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LONDON: MACMILLAN AND CO., LTD. IMPLICATION AND LINEAR INFERENCE MACMILLAN AND CO., Limited LONDON • BOMBAY • CALCUTTA - MADRAS MELBOURNE THE MACMILLAN COMPANY NEW YORK ■ BOSTON • CHICAGO DALLAS • SAN FRANCISCO THE MACMILLAN CO. OF CANADA, Ltd. TORONTO IMPLICATION AND LINEAR INFERENCE BY BERNARD BOSANQUET fellow of british academy author of 'the philosophical theory of the state' MACMILLAN AND CO., LIMITED ST. MARTIN'S STREET, LONDON 1920 " Knowledge starts neither from sense-data nor from general principles, but from the complex situation in which the human race finds itself at the dawn of self- consciousness." — Professor Norman Kemp Smith, A Commentary to Xanfs Critique of Pure Reason, p. xxxviii. . \-'A'\ )l() 1 . COPYRIGHT PREFACE My object in the present work is to develop and elucidate the non-syllogistic principle on which my Logic was founded. In order to make the central idea clear, I have permitted myself some detailed criticism of other writers, while I have abstained from comphcated systematic construction. Still following Mr. Bradley, and influenced further by Mr. Joseph, especially in the distinction between Syllogism and Deduction, I have laid even more stress than before on the principle of coherence, and have insisted on " imphcation " as a term free from reference to reasoning in its traditional shapes. I have thus been able, as I hope, to do much more justice to Mr. Bradley's positive accoimt of inference than was done in my former work. The contrast expressed in the title of the book has forced itself on me continually, not only in the logical studies of which specimens appear in my criticism, but in aU common-sense argument and observation, and in actual acquaintance with reasoning as conducted by great writers and capable publicists. It may be illustrated by contrast with such facts as are referred to in the following passage from Professor Sorley's Moral Values and the Idea of God : " Their method [that of the eighteenth-century vi IMPLICATION & LINEAR INFERENCE rationalists, both Deist and orthodox] if clear was also somewhat narrowly restricted. By ' reason ' they meant the passage from proposition to proposition by the ordinary processes of deduction and induction. They brought to light what could and what could not be arrived at in this way ; but they sought to apply to the interpretation of the universe as a whole the same kind of intellectual process by which one passes from part to part in the examination of finite things, or from proposition to proposition in a chain of reasoning. They ignored what has been called the synoptic method — ^the reason as distinguished from the understanding of Plato, Kant, and Hegel. They distrusted the intellectual insight which achieves a view of the whole, even although it is willing to test that view Jjy its adequacy to comprehend the facts." 1 What is here referred to as the synoptic method, if it were interpreted as including and conditioning those other methods which are contrasted with it, woidd be the mfethod of implication of which I am to speak. The distinction between reason and imder- standing should be taken in the same way. There is no argument in which both the aspects so designated are not present. There is a passage in Green's Prolegomena to Ethics (Sect. 174) which has always interested me for the same reason. He there speaks of his fundamental philosophical doctrine as something which cannot be proved, in the sense of being deduced from other established or conceded truths, but yet is the only way in which we can put the whole thing together and understand it. Obviously, I take it, supposing the claim to be established, this is the highest degree of proof. 1 p. 462. PREFACE vii " Implication," as I shall define it, may also help us to understand the conception that "clear and distinct " ideas must be true. I am not competent to criticise the conception as it stands in Descartes' system ; but in the form in which it appears in current philosophy it has always seemed to me plainly untenable. Huxley, for instance, has " seen clearly and distinctly, and in a manner which admits of no doubt, that all our knowledge is a knowledge of states of consciousness." ^ It seems plain that an affirmation ' may be in any ordinary sense clear and distinct before the mind, and yet absolutely false, or, to respect the refinements of theory, almost absolutely false. But if what the doctrine really intends, as, I suppose, in Spinoza's work referred to below, is an affirmation founded on a distinctly apprehended object, the relation of which object to the whole order of experi- ence is also distinctly apprehended, then it seems right to say that what is- clearly and distinctly en- visaged as inevitable within a ciertain complex (or a fortiori about a simple object if sucji were possible) must be true, conditionally or absolutely — condi- tionally if the object is a supposition, merely inter- preted by the " surviving reality " (see Chap. VIII.) ; absolutely if it is itself a factor necessitated by our ordered reahty as a whole. These distinctions are embodied in the apphcation of the principle to self- evidence and the a priori, especially in the case of Husserl's doctrine, and in the attitude adopted towards judgment and supposition; My argument, particularly in Chaps. VII. and VIII., is, I hope, in harmony with Spinoza's reasoning in the Tractatus de Intellectus Emendatione, to the general effect that you cannot but have truth where you have an ^ Methods and Results, Essays, p. 193. viii IMPLICATION & LINEAR INFERENCE expression of mind without confusion, but that in the details of the sense-world to exclude confusion would demand not abstraction but unlimited individual knowledge. " It is of the nature of a thinking being, prima facie, to form true and adequate thoughts " {op. cit. Van Vloten, i. p. 25). I should be more than content if my book should prove of some service in determining the direction in which a really non-syllogistic logic is to arise. I greatly regret the death of Dr. Mercier, for whose courage and abihty I had a genuine respect. The present work contains nothing, I think, inconsistent with this feeling. BERNARD BOSANQUET. OXSHOTT, Ootober 1919. P.S. — At the last moment there comes to me Professor Joachim's Inaugural Lecture, " Immediate Experience and Mediation." Besides much else that is valuable, it contains on pp. 15 and 16 a discussion which supports and explains my criticism of " linear inference." I welcome the coincidence. CONTENTS PAOE I. The General Nature of Implication . . i II. The Linear Conception of Inference . . 21 III. Critics of the Syllogism remain within Linear Inference . . . . . • 3^ IV. Implication, Presumption, and a priori . . 70 V. Natural Procedure in Argument, its Logical Ground, and its Climax in " Dialectic " . 105 ^ VI. "Threes" in Inference . . . . • 131 VII. In what sense Logic appeals to the Study of Mind ....... 141 VIII. Judgment and Supposition . . 166 Index. . . . . • - • i77 THE GENERAL NATURE OF IMPLICATION In attempting to ascertain the ultimate basis of Inference, it will be well to begin by noting the peculiar nature of the fact which makes knowledge, in principle, irrefragable. This fact may be expressed in different forms ; but its underlying character is perhaps best accented by sajdng that we find it a contradiction in terms to repudiate knowledge as a whole. Denial is a form of knowing, no less than affirmation, and can be applied, as experiment shows directly, only within the whole of knowledge, and not to the whole as such. This is very lucidly stated in a passage of Mr. Russell's writing, to which I shall refer again, and which has something of the effect of an admission from a hostile witness. "The philosophic scrutiny, therefore, though scep- tical in regard to every detail, is not sceptical as re- gards the whole [of our common knowledge.] That is to say, its criticism of details will only be based upon their relation to other details, not upon some external criterion which can be applied to all the details equally." ^ " Universal scepticism, though logically irrefutable, 2 is practically barren ; it can only, therefore, give a certain flavour of hesitancy to our 1 Lowell Lectures, p. 67. ^ This is what makes me call Mr. Russell a hostile witness. In my view, such scepticism contradicts itself. 1 B 2 IMPLICATION & LINEAR INFERENCE i beliefs, and cannot be used to substitute other beliefs for them." "Although data can only be criticised by other data, not by an outside standard " — This is otherwise expressed, and the inconsist- ency of a general scepticism is exhibited, in the old observation that it is a plain self-contradiction to say " There is no truth." And a general doubt will be found open to the same objections as a general denial. It must, that is, and yet cannot, offer itself on the basis of some knowledge of that reality the knowledge of which it declines to accept. A man can, of course, adopt ^ an attitude of general doubt in the sense that he pro- nounces himself to have found no certainty which satisfies him, and that as a personal resolve he has made up his mind to abandon theoretical enquiry. But he cannot support his position by reasoning with- out founding it upon some conviction which amounts to an assumption of knowledge as to the kind of thing that can be known. Now Inference, which is the subject of our enquiry, includes prima facie every operation by which know- ledge extends itself. When, by reason of one or more things that you know, you believe yourself to have^"^ arrived at the knowledge of something further, you claim to have effected an inference. : Sometimes there is a difficulty in disentangling the starting-point from the result, as when we say " Two straight lines cannot enclose a space," and a question may be raised whether an inferential transition has actually taken place. But for our present purpose these doubts are un- important ; we only want to trace the nature of Inference in xmquestionable examples. ' Bradley, Essays on Truth and Reality, p. 445. I GENERAL NATURE OF IMPLICATION 3 We seem to have it given, then, as the fundamental feature of certainty in knowledge, that it is impossible to doubt or deny the body of it as a whole. It is agreed in principle that we possess a province of assertion on the whole justified, which we call truth. The difficulty and pecuharity of it is, that when we come within it to any particular statement, doubt is liable to arise as to its justification, whether we suppose this to be intrinsic or to be derivative. Thus it would seem to be a natural assumption that in establishing the details of our knowledge we transfer the character of certainty which we primarily recognise in the province of truth as a whole, to the several matters which we progressively establish within it. And a general consideration which merely em- bodies this presumption might be rendered by some such formula as " This or nothing," which, empirically speaking, we do often make use of in representing the grounds of a conviction. The essence of an inference then would be in showing of any suggested assertion that unless we accepted it, our province of truth would as a whole be taken from us. , It is through such a conception, with the explanations and modifica- tions which it obviously demands, that I shall attempt to unite under a single point of view some recent contributions to the theory of Inference. I am hopeful that such a treatment may be of service in many ways. It may confirm what is justly advanced by those who censure the syllogism, and yet mitigate the antagonism which they rightly feel be- tween syllogistic logic and the natural processes of iargument, while at the same time pointing out that their own theories frequently do not in principle abandon the ground taken up by the logic which they attack. And it might explain the very real afiinity 4 IMPLICATION & LINEAR INFERENCE i which exists between the actual mode in which expert writers on general subjects develop their comprehen- sive arguments, and that " Dialectic " method which a too narrow theory has taught us to regard with superstitious repugnance. Thus in the prehminary explanation we start from the idea of a definite given complex within which, on scrutiny, conclusions emerge whose rejection would shatter the experienced world. Hence two totalities are concerned ; the special given complex whose consequences we desire to consider, and the total character of reality, which has to be respected and maintained in specifying those conse- quences. It is not, of course, that you adjust your given complex — your premises or data — ^to what you hold to be reality. You cannot at once infer from a premise and readjust it (except by a process Which includes and develops it). But though you must base your conclusion precisely on your given complex, whatever it may be, yet you can only draw a con- clusion by appljring the complex which is your premise to the reality which survives and transcends any modification introduced by the complex. Your given complex is self-contained ; your conclusion from it asserts about the world, and is false unless the world confirms its truth. Given a machine that can fly two hundred miles an hour, it can fly from London to Edinburgh in two hours. This depends on the dis- tance between London and Edinburgh, which the given complex does not modify. And however much you take the complex to modify reality, the con- clusion must always be an appeal to reality. Thus it follows from the nature of imphcation that every inference involves a judgment based on the whole of reaUty, though referring only to a partial system which need not even be actual. You cannot I GENERAL NATURE OF IMPLICATION 5 draw a conclusion from a mere and pure supposition, though you may draw one which explicitly refers to such a supposition and nothing more. Every asser- tion, when its expUcit condition is discounted, asserts absolutely of reality as a whole. This is the claim which truth makes ab initio, that you must either affirm this proposition or deny the whole of ex- perience. Apprehend this partial system — so an inference from a supposition says — as continuous with the real universe, and, reality being what it is, so and so must result. Without this reference you do not even know that reality is non-contradictory of itself.i By way of anticipation, and to arouse interest if possible in the idea of a principle pervading the region of contingent inference and insight which is the same as that operative in a priori thought or necessary matter, I will add some commonplace examples of everyday reasoning, stated so as to illustrate the analogy I am suggesting. I do not propose to discuss them at the present stage. In every case there is a definite given complex, the individual nature of which, con- sidered together with the system of reality, gives rise to special conclusions. According to the British Constitution, the king can only act through his ministers ; and therefore in and subject to that special complex, " the king can do no wrong." In the human circulating system the blood is driven through an intricate system of elastic tubes, therefore in that system there must be a powerful force-pump in continuous operation. In a good electrical installation, a fuse will be blown before any conducting wire can be overheated. 1 See Chapter VIII. on the hypothetical proposition. 6 IMPLICATION & LINEAR INFERENCE i In a country with large foreign trade, if you want to fix prices, you must control imports. " Where there is no property, there is no injustice " (Locke). Here the nature of the system within which the inference is to hold good is perhaps inadequately defined. , , In a body like that of any higher animal the separa- tion of the head from the trunk must be fatal to life. In such a body vitality must one day give way before the forces which obstruct it.^ Or the analogy may even be seen in examples where the system of content suggests no necessity in the conclusions — in the connection of fact with fact, say, as cause and effect, but where nevertheless the " circumstantial evidence " — say, the interpretation of a whole complex of facts, as necessitated by the nature of causality — ^forces an external necessity upon a conjunction of brute circumstances. On the basis of the given connection of circumstances he was the possible murderer and no one else was. Considering what is demonstrated and what excluded, i.e. the given system, it follows that the excision of the thyroid gland dulls the intelligence. Considering testimony causes and results there can be no doubt that Charles 1. was beheaded. This latter set of examples anticipates later dis- cussions. I will now return to the cases of simpler a priori apprehension or inference. Considering then the arithmetical and geometrical examples of apprehended connections within systems, we ought, if our suggestion is warranted, to have before us, in their case, the nerve of inference quite ' The presumption which lies beneath and reinforces the afftrma- tion " All men are mortals." I do not say it is absolutely right in theory. Such presumptions may be operative without being right. I GENERAL NATURE OF IMPLICATION 7 naked. What is it ? Is our vision of it a mere intuition in the mystic sense ; something that defies analysis ? Its necessity is certainly not reducible to sub- sumption under general formulae which can be arranged as schedules, dictating the arrangement of data and the type of conclusion after syllogistic fashion. Nevertheless, there are some general features which can be noted. a. In the first place, these complexes, the spatial triangle plus the construction necessary to exhibit this or that among its properties, and the arith- metical system, are typical of the nature of true wholes. I use this cumbrous expression, in prefer- ence to saying that they are true wholes, because their character of wholeness is bought at the price of a very extreme simplicity and the omission of nearly all the responsiveness that characterises for example an organic whole. Still, such as they are, they bear the features of genuine wholes, in which no part nor characteristic is indifferent to any other ; or perhaps it would be better to speak more moderately, and to say that there is no part nor characteristic which does not affect a number of others quite different from itself. But, owing to the imperfection which in some degree clings to all but the very highest conceivable kinds of system, there are features and modifications of features which are completely indifferent to each other — e.g. the magni- tude of a triangle and the comparative magnitude of its several angles. StiU, in a very great measure, the connection, as we said, lies naked before us. The three angles of a triangle are together equal to two right angles. If it is equilateral, it is equiangular, and vice versa. If a side 8 IMPLICATION & LINEAR INFERENCE i is lengthened ceteris paribus, the opposite angle is enlarged. So too in the numerical system. Alter the value of any combination, and some correlatives, and ultimately the whole system, must be altered. If 1 is 5, 2 is 10. AU is relevant to all. There is some- thing in each which runs through every point in the system, and makes each of them, though apparently unique and peculiar, respond to every other, and vary, though in its own individual manner, yet cor- respondingly to the variations of other points or traits. Complexes, in so far as they present this character, are true " wholes " or " universals." You can tell from the modification in which one feature of them is given in what modification another feature, though quite dissimilar in character, must be given at the same time. The essence of its nature lies, to repeat it in a sentence, in being a system with different features or properties,' such that without being at all similar or repetitions of each other they present varia- tions connected by law, and therefore the variation of one is an inde^ to the variation of others. Such laws are to be/ seen in simple forms in Euclid's theorems which develop the properties of triangles or in the statements of the midtiplication table. j8. In the second place, the connection with one another of such factors or elements within a system — let us call them terms and relations — ^might in some cases be causal, but obviously it is not so always. It is most adequately expressed by the word impHcation. Within a given complex,/^a system of terms and rela- tions, so far as it possesses the unity of a true universaj^ the presence or absence of certain terms in certain modifications enables us to be sure that certain other terms in certain determinate forms will be present or absent. Thus, if our suggestion is right, the funda- I GENERAL NATURE OF IMPLICATION 9 mental principle of inference will be implication.^ This is the general name for the relation which exists between one term or relation within a universal, or connected system of terms and relations, and the others, so far as their respective modifications afford a clue to one another. Its kinds and degrees depend of course upon the nature of the system, and as we saw above, it may be so direct that we are not aware of any operation intervening between starting-point and conclusion, such as we should call an inference. And yet the relation asserted may be far from a tautology. Such is " Two straight lines cannot enclose a space." Plainly, I think, the essential basis of an inference is present here, the nexus between genuine differents ; and the absence of an operation, if it is absent, is a mere matter of degree. We must, of course, imderstand the terms, and I add, we must scrutinise the relation in the light of the system, both immediate and ultimate, within which it is affirmed — here the nature of space or, ultimately, the abstract formal properties of all objects whatever. These requirements together constitute in fact what amounts to a simple and direct inferential operation. Thus, for our purpose, so long ^ In Dr. Mercier's interesting and acute New Logic the author's effort to transcend the syllogistic doctrine, of the narrowness of which he justly complains, is nullified, as it seems to me, by his failure to push home his theory of implication. Implication for him is the relation between two propositions which state the same thing in different words, and are therefore convertible. By this parody of the real nature of a system which is the basis of inference, he condemns Iiimself to restrict, implication within the bounds of a purely formal logic; unable to deal with the attainment of truth which transcends the premises. Thus he abandons the world-wide ground of the necessary nexus of truly different propositions within complex systems, and is reduced, like Mill, to substitute for the syllogism, which he justly impeaches, an inferior form of the same subsumptive reasoning under the name Of induction. 10 IMPLICATION & LINEAR INFERENCE i as there is no tautology, the apparent absence of inference is only apparent. The conditions of which we are speaking, and the insight based upon them, are the same throughout, whether a process can be detected or cannot. But, on the other hand, our description covers- the cases in which the detail of the system itself,: or of its special bearing on the relations which interest us, has to be elicited by putting data together or by the analysis of a system which is before us as a whole. And these are the typical cases in which we are clearly aware of an operation which we call inference. The implication, that is to say, is in these cases not the first thing we see, but is brought out by some dealing with factors which ave prima facie not given in complete systematic relations. " A to the right of B, B to the right of C, .•. A to the right of C." A is not given in immediate systematic relation with C. The very simple system C B A has first to be built up, and then the result, in the implied relation of A to C, to be read off. ^ y. All inference, then, is within a connected system, and consists in reading off the implications which this system, construed as one with the whole of knowledge so far as relevant, imposes upon some of its terms. The inference is founded upon our acceptance of the joint system so arising. Its necessity may be expressed, as we saw, in the formula " This or nothing." There is a given complex as starting-point, whether fact or supposition makes no difference. Construed along with the ordered whole of our experience, it affirms a certain result, and this result, its implication, you must admit as its implication, so long as you affirm the ordered whole to be real. You cannot escape from the ; implication as such by pointing out that you do not I GENERAL NATURE OF IMPLICATION 11 affirm as a fact the complex which is your starting- | point. On the contrary, you may decide to deny \ it as a fact just because its impUcation is inevitable. If the joint system has been rightly read, which we must assume, you could only annul the imphcation by ceasing to affirm the system of reality within which you are judging it to hold. If you have judged the relation rightly, you would in the end, in attempting to annul your judgment, have to deny the Law of Contradiction. \ That is to say, an implication rightly judged is guaranteed by the whole system of reality. If you deny it, you leave nothing standing. '^ " But if the implication seems outrageous you can modify some feature in your general view of reality, and so annul the implication ? " No doubt this is possible. You may have assumed in your general basis, e.g., a false estimate of the earth's diameter, and the implication resulting on that basis may lead you to re-examine this particular point. Only, in that case, prima facie, the implica- tion has shattered its basis, and so far, between " this " and " nothing " you have chosen " nothing." ^ You have thrown aside the reahty on which you founded your conclusion, and you can proceed no further until you have established a new one in its room. And you cannot do this on the ground of your distaste for the implication. For all you can tell, the re-examination may fail to modify your basal reality, and then you will be face to face with the full alternative dictated by our principle. " The implication stands, or your whole reality goes." * The same takes place at an earlier stage in illegitimate supposi- tion. In this case you suppose a state of things which flatly contradicts and destroys the reality in the light of which you would have to judge of it. See my Logic, i. 272 ff. 12 IMPLICATION & LINEAR INFERENCE i The question of fact, we must observe, " Is the given complex real, i.e. is our supposal true ? " cannot be before us while we are arguing on its implication. If we wish to decide it, it must itself be considered as the implication of some further complex. " Given such and such data, it follows that the British Con- stitution prevails in this country." The establish- ment of those data is again an implication of further data, until we reach facts which are guaranteed by our whole experience, e.g. the rehability of perception subject to certain tests. The impossibility of dealing at once with the implication and the fact is the root of what is called the disregard of truth in formal logic. You cannot establish a fact and point out its implication by one and the same process.