INTRODUCTION

I SHALL first[143] give a restatement, partly historical and partly explanatory, of Kant’s main argument as contained in the enlarged Introduction of the second edition.

There were two stages in the process by which Kant came to full realisation of the Critical problem. There is first the problem as formulated in his letter of 1772 to Herz: how the a priori can yield knowledge of the independently real.[144] This, as he there states it, is an essentially metaphysical problem. It is the problem of the possibility of transcendent metaphysics. He became aware of it when reflecting upon the function which he had ascribed to intellect in the Dissertation. Then, secondly, this problem was immeasurably deepened, and at the same time the proper line for its treatment was discovered, through the renewed influence which Hume at some date subsequent to February 1772 exercised upon Kant’s thought.[145] Hume awakened Kant to what may be called the immanent problem involved in the very conception of a priori knowledge as such. The primary problem to be solved is not how we advance by means of a priori ideas to the independently real, but how we are able to advance beyond a subject term to a predicate which it does not appear to contain. The problem is indeed capable of solution, just because it takes this logical form. Here as elsewhere, ontological questions are viewed by Kant as soluble only to the extent to which they can be restated in logical terms. Now also the enquiry becomes twofold: how and in what degree are a priori synthetic judgments possible, first in their employment within the empirical sphere (the problem of immanent metaphysics) and secondly in their application to things in themselves (the problem of transcendent metaphysics). The outcome of the Critical enquiry is to establish the legitimacy of immanent metaphysics and the impossibility of all transcendent speculation.

The argument of Kant’s Introduction follows the above sequence. It starts by defining the problem of metaphysical knowledge a priori, and through it leads up to the logical problem of the a priori synthetic judgment. In respect of time all knowledge begins with experience. But it does not therefore follow that it all arises from experience. Our experience may be a compound of that which we receive through impressions, and of that which pure reason supplies from itself.[146] The question as to whether or not any such a priori actually exists, is one that can be answered only after further enquiry. The two inseparable criteria of the a priori are necessity and universality. That neither can be imparted to a proposition by experience was Kant’s confirmed and unquestioned belief. He inherited this view both from Leibniz and from Hume. It is one of the presuppositions of his argument. Experience can reveal only co-existence or sequence. It enables us only to assert that so far as we have hitherto observed, there is no exception to this or that rule. A generalisation, based on observation, can never possess a wider universality than the limited experience for which it stands. If, therefore, necessary and universal judgments can anywhere be found in our knowledge, the existence of an a priori that originates independently of experience is ipso facto demonstrated.[147]

The contrast between empirical and a priori judgments, as formulated from the dogmatic standpoint, is the most significant and striking fact in the whole range of human knowledge. A priori judgments claim absolute necessity. They allow of no possible exception. They are valid not only for us, but also for all conceivable beings, however different the specific conditions of their existence, whether they live on the planet Mars or in some infinitely remote region of stellar space, and no matter how diversely their bodily senses may be organised. Through these judgments a creature five feet high, and correspondingly limited by temporal conditions, legislates for all existence and for all time. Empirical judgments, on the other hand, possess only a hypothetical certainty. We recognise that they may be overturned through some addition to our present experience, and that they may not hold for beings on other planets or for beings with senses differently constituted. Whereas the opposite of a rational judgment is not even conceivable, the opposite of an empirical judgment is always possible. The one depends upon the inherent and inalienable nature of our thinking; the other is bound up with the contingent material of sense. The one claims absolute or metaphysical truth: the other is a merely tentative résumé of a limited experience.

The possibility of such a priori judgments had hitherto been questioned only by those who sought to deny to them all possible objective validity. Kant, as a rationalist, has no doubt as to their actual existence. In the Introduction to the second edition he bluntly asserts their de facto existence, citing as instances the propositions of mathematics and the fundamental principles of physical science. Their possibility can be accounted for through the assumption of a priori forms and principles.[148] But with equal emphasis he questions the validity of their metaphysical employment. For that is an entirely different matter. We then completely transcend the world of the senses and pass into a sphere where experience can neither guide nor correct us. In this sphere the a priori is illegitimately taken as being at once the source of our professed knowledge and also the sole criterion of its own claims.

