Glass _ Book^ / SEMICENTENNIAL PUBLICATIONS OF THE UNIVERSITY OF CALIFORNIA 1868-1918 UNIVERSITY OF CALIFORNIA PUBLICATIONS PHILOSOPHY TOLUME 3 UNIVERSITY OF CALIFORNIA PRE! BERKELEY 1918 D. 3£f •f 2. 25 1920 FOOTNOTES FORMAL LOGIC by ,y^ CHARLES H.'rIEBER z m8J US* THE LIBRARY OF CONGRESS WASHINGTON CONTENTS PAGE Preface CHAPTER I Modern Indictment of Formal Logic S CHAPTER II Apprehension. Question and Assertion 31 CHAPTER III The Import of Judgment 46 CHAPTER IV Negation and the Infinite Judgment 68 CHAPTER V Nature of Inference 81 CHAPTER VI Immediate Inference 103 CHAPTER VII The Case Against the Syllogism 122 CHAPTER VIII Novelty and Identity in Inference 147 PREFACE The psychologist, on the one hand, and the metaphysician and the episteruologist, on the other, have crowded our present day discussions in the field of pure logic into a very narrow and uncomfortable position. No sooner does the logician raise the question as to the origin and nature of the thinking process, than the psychologist warns him that he is trespassing in fields not his. Especially is this true when we venture to discuss such questions as the process whereby judgment develops into infer- ence or is depressed into conception. This we are told is not logic, but genetic psychology. On the other hand, when the 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, except 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] FOOTNOTES TO FORMAL LOGIC for its life. Iii recent years, at Least four* important volumes have been entirely devoted to this modern indictment of tradi- tional logic. Saving 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 collect ion 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 killer, V. C. B., Formal Logic, London, Macmillan, 1912; Sidgwick, A., Elementary Lotpr, Cambridge, University Press, 1914; Dewey, John, Essays in Experimental Logic, Chicago, University of Chicago Press, 191(5; Mercier, Charles, .1 New Louie, Chicago, Open Court, 1912. PEE FACE 7 Logic that is without qualification ; for I have at times said some severe things about the ancient system. However, I think on the whole my efforts will be regarded as a defense of the Traditional Logic, and to that I shall not object. For, to use a very apt phrase of Dr. Mercier, if I have to choose between the New Logic and the Old Logic, I should "plump for'' the latter. CHAPTER I THE MODERN INDICTMENT OP FORMAL LOGIC I. 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 whence and the whither of thought. "What we have to reckon with,*' Professor Dewey writes, "is not the problem of How can I think iiber- hauptt 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 thai are certain and universally valid. Even the most zealous defender of the modern "flowing philosophy" admits the exist- ence of this logic iiberhaupt, alheit, he insists that it is a useless i Studies in Logical Theory (University of Chicago Press, 1903), p. 3. [8] THE MODERN INDICTMENT OF FORMAL LOGIC 9 pursuit. Another part of thought, which regards itself just as 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 judgment not only upon its own pragmatic process, but also upon the episte- mological aspirations of the Real Logic. And it is to this basic doctrine of the new school that the old school registers its earnest 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 pure intellectualism 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 be 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 that 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, but 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 studies I shall often speak of instrumentalisni, 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 insisted 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 instrumentalism declare that think- ing is instrumental or reconstructive and not constructive, as idealism always professes. They hold that thought finds real brute existences in the world of presented fact — structures that are not created but discovered. 10 FOOTNOTES TO FORMAL LOGIC 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, [nsighl is not for its own sake but for the sake of action. Knowledge turns not inward upon itself, but outward upon con- duct. It is practical; it is pragmatic. According to the sublime Platonic formula of life (even in its most modern interpretation by Caird, Royce, Eowison and others), knowledge is virtue, not, knowledge is knowledge. Plato w r ould 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 he sine, always expresses itself in a disjunctive judgment, as we shnll src 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 can yield true knowledge. An aggregate of particulars is just TEE MODEEX IXDICTMEXT 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 that the ideas are entities, genuine objects of knowledge, and that they must never be taken as states of con- sciousness merely. The New Logic cancels the distinction between origin and validity, between what we discover about a particular fact through an analysis of its present content, and what we learn about it by an historical study of the conditions of its birth and development. Professor Dewey 3 says of the orthodox logician : ' ' He deals with the question of the eternal nature of thought and its eternal validity in relation to an eternal reality. He is concerned, not 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 it prove them? But 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, no 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. L2 FOOTNOTES TO FORMAL LOGIC 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 enlarge- ment, hut only for the criticism !,<>!/><■; translated by T. H. Abbott (London, Long- . L885), j». 3. THE MODE EX IX DICE ME NT OF FOEMAL LOGIC 13 matism when I say that value cannot be regarded as the hidden worth within a situation, which needs only to be brought 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 are 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 see how the Xew 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 con- 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 Logic 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 be 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, but 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 LOGIC ality o\' 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 bu1 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." 5 On the view which I am presenting it is evident that the term nality 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 b Experimental Logic, p. 10. THE MODERN INDICTMENT OF FORMAL LOGIC 15 is never a part of the given; the idealist insists that the sug- gested fact is already in a profound sense a present fact, other- wise it would not be even suggested. Idealism provides, without contradiction, for both the discrete and the continuous aspect of the whole within which present thinking is set. Bradley and his followers, in making reality the ultimate subject in judg- ment have kept in mind these two uses of the word. 6 Moreover, I can not think it wholly just to the traditional theories of knowledge to say with Professor Dewey that they were concerned entirely with the ' ' question of the eternal nature of thought and its eternal validity in relation to an eternal reality — that they were engaged, not with the genesis but 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, that he did not teach that truth and falsity should be wholly divorced from the particular activities that we perform at a specific need. But he would reply to the pragmatists today in the spirit of his 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 aught." 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- sBosanquet says: "The subject in every judgment of Perception is some given spot or point in sensuous contact with the percipient self. But as all reality is continuous, the subject is not merely this given spot or point." Logic (ed. 2; Oxford, Clarendon Press, 1911), I, 78. 