 
 correlatives have something in common. In like manner there 
 must be something in common between the form and matter of 
 thought. 14 Bu1 it miisi nut be supposed thai we are here reaffirm- 
 ing tin- very old view thai the form is always the constanl and 
 the matter the changing characteristic. As I have jusl said the 
 form imi\ change and the matter remain fixed, or the matter may 
 change and the form remain fixed, or finally butli form and mat- 
 ter may vary. A wave, for instance, at no two moments of its 
 Life history has either the same form or the same content. Ye\ 
 the wave unquestionably has an identity thai persists amidsl its 
 changing form and matter. It is an individual because it is the 
 object of a will-alt itude. 
 
 since the time of the greal Stagirite, logic lias been looked at 
 under two aspects: (1) real logic, (2) formal louie. Loth of 
 these expressions are full of ambiguities — ambiguities that are, 
 however, hardly avoidable. Real Logic deals with the problem 
 of com spmuh nee, Formal Logic with the problem of consisti ncy. 
 The truth of correspondence joined with the truth of consistency 
 constitute total reasonableness. The question at issue is whether 
 these two aspects enter into total reasonableness in different 
 degrees of importance. Can the question of coherence be 
 divorced from the question of correspondence? Is correspond- 
 ence, at last, a kind of coherence? These two main senses in 
 which we may speak of the validity of thought, have been the 
 pivotal points around which the recent discussions regarding the 
 nature of inference have revolved. The Instrumental Logic of 
 today denies that there are these two aspects ; it dispenses entirely 
 with the ontological problem. Idealism has always insisted on 
 
 i* Windelband has clearly recognized the necessity of distinguishing 
 between these two points of view. "The two kinds of categories may lie 
 distinguished as transcendenl and immanent in their relation to truth; 
 
 thai I would Bay thai tli institutive categories are existential and the 
 
 reflective arc valid. It is the final task of the system of categories to 
 reunite the two divided series and to discover the forms of thought in which 
 the two fundamental categories, the valid and the existential, are combined 
 into a unity." Ency. Philos. ScL, I. 35.
 
 94 FOOTNOTES TO FORMAL LO<,l< 
 
 the distinction between the ontological and the epistemological 
 problem, even when (as in the case of Hegel) it asserts that 
 I)< nki nhhri ist audi Seinlehre. It declares that the relation of 
 thought to reality is a real problem, and that the recent attempts 
 to solve it by saying that there is no such problem or by asserting 
 that it is of no consequence, is a profound error 
 
 The question, "Is this particular instance of reasoning 
 accurate?" is at heart, always a duplex question. Although for 
 practical purposes we may ignore one or the other of these two 
 aspects, rigorous thought demands that we make the distinction. 
 We may have had in mind to ask whether the inference is itself 
 a manner of Being — whether we have laid hold of the real nature 
 of things through this mental operation. In the second aspect 
 of the duplex question, we disregard coincidence with reality 
 entirely ; we wish merely to know if our conclusion does follow 
 from the premises in accordance with non-contradictory princi- 
 ples. In the face of all these recent indictments we still declare 
 that Formal Logic is the science of that part of reason which 
 is concerned not with total reality and complete reasonableness 
 but with the truth which is contained in consistency. Consist- 
 ency is a part of truth, necessarily, but it is only a minor part. 
 
 The form of thought is unanalyzable and indefinable. The 
 best we can say of it is that it is the mode or manner in which 
 thought is. It is not an external matrix, independent of thought, 
 but is natural to thought. It is intrinsic in the nature of thought 
 itself, and in so far it is an expression of that nature. But it is 
 not a complete expression, any more than the form of a statue 
 is a complete expression of the statue. It is. however, a genuine 
 expression of the inner life of thought ; an expression that is 
 spontaneously taken by thought. To say that thought is deter- 
 mined by this form is inaccurate and insufficient. "What we 
 mean to say is that thought is self -determining in its form. The 
 form of thought is essential to thought, though not equivalent to 
 the fulness of thought ; thought does not subsist without thought-
 
 THE \ ATUBE 01 I \ I I Bl \< / 
 
 form. Thought, as thought, lias lliis form, and withoul it thoughl 
 in so far is non-existent. The form of thought is peculiar and 
 untranslatable. Serious misunderstanding has arisen from the 
 
 "wax and seal" illustration of matter and form of thought. It 
 would be well if this and all other similar figures of speech 
 could be expunged from logical discussions. These similes are 
 largely responsible \'"v confusion of logical form with temporal 
 sequt nee or spatial arrangi m< nt. 
 
 Furthermore, logical form is not the same as thai something 
 in objects that we call the beautiful nor is it thai other some- 
 thing in objects thai we call the good. We cannol escape the 
 conclusion thai there exist in consciousness more than one prin- 
 ciple of arrangement. Bui tins admission must not be regarded 
 an abandonment of our defense of Formal Logic. The elements 
 in a certain sort of consciousness are arranged in a particular 
 way. while the elements in another sort of consciousness are 
 arranged in another way. We have the time-principle, and the 
 space-principle, both existing and acting together in conscious- 
 ness. Also we have the est Ik tic and the moral prim ipli . Things 
 may be satisfactorily arranged in regard to time and space, but 
 yet not be beautiful; or they be harmonious as regards the 
 esthetic principle, and still be lacking in goodness. 
 
 But there is yet another principle thai we must add to the 
 foregoing list. Between the time and the space principle on the 
 one hand, and the esthetic and the moral principle on the other, 
 comes the truth principle, and it this principle with which 
 Formal Logic is concerned. Thus we gel the whole series of the 
 lir< principles of estimate, in which series the logic-principh is 
 the third. There are two aspects to this third principle: in its 
 nighesl aspect, the logical principle is that of truth absolute and 
 entire; in its other aspect it is susceptible of degree, h is not 
 in contradiction to what I have asserted elsewhere to say that 
 the principle of reality or truth lias degree: thai a state of judg- 
 ment may be on the way to the goal of complete truth and per-
 
 96 FOOTNOTES TO FORMAL LOGIC 
 
 feet reality, just as a thing may be on the way to the goal of 
 beauty or of goodness. 
 
 The new positivism which postulates a world of independent 
 objects — brute facts — rests back upon an unwarranted abstrac- 
 tion. It has taken this fundamental relation between form and 
 matter and pressed the correlation to the point of breaking. 
 The matter of thought is something that is finally foreign or 
 indifferent to its form. This indifference constitutes its inde- 
 pendence, since that aspect of thought which is indifferent to a 
 changing aspect, it would appear, cannot be otherwise than inde- 
 pendent. The fallacy in this reasoning, is due to a false analogy. 
 In the physical world, matter does lie in the form, like the 
 pudding in the mould. But the form of thought is not something 
 that is laid over the matter nor is the matter anything injected 
 into the form. The form is only the class of relations in which 
 the essential nature of matter man stand. The systematic view 
 of the ways in which its inner relations may express themselves is 
 thought's form. 
 
 It is unfair to the Traditional Logic to say that it has divorced 
 form from matter, that it has not held form in abeyance and 
 obliged it to wait upon matter. No one has been more explicit 
 on this point than Bosanquet who says, "We cannot and must 
 not exclude from the form of knowledge its modifications accord- 
 ing to 'matter' and its nature as existing only in 'matter.' 
 Again Joseph has said : ' ' The form' and content of thought are 
 not capable of separate consideration, like the mould and the 
 pudding; what from one point of view is form is from another 
 matter, and the same form in different kinds of content is not 
 altogether the same, any more than is the same genus in different 
 species." 10 
 
 It is often believed that any successful indictment of the 
 syllogism will carry with it the condemnation of Formal Logic, 
 
 is Essentials of Logic, p. 50. 
 ib Introduction to Logic, p. 214.
 
 THE NATUBE OF INFEBE \< / 97 
 
 as a whole. Bu1 this dors not follow. The two doctrines are not 
 so interdependent that they must stand or i';ill together. We 
 may, with Bradley, deny the univerality <>)' th.e syllogism, and 
 still hold thai "all reasoning is formal and is valid solely by 
 virtue of its form.*' Every inference belongs to a class. It 
 has its own type, and it moves in accordance with a principle thai 
 governs not only it. bu1 all other members of its class. Bradley 
 is*quite sure, however, that we can never determine the elass of 
 all such elasses. 17 lint this denial thai there is a universal form 
 of thoughl is itself just the final type for which we are Looking. 
 I confess that I see no other than the familiar traditional answer 
 to this difficulty. The agnostic who says there are no final formal 
 principles is asserting that there is at leasl one such principle, 
 namely, the principle that declares that there are no principles. 
 It is alleged that we cannot understand fully the essential 
 nature of the thinking process if we operate merely with symbols. 
 The form of thought is vitally affected hy that which is thought 
 ahout. But the opponents of Formal Logic ignore a distinction 
 that is of very ancient origin, namely, the distinction between the 
 two kinds of assertion that we may make. We either assert a 
 relation between things (or the attributes or condition of things . 
 or else we assert a relation between assertions. This distinction 
 between material implication and formal implication furnishes 
 the incontestable basis for Symbolic Logic. The calculus of 
 propositions — formal implication — is a study thai may he pur- 
 sued independently of any other implication. 
 
 IV 
 
 Many of the attempts that have been made to reconcile the 
 empirical and the idealistic theories of the relation between the 
 
 if Principles of Loi/ic, p. 471. ''No possible logic can supply us with 
 schemes of inference. Son may have classes and kinds and examples 
 reasoning, but you can not have a set of exhaustive types. The conclusion 
 refuses simply to (ill up the blanks you have supplied."
 
 98 FOOTNOTES TO FOBMAL LOOK 
 
 universal and the particular in thought have been reconciliations 
 in name only. They have generally allowed the opposing theories 
 to make assertions that are logically contradictory. And when 
 the pacifier happens to be one of the contesting parties, the recon- 
 ciliation that is effected involves the annihilation of his opponent. 
 But also, equally unsatisfactory has been the reconciliation when 
 the third, or benevolent neutral party, has stepped in. He has 
 generally cancelled all the outstanding differences between them, 
 and left the two theories standing "harmoniously" side by side 
 in the night of thought in which all cows are gray. Obviously the 
 idealist may accept no terms of peace which would deprive reason- 
 ing of its universal character. Nor may the empiricist abandon 
 his own central contention that all reasoning is from particular 
 to particular. The empiricist begins with the sense-presented 
 particular, and proceeds thence in quest of the universal. Failing, 
 however, to reach this goal by the way of the accumulation of 
 particulars — the only pathway he recognizes — he boldly declares 
 that the universal (even if it could be reached) would not be 
 needed. All reasoning is from particular to particular, the 
 universal is a convenience not a necessity. 
 
 The relation between the particulars and the universal may 
 be read off in three ways. We may read it (1) from particular 
 to universal, (2) from universal to particular, or (3) from par- 
 ticular to particular. It would seem therefore that there must 
 be as many different kinds of thinking as there are possible 
 relations here. Now Aristotle did clearly recognize this three- 
 fold relationship and on the basis of these distinctions declare 
 that there were three kinds of thinking. Reasoning from par- 
 ticular to particular he called irapaSei^fia, reasoning from par- 
 ticular to universal iira<ywvr], and finally reasoning from 
 universal to particular, avWoyiafxos. But Aristotle was not will- 
 ing to give to each of these types an independent or coordinate 
 function in knowledge. Although he recognized the importance 
 of analogy and induction, he was firmly convinced that these
 
 THE NAT! BE OF INFEBENl E 
 
 were merely operations subsidiary to real thinking which in the 
 lasl analysis was always syllogistic. Professor Adamson and 
 others have accepted Aristotle's threefold relationship bu1 have 
 se1 up three independent types of inference: namely, (1) from 
 particular to particular, analogical inferei ; (2) from par- 
 ticular to universal, inductive inference; (3 from universal to 
 particular, deductive or syllogistic inference. Bu1 I shall insist 
 
 that each of these types of reasoning expresses only in a partial 
 
 and one-directional way the reciprocating thoughl process thai is 
 
 at the basis of all three. 
 
 Adamson 18 has maintained that all inference is mediate. Bui 
 in setting up these three types of reasoning he has apparently 
 denied Hie necessity of mediation. In his account, each form 
 of thinking deals with two terms only. Bu1 on closer examina- 
 tion we find that each of these binary relations, from particular 
 to universal, from universal to particular, from particular to 
 particular, lias in reality a suppressed third term. When this 
 third term is properly supplied in each instance we discover that 
 the three forms of reasoning are really at bottom the same. No 
 reasoning is merely from particular to universal, nor from 
 universal to particular, nor from particular to particular. Bu1 
 in any complete act of reasoning we are always passing from 
 particular to particular via the universal. 1 '-' Tins pervading 
 identity is to be sure not always nor often overtly operative; 
 therefore by the popular mind and in some systems of philosophy 
 it is declared to be totally absent. Wherever there appears to 
 he inference from particular to particular it is because we do not 
 take the trouble to state the ground, either because, on the one 
 
 is "We may proceed either directly from particular to particular by 
 analogical inference, or indirectly from particular through universal to 
 particular by an inductive-deductive inference which might be called 
 'perduction.' On the whole, then, analogical, inductive ami deductive 
 
 inferences are not the same but three 1 similar ami closely connected 
 processes." Ency. Brit., XVI, 880. 
 
 is Cf. Rosanquet, Logic, II, •"><>. "The conception of inference from 
 particulars to particulars is thus an illusion arising from the activity in 
 inference of presupposed, superficial, or unanalysed universals. ' '
 
 100 FOOTNOTES TO FORMAL LOGIC 
 
 hand, it is so manifest or for the opposite reason, because it is 
 not immediately in view. 
 
 Consciousness is at first neither of a particular seen as a par- 
 ticular, nor of a universal seen as a universal. It is rather an 
 indistinct blending of the two. Succeeding pulsations of con- 
 sciousness are required to differentiate this confused primitive 
 perception into one or the other. Our earliest sense experiences 
 are definitely situated in space and in time. Every perception 
 is present here and now, and furthermore has its causal explana- 
 tion. This would seem to bestow on it individuality, but neither 
 space nor time are real principles of individualism. If spatial 
 and temporal relations were the only distinguishing character- 
 istics, we should never be able to declare that the object of a 
 present perception had not been seen elsewhere or at another 
 time. The perception of the individual or the universal as such 
 is impossible. They are differentiated aspects of a dual act of 
 consciousness. This two-edged act of consciousness is on one 
 side the discovery of certain attributes as uniquely characteristic 
 of one object and other attributes as common to many objects. 
 The particulars with which the empiricist deals are not really 
 particulars, they are the differences in which the universal has 
 exhibited itself. 
 
 Thought, then, always operates by means of a universal. 
 Furthermore, we do not think unless in knowing the part we do 
 also in a sense know the whole. All of our previous and sub- 
 sequent discussion turns upon this principle. Seasoning is never 
 from particular to particular. There is no thoroughfare from 
 one fact to another fact, except by the way of the universal. It 
 is true that in the psychological analysis of the process we cannot 
 discern the ascent to the universal nor the descent from the uni- 
 versal. We see only an apparent transition directly from par- 
 ticular to particular. But the logical analysis always discovers 
 the necessity of the universal. Reasoning can not possibly take 
 place unless there is a universal within which the particulars,
 
 I III: NATUEE OF TNFEEENCE L01 
 
 between which thoughl takes place, are embraced. If each 
 so-called particular were Locked up within the narrow Limits of 
 its own specific constitution, it would be idle to talk aboul pi 
 ing from one such particular to another. Yet this is the assump- 
 tion from which every form of associational theory of thoughl 
 sets out. Each idea reproduces in the contenl of another idea, 
 not only itself, hut in some mysterious way produces also the 
 connecting link between itself and that other idea. 
 
 Furthermore, ii can be shown thai the empiricisl is deluded 
 in his belief that he can make an assertion thai is absolutely 
 particular. No judgment has ever for its subject-matter just 
 bare concrete fact. A particular judgment would be no judg- 
 ment, because as Bradley has said, the subjed would be "com- 
 pletely shut up and confined in the predicate." Such a judg- 
 ment might almost be said to lie a stage prior to hare tautology, 
 it would tell us nothing else about the subject or predicate than 
 that each is just what it is. 
 
 We may, therefore, deny .Mill's contention that "the child 
 who having burnt his fingers, avoids thrusting them again into 
 the fire, has reasoned or inferred, though he never thought of the 
 general maxim, fire burns." When the child avoids thrusting 
 his fingers into the second fire, what warns it away is not the 
 sight of the second fire, as a hare isolated particular. If there 
 were oo more to this second fire than just its bare identical self, 
 the child would, of course, put its fingers into the flame and be 
 burned again. But the second fire is something more than just 
 a particular, it has something over and above its thisness. That 
 from which the child withdraws its fingers is in reality the first 
 fire, which it sees, by memory, in the second tire, [f it should 
 put its finger into the second tire and lie burned, we should chide 
 it with "You didn't think," which for the purpose of the >\<-\', - 
 of the universal, 1 concede is equivalent to "You didn't remem- 
 ber." We avoid the issue when we describe reasoning as a 
 passage from particular to particular, and blink at the universal
 
 102 FOOTNOTES TO FORMAL LO<.l< 
 
 which stares at us from behind the would-be particular. The 
 object of knowledge is never a pure this, it always has a fringe 
 of thatness. 
 
 Mill and the later-day associationists have said that ''what 
 justifies the transition from one particular to another is the 
 resemblance between the two particulars." "We reason by means 
 of the qualities which the two have in common. But this recogni- 
 tion, in the second particular, of the attributes which had pre- 
 viously been found in the first, is the tacit admission of the 
 universal for which we are contending. In the actual thought of 
 the moment we may not consciously distinguish the universal 
 from the concrete instance in which it is manifested. Never- 
 theless, subsequent reflection discovers that the general idea is 
 always there and constitutes the only bridge by means of which 
 we can reason from particular to particular. 20 
 
 20 Cf. Bradley, Principles of Logic, p. 36. "It is not true that par- 
 ticular images are ever associated. It is not true that among lower 
 animals universal ideas are never used. What is never used is a par- 
 ticular idea, and, as for association, nothing ever is associated without 
 in the process being shorn of particularity."
 
 < UAPTEB VI 
 
 [MMEDIATE [NFERENCE 
 
 I 
 
 15 1 'fore considering the question of the validity of immediate 
 inference, I wish to offer a revision of the names Eor the entire 
 system of the so-called immediate inferences. Assuming thai 
 objeets corresponding, to 8 and /' do exist, and furthermore thai 
 
 these classes do not exhaust the entire universe, then the various 
 relations in the universal affirmative proposition 'All N is ]'." 
 may be illustrated by the following diagram. The objections to 
 "Eider's circles" have now been presented over-many times. 
 No one who has ever taught elementary logic is unmindful that 
 the circle notation is incompetent to express properly the rela- 
 tion between species and genus. The genus is not a class thai is 
 divided up into sections called species. Eider's diagrams we 
 all know apply only to the static relations of inclusion and exclu- 
 sion. They are of service only in the calculus of classes and their 
 utility is entirely illustrative. They give no truths which could 
 not have been secured without their assistance. Bu1 they are. of 
 the highest service id students in elementary logic for the proper 
 understanding of the relations within the sphere where they are 
 applicable. 
 