This is the problem, semi-Critical, semi-dogmatic, which is formulated in the letter of 1772 to Herz.[149] What right have we to regard ideas, which as a priori originate from within, as being valid of things in themselves? In so doing we are assuming a pre-established harmony between our human faculties and the ultimately real; and that is an assumption which by its very nature is incapable of demonstration. The proofs offered by Malebranche and by Leibniz are themselves speculative, and consequently presuppose the conclusion which they profess to establish.[150] As above stated, Kant obtained his answer to this problem by way of the logical enquiry into the nature and conditions of a priori judgment.

One of the chief causes, Kant declares, why hitherto metaphysical speculation has passed unchallenged among those who practise it, is the confusion of two very different kinds of judgment, the analytic and the synthetic. Much the greater portion of what reason finds to do consists in the analysis of our concepts of objects.

“As this procedure yields real knowledge a priori, which progresses in secure and useful fashion, reason is so far misled as surreptitiously to introduce, without itself being aware of so doing, assertions of an entirely different order, in which reason attaches to given concepts others completely foreign to them—and moreover attaches them a priori. And yet one does not know how reason comes to do this. This is a question which is never as much as thought of.”[151]

The concepts which are analytically treated may be either empirical or a priori. When they are empirical, the judgments which they involve can have no wider application than the experience to which they give expression; and in any case can only reveal what has all along been thought, though confusedly, in the term which serves as subject of the proposition. They can never reveal anything different in kind from the contents actually experienced. This limitation, to which the analysis of empirical concepts is subject, was admitted by both empiricists and rationalists. The latter sought, however, to escape its consequences by basing their metaphysics upon concepts which are purely a priori, and which by their a priori content may carry us beyond the experienced. But here also Kant asserts a non possibile. A priori concepts, he seeks to show, are in all cases purely logical functions without content, and accordingly are as little capable as are empirical concepts of carrying us over to the supersensible. This is an objection which holds quite independently of that already noted, namely, that their objective validity would involve a pre-established harmony.

What, then, is the nature and what are the generating conditions of synthetic judgments that are also a priori? In all judgments there is a relation between subject and predicate, and that can be of two kinds. Either the predicate B belongs to the subject A, or B lies outside the sphere of the concept A though somehow connected with it. In the former case the judgment is analytic; in the latter it is synthetic. The one simply unfolds what has all along been conceived in the subject concept; the other ascribes to the concept of the subject a predicate which cannot be found in it by any process of analysis. Thus the judgment ‘all bodies are extended’ is analytic. The concept of body already contains that of extension, and is impossible save through it. On the other hand, the judgment ‘all bodies are heavy’ is synthetic. For not body as such, but only bodies which are in interaction with other bodies, are found to develop this property. Bodies can very well be conceived as not influencing one another in any such manner.

There is no difficulty in accounting for analytic judgments. They can all be justified by the principle of contradiction. Being analytic, they can be established a priori. Nor, Kant here claims, is there any difficulty in regard to synthetic judgments that are empirical. Though the predicate is not contained in the subject concept, they belong to each other (though accidentally) as parts of a given empirical whole. Experience is the x which lies beyond the concept A, and on which rests the possibility of the synthesis of B with A. In regard, however, to synthetic judgments which are likewise a priori, the matter is very different. Hitherto, both by the sensationalists and by the rationalists, all synthetic judgments have been regarded as empirical, and all a priori judgments as analytic. The only difference between the opposed schools lies in the relative value which they ascribe to the two types of judgment. For Hume the only really fruitful judgments are the synthetic judgments a posteriori; analytic judgments are of quite secondary value; they can never extend our knowledge, but only clarify its existing content. For Leibniz, on the other hand, true knowledge consists only in the analysis of our a priori concepts, which he regards as possessing an intrinsic and fruitful content; synthetic judgments are always empirical, and as such are purely contingent.[152]

Thus for pre-Kantian philosophy analytic is interchangeable with a priori, and synthetic with a posteriori. Kant’s Critical problem arose from the startling discovery that the a priori and the synthetic do not exclude one another. A judgment may be synthetic and yet also a priori. He appears to have made this discovery under the influence of Hume, through study of the general principle of causality—every event must have a cause.[153] In that judgment there seems to be no connection of any kind discoverable between the subject (the conception of an event as something happening in time) and the predicate (the conception of another event preceding it as an originating cause); and yet we not merely ascribe the one to the other but assert that they are necessarily connected. We can conceive an event as sequent upon a preceding empty time; none the less, in physical enquiry, the causal principle is accepted as an established truth. Here, then, is a new and altogether unique type of judgment, of thoroughly paradoxical nature. So entirely is it without apparent basis, that Hume, who first deciphered its strange character, felt constrained to ascribe our belief in it to an unreasoning and merely instinctive, ‘natural’ habit or custom.