7 Logical Theory, p. 14. L6 FOOTNOTES TO FORMAL LOGIC tain whether or not it is 'objective,' and whether other men (all or any) agree with himl H" lie docs, what arc they and what is their Logical valued Ii' he does not, why should not Ids 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 B more 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- sful 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 ns 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 Ear enough, as he lets facts recite their tale of explanation, he invariably brings us back to the point from which he set out. Be 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 yon explain the contradiction in experience? he replies naively, "There are no contradictions." Of course no contradic- ■ Mind, ii. b. .Will (1909), 402. THE MODEEX INDICTMENT OF FORMAL LOGIC 17 tion will ever be discovered in experience if he test 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 idealist the whole problem of knowledge reduces itself to the question. How are primary or internal 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 with 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 s Elementary Logic, p. 166. is FOOTNOTES TO FORMAL LOCK' grammat ical 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. Sidjrxviek 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 THE MODERN INDICTMENT OF FOEMAL LOGIC 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 the subject matter. But this I 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 Pinel 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, A New 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 that which Aristotle gave 10 Cf. Croce, Encyclopedia of Philosophical Sciences, I, 186. "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 Ave adopt in our deductions. * ' 20 FOOTNOTS8 TO FORMAL LOGIC in the Prior Analytics. Dr. Mercier maintains that there are three processes of reasoning — induction, deduction and analogy. Now. however much Logicians through the centuries max- have differed from Aristotle in their own personal opinions of the nature of the reasoning process, they have all admitted thai we owe to him the tripartite division of the reasoning process into analogy, deduction and induction. Although Dr. Mercier lias 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. Useless 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 uselexsness of the Traditional Logic in the discovery of facts, Dr. Mercier nevertheless accords to it a w r ide 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 w Logic, p. 11. "- Op. '-it., p. ] 7. THE MODEEX INDICTMENT OF FOEMAL LOGIC 21 the classification which Dr. Mercier suggests, instead of the one ordinarily found in textbooks, is itself not free from ambigu- ity of the very kind which he criticises. We are all of us at 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 not 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 origin in the 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 the 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. FOOTNOTES TO FORMAL LO<;ic V The genetic theory of judgment, upon which pragmatism rests its entire Logic, is stated most clearly and concisely by Mr. Schiller: I 1 cannot but conceive the reason as being, like the rest of our equip- ment, a weapon in the Btruggle for existence, and a means of achieving adaptation. It must follow that the practical use, which has developed it, must have stumped 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. 18 In the present essay 1 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 1898. I shall attempt to show, as I have maintained elsewhere" that thought is not merely an instrument in the struggle for existence, not simply one of the devices with which nature lias 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 pragma! ists have hestitated to commit themselves to the d net line that all judgments are practical. Such leaders, how- -■Humanism: "Philosophical essays (London, Macmillan, L903), p. 7. 14 "Pragmatism and the " priori," Present series, I H904), pp. 72-91 TILE MODEUX INDICTMENT OF FOBMAL LOGIC 23 ever, as Schiller, Sidgwick and Mercier have unhesitatingly declared, not only, that all truth works, but also that all that works is true. But Professor Dewey seems always to leave his readers in doubt as to precisely what view he holds. In his very latest utterances he has again failed to make his position clear. In an article entitled, "An Alleged New Discovery in Logic" Mr. D. S. Robinson criticises Professor Dewey's Experimental Logic and remarks 15 that he is in doubt 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 be practical." But when Professor Dewey "intimates" (not asserts), that "some" (not all) judgments "may be" (not are) practical, I, too, find myself in doubt. 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 judgment 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 16 has always declared that all definition presupposes a psychological treatment of mental states; and is Jour, philos. and psych., XIV, 225, April 26, 1917. i« There is an important sense in which every theory of 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 and most basic characteristics of the judging consciousness. Wherever we find the possi- bility of error, we are dealing with empirical facts. And there is this paradox about facts: to be real facts they must possess the inherent possi- bility of being different, and hence not facts. 24 FOOTNOTES TO FORMAL 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 ilberhaupt. 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 witli 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 THE MODEBX INDICTMENT OF FOKMAL LOGIC 25 true purpose ? Only when I have laid hold of a higher and ulti- mate purpose, namely, a criterion of this specific purpose. In short, I fail to see how purposes are capable of self-evaluation. Experimental Logic while emphasizing effects of action as tests of validity, does not furnish a criterion by means of which we may distinguish good from bad effects. Every judgment reconstructs reality, and thereby helps to continue the present order, say the defenders of the new theory of knowledge. We pronounce the judgment true if it contributes to the existing order, and false if it does not. But now, in order that we may distinguish a good effect from a bad one, we need some criterion extrinsic to the situation to tell us why it is best 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 «Cf. Windelband, Ency. Philos. Sci., I, 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 witli them. We may call the latter their value-in-themselves, the former their value-for-us. FOOTNOTES TO FORMAL LOGIC the rationality of this new elemenl is its compatibility with the old. [f it works it is pronounced true and is given its appropriate place in the established order. If it docs not fit in with the old i! is rejected as false. 1 > u t this definition of truth is more adroit than accurate. Is not the pragmafist all the while hogging 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- < l in ] ices, 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 w r orld 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 its.lf 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, hut what it eternally is, must furnish us with our deepest insight into the nature of thought. THE MODERN INDICTMENT OF FOBMAL LOGIC 27 VI The agnostic realism at the heart of every form of pragmatic logic is not easy to refute. It has descended directly from the agnosticism of the Critique of Pure Reason. The only way to dissolve this realism is to make use of Kant 's own discovery, and pursue his logic to the legitimate conclusion of its own movement. Kant pointed out the path that must be pursued in order to explain the inherent contradictions in the realistic conception of causality. He demonstrated, it would seem for all time, that the principle of efficient casuality cannot belong to reality, but that it is the mind's contribution to experience. However, he failed to see that for this very reason there can be no genuine datum in knowledge. If the facts of experience are really given, 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 FOOTNOTES TO FORMAL LOGIC ai the presenl time imposes this requiremenl on knowledge. Plato did not demand thai 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 be 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 stn ng-gegi fa nes, nothing genuinely novel or totally differ- ent. But the logic of naive realism declares that such a Streng- gegi fa nes 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 reaUzi 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 thoughl 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 acccu- THE MODERN INDICTMENT OF FORMAL LOGIC 29 rately before they knew the reason for their accurate reasoning. They followed out premises to their conclusion, or traced con- clusions back to 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 his primary purpose to make men rational — that, for the most part, they already were. He was interested to show men, by critical analysis, in what their existing rationality con- sisted. Thought does first 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 underived laws of its movement. Thought does find itself by the way 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, external, and object 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- FOOTNOTES TO FORMAL LOGIC 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 aires 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, 18 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« E.g., Windelband Bays: "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 oniverse as an articulated whole." Ency. Philos. 