 These relations between two classes and their negatives have 
 long been recognized and several different ways of naming them 
 have been suggested. In presenting this subject to elementary 
 students it is certainly conducive to clarity to have one name 
 stand for one only of these relations, and to have each of the 
 relations designated by a single term. In the majority of the 
 systems of the names so far offered, this has not always been 
 
 [103]
 
 104 
 
 FOOTNOTES TO FORMAL LOGIC 
 
 observed. The most of the names which I have proposed have 
 already been employed by different writers, but I am not aware 
 that any one has offered just this arrangement. If all of these 
 relations had now for the first time been discovered simultane- 
 ously, and a committee of philologists and logicians were set the 
 
 A 
 
 task of naming them, doubtless words derived from vcrto would 
 be used throughout, and probably some attempt would be made 
 to employ in each instance a word more or less suggestive of the 
 relations involved. I know of only one attempt to construct such 
 a simple and uniform terminology — that of Miss Jones. 1 
 
 A most radical departure was proposed by Miss Jones, in 
 substituting reverse for converse. If as I have said, these rela- 
 
 J Elements of Logic, p. 143.
 
 IMMEDIATE INFEBENl I L05 
 
 lions were named <l< novo, probably Miss Jones' suggestions 
 would be adopted. Reverse does suggest better than converse 
 the process of reading a proposition off from its predicate end< 
 Kiit the two names converst and contrapositivt have been sanc- 
 tioned now by so many generations of usage thai it would be 
 well-nigh impossible to make such a change. No one, so far 
 I am aware has adopted Miss .(ones' suggestion. For these two 
 fundamental relations I have therefore accepted the names of 
 established usage. Each of the other names which I have assigned 
 to tin' various relations 1 have found employed by some writer, 
 with the exception of oppositive. In Keynes-' admirable classi- 
 fication and naming of the immediate inferences, which has 
 been followed by Creighton and others, some of the relations have 
 compound designations, as obverted converse, partial contraposi- 
 tive, etc. Other writers have employed long and awkward expres- 
 sions for some of the relations, for example, "immediate infer- 
 ence by privative conception" — the name given to the obverse 
 by Jevons. 
 
 It would be interesting to ask which of these immediate infer- 
 ences the mind passes to first. The ordinary view is that, from 
 the original we step first either to the converse or the obverse and 
 proceed thence by successive obversions and conversions to the 
 others. But if these other relations are all immediate inferenci - 
 we should be aide to pass directly to them from the original. If, 
 however, there are two or more pulsations of thoughl in passing 
 out to the more remote inferences they ought not to be called 
 immediate In discussing the nature of judgmenl 1 have already 
 contended that all thought is in a sense mediate, that every judg- 
 ment is in the end an enthymeme. If the original proposition is 
 an abbreviated syllogism, and if each of the inferences is like- 
 wise an enthymeme, then the true explanation of the entire sys- 
 tem of immediate inferences will be found in the fundamental 
 conception of the syllogism which I shall propose later, namely. 
 
 2 Formal Logic, p. 140.
 
 106 FOOTNOTES TO FOEMAL LOGIC 
 
 thought manifesting itself through the threefold relation of 
 genus, species, and particular. The immediacy of the so-called 
 immediate inferences is psychological not logical. 
 
 Objections have been raised to all such extensions of Euler's 
 diagrams. These criticisms are for the most part based on the 
 existential import in the original proposition. It has been main- 
 tained by Venn 3 and other symbolic logicians that the two 
 assumptions that we have made concerning the original propo- 
 sition are unwarranted. The proposition from which we start 
 it is said, tells us neither (1) that 8 and P exist, nor (2) that 
 non-8 and non-P exist. But I think this is not a serious objec- 
 tion. Any explanation of immediate or mediate inferences is 
 confronted always with the fact of a multiple hypothesis con- 
 cerning existence, quantity and quality. We simply contend that 
 the operation of inference here involved is unconcerned with 
 these hypotheses. The process can carry along several hypo- 
 theses as well as one ; it accepts what is given it and passes it 
 along, unchanged, into the conclusion. This process of carrying 
 along a multiple hypothesis we shall find best illustrated in the 
 case of inversion — the most criticized of all the immediate infer- 
 ences. Venn has objected to the hypotheses of the Eulerian nota- 
 tion because they are very remote from the popular view. Formal 
 Logic, however, should not concern itself with the popular view, 
 but with the actual facts. All teachers of the subject bear testi- 
 mony to the fact that elementary students accept easily the 
 assumption of the existence of 8 and P and their negatives ; it is 
 the assertion that one or more of these classes may he non-existent 
 that comes as a surprise. 
 
 sCf. Venn, Symbolic Logic, (ed. 2, London, Macmillan, 1894), p. 154. 
 "From 'All X is Y' we are commonly allowed to derive 'All not-Y is 
 Not-X. ' But this being a universal affirmative must indicate that there 
 are instances of not-Y and not-X, as well as of Y and X. This is cer- 
 tainly very remote from the popular view, which never thinks of insisting 
 that X and Y must not only exist but must also abstain from comprising 
 all existence."
 
 IMMEDIATE INFEBE V< /. 107 
 
 II 
 
 In a previous chapter we saw thai the several definitions of 
 inference which were examined seemed all to be circular ; nor was 
 our own definition Eree from the suspicion of a return to itself. 
 In fact we accepted the circle in defining as by no means a 
 calamity. There are no ultimately simple units, or points, for 
 thought. It begins with circles, hut circles whose radii are zero, 
 so to speak — whose elements are concomitants, nol sequents. We 
 shall find the same difficulty confronting us when now we come 
 to look more closely into the nature of the so-called immediate 
 inferences. 
 
 Every proposition has a meaning, often several; and these 
 meanings have meanings. I have already spoken of these direct 
 and indirect meanings as first and second intensions of proposi- 
 tions. I employ these expressions, first and second intensions, in 
 quite the same sense as the scholastic usage. In the scholastic 
 terminology, the first intension is a judgmenl aboul a thing, and 
 the second intension a judgment aboul a judgment. Now the de- 
 hated question whether the immediate inferences of ordinary logic 
 are real inferences or just interpretations, transformations, or 
 to use another suggestive expression, alternati readings, depends 
 on whether we can estahlish any real distinction between the 
 first and second intensions, the direct and the indirect meanings 
 of propositions. The defense of Formal Logic depends upon the 
 validity of this distinction. If the second intensions are wholly 
 dependent upon the first intensions — if they have no domain 
 within which they may vary independently of the first inten- 
 sion — then the distinction between formal reasoning and material 
 reasoning breaks down. However, if such a distinction can be 
 made out, we shall be able to say that any movement of thought 
 in which we pass merely from one direct meaning to another 
 direct meaning, is only an alternate reading: whereas if thought 
 passed from a direct to an indirect meaning we should have a 
 true inference. Perhaps this distinction has already been in
 
 108 FOOTNOTES TO FOBMAL LOGIC 
 
 the minds of those authors of elementary textbooks who have 
 distinguished between implied and inf( rred judgments. But I 
 believe the distinction in kind, upon which I am here insisting, 
 can be described with a higher degree of accuracy by the terms 
 direct and indirect than by implied and inferred, or actual and 
 virtual. I have already tried to point out the failure of all those 
 definitions of inference which rely upon the pseudo-distinction 
 between the e>ld and the new, or that attempt to describe infer- 
 ence as progress of thought, without pointing out the necessity 
 of both identity and difference, action and reaction, in short, 
 genuine reciprocity. As an illustration of such a definition I 
 quote from Davis: 4 
 
 An implied judgment is one that actually exists together with the 
 given judgment, either merely in thought or involved covertly in the 
 expression. An inferred judgment is one that only virtually or poten- 
 tially exists in the given judgment, and is derived from it. The statement 
 of the one is nothing new; there is no advance, no progress of thought, 
 but only its full expression; that of the other contains something new, 
 there is a step forward, a progress of thought. In the inferred judgment 
 there is always either a different subject, or a different predicate, from 
 that of the premise, and perhaps both. 
 
 It seems unwise to use the terms implied and inferred to describe 
 the different moments in thought, since so many writers on 
 Symbolic Logic use implication and inference as synonyms, or 
 nearly so. And do not all such expressions as "step forward" 
 or -'covertly involved" themselves covertly involve the whole 
 problem that we are attempting to solve? I am of course fully 
 aware that the terms, first and second intensions, or direct and 
 indirect meanings, are by no means free from the objection I 
 have raised against the other terminology. 
 
 It is quite impossible, I think, to distinguish between imme- 
 diate and mediate inference on the ground of a numerical differ- 
 ence in the elements involved in the process. This is the most 
 ancient of all the distinctions. But when we assert that in an 
 immediate inference the conclusion is derived from one premise 
 
 * Theory of Thought (New York, Harper, 1878), p. 103.
 
 / 1/ \ll: HI ill: INFERENCE L09 
 
 alone, we have substituted one difficulty for another. The vital 
 
 point at issue is jusi the question aa to whal constitutes orn 
 proposition. It' the on< nrss of tin* judgment in tin- mind is 
 always to be round in the oneness of the spoken or printed 
 proposition then Logic is truly just another name for Grammar. 
 And this is. in fact, whal some philologists claim. Logic, they 
 say, being compelled to wait upon Language, is entirely a1 the 
 mercy of the accidents of speech. This obviously revives the 
 old question so prominent in the writings of Eamilton, Mill. 
 Mansel and Whately. whether Logic deals with language, thoughl 
 or things. Here, as I have remarked in an earlier chapter, is 
 where the doctrine of the quantification of the predicate has its 
 st rong hold, for that docl rine is precisely such a scheme for filling 
 out the shortcomings of language Won- it not for the inertia of 
 our human nature, which in language, as elsewhere, follows the 
 line of least resistance, the expression of thoughl would be ade- 
 quate to thought itself, and there would probahly be no such thing 
 as inference. When one goes into an East Side restaurant and 
 hears the waiter call out an order, "Hot cakes and" — or, "Ham 
 and," one has an illustration of Ihe economy of language. In 
 the mind of the cook in the adjoining kitchen one would find 
 the inference. However, the risk is taken, we economize effort 
 and say less than we think. But we pay the penalty for the 
 indolence of language in the perpetual necessity of making^good 
 the omissions by the process that we call inference. All efforts 
 to reduce Logic to Grammar have their origin in the failure to 
 observe this distinction, which I have already urged, between 
 the interpretation of a proposition and the deduction of in} 
 i net s from a judgnu nt. 
 
 To use a mathematical metaphor, which 1 admit is somewhat 
 riskful, we may say that there is both a one-dimensional and 
 two dimensional thought. One dimensional thought is repre 
 sented by the Aristotelian system of propositions with unquanti- 
 fied predicates. Two-dimensional thought is represented in the 
 Ilamiltonian system of propositions with quantified predical
 
 110 FOOTNOTES TO FOllMAL LOGIC 
 
 For example, in the universal affirmative proposition "All 8 is 
 P" in the one-dimensional system of thought we are told of one 
 relation which the predicate has. In this system when the predi- 
 cate attaches itself to the subject it reserves the privilege of 
 other attachments with which 8 is not concerned. Situations 
 might arise in which S would be justified in knowing P's other 
 attachments, and with such situations only the system of propo- 
 sitions with quantified predicates would be competent to deal. 
 If we regard the subject in extension and the predicate in inten- 
 sion, "All S is P" means that the objects in the class 8 all have 
 the attribute P ; but the proposition does not tell us, and we have 
 no right nor need to know whether P is an attribute of any 
 other object. P could be faithful to every requirement of a 
 qualifier of 8 and qualify other objects also. The question as to 
 what else, if anything, P does qualify is a perfectly proper ques- 
 tion, but this lies in a second dimension of thought. The query 
 arises "where or what is 8?" and the answer is "All 8 is P." 
 Then a second query arises "where or what is PV' This is 
 answered by the Hamiltonian A or U. But now it should be 
 noted that the second question does not arise simultaneously with 
 the first ; it is suggested by the answer to the first. The fact that 
 language has rarely provided the Hamiltonian forms, shows 
 clearly that the one-dimensional Aristotelian forms are entirely 
 adequate to the first questions. Now I believe this distinction 
 between first and second questions has an important bearing 
 on the question of the validity of immediate inference. An 
 immediate inference always involves the transition from the one- 
 dimensional system to the two-dimensional system. The only 
 genuine inference, therefore, is one in which thought passes 
 from a categorical to a problematic proposition. 5 
 
 5 Bradley, Principles of Logic, p. 390. "The truth is that, if you keep 
 to categorical affirmatives, your conversion or opposition is not rational, 
 but is simply grammatical. The one conversion which is real inference 
 is a modal conversion, and that presupposes a hypothetical character 
 in the original judgment. ' '
 
 IMMEDIATE I Ml. I: I. w / ill 
 
 III 
 
 As we have already had Erequenl occasion to remark, mosl 
 definitions say thai an inference is immediate, qo1 because it is 
 obvious or direct, or is grasped in a single beat of consciousness; 
 it is immediate no matter how many so-called steps are required 
 to reach it. provided no other information is used than what 
 was given in the one original proposition. The immediate infer- 
 ences have hem so denominated because thoughl seems to pass 
 from one judgmenl to another without the assistance of a middle 
 term. Bul this conventional distinction between mediate and 
 immediate inference is sadly defective in fundamental insight. 
 A common ground is required quite as much in immediate as 
 in mediate inference, as a means of bridging the gap between 
 the two judgments. We pass from one particular judgment 
 to another particular judgment only because both are embedded 
 in a universal. All thought is from particular to particular via 
 the universal; and moreover the certainty and value of the con- 
 clusion in any form of reasoning — immediate or mediate — 
 depends upon the grip we have upon the universal. 
 
 The logician therefore has to contend with this embarrassing 
 fact that propositions, as men use them, are not always univocal. 
 It is this ancient question of the precise determination of what 
 is implied in a proposition, and what is extraneous matter, that 
 is the cause of the difficulty which so many recent writers find 
 in these transformations of propositions which have now so long 
 been called immediate inferences. It is evident that, when one 
 of these ambiguous propositions is given to the logician to 
 operate upon, he must insist that yon shall announce beforehand 
 in which one of the several meanings he is to take the proposi- 
 tion. However, this task of determining the precise meanings 
 of propositions belongs to the person who announces it — to the 
 rhetorician or grammarian. If he does not fix the meaning, the 
 logician must not he blamed for drawing his inference from the
 
 112 FOOTNOTES TO FORMAL LOGIC 
 
 proposition in the form of hypothetical alternatives correspond- 
 ing to the alternatives implied in the original proposition. It 
 sometimes happens, however, that even where the proposition 
 from which we start seems unambiguous and categorical we can 
 not infer a truth equally unambiguous and categorical. This is 
 said to be the case with the relation which has commonly been 
 called inversion. The inverse may be defined as "a proposition 
 having the negative of the original proposition for its subject 
 and the original predicate for its predicate."'' The inverse of 
 "All 8 is P" is "Some non-8 is not P." The inverse has also 
 been confused with the eontrapositive, and I need only refer to 
 the many other special uses of the word in algebra, geometry, 
 mechanics, music, etc. 
 
 The opponents t»f immediate inference have attacked inver- 
 sion as, in their opinion, the weakest place in the system of imme- 
 diate inferences. But I submit that no logician of repute has 
 ever claimed universal categorical validity for the process of 
 inversion. Keynes, who was the first to give a thorough treat- 
 ment of this subject, most carefully pointed out the limits of 
 inversion. He says: "It is indeed quite impossible to justify 
 the process of inversion in any case without having some regard 
 to the existential interpretation of the propositions concerned. 7 
 Again, Welton says: "An inverse from a true proposition is 
 not necessarily true when stated categorically. ... It is thus 
 seen that these mediate inferences are of extremely small impor- 
 tance ; we give them chiefly for the sake of completeness. 8 
 
 c The word inverse is employed by mathematicians ami logicians in 
 several senses. Professor Royce defines the inverse as follows: "When- 
 ever the proposition (a R b) is true, there is always also a relation, often 
 symbolized by R, in which b stands to a. This may be called the inverse 
 relation of the relation R. Thus if: "a is father of b," "b is child 
 of a" ; and if one hereby means "child of a father" the relation child of 
 is, in so far, the inverse of the relation father of." Ency. Philos. Sri., I. 97. 
 
 7 Keynes, Studies and exercises in Formal Logic (ed. 4, London, Mac- 
 millan, 1906), p. 217. 
 
 s Ma a mi] of Logic, p. 305.
 
 IMMEDIATE INFEBENl I L13 
 
 Bui granted thai inversion is a process thai often yields a 
 hypothetical conclusion -sometimes even doubly conditional — 
 this docs qo1 destroy the practical value of these inferences. It 
 is no1 true thai a partial truth is no truth. The hypothetical 
 
 conclusion is distinctly "better than nothing." All Languages 
 are frill of "it's." and "if" they did no1 correspond to some- 
 thing practical and ;ds<> something theoretically defensible they 
 would have been eliminated long ago. In tin- business (if nar- 
 rowing down the complexities of alternatives which we meet 
 everywhere in the world of experience, we do not wait until we 
 have achieved certainty. In our search for truth it is greatly 
 worth while to be warned away from error by the destruction of 
 hypotheses one at a time. This we saw is the function of the 
 infinite judgmenl which some logicians have characterized as 
 meaningless and worthless. 
 
 There is a prevalent delusion among the enemies of tradition 
 that Formal Logic is a collection of rules which furnish guid- 
 ance of a positive character in the search for truth. But not 
 even its most ardent defenders have held that it is a direct 
 organon of knowledge. It is primarily by warning men away 
 from error, that Formal Logic helps them in their efforts 1<> reach 
 truth. In deducing the inverse the logician does not, as has 
 been asserted,''' attempt the absurdity of proving foxes do unt 
 hurl,- from all <1<></s bark. Now in the first place, before attempt- 
 ing to draw any of the immediate inferences from .1// dogs bark, 
 we must remember that this proposition is ambiguous, or to be 
 more accurate, it is brimful of suggestions, meanings and impli- 
 cations of meanings. It is in short a portmanteau proposition. 
 The Logician calls upon the grammarian to fix its meaning, for 
 not until then can he determine with accuracy the implications 
 or inferences from the meaning. We ask this proposition, among 
 others, these questions, Do d<></s exist; Is //"/•< <ni>ithi)i<i that 
 barks; An then beings other than </<><is: Is th< >■< anything 
 
 » Cf . L. E. Hicks, in an article mi "Euler'3 circles and adjacent 
 spare, •' Mind, a. s. -XXI | L912), 413.
 