Kant found, however, that the paradoxical characteristics of the causal principle also belong to mathematical and physical judgments. This fact makes it impossible to accept Hume’s sceptical conclusion. If even the assertion 7 + 5 = 12 is both synthetic and a priori, it is obviously impossible to question the validity of judgments that possess these characteristics. But they do not for that reason any the less urgently press for explanation. Such an enquiry might not, indeed, be necessary were we concerned only with scientific knowledge. For the natural sciences justify themselves by their practical successes and by their steady unbroken development. But metaphysical judgments are also of this type; and until the conditions which make a priori synthetic judgment possible have been discovered, the question as to the legitimacy of metaphysical speculation cannot be decided. Such judgments are plainly mysterious, and urgently call for further enquiry.

The problem to be solved concerns the ground of our ascription to the subject concept, as necessarily belonging to it, a predicate which seems to have no discoverable relation to it. What is the unknown x on which the understanding rests in asserting the connection? It cannot be repeated experience; for the judgments in question claim necessity. Nor can such judgments be proved by means of a logical test, such as the inconceivability of the opposite. The absence of all apparent connection between subject and predicate removes that possibility. These, however, are the only two methods of proof hitherto recognised in science and philosophy. The problem demands for its solution nothing less than the discovery and formulation of an entirely novel method of proof.

The three main classes of a priori synthetic judgments are, Kant proceeds, the mathematical, the physical, and the metaphysical. The synthetic character of mathematical judgments has hitherto escaped observation owing to their being proved (as is required of all apodictic certainty) according to the principle of contradiction. It is therefrom inferred that they rest on the authority of that principle, and are therefore analytic. That, however, is an illegitimate inference; for though the truth of a synthetic proposition can be thus demonstrated, that can only be if another synthetic principle is first presupposed. It can never be proved that its truth, as a separate judgment, is demanded by the principle of contradiction. That 7 + 5 must equal 12 does not follow analytically from the conception of the sum of seven and five. This conception contains nothing beyond the union of both numbers into one; it does not tell us what is the single number that combines both. That five should be added to seven is no doubt implied in the conception, but not that the sum should be twelve. To discover that, we must, Kant maintains, go beyond the concepts and appeal to intuition. This is more easily recognised when we take large numbers. We then clearly perceive that, turn and twist our concepts as we may, we can never, by means of mere analysis of them, and without the help of intuition, arrive at the sum that is wanted. The fundamental propositions of geometry, the so-called axioms, are similarly synthetic, e.g. that the straight line between two points is the shortest. The concept ‘straight’ only defines direction; it says nothing as to quantity.

As an instance of a synthetic a priori judgment in physical science Kant cites the principle: the quantity of matter remains constant throughout all changes. In the conception of matter we do not conceive its permanency, but only its presence in the space which it fills. The opposite of the principle is thoroughly conceivable.

Metaphysics is meant to contain a priori knowledge. For it seeks to determine that of which we can have no experience, as e.g. that the world must have a first beginning. And if, as will be proved, our a priori concepts have no content, which through analysis might yield such judgments, these judgments also must be synthetic.

Here, then, we find the essential problem of pure reason. Expressed in a single formula, it runs: How are synthetic a priori judgments possible? To ask this question is to enquire, first, how pure mathematics is possible; secondly, how pure natural science is possible; and thirdly, how metaphysics is possible. That philosophy has hitherto remained in so vacillating a state of ignorance and contradiction is entirely due to the neglect of this problem of a priori synthesis. “Its solution is the question of life and death to metaphysics.” Hume came nearest to realising the problem, but he discovered it in too narrow a form to appreciate its full significance and its revolutionary consequences.