^ They are distinct implications having different bases. But if you are arguing from a complex of facts already established, then their implication must also be a fact. The distinct basis, which implies, in its relation to the whole reality, I that this particular system is actual, has been already examined and its claim conceded, as e.g. in case of the data which implied the existence of Neptune. But implication as such is a relation of content to reality as a whole. 8. We may observe in this place how the view of inference which we are pursuing removes all temptation to an error which is not extinct though long ago exposed.^ Reasoning, it has been said, " is a mental vision reinstating unapparent details." Explanation " of a phenomenon by the discovery 1 Unless it is the indispensable premise of an established con- clusion. But that this cannot be shown by syllogism. 2 Cp. Lewes' Aristotle, p. 76, cited in Bradley's Principles of Logic, p. 490. I GENERAL NATURE OF IMPLICATION 18 of a cause is simply the completion of its description by the disclosure of some intermediate details which had escaped observation." I only go back upon this idea because the contrast with it throws so strong a light on the conception before us. In those most simple and naked inferential connections with which we have been deaUng there is no room for any detec- tion of unapparent detail. We are working with systems of plain and obvious relations and their nexus most unmistakably declares itself to be the mainspring of the inferential operation. Thus, in all inference the principle is the same. Fresh detail may be of service, if it fills a gap in the systematic connection, as do the additions in a EucKdean construction, or circumstances which supply a missing link in evidence. But the mere aggregation of facts, such as may facilitate imaginative transition between antecedent and consequent, is not essential to inference and may well be a hindrance to the insight which it demands. That is why diagrams are useful in scientific reasoning and why a crowded map may make discernment of strategic relations more difficult than it is on a skeleton plan. Our view of the essence of reasoning makes all this seem natural. Comparing this preliminary sketch with the char- acter of the simple illustrations employed in it, three points appear which are peculiar, and which I believe must be maintained. '^ (i.) All implication is in strict logical character, qua implication, a priori. Actual certainty is a matter of degree, depending on the distinctness of the systematic organisation within the immediate whole on which it reposes, and on the same character of that inunediate whole as referred to the ultimate whole. But the nature of implication is one and 14 IMPLICATION & LINEAR INFERENCE i one only. \It is the connection between terms or sets of terms in virtue of a common nature which binds them into parts within a continuous system such that you can tell from one part of it — or more ' modestly,! that there are parts of it from which you can tell— what the other parts of it, or some of them, are and how they are behaving. Thus, as we saw from our survey of examples, a certain continuity is established between inference in a priori matter and inference in contingent matter./ Not that the cer- tainty of the former is really impaired, nor that of the latter intensified by this comparison ; unless, as may well be the case, the current estimate of it has been affected by logical superstition apart from a careful reference to its actual formulation. Never- theless a certain vitality is awakened in the doctrine. We see the how and why of the a priori character, which lies simply in the absence of complication and confusion. We see the whole province of implications as a graduated scheme, in every part of which the same type of movement is active, subject to easily intelligible distinctions. And we may hope that from the removal of logical superstitions which favoured the special privilege of a formal and isolated self-evidence, dependent in great part on the sim- plicity or emptiness of the experience concerned, we shall tend to replace in their true rank as regards . certainty our valuations of the more concrete appear- ances of the world. The depth of experience on which some implications are founded, may compensate, by giving their basis a profounder root in the world of reality, for the natural directness which seems to confer pre-eminence on others ; and the self-contradic- tion of affirming that two straight lines can enclose 1 To meet the case of imperfect systems. I GENERAL NATURE OF IMPLICATION 15 a space will not necessarily seem more flagrant than that of saying, for example, that beauty is an illusion of the human mind. It is clear again, to take a very elementary case, that a judgment of our instructed perception upon a colour harmony is in principle as good an a priori judgment as that three angles of a triangle are equal to two right angles, and so with many other valuations. The system of factors is clear and distinct before you, and there is nothing to interfere with the appreciation. If it fails to be unanimous, that merely means that in many persons the perception is inadequately trained. Right appreciation is not every man's affair. (ii.) It has been said by a recent writer ^ that it is possible for a perfectly clear intuition, which I pre- sume is one with what we mean by an a priori truth, to conflict with such another intuition, and in the end to give way before its superior convincingness. It would follow that just as Whewell supposed Dalton's law " the discoverer of which was still living " (J. S. Mill) to have attained the rank of an a priori intuition, so too it would be possible for intuitions in the progress of knowledge to lose their self-evidence and their a priori character, and with these their claim to truth. Apparent examples of this type are emphasised by those who, like Mill, desire to overthrow altogether the conception of non-empirical truth. But neither the moral which they draw, nor that which might be drawn in favour of denying all a priori character to propositions which conflict with others claiming to be of the same type, and have in the end to give way, seem quite to do v justice to the facts. Both these conclusions alike v- would deprive us of all a priori truth ; the first in 1 Husserl, Jahrbuch, 1913, pp. 36-37. 16 IMPLICATION & LINEAR INFERENCE i principle, the second in practice. For the first uses cases of such truth alleged to have proved deceptive, to infer that it has no existence at aU. The second, admitting it in principle, throws doubt upon all examples of it which do not maintain ' their char- acter to the end. And how can we tell, except in certain cases to be mentioned presently, that any particular intuition is such as can never be super- seded ? What the facts suggest, in connection with the view here advocated, is rather something of this kind. The a priori character of an intuition depends on the distinctness of the whole which is its foundation, together with the depth or comprehensiveness which determines the degree of inherence with which that whole is rooted in reality. It is subordinated by the subordination of that whole to a wider or more truly real one, but is not destroyed. Under its own con- ditions or reservations it maintains its relative truth, whereas ultimate truth could belong only to intuitions founded upon the ultimate system, such as that of . the unreahty of the self-contradictory, which is necessary to the recognition of a whole in any sense. Obviously the character of the a priori can be brought by modification of content into complexes where it was not before, and can also be withdrawn from others. But no accumulation of external counter-evidence can modify it, unless the content of the complexes on which it rests is itself modified. You cannot get rid of " Two straight lines cannot enclose a space " unless you can alter the conception of the lines or of the spatial world. / For (iii.) even the acceptance of the blankest of brute facts which evidence compels us to believe, depends obviously in one degree, and to some slight I GENERAL NATURE OF IMPLICATION 17 extent at least always in a second also, on implication within a system. In one degree at least, because — to take Mr. Joseph's example — even if we cannot see how it is imphed in the system of the world, or in the psycho- physical system of man, that the excision of the thyroid gland must dull the inteUigence,^ yet it is a truism to say that if we accept the thing as a fact, it is because we see that the evidence is such as to shatter or overthrow om- system of knowledge if we did not accept it. We may not see that to deny it contradicts the content of our psycho-physical knowledge ; but we see that in face of the system of facts which are brought together it must contradict the logical conditions imposed by the nature of causation as necessary to the systematisation of our experience. And in the second degree of which I spoke, I am sure that the proposition of fact includes^ as such^ a presumption of necessary coherence ; and its general nature stands ready, so to speak, to incorporate in its meaning any particular grounds of presumption which its content may be found to offer. The mere requirement of relevance which governs the relation of subject-quahfication to content of predicate in ordinary speech proceeds from this imphed univer- sality of the proposition and connection. As I ^ pointed out many years ago, we consider ourselves warranted in charging any qualification of the subject with an implication, whether adversative or affirma- tive, bearing on the content of the predicate. And if such an implication is obviously absent, or is denied when imputed in argument, we resent the omission as a defect or deception in the expression. If we say, 1 Cp. Joseph, p. 437. 18 IMPLICATION & LINEAR INFERENCE i " The birches are lovely in spring," " those scoHindrels ought to be hung," " the male Lychnis is tall and leah, and the female shorter and stouter," we are imder- stood to maintain some " point " in the terms attached to the subject in each case ; and if we said that we meant nothing in partictilar about the birches or the scoundrels or the male Lychnis which connected them with their respective predicates otherwise than as mere brute facts conjoined with them, we should be held to have fallen short of the demands of intel- ligible language. Every proposition claims in form and conception to explain a law, and, as we shall see more fully below, every " association of ideas," how- ever casual and particular, does operate as a general connection of characters, such as must ultimately express itself in a system.^ To summarise the suggestions of the present chapter in the simplest form. All implication ^ is of the general type of the insight that two straight, lines cannot enclose a space. If inferential, in the strict sense of proceeding by an operation, it is of the same type, but brought to bear by an operation which unifies the data, as in the construction which exhibits the angles at the base of an isosceles triangle as equal. This conception has two factors, and it might be asked which of the two is prior. One of them is the consideration that the whole is all we have, relatitely in every case, and absolutely in the universe. In dealing, therefore, with what any whole complex forces upon us, we are confronted with the alternative " This or nothing." The other factor lies in the 1 Cp. BracJIey, Principles of Logic, p. 298 ft. i' Some reservation must be made on this statement for the case of subsmnption. I GENERAL NATURE OF IMPLICATION 19 character of a true whole as a connected system. This is evinced by the coherence which insight reveals, as, for instance, through the correlative modifications which the parts of a true whole exhibit. Our " This or nothing " is not merely a bare alterna- tive proposed to us by destiny. The whole is not merely all we have, but satisfies our intelligence by definite necessities. This view tends, as I hope, to restore the balance between abstract necessities and concrete valuations, which the common doctrine oiapriorism has weighted unduly in favour of the former ; and to furnish a unitary account of the apprehension of truth, which has been erroneously dissociated as between axiom and simple fact. If we ask whether the compelling feature of implication lies in the alternative " This , or nothing," or in the connectedness of genuine wholes, the answer must be that the two are insepar- able.i It would be the same, except in degree, if there were no connectedness, and if the connectedness were not with all we have. If there were no con- nectedness there would be no such consideration as, " K I deny this, I must deny that. ' ' If the connected- ness were not with all we have, we could never reach the final proof, " If I deny this, I must deny everything." And the degrees of stringency in implications of this type are what constitute the differences of a priori ' and empirical reasoning, and a survey of the types of impUcation is what constitutes the logical method. Subsumption alone stands out as no longer considered in the light of the sole mode of inference, but rather as an inferior and essentially second-hand process. Its place and nature will be discussed below. We shall see that everything turns on having the true universal nature precisely presented. What 20 IMPLICATION & LINEAR INFERENCE i distinguishes the more strictly a priori from the empirical basis of implication is that the latter is loaded with irrelevant matter, which in various degree embarrasses our insight into necessary con- nection, or, in other words, prevents the implications imposed by the empirically given complex from being such as could be sustained on the basis of a more comprehensive whole. But this, it must be remem- bered, does not make the implications of the narrower complex irrelevant to itself. Thus we are in the habit of thinking that number implies the possibility of enumeration ; but it appears that when number is taken in a wider sense the possibility of enumeiation ceases to be characteristic of it. But this doctrine, I imagine, makes no difference to the necessity of the truths which are expressed in the multiplication;; table, so long as we restrict our attention to such numbers as are there concerned. II THE LINEAR CONCEPTION OF INFERENCE The traditional conception of Inference is widely- different from that which I have outlined in the previous chapter. And its vices are far more wide- spread than most logicians have supposed. They appear not only in the syllogistic doctrine, but also in the theories of its most convinced opponents, as well as in those very modern views which insist on the one hand upon a "priori principles of inference, and, on the other, upon an Induction through repeti- tion of occurrences in experience. Wherever stress is laid upon argument " downward " or " upward," upon inference from indemonstrable premises, or generalisa- tion from recurrent particulars, we have before us the linear conception of inference with its inherent vices. By the linear conception of inference I mean that which is drawn from the analogy of the formal syllogism — I say, " from the analogy of it," and not merely "as an embodiment of its principle," because much of what is called Induction proceeds after the same type, and has the same general defects. In reasoning by the formal syllogism, in the typical case, the essence of Inference is placed in attaching to a subject a predicate or succession of predicates, linked with it by connections through 21 22 IMPLICATION & LINEAR INFERENCE ii predicates which are further used as subjects. A highly typical application of it is the Sorites, A is B, B is C, C is D, .-. A is D. In a syllogism under- stood after this ideal, the terms, it has been said, far from coalescing, rather tend to bid each other good-bye.^ What are employed are a series of statements of conjunctions, which simply serve to attach the terms named in them to the same primary term or subject ; or if the chain of reasoning is taken back through a series of narrower subjects, the argument remains of the same character ; the conjunction of a predicate' with a subject by means of a middle term. This linear ideal of inference, being thus identified with a series of terms connected by successive state- ments of conjunction, called a chain of reasoning, is apt to be taken as typical of deduction. But true deduction, which passes, for example, from the law of gravitation to particularisation of the move- ments of the moon, is obviously a very different thing from a chain of reasoning of the type of the Sorites, which can never particularise its predicate.% There is in such deduction a modification of the predicate of the conclusion, which vitiates the argu- ment from a syllogistic point of view. Moreover, even where there is no such formal; defect, it is still a mistake to apply the name of deduction to syllogism. It is not a true syllogism to argue that because A and C are each equal to B .-. they are equal to one another ; nor are any steps of reasoning from conditions to consequents truly syllogistic when the necessity of the major premise is seen in the complex before us at the moment, and ' Wallace, Proleg. to HegeVs Logic, p. 469. " See Sigwart, Logic, Eng. Tr. i. 357. II LINEAR CONCEPTION OF INFERENCE 23 is not bona fide borrowed by assumption or from a previous argument.^ From this tradition of the linear chain of reason- ing, usually identified with deduction, and very often with empirical induction also, two complementary errors seem to be derived. One of them is, that the ultimate premises of deduction must be indemonistrable. If deduction is a chain of syllogisms, each resting upon premises previously established, either the series must extend to infinity, or it must somewhere be attached to self- evident principles. Such; it is apt to be supposed, is the principle of the syllogism itself,^ together with a nimiber of self-evident truths, which furnish various starting-points for Logic and for Science. The other begins at the other end. It is the same vice in a more modern and fashionable form. You come upon A^ - Bj,, constantly repeated in experience. Out of it you abstract A - B, and from this you go to any particular case A^ Aj A3 etc. — Bj Bg Bg etc. And here you say that you have first argued " upwards " from the indefinite particulars Ac - Bj, to the generality A - B, and can then proceed " down- wards " syllogistically, using A - B as major premise. Or you can omit the step A - B and, relying simply on Ax -By, say that you are proceeding from par- ticidars to particulars, i.e. from a general impression, or from some striking conjunction. Now the first thing to grasp is that the processes of reasoning which appear to be formulated in these two opposite ways really are one and the same, resting on the same principle of a connection of attrib.utes from which you argue by predicating its 1 Joseph, Logic', pp. 294, 311, 524. • Russell, Lowell Lectures, pp. 37 and 57. 24 IMPLICATION & LINEAR INFERENCE ii subject of a prior subject, or a further predicate, of its predicate repeated as a subject. From whence we derive our certainty either of the connection of attributes itself, or of the reasoning which apphes it, is a further question, the answer to which divides from one another the two erroneous theories which have been indicated. But the essen- tial point, which separates the principle common to them both from the more comprehensive view of inference which was outlined above, lies in assuming that reasoning can only work by subsumption of new particulars under general connections borrowed from elsewhere. Whether the connection is explicitly stated in a premise introducing a middle term, or whether the reasoning goes, in the familiar phrase, " from particulars to particulars," is irrelevant to this antithesis. The difference is that between going from a presupposed connection to a new case taken to fall under it, and determining a conclusion from a system of relations which in the moment of determination is apprehended as making it inevitable. The former type of inference, whether explicit or implicit, I call linear ; the latter in all its forms, which can be shown to include what is often classed as linear, I call systematic. The second point, then, to grasp is the true place and interpretation of linear inference in the wider scheme I have suggested. What makes Inference linear is respect for the independence of the terms. On the traditional theory of the Syllogism, and according to any or all of the maxims which have been suggested as its ground, its terms are marks or properties which affect each other, so far as the technical purpose of the reasoning is concerned, only as indications of II LINEAR CONCEPTION OF INFERENCE 25 each other's presence and absence. If the predicate i. of the conclusion in Barbara is modified from the predicate of the major premise, because it is affected by the change of subject, the argument is vitiated. The rules forbid you to regard the argument as the construction of a system in which by their combina- tion the terms throw a new light upon one another. You cannot state a proportional argument in a syllo- gism, if, that is, the rule of proportion, which iiS predicate of the major, is to be applied in the predi- cate of the conclusion to the subject of the minor. The alteration of the predicate at once vitiates the form. A ton of coal costs thirty shillings ; this is half a ton ; therefore this costs fifteen shillings. The argument is formally bad in more ways than one. The law of gravitation involves such and such movements in general ; the moon obeys the law of gravitation ; therefore the moon shows such and such movements in particular. Again, the argument is formally bad. You cannot apply or extend a syllogistic argu- ment in this way. Each term must preserve its independent being, as if enclosed in a bracket, and can only react on others by indicating the conse- quences of its presence or absence in respect of the presence or absence of the others. Thus, to apply or extend a syllogistic argument, you must find a new term or series of terms which will let itself be added on to the succession which you _ already possess, either in the form of subjects included in the first given subject, or in predicates including the last given predicate. This side of the reasoning process depends on the fact that attributes can be conjoined, with a minimum of rational connection, simply by being found to 26 IMPLICATION & LINEAR INFERENCE n coexist in the same subject or subjects. And though, even here, undoubtedly a rational connection is presumed to imderhe the fact, yet all that is made explicit may be the bare fact itself, that A, which has X, has also y, as in Thackeray's well-known story of the Abbe ^ and the nobleman. In such arguments you get, technically recognised, no bearing of the import of one term upon another at all. They are, so to speak, in capsides, and all you can do with them is to note which lie in the same drawer, and which refuse to do so. You can extend the series ad infinitum either way ; but you cannot, ■ except by a felicitous choice of a middle term which gives the cause or the reason, deepen or express the rule, which you are taken to possess. And if you do so explain it, you are forbidden to express the result in your conclusion, e.g. by explaining what sort or quality of mortality characterises Socrates. It is the extremity of such a doctrine to suppose that the principle of the syllogism is its ultimate premise, and that a train of reasoning derives its force from having at its head an axiom about a class or a rule. When this extreme irrationality is rejected, and it is observed that the necessity of every syllogism is intrinsic to its form, and not borrowed from a rule under which it is subsumed, the way is paved for reconsidering its whole nature.^ The argument, " All organisms are mortal, Man is an organism, therefore 1 I repeat it in case any reader may not have met with it. The AbM, talking among friends, has just said, " Do you know, ladies, my first penitent was a murderer " ; and a nobleman of the neigh- bourhood, entering the room at the moment, exclaims, " You there, Abb6 ? Why, ladies, I was the Abba's first penitent, and I promise you my confession astonished him I " 2 Joseph, Logic^ p. 311. II LINEAR CONCEPTION OF INFERENCE 27 he is mortal," has as obvious a necessity as the prin- ciple that what satisfies the condition of a rule falls under the rule ; and could not be derived from it without using the type of argument which the deriva- tion is meant to justify. The syllogism, in short, contains its own necessity, and when this is seen, we are inclined to ask whether it can be as purely linear as extreme tradition makes it. And it has become obvious,^ as indeed Aristotle's accoimt of the first figure implied, that it is not so. The Syllogism at its best is not a mere marshalling of trains of predicates, which remain apart and unmodified. The syllogistic process, properly under- stood and taken in instances which reveal its full import, is an operation in which the terms come together, modify one another, and construct a systematic whole, within which the conclusion is obvious and explains itself. If you say, " Oxygen- ated blood is bright ; the blood in the arteries is oxygenated blood, therefore the blood in the arteries is bright," you have brought together yoiu- terms in the conception of the circulation of the blood, and your conclusion, although it implies a rule, shows also a system in which the terms are factors, their union is rationally explained, and their meaning developed. Such a term as " bright " acquires a new meaning in the construction, and it is a mere matter of convenience whether this demands a modification of expression. If it does not, it is only because general language enables us to imder stand such a change of meaning without altering the word. But a rule which is aimed, like that of the syllogism, at excluding in principle all modification, would really destroy the vital essence of reasoning. 1 Bradley's Logic, p. 398 ; author's Logic, ii. 202, 206. 