8ci., I, 65. THE MODE EX INDICTMENT OF FORMAL LOGIC 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 naive subjective idealism. However, it provides for a relax- ing of a too-rigid monistic ontology. When we declare that 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 fact and ground in thought. As has now frequently been pointed out, pragmatic Logic dispenses entirely with ontology in the historic sense of the word, and therefore, identifies the cause of the existence of serial facts — in their serial manifestation — and the ground 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 : it 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. FOOTNOTES TO FOBMAL LOGIC Professor Dewey has often admitted,' 1 ' by implication at any rate, that he lias not remained true to the Hegelian idealism of his earlier writings. And yel many of Ids 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 world — 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 a pari. The only truly explanatory continuity is found when !. Studies in Logical Theory, p. 36. "There is do 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 tie- "coherent" and more than the arithmetical sum of the two, that thought's activity can be evoked." THE MODE EX INDICTMENT OE FORMAL LOGIC 33 we read our way back at each instant to and through the project- ing power of the stereopticon itself. So, too, must the states of consciousness that appear chronologically in the instrumental theory of judgment be translated into a thought process that transcends time and of which that outer evolution is but the projection. A less concrete, and therefore in some ways a more satisfac- tory illustration may be taken from geometry to show the essen- tial discontinuity in the stream of consciousness. The points of a parabola, for example, take their places seriatim in obedience to the requirements of facts 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 we 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. It' 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, lias justly been called in question. That may always he regarded as one idea which includes within [ 34 | APPBEHEN SION, Q UESTION A X D . I S S EB TIOX 35 its synthetic grasp all the secondary ideas which a purposive will cares to make in it. It is the purpose to hold the multiplicity as a single object of attention that makes it 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, but it is not on that account simple. For this reason the expression simple apprehension is a misnomer. Apprehension may be of multiple content. For the purpose of the present discussion we need not go further into this controversy. It should be pointed out, however, that 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. ' ' Xo word in Logic has caused more confusion than the word idea. Even in ordinary usage it has been taken to stand for both a universal and a particular content of consciousness. 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 might be called my idea, of the tree, (2) the aggregate of inner qualities, (3) the ex- ternal reference or significance. 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 ielea 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. But 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 object is already an essential part of the idea. For Logic, the idea, or mental state is a one enwrapping a mam). It is a content contemplated from a mul- 36 FOOTNOTES TO FORMAL LOGIC tiple, that is. a dual viewpoint. Prom one of these points of view the idea or concept is a plurality; in its outward relation to the real 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 aet 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 ami 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 blue 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 Oroce seems to discredit unduly Buch an analysis of the content of consciousness. Be 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 B matter of fact, no one will ever succeed in thinking a concept, a real concept or B judgment which is not at the same time a conclusion, being Connected in B system with other conceptions and judgments." It is doubtless true as Uroee says that no one will ever think a concept by itself, but it Lfl not impossible to think the concept in its coordinated position within the whole of a specific content. Ency. Philos. Sri., I, 202. APPREHENSION, QUESTION AND ASSERTION 37 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 concept is the signi- fication or the fixed content. Berkeley and the other nominalists were plainly right in their criticism of Locke's doctrine of abstract 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 object in relation. Unre- lated objects are, as Hegel rightly said, indescribable ; they can- not even be named. The attributes in terms of which I describe any object immediately presented to consciousness, are all of them expressions of the relations of the presented object 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 object in existence we should not need a name for it, although we might need a word to distinguish between the existence and the non-existence 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. FOOTNOTES TO FORMAL LOGIC Bui prior to our knowledge of the objed as described, we know the object as merely apprehended. There is, to be sure, serious objection to Baying thai we know the object in this first simple awan ness. 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 arc 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- dict ory 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, QUESTION AND ASSERTION 39 tivity. And doubtless the same objection could be made to the term acceptance; the latter, however, is freer from the notion of activity, or decision. The expression "assertion of the object " already suggests that thought has gone out to meet the object with question, criticism, and decision. I think the word acknowl- edge is the most satisfactory for this 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 to them. 2 Every fact is, indeed, related to other facts in the real world, but I need not know this in order to proclaim my acceptance of one of the related facts as an isolated thing. I can take it at its face value : I can bow my acceptance or acknowledgment of it. When I merely contemplate the red rose, that is, when I appre- hend it simply. I acknowledge something immediately present, and nothing more. I am aware of the red color, but am not aware of the relation of the red color to anything else. When I say, the tree in my garden is tall, I am undoubtedly describing the object by means of its relation to other objects. I am also quite truly, although not so obviously, describing the tree through its rela- tions when I 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 the knots without thinking of the threads that run from knot to knot. I can gaze at the star, Sirius, con- template, accept, acknowledge it without consciously relating it to other stars. But as soon as I wish to describe — that is, com- - 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 Kard0eEncy. Philos. Set, I, 37. FOOTNOTES TO FORMAL LOGIC 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 the spurious meanings has been car- ried into the distinction between the problematic and the apo- deictic judgments. Professor Sidgwick lias 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." Bui the modal adverbs, I submit, have no intention to •intimidate the facts": they apply to the thought about the i'aets, 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 essendi. 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 reasons 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 ssed by a principle which is inherent in the other object. Bosanquet 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; hut when the entire content of the judgment becomes explicit ] i Eh in' ntary Logic, p. 71. THE IMPOST OF JUDGMEM 61 and it is made fully aware of its reasons, then comparison is seen always to lie at its heart. More is needed for an act of judgment than just the juxta- position of subject and predicate in consciousness. Comparison means more than simple association. The association theory of thought 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 state of consciousness is not always manifest. As Bosanquet has said: Its operation is extended throughout a series of the fugitive psychical facts or ideas, and although in logical thinking its operation is conscious, i.e., selects and modifies within the content of these ideas, yet it is not in itself necessarily a conscious activity. It acts in consciousness, but need not be conscious of its own principle of action.12 y 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. But every sentence has a mean- ing, even the imperative, optative, and exclamatory sentences; though these, to be 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 thought 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 12 Logic, II, 6. hi 1 FOOTNOTES TO FORMAL LOGIC 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 thai 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 emphasis 