 114 FOOTNOTES TO FOIiMAL LOGIC 
 
 that does not bark? Also we may inquire (note now the double 
 query), If there are beings other than dogs; are there any of 
 thesi beings that do not bark; also, // there are beings that bark 
 and if some of these are not dogs, are there beings that are not 
 dogs that do not bark, and how many. It is evident that some of 
 these are questions concerning the meanings of the propositions 
 and some are questions concerning the implications of the mean- 
 ings. Some are first intensions and some second intensions. 
 Among the former there is obviously the question of the existen- 
 tial import of the proposition. The logician can not, indeed, 
 peremptorily demand that these meanings be fixed, but he can 
 say categorically that if they are not so fixed any doubt that 
 remains will not affect the process of inference but only the 
 conclusion. The inferential process, he insists, is unerring; it 
 carries along unchanged any uncertainty that is handed to it. 
 Now to the latter question, which it will be observed is the 
 inverse, the logician replies, Yes, there are (on these conditions) 
 some beings that are not dogs that do not bark. We see, then 
 that the logician merely says he can warn you away from error 
 in your quest for an animal that does not bark. You have 
 been told that all dogs bark and you begin your search for an 
 animal that does not bark, whereupon the logician tells you 
 categorically that you must not look for the animal that does 
 not bark among dogs, but if you are to find it at all it will be 
 somewhere in the region of beings that arc not dogs. The inver- 
 sionist is prepared to treat a universal negative proposition in 
 a like manner, although there is greater uncertainty about the 
 meanings of the original proposition. As I have remarked, he 
 is not disturbed by the existential import of the proposition. It 
 is a matter of common observation that the predicate in the E 
 proposition need not exist in the same universe as the subject. 
 But this does not affect the process of inversion, or any other of 
 the immediate inferences. Such restrictions as are imposed by 
 the existential import of the proposition are passed on intact
 
 IMMEDIATE l\ FEEE \< I. 115 
 
 into the conclusion. We are challenged to find the inverse of 
 No mathematician can squan tht circU and we are told that 
 to do so we must perpetrate the absurdity of inferring from 
 No matin unit ician can squan tin circh thai 8onn om who is 
 not a mathematician run squan tin circle. If this is all thai the 
 process accomplishes it would, indeed, lie "inversion silliness." 
 But here again, the real function of inversion is to warn you 
 away from error. 5Tou set ou1 in search of some one to square 
 the circle Having discovered that no mathematician can per- 
 form the feat, you announce this to the inversionist, who there- 
 upon replies, "if that is so and you still persist in your search, 
 I can tell you most positively that if you are to find anybody 
 who can square the circle, // must bi someont among thos( who 
 art not mathematicians." No inhabitants of Thessaly ever saw 
 a centaur. The categorical inverse of this proposition, derived 
 from a thrice-conditioned premise, would read, //no inhabitant 
 of Thessaly ever saw a centaur ami if anybody ever did. it 
 must have been someone who was not an inhabitant of Thessaly, 
 if there are any such. Dr. Mercier disposes of the inverse in 
 his customary cavalier fashion. He says the inverse 
 
 ... is arrived at by a method so complicated that T will not trust myself 
 to attempt it, but will take, from a standard textbook, the following 
 example: "Every truthful man is trusted" — Inverse, "Some untruthful 
 men are not trusted." Some logicians doubt the legitimacy of this form 
 of Inference; and I must confess to misgivings about it; for, if it is 
 valid, 1 see no reason why it is not equally valid to infer from "Every 
 truthful man is mortal" to "Some untruthful men are not mortal." This 
 puts on inveracity a premium, which is scarcely to lie expected from the 
 justice of Providence; and, what i^ more to the purpose, does not seem 
 to me to be implied in the postulate. 10 
 
 Bu1 a valid non-contradictory inference of the hypothetical sort 
 that I have described can be drawn by inversion from Dr. 
 Mercier's example. Every truthful man is mortal, as follows: If 
 v\('vy truthful man is mortal then if there are any beings that 
 arc not mortal thev will be some of those beings that are qo1 
 
 i" Nt w Logic, p. 290.
 
 lit! FOOTNOTES TO FORMAL LOGIC 
 
 truthful men. And this is an inference that a just Providence, 
 to whom Dr. Merrier appeals, may safely accept. 
 
 It is evident that the process of inversion is adequate to any 
 of the several possible situations which the existential import 
 of judgment imposes. Both subject and predicate and their 
 negatives are existent in the same universe of discourse. This 
 is assumed to be the case where no information to the contrary 
 is furnished the logician when he begins his task of inferring. 
 If any other meaning is intended by the original proposition the 
 logician expects to be informed, for example (1) that neither 
 subject nor predicate exists, (2) that one exists but not the 
 other, (3) that either subject or predicate may be practically 
 and perhaps theoretically without a contradictory. 
 
 Xow it should be remarked that we are not here concerned 
 with the question whether this conclusion is a "new" truth; 
 that is a question which concerns the whole class of so-called 
 immediate inferences. Nor should we object seriously if some 
 one should maintain that this process of inversion is neither an 
 immediate nor a mediate inference as those operations are com- 
 monly defined. There is a striking resemblance between inver- 
 sion, when it is expanded into a form that exhibits all of its 
 parts, and that one of Russell's "ten axioms'" of Symbolic Logic 
 which he has called the Principle of Importation. "The prin- 
 ciple states that if p implies that q implies r, then r follows from 
 the joint assertion of p and q. For example : ' If I call on 
 so-and-so, then if she is at home I shall be admitted" implies 
 "If I call on so-and-so and she is at home, I shall be admitted." 11 
 
 IV 
 
 The criticisms of inversion which I have attempted to answer 
 all rest back upon an alleged failure to regard the existential 
 import of propositions. Another objection has been raised, 
 
 ii Principles of Mathematics, p. 16.
 
 IMMEDIATE I Mil; I. Ml. 117 
 
 namely, thai the process involves an illicil distribution. In "All 
 8 is /'," P is undistributed while in the inverse "Some no 
 is not /'." /' lias become distributed. I think there is here a 
 serious misunderstanding as to the meaning of distribution. The 
 medieval law concerning distribution stated that oo term musl be 
 distributed in the converse if it was not distributed in the con- 
 vertend. But now it should be observed thai i his law was 
 intended only to apply to conversion, where the prior require- 
 ment had been imposed, namely, thai the quality of the proposi- 
 tion must not be changed. However, in the obverse, retrovei 
 contraverse, inverse, the quality of the proposition has suffered 
 a change in passing to the inference; and here a differenl inter- 
 pretation of distribution is required. The distribution of terms 
 in negative propositions does not. mean the same thing as the 
 distribution in the affirmative proposition. The failure to 
 recognize this fact, has brought confusion into discussions con- 
 cerning the validity of inversion, as we shall see presently. A 
 term is said to be distributed when we know something about 
 every member of the class designated by the term. In the propo- 
 sition "All S is P," S is distributed because we know something 
 about every member of the class S, namely, that it is a /'. 
 
 But in the E proposition, "No 8 is /'." while we may say 
 again that S is distributed because we know something about 
 every member of the class, this knowledge is of a differenl kind 
 from what we bad in the case of the .1 proposition. In "No S 
 is I'," I know something about every S, namely that it is not a /'. 
 and this I know indirectly. This indirect process, when mad'' 
 explicit is as follows: first and most fundamentally I know 
 thai "»s Y is not non-8" and then because /' happens to be some- 
 where in the region of non-8 (though 1 am quite ignoranl of 
 just where it is) 1 know that "S is not /'." We met this diffi- 
 culty in the chapter on the infinite judgment. We saw thai 
 negation is always a degree more remote from reality than 
 affirmation. Every significanl negation, when fully expanded
 
 118 FOOTNOTES TO FORMAL LOGIC 
 
 reads: Since P is in the region of non-S, and since 8 excludes 
 non-8 it excludes that which is included in non-8, namely P. 
 
 But now, referring to the diagram for the universal affirma- 
 tive proposition on page it would seem that if P is undis- 
 tributed, non-P should likewise be undistributed. This non-dis- 
 tribution of P we have represented in the diagram by the dotted 
 lines, indicating that the class P is undefined. So far as 8 is 
 concerned, P might widen its sphere of application as far as it 
 pleased, even to the extent of pushing non-P off the map of 
 existence. However, if this dotted line marks the boundary 
 between the two classes P and non-P, it would seem that non-P 
 should have the same indefinite range as P. But we have not 
 told the whole truth about the circle P when we have said that 
 its expansion outward is unlimited, we must observe that its 
 contraction inward is definitely limited. It is this lower limit 
 which the very nature of the universal affirmative proposition 
 permits us to disregard, that in turn becomes an upper limit for 
 the expanding class non-P. Non-P may expand only to the 
 limit to which P may contract. This anomalous fact is exhibited 
 also in the process of obversion. In "All 8 is P," P is undis- 
 tributed, but in its equivalent ''No S is non-P/' the non-P is 
 distributed. 
 
 But this apparent contradiction in the medieval law of dis- 
 tribution when it was applied beyond conversion, did not attract 
 the attention of logicians until the process of inversion was 
 reached. Now although the difficulty has become more acute 
 in the case of inversion, it is nevertheless in my opinion, precisely 
 the same difficulty that has just been pointed out. Keynes 
 noticed this difficulty in the apparent violation of the Law of 
 Distribution and gave an explanation of it that has been followed 
 by Creighton and others. 
 
 It will be remembered that we are at present working on the assump- 
 tion that each class represented by a simple term exists in the universe 
 of discourse, while at the same time it does not exhaust that universe;
 
 IMMEDIATE INFEBE \< I. 
 
 in other words, we assume thai 8, not 8, not /', .-ill represenl existing 
 
 classes. Tliis assumption is perhaps specially important in tl ase of 
 
 inversion, and it is connected with certain difficulties thai may I 
 already occurred to the reader. In passing from All 8 is P to its In 
 Bom* not S is not P there is an apparent illicit pr< which it is aot 
 
 quite easy either to account Cor oi explain away. For the term /'. which 
 is undistributed in tin 1 premiss, is distributed in the conclusion, and 
 if the universal validity of obversion and conversion is granted, it is 
 impossible to detect any flaw in the argument by which the conclusion 
 is reached. It is in the assumption of the existence of the contradict) 
 of the original predicate that an explanation of the a].]. aunt anomaly 
 may be found. That assumption may be expressed in tin- form 8onn 
 things an not P. The conclusion Somt not-8 is not I' may accordingly be 
 regarded as based on this premiss combined with the explicit premiss. 
 All S is P, and it will be observed that, in the additional premise P 
 is distributed. 12 
 
 But now this is merely an elucidation of the difficulty not 
 an explanation oi' it. The true explanation is to be found in the 
 double meaning of distribution. Eacli term in a proposition, as 
 we have just stated, has an tipper and a lower limit to its extru- 
 sion. Our attention need be directed towards only one of tl 
 limits, the other is ignored. For practical purposes we may say 
 that we do have some genuine knowledge even if our class is 
 bounded merely on one side. But for the purposes of exact 
 thinking both the upper and lower limits must be observed, and 
 this is what the doctrine of the quantification of the predicate 
 attempted to accomplish. The inverse of the affirmative proposi- 
 tion "All 8 is P" is as Keynes has said. "Some non-S, is not /'." 
 It is indeed one and the same class P that is considered first with 
 S and then with non-S as subject. But in the one case we see 
 P on its bounded or limited side and in the other the unlimited 
 side. There is no contradiction, according to our point of view, 
 in asserting that /' is both distributed and undistributed. The 
 quantification of the predicate is a device for looking at /' 
 from both sides at once. 
 
 12 Formal Logic, p. 139.
 
 120 FOOTNOTES TO FORMAL LOOK 
 
 X 
 
 The theory of inference which I have proposed in these pages, 
 namely, that every true inference must mark a transition from 
 a categorical to a modal proposition, removes some of the diffi- 
 culties about the particular proposition. It is evident that, since 
 the true particular is always a modal assertion the passage to 
 such a particular is always a true inference. The particular 
 judgment is always a problematic judgment in disguise. "Some 
 8 is P" is equivalent to "S may be P." Venn, and other sym- 
 bolic logicians after him, have defined sonic as not none. This 
 is quite in agreement with one side of the popular meaning of 
 the word. This definition provides an unambiguous relation of 
 somi to its lower limit nom . but there is still an ambiguity in its 
 relation to the upper limit, all. It may include or exclude all. 
 This latter ambiguity, the popular mind also aims to avoid and 
 so prefers the interpretation of some as not all. as well as not 
 none. 
 
 Some is a variable moving toward a limit in two directions, 
 but in different senses. In the downward direction toward none 
 it can not reach its limit, while in the upward direction toward 
 all it may reach the limit. The particular proposition of ordi- 
 nary logic on this view, is semi-indefinite, being defined by its 
 exclusion of none and yet undefined by its inclusion of all. There 
 are thus seen to be, theoretically at least, four possible relations 
 between some and its limiting classes: (1) Some includes none 
 and all, or (2) it excludes them both, or (3) it includes the all 
 and excludes none, or (4) it includes none and excludes all. 
 Some has been identified with the indeterminate class of Symbolic 
 Logic. This is, I think a mischievous error. The some of Tra- 
 ditional Logic has never, even its most liberal interpretation 
 included more than two of the four possible relations between the 
 indeterminate class and its limiting classes, none and all. 
 
 Every such discussion of the meaning of some that intends to
 
 IMMED1 ill. INFEBENt / li'l 
 
 define it in terms of either its limits, all and none, presupposes 
 that these Limits themselves have already been denned. Bui now 
 we should find it difficult to define nom in any other way than 
 by reference to sunn, and it' noTn implies some, we move in a 
 vicious circle in defining sonn as not none. We have here 
 another illustration of what has so often been pointed oul in the 
 recenl discussions, especially those inquiries into the nature of 
 the fundamental concepts of mathematics, thai when we deal 
 with ultimate concepts it is impossible to avoid the circle in 
 defining. 
 
 It lias been alleged thai the particular proposition has for its 
 collateral aim — if not its distinctive purpose —to asserl thai 
 objects referred to by the subjecl do exist. When, for example, 
 I say. "Some California Poppies are scarlet," my primary pur- 
 pose is to assert the existence of such flowers and secondarily 
 only am I concerned to give the information thai their color is 
 scarlet. It is evident that the primary function of the particular 
 proposition is in reality what appeals to he merely its secondary 
 or indirect function. The particular affirmative proposition, 
 "Some X is P," taken at its face value, means to affirm, bu1 in 
 practice its intentions is to deny I he universal negative. Like- 
 wise, the particular negative is employed to deny the universal 
 affirmative. This latter fad is disclosed l>\ the form which the 
 particular negative so often takes in all Languages, " All S is nol 
 P," "Not All 8 is /'." These forms, which perplex the student of 
 elementary Logic, are only rightly understood when the purp 
 to overthrow the universal is considered.
 
 CHAPTER VII 
 
 THE CASE AGAINST THE SYLLOGISM 
 
 I 
 
 The syllogism has always been attacked on two scores. It is 
 alleged, in the first place, that it is structurally defective — it 
 begs the question. Secondly, it is held that it is not universally 
 applicable. Mill criticized the syllogism on the former count 
 and Bradley on the latter. In view of the various attacks, both 
 upon the validity and the universality of the syllogism since Mill, 
 and more particularly in view of the recent developments of 
 Symbolic Logic the Aristotelian account of the subject demands 
 a new interpretation. Aristotle defined syllogism as ''discourse 
 in which certain things being posited, something else than what 
 is posited necessarily follows merely from them." This defini- 
 tion contains five words each of which to say the least, is moder- 
 ately ambiguous. Before the exact scope of this definition can 
 be understood we must know (1) the nature of the "things 
 posited"; (2) what we mean by "positing" or "laying down"; 
 
 (3) in what the difference of the "something other" consists; 
 
 (4) and what is meant by "following," especially (5) "neces- 
 sarily following"? 
 
 We may ask two questions concerning Aristotle's own account 
 of the syllogism. First, what precisely did he himself mean by 
 the definition, as shown by the context. Secondly, granted that 
 Aristotle's own discussion of the syllogism left certain forms of 
 thought outstanding, is it possible to give a wider interpretation 
 to the several words of his definition than he himself gave, so that 
 the so-called asyllogistic types of reasoning may be encompassed 
 by it? If we give to each of these five elements of the definition 
 
 [122]
 
 TEE case AGAINST THE SYLLOGISM 123 
 
 its most liberal interpretation, I believe it can be shown thai the 
 case against the syllogism is not so damaging as tbe New Logic 
 believes. 
 
 The ordinary account of the syllogism as mediate inference 
 is unsatisfactory because it is too vague. The difficulty of dis- 
 tinguishing between the immediate and the mediate in thought, 
 I have dwelt upon elsewhere. So, too. the description of the 
 syllogistic process as a comparison of concepts lacks in explicit 
 ness. Again, Sidgwick, who differs from the other opponents of 
 Formal Logic in his belief that the syllogism is the universal 
 form of thought, proposes a definition which has a number of 
 ill-defined terms. "A syllogism may thus be regarded as con- 
 sisting of three parts: the rule ("major premiss") ; the identi- 
 fication of a case as coming under it ("minor premiss") ; and 
 the conclusion inferred as a result of applying the rule to the 
 ease." 1 If we interpret each of the words in the Aristotelian 
 definition liberally, I think it can be shown that the syllogism is 
 the universal form of thought. In its widest possible meaning 
 it will be found always to consist in tin correlation of genus, 
 species, particular; or universal, particular, singular. I believe 
 thai every thought, be it true or false, will conform to this con- 
 ception of syllogism. It is impossible to think otherwise than 
 in this form. It is hardly necessary to say that this interpreta- 
 tion of the syllogism is meaningless, or at least is plainly open 
 to the two criticisms of lack of universality and begging the 
 question, if the relation between particular and species, and 
 species and genus is taken in pure extension. These relations 
 are sui generis; they are not to be confused with numerical or 
 quantitative relations as ordinarily understood. The relation 
 of particular to species is not the indifferent relation of the one 
 to the many, nor is the relation of species to genus the merely 
 associative relation of part to whole. The relation is vital and 
 reciprocal. This relation might be expressed as universal, par- 
 
 i /•.'/< mi nhirii Logic, p
 
 124 FOOTNOTES TO FOBMAL LOGIC 
 
 ticular, individual ; but we should avoid this designation, because 
 the term individual is highly ambiguous in philosophy. In the 
 nomenclature of Logic singular is j^referable to individual. We 
 should notice also that the term particular is ambiguous. For 
 in the threefold designation, genius, species, particular, and 
 universal, particular, singular, the word particular in the latter 
 series corresponds to species in the former. But this ambiguity 
 in the use of particular is in our common speech as well. We 
 say, "Give me the particulars of this affair"; and again, "What 
 particular sort of flower do you mean?" However, this am- 
 biguity is not so important as in the case of individual. The 
 latter is a difference in kind, the former simply a difference in 
 degree. Individual usually means a single case. When I ask 
 "What particular individual occupies that seat?" I mean to 
 identify or to designate some particular one. But the word is 
 likewise used in an entirely different sense, as when one says, 
 "I like individuality." By this we mean the singular plus the 
 evidences of self -activity. In this sense individual stands for 
 spontaneity, life, growth. An individual is a fountain of ever- 
 increasing newness and originality. This latter use of individual 
 is not pertinent to Formal Logic, where a stick or stone is as 
 good an individual as a soul. Thinking is always viewing in the 
 light of genus, species, particular, or considering the relation of 
 universal, particular, singular. "I think," means that I see 
 this particular in the light of that species, and the species in the 
 light of the genus, or else that I am carrying on the reverse 
 process, seeing the whole or genus, and taking under it the 
 species, and seeing the particular as under the species. Both 
 the rigid syllogism of deduction and the uu-rigid syllogism of 
 induction are consistencies, and must be explained in terms of the 
 threefold relation, genus, species, particular. 2 Syllogizing, or 
 
 2 This view of pan-syllogism I owe to the lectures of Professor Howi- 
 son. An interpretation very like this has been given by Mr. Joseph, 
 although he denies its universality. He says: "The central idea of 
 syllogism is that it works through concepts, or universals. The major
 
 ////•; i .isi: AGAINST THE SYLLOGISM L25 
 
 thinking together, therefore, always involves classification. We 
 can think inwardly from the whole, through the members, to 
 the minutesl members; or outwardly from the minutesl member, 
 1<> the larger member, then to the class, and to the Largesl cla 
 I am not unmindful of whal I am committed to in the assertion 
 thai all thinking is syllogistic and thai this always implies classi- 
 fication. Symbolic' Logic lias shown that the definition of a class 
 is the must importanl and difficull of all the problems of Logic. 
 We may condemn the class view of predication, bu1 we cannot 
 escape from the fundamental fact of comparison that lies some- 
 where ;it the heart of all judgmenl and all judgment about judg- 
 ment, h may be, as Russell and McColl have asserted, that 
 propositions arc more fundamental than classes; this would not, 
 however, affed the theory of pan-syllogism. Thought is a 
 "'relating activity"; from this there seems no escape. But an 
 analysis of any act of comparison or the definition of relation 
 reveals a number of difficulties. We cannot compare on the one 
 hand total identities nor on the other hand complete disparates. 
 Sameness without difference or difference without sameness makes 
 comparison, judgment, or classification impossible. 
 