28 IMPLICATION & LINEAR INFERENCE ii Thus even the syllogism is really a case of the general character which our theory ascribes to inference. It is true that it possesses a side in which that character is minimised. That is the side which insists on the mere fact that three terms are brought together within the unity of a single subject, or, in the case of one negative premise, at least referred to it. So in the story quoted above,i what we have is two events united in a single subject, and all that we do is to recognise that the subject in the two is the same. We do not attempt to elicit further conclu- sions from the combination of the contents with one another, as we might if the subject were, say, an army, and the two events were two features of its military position. But, of course, there is a reaction between the natures of the terms, though there is no formal means of expressing it. The interest or " point " of the story consists wholly in this reaction — that such a person should have united in himself such, features and revealed them in such a way. And so with all syllogisms. All they say is that by certain rules of connection certain terms must come together or be separate. Bjit if the arguments are worth making, of course there is a " point," a something that follows from the construction, which its logical form does not adequately exhibit. For even the linear reasoning is in some sense a construction, from which the conclusion can be read oft. Our criticism amounts to saying that it is a construction in which nothing operates beyond the most formal relations of the terms. Something more may be seen in syllogism at its best, when its linear aspect is least and its system- atic aspect strongest, when it is least like a case under a borrowed rule and most like an explanation 1 See p. 26. II LINEAR CONCEPTION OF INFERENCE 29 of two points by a complex which includes them both.i Now it is a remarkable fact that in all cases, so far as I know, but one or two,^ the enemies of the syllo- gism have selected as the true type of progressive knowledge to be set up in its place simply that weaker form of itself which consists in tmiversal connections established by recurrence of conjoined events. Thus while their adverse criticism of the syllogism has been to a great extent justified,^ yet they have missed a great opportunity. There is a principle of progressive knowledge which explains its relation to experience, and goes far beyond the limits of syllogistic reasoning ; but it is not to be discovered so long as we remain within the linear doctrine of inference, and find the antithesis upon which our doctrine turns in the opposition of a priori and a posteriori or of downward and upward argiunent. When this fatal position has been adopted, it is impossible to arrive at a tenable doctrine, whether with the older empiricists we resolve the whole of reasoning into an upward (Inductive) followed by a downward (Deductive) movement, or whether, as is more fashionable among recent theorists, we begin at both ends at once, basing syllogistic argument on one self-evident a priori principle, and Induction by Simple Enimieration on another. In truth, the older assumption that syllogistic reasoning is one with deductive inference, which is common to Mill and Bain with many believers in the syllogism, contains the germs of the fallacy we are criticising. Syllogism, 1 See example, p. 27 above. » Mr. Biadley and Mr. Joseph. It is a question how far either of them should be called an enemy of the syllogism. » Not in so far as it alleges a pelitio principii ; when a imiversal is recognised as opposed to an enmneration this falls to the ground. 80 IMPLICATION & LINEAR INFERENCE ii as an argument depending on the relation of subject and attribute, does not cover the ground of Deduction and Demonstration ; and, strictly speaking, we are not syllogising when we reason from an intrinsic necessity, exhibited, for example, in a spatial or numerical construction. Syllogism and enumerative Induction bear the distinctive character of linear inference. They begin to pass into something different as they develop an aspect of systematic necessity involving transformation of the terms ; but when reasoning begins to depend on the intrinsic necessity of a transparent system, to be systematic instead of linear, we are in a wider region, of which syllogism is an outlying province ; and no escape from syllogism is open in principle by a passage to enumerative Induction. We have to look away altogether from this region of connections accepted as general rules, whether empirical or a priori, and applied by subsumption to more particular cases. We have to enter upon the wider world of implication which our preliminary chapter has outlined. Ill CRITICS OF THE SYLLOGISM REMAIN WITHIN LINEAR INFERENCE If the discussions of the two previous chapters are sound, any serious amendment of the theory of reasoning has to go much further than the hostile critics of the syllogism appear to have perceived. This may be seen in a moment from the fact that while their criticism often insists on some principle of reasoning which they suppose to differ from that of the syllogism, it has not in the majority of cases travelled outside the linear conception of inference. For, apart from mere modification of syllogistic formulae which in no way widen their principle,^ the extension of logic proffered as non-syllogistic by the reformers consists in nothing more than a theory of Induction, and that founded upon subsiimption or upon relations of similars. Now a theory of Induction might be quite other than this ; and in Mill at his best a different line of advance is indicated.^ But so long as aU that is offered is a theory of Induc- tion working by exphcit or implicit subsumption of 1 Such as those of Symbolic Logic. * I think that this is true in some degree of Dr. Mercier's Nesv Logic, and still more so of his work on Causation and Belief, in so far as Causation is recognised by other evidence than constancy of repetition. 31 32 IMPLICATION & LINEAR INFERENCE iii new cases under a principle gathered from previous experience, so long we are within the linear concep- tion, and have passed, at furthest, from an explicit to an implicit syllogism. Especially this is so, if the link between the new and the old cases is stated in terms of resemblance. Any connection of attributes, employed as a premise to determine particular cases, is prima facie of a syllogistic nature, though it may itself have been obtained by a better inductive procedure than the observation of resemblances. But if it is laid down, not merely that Induction makes a practice of using a universal connection, but that its universal connection is obtained by noting the similarity of an example before us to a previous example, or to many which are themselves similar to each other, then we are in presence not merely of a syllogistic logic, but of a syllogistic logic founded on a vicious theory of the syllogism, which, so far as applied to Induction, absolutely precludes an advance at any point beyond the method of simple enumeration. Later we shall see in detail how this maxim confines reasoning ab initio to a linear method, in the way of ranking example along with example because of an uncriticised resemblance which seems to link the subsequent examples with that which was first observed. In such a method you are tied down to likeness between cases, and at every point you are forbidden to apprehend and analyse the relation between the point of similarity and the case, or between the case and its total conditions. These preliminary observations may be supported by a very simple fact. With the exceptions indicated above, none of the recent critics give us any help if we ask whether syllogism is really one with deduc- Ill CRITICS OF THE SYLLOGISM 33 tion. That deduction and demonstration go from generals to particulars in a " descending " argument, and that syllogism is their instrument, is the tradi- tional assumption. And yet its difficulties stare us in the face. But what we find is that an inherited opposition between Syllogism and Induction has caused them to be regarded as the protagonists in the logical controversy, even when, as with Mill, the solution took the shape of reducing one of them in ultimate principle to the other. So that if Deduc- tion was not Induction, it seemed to follow that it must be Syllogism. Hence no attention was given to the really important facts of deduction and demon- stration which prove a wider explanation of reasoning to be necessary, than that of attribute linked to attribute or resemblance to resemblance, whether in the ejctemal shape of Syllogism or of Induction. It is an extraordinary thing to notice the continual repetition in text-books of the double statement that deduction is syllogistic and that deduction leads to particiilars. So far as I can see, a true syllogistic ' process cannot take us to particulars, in the sense in which a genuine deduction or demonstration does so. It can prove a general predicate of a particular - subject ; but it cannot specify and particularise the general predicate itself in accordance with the special conditions which apply to the particular subject. It follows by syllogism from " The bodies of the solar system are subject to the law of gravitation," and " The moon is a body of the solar system " that " the movements of the moon are in accordance with the law of gravitation " ; but I do not see how, by syllogistic procedure, you can fill in the astro- nomical data affecting the moon in particular, and infer from these data her movements to be true of 34 IMPLICATION & LINEAR INFERENCE in her as the exhibition of the law of gravitation in her particular case. You would have, surely, first to assign the data and calculate the movements, and then to invent a major premise saying that from such and such data such and such results could be drawn by calculation. But you could never, by a syllogism, limit the major term " subject to the law of gravitation " to the predicate of a conclusion specifying the movements resulting from gravitation in the case of the moon only. The syllogism would have four terms. And moreover, no reasoning can be syllogistic in which the operation justifies itself without reliance on a universal connection of attributes such that the conclusion follows from it by mere subsumption ; that is, the nerve of the connection being taken upon trust, and not apprehended in the inference. This has often been pointed out in the case of the axiom of things equal to the same thing. Any one who would deny that if A = B and B = C, .-. A = C would just as much deny the axiom in its abstract form. Placed as a major premise, it does no work, and therefore the argument is not a syllogism. So with calculations ; for example, with multiplications ; of large numbers. " The multiplication table up to 12 X 12 might be said to contain principles, and the multiplication of 266 x 566 to apply them " ; but whatever reason there is to doubt that 60x60 = 3600, there will be the same reason to doubt whether 6x6 = 36.1 At all events, the assumption that syllogism and deduction are one and the same, together with the assumption that the opposition between syllogism 1 Joseph, Logic^, p. 549. I have modified the latter half of the sentence to suit my point. Ill CRITICS OF THE SYLLOGISM 35 and induction is the principal crux of logic, seem to me to show a strange unconsciousness of the real issue. The true point surely is that whereas the linear type of inference includes both syllogism and induction as a single method, differing only in degrees of explicitness, there is a wholly different way of regarding the basis of reasoning which is suggested by the antithesis, among others, of syllogism and deduction. The book tradition, which I imagine to be Aris- totelian in its origin, regards syllogism and deduction as practically one. And it is worth while to insist upon the insensibility of logical writers to the glaring difficulties of this doctrine. The recent history of the question shows a curious double reaction. I read it thus. The logical book tradition had narrowed itself into a linear interpreta- tion of the syllogism. In this form it seduced by its simplicity its main antagonists, notably J. S. Mill, so that they, in pushing home their own favourite principle of induction, adopted as its essence a linear type borrowed from that syllogism which they con- ceived it to supersede. Thus their entire doctrine, aimed at overthrowing the syllogistic book tradition, reaUy remained ^ within a narrow province of their subject into which that tradition had itself inveigled them — the province which I have called that of linear inference. The foundation of Mill's theory, for example, on the appeal to resemblances between given and recalled particulars of experience, was very suitable to the syllogism in its degraded form as a doctrine of class inclusion. The major premise, as we know, was to be simply a record of the similar experiences 1 I shall point out below slight reservations on this statement. 36 IMPLICATION & LINEAR INFERENCE iii which, record or no record, were operative upon the new given particular resembling them. And the result was in Mill's case to establish linear inference as the whole secret of induction and of deduction aUke, while the identity of the latter with syllogism was not merely not repudiated, but was held to be triumphantly demonstrated in terms of the very doctrine which established induction as the funda- mental principle in both; In the meantime a remarkable counter-plot was developing. Some interpreters of the book tradition, being through its philosophical aspect in posses- sion of a wider rationale of inference and con- ception of the universal, took note of the obvious objections to finding a general type of inference in the syllogism. Their insight was stimulated, beyond a doubt, by the vigorous criticism levelled by others at the syllogism so far as it was held to be founded on class relations. And through this insight they began to urge, first, that many types of inference, and especially deduction, could obviously not be identified with syllogism ; and secondly, that syl- logism itself, when looked at more carefully, revealed a character passing beyond that ascribed to it by the tradition, and therefore was not properly appreciated so far as it was taken to be the deductive aspect of a Unear Induction.^ On the one hand, it was different from deduction; on the other hand, it was not completely linear. Thus the final dispossession of the syllogism and vital reconstruction of the doctrine of reasoning came from the traditional supporters of the former, while the fallacious re-establishment of it on the throne of ' I mean an Induction which argues from case to case on the ground of their similarity or of an identical attribute in them. Ill CRITICS OF THE SYLLOGISM 87 inference was due to its old enemies. In saying this, I do not deny that its enemies, to use that word for shortness' sake, co-operated vigorously in destroying the fossilised tradition for which Euler's circles represented the nerve of reasoning. To illustrate the situation, and not for the sake of controversy, I will indicate my meaning more precisely by one or two examples from either side. The logical theory of J. S. Mill has been restated and criticised ad nauseam ; and fortunately it is not necessary for me to retraverse the familiar ground. It is enough to recall what for him was the universal type of the reasoning process ; ^ " certain individuals have a given attribute ; an individual or individuals resemble the former in certain other attributes ; therefore they resemble them also in the given attribute." ^ Inference, that is, always proceeds from known sets of resemblances between cases to a resemblance which in one part of a set is unknown. And this is what I have spoken of as linear inference. With the experimental methods, as I have suggested, there begins a transition towards other types of reasoning. But we are concerned with a quite simple point, which has passed, I think, nearly unnoticed. It is that syllogism, for MiU, being once reduced to a vehicle of induction, covers completely the whole field of inference beyond the primary induction itself. All inference is induction or the application of indue- - tion ; and the application of induction is syllogism. Geometrical and arithmetical reasoning, of course, are not excluded. Nothing is more remarkable than 1 Mill's Lo^, Bk. II. iii. 6. * Cp. II. iv. 3, " The real premises are the individual observa- tions," etc. 38 IMPLICATION & LINEAR INFERENCE in the energy and persistence with which Mill explains and analyses every possible deductive process — ^from EucUd's theorems ^ to every step of an arithmetical or algebraical calculation ^ — ^into cases under the maxim nota notae which he has adopted as the syllogistic rule. " Deduction as we have seen con- sists of a series of inferences in this form — a is a mark of b, h oi c, c of d, therefore a is a mark of d, which last may be a truth inaccessible to direct observation." ^ The identification of the Syllogism with Deduction prima facie introduces a cross division to Mill's well- known distinction between the logic of consistency and the logic of truth. The logic of consistency becomes the logic of deduction and demonstration, while the logic of truth becomes the logic of observa- tion or apprehension (in Mill's phrase, of experimental science, Logic, II. iv. 5). On the one side he holds that Formal Logic, principally the doctrine of the Syllogism, is nothing more than the logic of consist- ency ; and it is the theory of induction which constitutes the logic of truth. On the other side, the instrument of all deductive and demonstrative science is for him the syllogism; and what belongs ' Mill's Logic, Bk. II. iv. 4. = h. yi. 2. ^ II. vi. 4 ; cp. II. iv. 1. The common sorites, given in this quotation, as the general form of Deduction, which we rather expect to go from general to particular, excites surprise at first sight, having all the appearance of a reasoning to more and more general predicates. (Cp. Sigwart's Logic, Eng. Tr. i. 357.) " What do we gain by this process of continuous ascent to higher concepts ? If our object is to extend our knowledge by means of judgements, we are moving in the wrong direction ; our predications become less and less significant, we learn less about our subjects," etc. I take it, judging from Mill's instances, that he thought of the process as departing from c is d, and finding a narrower middle term to prove the minor premise a c. This would be the Goclenian sorites. (Sigwart, ii. 184.) No effective deduction is gained by it. in CRITICS OF THE SYLLOGISM 39 to Induction pure and simple is confined to sciences which are in a comparatively elementary stage, and to the ascertainment of relatively few general pro- positions out of which the vast structures of deductive science arise by syllogistic manipulation. The services which consistency is thus represented as rendering to truth are but meagrely acknowledged when the former kind of logic is treated as " a neces- sary auxiliary " ^ to the latter, by providing for " the correctness of the application to particular cases " of inference drawn from experience in the course of " experimental " investigation. The fact is, that Mill's preoccupation with the antithesis of Syllogism and Induction has disturbed his whole scheme for the treatment of reasoning. Induction carniot possibly meet the demands of the logic of truth. Syllogism cannot possibly cover the ground of Deduction and Demonstration. They are really the two extremes of the same inferential type ; that very limited one, which operates through ascending and descending lines of predicates. If, with Mill, we insist on dividing the world of inference between them according to the nearest affinities of its constituents, we find that we have assigned nearly all the province of science to the deductive logic of mere consistency, and that nothing remains for the inductive logic of truth but to subject postulates and perceptions to a kindred organising process, in entire disregard of its claim to proceed by linkage of resem- blances. The experimental methods are a confession of this necessity. It is only when we apply the conception of systematic inference that we are able to co-ordinate the types for which the linear conception offered no appropriate places, and we see the logic » Mill's Logic, Bk. 11. Hi. 9. 40 IMPLICATION & LINEAR INFERENCE iii of system including with modifications both that of consistency and that of truth. The same fundamental position is retained not only by Mill's immediate followers,^ but, for example, by Dr. Thomas Case.^ His view represents, if my outline of the whole development is correct, the book tradition fossilised into a doctrine of class inclusion, and ready, in consequence, to amalgamate with a theory founded upon similarity. For him there are three forms of Inference and no more, Analogy, Induction, Syllogism ; and all of these are " applica- tions of the principle of similarity." " Analogical Inference requires that one particular is similar to another, induction that a whole number or class is similar to its particular instances, deduction that each particular is similar to the whole number or class." ' Thus, prima facie, he is altogether within the method of linear inference, and deduction remains purely syllogistic, as an affair of applying predicates true of classes to their members. So with the serial inferences which, insisted on, I think, first in recent times by Mr. Bradley, have figured in all logical treatises since his Principles of Logic appeared in 1883. Dr. Case does not shrink from assigning them major premises and calling them syllogistic reason- ings. The difficulty here, which he appears to neglect, is not that the major premise is cumbrous, but that it does no work, and the inference is com- plete without it. It is impossible, as we have seen, to explain deduction and demonstration by help of a major premise. But here again we have, as it seems to me, an entire insensibility on the logician's part (and he is one exceptionally well versed in the book 1 E.g. Fowler and B^in. 2 Eruyy. Brit. art. " Logic." ^ Ibid. xvi. 880. Ill CRITICS OF THE SYLLOGISM 41 tradition), to the significance of inferential method outside the procedure by borrowed general connec- tions from instance to instance.^ Dr. Schiller's purpose in his work on Formal Logic is so alien to my present argument that I may seem to do him an injustice by referring to him in this connection. The fact is, I imagine, that he is so- wholly an enemy of form as not much to care whether logic receives or does not receive a reinterpretation with reference to the form which it recognises. But the refusal to use the strongest of all weapons against the traditional linear syllogism is on his part so striking that I feel obliged to notice it. We may start from his dealing with the spatial and serial forms of non-syllogistic inference.^ All that interests him about them, I think it is fair to say, is that they are not vaUd because of their form. He holds, however, that their reasoning may always be reduced to a syllogistic type. So far, I think, as he considers form worth enquiring into at all,^ he recog- nises no other than linear inference. " Every argument, whether inductive or deductive, is really analogical.* In ' induction ' we argue from a number of cases to a ' law ' or ' rule.' In ' deduction ' we apply a rule or law to a number of cases, or, more precisely, extend the rule's application to fresh cases. 1 It is notable, however, that he allows us in some cases of in- duction concerned with objects capable of abstraction and simplifica- tion " a power of identification by which we can say that the same thing has two aspects which are inseparable." This power would take us into a new region of inference ; i.e. " not a prion, but in the act of inducing a conclusion." (See Ency. Brit. xvi. 880-81.) 2 Formal Logic, p. 214. Perhaps I may here refer to my Know- ledge and Reality, pp. 316 ff., where I tried to show that argument by subsumption in these cases is always a second-class inference. But I do not now think that I saw their full logical significance. ' E.g. Formal Logic, p. 247. * Ibid. p. 342. 42 IMPLICATION & LINEAR INFERENCE lu In both, therefore, several ' cases ' of a law are involved. But no two cases are ever absolutely 'identical'; they are known to be only 'similar,' and their ' identity ' is always constituted by abstract- ing from their differences, which are judged to be irrelevant. Hence every argument from case to case must rest upon an analogy." For him, then, I think, as for so many others, inference goes simply up and down. We can see by his treatment of explanation,^ that the idea of system, which for us gains its value from approxima- tion to the whole, has for him no special bearing on the nature of inference. He is occupied- more in refuting the idea of deduction or derivation from a single principle than in analysing the relation of system to reality and experience. Thus, in com- menting^ on the alternative of infinite regress and of intuition as bases of certainty, an alternative which depends entirely on the restriction to linear inference, he sees no third course but to dispense with certainty and to make reasoning tentative. And with this, as a general warning, I have no fault to find. It agrees in principle, though perhaps not in the degree of its application, with the thesis I am maintaining. But as a mere general warning it seems to me out of place when the question is one of relative inferential values as between different ways of looking at our experience. Much of Dr. Schiller's language is calculated to raise a doubt whether he admits in principle that there can be justified inference at all. To say that it is tentative, difficult and hazardous is to say in principle nothing at all. The question is whether under the most favourable conditions you can know 1 Formal Logic, p. 342. 2 p. 247. Ill CRITICS OF THE SYLLOGISM 43 one thing by knowing another. We all quite under- stand that you may be wrong ; unhappily, experience leaves no doubt of that. But is there any nature in" things in virtue of which it is ever possible to be right, otherwise than by a mere chance coincidence ? Can an element of experience imply something beyond itself ? If it can. Dr. Schiller's arguments about the paradox of the syllogism ^ fall to the ground. If it cannot, inference is not merely hazardous ; it is, as inference, impossible ; and what Dr. Schiller is talking about is not really inference but guesswork, and the only way of judging its value is to wait and see how it turns out. But if there is something on which inference can be founded, it seems necessary to consider fully what that something is. There is no ground for enquiring only into a restricted type of it, say, into laws and cases, and neglecting system and structure. The emphasis on relevance as the true desideratum in Induction ^ shows indeed, as Mill also showed at this point, a tendency to escape from the limits of case -to -case similarity. Relevance implies, surely, the formulation of a whole of conditions, within which you can see the more or less intimate connec- tion of the elements. It is an introduction to the logic of system. Intuition, I should add, used of insight within such constructions, is not liable to the criticisms which are fatal to it in its current applica- tion. Dr. Schiller's account of mathematical cer- tainty shows an appreciation of this point, although he does not make it clear whether he conceives the method of mathematics to be syllogistic, and from some of his utterances I should imagine that he does.^ In short, the same thing is true here which we 1 Ftninal Logic, p. 208. * P. 269. = Pp. 214, 249. 44 IMPLICATION & LINEAR INFERENCE iii have seen to be true of Mill. The critic stands in principle on the same ground with what he is criti- cising. His view is confined to ascending and descending lines of inference ; and in his polemic against what he considers the mistakes of abstract form, he does not think it worth while to advert to the question what there is in the experienced world which makes inference possible at all, and whether that character has hitherto been adequately por- trayed. And the same peculiarity reaches a climax in Dr. Mercier's brilliant treatise.