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 cxponible which was given by the older logicians to these propositions with multiple meanings w r as 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, for a non-committal atti- tude toward the question of the existence of the subject. It is often said that 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 least 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 an interesting and important work, but it is no more the special business of Logic than the transla- tion of a foreign language would be. The translations of propo- sitions should be distinguished from their transformations. The 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 science of inference, not the art 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 exhibit more truly the proper scope of Logic, than does Genetic or Instrumental Logic. I repeat the criticism so often made, that the latter is not Logic but Psychology. An excellent illustration of the failure to distinguish between Grammar and Logic is found in Dr. Mercier's treatment of propositions. He writes: For logical purposes, the most important distinction between different propositions is that between the Incomplete and the Complete. This is a distinction new to Logic, but 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, • it FOOTNOTI-S TO FORMAL LOGIC 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 ntav be missing; but we can keep the proposition in form until the missing element can be supplied, and at the Bame 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 questions 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. !3 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. w Logic, p. 30. THE IMPOST OF JUDGMEN I 65 VI Every judgment claims to be true ; if it did not, it would forfeit its right to be called a judgment. This claim to be true, means that the mind that judges distinguishes between idea and object, in recognizing that it might have an idea which is not in agreement with the object. Here, again, it is necessary to dis- tinguish between a judging consciousness and one that merely apprehends. The difference between the two is that one con- fesses the possibility of error, while the other knows nothing of the distinction between truth and falsity. There is an essen- tial difference between the simple apprehension "This is A," and the judgment, "This is A." The judgment is never merely the awareness of something present. It asserts qualities that 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 which differentiates the judgment 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 I* On this point see Sidgwick, Elementary Logic, p. 196. "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 pay for the power either of generalising or of describing a Subject; it is a defect that belongs to a quality. ' ' I 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'.xat is just as essential as the risk. 66 FOOTNOTES TO FORMAL LOOIC bare identical sell', something genuinely different from it. But we do take the risk and must lake 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? 1 ' 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 w r ell 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 w T e 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 lh on f/ht. 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 can not belong to appearance, because that, with all its contents, cannot fall outside the Absolute. An appearance THE IMPOST OF JUDGMENT (37 entirely outside of Reality is naught. The essential character- istic of falsehood, error, fiction, is that an actuality should 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 about something that never happened. It will be observed that I have differed from Bradley as to the place of error in judgment. He con- tends 15 that we can not, while making a judgment entertain the possibility of its error. One can not judge and doubt at the same time. I have insisted that one does not judge unless one does feel the actual constraint of a doubt. is Mind, n. s. XVII (1908), 154. 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, omnis deterndnatio 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. Tli is view makes possible, it seems to me, a genuine reconciliation of the divergent claims of (2) and (3). Sigwart 'a view that every negation presupposes an affirm- ation, has been characterized as "monstrous" by Bosanquet. [68] NEGATION AND THE INFINITE JUDGMENT 69 However, we must admit this is a true and accurate description of a stage in the complex whole of the judging process. That reality is a system of inter-related facts is a postulate of every judgment. This affirmation of an orderly whole which is the logical presupposition of every specific judgment, always takes the form of a disjunctive judgment. It is an assertion to the effect that reality offers alternative possibilities to the judging consciousness. "S is either P or non-P." Bosanquet 1 and Bradley 2 are doubtless right, however, in saying that this 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 the balanced terms 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. But the one is an ideal construction and the other an affirmation of fact. The prior disjunctive judgment 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, but this is clearly untenable. We can not say, as Sigwart's view would have us say, that negation is the rejection of an actual judgment. The acceptance of the bare 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." But now we may properly ask "At what stage has the exclusion taken place?" i Logic, I, 321. -Principles of Logic (London, Paul, 1883), p. 110. FOOTNOTES TO FOBMAL LOGIC [f there is no necessity for putting the verb is and excludes in tlic same tense, we may consider the exclusion to have been per- formed first and thereafter the discovery made thai the inclu- sion of .1 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: .1 (in being X) 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. 8 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 tie- prior position in Logic, in Psychology he places negation b Cf . Bradley, "Principles of Logic, p. 118. XEGATIOX AXD THE INFINITE JTDGMENT 71 after affirmation. Since negation presupposes a positive ground, he says, "it stands at a different 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 that negation is a thwarted affirmation. It is true, as has already been shown, that the prior affirmation which he concedes does not refer the ideal content to reality with the same claim to truth as the later affirmation, namely, that which selects from among the presented alternatives. The first is a suggested affirmation while the second is an asserted affirmation. But Sigwart himself recognizes the essential difference between these two forms of affirmation when he says, "The primitive judgment should not be called affirmative at all ; it would be 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 statement I do not see why Bradley finds Sigwart 's doctrine so "obviously absurd.*' There is a prevalent tendency, especially in the elementary textbooks of Logic, to define affirmation and negation in terms of approval and disapproval. This is not precisely accurate, for 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- * On this point see Sigwart. Logic; translated by Dendy (ed. 2; London, Macmillan, 1895), I, 381. 72 FOOTNOTES TO FORMAL LOGIC edgment of a contenl without critical reaction, and true judg- ment or acceptance through criticism. Bui 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 lias 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 cnretpov 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 5 Bosanquel 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 NEGA TIOX AND THE INFINITE J I DO .17 EN T 73 It is alleged to be a self-contradiction to say that 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 of bare denial, that no term can be purely negative. But now it 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 different sort it does possess. The negative term denotes an object which in the first place lacks the qualities denied by the negative term but has other qualities in terms of which that 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 might be P, 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, and 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. But 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, but none the less genuinely. In a later chapter on immediate inference I shall as at any rate capable of contributing some factor to the ideal fabric of reality. But it assumes the external shape of ignorance, or at least of failure, and the paradox consists of this — that in negation the -work of positive knowledge appears to be performed by ignorance. The contradic- tion arises, as we have seen other contradictions arise, from the adoption by thought of a shape which at best expresses it but partially, and the reten- tion of that shape when the aspect which it did express has come to be dwarfed by other aspects of knowledge. ' ' Logic, I, 293. 