 This syllogistic process is distinct from that of just perceiv- 
 ing with the senses. The perceptive judgment is different from 
 the cognitive judgment — the former is not a stage on the way to 
 the latter. We do not classify when we see, or bear, or smell, 
 that is to say we do not correlate, or see in a higher unity. In 
 sense as such we do not have unity, only separateness. We may 
 have a pseudo-unity in the association of sensations. Thought 
 is the process of unification in which we harmonize so as not to 
 obliterate the items. We retain their distinctness and discover 
 the harmony between them. Or again, thought is a unifying 
 process, by which we retain the clearness of each part in obtain- 
 ing the whole. Moreover, the two processes of unification and 
 
 premiss asserts, not tlic presence of .1 in every /.' (and therefore in < . 
 among them), but the connection of I :i- such with /.' :is such: hence 
 wherever we find />'. we must find .1." Introduction to Logic, \<. 284.
 
 126 FOOTNOTES TO FORMAL LOGIC 
 
 separation vary inversely, paradoxical as it may seem. The more 
 firmly the integrating power clutches the items the more clearly 
 does the separating actively differentiate them. All this is appro- 
 priately expressed in the name syllogism and without doing 
 violence to its etymology or to Aristotle's own conception of its 
 scope. 
 
 I have already referred to the other aspects of this syllogistic 
 fact which we need to notice before we can obtain a complete 
 view. We still find the statement in textbooks that besides this 
 one form, there are two others ; that the syllogism is only one of 
 three forms of thought, namely: (1) conceptions or notions, (2) 
 judgments, (3) the syllogism. The impression is still too often 
 left with the student that we first have conceptions, and that we 
 then pass on to the combination of these in judgment, and finally 
 to the higher form in which three judgments are connected in a 
 syllogism. Any such mechanical or corpuscular theory of thought 
 is faulty. Thought is not a mere aggregation of symbols of 
 thought. Tin nature of thought is to produce its men > L m< ids; 
 it creates both itself, and its numbers. Thought is a whole, so 
 whole that it furnishes to itself its own members and also com- 
 bines them. The reciprocal process of determining the whole 
 into its elements and the elements into the whole, constitutes the 
 fundamental distinction of deduction and induction — the rigid 
 and the un-rigid syllogism. 
 
 But hereupon it may justly be asked where do we get the 
 distinction between the relation, conception, judgment and 
 reason, and the relation genus, species and individual? To this 
 query we can only reply that both relations are fundamental, 
 unanalyzable and indefinable. We just think our thoughts, and 
 cannot but think them. Every conscious experience that we call 
 thought must stand the light of a syllogism, else it is not a real 
 experience. If we cannot think, that is, syllogize our experience, 
 we do not have any. As to the series, concept, judgment, 
 syllogism, we cannot get along without these names, but the
 
 THE CASE AGAINST THE >) LLOGISM 127 
 
 syllogism is not the last result or producl from the union of 
 judgments, thai were themselves the products of concepts. The 
 concept is not the ultimate elemenl of thought; on the contrary 
 the thought unit is tin- syllogism itself. 
 
 The syllogism is the omnipresent, all-embracing form, denned 
 as the thought that casts itself in the correlated distinction of 
 particular, species, genus, or universal, particular, singular. 
 These three 1 1 ist iuci ions each depend for their meaning on the 
 correlation of the three. A significant, "just this" always pro- 
 vokes the query "just this what?" Hence ii is necessary to tell 
 the species. Someone says to me, "I want you to see this"; I 
 immediately ask, "this what?" Now if I really do see it, it is 
 this or that or the other object that I see. It has correlation 
 (shape, size, color, etc.), and through this con-elation it is con- 
 nected with the species. In looking for the this, we see the color 
 or the shape, and so we connect it directly with species. If we 
 did not take in the others of the species we would not see the 
 this. The singular means nothing except in the light of the 
 particular, and the particular means nothing except in the light 
 of the universal. All perception, all intelligence, is knowing in 
 the light of the whole. Conversely, the whole means nothing 
 without the final this. Without the descending steps in the cor- 
 related things, it is not a whole, it is nothing. The universal 
 without the species and the genus, is an abstraction, is nothing. 
 The abstract singular and the abstract universal are alike noth- 
 ing. Hence a thing that does not contain its own differentia does 
 not exist. 
 
 The syllogism cannot proceed without having parts and a 
 whole upon which to operate. Parts that are just parts — that 
 have no relation to any whole, have no meaning. They are parts 
 of nothing and so are themselves nothings about which nothing 
 can be asserted. Furthermore no judgment is ever just the sum 
 of units that existed prior to the whole which they constitute. 
 The quantitative whole which seems to be composed of units
 
 128 FOOTNOTES TO FOBMAL LOGIC 
 
 qualitatively alike is no exception. This is reached by a process 
 of abstraction in which the parts, having become qualitatively 
 indifferent to each other, have also sacrificed their unique rela- 
 tions to the whole. The whole is thus lost to sight when it is no 
 longer required as the synthesis of the different and differing 
 facts. But no whole, not even the abstract quantitative whole, 
 may disappear entirely. Quantity is just the latent device for 
 holding asunder parts which are qualitatively alike. This thought 
 I shall develop further presently. 
 
 The singular is not made up out of the universal, nor the uni- 
 versal out of the singular, nor the particular out of either. 
 Neither can we start with the all (which is an empty name when 
 taken alone) and from it arrive at the particular, and so pass 
 on to the singular. For this is equivalent to starting with noth- 
 ing, and trying to make of it a lower class, and of this in turn 
 still a lower class, the final result will still be nothing. "We cannot 
 think these things apart ; without the particular and the singular, 
 the whole is nothing, they are all intrinsically correlated, and are 
 not to be taken apart. The syllogism is not a composite, nor an 
 analysis of a composite, but an individual whole furnishing 
 intrinsically its own elements. Thus it is clear that no one of 
 the three forms of thought sets out with one unanalyzable ele- 
 ment. "We do not begin, as the empirical theory of association 
 would have us begin, with thought atoms, then proceed with 
 combinations of these. The syllogism is a harmonic unity, a 
 unity of correlated elements existing intrinsically in correlation. 
 The syllogism in this sense, we repeat with insistent emphasis, 
 is the cardinal fact wherever there is a thought ; it is the universal 
 type of thought. 
 
 II 
 
 It is however, insufficient to say that the syllogism is the uni- 
 versal form of thought, differentiating itself into the syllogism 
 as concept, the syllogism as judgment, and the syllogism as argu-
 
 THE CASE AGAINST THE SYLLOGISM L29 
 
 merit, or that il is the universal, omnipresenl form of thought, 
 the indivisible, correlated unity embracing universal, particular 
 and singular. We musl show how and why this correlation 
 appears in three differenl ways. There is ueed in short of dis- 
 tinguishing between the implicit and the explicit presence of the 
 syllogism. In the concept, the syllogism is only implicitly pre- 
 sent. To bring the implication out in the clearest way, it is 
 uecessary to show, as we have in pari already shown, thai judg- 
 ment is implied in the concept. It is so implied, since the con- 
 cept means nothing unless it is a whole, ensphering a great many 
 marks, or implicit judgments. And it has therefore rightly been 
 
 said that in judg nt, we explicate the corresponding concept, 
 
 winch is the subject of the judgment. In the judgmenl we say 
 that the concept is so and so. If I assert that I have a concep- 
 tion, and I am asked what my conception is. I answer by making 
 a series of judgments. For example, [ am asked, "What is a 
 salamander?" I reply, "It is a reptile, it is scaly, it can stay 
 in the fire without being burnt, etc." Here I am explicating the 
 concept, salamander, by making a number of judgments bring- 
 ing out the various characteristics of the salamander, in each of 
 which judgments I employ a predicate and connect it with the 
 concept by a copula. The concept (as a thought ' is therefore an 
 implicit bundle of judgments. So, also it may be shown that 
 every judgment is an implicit syllogism. Suppose that I assert 
 "X is Y." Yon ask, "What is it to be Y?" I answer " F is Z." 
 Then of course "X is Z." The filling out of the required mean- 
 ing of the judgment makes us go on and complete the syllogism. 
 We can continue in this way indefinitely, until we come to a 
 predicate beyond which we cannot go. This implied process in 
 thought is seeking the real whole, from which each pari takes its 
 significance. 
 
 Every thought implies two elements and their union in a 
 third. All reasoning is from particular to particular via the 
 universal. This uniting act Formal Logic has always preferred
 
 130 FOOTNOTES TO FORMAL LOGIC 
 
 to call the copula. The word is appropriate, yet in one sense 
 quite inappropriate, for copula really means a link or yoke, and 
 suggests an artificial union ; we are apt to think of it as uniting 
 two distinct things. But the elements united in thought are not 
 two distinct things. The truth is, the syllogism is an indivisible, 
 complex, unitary act, and the copula furnishes the principle 
 which both joins and separates the parts of the whole. It is the 
 function of the copula to "couple apart." Bosanquet writes: 
 "In analysing the judgment as an act of thought we may begin 
 by dismissing the separate coupla. " 3 To this we may yield a 
 hearty assent, but there is no good reason why the word itself 
 should not be retained to designate the real act involved in the 
 synthesis of subject and predicate. The copula is the inner activ- 
 ity that permeates each of the two parts and grips them into 
 a whole. Two pieces of magnetized iron that cohere are a better 
 illustration of the function of the copula than the link between 
 two cars. In the case of the two pieces of iron, every molecule 
 in each piece takes part in the enwholing grip. In terms of this 
 act of joining through the copula, we can determine the distinc- 
 tion between the concept, the judgment, and the syllogism. The 
 difference between these three is a difference in the degree of 
 explication of the copula. In the concept, the copula is not 
 explicit at all, but implicit. In the judgment, the copula is 
 explicit, but appears simple, as though on the surface, having no 
 complexity. In the syllogism, the complexity of the copula comes 
 entirely into light. 
 
 It is not only convenient, but necessary for the purposes of 
 exposition and communication of thought, to adhere to the dis- 
 tinction between dynamic and static relations and to say that 
 the syllogism is competent to deal only with the latter. This is, 
 however, a distinction that has to do with "thought expressed"; 
 it does not concern "thought in reality." Such a distinction 
 1)1 inks at the real difficult v. The dynamic relations themselves 
 
 3 Essentials of Logic, p. 99.
 
 THE CASE AGAINST THE SYLLOGISM L3] 
 
 cannot exist, or a1 leasl cannol be thought, withoul a universal 
 within which the apparently intransitive relations are enclosed. 
 Now there are in reality no purely intransitive relations. Even 
 in the temporal series the present harks back to the cast — the 
 effect in a sense causes the cause. 5Te1 the dynamic order and 
 the static order bave something in common, and it is the task 
 of Logic to discover this pervading element. It is, of course 
 true that any reasoning which explains phenomena through 
 causes is not syllogistic in the narrower interpretation. Bui 
 when we take the larger view of syllogism as thoughl exhibiting 
 itself in the threefold relation of singular, particular and uni- 
 versal; or particular, species and genus, we find thai reasoning 
 through causal determination is n<> exception to its scope. 
 
 Common sense reads class relationships in one direction only. 
 It supposes that in any scries of more and more inclusive groups 
 the stability of the smaller group must give way if it interferes 
 with the stability of the larger. The pari is subordinate to the 
 whole. This seems an elemental truth. But the discernment of 
 this truth as an axiomatic principle is a far 1 simpler matter than 
 its practical application. In what does the stability of any group 
 consist, and what constitutes interference with the stability of a 
 larger group, and what precisely constitutes a larger and a 
 smaller group? Merely a cursory examination of group rela- 
 tions reveals the hidden truth that some aspects may always be 
 found in which the smaller includes the larger. In extension the 
 species is included in the genus, but in intension the genus is 
 included in the species. The principle of total one-way inclusion 
 seems a chimera. There appear to be no groups such that the one 
 is in every way included within the other. Real groups involve 
 only transitive and symmetrical relations. The relation between 
 a so-called small group and its including larger group must ever 
 exhibit the fundamental relation between part and whole, in 
 which, as we have seen, the parts and the whole are equally real ; 
 each includes and is included by the other. Neither presupposes
 
 132 FOOTNOTES TO FORMAL LOGIC 
 
 the other, nor is either more real than the other. Neither has a 
 stability to which the other owes, in every way, unquestioned 
 allegiance. Such a view of class relations will, I believe, go far 
 toward vindicating the universality of the syllogism. 
 
 The most difficult and, I believe, the most important of all the 
 problems of Logic is the relation of extension to intension. Upon 
 this distinction depend the vital questions of the meaning of 
 class, the import of judgment, the fundamental metaphysical 
 question of the relation of quantity to quality, and above all the 
 question of the validity and universality of the syllogism. The 
 elementary textbooks find little difficulty with this subject for 
 there is a superficial definition of these words that makes this 
 relation simple and comprehensible enough. Some writers have 
 been aware of the difficulty of defining each of these words in a 
 way that would make their relation in one object intelligible. 
 Jevons, for example, says "I believe that the reader who once 
 acquires a thorough apprehension of the difference of these mean- 
 ings, and learns to bear it always in mind, will experience but 
 little further difficulty in the study of Logic." 4 However, 
 Jevons' own treatment of the subject is most naive and ignores 
 entirely the real issue, namely, the essential incommensurability 
 of the extensive and the intensive series. Aristotle taught that 
 the extensive and the intensive modes of predication were, at 
 bottom, equivalent and the question of priority meaningless. He 
 declares most explicitly that there is no difference between saying 
 that one thing is entirely included in another and saying that 
 the other thing is always a predicate of the one. 5 Mathematics, 
 until very recent times, has always glorified quantity, and the 
 older symbolic logicians taught that the point of view of extension 
 was so fundamental in all our thinking that intension might be 
 entirely disregarded. The philosophers, on the other hand, 
 insisted on the primacy of quality, and declared that the relation 
 
 * Elementary Lessons in Logie (New York, Macmillan, 1914), p. 37. 
 5 C.f. Prior Analytics, I.
 
 THE CASE AGAINST THE 87LL0GISM L33 
 
 between subject and predicate was distorted from truth in the 
 extensive interpretation of judgment. Mill and many writers 
 
 since have insisted that the intension of terms must be taken as 
 both psychologically and logically primary, and extension as 
 secondary. Mill, to be sure, held that some teems have no conno- 
 tation, but only denotation, and thai such terms always denoted 
 the subject directly and connoted its attributes indirectly. Bu1 
 this was the interpretation of the relation for the purpose of 
 communication. Mill himself plainly implied that in thought 
 connotation is primary; but since we rarely have the finalities 
 in a sufficiently definite and tangible grasp, we resort to the 
 denotation in defining or describing the object. A familiar illus- 
 tration of this is found in ordinary intercourse where we often 
 find it more convenient to describe an object by telling when 
 it is than what it is. Hut in all these debates concerning the 
 meaning of extension and intension and the nature of their 
 relation, the contestants never suspected that there might be 
 intermediate positions between extension and intension; or, that 
 since a good case could be made out for the priority of each, 
 perhaps neither was fundamental but that both were correlated 
 aspects of a more fundamental point of view. 
 
 The first difficulty that the naive treatment of the relation 
 of connotation to denotation met was the obvious fact that the 
 law of inverse variation was not universally applicable. It is not 
 strictly accurate to say that as the extension increases the inten- 
 sion decreases and vice versa. I n the calculus of classes where the 
 distinction between subject and predicate is effaced and the con- 
 tent of proposition represented diagramniatically as by Euler 
 and Venn, this may be partly true. However, it is not a faithful 
 account of the psychological process involved. The power of 
 thought to widen its field of attention is not incompatible with a 
 simultaneous deepening of its intensive insight. It is a common 
 practical occurrence and one that has a deep-seated theoretical 
 justification, that, in extending its synthetic grasp over new
 
 134 FOOTNOTES TO FOBMAL LOGIC 
 
 instances, thought is continually discovering attributes hitherto 
 latent. In considering the subject of analysis and synthesis in 
 judgment, and the correlated question of novelty and sameness, 
 I attempted to point out how essential it was to any right under- 
 standing of the import of judgment to see that the synthetic 
 and the analytic functions of thought may both operate each in 
 its own opposite direction. No antinomy is involved in describ- 
 ing certain systems as exhibiting simultaneously integration and 
 differentiation. 
 
 The relation of extension to intension, of quantity to quality 
 is of such vital importance that I wish to pursue this matter still 
 farther even at the risk of indulging in subtleties that may appear 
 to the reader quite out of place in the present discussion of the 
 nature and validity of the syllogism. No idea, which is in the 
 least extended — that is, no quantitative idea can be brought into 
 consciousness by one indivisible act. Any single pulsation of 
 consciousness does yield size, that is Gestalt-Qualitat or form, 
 just as it does quality ; but such a simple act of consciousness can- 
 not give us the notion of extension regarded as a system of. inter- 
 related parts. The notion of true quantity never comes to us 
 in a single beat of consciousness. It is a continuous manifold, 
 and yet a manifold which, though never grasped by one indivi- 
 sible act of mind, is on the other hand equally incapable of being 
 produced by a mere repetition of units, or ultimate, simple ele- 
 ments. We have here, again, the perennial problem of the rela- 
 tion of the part to the whole, of individual to species, of a term 
 to the class of which it is a member. This problem is so closely 
 connected with the question of the relation of quantity to quality, 
 that we may partially solve the difficulty, I think, if we examine 
 it where it appears in another form, namely, in the relation of 
 the arithmetical to the geometrical continuum. 
 
 [Modern mathematics has discovered that the arithmetical 
 and the geometrical continuum are different facts, both for 
 description and explanation. We never pass directly from one
 
 THE CASE AGAINST THE SYLLOGISM 135 
 
 to the other either in practice or in theory. The geometrical 
 continuum resists any attem.p1 numerically to exhausl its mean- 
 ing; and the arithmetical continuum can never be regarded as 
 the first step in the Logical process of the developmenl of the 
 geometrical continuum. All such attempts to derive one con- 
 tinuum from the other are vicious circles. When we respond to 
 the demand for an absolutely single and simple element, we find 
 thai the spatial continuum, which is quantity or extension par 
 < xci III in i . presents insuperable difficulties i < > concept mil analysis. 
 The mathematician responds to this challenge to find ultimate 
 elements by declaring, "There are points." But, when required 
 to define these points, he finds thai they are just the self-con- 
 tradictory outcome of this search for the ultimate elements. This 
 definition is self-contradictory for the reason that when the 
 mathematician reverses the process, he discovers that he cannot 
 get back from his points to the continuum from which he started. 
 No repetition of the point, as such, can give rise to the line, thai 
 is, not the conl inuous or quantital ive aspect of the line. We have 
 here the familiar paradox concerning the discrete and the con- 
 tinuous aspects of quantity. Because of its incapacity to pene- 
 trate things to the bottom of their real natures an imperfect 
 mind must resort to a quantification of them. Let me illustrate: 
 and 0' are two objects which are qualitatively alike differing 
 only in quantity, that is. they are members of a lowest species. 
 Thought first contemplates the object by itself. It discovers 
 that it is unable to penetrate the object to the core of its mean- 
 ing. A certain opacity prevents the finite mind from ever reach- 
 ing the essential, individual nature of 0. But is not yet a 
 quantity, for quantity is never the content of such a single pul- 
 sation of consciousness. Baffled in its attempt to discover the 
 true nature of by internal searching, thought seeks for thai 
 desired information from an external source. It betakes itself 
 to the other of 0, or ()'. which is. however, in itself jusl as 
 impenetrable for thoughl as () was. o and 0' are conceptually
 
 136 FOOTNOTES TO FOBHAL LOGIC 
 
 alike, and yet the mind perceives a difference between thou. 
 Every attempt to explain this difference lands us in an inevitable 
 contradiction. 
 