^ If a complete survey of this work came within my plan, I should have much to say of the acuteness which it displays in raising logical difficulties, and the vigour with which the author's own conceptions are pressed home. But for my immediate purpose in the present work, all his vigour and acuteness serve principally to throw into relief the fundamental point which I am en- deavouring to make clear, and which his very courage and energy have only emphasised. Dr. Mercier's acuteness, exercised upon the work of his predecessors in similar views, has saved him from some obvious pitfalls. But, in avoiding these, he has recognised facts which plainly reveal the bank- ruptcy of their common theory. In his doctrine we still have the Logic of Consist- ency, that is, of Syllogism or Deduction, called Inference par excellence, and that of Truth, or Induction, or Empirical or Material Reasoning, as protagonists in the logical drama. But, though he verbally identifies Syllogism with Deduction, he is aware, apparently, of the fatal result, for his views, of treating mathematical reasoning as syllogistic, and so 1 New Logic. in CRITICS OF THE SYLLOGISM 45 insists that this kind of reasoning is not deductive — he means merely, I think, not syllogistic. And if this is his meaning, I take it he is perfectly right. We noted Mill's paradox on this head, and Dr. Case's concession. So with the test cases of the serial type, A>B, B>C, -•. A>C. He will not, with Dr. Case or Dr. Schiller, force these under major premises ; and here again I take it he is perfectly right. Whether " substitution " is a satisfactory method of inference is a further question. I should say that he admits it to be a mere result of deductive insight ; not, you can infer where you can substitute, but, you can substitute where you can infer. But the net result is this. We have on our hands Induc- tion and Deduction (Syllogism) sharply opposed as before ; but a great part of our knowledge falls under a third category, or more than one ; and of this or these categories, and their moral for logical - theoiy as a whole, we hear much less than we could wish. They suggest some form of inference genuinely outside syllogistic and linear limits, some non- syllogistic deduction and induction. For Dr. Mercier, however, as for Mill, the pro- tagonists, as we said, are Induction and Syllogism. - Induction is the appeal to experience, and may be inunediate by direct observation or experiment, but as a rule, is mediate. " Inference " may also be inunediate or mediate, but mediate Inference ( = Deduction or Syllogism) is the principal form of " Inference " discussed. The radical difference be- tween " Inference " and Induction is that Inference starts from postulates only, and takes no account of truth or of experience, while Induction rests on experience alone.^ ^ New Logic, p. 204. 46 IMPLICATION & LINEAR INFERENCE in Inference consists in the explication of implica- tions. It is therefore purely verbal. " The one statement is impUed in the other ; and the meanings cannot therefore be diverse. But the two proposi- tions look at the same fact from different points of view. The attention is directed to different aspects of the same fact " ^ (cp. on Dr. Case's " identification " above). Implication, then, is confined to a verbal procedure, and can never hold from one meaning to another that is bona fide different. " In my view Deductive Logic is purely formal, on this ground, and in this sense, that it consists solely in casting the matter of the Postulate into different forms. The Postulate gives us the matter in one form, and the task, the sole task, of Deduction, is to convert the Postulate, or part of it, into another form and to ensure that the two forms are consistent with one another." ^ It is plain that such an account of deduction could not stand for a moment if niathe- matics were taken to be deductive. But Dr. Mercier, aware of this consequence, and admitting it, denies, as we saw, not only that mathematics are syllogistic, but that they are deductive.* I have said, that if by the latter term he only means the former, he seems to me to be right. But the fact of deduction in a non-syllogistic sense would remain for him to deal with as a form of the problem which I suggest that the enemies of the syllogism neglect throughout. [ There would seem to be, then, a nexus of inference which is neither syllogism nor induction, but might conceivably throw a light on both.* But in any case, the careful reader of the above sentences will note, I think, that the attitude to 1 New Logic, p. 246 ; cp. p. 302. 2 IMd. p. 261. » P. 328. " Pp. 209, 348. Ill CRITICS OF THE SYLLOGISM 47 implication is impossible, as the obvious slurring of the facts betrays. What is for me the root of all know- ledge and reasoning is described in so many words as the same fact seen in different aspects — ^what I should call identity in difference — only to have its real import denied. Given certain premises you can go by deduction in Dr. Mercier's sense from one aspect of a fact to another, '^ e.g. from the aspect of Lord X, in which he was the priest's first penitent, to that other aspect in which he was a murderer. Only you must remember to say that the meaning is un- changed and the transition is purely verbal.^ Mediate Induction, " Empirical Reasoning," or " Material Reasoning " is the full opposite of mediate " Inference." It always appeals to experience in the form of a previous instance to which that before us is similar,^ and has foiu: terms to the three of the syllogism. " The reasoning may be represented thus ; the mark || being the sign of assimilation : Jenny Brown's illness was caused by foul drains Johnny Jones's illness was caused by (a;) foul drains." This is the first and simple statement. The going round explicitly through a similar case, actually experienced, and compared with the case to be deter- mined, is fundamental in the sharp contrast with " Inference." And we have seen that this, the distinction between cases and a rule, is the only possible distinction when you argue from similarity. You must go to previous cases, and the only possible ^ Cp. Dr. Case's " identification," by which he explains mathe- matical reasoning. 2 The example is mine. ' New Logic, p. 202. 48 IMPLICATION & LINEAR INFERENCE iii question is whether you cite them, or go by the general impression they leave on your mind (a general rule). Dr. Mercier leaves no doubt on this head.^ Now my point here is twofold. First, to proceed upon likeness ties you down ab initio to linear infer- ence, and secondly, taken as within linear infer- ence. Induction and Syllogism, so far from being opposed, are the same process. The peculiarities which are alleged as distinguishing them are bound to vanish in proportion as the connection assumes a shape which can be operative. I will say a word on these two points. (i.) Dr. Mercier puts the fundamental issue quite plainly.^ " The formation of relations of likeness and unlikeness is at the base of all reasoning. In Induction the first step, upon which the whole depends, is the discovery of a datum, that is to say, the discernment of likeness between an element in the Problem [the case some point in which is to be determined 3] and an homologous element in some proposition derived from previous experience. The next step is the establishment of identity, that is, of complete likeness, between the second element of the Problem and its homologous element in the Pre- mise. The third step is the assimilation of the third element in the Premise to the Quaesitum. In Infer- ence, if one proposition or ratio * or term is equivalent to or included or implied in another, the equivalence or inclusion or implication rests upon likeness, etc." 1 See loc. cii. just below and cp. Nem Logic, p. 348. » Op. cit. p. 348. » See statement of terms and " ratio " (e.g. causation) set out on previous page. « Dr. Mercier's name for what has been called the relating relation between the two terms of a proposition, as " was caused by " in the formula on previous page. Ill CRITICS OF THE SYLLOGISM 49 It is plain at once that this kind of inference is what has been described as linear. What you look for from the beginning is a similarity to a case before you, in an element of a connection which for some tmknown reason was accepted in a former case in experience. Out of an element (term or " ratio ") in that previous connection you fill in an element in the connection, of which the starting-point is now presented to you. Ex hypothesi you do not examine the direct arguments and presumptions arising from the whole complex of conditions in the case to be determined. The appeal to similarity with a previous instance prohibits that course ab initio. But what is stranger, you do not examine them in the previous case either. Not a word is said of criticising or testing the " ratio " between the two different terms in that previous case, e.g. the illness and its cause. That is taken for granted, and you argue purely from the likeness between Jenny's illness and Johnny's illness to a cause of Johnny's illness resembling the cause of Jenny's. Is not the type of argument unmistak- able ? You are applying to a new case a connection which you are under the impression that you have derived from past experience, and which as applied to a new case does the work of a general rule. Of course this is linear inference. There is no idea of testing the connection in either case ; no word of criticising it in its relations to the surrounding world of knowledge or of experience. And if, retaining the same method, you claim for the observed relation constancy in experience, you are merely referring to the same likeness as linking the first previous case with indefinite other previous cases as uncriticised as itself, in short, to inductioii by simple enumera- tion. There cannot be a shadow of doubt that this 50 IMPLICATION & LINEAR INFERENCE iii reasoning works by applying an uncriticised general connection, dn the ground of a resemblance of char- acters, to a new particular case. And that is linear inference ; and so long as an argument is founded on likeness you cannot escape from it, if you adduce a million previous cases. You are forbidden in any one of them to test the alleged connection by a precise analysis of the case and its whole conditions, so as to ascertain the true constant relation. (ii.) And my second point is, that this is essentially syllogistic argument, or what Dr. Mercier calls deductive.^ Not that this account is strictly true of Syllogism or of any re^Sjoning, because sameness and not similarity is their real principle. But as Dr. Mercier has told us, he offers it as representing the common basis of all reasoning ; and we say that on this assumption his Induction is one with Syllogism! To test this matter let us follow the fortunes of Jenny's and Johnny's respective illnesses from p. 201 to p. 209.2 Is it not plain that by 209 the Assimilation of Jenny's illness to Johnny's has become the subsumption of the latter under a universal relation of characteristics, causal, and constant in experience ? But then, with the appearance of these characteristics, the relation is no longer derivable from Jenny's illness as given in experience. Con- stancy in experience certainly cannot be revealed by a single instance; nor can causation be so revealed so long as the connection of the terms is not specially investigated ; and this falls beyond an induction based on likeness. 1 Cp. the criticism referred to, N&a Logic, pp. 239 ff. Dr. Mercier's reply does not, I think, touch the point, which is, whether the universal is borrowed aliunde, or apprehended as intrinsic to the argument. His " constancy in experience," moreover, dissolves under criticism, « And cp. p. 404. Ill CRITICS OF THE SYLLOGISM 51 What we have now arrived at is thus expressed by the author:^ "In formal propositions we may state the argument thus : "Since men have constantly in experience been found mortal, and since Socrates resembles in respects material to the argument men who have died, .•. Socrates will die. In this argument will be found certain characters that are common to all mediate Induction, and that form the conditions of validity of all such Induction." He has followed the same necessity which Mill followed in formulating his universal type of reason- ing. I repeat Mill's formula for comparison.^ " Certain individuals have a given attribute ; an individual or individuals resemble the other in certain other attributes ; therefore they resemble them also in the given attribute." Of course the phrase " other attributes " in the second clause implies a first set of attributes possessed by the " certain individuals " but not mentioned in the first clause. It is worth noting that the qualifications " con- stantly in experience " and " material to the argu- ment " betray a mind divided between two divergent considerations of which one must strictly be sur- plusage. What you want to know is whether the connection can be relied on to hold good. If you say " it is constant in experience " you tie yourself down, as we remarked above, to simple enumeration, and, of course, assert something that no case and no number of cases can, strictly speaking, tell you. If you say " resemblance in material respects " (and this or its equivalent is a very frequent expression of the author) you mean one of two things, which I 1 New Logic, p. 209. * See p. 37 above. 52 IMPLICATION & LINEAR INFERENCE in do not think that the author habitually distinguishes. One is "in respects which are generally a reliable index of the remaining properties of the things in which they occur." Then you are appeahng to the doctrine of essence or importance, and the allegation that, say, large numbers of men have died retains some bearing on the conclusion ; because such index " respects " do not show directly that the possessors of these properties are likely to die, but only that what one such creature does, another is likely to do.^ This already goes beyond similarity in the direction of examination of the connection, but leaves some value to numbers. The other is that you have direct reason to think that the " material respects " are indications of the predicate of the conclusion, here "liability to die,*' and not merely of a tendency to fare as other similar creatures fare. Then the mention of men who have died does not operate in the argument at all, and the reasoning ought to run ; x (organisms ?) are sure to die, Socrates is x -*. Socrates is sure to die. Obvi- ously constancy in experience is of no use except as furnishing a presumption that the respects are material and the connection therefore reliable. But there can be little doubt that the respects being held material often operate as an unacknowledged presump- tion in favour of constancy in experience. E.g. it cannot possibly be said that no one has ever believed in a man's exemption from death ; and I take it that the belief in a past absolute constancy of mortality itself rests to a great extent on a presumption that 1 Dt Mercier repudiates the idea of essence, but in trying to explain what he means is driven at last to the hardly less obscure term " nature " {New Logic, p. 217). He is there interpreting the " material respects " appealed to in the argument about Socrates cited above. Ill CRITICS OF THE SYLLOGISM 53 creatures like us must be perishable. In all these enumerative arguments the conclusion is very apt to get into the premise. In any case, we have it admitted that you argue in Induction (Dr. Mercier's Induction), not from a particular case previously experienced, the thesis from which he started, but from a universal connection, universal either by repetition or by some special necessity ; the former of which transcends any single case, and the latter of which, if asserted on the basis of Induction through similarity, cannot be investigated. The reasoning is plainly syllogistic ; an application of a rule to a case.^ But here we are met by the author's reiterated complaint, " The Universal of Induction, as a relation found in experience to be constant, has never been clearly or consistently distinguished from the Univer- sal of Deduction, which is a general rule postulated for the purpose of the argument." Except for a single point, we have already seen enough to destroy this distinction ; remembering that Deduction means for the author, not non- syllogistic synthesis or analysis, but syllogistic reasoning from a universal major premise. We have observed that the inductive connection, in proportion as it comes to be recognised and employed as a premise in its own right, becomes also determinate as between certain qualities (that is " universal ") and sloughs off the peculiarities of particular cases. It becomes, in fact, a general law, and is used precisely as a major premise is used in syllogism. And this is so in the psychology of inductive argument, as we might have said at once and cut the knot. The account of the use of instances from 1 New Logic, p. 404. 54 IMPLICATION & LINEAR INFERENCE iii experience on pp. 202-3 ^ recalls to us something that may sometimes happen, but it gives neither the true connection nor the normal fact. It is possible, if a detailed memory is awakened, to attach an argument about a case before us to a particular case in past experience, but as a rule it does not happen, and there is no reason for it. The connection is general from the first, even in the particular case, if there is one, which is recalled to memory. The connection between determinate qualities is inevitably general. And as to the fact, with all respect for Dr. Mercier's special knowledge, I cannot believe that a doctor who has treated perhaps a thousand cases of a certain ailment goes back to a particular past case in order to diagnose it in me.^ ^The connection of definite qualities has established itself in his mind, and defined itself by a continual process of adjust- ment and correction, and he goes at once from certain determinate appearances to the cause or nature or treatment which they " indicate.ji Daily experience leaves no doubt on this head. In judging of the weather, or of the action of a familiar poison, or of the strains which different materials will bear, or of the temper of a public meeting, what expert ever refers back to a particular previous occasion? He possesses the connection gathered by selection and adjustment from a long and wide experience, and also from books, the sifted and generahsed experience of others, and goes straight from the ^appearance to his conclusion. 1 Op. cit. ' Not long since, a fiiend, who is a G.P. in a working-class dis- trict, peimitted me to see certain generalisations which he had formulated after attending five thousand confinements. Am I to suppose he had in mind all the particular cases that had gone to form his conclusions ? Ill CRITICS OF THE SYLLOGISM 55 So long as reasoning is linear, that is, relies on a determinate connection applied by subsumption as a premise, you cannot possibly distinguish the prin- ciples of induction and of syllogism. But in deduction or syllogism, we are told, the universal is a mere postulate for the purpose of the argument.^ " ' The earth is larger than the sun ' is a proposition having a definite meaning, and capable of entering into a logical argument, but it does not, to me at least, imply a beUef in the statement made, nor do I in making it claim the assent of the hearer." " The ^ task of Inference is the extraction of the implications of propositions, etc." The author has here made use of a special case to support an incorrect general inference, just as he did in attaching the reference to a previous particular instance to the application of an inductive universal. Judging in make-beUeve, or subject "to reservations of many kinds, as in artistic fiction, or again in mathematics, is a well-known practice, the theory of which has been carefully studied. But to say that every general judgment, the moment you argue from it as from a premise, acquires so total a reserva- tion that it ceases altogether to be an assertion, is surely the very madness of method. Indeed, the whole conception of ideas entertained and not aflfirmed I beUeve to be untenable.' It is true thAt if Dr. Mercier told me that the earth is larger than the sun I should probably assume him to be speaking with some hidden purpose ; but it is not certain that every one would make for every one the same allowance. The theory and usage are 1 New Logic, pp. 26, 239, 404. ' Jbid. pp. 194-5. » See Bradley, Essays on Truth and Reality, p. 29 ; cp. my Know- ledge and Reality, p. 146. 56 IMPLICATION & LINEAR INFERENCE iii surely quite simple. A complete enunciative sentence is an assertion and the speaker is committed to it. Any reservation is indicated by some one of numerous conventions, of which inverted commas are the simplest, and the mere extravagance of the statement is one of the hardest to interpret. You can take any content of judgment as an assumption ; as some- thing prefaced by a " that " and as not asserted ; but so taken it cannot strictly be expressed by a complete enunciative sentence, nor form a tru^ unit of thought. Even the most extravagant proposition or one made under the completest reservation, ex- presses some amount of truth about things. Other- wise it could not be argued from. For the conclusion of an argument always follows not from the " postu- late " alone, but from the relation of the post\ilate to fact. Otherwise there would be no conclusion, but the whole sequence of affirmations, conclusion and all, would be pure fancy. From " the earth is larger than the sun," as from any other proposition, nothing follows except by its relation to facts and to the system of the world in general. You may, if you specially desire to, suppose the premises, but if you mean to make any pretence of arguing, you must draw the conclusion. That is, you must find out what the premises demand, when combined within the system of such a world as ours. It is, then, possible to use a proposition as a postulate from which to reason ; but even so some- thing more than the postulate, viz. the world of fact, has to be accepted before reasoning can take place. And in normal usage the universal connections applied to cases, which guide our thought and action every day and all day long, may indeed be truly said to be taken for granted as drawn from previous Ill CRITICS OF THE SYLLOGISM 57 experience,^ but are certainly not postulated merely with a view to argument. The link between syllogism and induction by subsumption or similarity is the use, in both, of these relations which have been gathered from experience and possess no intrinsic necessity — ^no implication, visible at the moment of consideration, from any systematic complex. And it is plain that the alleged distinctions between the two are untenable.^ They obviously form a single class in contrast to non-syllogistic reasoning in which there is true deduction and demonstration ; in which, that is, intrinsic necessity is operative. And in any case, admitting postulation to be pos- sible, it is a mere misconception by which Dr. Mercier labours to fix it on the premises of syllogism as opposed to the premises of induction. This feature really belongs, as it seems to me, no more to the one of them than to the other, and depends, so far as it exists at all, on the mere fact that they can both be used as examples in logical text-books.^ This is one of the simple conventions which govern our interpretation of propositions. It is true that we do not demand truth to fact from an example in a Latin grammar or in a logical text-book. And we can see this char^acter at once in Dr. Mercier's own instances of induction. Who supposes that the cases of Johnny Jones and Jenny Brown * are cases drawn as they stand from actual experience, and what possible difference can it make to the reader's understanding of the description whether they are so or not ? In a working induction, no doubt, we expect veracity from the exponent, though 1 To which, as we have seen, they are seldom explicitly referred. " Cp. New Logic. Answer to a critic, pp. 239-41. ' Cp. Joseph, Logie^ pp. 254-5. * New Logic, p. 202. 58 IMPLICATION & LINEAR INFERENCE in it must be remembered that his veracity or bona fides does not in the least guarantee that his examples are truly founded on experience, but merely, if assumed, save us some trouble in investigation by excluding one cause of error. All possible absurdities are founded on experience, if you believe their advocates, who may be perfectly honest. To determine the rela- tion of an alleged fact to experience is a matter not of assurance but of methodical analysis, which is out- side the process of subsumptive induction which Dr. Mercier is describing, and, as we have seen, is excluded by it. In analysing thought you must begin some- where, and you cannot begin before your beginning. You might indicate an appeal to a different method as preceding, but Dr. Mercier's language, as we see, excludes such an appeal. With the syllogistic premise it is just the same ; no more so, and no less. In a text -book example of a logical process we are illustrat- ing forward, so to speak; we are taking up the description of an argument at a certain point for didactic purposes. We cannot begin before our be- ginning, and include in our analysis of the argument forward the proofs which lie behind the initial step. Dr. Mercier has taken the inductive premise as if out- side the logical text-book, and the syllogistic premise as if within it. But if we come upon a syllogism in a serious economic or critical treatise, we do not suppose the premises to lose their quality of categorical affirmatives or negatives just because they are argued from. I think" that there is a tendency to forget that the business of logic is not to be science or reasoning, but to understand and analyse them. In doing this, it necessarily breaks them up into specimens, which, as specimens must, differ in certain features from the complete construction which is being analysed. But Ill CRITICS OF THE SYLLOGISM 59 it is the latter, the actual argument as found in knowledge, and not the former, whose character has to be estabUshed by logic. And this character cer- tainly cannot involve the denial of affirmative quality to propositions in so far as they are employed as premises in the actual body of knowledge. It must be remembered that the suggested dis- tinction is not one that could be produced by mere bona fides or detected by simple inspection. There is no point at which facts can be infallibly perceived as rooted in experience. When called upon to justify an affirmation you can only appeal to systems upon systems of propositions, describing the conditions which you hold to make the proposition reliable, and behind these the propositions which corroborate these first conditions. Dr. Mercier speaks as if to establish that a statement is founded on experience were as simple a matter as to beUeve in a witness's veracity. But veracity is no guarantee of competence, and can itself only be established on the whole by reasoning from our systematic knowledge to the substance of what is alleged. It appears then to me to be plain that in principle subsumptive induction — induction from similarity of repeated cases or by simple enumeration — is of the same class as syllogism, and that both are in contrast with true deduction or demonstration which come imder the category of systematic reasoning. The doctrine of implication has to be freed from the limitations which have been imposed upon it, and has to be recognised as applicable to the whole of system- atic reasoning, and beyond that, to all argument in which any presumption of necessity or causation is traceable. All this is suggested by Dr. Mercier's exposition, and is rendered inevitable, I think, by the 60 IMPLICATION & LINEAR INFERENCE in failure of the attempt to hold apart the provinces of syllogism and induction, and to restrict imphcation to meaningless formality, combined with the just recognition of non-syllogistic inference in certain serial arguments and in mathematics. The principle of mathematical reasoning for him is quantitative analogy. I do not suppose that this would cover the ground of the facts of non-syllogistic deduction. If the story of induction by enumeration had ended here, I do not know that it would have been worth the telling.i But it is a remarkable fact that among very distinguished philosophers whose modes of thought differ profoimdly from each other and from those above mentioned, the same conception has re- appeared, inset in quite other philosophies than that of its origin. I have in mind M. Bergson, Mr. Russell, and Dr. M'Taggart.