“Greater firmness will be required if we are not to be deterred by inward difficulties and outward opposition from endeavouring, through application of a method entirely different from any hitherto employed, to further the growth and fruitfulness of a science indispensable to human reason—a science whose every branch may be cut away but whose root cannot be destroyed.”[154]

These statements are decidedly ambiguous, owing to Kant’s failure to distinguish in any uniform and definite manner between immanent and transcendent metaphysics.[155] The term metaphysics is used to cover both. Sometimes it signifies the one, sometimes the other; while in still other passages its meaning is neutral. But if we draw the distinction, Kant’s answer is that a genuine and valid immanent metaphysics is for the first time rendered possible by his Critique; its positive content is expounded in the Analytic. Transcendent metaphysics, on the other hand, is criticised in the Dialectic; it is never possible. The existing speculative sciences transgress the limits of experience and yield only a pretence of knowledge. This determination of the limits of our possible a priori knowledge is the second great achievement of the Critique. Thus the Critique serves a twofold purpose. It establishes a new a priori system of metaphysics, and also determines on principles equally a priori the ultimate limits beyond which metaphysics can never advance. The two results, positive and negative, are inseparable and complementary. Neither should be emphasised to the neglect of the other.

Comment on the Argument of Kant’s Introduction

This Introduction, though a document of great historical importance as being the first definite formulation of the generating problem of Kant’s new philosophy, is extremely unsatisfactory as a statement of Critical teaching. The argument is developed in terms of distinctions which are borrowed from the traditional logic, and which are not in accordance with the transcendental principles that Kant is professing to establish. This is, indeed, a criticism which may be passed upon the Critique as a whole. Though Kant was conscious of opening a new era in the history of philosophy, and compares his task with that of Thales, Copernicus, Bacon and Galileo, it may still be said that he never fully appreciated the greatness of his own achievement. He invariably assumes that the revolutionary consequences of his teaching will not extend to the sphere of pure logic. They concern, as he believed, only our metaphysical theories regarding the nature of reality and the determining conditions of our human experience. As formal logic prescribes the axiomatic principles according to which all thinking must proceed, its validity is not affected by the other philosophical disciplines, and is superior to the considerations that determine their truth or falsity. Its distinctions may be securely relied upon in the pioneer labours of Critical investigation. This was, of course, a very natural assumption for Kant to make; and many present-day thinkers will maintain that it is entirely justified. Should that be our attitude, we may approve of Kant’s general method of procedure, but shall be compelled to dissent from much in his argument and from many of his chief conclusions. If, on the other hand, we regard formal logic as in any degree adequate only as a theory of the thought processes involved in the formation and application of the generic or class concept,[156] we shall be prepared to find that the equating of this highly specialised logic with logic in general has resulted in the adoption of distinctions which may be fairly adequate for the purposes in view of which they have been formulated, but which must break down when tested over a wider field. So far from condemning Kant for departing in his later teaching from these hard and fast distinctions, we shall welcome every sign of his increasing independence.

Kant was not, of course, so blind to the real bearing of his principles as to fail to recognise that they have logical implications.[157] He speaks of the new metaphysics which he has created as being a transcendental logic. It is very clear, however, that even while so doing he does not regard it as in any way alternative to the older logic, but as moving upon a different plane, and as yielding results which in no way conflict with anything that formal logic may teach. Indeed Kant ascribes to the traditional logic an almost sacrosanct validity. Both the general framework of the Critique and the arrangement of the minor subdivisions are derived from it. It is supposed to afford an adequate account of discursive thinking, and such supplement as it may receive is regarded as simply an extension of its carefully delimited field. There are two logics, that of discursive or analytic reasoning, and that of synthetic interpretation. The one is formal; the other is transcendental. The one was created by Aristotle, complete at a stroke; Kant professes to have formulated the other in an equally complete and final manner.

This latter claim, which is expressed in the most unqualified terms in the Prefaces to the first and second editions, is somewhat startling to a modern reader, and would seem to imply the adoption of an ultra-rationalistic attitude, closely akin to that of Wolff.