 But now in this second pulsation of consciousness the quanti- 
 tative aspect of and 0' has suddenly appeared. Quantity is 
 that mysterious somewhat that can not be found in either or O f 
 when contemplated alone but does somehow seem to exist in 
 each when both are viewed together. Quantification might then 
 be described as the result of our finite efforts to discover exter- 
 nally the inaccessible internal meanings of things. Or I might 
 say it is the search for a mediator between objects where the com- 
 plete understanding of each is by the very nature of things 
 impossible. 
 
 Herein lies also the solution of the apparent contradictions 
 in the discreteness and the continuity of quantity. The dis- 
 creteness arises from the necessary duality of the thought pro- 
 cess that produces the quantitative way of viewing things. The 
 continuity is simply the compulsion under which thought lies of 
 holding the two objects and 0' in a unitary grasp of conscious- 
 ness in order to explain the unfathomable mystery of each. From 
 the absolute point of view and 0' of our illustration, instead 
 of being covered by one concept, are provided each with a con- 
 cept of its own which is adequate to its essential nature. A 
 perfect mind has no need to view things under the category of 
 quantity. For finite thought quantity is simply the ever present 
 reminder of the irrationality of sense. Finite thought is, once 
 for all, inadequate to sense. Every this that it contemplates is a 
 this only in appearance. To our limited minds the this reveals 
 only its thisness. But, as I have already pointed out, the thisness 
 of the this contains as a part of its meaning a reference to a that. 
 And now comes the crucial point. Finite thought feels itself 
 irresistibly impelled to search for the that to which the this 
 points, which in reality it must mean to be a this. The mind 
 at once discovers that it has entered upon a hopeless, an unending
 
 THE CASE AGAINST THE SYLLOGISM 137 
 
 task; for, no sooner do we discover the that, which we had hoped 
 would solve the inexplicable mystery thai enshrouds the this, 
 than it turns out to be ool a thai a1 all, bu1 the identical this 
 
 from which our thoughl started. Thoughl has in a fashion, to be 
 sure, solved the puzzle; hut in the solution it has likewise rein- 
 stated its original question. Here we find an explanation not 
 
 Only for the discreteness of extension and its continuity, hut also 
 
 for its infinitude. The process described is evidently of the 
 recurrent type, hut I think il differs in one essential feature from 
 the KetU that Professor Royce has so often described. In the 
 present h'<ttc, the process is in the end a tautological one. Each 
 new member of the KetU has novelty only so long as it is con- 
 templated as a fact still external to the series, that is. as the goal 
 toward which each individual pulsation of thought strives for 
 the moment. Hut as soon as the goal is reached— when once thai 
 new link has been welded into connection with the rest — the 
 novelty it formerly possessed vanishes into an inevitable same- 
 ness with the whole. The novelty is only a transitory aspect of 
 
 'I ssential tautology in the process. The novelty is accountable 
 
 for the discreteness of extension, the tautology for its continuity. 
 
 Ill 
 
 If the syllogism is merely an expression of the relation of 
 classes, where each class is taken in extension only, that is, where 
 the thought is uni-directional, it will truly not compass all the 
 forms in which we may reason. Such class reasoning always con- 
 forms to the following type : (1) the major premise is an enum- 
 erative, universal proposition in which we affirm that each .1/ 
 is seen (by actual observation) to he in the class /',• and (2) the 
 minor premise states that S is observed to he one of these .1/ "s : 
 then (3) the conclusion, X will he in class P. This view of the 
 syllogism has rightly been condemned, firstly, because of its 
 evident tautology and secondly, because it is not universally 
 applicable. The first of these criticisms, namelv. that it is a
 
 138 FOOTNOTES TO FORMAL LOGIC 
 
 pi titio appeared long before Mill's classic assault. It was 
 advanced frequently by Aristotle's own students. The second of 
 the criticisms is very prevalent in recent discussions. As has 
 now so often been pointed out by Bradley, and others, there are 
 many forms of inference, for example, those that are concerned 
 with dynamic relations, in which there are no class relationships, 
 or in which we are not conscious of any such relations. I think, 
 however, that all such relations can be compassed by the class 
 relations when they are given the interpretation I have offered. 
 It is an unwarranted limitation of the scope of the syllogism 
 to restrict its application to the old class view of judgment. 
 There is no mention of classes, that is, classes in extension, in 
 Aristotle's definition of the syllogism: "Syllogism is discourse 
 in which from certain things laid down other, different things 
 follow." The things "laid down" in the major premise are not 
 "laid down" according to any principle of inclusion or exclu- 
 sion. Aristotle was obliged to distinguish (as every logician 
 must) between thought and language. In the actual thought 
 process the relation of an individual to a class was for Aristotle 
 always a relation in intension. But when this intensive relation 
 was translated by him into a form available for exposition and 
 communication it took the inevitable form of a relation in exten- 
 sion. The charge of a petitio can not be brought against the 
 present pan-syllogism. It employs the true universal which is 
 an assertion about things before they have been experienced, 
 and which is in a sense, therefore, always hypothetical. Now 
 since the major premise is hypothetical, and the conclusion is 
 categorical, it is impossible that the latter could have been con- 
 tained in the former. Moreover, when it is said that the conclu- 
 sion contains "new" knowledge, it is not knowledge that is 
 totally disconnected from the premises ; for no process of infer- 
 ence, mediate or immediate can ever deliver such new knowledge. 
 It is new knowledge in the sense that it is then for the first time 
 observed.
 
 TEE CASE AGAINST THE SYLLOGISM 139 
 
 There is abundanl evidence everywhere in Aristotle's treat- 
 ment of the subject Ilia! lie was fully aware of the two kinds of 
 universal propositions— the abstract or pseudo-universal which 
 
 is a collection of actually observed particulars, and the true or 
 concrete universal, which (by asserting a connection of attri- 
 butes) refers not to any definite group of individuals, but to an 
 entirely indefinite group. The pseudo-universal, "All 8 is /'," 
 means, ''Each S (and I have examined and counted them) is a 
 P." The true universal "All 8 is /'." means " 8 as such is P, or 
 if 8 then /'. The question whether the syllogism in its applica- 
 tion of the dictum de omni et nullo involves a petitio as I have 
 said hinges on the sense in which we take the major premise. If 
 this is construed as an historical or enumerative judgment, then 
 manifestly the conclusion is just one of the particulars which 
 has gone into the aggregate, bound together by the all in the 
 major premise. The so-called universal, that is, the enumerative 
 or historical universal is itself merely an aggregate of particular 
 truths and has no greater validity than the particulars which 
 constitute it — it is itself another particular. Aristotle pointed 
 out, and it was an insight that always seemed irrefutably clear 
 to him, that the universal nature of an object could never be 
 reached by examining and counting particular instances. 
 
 But even in a syllogism, where the major premise is a pseudo- 
 universal, just an aggregate of observed individuals, there is 
 often a movement in thought, in which there is novelty in the 
 conclusion. The major premise although strictly an enumerative 
 universal, does not contain the conclusion nor even predict it. 
 The two premises have come to us by different routes and it is 
 only in the combination of the two that the conclusion is reached. 
 For example, if a man should learn from the telegraphic reports 
 that the entire Second Regiment were taken prisoners in the 
 battle of the Marne, and then on consulting the lists in the War 
 Office should find that his son was enlisted in this Second Regi- 
 ment, the conclusion that his son was captured is something over 
 and above the agony of suspense that came from the unsupported
 
 140 FOOTNOTES TO FORMAL LOGIC 
 
 major premise. To the authorities in the War Office, who have 
 before them at one time, both the telegraphic report and the 
 record of enlistments, there is not the novelty in the conclusion 
 that there is for the anxious parent. 
 
 In the perfect mind premises and conclusions are concomit- 
 ants not sequents, and hence all reasoning in such a mind would 
 involve an essential tautology. But for the purpose of com- 
 municating its intuitive knowledge to minds on lower levels of 
 insight the perfect mind would employ the syllogism and the 
 accusation of tautology would be unjustified. On this view, then, 
 the syllogism is the instrument of communication between 
 minds having different degrees of insight into the relations among 
 things. The perfect mind would not syllogize, nor would imper- 
 fect minds, if they all had simultaneously the same degree of 
 knowledge of facts. 
 
 Bradley has condemned the syllogism at times with vitriolic 
 vocabulary. The mildest of the epithets that he has applied to 
 it is "a chimera." And yet he often comes quite near to con- 
 ceding all that its defenders have thought worth contending for. 
 He says: "If it were admitted, on one side, that the syllogism 
 supplies no general type of the reasoning act, it might be allowed, 
 on the other side, that it is a mode of stating the principle which 
 is used in that act. It is universal as a form for showing the 
 explicit and conscious exercise of a function."' This is an admis- 
 sion both of a form and of its univ< rsality. The formalists have 
 never claimed for any of the forms of thought an existence prior 
 to and separated from its concrete setting. They have granted 
 freely that there are no antecedent types or schemes for thought. 
 The form of thought as we have shown in an earlier chapter 
 is a vital constructive principle within the so-called object matter 
 of thought itself. There is some thing in every concrete act of 
 thought that always detaches itself from the thought, something, 
 as Bradley himself has said, that is "more abstract than the 
 argument itself." 
 
 6 Principles of Logic, p. 4s2.
 
 THE CASE AGAINST THE SYLLOGISM 111 
 
 IV 
 
 It may not be evidenl to the reader how much the foregoing 
 
 discussion owes to Kant's well-known defense of the syllogism. 
 The logical doctrine of marks taughl by Kani has bad contempl 
 heaped upon it, particularly by Hegel, who holds it responsible 
 for much of the confusion in tin- discussion of the nature of im- 
 mediate and mediate inference. Hegel said : 'There is no more 
 striking mark of the formalism and decay of logic than the 
 favorite category of the 'mark.' Kant's account of the doc- 
 
 trine has, I venture to think, been much misunderstood and 
 maligned. It will he remembered thai lie defined judgment as 
 the comparison of a thing with some mark, and ratiocination as 
 a judgment by means of a mediate attribute. And, the supreme 
 rule of all ratiocination he stated thus: "A mark of a mark is 
 a mark of a thing itself." Nota n<>!<t< i si nota rei ipsius. 
 
 The criticism that Kant did not prove his dictum deserves 
 only passing attention. It would not be the highest or final 
 rule if it were capable of proof. Any attempt to prove the 
 supreme formula of all ratiocination would be to reason in a 
 circle. Proof would be possible only by means of one or more 
 inferences. This principle claims to be the final anchorage of 
 all certainty in reasoning and can no more be challenged than 
 the indemonstrable propositions of Symbolic Logic. The two 
 criticisms which Joseph 7 has urged against Kant 's principle are 
 more pertinent. However, neither of his objections appears to 
 me a serious indictment. The first is that the rule assumes the 
 minor term is always a concrete thing. Kant would have 
 admitted, 1 think, that this was precisely his intention and would 
 not have differed widely from Bradley's view that the subject in 
 every judgmenl is reality or some definite and therefore con- 
 crete portion of reality. The ipsa res of Kant's formula is just 
 this presented reality to which the ideal content is referred. 
 
 Introduction in Logic, ed. 2, p. 307.
 
 142 FOOTNOTES TO FOBMAL LOGIC 
 
 However much we may differ from Bradley's theory of judg- 
 ment, it seems to me that his central contention that the subject 
 is a concrete datum is unescapable. I do not see therefore that 
 Kant's supreme rule differs essentially from Bradley's definition 
 of inference as the indirect reference of a content to reality. 
 The ideal content, meaning, or attribute is attached to reality, 
 not directly but indirectly by being joined to a meaning already 
 attached. 
 
 The second objection to the formula is that it makes one attri- 
 bute qualify another. This, too, seems an immaterial criticism. 
 In the first place we may contend that there is nothing contra- 
 dictory in the statement that there may be an attribute of an 
 attribute, as Joseph seems to imply. Wherever an object admits 
 rank or psychological priority among its attributes, a later attri- 
 bute, being an attribute of an object already qualified, is in 
 reality an attribute of an attribute. Also the varying degrees 
 in intensity of the quale of sensations are in a sense qualities 
 of qualities. But admitting that there may be an inherent diffi- 
 culty with the conception of an attribute of an attribute (con- 
 struing the expression literally) I think this is not precisely the 
 meaning that Kant intended by the expression nota notae. Mark 
 of a mark, is the better rendering of nota notae than attribute 
 of an attribute. 8 The working of Kant's formula may be illus- 
 trated in the syllogism, Savages are cunning, Indians are savages, 
 therefore Indians are cunning. Cunning is the mark of savagery, 
 and savagery is the mark of the Indian, therefore cunning is 
 the mark of the Indian. Of the three terms in the syllogism two 
 are always taken in connotation, namely, the major and the 
 middle. The minor must always be taken in denotation. In the 
 major premise, both subject and predicate are taken in connota- 
 
 8 It must be observed that the word marie has two meanings. It points 
 both forward and backward ; it is the sign or evidence of something that 
 has been, as well as the prophecy of something yet to come. The glacial 
 scorings are the marks of the ice-age, while a red sunset is the mark of an 
 impending storm.
 
 Till-. CASE AGAINST THE SYLLOGISM L43 
 
 lion ; it affirms thai the attribute of cunning accompanies the 
 attribute of savagery. Bui in tin- minor premise only the i n<-< 1 i- 
 cate is taken in connotation. 
 
 Kant maintained thai the dictum dt omni was subordinate 
 to bis formula, "Whatever is a mark <>1 a mark of a thing is a 
 mark of the thing itself." The former declares thai whatever is 
 true of the concept is true of everything contained under it. 
 This, according to Kant represents a stage in the process of 
 abstraction one step removed from the formula. The concepl 
 itself was derived in the first instance by abstraction from the 
 things which came under it. Thus whatever belongs to this 
 eoneepl will in 1 rut 1 1 be an attribute of an at trihi it e and therefore 
 an attribute of the things from which it has been ahstraeted. 
 
 Kant drew a distinction between pure and hybrid mediate 
 inferences, that we have lost sight of in our later discussions 
 about the universality of the syllogism. The pure inferences 
 are those which require but three propositions. We have a hybrid 
 inference when between two of the main propositions there 
 must be interposed a fourth proposition which is itself an imme- 
 diate inference from one of the others. Kant made this distinc- 
 tion the starting point of his essay on •"The Mistaken Subtlety of 
 the Four Figures." He regarded the first figure only as pure 
 rationcination, since it involved never more than three propo- 
 sitions. 
 
 It is not my purpose to enter into a long discussion of the 
 relation of the later figures to the first. "Without detailed proof 
 I shall say that I believe Kant's position to be fundamentally 
 correct. I am sure, also, that Kant would have explained all of 
 the modern asyllogistic types of reasoning as "hybrid inferences." 
 In his exposition of the fundamentals of Symbolic Logic. Russell 
 has postulated ten indemonstrable axioms, the sixth of which is 
 the syllogism as it is commonly understood. But on our wider 
 interpretation of the syllogism, I believe, all of the other axioms 
 can be explained as either abbreviated or expanded forms of
 
 144 FOOTNOTES TO FORMAL LOGIC 
 
 the fundamental syllogistic fact — thought exhibiting itself in 
 the triadic relationship of universal particular and singular. 
 Let me explain by quoting Russell's seventh axiom: "If q 
 implies q and r implies r, and if p implies that q implies /•, then 
 pq implies r. This is the principle of importation. In the hypo- 
 thesis we have a product of three propositions ; but this can of 
 course be defined by means of the product of two. The principle 
 states that if p implies that q implies r, then r follows from the 
 joint assertion of p and q. For example: 'If I call on so-and-so, 
 then if she is at home, I shall be admitted. ' " ,J I fail to see why 
 this can not be explained as a triadic relation. In fact, Russell 
 seems to resort to such an explanation himself when he says 
 that the hypothesis, although it has three propositions, can be 
 defined by two. Every thought contains three and only three 
 terms, that is, there are only three fundamental nodes or beats. 
 This needs further elucidation. All reasoning is (as we have 
 often had occasion to remark) a movement from particular to 
 particular via the universal. It follows that every inference 
 must have three terms, and that no inference can have less nor 
 more. Inferences have often to do with more than three facts. 
 But it is important to distinguish between terms of inference, 
 that is the significant nodes in the movement of thought and the 
 data of inference, that is, any accidental halting-places. Each 
 of the three terms may be viewed as a system and when its 
 secondary data are combined with the secondary data of each of 
 the others, we get hybrid inferences with apparently more than 
 three terms. To use a railway figure of speech, the main trunk 
 line of thought has three stations where the "train of thought'' 
 must stop. There may, be any number of intermediate stations, 
 however, where it may stop. 
 
 There have been many attempts to give a syllogistic demon- 
 stration of the so-called axiomatic truths and many refutations 
 of these attempts. Bradley has said, "To prove syllogistieally 
 
 9 Principles of Mathematics, p. 16.
 
 rill-. CASE AGAINST Till-: 8YLL0GISM 145 
 
 that, because .1 and C are both equal to />'. they are equal to one 
 another, is quite impossible." Also, "I may suggesl to the 
 mathematical logician that, so Long as be fails to treal (for 
 example I such simple arguments as ".1 before />', and /»' with C, 
 therefore .1 before C," he lias no strict right to demand a hear- 
 ing." 10 Euclid's first axiom, "Things equal to the same thing 
 are equal to each other," has been written in syllogistic form 
 
 thus: 
 
 Things equal to the same thing arc equal to cadi other. 
 
 .1 ami (' arc things equal to the same thing. 
 
 Ami .-. .1 C are equal to each <>t her. 
 
 Hut in this syllogism both the major and the minor premises 
 are defective. The major premise in the syllogism is the axiom 
 itself, and hence not a major premise in the required sense of the 
 word. It would be circular reasoning, vicious in the first degree 
 to use the identical proposition, which is to be proved. The 
 major premise ought properly to read, Things equal t*> II an 
 equal to each otlnr. Bui a more serious fault we find in the 
 minor term, ^1 and C. In the concrete instance of the axiom 
 A = B, B = C .-. A = C. A and C function separately each as 
 a distinct subject. But in the minor premise of the syllogism, 
 by means of which we attempt to validate the axiom, we take 
 unwarranted liberties with .1 and C by attempting to make 
 them function conjointly as a single subject. A and B are. is not 
 the same as A is and 11 is. It is not the intention of the axiom to 
 assert a predicate of A and B as one, but to declare a relation 
 between them. The distinction between the collective and the 
 distributive use of the terms is here in question and it is a form 
 of the familiar fallacy of composition of elementary logic that is 
 committed. 
 
 The argument a fortiori," A is greater than B,""B is greater 
 than C," therefore, "A is greater than r." has 1 n offered as an 
 
 i" Principles of Logic, pp. •"'(!». 360.
 
 146 FOOTNOTES TO FORMAL LOOK 
 
 illustration of asyllogistic reasoning. This, however, may be 
 expressed in the following valid syllogism. Major premise. All 
 cases where, of three things, the first is greater than the second 
 and the second greater than the third, are cases where the first 
 is greater than the third. Minor -pre mist. A, B, C, is a case 
 where, of three things, the first is greater than the second and 
 the second greater than the third. Conclusion. A, B, C, is a case 
 where the first is greater than the third. 
 
 Here again a criticism has been raised similar to that which 
 we have just examined in the case of the. axiom of equals. It is 
 true that these so-called asyllogistic forms of reasoning are not, 
 when reduced to the syllogism, strictly formal. But neither are 
 they strictly material. From the two propositions "A is the son 
 of C," and "C is the son of D," we may infer that "D is the 
 grandfather of A." This is semiformal. It is a valid infer- 
 ence only to one who also knows the "system of relationships." 
 But granted this prior knowledge, the inference within this 
 "system" is evidently formal and capable of reduction to the 
 syllogism. The same is true of the other a fortiori arguments.
 