74 FOOTNOTES TO FORMAL LOGIC advance a new interpretation of the ancienl 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 lias to do with the "relational way" of thinking. We begin with what appears a mere couple, a two in relation. Bui the "endless fission' ' breaks out and we discover that no relation is purely diadic. Relations are ahvays within as well as hi twi i n : 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 wiiole. 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 XEGA TION AND THE IX FINITE J I WG M K V T 7.-) 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's and the non-P's lying about ready made and then proceed to affirmations or denials about them. These negative terms are the by-products of the reverse process. We first observe that P cannot be attributed to 8 and state this fact in the negative judgment "S is not P." Whereupon the query arises, if P can not be attributed to S, what can be ? In answer to this question, non-P is created and the response is embodied in the pseudo-affirmative judgment "S is non-P." The nega- tive judgment "S is non-P" affirms something indefinite. There is, therefore, abundant reason to assert with Lotze that the true meaning of this latter judgment 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 distribution falls to the ground. To say that non-P 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, but 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 FOOTNOTES TO FOBMAL Lome of it in his theoretical thinking, and the empirical scientist applies it continually ill his search for causal connections. The sciential narrows the field in any inquiry by destroying, one by one. the possibilities 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 hare denial, lint it is precisely these exceptional cases where it dot's halt at bare denial, however rare they may he. 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. XEGATIOX AXD THE INFINITE JUDGMENT 77 At an election the counter records the "ayes'' and "noes" and also the "not voting." And in Psychology we are told often of the indifferent zone that lies between the extremes in sensa- tion. It is an answer not to the point to say that the state of consciousness called indecision is decision not to decide. The question is, Why do we require for Psychology and practical life a threefold division and for Logic a twofold division ? We see, therefore, that a careful examination of these con- siderations which seem to militate against the infinite judgment shows that they are unfounded. In the first 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 be retraced, that is to say, a second infinite judgment in the next stage of division proceeds from where the first left off. 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 number 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 summum genus to a very definite infima species. 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 negative 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 FOBMAL LOGIC surely not without value. The scientist assumes that the object o\' his search will be found in a certain field, but after laborious investigation discovers thai he has set up a false hypothesis, and must seek elsewhere for the cause of the phenomenon under investigation. lie registers this fact in the infinite judgment. "S is )io)i-r." And lie 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 f 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 )io)i-J } 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 w T hen 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 /' 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 Kant'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 "S is P," "S is not P," and S is non-P have their origin not in any strict doctrine of negation, bnt in the practical convention of something less than complete negation, 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, that is, terms which mutually exclude each other, as do contradictories, but which do not together include the entire universe of think- able objects. The class of infinite judgments is a concession to contrary negation, and to the attributive view of predication. And this view, as I have already tried to show, is merely a neces- 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 true. 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 the 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 nothing. 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. so FOOTNOTES TO FORMAL LOGIC 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 .1 to non-A by imperceptible gradations within the same qualitative sphere. However far apart we place A and non-A t they will have something in common, otherwise they could not be thought together. The same norm that defines A will also define non-A. CHAPTER V The Nature of Inference I The dictionaries have found it necessary to give a score or more of synonyms to cover the many uses of the word inference by philosophers and laymen. 1 Logicians have not been so much concerned with the ambiguity in the word, as with the contradictions that seem to lie at the heart of the process of inference itself. Aristotle, very early in his thinking about the fundamental problems of Logic, 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 that "A is B," but only that "A is A." This dilemma arises then, in saying "A is B," you predicate what the object A is not, and you therefore speak falsely; but on the other hand, if you say "A is A/' you indeed predicate what it is, but you 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 inference in ways 1 Some of the 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, generalization, guess, hypothesis, illa- tion, induction, inquiry, investigation, judgment, lemma, moral, persua- sion, porism, prediction, prevision, presumption, probation, prognostica- tion, proof, ratiocination, reasoning, research, sifting, surmise, test, theorem, verdict. [81] B2 FOOTNOTES TO FORMAL 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 he (mother, or a new, or a differ- ent, or a fresh proposition. Bui 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 1 ' 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: i Ency. Brit. XVI, S79. TEE XATUHE OF IXFEBEXCE 83 Inference is a process of thought which, starting with one or more judgements, ends with another judgement made necessary 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 be a new judgement; to repeat in fresh words our original statement is not inference, any more than translation is inference. For the most part a new judgement is only got by putting together two judgements, and, as it were, extracting what they yield. But there are a few con- clusions 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 immediate infer- ence^ Welt oil's definition reads: "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, "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." 5 Bosanquet'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 Windelband insists that "Inference is nothing else than a way of establishing judgments, and is indeed a judgment by means of judgment."- This definition is satisfactory until we come to see that the whole question at issue is just the meaning of this * Introduction to Logic (Oxford, Clarendon, 1906), p. 209. * Manual of Logic (London, Clive, 1891), V, 24. •-■ Ibid., I. 256. « Logic, I. 4. " Jones, E. E. C, Elements of Logic (Edinburgh, Clarke, 1890), p. 139. b Ency. Philos. Sci., I, 27. M FOOTXOTES TO FORMAL LOGIC process of "establishing" judgments. Inference lias 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. One of the commonest of all the vagne 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." 10 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 the premise? Again we may ask, What have we added to the "old" when we say that thought lias been "active" in "stepping" to the new point of view? » e.g. Russell says: "A definition of implication is quite impossible. If ji implies q, then if p is true q is true, i.e., p's truth implies g'a truth; also if q is false p is false, Le., q*B falsehood implies p'n falsehood. Thus truth and falsehood give us merely new implications, not a definition of implication.' 1 Principles of Mathematics, p. 14. 