“In this work I have made completeness my chief aim, and I venture to assert that there is not a single metaphysical problem which has not been solved, or for the solution of which the key at least has not been supplied. Reason is, indeed, so perfect a unity that if its principle were insufficient for the solution of even a single one of all the questions to which it itself gives birth, we should be justified in forthwith rejecting it as incompetent to answer, with perfect certainty, any one of the other questions.”[158] “Metaphysics has this singular advantage, such as falls to the lot of no other science which deals with objects (for logic is concerned only with the form of thought in general), that should it, through this Critique, be set upon the secure path of science, it is capable of acquiring exhaustive knowledge of its entire field. It can finish its work and bequeath it to posterity as a capital that can never be added to. For metaphysics has to deal only with principles, and with the limits of their employment as determined by these principles themselves. Since it is a fundamental science, it is under obligation to achieve this completeness. We must be able to say of it: nil actum reputans, si quid superesset agendum.”[159]

These sanguine expectations—by no means supported by the after-history of Kant’s system—are not really due to Kant’s immodest over-estimate of the importance of his work. They would rather seem to be traceable, on the one hand to his continuing acceptance of rationalistic assumptions proper only to the philosophy which he is displacing, and on the other to his failure to appreciate the full extent of the revolutionary consequences which his teaching was destined to produce in the then existing philosophical disciplines. Kant, like all the greatest reformers, left his work in the making. Both his results and his methods call for modification and extension in the light of the insight which they have themselves rendered possible. Indeed, Kant was himself constantly occupied in criticising and correcting his own acquired views; and this is nowhere more evident than in the contrast between the teaching of this Introduction and that of the central portions of the Analytic. But even the later expressions of his maturer views reveal the persisting conflict. They betray the need for further reconstruction, even in the very act of disavowing it. Not an additional logic, but the demonstration of the imperative need for a complete revisal of the whole body of logical science, is the first, and in many respects the chief, outcome of his Critical enquiries.

The broader bearings of the situation may perhaps be indicated as follows. If our account of Kant’s awakening from his dogmatic slumber[160] be correct, it consisted in his recognition that self-evidence will not suffice to guarantee any general principle. The fundamental principles of our experience are synthetic. That is to say, their opposite is in all cases conceivable. Combining this conclusion with his previous conviction that they can never be proved by induction from observed facts, he was faced with the task of establishing rationalism upon a new and altogether novel basis. If neither empirical facts nor intuitive self-evidence may be appealed to, in what manner can proof proceed? And how can we make even a beginning of demonstration, if our very principles have themselves to be established? Principles are never self-evident, and yet principles are indispensable. Such was Kant’s unwavering conviction as regards the fundamental postulates alike of knowledge and of conduct.

This is only another way of stating that Kant is the real founder of the Coherence theory of truth.[161] He never himself employs the term Coherence, and he constantly adopts positions which are more in harmony with a Correspondence view of the nature and conditions of knowledge. But all that is most vital in his teaching, and has proved really fruitful in its after-history, would seem to be in line with the positions which have since been more explicitly developed by such writers as Lotze, Sigwart, Green, Bradley, Bosanquet, Jones and Dewey, and which in their tenets all derive from Hegel’s restatement of Kant’s logical doctrines. From this point of view principles and facts mutually establish one another, the former proving themselves by their capacity to account for the relevant phenomena, and the latter distinguishing themselves from irrelevant accompaniments by their conformity to the principles which make insight possible. In other words, all proof conforms in general type to the hypothetical method of the natural sciences. Kant’s so-called transcendental method, the method by which he establishes the validity of the categories, is itself, as we have already observed,[162] of this character. Secondly, the distinction between the empirical and the a priori must not be taken (as Kant himself takes it in his earlier, and occasionally even in his later utterances) as marking a distinction between two kinds of knowledge. They are elements inseparably involved in all knowledge. And lastly, the contrast between analysis and synthesis becomes a difference not of kind but of degree. Nothing can exist or be conceived save as fitted into a system which gives it meaning and decides as to its truth. In the degree to which it can be studied in relative independence of the supporting system analysis will suffice; in the degree to which it refers us to this system it calls for synthetic interpretation. But ultimately the needs of adequate understanding must constrain us to the employment of both methods of enquiry. Nothing can be known save in terms of the wider whole to which it belongs.