^ I have discussed M. Bergson's doctrine in another work,^ and need here only point out that it is a view expressly hostile to intelligence. Intelligence, for him, deals naturally and solely with repetitions. Its func- tion is to bind the same to the same. The probability of a connection affirmed on inductive grounds is according to such a view proportional to the number of cases in which the alleged connection is precisely repeated. As repetition is never precise, and as the doctrine attaches no importance to the extension of a principle by adaptation over a widening area of 1 I do not mean to be discourteous to Dr. Schiller and Dr. Mercier, but the former, I am sure, is not specially interested in the question, and the value of the latter's brilliant book is due to his beginning to diverge from the doctrine. 2 Dr. M'Taggart's attitude appears in separating the a priori sharply flrom the empirical implication, and making the latter dependent on repetition. Mind, No. 95, p. 330. » Logic^, ii. 174. Ill CRITICS OF THE SYLLOGISM 61 experience, and over an expanding field of differing constituents, it naturally throws a disparaging light upon the intellect as in the main an observer of tautologies. I should imagine that the conception has in this case arisen independently of the English inductive school, and rests on a deep foundation of imperfect logic derived from the " imitation " theorists of the school of M. Tarde.^ Mr. Russell's doctrine again, and of course that of Dr. M'Taggart, differ fundamentally from that of Mill in not suggesting that the inductive principle can be proved by simple emuneration. They are agreed that if the conclusions of induction are to be valid, it must rest on an a priori principle. Linear inference still in them has its independent basis apart from any other, but is founded, not on a continuation ad in- finitum of itself, but on an a priori principle specially appropriated and framed for it. But what survives in this doctrine, and, as it seems to me, in a form that suggests inheritance from Mill,^ is the pecuhar nature of the experience to which it takes the degree of inductive probability to be proportional, with the result, I think, of a needless speddlty and isolation in the a priori principle to be assumed, and of a serious failure to unify the doctrine of inference. Mr. RusseU's statement ^ of the problem of induc- tion begins with the opposition of past and future. " If we are asked why the sim will rise to-morrow, we shall naturally answer, ' Because it always has risen every day.' We have a firm belief that it will rise in the future because it has risen in the past." 1 See my Logic'', ii. p. 240. 2 Russell, The Problem of Philosophy, p. 94, " a sign of . . . " recalling the phrase nota notae. ' Op. cit. pp. 95 ff. 62 IMPLICATION & LINEAR INFERENCE in We may refer our belief further to the laws of motion, "but the interesting doubt is whether the laws of motion will remain in operation until to-morrow." " The only ^ reason for believing that the laws of motion will remain in operation is that they have operated hitherto, so far as our knowledge of the past enables us to judge." " The real question is, do any"^ number of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future ? " He distinguishes the cause of expectations from the reasonable ground for them. " The ^ mere fact that something has happened a certain number of times causes animals and men to expect that it may happen again." Then we come to the recognition that the reference to the future is not essential. " The question ^ we really have to ask is, ' When two things have been found to be often associated, and no instance is known of the one occurring without the other, does the occurrence of one of the two, in a fresh instance, give any good ground for expecting the other ? " The reign of law * cannot be used to prove the certainty of induction, for it is itself only probable, and our belief in it rests on the very principle we are examining. This is the principle of induction, and is stated in two forms, as regards a single fresh case, and as regards a general law. I quote the latter. " (a) ^ The greater the number of cases in which a thing of the sort A has been found associated with a thing of the sort B, the more probable is it (if no cases of failure of association are known) that A is always associated with B. " (6) Under the same circumstances, a sufficient 1 Mr. Russell's italics. := Op. dt. p. 98. » P. 101. * P. 102. 6 P. 104. in CRITICS OF THE SYLLOGISM 68 number of cases of the association of A with B will make it nearly certain that A is always associated with B, and will make this general law approach cer- tainty without limit." I will add an observation from the chapter on a priori knowledge. " Thus ^ our knowledge of the general propositions of mathematics (and the same applies to logic) must be accounted for otherwise than our (merely probable) knowledge of empirical generaUsations such as ' all men are mortal.' The problem arises through the fact that such know- ledge is general, whereas aU experience is particular." The principle of induction is, as I understand, an a priori principle. The points which concern my argument in the doctrine thus exhibited are reducible to two — (i.) The relation between nupiber of cases and in- ductive probability, and (ii.) The consequent specialisation of the form given to the a priori principle of induction. It is my object to show that (i.) inductive probability depends rather on the unification of a region of ex- perience than on the number of cases in which similar conjunctions are repeated, and that (ii.) the principle of induction is not a separate and special a priori principle, but the fundamental assumption that the universe is a connected whole ; and that therefore, though it may be called a priori, it is not a priori in the sense in which supposed separate axioms, con- sidered to be severally self-evident, are a priori. (i.) The assumption is ab initio that experience is of particulars only. This governs both a the type assigned to inductive belief and ;S the character assigned to the instances on which it is held to depend. a. It is assumed that if we are asked why we believe 1 P. 131. 64 IMPLICATION &. LINEAR INFERENCE iii that the sun wUl rise to-morrow, we shall naturally answer, " Because it has risen every day." It is pretty much a chance what an unreflective person would answer, but I should say that a better answer, and one equally likely, would be, " Why not ? " That is to say, if the world in general is going on, why, apart from any special menace, pick out the sun ^ as hkely to stop ? Our beliefs through natural induction do not depend, I think, on conjunctions separated from the context of our one world, each series within itself, like successive couples of chain-shot, having no internal structure, and interwoven with no general scene and background. No experience, I should affirm, is particular, but every one is general ; and a more careful observation of natural inductive beliefs reveals this feature within them in a degree which has logical importance. From the first, the beliefs we form do not embody tautologous repetitions, but ideas or practical readinesses extending through con- siderable variations of context, and including system- atic modifications.^ And besides being systematic within, they are interwoven in a system without. They are established on the presupposed basis of the whole normal world,^ from which it is not logically nor factually correct to dissociate them. The argu- ment is in effect : " If all this goes on, why not that which seems to be inseparable from it, unless you can show a special exception against it ? " If you suggest that perhaps nothing is to go on, that surely requires very special explanation and motivation. It might be 1 Or the earth's rotation. 2 Bradley, Principles of Logic, p. 302. I think this feature of association — ^that it is a general connection — is logically important, and that natural induction is treated far too much on the lines of particularised memory ; see above on Mercier's view, p. 34. ^ See Bradley, Appearance, p. 602. Ill CRITICS OF THE. SYLLOGISM 65 questioned whether it has any meaning.^ The more the systematic connection includes, the more force this contention acquires, as e.g. if we refer the sun's rising to the laws of motion. The sceptic may be asked, Do you admit that anything goes on, and, if so, why select, whatever you do select, as in danger of stopping ? 2 p. We notice that the instances, on the repetition of which inductive probability is held to depend, are described as connections of " things " or " sorts of thi&gs " (this recognises the non-particular nature of experience ; eoery experienced coimeetion is between sorts of things) and have effectiveness through their nimabers. It is striking that the introduction to the argument should state it as a question of past resembling future, a phraseology soon abandoned. This makes a considerable difference in estimating the logic actually used in the argument. " WiU the future resemble the past ? " assumes that the past is solidly given ; while we know that as a rule it is not, and the constancy of the past experience is itself constructed by the same means as the resemblance hoped for from the future. We are not in possession of detailed experience that all men have died. We assume it on the ground of very various experiences and very comphcated presumptions. It has not been an absolutely unopposed conviction. Thus even in the most commonplace causation of beliefs, numbers ' As Bergson has in fact questioned, L'^volution eriairice, p. 318. " It is important, I think, not to put the improbability of an apparent change or lapse in the world system supematurally high. To do so weakens oui argument, by introducing an element of the miraculous. Our e:qpectation of de facto constancy is relative to the exhaustion of possibilities by our positive Imowledge, and that, I presume, is very trifling. Still change, like persistence, can only be rationally suggested by positive knowledge. 66 IMPLICATION & LINEAR INFERENCE m play a smaller part than we are apt to suppose. The alleged numbers of instances belong to the conclusion nearly as much to the premises.^ » And if we examine the question rationally the point is still clearer. What can a tautologous re- petition possibly teach us ? If we note a repetition imder changed conditions, then of course it is a help to abstracting the true form of the repeated connec- tion from the complex of circumstances. But apart from this it is surely plain that mere repetition does not and cannot advance our conviction. By the hypothesis we have had AB before, the very con- junction which we are to learn to believe in as a connection. Where this is assumed, there can no longer be a question of elimination of error. It is, then, ah initio what we are looking for, and what can be the use of giving it us again ? What happens in fact is that we assume a real connection of qualities everywhere ; and that which seems constant through varying conditions, or adapted in application to them, appears most likely to approximate to the real one. (ii.) The principle of induction, in the form cited above,^ embodies in itself the appeal to number of repetitions. It therefore appears to me to deviate from the true ground of inference in two respects, by claiming for itself a priori truth or self-evidence within its four corners, and by offering support to an inductive behef which rests on an accumulation of particular experi- enced conjunctions. If the character of experienced conjunctions were carefully scrutinised and the ulti- mate ground of knowledge considered in its full import, I beheve that this recurrence to a linear scheme of ' See Joseph, Logk\ p. 422. ' P. 62. Cp. Problems of Philosophy, p. 167. in CRITICS OF THE SYLLOGISM 67 inference would appear unnatural and contrary to logical unity. Mr. RusseU refuses, as we saw, to rest inductive probability on the reign of law, because in his view the reign of law itself is only probable and rests on the ground of inductive probabihty, which for him is an a priori law. But all that is needed for the "basis of inductive inference is surely taken for granted when we assume in any form that the whole of ex- perience furnishes a criterion, which we cannot doubt, for all its details.^ This is a position which we know cannot be denied without self-contradiction. If so, we have only to say, what follows from the above, and what Mr. Russell has implied elsewhere,^ that about everything there is a true proposition, whether I we know it or not ; and to add to this that an ex- pansion towards totality is a guarantee of relative approximation to the truth ; and we have all that is^ required for genuine induction. We thus get rid of the disorderly crowd of a priori principles, and we imderstand that the degrees of self-evidence, which Mr. Russell most suggestively mentions,^ are simply degrees of implication in the whole system which is the ultimate criterion. Induction then ceases to be, in accordance with the linear scheme of reasoning, a weakened syllogism proceeding on a connection drawn through similarity from previous cases, and returns to its natural place as the procedure by which — a universal connection being in every case assumed * — any suggested connec- tion is tested and modified according to the support or modification which the whole system of experience offers to it. Any special inductive principle, drawn 1 LoweU Lectures, p. 67. ^ Problems, p. 89. ' Ibid. p. 183. * Joseph, Logic'', pp. 406 £f. 68 IMPLICATION & LINEAR INFERENCE in so as to justify an enumerative procedure, falls to the ground with the enumerative procedure itself. The general character of the criterion is traceable from the first in the natural expansion of experienced' connections towards systematic completeness, just as even with animals, even in what would be set down as the mere causation of associations, they are much less particular and much more capable of including adapted variations than is commonly observed.^ And the sharp distinction between the empirical and the a priori universal ^ is also untenable, as indeed the admission that self-evidence has degrees very strongly suggests. It is not necessary to show that any of the simpler a priori principles are practically doubtful. It is enough to point out that all of them owe their self-evidence to their extreme simplicity and distinctness, and that it is altogether illogical to assume their truth apart from existence — ^the exist- ence, for example, of the universe. It is enough to rely on the insight that nothing is really certain except the whole, for it is impossible to say that apart from the conditions which the whole furnishes, anything would be what it is. On the other hand, in order to maintain the unity of the method of knowledge, it is not necessary to claim for empirical universals any degree of intrinsic certainty which is usually denied them. It is enough to say that all of them represent a presumption forced upon us by the order of our experience, that we have in them the best approximation which our present resources afford to the intrinsic connection which we divine and which our entire experience is an attempt to approach. None of these are given as a linkage of separate solids. All of them are selections out 1 Above, p. 64. 2 Problems, p. 167. Ill CRITICS OF THE SYLLOGISM 69 of the mass of a vital and indivisible whole, which persists throughout and underneath the coimections which we trace in it. And it may be said that in a sense the concrete experiences which carry the higher values are more certain than the simpler and more abstract relations which we are apt to call self- evident, because they carry with them more of the whole.^ The linear scheme of inference naturally leads to a disruption of the theory of reasoning, and with that to an isolation of a priori principles from each other, and of the whole a priori world from the whole of that which is called empirical — of certainty from value. And this I believe to be a profound philo- sophical error. * Cp. Principle of Individuality and Value, p. 51. IV IMPLICATION, PRESUMPTION, AND A PRIORI We have noted the broad distinction between a theory of inference based on implication, and theories which, however critical of the syllogism, in truth confine themselves within its characteristic principle of sub- sumption under a borrowed premise. We are now free to develop the idea of implica- tion as it operates, under the various circumstances which experience offers to us, at all points between the extreme poles of the regions which have for- merly been known as those of necessary and contin- gent matter. Our guiding notion is perfectly simple. It is to trace the fundamental character of infer- ence throughout our efforts to establish truth, on the hypothesis that it is essentially the same with the principle in virtue of which we affirm unhesitatingly that if a triangle is equilateral it is equiangular and vice versa, that 2 + 2 = 4, or that the same thing cannot possess differing qualities except in distinct relations. In the present chapter I shall attempt to make quite plain what I have in mind by help of a graduated set of examples, briefly commented on in passing; and then, as I hope, further elucidated by a short 70 IV IMPLICATION AND PRESUMPTION 71 discussion of a divergent opinion offered by a first- rate logician. I wiU begin in the middle, so as to hit, I if can, the meeting point of extremes. Thus I hope to start with cases which are both important, as representing practically all the inferences we use from day to day, and illimiinating, as exhibiting the common nature which links a -priori necessity at the one extreme to the faintest presumption of rationality at the other. 1. I oifer three examples from this middle region. The principle to be illustrated, it will be remembered, < is that within any complex of terms and relations, which is distinctly before our apprehension, connec- tions can be seen as between antecedents and conse- quents which are necessary and relatively a priori so long as that complex is assumed.^ I have previously suggested ^ that legal or political systems form an excellent himting ground for examples of inferential necessity outside mathematics and formal logic. Such a case we may observe in the British Constitution when analysed as a complex governed by the fact and principle of the rule of law.^ The logical point is, that in order to apprehend the relative necessity of a number of connections between antecedent and consequent which arise within such a complex, it must be envisaged as an organised whole, in sufficient detail to render the reciprocal operation of its parts or factors intelligible.* Thus in this example you have presented a com- 1 On tte distinction between such connections and the bare facts of the complex, see below, pp. 73 ff. 2 Log^; ii. p. 18. ' See A. V. Dieey's Lectures Introdvctory to the Study of the Law of the CoMtituiion, 1886. I am taking the system as Prof. Dicey presents it, and am not writing as a politician or social reformer. ' Cp. J). 8 supra. 72 IMPLICATION & LINEAR INFERENCE iv mimity of persons with a machinery for self-expression through a legislature, by which self-expression called the law, and by it alone, authority to control the actions of individuals is conferred. For every act of authority some one, e.g. in the case of the Crown a Secretary of State, is responsible, and no agent of authority can be protected, say, by superior orders, from liability to answer before an ordinary l^w court for action which may violate that comm>inal self- expression. Thus no individual can be /interfered with, to use the most general expression, except in the name of the law ; and if he suspecp that the agent of authority has overstepped the law, he has his remedy by stated processes, open alike to every one. ' From such a complex we can read oft as a necessary connection that if administrative authority becomes oppressive it can appeal for support jo no separate and peculiar law of its own, such as in some coimtries protects official conduct. Its agents are liable to actions before a judge and jury, by tie same law and procedure as every man. Or more generally, if the actions and demands of the administration conflict with a judge's construction of the law, the ordinary law, it is the latter that prevails and takes effect. This consecution can be exhibited in manyjproblems ; for example, in issues affecting personal f:^eedoi;n, or the right to freedom of discussion, or thfe right of public meeting or other analogous rights.^ 1 It is not the case that they are recognised in a constitution of this type by particular legal provisions, and they are better secured by not being so. They are not special concessions conquered one by one from an autocratic power. They follow from the rule, and the restric- » Cp. Le 2, we generalise and say that if x be any number there exists some number (or numbers) y such that y>x. We may remark in passing . . . that this latter assumption is of vital importance both to philosophy and to mathematics ; for by it the notion of infinity is introduced." Now from a logical point of view, what are we doing when we are thus smoothly carried on from apparent tautologies to statements which assume grave importance, and shortly become too complex for the layman to foUow ? Nothing can come of nothing. You could not get a significant science by simply considering a tautology. In speaking of arithmetic as a source of mathematical propositions Mr. Whitehead says,^ " The natm-e of the things is perfectly indifferent. Of aU things it is true that two and two make four. Thus we write down as the leading characteristic of mathematics that it deals with properties and ideas which are apphcable to things just because they are things, and apart from any particular feelings, etc." These properties are " the abstract formal properties of things." Now why, on the basis of properties like th^se, is it self-evident that 2 + 3 = 3 + 2 or, generahsing, that x + y = y + x'i It is not self-evident that 15 = 51. We cannot say that the order of elements is never significant. It is simply, is it not ? — ^that we are reading off the character of a series defined by a simple operation which the sign + indicates. And we know, by insight founded on ideal experiment, that a series of this kind can be applied to all dis- tinguishable things, because the peculiar nature of 1 Whitehead, pp. 151-6. ^ Ibid. p. 13. 112 IMPLICATION & LINEAR INFERENCE v different things cannot affect their distinctness.^ And we further know, from the nature of the operation, that the order in which the elements are set down makes in this case no difference, while in other statements of steps in a series it may be all-important. And when we pass on to the statement which brings in numerical infinity,^ it is obvious that we are affirming the definite nature of a series which we can see, by trying, to be rooted in the formal properties which have been mentioned, and to find in them, as we discover by trying, nothing to contradict it. To the layman it is one of the most extraordinary things in all experience that a series possessing, as it seems to him, all sorts of oddities and startling idiosyncrasies,* should arise in this almost immediate way out of the mere distinctness of everything from everything else. But in truth the arithmetical propositions and algebraical generalisations are features of a whole which has a perfectly definite structure and character, whose texture is very simple, though its entangle- ments are extraordinarily intricate. We are not deducing something significant from tautological premises ; we are building it up according to the definite law of a certain system, which reveals itself as we experiment, and which we see to admit of no alternative. ^ It is arguable, as I think Dr. Schiller has urged, that there might be experiences which shotild not admit of numeration. Mr. Broad has put a case of the kind. But it makes no ultimate difference. '^ I do not see why this should be called an assumption. It seems visible in the nature of the series. ' I am thinking, e.g., of the problem of prime numbers. And there are the brute facts of the multiplication table, which seem to make it hard to say that formal principles alone cannot give facts, if you hold to the traditional view of Deduction and treat the formal premises as the real source of all the conclusions. V NATURAL PROCEDURE IN ARGUMENT 113 That is all we want for our logical purpose. We are not being tricked into inferring determinate facts from a tautology. Mr. Whitehead's statements have each its individual meaning from the beginning, which becomes more marked and complicated as he proceeds. The connection is in essence systematic and not linear. Though gradually developed, it is intrinsic to an individual whole or " subject." ^ (ii.) Thus I believe that our natural method of " opening the case " descriptively, and placing the reader or hearer within the system which is the development of our " subject," not merely follows an instinct of common sense, but is a well-grounded logical procedure and idtimately fundamental. It seems to me probable that it is, as explicitly employed, a peculiarly modern method, owing to the feeling for impartial system and the repugnance to deduc- tion " from above," which have grown up with the empirical attitude and have indeed been exaggerated by it into falsehood. I will refer to this method briefly, for it is normal and familiar. Bishop Butler's approach to the subject of human nature explicitly adopts and defends this method. He heads his argument ^ with this sentence, " A nature is an integer ; its parts having reciprocal relaiions needful to be known," and proceeds, " whoever thinks it worth while to consider this matter thoroughly, should begin with stating to himself exactly the icT&a of a system, economy, or constitution of any parti- cular nature, or particular anything ; and he wiU, I suppose, find that it is an one or whole made up of • We may note that this can often be shown of so-called a priori apprehensions, by the simple Teminder that " you must understand the terms," i.e. you must place yourself within the individual system. Cp. Whewell, cit. in my Logic\ ii. p. 227. * Butler's Sermons, Preface, sect. 10. I 114 IMPLICATION & LINEAR INFERENCE v several parts ; but yet, that the several parts even considered as a whole do not complete the idea, unless in the notion of a whole you include the relations and respects which those parts have to each other. Every work both of nature and of art is a system." There is however one ancient example which anticipates this method, an example of immense importance in the history of thought. And this is Plato's appeal from inferences based on abstract premises in Republic I. to the constructive argument from a whole which supplies in the rest of the treatise the typical environment necessary to make man's nature intelligible. That no inferences about man's nature are sound which neglect the fact that he is a social being, and that you get to understand him by observing the play of his functions and not by apply- .jpg*¥horal axioms to his conduct, is so obvious when suggested that it easily seems commonplace. But it is really the primary type of a sound logical method. You draw out a construction, supplying the relations necessary to make your subject intelligible, and you read off your conclusions from the result. There is something of a similar contrast between the first book of Locke's Essay and the remainder of the treatise. The first book is essentially a syllogistic argument. Locke had got it fixed in his mind that inherent ideas would be explicit ab initio, and argued that as no ideas are explicit a6 initio none can be inherent. When he comes to develop his positive view of the structure and working of the mind, whatever we may think of his conclusions, his method is a more fruitful one. It seems unnecessary to furnish further examples. I had thought of adducing the first four chapters of the Origin of Species, as a whole, together with such V NATURAL PROCEDURE IN ARGUMENT 115 special cases of interrelation as those of the wood- pecker with trees and of the mistletoe ^ " with its relations to several distinct species of organic beings " ; or, again, the familiar story of the dependence of clover upon cats.