10 Introduction ><> Logic, p. 217. TEE NATURE OF INFERENCE 85 When is the change not a step ? It is said, that the obviousness 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, it is evident that a conclusion will not lose its character as inference as soon as it becomes obvious. Inference involves discovery but it does not cease to be inference when (the discovery having been made) thought vindicates the infer- ence by proof. As Bosanquet has so well said, "Discovery ivith- out proof is conjecture; an element 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 that the ele- ments which are indirectly referred to reality should also be directly referred to reality. ' ni 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 facts, as long as they are distinct to pass from the one to the other is to make a new assertion. ' ' 12 But it seems to me that Hobhouse has not reached the central issue either. To define the "new" as that 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- 11 Logic, II, 8. i 2 Hobhouse, Theory of Knowledge (London, Methuen, 1896), p. 216. FOOTNOTES TO FORMAL LOGIC ence must finally go back to the world-old Platonic Doctrine of Recollection, [nference is the process of discovering what we already logically possess but did not observe thai we possessed until we psychologically came upon it. It' 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. We It on says, "Inference involves 'mental process, 9 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 1 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 mere 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 oilers a theory of induction that attempts the self-vindication of its own processes has on his hands this THE XATUEE OF INFERENCE 87 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 out by its earliest critics, is indeed incompetent 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 from which it proposes to relieve deduction. Induction 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 !3 Cf. Bussell, Principles of Mathematics, p. 11. "What is called induc- tion appears to me to be either disguised deduction or a method of mak- ing plausible guesses." Also Shearman, Scope of Formal Logic (London, 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, thev are not Logic at all." FOOTNOTES TO FORMAL LOGIC conscious processes pass through various stages of development. When we take inference al its early, rudimentary and uncon- scious beginning, we shall find it of a lower order than judgment, if at the same time judgmenl 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 judgmenl t lie given fact, the process of its just itieat ion, 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 <; 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 fads — rests back upon an unwarranted abstrac- tion. It has taken this fundamental relation between form and matter and pressed the con-elation 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 flu essential nature of matter may 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.' " 1,r ' 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 [natter, and the same form in different kinds of content is not altogether the same, any more than is the same genus in different Sprcirs.'*"'' 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. u Introduction to Logic, p. 214. THE XATUEE OF INFERENCE 97 as a whole. But this does not follow. The two doctrines are not so interdependent that they must stand or fall together. We may, with Bradley, deny the univerality of the syllogism, and still hold that "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 that governs not only it, but all other members of its class. Bradley is quite sure, however, that we can never determine the class of all such classes. 17 But this denial that there is a universal form of thought 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 least 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 by that which is thought about. 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 that may be 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 i" Principles of Logic, p. 471. "No possible logic can supply us with schemes of inference. You may have classes and kinds and examples of reasoning, but you can not have a set of exhaustive types. The conclusion refuses simply to fill up the blanks you have supplied." FOOTNOTES TO FORMAL LOGIC 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. Bu1 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 ma}' 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 t<» particular he called TrapaSeLj/xa. reasoning from par- ticular to universal eiraycovrj , and finally reasoning from universal to particular. avWoyia/jio^. 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 X ATE BE OF IXEEEEXCE 99 were merely operations subsidiary to real thinking which in the last analysis was always syllogistic. Professor Adamson and others have accepted Aristotle's threefold relationship but have set up three independent types of inference : namely, ( 1 ) from particular to particular, analogical inference; (2) from par- ticular to universal, inductive inference; (3) from universal to particular, deductive or syllogistic inference. But I shall insist that each of these types of reasoning expresses only in a partial and one-directional way the reciprocating thought process that is at the basis of all three. Adamson 1 8 has maintained that all inference is mediate. But in setting up these three types of reasoning he has apparently denied the necessity of mediation. In his account, each form of thinking deals with two terms only. But on closer examina- tion we find that each of these binary relations, from particular to universal, from universal to particular, from particular to particular, has 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. Xo reasoning is merely from particular to universal, nor from universal to particular, nor from particular to particular. But in any complete act of reasoning we are always passing from particular to particular via the universal. 19 This 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 be inference from particular to particular it is because we do not take the trouble to state the ground, either because, on the one 18 "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 and deductive inferences are not the same but three similar and closely connected processes." Ency. Brit., XVI, 880. is Cf. Bosanquet, Logic, II, 30. "The conception of inference from particulars to particulars is thus an illusion arising from the activity in inference of presupposed, superficial, or unanalysed universals. " LOO FOOTNOTES TO FORMAL LOCK' 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. Reasoning 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- v. isal. We see only an apparent transition directly from par- ticular to particular. But the logical analysis always discovers the necessity of tie- universal. Reasoning can not possibly take place unhss there is a universal within which the particulars, THE NATURE OF INFERENCE 101 between which thought 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 about pass- ing from one such particular to another. Yet this is the assump- tion from which every form of associational theory of thought sets out. Each idea reproduces in the content of another idea, not only itself, but in some mysterious way produces also the connecting link between itself and that other idea. Furthermore, it can be shown that the empiricist is deluded in his belief that he can make an assertion that 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 subject would be "com- pletely shut up and confined in the predicate." Such a judg- ment might almost be said to be a stage prior to bare 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 bare isolated particular. If there were no 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 fire. If it should put its finger into the second fire and be burned, we should chide it with "You didn't think," which for the purpose of the defense of the universal, I 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 LOGIC which stares at us from behind the WOllld-be particular. The object o\' knowledge is never a pure this, it always has a fringe Of Ihdhh SS. Mill and the later-day associationists have said that ''what justities 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." CHAPTER VI IMMEDIATE INFERENCE I Before considering the question of the validity of immediate inference, I wish to offer a revision of the names for the entire system of the so-called immediate inferences. Assuming that objects corresponding, to S and P do exist, and furthermore that these classes do not exhaust the entire universe, then the various relations in the universal affirmative proposition "All 8 is P," may be illustrated by the following diagram. The objections to "Euler'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 that is divided up into sections called species. Euler'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. But they are of the highest service to 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 1 have proposed have already been employed by differenl writers, but I am not aware thai any one lias 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 sel the A Oppositive § Contrapositive task of naming them, doubtless words derived from vrrto 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 reversi for converse. If as I have said, these rela- i l-.h nu nts "i Loan-, p. 14:;. IMMEDIATE INFEBENCE 105 tions were named de 