There is, however, one important respect in which Kant diverges in very radical fashion from the position of Hegel. The final whole to which all things must be referred is represented to us only through an “Idea,” for which no corresponding reality can ever be found. The system which decides what is to be regarded as empirically real is the mechanical system of natural science. We have no sufficient theoretical criterion of absolute reality.

These somewhat general considerations may be made more definite if we now endeavour to determine in what specific respects the distinctions employed in the Introduction fail to harmonise with the central doctrines of the Analytic.

In the first place, Kant states his problem in reference only to the attributive judgment. The other types of relational judgment are entirely ignored. For even when he cites judgments of other relational types, such as the propositions of arithmetic and geometry, or that which gives expression to the causal axiom, he interprets them on the lines of the traditional theory of the categorical proposition. As we shall find,[163] it is with the relational categories, and consequently with the various types of relational judgment to which they give rise, that the Critique is alone directly concerned. Even the attributive judgment is found on examination to be of this nature. What it expresses is not the inclusion of an attribute within a given group of attributes, but the organisation of a complex manifold in terms of the dual category of substance and attribute.

Secondly, this exclusively attributive interpretation of the judgment leads Kant to draw, in his Introduction, a hard and fast distinction between the analytic and the synthetic proposition—a distinction which, when stated in such extreme fashion, obscures the real implications of the argument of the Analytic. For Kant here propounds[164] as an exhaustive division the two alternatives: (a) inclusion of the predicate concept within the subject concept, and (b) the falling of the predicate concept entirely outside it. He adds, indeed, that in the latter case the two concepts may still be in some way connected with one another; but this is a concession of which he takes no account in his subsequent argument. He leaves unconsidered the third possibility, that every judgment is both analytic and synthetic. If concepts are not independent entities,[165] as Kant, in agreement with Leibniz, still continues to maintain, but can function only as members of an articulated system, concepts will be distinguishable from one another, and yet will none the less involve one another. In so far as the distinguishable elements in a judgment are directly related, the judgment may seem purely analytic; in so far as they are related only in an indirect manner through a number of intermediaries, they may seem to be purely synthetic. But in every case there is an internal articulation which is describable as synthesis, and an underlying unity that in subordinating all differences realises more adequately than any mere identity the demand for connection between subject and predicate. In other words, all judgments will, on this view, be of the relational type. Even the attributive judgment, as above noted, is no mere assertion of identity. It is always expressed in terms of the dual category of substance and attribute, connecting by a relation contents that as contents may be extremely diverse.

This would seem to be the view to which Kant’s Critical teaching, when consistently developed, is bound to lead. For in insisting that the synthetic character of a judgment need not render it invalid, and that all the fundamental principles and most of the derivative judgments of the positive sciences are of this nature, Kant is really maintaining that the justification of a judgment is always to be looked for beyond its own boundaries in some implied context of coherent experience. But though the value of his argument lies in clear-sighted recognition of the synthetic factor in all genuine knowledge, its cogency is greatly obscured by his continued acceptance of the possibility of judgments that are purely analytic. Thus there is little difficulty in detecting the synthetic character of the proposition: all bodies are heavy. Yet the reader has first been required to admit the analytic character of the proposition: all bodies are extended. The two propositions are really identical in logical character. Neither can be recognised as true save in terms of a comprehensive theory of physical existence. If matter must exist in a state of distribution in order that its parts may acquire through mutual attraction the property of weight, the size of a body, or even its possessing any extension whatsoever, may similarly depend upon specific conditions such as may conceivably not be universally realised. We find the same difficulty when we are called upon to decide whether the judgment 7 + 5 = 12 is analytic or purely synthetic. Kant speaks as if the concepts of 7, 5, and 12 were independent entities, each with its own quite separate connotation. But obviously they can only be formed in the light of the various connected concepts which go to constitute our system of numeration. The proposition has meaning only when interpreted in the light of this conceptual system. It is not, indeed, a self-evident identical proposition; but neither is the connection asserted so entirely synthetic that intuition will alone account for its possibility. That, however, brings us to the third main defect in Kant’s argument.