 CHAPTEB VIM 
 NOVELTY AM) [DENTITY IN [NFERENCE 
 
 I 
 
 I find deplorable disorder and obscurity in currenl discus- 
 sion concerning novelty and sameness, difference and identity, 
 objectivity and subjectivity, independence and dependence in 
 judgment. Some of these difficulties we mel in the previous 
 essay. 1 wish now to call attention to some further related 
 problems. 
 
 The New Logic asserts thai the uniqueness of any mental 
 fact is always of vital importance for some specific purpose; 
 thai in truth, its uniqueness or individuality is driven in upon it 
 from out of that external purpose. We have, here, a new and 
 revolutionary definition of essence. The essence of the fad 
 depends for its essential essence (if one may be permitted such 
 reduplication) upon the varying purpose to which it may be 
 put. In other words there is no essence in the traditional sense, 
 since the fad has no individuality, no character of its own. 
 This doctrine, when applied without reserve, leads inevitably 
 to the conclusion thai there is no stability within the states of 
 consciousness — that there are no laws of thought. And this 
 issue the pragmatist accepls not reluctantly, but even more joy- 
 fully than the ancienl sceptics. In so far as we must take a risk 
 in judgment, each situation is a law unto itself. The old ideal- 
 ists uphold the law thai there shall be law. The new theory 
 recognizes only one law, namely, the law that there shall be no 
 law. However, as we saw when discussing the nature of judg- 
 ment, no idealistic theory of predication denies the novelty that 
 comes with the predicate. Some risk we do take, and must take. 
 
 ■ | 147 |
 
 148 FOOTNOTES TO FORMAL LOGIC 
 
 But something over and above risk there must he in every judg- 
 ment. That which enables the risk to know itself to be a risk is 
 a stable principle of values. 
 
 There are three possible views that we may take upon the 
 question of the relation of stability to risk : Either there is all 
 stability and no risk, as an absolute idealist might aver ; or there 
 is no stability and all risk as the pragmatist in my opinion is 
 compelled to say ; or there is some stability and some risk as the 
 dynamic idealist holds. If practical consequences are the sole 
 test of truth — if the object-matter of judgment is brute force — 
 then thinking is indeed pure adventure. But I submit that it is 
 one thing to say that judgment is practical and hence riskful, 
 and quite a different thing to say that there is nothing else to 
 judgment but its utility and risk. 1 As Professor Hocking has 
 said with such picturesque vigor: "Only he who has tried (or 
 tried to imagine) a pure adventure knows that there is no such 
 thing as a pure adventure; for when you have cancelled path, 
 peak, sky, star, all distinguishable points in space, the adventure 
 itself is abolished. 1 ' 1 " 
 
 We have sufficiently insisted that no relation can dispense 
 with either of the two aspects the within or the between. A 
 relation that attempts to exhibit identity without difference, or 
 difference without identity is no genuine relation, since it omits 
 one or the other of these two aspects. For this reason, as Bosan- 
 quet has pointed out, no single judgment can exhibit a com- 
 plete comparison ; a disjunctive judgment either implied or 
 expressed is required. Every act of relating is an act of com- 
 parison, and comparison always affirms the interdependence of 
 identity and difference — it is redintegration. When we assert 
 
 1 Cf. Bradley, Principles of Logic, pp. 18, 499. ' ' The assertion we are 
 to examine is not that practical influence induces us to judge, or results 
 from a judgment: What is asserted is that judgment is nothing else 
 whatever. . . . We do not mean to ask what sound performances of 
 reasoning are practicable, but what types of argument are flawless in 
 themselves, without regard to the question if any one, or no one, can use 
 them in his work." 
 
 i" Meaning of God i)i Human Experience, p. xii.
 
 NOVELTY AND TDENTI1 ) IX TNFEBENi / L49 
 
 that every judgment affirms or denies an identity in the midst of 
 difference, and difference in the midsl of identity, this must be 
 taken to mean thai we cannol begin with one alone and super- 
 impose the other upon it as an after-effect. Both are presenl in 
 one indivisible moment of consciousness. Although the differ- 
 ence and the identity arc concomitants in every judgment, the 
 dominant emphasis may be shifted from one componenl to the 
 other. Both may be quite indistinct in the first suggestion and 
 the judgmenl may be aimed primarily to develop this inchoate 
 distinction. Again one aspect in the presented con-elation may 
 be faint and the other vivid; here the judgment will aim to 
 reestablish the balance by emphasizing the weaker aspect. - 
 
 In his criticism of the three fundamental laws of thought of 
 Traditional Logic, Hegel proved that the Law of Identity liter- 
 ally interpreted, cannot possibly he an expression of the activity 
 in any phase of a living judgment. If A is A, states a sheer 
 tautology, it is no judgment. It proposes to say something, hut 
 ends by saying nothing. It is worse than idle breath, for it has 
 not even asserted identity. The real Law of Identity "A is .1 ' 
 means that, whatever is true of A in one reference is true in 
 another. 3 
 
 The difficulty about the conception of identity and difference 
 would be less puzzling if instead of the conjunction <nnl. we 
 used some other word to describe the relation involved, for 
 example, identity in or with, or because of difference. And is a 
 highly ambiguous word. In Symbolic Logic it has been found 
 very accessary to distinguish among its several meanings. For 
 the present discussion the obvious warning is that uinl must not 
 
 - Bosanquet, L<><ii<-. I, .'50. "As regards the affinity between Distinc- 
 tion and Identification, they are obviously two sides of the same pro 
 and it is idle to ask which came first. So far as we ran see, Conscious] 
 or at least Intelligence, must begin with both." 
 
 3 Symbolic Logic which is rendering a most important service to exact 
 thinking offers a definition of identity that is quite free from the per- 
 plexing ambiguities that have beclouded it in the past. Cf. Russell, 
 Principles of Mathematics, p. 20. "X is identical with Y if V belongs to 
 every class to which X belongs."
 
 150 FOOTNOTES TO F011MAL LOOK 
 
 be taken to indicate mere juxtaposition. If that were all the 
 and signified, then the whole, within which the identity and 
 difference are aspects, would be no genuine whole : for either 
 aspect might be removed and the other would suffer no change 
 in meaning. The limiting conceptions for identity in differenct 
 are at the lower limit, pure tautology, at the upper limit, entire 
 difference. But obviously these limits can never actually be 
 reached by the judgment without sacrificing its essential char- 
 acter. The judgment indeed, aims both at mere tautology, and 
 mere difference, but if it found its goal it would lose its life — 
 the reverse of the scriptural experience of losing life to find it. 
 
 In this modern indictment of the old Logic a most serious 
 arraignment on all sides is made against the traditional laws of 
 thought. But every argument against any one of these three 
 laws always presupposes one or all of them. Every argument 
 against identity assumes a principle of identity. The opponent 
 of the Law of Identity must be standing upon a platform sup- 
 ported by stable values when he assaults identity, otherwise his 
 aim will be uncertain and he will miss the mark as widely as a 
 Jiowitzer anchored upon a drifting cloud. These attacks upon 
 the law of identity are most surprising instances of oversight. 
 Reason cannot commit suicide. A law of thought is reinstated in 
 each attempt to remove it. The Aristotlian logic is the founda- 
 tion of all logic even of those which attempt to overthrow it. 4 
 
 No judgment affirms mere identity. If any collection of 
 words should aim to assert identity they would not constitute a 
 judgment, for as Hegel said, they would sin against the essential 
 
 4 Sidgwick, Elementary Louie: ' ' It is indisputable, e.g., that every 
 A is A, but this leaves it quite uncertain whether any actual case of 'A' 
 that we meet with is the genuine thing or not. Such a 'law' therefore 
 has no application except on the assumption that we no longer need the 
 information that it is supposed to give. This kind of indisputability i-; 
 common enough, and we can all manufacture as much of it as may 
 content us." (p. 120.) "A is prima facit A. and not non-A, and clearly 
 distinct from B. But if A can be A for one purpose and non-A for another 
 the supposed authority of these rules in application crumbles away to 
 nothing." (p. 157.)
 
 \<>l I II Y AM) IDENTITY IS INFEBEm E 151 
 
 characteristic of judgment. But, on the other hand, withoul the 
 tacil assumption of identity, do affirmation or denial could ever 
 
 bo made Sameness and dillm-ence are so inter related thai they 
 are in reality differenl sides of the self-same content. Any two 
 facts thai fall within the same whole arealike and yel different. 
 Nevertheless, although likeness is a fad and difference is a fact, 
 we never mean to asserl jusl the fact of likeness or the fact of 
 difference. This is the puzzle which Professor Dewey lias made 
 the basis of Ids criticism of all conceptual logic. lit- says, in 
 
 criticis E ;ill such Logics, "The rock against which i'\t-iy such 
 
 logic splits is either thai reality already has the statemenl which 
 t houghl is endeavoring to give it or else it has not. In the former 
 case thoughl is futilely reiterative; in the Latter it is falsinca- 
 tory." 1 shall attempt to show in detail. Later that these two 
 alternatives do not exhaust the possible points of view. We may 
 answer both charges of futility and falsity by saying that tie- 
 predicate is something which the subject already is or has, bu1 
 which it was not known to be or to have prior to the predication. 
 In his defense of independence the realist assumes a mind 
 which is to know a totally independent and hitherto unknown 
 object. He then gradually brings that object, so to say, toward 
 the mind until the mind observing it. seizes it. and knows it. He 
 admits that in any such act of normal thinking, when the object 
 is known, that knowing of it causes it to enter into a new relal ion. 
 But he emphatically declares that certain other relations the 
 object retains, and that these are in no wise influenced by the 
 new relation of the knowledge it has permitted to be set up. Bui 
 now is it not an unwarranted abstraction by means of which the 
 realist transcends the unity of knowing and being, and imagines. 
 or conceives, or thinks an object independent of all knowing? 
 "When we separate being from knowing, reality from thought, 
 what is Left is not jusl an independent unknowable something, 
 but real non-being. Whoever declares that the objects of sm^ 
 perception— or the objects of thought — are not in themselves as
 
 152 FOOTNOTES TO FORMAL LOGIC 
 
 they appear to us is making an assertion for which there is no 
 logical defense whatever. In order to pronounce the things in 
 themselves other than, or independent of, the appearances, we 
 must previously have compared the things as they are with the 
 things as they appear. If this can be done then the independ- 
 ence has been disproved before we begin, and we are guilty of a 
 negative petitio. 
 
 The realist in every age has put the burden of proof or dis- 
 proof, upon the idealist." He says that entities are independent, 
 unless they are proved dependent. This is analogous to the 
 familiar legal procedure of regarding a man innocent until he is 
 proved guilty. That there is an important element of truth in 
 this principle in legal practice I am not concerned to deny. In 
 the law with which we are dealing, approximations to certainty 
 merely, and the principle of the presumption of innocence is all 
 we have. But in logical problems where rigorous demonstration 
 is sought, it is a confession of weakness to give external evidence 
 where internal proof should be forthcoming. 
 
 The realist's definition of independence as equivalent to non- 
 ilt'jtendence is open to serious objections. In this definition he 
 has failed to distinguish between the absence of dependence and 
 the opposite of dependence. The realist admits that he cannot 
 prove independence until the idealist has failed to prove depend- 
 ence. Let us accept his challenge and attempt to prove that 
 there is ineffaceable dependence between idea and object. The 
 realist asks us to go to experience for the confirmation of his 
 doctrine. Objects in the world of matter he says are independent 
 of one another ; so too are ideas in the world of mind. Up in 
 Lake Superior, and quite on the bottom, he tells us, is a drop of 
 water, and here are pages in a book. They are totally inde- 
 pendent, are they not ? The turning of the pages in no wise 
 disturbs the essential being of that drop of water. And there is 
 
 5 E.g., E. B. Perry, "Bealistic theory of independence, " New Realism 
 (New York, Maemillan, 1912), p. 99.
 
 NOVELTY AND IDENTITY IN INFEBENi / L53 
 
 Halley's Comet, winging its way through space preparatory to 
 coming back to us again in seventy years. That, too, the realisl 
 says is independent <>i* this page. Bu1 now when we enter the 
 realm of possibilities, are these facts of our illustration so inde- 
 pendent as they seem a1 first sight? The drop of water at the 
 bottom of Lake Superior may come to the surface, evaporate, 
 enter the atmosphere, be carried to this spot and fall upon this 
 page and blur the ink — tbat is a possibility. Therefore, in 
 criticism of New Realism the idealisl insists that this possibility 
 which is a1 the heart of the drop of water is already a part of 
 its being, as ii lies there at the bottom of the lake. The very 
 possibility of its entering into harmful relations with my paper, 
 prevents it from being regarded as an absolutely independent 
 existence. It is an uncombatted possibility and therefore an 
 actuality. Hence the idealist refuses to admit that even in our 
 concrete human experience, we can ever find two physical objects 
 which are so utterly independent of each other that no conceivable 
 change in one of them can effect the other in any wise. 
 
 But we need not rely alone upon this argument from the 
 possibilities that lie inherent in the drop of water. That drop 
 of water has, at this very moment, a relation to this paper — a 
 relation that differs only in degree and not in kind from the 
 relation which it would have to the paper if it were actually 
 lying here now and blurring the words as they are being read. 
 The realist would hardly venture to claim that space is more 
 than a principle of differentiation. As I have already said, the 
 realisl declares that whenever we know any object (not our- 
 selves) this object is existent ially absolutely independent of our 
 knowledge of the object. So that the ideas that constitute our 
 knowledge may come and go, they may be true or false, and 
 yet the object will remain forever what it was. In knowing the 
 rest of the universe other than ourselves, we know something 
 thai is different from that knowledge, ami because different is 
 independent of that knowledge. And here is the novelty, the 
 risk, the objectivity in judgment that can oever be effaced.
 
 1.14 FOOT SOT J-:s TO FOEMAL LOCK 
 
 For further, proof of this metaphysical doctrine of independ- 
 ence, the new realist refers us to the mathematical theory of prob- 
 abilities, where events are said to be mutually independent. In 
 the throwing of dice, for example, each throw is independent of 
 the others. But again we should insist that when we look closely 
 at all such illustrations of independence, we find that, in the last 
 analysis, the objects so defined are always relative. This is 
 pseudo-independence ; we are looking merely at special aspects 
 of our objects. To use a crude but pertinent illustration — -our 
 fingers ma}' be said to be separate and independent when we view 
 them at their tips, and do not follow them back to their physio- 
 logical connection at the palm. The two throws of the dice which 
 the realist uses to support him in his metaphysical gamble in 
 the search for independence, are connected in the general causal 
 arrangement of our universe ; they are really not wholly inde- 
 pendent. We merely do not happen to know what the causal 
 connection is. When we speak of pure chance we overlook these 
 causal features and fail to observe that any two physical events 
 occur in the same space, and in the same time. The parts of 
 space and the moments of time, are perceptually, genuinely inter- 
 dependent. Space and time are not principles of individuation, 
 and nothing short of the individual can be regarded as genuinely 
 independent. However far apart two objects are placed, they are 
 still clutched in the enwholing grasp of space and cannot be 
 totally indifferent to each other. Space is a principle by means 
 of which things are "coupled apart.'' In the theory of probabili- 
 ties, we do, to be sure, call two events that happen in' the same 
 space and in the same time independent events. What Ave mean 
 is, not that these two events are absolutely independent, but that 
 there is an aspect in which we may treat them as independent. 
 For certain purposes, we may ignore their interdependence or 
 at any rate treat it as insignificant, and thus secure an apparent 
 independence. 
 
 It is precisely this pseudo-independence which the new realist
 
 NOVELTY AND IDENTITY l\ / Y /■/•/,'/•. w I 155 
 
 has seized upon and magnified into a genuine independence. The 
 realist \s explanation of the process of knowing, as Bradley would 
 say, is a "makeshift, a device, a mere practical compromise," 
 which cannot be logically defended. From one poinl of view we 
 
 have to take reality as many, and from another, as on< — an 
 Ontological dualism and an epistemological monism. We insisl 
 on dividing reality for the purposes of existence, or to take it, if 
 we wish, as indivisible for the purpose of knowledge. 
 
 The idealist says thai the alleged objects independent- of 
 consciousness are objective and independent only in the sense 
 thai they are the externalization of an internal constraint. They 
 are what we must think, it* thoughl is to be self -consistent. Our 
 apparent success is won by a perpetual shifting of the ground, 
 so as to turn our backs upon the aspect we desire to ignore. But 
 when these inconsistencies are brought together, as in rigid Logic 
 they must be. the result is an incurable discrepancy. The inde- 
 pendent beings of which the realist speaks are beings that have 
 no common features, no ties, no relations, or at any rate only thai 
 mysterious kind of relation which he calls mere dependence. They 
 are separated one from the other by an absolutely impassable 
 chasm. But such beings, we insistently repeat, cannot be in the 
 same space or the same time, or be members of the same con- 
 ceptual realm. They are false existences, and vanish at the touch 
 of thought into the realm of non-being. They are not one. nor 
 many, but just impossible nothings — just the drapery folded 
 around the empty outline of ghosts of beings. 
 
 The realist insists that real beings must be essentially and 
 absolutely independent. In order to get such independent beings, 
 he first declares that certain gaps or barriers are absolute. But 
 he forthwith proceeds to make thought transcend these very 
 barriers. He accomplishes this feal by an actual union of those 
 parts of being, which in the first instance he attempted to put 
 forever asunder. Realism attempts to divide the what of an 
 
 object from its Hint — the meaning from its existenci — a vivi-
 
 156 FOOTNOTES TO FORMAL LOGIC 
 
 section that must always prove fatal. It is true that a psycho- 
 logical dualism is implied in the very conception of conscious- 
 ness. But as we have seen earlier this postulated objectivity does 
 not imply the ontological pluralism which the New Realism seems 
 to demand. 
 
 In the new realist's philosophy, quite closely related to the 
 doctrine of independence and the problem of error, there is a 
 third problem which is also one of the crucial test problems of 
 the realistic metaphysics — the ancient problem of the one and 
 the many, the whole and the part. One phase of this problem 
 I have already discussed in considering the doctrine of inde- 
 pendence. The realist's explanation of the relation between the 
 one and the many seems to me to be a complicated linkage of 
 circular reasoning, in which the inquirer is continually deluded 
 by an apparent approach to valid conclusions, and is yet all the 
 while led back to the point from which he set out. The realist 
 fails to reach any satisfactory solution of the problem of the 
 one and the many, I venture to think, because he is applying an 
 inadequate and imperfect conception of the relation of whole to 
 part, and of the function of analysis and synthesis in judgment. 
 In the world in which the pragmatist and the new realist first 
 find themselves and beyond which they hold they can not go — 
 the empirical, quantitative world — the parts of every whole, the 
 elements of every multiplicity, stand in purely external relations 
 to each other. This is one of the vital axioms of every form of 
 realism. Every other principle or category that it employs, must 
 conform to, or be a genuine expression of the fundamental char- 
 acteristic of this phenomenal world, the mutual exclusiveness, the 
 utter isolation of its elements. 
 
 But in the world of thought, in the qualitative order, a funda- 
 mentally different axiom is discovered. Consciousness is not a 
 mere collection or aggregate of states, existing seriatim, each 
 self-sufficient ; but it is an organic whole, a genuine system, every 
 part of which has meaning only in so far as it is related to the
 
 NO) ELI ) AND IDENTITY IN INFEBENi E L57 
 
 rest. The new realist's problem of independence presents no 
 difficulty if we accepl Aristotle's definition of a true whole, thai 
 is, a whole such that ii' any part is modified or removed the total 
 is entirely altered; dor that of which the presence or absence 
 makes qo difference is no true pari of the whole. In the deeper 
 Life of self-active mind, there is both multiplicity or diversity; 
 but it is the multiplicity or diversity thai is not of parts, opposed 
 to each other and const ii uting a whole by juxtaposition. In the 
 organic whole of thought no part has an intelligible existence by 
 itself in separation from the rest. Objects in the material order 
 are by their very definition mutually exclusive. Each object in 
 space lies outside of every other, and can be only externally 
 related to them. But the independence of the elements in the 
 thought system is the independence of that which although 
 always limited is limited only by what is of the same essence with 
 itself. The element in the scientific order is an (dement winch 
 declares its independence of all tliat lies without it. The element 
 of thought, however, is an element which is ever discovering itself 
 in that which apparently limits, or lies beyond it. 
 