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. But the two names converse and contra positive have been sanc- tioned now by so many generations of usage that it \vould be well-nigh impossible to make such a change. No one, so far as I am aware, has adopted Miss Jones' 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 the various relations I have found employed by some writer, with the exception of oppositive. In Keynes 2 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 obvcrtecl 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 inferences we should be able to pass directly to them from the original. If, however, there are two or more pulsations of thought in passing out to the more remote inferences they ought not to be called immediate. In discussing the nature of judgment I 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, Formal Logic, p. 140. L06 FOOTNOTES TO FORMAL 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, 'rinse criticisms are for the most part based on the existential import in the original proposition. It has been main- tained by Venn 8 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 confront ihI 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 S and P and their negatives; it is the assertion that one or more of these classes may be non-existent that comes as a surprise. • <•(■. Venn, Symbolic Logic, (ed. 2, London, Macmillan, 1894), p. 154. "Prom 'All X is ST' 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 V must not only exist but must also abstain from comprising all existence. " IMMEDIATE INFERENCE 107 II In a previous chapter we saw that the several definitions of inference which were examined seemed all to be circular ; nor was our own definition free 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, but circles whose radii are zero, so to speak — whose elements are concomitants, not 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 judgment about a thing, and the second intension a judgment about a judgment. Now the de- bated question whether the immediate inferences of ordinary logic are real inferences or just interpretations, transformations, or to use another suggestive expression, alternate readings, depends on whether we can establish 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 L08 KO0TNOTE8 VO t'OUMAL LOGIC tin- minds of those authors of elementary textbooks who have distinguished betweeu implied and inferred 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 oul the failure of all those definitions of inference which rely upon the pseudo-distinction between the old 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 1 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 i Theory oj Thought (New York, Barper, 1878), p. 10.'}. I Mil EDI ATE INFERENCE 109 alone, we have substituted one difficulty for another. The vital point at issue is just the question as to what constitutes one proposition. If the oneness of the judgment in the mind is always to be found in the oneness of the spoken or printed proposition then Logic is truly just another name for Grammar. And this is, in fact, what some philologists claim. Logic, they say, being compelled to wait upon language, is entirely at the mercy of the accidents of speech. This obviously revives the old question so prominent in the writings of Hamilton, Mill, Mansel and Whately, whether Logic deals with language, thought or things. Here, as I have remarked in an earlier chapter, is where the doctrine of the quantification of the predicate has its strong hold, for that doctrine is precisely such a scheme for filling out the shortcomings of language. Were it not for the inertia of our human nature, which in language, as elsewhere, follows the line of least resistance, the expression of thought would be ade- quate to thought itself, and there would probably 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 the 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 infer- ( nces from a judgment. To use a mathematical metaphor, which I 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 unquali- fied predicates. Two-dimensional thought is represented in the Hamiltonian system of propositions with quantified predicates. no FOOTNOTES TO FOBMAL LOGIC For example, in the universal affirmative proposition "All 8 is /'" 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 ether attachments with which 8 is not concerned. Situations mighl arise in which 8 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. [f we regard the subject in extension and the predicate in inten- sion, "All 8 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 S 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 Pf" 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. b 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 18 ,-i modal con version, and that presupposes a hypothetical character in the original judgment. M IMMEDIATE INFERENCE 111 III As we have already had frequent occasion to remark, most definitions say that an inference is immediate, not 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 been so denominated because thought seems to pass from one judgment to another without the assistance of a middle term. But 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 you 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 be blamed for drawing his inference from the L12 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, thai 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 contra/positive, and I need only refer to the many other special uses of the word in algebra, geometry, mechanics, music, etc. The opponents of 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 b The word inverst is employed by mathematicians and 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 B, in which 6 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 menus ''child of a father" the relation child of is, in bo far, the inverse of the relation father of." Ency. Philos. Sri., r, 97. 1 Keynes, Studies and exercises in Formal Logic (ed. 4, London, Mac- millan. 1906), p. 217. - Manual of Logic, p. 305. IMMEDIATE INFERENCE 113 But granted that inversion is a process that often yields a hypothetical conclusion — sometimes even doubly conditional — this does not destroy the practical value of these inferences. It is not true that a partial truth is no truth. The hypothetical conclusion is distinctly "better than nothing." All languages are full of ' * if s, and "if" they did not correspond to some- thing practical and also something theoretically defensible they would have been eliminated long ago. In the business of 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 judgment 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 to reach truth. In deducing the inverse the logician does not, as has been asserted, 9 attempt the absurdity of proving foxes do not bark from all dogs bark. Now in the first place, before attempt- ing to draw any of the immediate inferences from All 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 dogs exist; Is there anything that barks; Arc then brings other than dogs; Is there anything »Cf. L. E. Hicks, in an article on "Euler'a circles and adjacent space," Mind, n. s. XXI (1912), 413. Ill FOOTNOTES TO FORMAL LOCK' that dots not hark/ Also we may inquire (note now the double query), If then an beings other than dogs; are there any of Ik int/s that do not bark ; also, If there are beings that bark and if sown of these an not dogs, are there beings that art 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 Bay 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) sonu 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 are not dogs. The inver- sionist is prepared to treat a universal negative proposition in a like manner, although there is greater uncertainty about the neai lings 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. lint 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 INFERENCE 115 into the conclusion. We are challenged to find the inverse of No mathematician can square the circle and we are told that to do so we must perpetrate the absurdity of inferring from No mathematician can square the circle that Some one who is not a mathematician can square the circle. If this is all that the process accomplishes it would, indeed, he "inversion silliness." But here again, the real function of inversion is to warn you away from error. You set out 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, it must he someone among those iclw are not mathematicians." No inhabitants of Thessaly ever saw a centaur. The categorical inverse of this proposition, derived from a thrice-conditioned premise, would read. If no inhabitant of Thessaly ever saw a centaur and 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 I 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, I 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 be expected from the justice of Providence; and, what is more to the purpose, does not seem to me to be implied in the postulate. 