^ Or in another sphere one might have referred to Professor Dicey's book, already laid under contribution,* and insisted again on the ■ intrinsic relations and properties which become necessary when the complex of the British Constitu- tion, with its governing principle of the rule of law, is exhibited before us. But more does not seem necessary, and we shall see below that " the development of a subject " * is not only the natural method of everyday argument, but is also pronounced by logical theory to be the central feature of inference. 2. The above suggestion is confirmed when we bring before us in a single survey the phases of this develop- ment, as it embodies itself in the several special shapes assumed by inference. It is here that in an enquiry which has been unaccountably neglected by logicians,^ Mr. Bradley has practically laid the foundations of a " New Logic." Here, so far as I know, for the first time, the rules of syllogism and of the kindred methods which share its limitations were flung to the winds. What was 1 Origin of Species, p. 2. 2 Ibid. p. 57. ' P. 71 supra. ' Bradley's Principles of Logic, p. 454. " What, then, was the present writer about when, in earlier days, he attempted to follow Mr. Bradley's lead ? He can only answer, that while he beUeves hinlself, in his Logic, to have embodied truly the most significant principles of the enquiry, he now recognises that he ought to have apprehended more completely the plot, so to speak, and spirit which made the story of inference a new thing. This section is a belated attempt to do it partial justice. 116 IMPLICATION & LINEAR INFERENCE v brought before us in their place was an inspiring vision of the expanding subject, alive with the implicit system of the mind. We see it first as the given minor term which passes unchanged into a new relation with another given term in the conclu- sion of a common subsumptive inference. And we apprehend it more pregnantly through its working at the other extreme, where the implicit whole of mind forces us forward through the dialectic process from less complete to completer affirmations about the real world. From the very first, in the formal syllogism itself, of which the data are furnished ah initio, and cannot be modified without a formal fallacy, there is yet a fusion and an enlargement which develops their meaning. The subject of the conclusion, the minor term, appropriates to itself an import and an ampli- fication which, as first presented, it did not possess. Even here we can see the three phases which we shall find to be characteristic of all reasoning : " the starting-place, the operation, and the modification of the starting-place."^ And in the operation the original subject has begun to expand, and prepares to appropriate its new predicates through this expansion. In the more plainly constructional reasonings'' where we are outside subsumption and the category of subject and attribute, we begin further to note an increased vitality springing from the juxtaposition of the original data. A fresh datum — a premise which partakes of the nature of a conclusion — may arise out of the necessities which impose themselves when the original facts are synthetically grouped. A new interpretation arises which transforms them, and along with that a new demand which forces us 1 Bradley's Logic, p. 396. V NATURAL PROCEDURE IN ARGUMENT 117 to affirm of reality something not observed and therefore not a primary datimi. Such was, in our example of Harvey's discovery, the passage of blood through the capillaries from the arteries to the veins ; or, in a different field, the discovery of Uranus ; or, again, all the detail, so far as new to a given enquirer, which arises from the supremacy of law in the British Constitution.^ The feature of a conclusion seeming to arise among the premises is natural to the aspect of inference which we are now considering, and it will be found to characterise especially those procedures in which the expansion of the subject is most strikingly exhibited. In an early and imrecognised form it is responsible for a good deal of misconception, as when, in what professes to be enumerative induction, we are offered conjunctions as constant in experience, whose alleged constancy is not actually observed but depends, for example, on causal presumption. " Again, the uniformities which are said to be the basis of our 'generalisation, are not really matters of direct experience. We have said above, that the particular connections which we believe to prevail in nature have been inferred with the help of the assumption that all changes occur in accordance with laws. But if any one likes to question this, he must at any rate agree that most of the uniformities in which we believe have been inferred somehow ; very little has come directly under our observation. We beUeve that winds are caused by differences of atmo- 1 I may note that it is cases of this kind which fully justify my definition of inference in Logic^, ii. p. 3, as. affirming of reality in the conclusion differences only mediately referred to it before. When all your terms are given, as in the formal syllogism, all have been as data immediately referred to reality, though not all im- mediately to the subject of the conclusion. 118 IMPLICATION & LINEAR INFERENCE v spheric pressure : difference of atmospheric pressure is itself inferred rather than observed ; but waiving that, for what proportion of winds have such differences been noted ? We believe the sounds of a piano to be caused by the striking of strings ; for what proportion of such soiuids have we first seen the strings struck by the hammer ? " ^ In these constructional inferences, then, the con- clusion need not be simply a new relation of those terms which were explicitly there at the beginning. And if it is so, as it still may be where the synthesis demands no new term or quality, the expansion of the subject is nevertheless obvious and necessary. For indeed there may be among the explicit original data two or more given subjects, seeing that with the rejection of the major premise there ceases to be a single predestined subject of the conclusion. So, too, in a comparison of distinct subjects. In all these cases the true implicit individual centre of the infer- ence is what comes out in the sjoithetic operation — in the argument " A to right of B," for instance, the total space within which the subjects A, B, and C are fused into one ; in quahtative comparison the unity of quality within which the subjects to be compared are identified or discriminated ; or in a construction like Harvey's discovery, the whole " circulating system " which exhibited itself in the progress of his reasoning and gave connection and significance to his eight new data or conclusions, thus, moreover, confirming their truth, or re-establish- ing it in an extended sense. It is necessary, of course, that the change in the original subject or the apparent emergence of a new one should be due simply to the vision of what is ' Joseph, lMgic\ p. 422 ; see above, p. 52. V NATURAL PROCEDURE IN ARGUMENT 119 necessary to make the one or the other intelligible. If the change is more and other than this ; if, in drawing the conclusion, we omit, for example, elements from the full construction without special experiment to ensure that nothing material is removed, then the change comes to be due to ova interference and not merely to the subject's necessary expansion, and the result is falsified. Thus, if in constructing the conception of freedom you assxime that the environ- ment must necessarily be oppressive, you will get an emphasis on caprice or rebellion in the idea — on its negative side — which does not really belong to it. And you can see that this is so, not merely by the fact that environments can be observed which are not oppressive or hostile, but by your insight that in the construction the work of an environment can be done and its place be filled by an element which is not negative towards the agent, but is ready to forward its expansion. Erroneous assertions of im- plication are very common, and they depend in this way on the failure to discriminate the true lines of connection in a construction — ^to see what really depends on what. The proof of the true relation can only be afforded by a distinct envisagement of the system in question. Is there a moral govern- ment of the world conducted by rewards and punish- ments ? No, because when we look close at the system which we call morality, we see that such inducements cannot be adapted to its functioning, but rather destroy its nature. The important point is that we are not convinced of our error by mere instances which appear to indicate the contrary, though such instances may be the first thing which calls our attention to it. As in recognition we get an inference from 120 IMPLICATION & LINEAR INFERENCE v reproduction, so in the hypothetical judgment we get one from supposition. As a face, given in perception, recalls a name, which being a new datum becomes the predicate of a conclusion, so a quality or relation, attached to reality by a supposition, gives a further quality or relation which again becornes one of the equivocal premise-conclusions we have noticed. We are familiar with the analysis of the hypothetical judg- ment. It stands for one of the commonest of our every- day inferential procedures.^ We are in presence of a real thing or situation more or less explicitly, given, and we wish to judge how it is likely to react to our manipulation. We ideally apply a condition to it, and get a conclusion which claims to be true, subject to that condition. So what is positively asserted is not exactly our conclusion. And yet we have acquired some knowledge. What is positively asserted is something which underlies our conclusion and is not necessarily made explicit. The old simple instance is the clearest : "If you ask him he will refuse." The conclusion as it stands affirms no actual fact ; it is conditional. The categorical conclusion is about something in him. You have brought to bear your mind on him and the situation seen in a certain light, and the subject^the theme or situation — as a whole has responded and carried you to a result. In these latter cases, such as recognition or the hypothetical judgment, the self - development of the subject is plain. You apply to it your mind, which' is itself naturally a system, carrying with it in these cases a sense-perception or a supposition as a stimulus to the given complex to rearrange and requalify itself, and you get a response consisting of a new predicate which was not given at all in any data at the begin- ' Bradley, Logic, pp. 378-9 ; Bosanquet, Logic, i. p. 267. V NATURAL PROCEDURE IN ARGUMENT 121 ning. You have invited the subject, the complex which constitutes the situation inspired by the Uving system of your mind, to react in view of a special modification, and it has reacted, giving you some- thing new. Or, one might say, in the procedure of construction the nature of the subject has " taken charge," and has not needed to be put together out of data accepted ab extra. Thus the synthetic principle which was present even in the most formal and apparently analytic types of inference has in the end become unmistakable. Inference is the life of a " subject." All that it needs in the way of pre- mises or data is, in principle, a stimulus to the special line of development which interests us at the moment as promising the answer to om- question. This is what has been so much insisted on as " the purpose of the argument," as though it were something by which oiu" wishes could influence the inferential nexus. But it is evident that such a purpose is merely selected within a total necessary development, and cannot affect the conclusion otherwise than by selective attention. A problem seems to arise whether, if this is aU the premise or datiun need supply, the subject could not develop itself without any such suggestion — whether you could not infer without a premise or datum. The answer is simple. You cannot infer without knowing on what basis you are inferring. Now the premise or datum, however slight and simple, is all that indicates to you both what subject you are dealing with, and in what direction it_is possible pr desirable for it at the moment to develop. If you had no premise or datum you could feid no starting- place. But, on the other hand, you might say that in a sense you need no special datum, when your 122 IMPLICATION & LINEAR INFERENCE v starting-place is in any way indicated to be the implicit whole itself in a certain phase. Such a case you have in a stage or situation within a science. Then the whole conation of your mind is as nearly as possible identified with a comprehensive body of organised data and relations, and these of themselves dictate their further development. You have, you may say, no single datum, because the developing whole is itself in union with you, and is, indeed, in so far as it comprises particular terms and relations, itself your total premise and datum. Here the true insignificance of the special purpose of the argument becomes evident. In presence of the whole there is no special or partial purpose. The scientific conation defines its own purpose as it advances, and your only purpose, as a man of science, is to follow its evolution as completely as you can. You want no new single premise to start you on a special argument ' in the middle of a treatise on logic or economics or biology ; nor would any single premise be of service to you. What you want is to apprehend the whole up to a certain point, and then to carry it forward in the way it demands. Of course an amateur can put, say, to an economist, a special case, such as, " In what sense is a payment thus and thus defined to be called rent ? " That would give an arbitrary special purpose to his answer, namely, to convey to you the information you require. But left to him- self, he would develop his theory of rent in its natural place in his system, treating it in all its senses, and starting, not from a question like yours, but from all the considerations which the largest survey had presented to his mind. The subject, in one complete phase, would be the only datum necessary for an advance to a further phase. V NATURAL PROCEDURE IN ARGUMENT 123 3. It will complete the line of thought which we have been pursuing if I indicate briefly the continuity between what we have seen to be the commonest and most natural procedure in argument, and the rationale of a method so rare and difficult that its very existence has been doubted. The latter method, I shall suggest, is merely the pure spirit of the former, being the complete expression of the inferential movement which we have traced as the self-develop- ment of the subject. What has been called Dialectic, then, may be exhibited as the essential principle which is obscured in the formal syllogism, but is tolerably obvious in the natural course of argument as it is introduced by complete exposition. (i.) We saw at the beginning of this chapter that the impulse of the natural man in opening an argu- ment is not to lay down a first premise but to explain the situation at large. Here, it appeared to us, the natural man was right, and the argument " from above," we thought, was only valuable when it simimed up the essence of the situation, or led to its revelation by gradual increments. When it is put before us among the foundations of mathematics that 3 + 2 = 2 + 3, this is no heaven-sent revelation per se, but the expression of our judgment upon a certain kind of operation within a certain type of complex. When at the other extreme of single thought-opera- tions we infer that if a man is beheaded he is killed, this is not merely a fact which we accept because facts like it have occurred before. It is an over- whelming presumption drawn firom our knowledge of the structures and relations by which life is carried on within the organic world in general and among vertebrate animals in particular. It represents, once 124 IMPLICATION & LINEAR INFERENCE v more, our judgment upon a certain kind of operation within a certain type of complex. When,' again, a barrister opens his case, under- taking to exhibit a situation from which, if he proves his facts, only one conclusion can emerge, the root of his argument is the same. ' A complex, a whole of the relations and properties of things, is to be estab- lished before us, and it is expected that taking it all together we shall be carried without alternative to a certain determinate insight. The systematic char- acter of our mind unites itself with the systematic material laid before it, and, aspiring to complete and harmonise the system, necessarily proceeds — such is the reasoner's hope and expectation — in a certain way to a certain result. What governs the procedure is the unity of the " subject " — the interrelation of circumstances round a common centre — ^it may be a personal, geographical, financial, military, or any other complication. The only necessity is — and I am aware that I am merely illustrating the same point by a different expression — that it must be such that from terms or relations included in it you may hope to read off something about other terms and relations included in it. They must all fall within the universal nature of a single subject, although as we saw the single subject may not be any one of the terms apparent at first sight, but may only emerge, as in Harvey's discovery, or in any detective story, in proportion as the operation of inference begins to succeed, and the centre of the plot, so to speak, to reveal itself. Such a doctrine may appear to have the effect of exempting inference from criticism.^ My insight 1 ^ Pickard-Cambridge in Mind, no. 102, pp. 207-8. Cp. Bradley's Logic, p. 479 ; Bosanquet, Logic\ ii. p. 36 ; Knowledge and Reality, pp. 316 tt. V NATURAL PROCEDURE IN ARGUMENT 125 carries me to this conclusion, and yours to that, and how are we to reason upon them ? But this point has often been discussed, and the answer is, I think, quite plain. There is a medium between the universal form of the formal syllogism, and the total absence of appeal to any principle beyond the given complex. The syllogism " professed to control from a central office every possible event in all parts of its kingdom. It issued some two dozen forms of reasoning, to which all inference was expected to conform." ^ This pre- tension is self-contradictory, because it woidd imply that all possible combinations of relations had been exhausted and classified along with their results. But, on the other hand, an inference always proceeds on a general principle, though not necessarily /rom a general principle. When challenged, you could always exhibit the form of yoiu: argument ^ and illustrate it by a parallel instance. You could point out that if a man would deny the one he must be prepared to deny the other, as e.g. with the arguments from a spatial series, so often referred to in recent logical discussion. The point is not that there is in infer- ence no principle, but that the principle is established by the observed working of the inference, and not the inference by the independent assumption of the principle. This has been sufficiently explained above.^ How can you prove that 12x12=144? Only by working out the combination in all possible ways, and showing that to deny the result upsets the multiplication table. Thus we recur without misgiving to the description of inference as in its essence the self-development of a single subject. And we see that this is a character 1 Bradley, op. cit. p. 245. ^ Ibid. pp. 472 ff. " P. 34 supra ; Joseph, Logie\ pp. 311 and 345. 126 IMPLICATION & LINEAR INFERENCE v common to the natural procedure of reasoning from wholly given data — ^from a whole which is prima facie entirely new to us — and to reasoning which requires only a suggestion to set the development in motion. If an agent is to be free, we say without hesitation, he must have a will. We are here appealing to a whole so far one with our mind's own nature that a supposition conveyed by a single word places us in the central track and is all the data or premises that we need. " Free " imphes " will " ; " will " implies something more ; and we could build up a complex construction on this single supposition. We have seen that the self-supplying premise, the premise which is half a conclusion, cannot be kept out of inference even when very much more dependent on what is given ah extra. In a development like the above we have something which in principle is not far removed from dialectic. External data are not needed more than to let you know just at what point you are. Then you pick up the development as a matter of course, hke a mathematician or economist whom you " put on " at a certain knot in a problem familiar to him. The whole, in its relevant phase, awakes as one thing with his intelligence, and he is prepared to proceed as by a native impulse. This, but for its limited material, is the pure essence of inference to which our account of it carried us forward. The external data, neces- sary where no whole had been constructed, showed themselves superfluous when the whole was intrinsic to us. But none the less, when no whole was present to us, the natural impulse to build one up before our mind was right and logical. Exposition of a case supplies the same demand which dialectic copes with out of the mind's own resources. It is of course not V NATURAL PROCEDURE IN ARGUMENT 127 implied that these resources are independent of ex- perience. The a priori is merely what comes clear and connected out of the mass of the a posteriori. (ii.) There is one distinction which calls for a moment's consideration. In a normal and natural inference you remain, subject to a very limited reser- vation,' within a single category. You argue from relations in space or time to a relation in space or time ; from relations in degree to a relation in degree ; from effect to cause, or from cause to effect, alike within the category of causality. In the dialectic the opposite rule prevails : you pass at every step, if not from category to category, at least from sub- category to sub-category. You do not remain at the same level of thought-connection for two steps together. You do not argue from a given effect to a hypothetical cause, but perhaps you may argue from one sense or usage of the correlatives " cause" and " effect " to another which is different and treats them, it may be, as more of a unity than they seemed at first. How is this difference compatible with that essen- tial identity between dialectic and everyday inference which has been suggested ? In the first place, we have seen suflBciently that in no inference do data and conclusion abide on the same level of unity. Even the argument in Barbara leaves the minor term larger, more concrete, and more articulate than it found it. You begin with sporadic facts and you end with a concentrated " plot " and its " solution," to borrow dramatic language. You begin with related points in space ^ See Bradley's Logic, p. 241, on types of synthesis, and on cross- ing from category to category if one of them is that of subject and attribute. 128 IMPLICATION & LINEAR INFERENCE v and you end with a figure which relates points for you that were previously unrelated. The fact seems to be that every category admits within itself of an advance which is of the same type as the advance from category to category, but so much less in degree as to show a marked difference of kind.