 II 
 
 All vocabulary, and particularly English vocabulary, is defec- 
 tive in words to designate the highest type of synthesis, that is. 
 the synthesis which does not entirely efface the parts in the 
 achievement of the whole. Also, we have no good single word 
 to embrace the two aspects of the highest type of analysis, which, 
 in winning its part is not totally disruptive of the whole. We 
 greatly need in this discussion of the essential import of judg- 
 ment what Philosophy in every language through all the aires 
 has felt the lack, namely a single word to denote analysis in 
 synthesis, or synthesis in anal ysis — the process in which an 
 identity is preserved in the midst of difference. 
 
 In the dialectic process, thesis, antithesis, and synthesis, 
 namely, the positing of an object, the placing over against it its
 
 158 FOOTNOTES TO FORMAL LOGIC 
 
 negative, and then the reconciling of the two, vocabulary follows 
 thought with an abundance of adequate words up to the second 
 stage. Language is rich in words that distinguish the first two 
 stages, thesis and antithesis; affirmation and denial, inclusion and 
 exclusion, and their many synonyms and antonyms cover satis- 
 factorily all of the various shades of meaning of the first two 
 steps in thought's movement of increasing complexity. But, 
 when we pass to the third stage of synthesis and think in terms 
 of a genuine reconciliation of a concept with its negative, 
 language refuses to follow, or at any rate fails to provide a new 
 and unambiguous word to denote the essential characteristic of 
 the complex thought process of this third stage — the stage of 
 higher synthesis. The word which seems most nearly to express 
 the double-acting character, the analytic-synthetic or synthetic- 
 analytic process, in all judgments, or is eonstr'efinn. As Bosan- 
 quet says: "The process of construction is always that of ex- 
 hibiting a whole in its parts, an identity in its differences ; that is 
 to say, it is always both analytic and synthetic.'* 
 
 On the higher level of synthesis, when we attempt to exhibit 
 the results of reflective insight, we express ourselves imperfectly 
 by circumlocution. If we are pressed for a single term to describe 
 the third stage, we invariably employ the same words to designate 
 the synthesis, or reconciliation of the thesis with its antithesis, 
 that we have already employed to designate the thesis. This has 
 given rise to endless confusion and misunderstanding in philo- 
 sophical discussions. In the time-series, for instance, we posit 
 as thesis is, then over against the is, we place its antithesis, was. 
 But now, when we are called upon to reconcile the two. when we 
 comply with the inevitable demand of thought to discover what 
 tJusis and antithesis here have in common, we find not a third 
 new word, but one of the two already employed, namely, is. In 
 like manner, necessity and contingency are synthesized by neces- 
 sity ; the one and the many by the one. We generally mark the 
 distinction, by capitalizing the one word in the position of
 
 NOVELTY AND IDENTITY IN INFEBENCE 159 
 
 synthesis. Or by way of explanation, we say thai aecessity is a 
 higher aecessity which is the reconciliation of itself with the 
 contingent ; or thai unity is a higher unity which is reconciliation 
 of itself with the many. The distinction between these two mean- 
 ings of is, we find illustrated in the sentence "Before Abraham 
 
 was, 1 inn." 
 
 Of all our English synonyms of analysis ami synthesis, the 
 words differentiation ami construction, besl bring ou1 the revers 
 ible ami transitive character of the process. Any process of 
 genuine const ruction always exhibits the final whole in and 
 through its parts. It sets forth an identity in the midst of its 
 difference. That is to say. as Bradley, Bosanquel and other 
 recent writers have pointed out, it is always both analytic and 
 synthetic. In any discussion of the interrelationship between 
 analysis and synthesis it is important to distinguish between 
 perceptual synthesis of parts into a whole in space and time, and 
 conceptual synthesis of parts and whole in a non-temporal order. 
 The result of the former process is always a mechanical, purely 
 quantitative aggregale. The mathematician has ever had a clear 
 conception of this interdependence of analysis and synthesis. His 
 terms, integration and differentiation, are always employed in full 
 view of the vital correlation of parts and whole. It is mani- 
 festly impossible in the non-metrical reaches of geometry to think 
 of this relation as one subsisting between parts and whole without 
 confusion, because of the quantitative connotation of the terms 
 pari and whoh as we ordinarily employ them. The mathema- 
 tician has therefore wisely come to prefer the terms element and 
 system. Moreover, in describing the process of integration, he 
 is careful to point out that in the complex entirety into which 
 the elements have been combined, the elements are never impotenl 
 and indistinguishable. And conversely, in the process of dif- 
 ferentiation into elements the system is never dismembered or 
 multilated. 
 
 The doctrine that a proposition is analytic when the predicate
 
 160 FOOTNOTES TO FORMAL LOGIC 
 
 is a genus or differentia of the subject, and synthetic when the 
 predicate is a proprium, or accidens, is maintained by Welton. G 
 This view obviously defines in a circle. It presupposes that we 
 can distinguish between the accidental and the essential attributes 
 of the subject, without invoking the assistance of the very con- 
 ception of analysis and synthesis which this distinction is called 
 upon to define. If the so-called accidental attribute is accidental 
 in the literal sense of the word — if it has drifted in upon the 
 subject like a snowflake out of an unknown sky — then it is not 
 even a synthetic judgment, it is not a judgment at all. It is 
 worse than sheer falsehood, it is empty breath. However, if 
 instead of the terms accidental and essential attributes, we use 
 the terms external and internal meanings, we may discover a 
 sense in which we can properly speak of analytic judgment as 
 the explication, or determination of internal meanings, and 
 synthetic judgment as the implication or determination of 
 external meanings. But then, we should be obliged to return to 
 the view for which we are here contending, that analysis and 
 synthesis are inseparable, correlated aspects of every act of judg- 
 ment. But it should be pointed out again that on this view the 
 so-called accidental attributes or external meanings are not so 
 accidental and external as at first sight they appear to be. 
 
 The problem of the true import of judgment rests back finally 
 upon this distinction between external and internal meaning. If 
 we are to rescue judgment from the fatal paradox of being either 
 false or idle, we must show that it is possible for the subject to 
 have an internal meaning consistent with an external meaning 
 brought to it by the predicate. Let us take any diyadic relation 
 in a pluralistic universe. Let us assume, for example, that A 
 and B are two minds or souls (Kantian ends), in such a pluralis- 
 tic universe. A has its internal meanings, namely, a, b, c, d, etc., 
 and likewise its external meaning m, n, o, p. But on closer 
 analysis it is discovered that these external relations m, n, o, p 
 
 6 Manual of Logic, p. 104.
 
 NOVELTY AND IDENTITY IN INFEBE VCE 161 
 
 are only the demands thai are made upon .1 by />' and these 
 demands of B are B's own internal meanings, which are pre- 
 cisely the aforesaid m, n. o, p. And in tin- same way B's external 
 meanings will be a demand made upon /»' by -1 through its 
 interna] meaning a. h, c, d. In short. .1 r s external meanings are 
 />'\s internal meanings; and vice versa, B's external meanings 
 are -l's internal meanings. This Logical doctrine, thus expressed 
 symbolically is analogous to the definition of a true person in 
 explanatory ethics. There too, the true insight is reached by a 
 reciprocal determination of internal and external meanings. A 
 person is being endowed with rights (internal meanings) that are 
 inalienable, and duties (external meanings) that are absolutely 
 binding. 
 
 It must be observed that we deal with the same reality whether 
 we approach it analytically or synthetically. This true insight 
 into the real nature of analysis and synthesis in judgment settles 
 finally, in my opinion, the much debated question whether the 
 analytic judgment is really a judgment, that is to say, whether 
 it is not in the last analysis idh ; and the correlated question, 
 whether the synthetic judgment, which is supposed to bring 
 novelty in the predicate is not false. The subjed is indeed given 
 to us by one act of analytic attention, and the predicate by 
 another. But to know the parts and to know the whole separately 
 is not the same as to know the parts in the whole, or the whole 
 containing the parts. 7 
 
 Now it must be confessed that it is difficult to tell, in the 
 analytic judgment precisely where its Latent synthetic aspects 
 begin to operate, and. in the synthetic judgment, it is difficult 
 to tell at precisely what point the analysis begins. But I believe 
 that careful psychological study of the thinking process would 
 
 7 Cf. Bradley, Principles <>f Logic, p. 447. "Unawares then we strive 
 to realize a completion, single and self-contained, where difference and 
 identity are two aspects of one process in a self-same Bubstance, and 
 where construction is self-diremption and analysis self-synthesis. This 
 idea of sy>t-.'in is the goal of our thoughts."
 
 162 FOOTNOTES TO FOBMAL LOCK 
 
 show that we often reverse the process several times in a single 
 judgment. We find an analogy in the physical world in the 
 solution of the familiar Japanese puzzles. We often take out 
 several sticks and then restore them to their respective positions 
 in order to make sure that we may in the end bring the pieces all 
 together again. So too, in pursuing an unknown path through 
 the woods, we glance back often over our shoulders in order that 
 the path may be familiar on the return journey. 
 
 As I have already remarked, of all our English synonyms for 
 analysis and synthesis, differentiation and construction, or inte- 
 gration seem best to bring out the reversible and transitive char- 
 acter involved. Any process of genuine construction, always 
 exhibits the final whole in and through its parts, as many genera- 
 tions of idealists from Plato to Hegel have taught. It is both 
 analytic and synthetic, therefore not just idle nor yet false. 
 
 Among the various attempts to preserve for analysis and syn- 
 thesis separate and entirely independent functions, that which 
 rests upon the distinction between ground and consequence has 
 had many defenders. 8 It is maintained that whenever thought 
 follows out a premise to a conclusion, or passes from cause to 
 effect, the process is synthetic. But when the movement is in 
 the reverse direction, namely, from consequence to ground, or 
 effect to cause, the process is analytic. But obviously this view 
 presupposes a transformation of the judgment in which its essen- 
 tial non-temporal character is disregarded. The relation of cause 
 to effect, of ground to consequence, is a transitive and reversible 
 relation. This reciprocal relationship is the vital characteristic 
 of inference and judgment, and even of conception. In the 
 relation of cause and effect, the cause is quite as much condi- 
 tioned by the effect as the effect by the cause. This basal truth 
 is continually overlooked in the instrumental theories of judg- 
 ment. And the fallacy when carried on into the discussions of 
 mediate inference causes endless confusion. 
 
 8 Cf . Mellone, Introductory Text-Bool- of Logic (ed. 2; Loudon, Blacks- 
 wood, 1895), p. 99.
 
 N0VEL1 ) AND WE \ III ) I \ INFEBENi E 163 
 
 Subject and predicate, premises and conclusion, are together 
 in the mind; on the printed page they are necessarily spread out 
 seriatim. The proposition and the syllogism are in time, bu1 the 
 judgmenl and the inference, of which they are the outward 
 expressions, arc not in time. The judgmenl is no1 transition 
 from subject to predicate, nor is the inference a transition from 
 premise to conclusion. The parts of the judgmenl do no1 follow 
 each other like the parts of the proposition. The relation is not 
 merely between two mental states, hut is within a single enwhol 
 
 ing mental state. This single idea within which the elements of 
 the judgmenl arc held, not only permits hut compels a transitive, 
 reversible relationship between those parts.'' 
 
 The presented facts which constitute the subject in the judg- 
 menl contain two groups of elements, those which are explicil 
 in the primary apprehension or perception and those wide]) are 
 implicit. 10 Now the analytic judgment, is on the one hand, 
 overtly the explication of these implications, and. on the other 
 side, tacitly the synthesis of these same elements. The word 
 analytic with its usual connotations as 1 have pointed out. is 
 incompetent to exhibit 1 his redintegration in the so-called analyt ic 
 judgmenl ->>n rl introspection (inward looking) with tacit retro- 
 spect] outward looking). We likewise discover in the syn- 
 thetic judgmenl the same essential dual process. The only differ- 
 ence here is, that the group of presented facts, which again takes 
 its place as the subjeel in the judgment, is now seen to be a con- 
 stituent clement of the whole which in the primary apprehension 
 was implied. This Larger whole now becomes implicit; it is dis- 
 covered that the subject which in the primary apprehension 
 
 '■' Tli is is the mm familiar doctrine, so tony and so ably defended by 
 Bosanquet. The essential concomitancy of the parts of judgment had 
 of course, been pointed out many times before, in the history of Logic, 
 but no one had ever Insisted upon the principle with Buch repeated 
 emphasis. 
 
 '"It must l>e admitted, of course, that there i-; -nun 1 difficulty in 
 Speaking of these elements as being implied in tin- original 'latum. The 
 enormously complicated question of the meaning of implies is here involved.
 
 164 FOOTNOTES TO FOBMAL LOGIC 
 
 seemed single and isolated is in reality correlated with at least one 
 other group of elements into a larger concept, or idea. Thought 
 is continually bringing together at one moment the result of the 
 abstraction of a previous moment. Thought begins with a whole 
 — with reality in some sense grasped as an entirety. It then pro- 
 ceeds to disperse this whole by analysis (not a complete dispersion 
 however) and then gathers the dispersed elements into a whole. 11 
 "We first "grasp the sorry scheme of things entire," then "shatter 
 it to bits" and finally "remold it nearer to the heart's desire." 
 A vital question now arises which Professor Dewey asks as 
 follows: 12 "Why and how should perfect, absolute, complete, 
 finished thought find it necessary to submit to alien, disturbing, 
 and corrupting conditions in order, in the end, to recover through 
 reflective thought in a partial, piecemeal, wholly inadequate way 
 what it possessed at the outset in a much more satisfactory way ?" 
 But no serious idealist has ever been willing to admit that thought 
 is as Dewey says, perfect, absolute, complete, and finished, before 
 it has submitted to these apparently alien, disturbing conditions 
 of judgment. It is not truly itself until it has discovered itself 
 by passing, in a piecemeal fashion, through these seeming foreign 
 conditions. This reflective process through which thought passes 
 is not partial and inadequate ; it is the highest type of adequacy, 
 namely, self-completing adequacy. You may try to condemn 
 thought by calling it finite, relative, conditioned, imperfect, frag- 
 mentary, since it is obliged to reconstruct reality by the device 
 of judgment, In fact thought will join you in such a condemna- 
 tion of itself ; but forthwith it produces from within the principle 
 of its own self-perfection, by means of which it escapes from all 
 of these self-imposed limitations. 
 
 11 Bradley has expressed this thought with his usual clarity and 
 vigor: "Analysis is the inward synthesis of a datum, in which its unseen 
 internal elements become explicit. Synthesis is the analysis of a latent 
 whole beyond the datum, in which the datum becomes explicit as a con- 
 stituent element, bound by interrelation to one or more elements likewise 
 constituent." Principles of Logic, p. 432. 
 
 12 Logical Theory, p. 45.
 
 NO) I.I.I V AND IDENTITY IS INFEBENi I. 165 
 
 In this discussion of the essential identity or a1 leasl the 
 inseparable eorrelativity between analysis and synthesis, it is 
 important to point out that the thought process exhibited in 
 the relationship is one that always involves a triadic relation. I 
 have already spoken of the duality of the relation bu1 there are 
 really three centers of separate attention. Analysis not only dis- 
 tinguishes each element from the other, hut also distinguishes 
 each element from the whole. Also, when we read off the con- 
 tent in the reverse direction, we find that synthesis so combines 
 parts into wholes that the relations of the whole to each of the 
 several parts, as well as of the parts to each other is never obliter- 
 ated. Both analysis and synthesis estahlishes and maintains 
 relations, but the relations here involved, I repeat, are essentially 
 triadic, because every such relation involves both a h< tun i n and 
 a within. If the relations between two terms .1 and />'. be 
 expressed by R, then W would express the whole within which 
 this relation is embedded, and R, the relation between A and .1/ 
 and also between B and M. The triadic relationship would run 
 thus: A-R-B, A-R-M, B-B-M. While it is true that every 
 judgment is both analytic and synthetic, we may yet assert 
 (without yielding any essential part of the position we are 
 advancing), that judgments of sense are synthetic and judgments 
 of reason are analytic. The former do transcend the sense-pre- 
 sented content ; they are more than simple apprehension. The 
 latter always start with a whole or system, in which differences, 
 already existing are further developed. 
 
 Some writers have attempted to overcome the apparently 
 vitiating tautology of the analytic proposition by making two 
 classes of so-called verbal proposition — analytic and synon- 
 OmOUS. 18 In the one class the predicate aims at an exposition. 
 or analysis of the intension of the subject, for example, B<>di>s 
 an extended, An equilateral triangh is a triangU having threi 
 
 equal sides. These are regarded as the true type of what should 
 
 !3 Cf. Keynes, Formal Logic, p. 50.
 
 166 FOOTNOTES TO FOEMAL LOGIC 
 
 be called analytic propositions. They are never tautologies or 
 bare identities and therefore may never be condemned as trivial. 
 Even where the exposition of the intension of the subject is com- 
 plete and the proposition becomes a definition, such propositions 
 are still to be distinguished from the other group which Keynes 
 calls ' ' synonymous. ' ' In this class the predicate is not an exposi- 
 tion of the intension of the subject ; it gives information only in 
 regard to the external reference of the subject or is its dictionary 
 synonym, for instance, Tulhj is Cicero, or A story is a tale. This 
 is a distinction that for practical purposes may be useful, but it is 
 hardly defensible theoretically. The class of synonomous propo- 
 sitions that is here interpolated, is provided with no precise line 
 of logical demarcation from the analytic and the synthetic class. 
 A third class is not strictly needed. Even in tbose propositions 
 where subject and predicate are both singular terms we may, 
 and in truth, must regard the judgment, which the proposition 
 expresses as an equating of synonyms, as conforming to the funda- 
 mental principle of all judgment, namely, the assertion of an 
 identity in difference. Neither in judgment nor in inference 
 can thought pass from particular to particular ; for example the 
 proposition tliis is that corresponds to no actual judgment any 
 more than tli is is th is. We do violence to the real judgment when- 
 ever we attempt to interpret it in any other way than that of a 
 universal, exhibiting itself in and through its differences. The 
 challenge to describe these synonomous propositions as either 
 analytic or synthetic can not be met, indeed, if it means that 
 they are to be either one to the exclusion of the other. But they 
 can all be described as analytic-synthetic. Even Tully is Clara 
 or A star y is a tale are assertions of identity in the midst of a 
 difference ; we pass out beyond the judgment at the one link into 
 bare tautology and at the other into falsity. 
 
 The results on which we would insist may now be briefly 
 summarized. The relation of judgment to conception is recip- 
 procal. The judgment expands the conception and in expanding:
 
 NOVELTY AND IDENTITY IN INFEBENi / 167 
 
 enriches its meaning. It does this by adding new relations to the 
 group of references thai it already lias. Every judgment asserts 
 both identity and difference. An assertion thai is merely identical 
 is no judgment. So, too, if a judgmenl is merely synthetic, and 
 no bond is perceived between the subjed and predicate, thai is, it' 
 the two arc not situ to be embedded within a whole there is no 
 real judgment, bul only association. Every judgmenl purports 
 to be both a unity and a multiplicity. If ii did no1 fulfil its 
 purpose to exhibit an identity, it would cease to exist. Bu1 this 
 external unity a1 which ii aims is not inconsistent with endless 
 multiplicity within. The content of judgment, though a single 
 definite idea in any external reference, is when viewed interiorly, 
 capable of manifesting itself in an endless variety of meanings. 
 Judgmenl is a self-enclosing expansion, a unifying of the many 
 and a multiplying of the one. The reality with which judgmenl 
 is concerned is a whole, completely revealing itself in each of its 
 parts. Judgmenl is a unity breaking itself up into a multiplicity 
 and then reasserting itself as a unity. It is the highest type of 
 redintegration. It is both true and false and neither. 
 