10 But 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: // every truthful man is mortal then if there are any beings that are not mortal they will be some of those beings that are not u>New Logic, p. 290. in; FOOTNOTES TO FORMAL LOGIC truthful men. And this is an inference thai a just Providence, to whom Dr. Mercier appeals, may safely accept. It is evident that the process of inversion is adequate to any o\' 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 ease where no information to the contrary is furnished the Logician when lie 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. Now 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 resl bach upon an alleged failure to regard the existential import of propositions. Another objection has been raised, ;i Principles of Mathematics, p. 10. IMMEDIATE INFEBENCE 117 namely, that the process involves an illicit distribution. In "All 8 is P," P is undistributed while in the inverse "Some non-S is not P," P has become distributed. I think there is here a serious misunderstanding as to the meaning of distribution. The medieval law concerning distribution stated that no term must be distributed in the converse if it was not distributed in the con- veriend. But now it should be observed that this law was intended only to apply to conversion, where the prior require- ment had been imposed, namely, that the quality of the proposi- tion must not be changed. However, in the obverse, retroverse, contraverse, inverse, the quality of the proposition has suffered a change in passing to the inference ; and here a different 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 P. But in the E proposition, "No S is P," while we may say again that S is distributed because we know something about every member of the class, this knowledge is of a different kind from what we had in the case of the A proposition. In "No S is P," I know something about every S, namely that it is not a P, and this I know indirectly. This indirect process, when made explicit is as follows : first and most fundamentally I know that "S is not non-S" and then because P happens to be some- where in the region of non-S (though I am quite ignorant of just where it is) I know that "S is not P." We met this diffi- culty in the chapter on the infinite judgment. We saw that negation is always a degree more remote from reality than affirmation. Every significant negation, when fully expanded L18 FOOTNOTES TO FORMAL LOGIC reads: Since P is in the region of non-8, and since 8 excludes //"//->' it excludes thai which is included in non-8, namely P. Hut 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 w r e 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 ob version. In "All S 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 Oeighton 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 INFERENCE 119 in other words, we assume that S, not-S, not-P, all represent existing classes. This assumption is perhaps specially important in the case of inversion, and it is connected with certain difficulties that may have already occurred to the reader. In passing from Ail S is P to its inverse Some not-S is not P there is an apparent illicit process, which it is not quite easy either to account for or explain away. For the term P, which is undistributed in the premiss, is distributed in the conclusion, and yet 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 contradictory of the original predicate that an explanation of the apparent anomaly may be found. That assumption may be expressed in the form Some things are not P. The conclusion Some not-S is not P 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 of it. The true explanation is to be found in the double meaning of distribution. Each term in a proposition, as we have just stated, has an upper and a lower limit to its exten- sion. Our attention need be directed towards only one of these 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 S is P" is as Keynes has said, "Some non-S, is not P." It is indeed one and the same class P that is considered first with 8 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 P is both distributed and undistributed. The quantification of the predicate is a device for looking at P from both sides at once. a Formal Logic, p. 139. 120 FOOTNOTES TO FORMAL LOGIC V The theory of inference which I have proposed in these pages, namely, thai 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 judgmenl 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 denned some 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 smiif to its lower limit none, 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 HOIK . Some is a variable moving toward a limit in two directions, but in different senses. In the downward direction tow r ard 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. 8onu lias been identified w r ith the indeterminate class of Symbolic Logic. This is, I think a mischievous error. The some of Tra- ditional Logics 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 IMMEDIATE INFEEENCE 121 define it in terms of either its limits, all and none, presupposes that these limits themselves have already been defined. But now we should find it difficult to define none in any other way than by reference to some, and if none implies some, we move in a vicious circle in defining some as not none. We have here another illustration of what has so often been pointed out in the recent discussions, especially those inquiries into the nature of the fundamental concepts of mathematics, that when we deal with ultimate concepts it is impossible to avoid the circle in defining. It has been alleged that the particular proposition has for its collateral aim — if not its distinctive purpose — to assert that objects referred to by the subject 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 that their color is scarlet. It is evident that the primary function of the particular proposition is in reality what appears to be merely its secondary or indirect function. The particular affirmative proposition, ''Some 8 is P," taken at its face value, means to affirm, but in practice its intentions is to deny the universal negative. Like- wise, the particular negative is employed to deny the universal affirmative. This latter fact is disclosed by the form which the particular negative so often takes in all languages, ' ' All S is not P," "Not All 8 is P." These forms, which perplex the student of elementary logic, are only rightly understood when the purpose 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 ui)on 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 I THE CASE AGAINST THE SYLLOGISM 123 its most liberal interpretation, I believe it ean be shown that the case against the syllogism is not so damaging as the 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 case." 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 the correlation of genus, species, particular: or universal, particular, singular. I believe that 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 Elementary Logic, p. 227. L24 FOOTNOTES TO FORMAL 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 preferable to individual. We should notice also thai ilu' term particular is ambiguous. For in the three fold 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, "(Jive 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 un-rigid syllogism of induction are consistencies, and must be explained in terms of the threefold relation, genus, species, particular. 2 Syllogizing, or - This view of pan-syllogism I owe to the lectures of Professor Howi- Bon. An interpretation very like this has been given by Mr. Joseph, although he denies its universality. He says: "The central idea of Byllogism is that it works through concepts, or universals. The major THE CASE AGAIXST THE SYLLOGISM 125 thinking together, therefore, always involves classification. "We can think inwardly from the whole, through the members, to the minutest members ; or outwardly from the minutest member, to the larger member, then to the class, and to the largest class. I am not unmindful of what I am committed to in the assertion that all thinking is syllogistic and that this always implies classi- fication. Symbolic Logic has shown that the definition of a class is the most important and difficult of all the problems of Logic. We may condemn the class view of predication, but we cannot escape from the fundamental fact of comparison that lies some- where at the heart of all judgment and all judgment about judg- ment. It may be, as Russell and McColl have asserted, that propositions are more fundamental than classes; this would not, however, affect 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 hear, 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 wholp. Moreover, the two processes of unification and premiss asserts, not the presence of A in every f! (and therefore in C, among them), but the connection of A as such with B as such: hence wherever we fin