^ The spatial figure which introduces new relations is a simple case. Or you may track a causal relation from non-reciprocating to reciprocating causality, and find yourself at the end in possession, no longer of a chain of events, but of a solid system thoroughly apprehended. The distinction between mechanism and life seems strikingly relevant to our problem. Can the most thorough reciprocating con- nection between the elements of a causal whole give as a conclusion the relation or unity of life ? The doubt whether it can or cannot is precisely our question whether there is a limit of principle which separates everyday inference from dialectic. If spatial data cannot give a conclusion in terms of time, nor temporal in terms of causation, nor causal in terms of life, then dialectic can do what everyday inference cannot. Dialectic, it would seem, marches with seven-league boots, passing an interval of kind at every stride. Everyday inference begins, one might suggest, before any category is discerned as immanent in the facts, and reaches its limit when the completest unity is attained which some single category can offer. Dialectic begins, on the contrary, with an explicit category, presses it to its failure, and proceeds necessarily to another. So that, supposing the dispute about life and mechanism in biology to turn in favour of the former, we should see a case ^ Every difference in degree is also a difference in quality, though it may be negligible. V NATURAL PROCEDURE IN ARGUMENT 129 where everyday inference, by its failure to construct out of its premises, chosen on prima fade appearance, the required solution, has been forced to make an advance on the grand scale from phase to phase which is in its nature dialectical. So here a further difficulty is very simply solved ; that is, the peculiarity known as the negative factor in dialectic. This negative factor is what blocks the way, as we saw just now, when everyday inference can get no further. " I have done all I can," common logic seems to tell us in face of certain experiences, " with space or time or quantity or mechanism, or with aU of them together, but I cannot get a conclu- sion which represents what the movement of experi- ence at a certain point demands." There is an intractable element in the problem, an element of totality, in which the whole seems to find itself and to answer for itself. We can go no further till we have brought freedom — by itself again, an inadequate idea — ^together with causal necessity in a conception which will enable us to fuse aU our data in conclusions adequate to them. But in the end the two procedures are the same. Each of them consists in a subject, inspired by the impUcit totality of the mind, developing itself whether from sporadic given suggestions into a unity within a single category, or from a given category, through considerations estabhshing its inadequacy, to one more complete. It is easy to see the different position of a posteriori data or single premises in the two, and in the procedures which rank between them. In the one extreme the inferring mind has to discover unity, and evaluate a whole given only in fragments ; in the other, the mind is set going at some critical point of the system which is one with its own implicit 130 IMPLICATION & LINEAR INFERENCE v nature, and ascends the great stairway of that system by the force of considerations which the nature of each given step brings automatically into operation. All through, in both cases, the method is ideal experi- ment, and the driving force is the operation of the mind, as an implicit system, on a definite complex or situation. This may be suggested ab initio, through isolated data, more or less complete, or may grow naturally out of a mere suggestion sufficient to indicate the track and phase of the necessary advance. VI " THREES " IN INFERENCE 1. Is it, as has been said, altogether a superstition to attach importance to the tradition which finds in every inference three terms only, and three pro- positions ; two premises, that is to say, and one conclusion ? Taken in a rigid sense, it may be a superstition ; for example, the syllogism itself admits that a weaker conclusion may sometimes be drawn where a stronger one is possible. From a complex inferential context more than one conclusion may certainly be drawn. This may be so, and yet all the possible conclusions really rest on a single insight. And a discussion of the place of tripUcity in inference may at least throw light on the process analysed in the previous chapters. 2. We may begin by looking at the connection between " data " and " terms." a. We might suggest as a hmiting conception some such idea as that of sheer data or data datissima. They would be the actual starting-point of an infer- ence, not yet modified by investigation. " Not yet ' modified," but selected at least they must be, or how [ and why treat them more than anything else as data ? \ Well then, grant that they must be selected, but by 131 132 IMPLICATION & LINEAR INFERENCE vi a prima facie selection ; they constitute the situation in face of which the cognitive impulse first emerges. In Harvey's argument, for instance, it appears to me that the data datissima, or true starting-point, must have been his predecessors' alleged facts and ideas, which he must have found before him on enter- ing upon the subject, e.g. the alleged porous septum of the heart. Here at once we are led to a remark which, if I am right, has importance. KJiowledge does not merely find and accept ; from the very beginning it modifies and constructs. You would not set to work to know, if given ideas and appearances satisfied you. You would never proceed to infer, if your data were satisfactory as they stand. Now, of these data there may obviously be any number ; and indeed what the number is becomes a verbal question. Is a full description of the heart's functioning one datum or a dozen ? And if you call these data terms the same is true of them. " Perhaps we may say without exaggeration that a man who cannot use more than three terms in reasoning, is unlikely to do much in any subject. But however that may be, the limit is psychological and not logical." ^ Take " A to right of B " in space. As mere distinct points in space A, B, and C are all logically on the same level, and there is no possible reason for limiting their number. Note Mr. Bradley's A 10 miles N. D 10 miles construction C B 10 miles B. this uses four spatial points, and there can be no reason why such a construction should not use a hundred. Observe ^ Bradley, Principles of Logic, p. 239. VI " THREES " IN INFERENCE 133 however in passing that "we first complete our construction and then go on to D-A." This cuts both ways. We do not stop at three terms (or two premises). But all the terms and premises belong to one section of the procedure, and this has a sequel which is different from it. And one more remark. The number is not restricted, but a difference has already appeared which affects the number. B and C are pec\iliar and pre-eminent as points of junction ; and each doing double duty operates to reduce the number of distinct terms which can be used. j8. Obviously some of the data datissima may fall out the moment we apply serious consideration to them ; and it might be convenient to say that terms are what can enter into a construction relevant to the logical purpose,^ while data are still subject to criticism and rejection. The distinction, no doubt, is one of degree. Terms remain modifiable through- out the inferences. Still data are rejected at the outset of every enquiry. Irrelevant symptoms in view of a medical diagnosis are a sufficient example. Or if you say A and B are both greater than C, these are not terms in a construction to tell you whether A and B are equal. Or there is such a datum as that which by its inclusion vitiates the argument that if a is due N. of b, and b E. of c, then a is N.E. of c. For if a is at the North Pole, it is due N. both of b and c.^ The terms would have to be selected so as to omit this datum. Detective stories, as I observed above, have made these distinctions familiar to us all. We are accustomed to ask, " Is this or that datum ^ It is very necessary to distinguish logical purpose, i.e. the nature of the problem proposed, from subjective purpose, i.e. personal interest which may or may not incite to consideration of a certain problem. See Philos. Review, May 1917, pp. 266-7. 2 Pickard-Cambridge, Mind, 102, p. 206. 134 IMPLICATION & LINEAR INFERENCE vi datissimum a term in the enquiry, or is it, so far as that is concerned, a blind alley ? " We come to this then. Terms are data which are selected as bearing on the logical purpose. There is no theoretical limit to their number, but the very criterion just mentioned, of their claim to be terms, is connected with their character as points of junction or centrality, which again has a certain bearing on their number. This character may lie either in the given relations of the term, as if it is central in a spatial figure, or in its intrinsic properties if these involve external relations, like the working of the heart in Harvey's problem. Terms are not all on the same logical level, as data datissima are. The points of junction have a significance beyond the others. 3. The last observation suggests to us a comparison between terms and premises. You must have judgments in order to posit either data or terms. But not every judgment is a premise. " Socrates existed ; there are men ; there are mortals," would state facts, possible data or terms, but would not be premises in reasoning. Premises do not posit single terms only, but allege conjunctions between them, or properties which imply conjunc- tions. Indeed, premises are got at in some cases by working back from a given construction or con- clusion, and asking what premises are necessary to account for it. Thus, though they may be on the same logical level each to each, taken separately, and their number thus unrestricted, yet they can hardly remain so. Their order may be indifferent, as in A to the right of B, etc. ; but any order wiU reveal a progress which confers importance on the later by mere accretion. As we saw, in the combina- tion of your premises there may even arise a new VI " THREES " IN INFERENCE 135 quasi-premise which was not in the data at all, just as drawing a + over a x gives a * which has a quality of appearance not in the least like either.^ And, as in the old idea of the syllogistic middle term, this comphcation of the premises modifies one or more of the terms, or unites some of them into one. The premises must be read together ; that is what they are there for, and the grammatical separa- tion of them is really deceptive,- or may be taken as indicating a preliminary phase of the procedure. So read, they advance towards the specification of the construction, and the construction towards the conclusion. All the terms tend to fuse and at the same time to articulate themselves till we see the self-development of a subject, of which we have said so much. In Harvey's enquiry, the eight " conclu- sions," which might just as well be called acquired data or secondary premises, illustrate this phase of the procedure. With some of these " conclusions," as the results in the main of appropriate observation, are connected as on the same logical level others which are unobserved necessary consequences of the rest taken together, as we noted in the case of the passage from arteries to veins. We called this a premise- conclusion. It is not in the data datissima, and it is not the whole conclusion of the problem. It is a partial novelty, arising by the way. We found the same kind of thing in many of our supposed premises which are received as data datissima, e.g. the deaths of all men who were bom, say, before 1800. The alleged datum is at least half of it a conclusion and not a datum. So it is as we begin to discern why a Euclidean construction takes the form it does, or to get on the track of a Sherlock Holmes discovery. 1 Cp. Bradley's Logic, p. 367. 136 IMPLICATION & LINEAR INFERENCE vi Our premises, especially as connected in an order, embody an advancing insight. 4. We may go on to consider the connection between Premises and Phases. So far the number of terms and premises has not been taken as restricted, although in terms which were junction-points, and premises which embodied constructive insight, we saw a tendency to a certain economy. But now, as we have noted a movement of liaison in the premises, with a corresponding expansive character in the terms, we are led to com- pare this movement with the recognition that in all inference there are three main phases to be dis- tinguished ; ^ the starting-place, the middle operation, and the modification of the starting-place. , And to do justice to the formal syllogism at its best, we can see that a recognition of this character of inference was the ground of its three terms, and three propositions. " Three propositions," for the assimilation of the conclusion to the premises is a consequence of the way in which we have stated the inferential development. The minor term gave the starting-place, which might be a more or less acci- dental datum ; the middle term, recurring as a point of jmiction, and emphasised as such in the two premises, represented the content and process of a middle operation ; and the major term, attached to the minor in the conclusion, was taken as a modifica- tion whose attachment to the minor was rendered possible by the process-content which the middle term, as cause or reason, represented. That the three propositions contained, not each of them a single separate phase of the whole inference, but the typical advances which we have noted from phase to phase, 1 Bradley, pp. 396-7. VI " THREES " IN INFERENCE 137 and finally the penetrating connection or attachment which is the axis that binds the two extremes together, seems really a merit and not a defect. It is so ; the construction is a transition from the starting-place, and the modification a transition from the construction. The three propositions represent the connections, and the three terms the connected phases. Thus we can see what the " threes " of terms or propositions indicate. And it is a verbal question whether we treat all data terms or premises as belong- ing to the starting-place, and say that their number is unrestricted, and that the subsequent phases are beyond the stage of premises and data, and above their logical level ; or whether we recognise them as retaining or attaining an identity as they fuse and advance. So that the triple rhythm, which seems after all inevitable, may be represented in two parallel forms, (i.) In three terms, viz. a the whole set of constituents ^ of the immanent subject given in a fragmentary form, j8 the explicit construction of the immanent subject, y the modification with which a as defined through )8 must now be read, (ii.) In three propositions, a. The proposition which exhibits the constituent fragments passing towards unity in the immanent subject. )8. The proppsition which ex- 1 Compare, for the different ways of legarding premises, the comment on Lotze's inductive syllogism in my iogic*, ii. p. 53, note 2. The point is that he treats each inductive instance with the same predicate as a separate premise, and so speaks of the premises as being unrestricted in number. I am inclined, on the other hand, to treat as a single premise all the data s^m, s^m, s^m, etc., which supported the same general proposition SM ; that is, to take it, SM, one whole limb or link of the argument, as a single premise. The old syllogism, I suggest, was right, or at least significant, in attempting to treat the several premises as on difierent levels of the reasoning. 138 IMPLICATION & LINEAR INFERENCE vi hibits the subject as involving the final modification, and 7 the proposition which refers the modification back to the original constituents a in the unity which they have been found to imply. In dialectic, and the direct inferences compared with it, such as recognition, the principle is obviously the same. You may consider for instance some datum which is simply actual, and not prima facie self -contradictory. This is so far " contingent " ; that is, for all you can say anything else might have taken its place. In pursuing the track of the whole, immanent as we saw in mind, the intelligence cannot help passing to some connected factor, which justifies the first actuality by the nature of some system which includes it, and is related to it therefore as a " ground " ; and finally, attaching the possession of a ground to the original datum which was pronounced " contingent " you affirm it to have revealed in itself as thus connected the character no longer of contin- gency but of " necessity." Your first premise leads you to a second, and the result of the second attaches to the original starting-point. Thus too the traditional syllogism seems to have a tjrpical value, and it is impossible altogether to get away from " threes " in inference. It is the number of synthesis. And we may end by admitting that in a certain practical and rhetorical sense the old syllogism will probably never pass out of use. Besides typify- ing in a crude and naive manner the triplicity which we feel to be inevitable in inference, it, and I think it only, justifies unambiguously and directly the plain and central answer to the plain and central question which every assertion raises about which we can ask " Why ? " For a practical and rhetorical answer we do not want an elaborate demonstration depending VI " THREES " IN INFERENCE 139 on complete and necessary insight. We want a sufficient clue to the cause or reason of the conjunc- tion asserted, to indicate the line of demonstration that would be followed if we were to complete the proof. We want to discriminate the general nature of the real cause or reason from wholly false or superstitious suggestions and to show our awareness that the principle which justifies a universal connec- tion must be a universal principle. Every direct answer to the demand for an adequate cause or reason imphes a possible syllogistic form, and is false if it cannot meet the test imposed by that form. " Why does spraying with sulphate of copper cure potato bUght ? Because it kiUs the fimgus." This appeals to the major premise, "Whatever kills the fungus will cure potato blight." " Why does the blood circulate ? Because the heart is a force-pump which propels it." That is, " Whatever acts as a force-pump can maintain a circulating system." " Why is man a social being ? Because his mind is a general centre of relations." That is, " A general centre of relations is a centre of social relations." " Why do you hold that war is murder ? Because God has said so " (Biglow Papers). That is, " What- ever God has said is true." In cases of this kind, the distinction between a borrowed premise and an insight at the moment is of little importance, for the purpose is only popular, and probably the reasoning is always of the former or true syllogistic type. You do not in this way get a full and accurate demonstra- tion. But you do get clearly selected the main point on which the disputant rehes, along with a plain understanding that unless he can affirm it as a imiversal connection of the attribute it is no explana- tion, no rationale. I am not harking back to the 140 IMPLICATION & LINEAR INFERENCE vi ancient syllogism, but I am doing justice to the point which Mr. Pickard-Cambridge raised in Mind,^ and which I have argued previously, that however original and individual may be your demonstration or insight, you ought to be able to say in a few words what is the leading plot or principle of your argument as distinct from other arguments which you reject as inadequate or fallacious, and in common with arguments which you regard as sound. The rough and ready demand of the old syllogism with its " Why ? " comes to me at least as refreshing from this point of view. Every sound argument has a core or special type of connection, and though the core is an abstraction and useless by itself, the special apprehension of it is a very desirable factor in addi- tion to the detail of a complicated demonstration. ' No. 96. Cp. Knowledge and Reality, p. 316. VII IN WHAT SENSE LOGIC APPEALS TO THE STUDY OF MIND 1. Professor Mackenzie, in his Elements of Con- structive Philosophy,^ censures the practice of mixing up psychological enquiries into the process of thinking •with the strictly logical theory of implication. Pro- fessor Husserl, in his very brilliant Logische Unter- sv^hungen, has directed an acute criticism against the doctrine that logic is founded on psychology, which he finds exemplified not merely in Mill and Spencer, but in Sigwart and other distinguished countrymen of his own. I wish to discuss the question in what sense the study of logic must appeal to mental experience (" Erlebnisse," experienced facts and operations of mind). To deny that logic is founded on psycho- logy is one thing. To deny that " pure logic " involves propositions about mental process is quite another thing. The former negation seems to me unquestionably true, but the latter unquestionably false. 2. For the sake of argument I will take Husserl's indictment of " Psychologismus " in logic at its face value. I should suppose that at least as far as ' P. 103. 141 142 IMPLICATION & LINEAR INFERENCE vii Herbert Spencer is concerned the indictment is just. With regard to MiD, Sigwart, and others whom he mentions in the same Ught, I beheve that a critical discussion would be troublesome and unremunerative.i I do not want to burden my treatment with historical controversy. The nature of my contention will show how very difficult it is to avoid misunderstanding in this discussion. In justice, however, to English logic after Mill, with which Husserl does not appear to be acquainted, I cite a passage from Bradley's Principles of Logic^ (1883), which is decisive of his attitude : " A simple method of stating the principle [of Contradiction] is to say ' Denial and affirmation of the self -same judgment is wholly inadmissible.' And this does not mean that if a miracle in psychology were brought about, and the mind did judge both affirmatively and negatively, both judgments might be true. It means that if at once you affirm and deny, you must be speaking falsely. For denial asserts the positive contrary of affirmation. In the nature of things (this is what it all comes to) there are certain elements which either can not be conjoined at aU, or can not be conjoined in some special way ; and the nature of things must be respected by logic." But to illustrate Husserl's contention I cite part of the passage from Herbert Spencer which Mill has certainly quoted in two places ^ with complete approval, and I italicise the sentence which Husserl has selected as typical. " The Law of Excluded Middle, then, is simply a generalisation of the universal experience that some mental states are directly destructive of other states. It formulates an abso- 1 For my view of Mill's attitude to necessary truth see Logic^, ii. p. 229. « P. 137. » Logic, II. vii. p. 184 ; Exam, of Hamilton, p. 475. VII LOGIC AND THE STUDY OF MIND 143 lutely constant law, that the appearance of any positive mode of consciousness cannot occur without excluding a correlative negative mode, the antithesis of positive and negative being indeed merely an expression of this consciousness. Hence it follows that if consciousness is not in one of the two modes it must be in the other." By such a doctrine, the obvious criticism runs, the laws of pure togic, say, the Law of Contradiction or the Law of Excluded Middle, are based upon alleged psychical phenomena. They would then have to be regarded as empirical laws of fact, and this fact would not be a fact about the real world, but about the mental habits or constitution of a certain species of animals. But this is not the sort of thing that logical laws affirm.^ The Law of Contradiction does not say, you caimot entertain at once the idea or belief that A is 6 and that A is not b.^ It says nothing about your states of consciousness and their correlations. What it says is that " A is 6 " and " A is not b " cannot both be true. It is an " ideal " law, true time- lessly and apart from the facts of your thought or of mine. A timeless law, it is urged on the side of pure logic, can make no primary statement about facts in time, nor can it be derived from them. This gives in a single case the whole indictment against " psychologism." It amounts to this, that by it the laws of logic are taken as founded on the observed psychical habits of minds in a certain species of animals.^ The consequence seems inevit- able, that these psychical habits might be accidentally 1 Husserl, L.U. i. p. 99. ' I add, what Husserl does not say, that taking them as mere ideas entertained, it is arguable that they must, or at least may, be complementary parts of the same thought. » Husserl, L.U. i. p. 125 ff. 144 IMPLICATION & LINEAR INFERENCE vn related to the real world, and that either for us, or for some other species, it might happen that the laws of thought were not in harmony with the laws of things. The basis of all logic would be an Inductio per enumerationem simplicem, without a principle behind it. Obviously, such a doctrine is fatal. That is to say, if we take psychology as an empirical or natural science, and logic as founded on the mental habits which that science observes and treats by induction, we have cut the connection between the laws of logic and the real world. No laws which speak in the tone of first principles of thought and reality can be founded on the observation of the psychical habits of a species. It seems impossible to hold in this sense that logic is founded on Psychology. 3. " Pure Logic " represents an opposite extreme. It relies on the distinction between truth or necessity and the mental apprehension of truth or necessity. Logic speaks about concepts, judgments, and infer- ences, which sound like mental facts ; but in so speaking, it does not really refer to the facts of psychical life, but to the meanings, propositions, and necessary connections which, true independently of mental apprehension, are discovered and accepted in the mental processes just referred to. " Its laws are all the ideal laws which are grounded purely in the meaning ('essence,' 'content') of the notions truth, proposition, object, constitution, relation, connection, law, fact,i etc." They include the so-called laws of thought, the principles of syllogistic reasoning, of the calculus of probabilities, of arithmetic and ultimately of mathematics." * All these truths depend in one sense on psychical 1 Husserl, L.U. p. 122. a Jbid. p. 63. VII LOGIC AND THE STUDY OF MIND 145 processes,^ some on activities of reference and con- nection, some on addition and multiplication, sub- traction and division. But no one suggests that for this reason arithmetical or mathematical truth should be brought within the scope of psychology. And the same applies to the principles and combinations of pure logic, which are of the same general character if not absolutely one with those referred to. Pure logic deals always with meanings, not with mental pro- cesses ; and, as I understand, with the more formal properties of possible collections or complications of meanings. Thus, for instance, the conjunctive, dis- junctive and hypothetical interconnection of proposi- tions ^ will be considered by it, not as types of reason- ing which we habitually adopt in our thoughts, but as necessary steps in the complication of propositional forms. The ultimate goal of the science woidd be, as I . understand, a general theory of the possible types of theories, or a construction and survey of all conceivable systems of order which a consideration of the formal properties of objects would generate. AH this is opposed to the consideration of Logic as the study of " our thinking," and to the treatment of pure principles, such as that of Contradiction or of Ground and Consequence as " Laws of Function " or as " Fundamental Forms of Movement " of our thought.^ Such language involves an " anthropolo- gistic " fallacy, and, as we saw above, makes triith dependent on the mental characteristics of certain classes of beings.* It is incompatible with the sub- sistence of valid truths which nobody knows. The point of view implies a sharp distinction between real and ideal, and, in a certain sense, a 1 Husserl, p. 169. " Ibid. pp. 243, 247. a Ibid. p. 126, on Sigwart, * Ibid. L.V. i. p. 127. L 146 IMPLICATION & LINEAR INFERENCE vii rehabilitation of apriorism. Apriorism, indeed, as a mere necessity of our mental process, is rejected (rightly in my judgment) as a form of relativism ; ^ but a different kind of apriorism, which rests on the ideality of truth and the severance of real and ideal, is the foundation of the doctrine. " If all the beings of a genus ^ are by their con-" stitution compelled to identical judgments, then they ■ empirically agree together ; but in the ideal sense of the logic which is exalted above everything empirical they may yet be in that case judging not unanimously but contrary to the conditions of meaning (wider- sinnig)." Sigwart does not carry out " the most essential discrimination, which precisely presupposes the sharp severance between ideal and real.