 Ill 
 
 The lirst of all the prerequisites for judgmenl is a world of 
 reality different from, or at least distinguishable from the world 
 of ideas. A judgment always claims to be true. It is idle to talk 
 
 about judgment until we have distinguished between idea or 
 psychical fact and the reference of idea to objective fact or 
 reality. One of the purposes of these studies is to show how and 
 why this distinction is made. This claims to I" trUi . which is one 
 of the several correlated factors in all judgment, might also he 
 described as judgment's intrinsic )><<■< ssih/. It would also be 
 equally accurate to speak of it as the objectivity in judgmenl. 
 Objectivity in judgment is nothing else than its necessity. What 
 we are obliged to think, through this self-compulsion of thought.
 
 168 FOOTNOTES TO FOBMAL LOGIC 
 
 constitutes its objectivity. These are truths that the history of 
 Logic has repeatedly been compelled to recognize. No one can 
 understand thought as an instrument of conviction until he has 
 studied it in its relation to its subject matter. There is an inter- 
 structural correspondence between thought and facts. 14 Every 
 judgment therefore has objectivity even if it has no object. And 
 such a view of objectivity allows us to say that the conditions of 
 actual and possible thought do correspond with the conditions of 
 actual and possible being, and that, therefore, what we think 
 exists and what we can not think does not exist. 
 
 Since judgment always refers to something other than itself, 
 it has been maintained that Logic is the science of thought when 
 engaged upon an object other than Logic. This is a doctrine 
 which I think is entirely defensible although the common under- 
 standing of it leads to all manner of contradictions. The living 
 judgment, perhaps, can not become its own object and still live. 
 The Hegelians have always held that immediate consciousness is 
 self-contradictory. For them there is no such thing as the vivi- 
 section of a thought. But, continuing this metaphor, may we 
 not say that there can be a postmortem examination of departed 
 thinking by its own resurrected self ? 
 
 The attempt to make a distinction between the judgment of 
 perception and cognitive judgment breaks down with any care- 
 ful analysis of psychical facts. There is no difference in kind, 
 on our theory, between perceiving and perceiving that I per- 
 ceive, or between thinking and thinking that that is one of my 
 thoughts. Idealism of every form declares that objects of 
 thought, just because they are thought, have a different kind of 
 existence from what belongs to them when they are not thought — 
 if that may ever be. Mind is, in other words, in some sense 
 creative. The realist says that the validity of thought depeods 
 quite as finally upon the object thought about, as upon the 
 
 I* On this point we are in cordial agreement with the instrumental 
 pragmatist; we differ, as I have tried to point out in an earlier chapter, 
 on the wav in which the relation is read off.
 
 N0VEL1 r AND lhi:\ ill) IS INFEBENi I. L69 
 
 thoughl itself. He contends for a fundamental distinction 
 between idea and object. He grants the idealist's main <•< n 1 1 • -i i - 
 lion thai certain objects of thoughl do qo1 exisl outside of the 
 mind, bu1 he denies thai therefore the mind creates these objects. 
 When reduced to its Lowesl terms and stripped of all unnecessary 
 verbiage, there is, one fundamental difference between the old and 
 new Logic Every form of idealism has asserted thai experience 
 does create its object, thai the self does begel the not-self. 
 
 Professor Dewey 1, has stated in a very concise form what he 
 tak"s to he "the poinl of contact and In nee of conflict " between 
 
 idealism and instrumentalism. The significant sentence reads: 
 
 "The idealistic logic started from the distinction between imme- 
 diate plural data unifying, rationalizing meanings as a dis- 
 tinction ready made in experience, and it set up as the goal of 
 knowledge (and hence as the definition of true reality a com- 
 plete, exhaustive, comprehensive, and eternal system in which 
 plural and immediate data are forever woven into a fabric and 
 pattern of self-luminous meaning." A liberal idealist could 
 accept this statement by changing the one word "self-luminous" 
 to "self illuminating." This would make the difference between 
 static and dynamic idealism. Thought is not perfed bul self- 
 perfecting. Thought strives for something; it needs something 
 apparently beyond itself; it is permeated with wonder, with 
 curiosity, which points to a fundamental defect in its nature. 
 But in this never-ending aim to be a whole, to be self-complete, 
 thought is incessantly discovering that there is nothing genuinely 
 outside of itself. If in this striving for self-completeness, it 
 should actually reach its goal, thought as such would obviously 
 be destroyed. Thought's aim is to get hold of an object as a 
 whole, the separate elements of which it already has. Now ii is 
 precisely this self-completion of thought beyond itself, which 
 constitutes the object, the independent thing in every type of 
 realism. In the subject -object relation, then, tin expected self- 
 
 is Experimental Logic, i>. -i
 
 170 FOOTNOTES TO FOEMAL LOGK 
 
 transcendency of th( subject constitutes tJu object. Thought 
 moves by means of relations toward a goal which lies beyond 
 relations. The attainment of its goal by transcending relations 
 would be the annihilation of thought. 
 
 What Idealistic Logic discovers when it reaches final reality 
 is a whole in which distinctions can be made and are made, but 
 in which the genuine diversity — the bona fide independence — 
 demanded by the New Realism does not exist. The position of 
 modern realism on this central question of Logic can be stated 
 briefly, but with rough justice thus : The perception of relations, 
 which is the fundamental characteristic of the judging conscious- 
 ness, is a self-contradictory but necessary blending of the one 
 and the many, unity and variety. This relation is unique, 
 logically indefensible and undefinable. Consciousness, it is 
 asserted, lias the undeniable feature of immediacy. The idea 
 has hold of its object. This establishes continuity. But equally 
 undeniable is the characteristic of self-dependence, or independ- 
 ence. The terms which consciousness unites in the relating 
 activity of judgment are. in truth, given to it. and not actually 
 made by it. This given reality with which it deals is therefore 
 i issentially pluralistic. 
 
 But I submit that at this point The modern realist has allowed 
 his dialectic to halt. He has stated only half of the whole truth. 
 The other half is the indisputable fact that this cognition which 
 binds together the many, represents at its center an original 
 underived whole. It is a synthesis, a unity, which is not made 
 by the original differences in the presented facts, but is- placed 
 upon them. The whole is not just composed of its parts, it con- 
 stitutes them and is legislatively sovereign over them. Now it is 
 this characteristic and apparently paradoxical feature of thought 
 that neither the Instrumental Logic nor the analytic realism 
 seems able to surmount. Thought does aim to retain these two 
 features, unity and plurality, and at the same time weld them into 
 a higher harmony. It strives to reach an all-embracing whole
 
 NOVELTY AND IDENTITY IN INFEBE V< /. 171 
 
 which shall not in any way conflict with the Immediate fl.-in.-nts. 
 
 It therefore bestows upon its elements a kind of independence. 
 I'.ui at the same time it seeks for elements thai shall be sub- 
 ordinated to the entirely independenl (i.e., superior) whole 
 
 There is, then, this paradoxical fad aboul thoughl and its 
 object; they are two and ye1 can aever be studied in isolation. 
 Thinking, is always thinking aboul something, and thought can 
 aever be divorced from this postulated objectivity and treated as 
 purr subjectivity. This point, which has now so often been 
 insisted upon, seems invariably to be ignored by realists and 
 pragmatists in their criticism of idealism. Thought can aever be 
 investigated in abstraction from its objective reference. Such 
 a view- as I am here stating, concerning the relation of subject 
 to object, may when taken at its face value, appeal' to be a con- 
 cession to the central thesis of pragmatic logic namely, that the 
 form of thoughl must wait upon its matter. On this view, it will 
 be asked, how can Lo^ic be regarded as the study of the forms 
 of thought? If the form and the matter are thus inseparable. 
 inter-related in each concrete instance of thought, how can there 
 be any form in general? I cannot think the answer to these 
 questions and the justification of Formal Logic is far to find. 
 Just as we can inquire into the laws of gravitation without 
 examining all the objects that have ever fallen, so we may study 
 the laws of thought without studying all the objects thai may 
 conceivably be discovered at the other end of the subject-objeel 
 relation. 
 
 IV 
 
 There now arises a question of singular gravity, the central 
 question of speculative Logic through all the centuries. That 
 portion of thought's content which constitutes its meaning or 
 external reference as distinguished from its existence, we have 
 insisted, is a systematic totality. This is what we mean when 
 we speak of the world of all possible objects of thought. How
 
 172 FOOTNOTES TO FOEMAL LOGIC 
 
 far into this realm of objective reference must thought go before 
 it can claim finality for its deliverance ? One school of philosophy 
 has held that perfect validity of thought would require perfect 
 insight into the objective system. Bosanquet has said. "Ulti- 
 mately nothing can be rightly known without knowing all else 
 rightly." Others insist that w T e have some knowledge that is in- 
 complete and yet perfect, and that we can pronounce judgments 
 that are not subject to future revision. The agnostics, from the 
 ancient sophists to the new realists have declared that never in 
 the growth of knowledge do we reach a stage at which we may 
 say, "The evidence is now all in, and the judgment of finality 
 can be pronounced. We do not have perfect control over the 
 object ; if we did it would cease to be an object. It is just this 
 alien character that constitutes its objectivity. 
 
 The Idealists have always given a decisive affirmative answer 
 to this fundamental question; we do have perfect knowledge in 
 part. Professor Hocking has defended this cardinal tenet of 
 traditional idealism with impressive clarity of illustration. He 
 pointedly tells us that unfinishedness is not itself a blemish, and 
 says: ''There are tolerable and intolerable kinds of unfinished- 
 ness. A thing is properly unfinished when it is linishable ; and 
 it has an identity that finishing will not change. Let an artist 
 sketch a face with all conceivable haste and roughness. The 
 unfinishedness is justified if only it is a thing, if only it has a 
 character and a significance that all later finishing does but 
 develop without displacement or substitution." 1 " 
 
 The truth about our fragmentary thought, as it comes to us 
 by the pathway of experience, is not that it is imperfect or incon- 
 sistent, but that it is incomplete. It is indeed not adequate to the 
 whole of reality, but what it does deliver is genuine. From its 
 one shore, thought bridges the gulf between it and reality by 
 pushing out cumulative cantilever arches, each firmly and 
 unchangeably anchored. It is not a pontoon bridge whose units 
 
 i« The Meaning of God in Human Experience (New Haven. Yale 
 University Press, 1912), p. x.
 
 NOVELTY AND IDENTITY IN INFEBENl I L73 
 
 are swayed by the dashing tide, and whose mooring to the shore 
 may require to be changed as its length increases. 
 
 Actuality, which is just one asped of objectivity, is the 
 necessitated possible. This is Bradley's well-known view. The 
 most fundamental Law of thought is the law by which we assume 
 thai every isolated, unique possibility is also real. In other 
 words, the uncombatted possibli is the actual. This law, cannot 
 be exhibited as the operation of either analysis or synthesis or 
 both correlated, and ye1 it is a normal, universal way of thought 's 
 functioning. Every time reality presents itself as a subjed for 
 a possible judgment, and reaches out among the possible predi- 
 cates, thai one of these possible predicates which finally stands 
 alone, either because there are no other possihle predicates, or 
 because other competing possibilities have been rejected, is appro- 
 priated by the subject. This appropriation elevates the predicate 
 from possihility to actuality. We may not he cognizant of the 
 operation of this law. and may indeed when out- attention is 
 directed to its operation, be inclined to disclaim it, hut we 
 nevertheless do finally and always owe allegiance to it. Instead 
 of saying that the mind selects one of the several alternatives 
 and so depresses the others, it would he more accurate to say 
 that the several impossible possibilities having been destroyed 
 the single uncomhatted possihility stands self-affirmed. The 
 actual, the real, the object, is that which resists the subject. A 
 thing has objectivity if it exhibits, in its own name, any force 
 or necessity. 
 
 This doct rine again must not he confused with the teaching of 
 pragmatic Logic, which at litst sight it resembles. The Logic 
 of Pragmatism tries out the various possihilities and tests truth 
 by acting as if. When the question arises whether the new 
 possibilities which are applying for acceptance are true, or real 
 we must test them, one by one, by acting as if they were true, 
 and accept in each instance those that work in with the old. Bu1 
 this pragmatic test of truth, as 1 have shown elsewhere, assumes
 
 174 FOOTNOTES TO FOEMAL LOGIC 
 
 the rationality of the old, and asserts that the new which works 
 in with this, is true. Of course, if we start with an original 
 matrix of truth, then whatever this accepts as true, will be true, 
 and whatever it rejects because it does not work, will be false. 
 But the Pragmatic Logic is incapable of endowing this original 
 mass with the essential truth necessary to make the principle 
 as if operate. Bradley's doctrine does on the surface seem 
 identical with the pragmatic test — wherever a suggestion is not 
 rejected by the facts with which we start, or again by some other 
 suggested quality, and we are left not with disparate possibilities, 
 but with one uncombatted maybe, that suggestion must always 
 be taken as fact. The facts with winch the pragmatist starts are 
 not possessed of universality; with Bradley they are. He says: 
 "The striving for perfection, the desire of the mind for an 
 infinite totality is indeed the impulse which moves our intellect 
 to appropriate everything from which it is not forced off." 
 Possibility is a kind of necessity, and consequently there is no 
 difference in kind between the problematic and the apodeictic 
 judgment. A thing is possible when at least one of its conditions 
 is present, and actual when none of its conditions is absent. 
 
 V 
 
 As a typical illustration of the sceptical attitude of the new 
 movement toward reality, objectivity, or necessity, we may quote 
 two Protagorean passages from Professor Sidgwick : ' ' Absolute 
 truth is never attained but that further improvement is always 
 possible. " " There is no need to make any pretence of securing 
 infallibility of judgment, even in a single instance. If Absolute 
 Truth means Truth as it would appear to a superhuman mind, 
 how can we presume to have reached it ? Or, if by any chance 
 we did reach it, what means would we have of distinguishing 
 between it and the truth that merely suffices for human pur- 
 poses?" 17 The modern idealist always replies to this agnosticism 
 
 Elementary Logic, pp. 123, 170.
 
 NOVELTY AND IDENTITY IN INFERENCE 17.", 
 
 in the spirit of Socrates' reply to the ancient sceptics. Knowl- 
 edge has this peculiar paradox aboul ii : We have a criterion 
 of truth — we know what valid knowledge oughl to be; and ye1 
 we can aever in our practical experience reach any such knowl- 
 edge as is guaranteed by this criticism of validity. 
 
 Professor Sidgwiek's own statemenl thai "absolute truth is 
 
 never attained hut that further improvemenl is always possible" 
 is itself an illustration of this "self-perfecting" criterion of 
 knowledge. When we assert that further improvement is possible, 
 we imply a criterion of stable values, or else the word improve 
 
 incut does not mean what it purports. Improvement and pro- 
 gress are indeed dignified words hut no one has any righl to use 
 them, either in Logic or Ethics, who does not admil something 
 absolute, some definable standards of value. The modern enemy 
 of Traditional Logie and Ethics declares that knowledge is 
 Limited in a world of comparatives, whose superlatives are never 
 in sight. We do not know the beautiful, the true, the right, and 
 never can know them, for there are no esthetic, logical, or ethical 
 standards. We simply have knowledge of the first two decrees, 
 namely, the good and the better; and from these as a base we 
 must triangulate our journey. But in full view of all the many 
 indictments the idealist still asserts, with renewed emphasis, 
 that any genuine improvement implies direction, a goal. If we 
 are in the least degree uncertain about the goal, we must in the 
 same degree he uncertain about the improvement. Improvement 
 is not measured in terms of mere movement. We can he much 
 "on the go" without making any improvement — witness many 
 aspects of our present civilization. In other words, briefly, 
 improvement is estimated not by the distance one has gone, but 
 by the distance one has yet to go. 
 
 "There are probably few people at the present day," says 
 Sidgwick. "who would confess to holding that the general rules 
 by which our thoughts and our lives are mostly guided deserve 
 to be applied through thick and thin." 18 One may agree with 
 
 i s Element aril Lmjic, pp. Kid, Hit.
 
 176 FOOTNOTES TO FOEMAL LOGIC 
 
 this statement so far as the word "mostly" is concerned, and 
 admit that humanity does depend for its practical faiths very 
 largely upon insights that are transitory, partial and for the 
 most part subconscious. We act most often before the arrival 
 of certainty and under the guidance of shifting standards. But 
 surely Professor Sidgwick must believe in some things that abide. 
 Can the solemn agreements among men never be final? Is there 
 no pact that deserves to be applied through thick and thin? If 
 not, then the most pragmatically consistent of the nations in the 
 great world-war is Germany. A treaty is indeed merely a scrap 
 of paper to be respected only so long as it is convenient to 
 respect it. 
 
 Another illustration of how the pragmatist fails, it seems to 
 me, to grasp the idealistic notion of a self-perfecting control of 
 the object, I may quote from Mr. H. 0. Knox: "We simply 
 deprecate as futile the assuming of a transcendent and absolute 
 reality as the standard to which our actual judgments are to 
 correspond. For (a) if an absolute standard were available for 
 actual comparison the comparison itself would be purely super- 
 fluous. We should already be de facto in possession of absolute 
 and infallible certitude. And (b) to say, that reality is trans- 
 cendent is simply to say that it is not available as a standard at 
 all" 19 This is clearly a restatement of the ancient paradox of 
 the apparent futility or idleness in judgment which I have 
 attempted to answer in the chapter on "The Import of Judg- 
 ment. ' ' 
 
 All necessity is in the end conditional, since every must be 
 rests back upon a because. All objectivity is in the end sub- 
 jectivity since reality is continuous and since the thinking self 
 (apud Cartesianism) is the initial indefeasible reality. If the 
 object lay genuinely outside the system of thought it could never 
 be reached by thought. The knowing process does not involve 
 a transition from subject to object ; it consists in a progressive 
 
 10 Mind, n. s., XVIII (1909), 602.
 
 NOVELTY AND IDENTITY IS INFERENCE 177 
 
 analysis and developmenl of the objective aspecl of the total con- 
 tinuous reality. This view will seem to resemble Professor 
 Dewey's account of the sub ject-object relation. Be writes: "The 
 distinction between subjectivity and objectivity is not one 
 between meaning .-is such and datum as such. It is a specifica- 
 tion thai emerges, correspondently, in both datum and ideatum, 
 as affairs of the direction of logical movement." 20 There is, 
 however, an essential difference between this position and that 
 which I have now urged from several points of view in these 
 pages. A cross-section of the stream of consciousness in Pro- 
 fessor Dewey's doctrine, it seems to me. does not raise the vital 
 question of the correspondence or coherence in the longitudinal 
 section of the thinking process. No matter how completely we 
 may seem to explain the subject-object in any situation as the 
 meeting point of converging forces, we still need the help of a 
 principle outside of the pragmatic movement to explain the 
 identity that persists in the spatial or temporal series. Spatial 
 judgments are far from being as particular or factual as on the 
 surface they appear to be. Every lure contains a there and 
 hence it is never a particular. Spatial references in judgment 
 are always universal. There is never given to thought a genuine 
 this or that, but always thisness and lliatmss. "We may say the 
 same of our temporal judgments. It has justly been maintained 
 that every present includes a past, and therefore no temporal 
 judgment can be strictly particular. 
 
 so Experimental Logic, p. 55.
 

 
 Tliis book is DUE on the lar '
 
 UC SOUTHERN REGIONAL LIBRARY FACILITY 
 I 
 
 v7 
 LjOS ai AA~ 000 512660 2 

 
 il 
 
 ■