* This is enough to explain the attitude of Pure Logic so far as concerns the connections between logic and psychology. It is obvious, of course, and Pure Logic fully accepts the necessity, that in order to the discovery and demonstration of truth the human mind in its operations must in some way dis- criminate true from false, and some account must be given of this discrimination. And when we come to estimate the justice of its contention on the whole, it will be necessary to speak of what it postulates under the titles of " insight " and " self-evidence." But prima facie there is reason in its argument that if we can see that 2 + 2 = 4, which involves a process of addition, without psychological analysis of that pro- cess, we should be able to do the same for the Law of Contradiction or the principle of the syllogism. It is not the habits of human thought that Logic in- vestigates or depends upon ; it is the content of ideal truths — ^truth founded upon the characters of con- 1 Husserl, 1. p. 124. ^ Uyici. i. p. 131. a ji^^^ p. 133, VII LOGIC AND THE STUDY OF MIND 147 ceived objects and the laws and structure of their interconnection. Ideal truth is vahd and immutable, whatever capacity for its apprehension this or that thinking being may display. 4. We admitted the falsehood of the extreme psychological position, according to which the funda- mental truths of logic depended upon the facts and habits of a species of animal mind. But when we look again at the correlative extreme of doctrine which has just been sketched we seem to discover between the two a remarkable affinity. Is not the root of both these rather starthng contentions actually one and the same, that is, the severance of real from ideal, or the suggestion that what operates in mental functions and in the conjunctions of temporal fact may be something other than what is revealed in the structure of ideal truth ? ^ Pure Logic seems to in- volve the same Psychologism as it charges upon others. It is a postulate common to both contentions that functions of actual thinking are not necessarily to be considered as expressions of the truth of things ; that the processes of mind are one thing, belonging to the facts of nature ; and that the first principles of truth are another thing, belonging to the ideal system, severed from facts in time and compatible with differences in these facts to an unknown degree. It is one and the same thing to say, with the psycho- logical logician, that thought has its own necessity which gives no warrant that its truth is true of being ; and to say with pure logic that the truth of being is a self-subsistent system which does not necessarily^ 1 Husserl, L.V. i. p. 122. " Facts are contingent, they might just as well not be ; they might be different." I miderstand Husserl to adopt this assertion, using it of course as an argument that logical principles cannot depend on facts. 148 IMPLICATION & LINEAR INFERENCE vii reveal its character in the facts of mind.^ Truth is inherently two-sided ; and each of these contentions divorces its essential factors of reality and ideas. Ideas, the former says, may be psychically neces- sary without being true of what is real. Truth, the other says, may be logically necessary, the ultimate nature of the real, without appearing in facts either of a given world or of mind. What impresses me in this situation is that any reasonable account either of truth or of reality has been made impossible. Truth seems to me to have no meaning unless (1) it is reality ; ^ (2) is in the form of ideas. It is the form which reality assumes when expressed through ideas in particular minds. It is unintelligible if this unity is broken up. If you suppose a course of ideas inexpressive of reality, or a reality which has no expression in ideal form, you have destroyed the essence of truth. This is the only way of understanding the paradox about the making of truth and its discovery. You can hammer upon either side of this antithesis for ever ; but you cannot possibly make sense without both. Certainly truth comes to be when we find it out ;"" the very determinations in which it consists, the selection and connection of things and relations, had for all we know no emphasis, no distinguished place in the scheme of the universe before or apart from our mental opera- tions. But no less certainly it was true before it was found out ; if it was not true before it could not be true when it was found out?^ It is of no use to deny either of these paradoxes ; they naturally affirm ^ Dr. Mackenzie, for instance, seems to me bound to hold both these views. Elements of Constructive Philosophy, p. 83. " The phrase " it is about reality " suggests that its quality depends on representing something outside it. But this is upside down ; it is reality which becomes truth when it takes ideal form. vii LOGIC AND THE STUDY OF MIND 149 themselves if we insist on dismembering an essential unity. Thus we are led to reject both the positions we have considered. You cannot have truth except as reaUty in ideal form. And you cannot know reality except by apprehending the ideal form in its concrete spirit and all its detail. This does not mean that reality is qualified as or by a series of psychical events. The qualification of reality by ideas is from the beginning a qualification by meanings. This is the significance of thought, which is in its essence an effort to define the imiverse by meanings adequately conditioned ; to reconstruct the unity of the real in ideal or discursive form. This is why, as it seems to me, there can be no complete account of the system and structure of truth apart from an exhibition — not merely of its general forms by enumeration, but of the vital effort and process by which the needs of apprehension express themselves in the succession of forms, while and because they are wrestling with types of content in their concrete peculiarities. The forms, in short, must be interpreted as the spirit which, operating within the content, creates the system. I wiU attempt to draw out this conception in detail, and to explain why logic has to take account of mental process in a way which is not necessary for special sciences. I may say at once that in the main it is merely because logic claims to deal with the whole system of truth-forms in connection, while any particular science only applies a few of them. Write down the whole system of truth-forms and you have, ipso facto, a large-scale though very diagrammatic map of the thinking mind. To connect them together by noting their vital process, to observe their critical 150 IMPLICATION & LINEAR INFERENCE vii and complementary reactions on one another, and the suggestions which they furnish as to the possi- bihty or the reverse of isolated or interdependent validity — to do all this is ipso facto to study logic in the light of the mind. 5. I proceed to indicate a view of truth in its relation to mind and reality which may, I hope, prove less one-sided than either of those from which we started. Truth, we suggest, is reality as it makes itself known through particular minds in the form of ^ ideas. Ideas are pronounced by discursive thought to belong to or express the nature of reality ; and^ this character of thought, which claims the title of truth, is a mode in which reality, the nature of the universe, manifests itself, and is present and living ; just as it does in other modes, such as volitional and aesthetic experience. I will point out some con- siderations which support this view and illustrate its significance. a. The essence of the judgment is the adequate and coherent qualification of reality by meanings, that is, by ideas apprehended as conveying meanings. The term adequate conveys that the impulse of thought is to include in its affirmation as much as possible of the nature of the real world. The term coherent conveys that this same impulse involves the requirement of systematic connection between the ideal determinations employed in the expression. Every judgment which is inadequately determined by the standard of the whole as recognised ad hoc, or which is inadequately conditioned by the standard of the system as recognised ad hoc, is suspected to be error, and is received, when so suspected, with an uneasiness and dissatisfaction which develop into the awareness of falsehood. Although in practical life ■\ VII LOGIC AND THE STUDY OF MIND 151 the demand for adequateness of conditioning is largely- obscured by what appear to be conjunctions of bare fact, or adapted to special needs, yet it is always present in the mind, and much of the aptness and force of idiom depends on it. We do not say " the horse runs " or " the man gallops," " the donkey neighs " or " the jay sings." The conditioning sub- jects would refuse to justify such predicates. Nor do we say " that liar said you were here " when it was the truth he told, nor " that stupid ass has brought the car " when it was the right thing to do. And yet in bare fact, but for the demand of relevance, all these statements might be correct. We may indeed insist on a counter-relevance. " That villain really loved his wife " ; but that is a relevance still. We are expressing surprise at a counter-condition which presents a problem. As we approach the precise formulation of knowledge the demand becomes more imperious. It is an error, though it may be a " fact," to say " a metallic object attracts the lightning " if you only mean that it attracts it as any other object may, perhaps in virtue of being in motion ; or to say " an isosceles triangle has its three angles equal to two right angles," when the condition isosceles has nothing to do with the matter. It is inaccurate to say " water boils at 212° Fahrenheit," though we constantly see it do so. An essential condition, the atmospheric pressure, is omitted. How can we know that our judgment is thus an expression of reality through our mind ? How can we know that the habits of our mind are not merely ways of conjoining particulars, which are accidental facts of its hfe, and quite other than connections valid in the real world ? Here there are several points to note. 152 IMPLICATION & LINEAR INFERENCE vii First, my mind does not come to me as a separable source that judges by connecting particulars ab extra. It comes to me as a full world which reshapes itself by its own impulse, involving, as it does so in certain respects, more or less of a peculiar satisfaction which attends upon adequacy and coherence. So far from misrepresenting the world, my mind as a volitional or capricious being cannot in the least affect that reshaping by the world of its own meanings which is judgment. If I am in a motor colhsion I shall probably be badly hurt. How am I to think other- wise ? I only wish I could. Further, my mind has nothing but the world's reality to draw from ; and, again, the world has no way of becoming ideally determinate but through it. j8. There is something more. The separation of Psychology from Logic has largely been due to a vicious doctrine of Association. Mind, it has been thought, begins with chance conjunctions of particu- lars ;' and the laws of association are mere causal laws of conditions under which presented particulars come to be conjoined and reproduced in connection. ' If this were true there would be a chasm between logic and psychology which could hardly be bridged, and it would be true that the facts of mind were mere causal conjunctions of facts caused by some in- scrutable natural mechanism or spontaneity. But this is not so, and with the refutation of this point of view the plausibility of the severance between real and ideal vanishes, as its truth has vanished before. It would be true in the main and in principle to say that no judgment can express a mere fact, and no association can reproduce one. What operates from the first in mind, long before explicit judgment, long before memory or the discrimination of particular VII LOGIC AND THE STUDY OF MIND 153 facts, is the reproduction of universal connections. " Association marries only universals." Every judgment expresses a law of systematic connection. The explicit conditioning may be in any degree false or irrelevant, and may appear in the guise of a mere factual conjunction. But the spirit of the ideal is always there, and can be traced if not awakened by appropriate research into impUcations and by proper introspection. This is all-important for the connection of psycho- logy and logic, of mind de facto and reality de jure. The logician takes over, so to speak, the mental development from the psychologist at the point where instinctive self-guidance and self-adaptation by rnii- versal connections within reaUty ^ pass with the de- velopment of expKcit thought into the act of quaUfy- ing reality by meanings, systematically connected and complete. He traces the spirit of the real operating through the mind not merely in every " form " or ex- ternal shape of judgment and inference, as assertion, negation, conjunction, hypothesis, or disjunction are forms, but within every connection of content which is tjrpical of actual affirmations. The apparent facts are only conditions within this system. They are means of specifying the laws. In every such typical connection the germinating system makes itself felt by peculiar demands, pecuhar directions of satisfac- tion and dissatisfaction, pecuUar pressxires towards advance. It is essential to an account of truth to know by careful reflection what in every kind of judgment we really want to say. Great systems indeed separate themselves off, and profess to be independent of the real which is determining itself as a whole ; but when held together with the self- 1 As in a bird's behaviour on the recurrence of spring. 154 IMPLICATION & LINEAR INFERENCE vii completing totality they evince their pretended in- dependence, though practically actual, yet as ulti- mately precarious and conditional. There is no truth which does not qualify the real, and no real apart from that which shows itself ideal in truth. There is no other truth and no other real. Where else should they come from or reveal themselves ? Where is the positive something which not being a qualification of the one reality could appear as predicated through mind and constitute a falsification of our thoughts out of some private and peculiar spring or source ? y. Thus an intelligent view of the relation between logic and the mind demands, in addition to a right analysis of association as the naarriage of universals, a true theory of error as the qualification of reality by genuine meanings inadequately systematised. The problem of error is just as urgent in the shape of the question " How is it possible to be wrong ? " as in the question " How is it possible to be right ? " It applies to the situation in this way. We suggest that all mental affirmation of meanings qualifies reality by something discriminated within its system. The mind is not a creative factory of error and has no private source of unrealities. But then the question stares us in the face, " Why are not all your judgments right and your conclusions sound ? " "If you say there is nowhere for error to come from, why are you nearly always wrong ? " If it were the case that truth and falsehood were scattered through our assertions and reasonings hke black and white squares on a chess-board, some absolutely one thing and some absolutely the other, and no gradation between the other and the one, the situation would indeed be inexplicable. But it is not so ; and the full answer in principle to the problem vii LOGIC AND THE STUDY OF MIND 155 set by error is that the mental determination of reality by ideas is never wholly wrong and never wholly right. It is never wholly wrong, because there can be nothing in experience which falls outside reality and so fails, under one condition or another, to quahfy it. It is never wholly right, because in every deter- mination — ^in every judgment — ^there is operative the life of the whole, and in it the ambition to qualify the whole completely, carrying with it the conviction of failure because of the shortcoming which it confesses. I am strongly convinced that introspection emphatic- ally confirms this principle. Think of any serious effort to formulate compUcated truth. Not only the poet and the truth-seeker, but the commonest man in the street, constantly feels tongue-tied before all that he wants to say. The theory of error has to deal with the various degrees of inadequate qualification of reality within the world of abstraction, of imagination, and even within the world of self-contradiction. In all error a reaUty is qualified by a meaning, but the condition of the qualification is in various degrees inadequate and therefore resists literal inclusion in the total system of experience. This is the only method on which justice can be' done to the status of imagination and of the various and conflicting systems of working ideas. If you set up a disconnected triple scheme — say of absolute ideal truth, of contingent fact, and of pure falsehood chimera and self-contradiction (which latter is intelligible but does not quahfy reality) — it is altogether impossible to deal with the demand for justification of the hmits which you assign to the real world. Is there, for instance, an unreal world outside that whicb is real and additional to it in some fan- tastic way ? 156 IMPLICATION & LINEAR INFERENCE vii Clearly this will not do. Error is a side of truth, and truth implies error. Error is truth inadequately conditioned in the statement. But every assertory thought qualifies reality by a connection of meanings which in some degree belongs to it ; and this appre- hension of typical or universal nexus is the central feature of mind throughout from the point where its self-guidance first makes its appearance. S. Thus then in the assertory and inferential thought-function, from beginning to end, we are deal- ing with, and, I reiterate, we are distinctly conscious of and inspired by, an imptdse to the ideal and adequate quahfication of reality. When we have mentioned the word " thought " we have disposed of the distinction between psychical occurrences and the assertion of meanings. To think is to mean — ^to direct the mind's intention to an object through the instrumentahty of a psychical state. But having admitted the practically unhmited scope of error — ^though in every error the impulse to truth is implied, which, ordering a finite experience, must obviously proceed on the cy prds principle, using what it has — we are obviously bound to indicate how truth can be discriminated from or within it. There are certain conceptions which are nominally common to all sides in this discussion. But the question is who really has a right to them, and can demonstrate it by giving an adequate account of them. Necessity, intuition a priori, self-evidence ; these are the typical phrases which are used to indicate the character by which assertory truths or sound reasoning vindicate themselves. But when employed by the extreme psychological logician, whose conception we sketched at starting, none of these terms can convey a satisfactory indica- VII LOGIC AND THE STUDY OF MIND 157 tion. We are confined ex hypothesi to the characters of our private mentality, or of that which we share as specific, it makes no difference. Therefore our intuition is a mere apparent clearness in our private mind ; our necessity is a subjective or nature-caused compulsion ; our self-evidence is some kind of feeUng which attaches ab extra to some of our assertions for unknown reasons, perhaps merely by habit and famiharity. Such is the criticism launched at them by pure logic and it can hardly be denied. In the mouth of pure logic itself we hope to find that they have a more pregnant significance. Truth is now something which subsists, independently of the apprehensive process, and we may expect it to present characters by which it may certainly be dis- tinguished. But so far as I have seen, pure logic is not strong on this side of the matter. Intuition which perceives self-evidence seems in the first place to be confined to abstract principles — ^the unity of the character of imphcation throughout knowledge cannot be appreciated where the character of judgment as a law of connection is ignored ; and in the second place to seize in its act of perception the convincing char- acter of truth, but what this character is does not seem to be distinctly determined. The crucial ques- tion, as I argued long ago, is whether self -evidence is conceived as belonging to principles as they stand within their own four corners, or whether it is a perception or presumption of some further relation which they hold to the entire system of knowledge.* 1 My Logic", ii. pp. 224 ft. Mill's theory of " evidence " is of course his "larger logic," the doctrine of Induction or Logic of Truth (Examination of Hamilton, pp. 459 ff.); it has not, as Husserl supposes, to do with " evidence " = self-evidence. So far Mill's doctrine is opposed to that which Husserl ascribes to him (L.U. i. pp. 181, 189). There is nothing " psychological " about it. 158 IMPLICATION & LINEAR INFERENCE vii For us the question of self-evidence is entirely one of the presence and presumption of implication, and applies in its degree to systems of fact, being all ultimately alleged connections of laws, no less than to abstract principles. How far in judgment we ultimately affirm mere facts is again a point on which introspection is helpful. ^ Implication is, in other words, a relation of any determination to the whole to which it belongs, and ultimately to the whole system of experience, such that the assertion of the latter affirms the former, and the denial of the former denies the latter. It follows that self-evidence in isolation is really a contradictio in adjecto, and it is not difficult to show ^ that the fundamental law of thought and those elementary truths which affirm themselves in being denied derive their character from the simple alternative between the affirmation of a coherent system which directly implies them, and the impossibility of maintaining any affirmation at all. 6. Thus implications which are rooted in very general or abstractly formal properties of objects may confer an appearance of self-evidence in isolation which a more complete considera,tion would dispel. Practically, I take it, we do not care on what grounds we assert the necessity of the Laws of Thought or of such propositions as 2 + 2 = 4 or " two straight lines cannot enclose a space." If they were challenged, we should probably answer to the effect that if you are prepared to deny them you are prepared to deny anything, so that it is futile to enter on an argument. But this does not mean that each of them is a separate vision or intuition or revelation, standing within its own four corners and upon its separate merits. It means that we are aware that what these propositions 1 Logic\ ii. loc. cii. ; Principles of Indimduality, pp. 44 ff. VII LOGIC AND THE STUDY OF MIND 159 assert amounts to such a minimum of reality that, if it can be denied, there is nothing that will be left standing. So that the character of being affirmed by its own denial, which belongs ultimately to every proposition that can be proved, is in them especially visible with the least possible mediation or with none at aU. But if such propositions could be truly denied, the Law of Contradiction would have to go, and it could not be the fact that things are one way only ; it becomes an open chance that they may be two or more ways at once in the same respect, and so the conception of determinate experience would have to be, though it cannot be, abandoned. It is a very significant feature of pure logic that it insists on the importance of highly formal char- acters and of apparent triviaUties, e.g. a + b = b + a.^ It is just these which present the delusive appear- ance of isolated self-evidence or necessity, so as to support the idea of an intuition other than the insight into implications. Thus, e.g., the sciences of mathe- matics or of symbolic logic may claim an independent status of necessity, which is incompatible with the real basis of truth. At the other extreme of knowledge the same may appear to be the case with simple hard facts. What has happened here is that a very limited but appar- ently self-contained system has been erected ad hoc by a practical interest or an arbitrary intellectual objective. Then the reply, which satisfies this interest or attains this objective, appears to be complete in its isolation. The growing point of the serious judg- ment is artificially broken off.^ A conventional end 1 Husserl, Jahrbuch, 1913, p. 38 ; cp. Whitehead, Introduction to Mathematics, pp. 15 ff., on which see above, p. 110. « See p. 122 above. 160 IMPLICATION & LINEAR INFERENCE vii is imposed upon the aspiration of knowledge. " What is your brother ? " "A college tutor ; really a dis- tinguished man ; he has written " " Thank you, a college tutor ; that is quite enough." Or again, " How do you know that is so ? " " A. B. told me ; of course he may be wrong." " Oh, well ; A. B. is good enough for me ; his authority will justify me, and I need not enquire further." This is really the type of absolute facts which set up to be true by them- selves, both as to their completeness and as to their evidence. They are true because they are all we want to know in their direction. Their isolated necessity means that they are good enough for our immediate purpose ; but of course the connections motived by them are at the mercy of criticism. When we come to the concrete sciences — biology, politics, philosophy — the theoretical unity of the system of experience awakens and becomes practical, and we find that we know nothing at all worth speaking of unless we know it in its full systematic connections. In economics, it has been said, you know nothing if you do not know it all. Apriorism then has no meaning unless it indicates connection with the system of experience as organised and understood. Intuition and self-evidence, though they may appear to characterise isolated principles and provinces of knowledge, really refer to the vision of implication in the system of experience, and nothing more nor less. 6. In what sense then are we to conclude that Logic is concerned with the mind ? We held that, in truth, reality and ideas are inseparably conjoined, and we suggested that, even by pursuing to the end the scheme of a pure logic, and arraying in order and sequence the constituent forms of truth, we should VII LOGIC AND THE STUDY OF MIND 161 obtain a large-scale map of the mind, though in its detail a mere outline, and moreover a mere diagram instead of the experience of a life. Therefore, for a complete logic, it appears to me essential to trace and master the thinking fui^ction which eUcits in ideal shape at once the nature of reality and its own, throughout all the nexus of its working, and not merely in its given results ranged side by side in the sciences and disguised in their detail. This is not to base logic upon psychology in the sense of accepting mental facts and habits as the evidence for real laws; it might rather be de- scribed as exploring the psychological field in search of the complete and continuous developments in which the thinking function proper reveals its nisus an