When Kant states[166] that in synthetic judgments we require, besides the concept of the subject, something else on which the understanding can rely in knowing that a predicate, not contained in the concept, nevertheless belongs to it, he entitles this something x. In the case of empirical judgments, this x is brute experience. Such judgments, Kant implies, are merely empirical. No element of necessity is involved, not even in an indirect manner; in reference to empirical judgments there is no problem of a priori synthesis. Now in formulating the issue in this way, Kant is obscuring the essential purpose of his whole enquiry. He may, without essential detriment to his central position, still continue to preserve a hard-and-fast distinction between analytic and synthetic judgments. In so doing he is only failing to perceive the ultimate consequences of his final results. But in viewing empirical judgments as lacking in every element of necessity, he is destroying the very ground upon which he professes to base the a priori validity of general principles. All judgments involve relational factors of an a priori character. The appeal to experience is the appeal to an implied system of nature. Only when fitted into the context yielded by such a system can an empirical proposition have meaning, and only in the light of such a presupposed system can its truth be determined. It can be true at all, only if it can be regarded as necessarily holding, under the same conditions, for all minds constituted like our own. Assertion of a contingent relation—as in the proposition: this horse is white—is not equivalent to contingency of assertion. Colour is a variable quality of the genus horse, but in the individual horse is necessarily determined in some particular mode. If a horse is naturally white, it is necessarily white. Though, therefore, in the above proposition, necessity receives no explicit verbal expression, it is none the less implied.

In other words, the distinction between the empirical and the a priori is not, as Kant inconsistently assumes in this Introduction, a distinction between two kinds of synthesis or judgment, but between two elements inseparably involved in every judgment. Experience is transcendentally conditioned. Judgment is in all cases the expression of a relation which implies an organised system of supporting propositions; and for the articulation of this system a priori factors are indispensably necessary.

But the most flagrant example of Kant’s failure to live up to his own Critical principles is to be found in his doctrine of pure intuition. It represents a position which he adopted in the pre-Critical period. It is prefigured in Ueber die Deutlichkeit der Grundsätze (1764),[167] and in Von dem ersten Grunde des Unterschiedes der Gegenden im Raume (1768),[168] and is definitely expounded in the Dissertation (1770).[169] That Kant continued to hold this doctrine, and that he himself regarded it as an integral part of his system, does not, of course, suffice to render it genuinely Critical. As a matter of fact, it is really as completely inconsistent with his Critical standpoint as is the view of the empirical proposition which we have just been considering. An appeal to our fingers or to points[170] is as little capable, in and by itself, of justifying any a priori judgment as are the sense-contents of grounding an empirical judgment. Even when Kant is allowed the benefit of his own more careful statements,[171] and is taken as asserting that arithmetical propositions are based on a pure a priori intuition which can find only approximate expression in sensuous terms, his statements run counter to the main tendencies of his Critical teaching, as well as to the recognised methods of the mathematical sciences. Intuition may, as Poincaré and others have maintained, be an indispensable element in all mathematical concepts; it cannot afford proof of any general theorem. The conceptual system which directs our methods of decimal counting is what gives meaning to the judgment 7 + 5 = 12; it is also what determines that judgment as true. The appeal to intuition in numerical judgments must be regarded only as a means of imaginatively realising in a concrete form the abstract relations of some such governing system, or else as a means of detecting relations not previously known. The last thing in the world which such a method can yield is universal demonstration. This is equally evident in regard to geometrical propositions. That a straight line is the shortest distance between two points, cannot be proved by any mere appeal to intuition. The judgment will hold if it can be assumed that space is Euclidean in character; and to justify that assumption it must be shown that Euclidean concepts are adequate to the interpretation of our intuitional data. Should space possess a curvature, the above proposition might cease to be universally valid. Space is not a simple, unanalysable datum. Though intuitionally apprehended, it demands for its precise determination the whole body of geometrical science.[172]

The comparative simplicity of Kant’s intuitional theory of mathematical science, supported as it is by the seemingly fundamental distinction between abstract concepts of reflective thinking and the construction of concepts[173] in geometry and arithmetic, has made it intelligible even to those to whom the very complicated argument of the Analytic makes no appeal. It would also seem to be inseparably bound up with what from the popular point of view is the most striking of all Kant’s theoretical doctrines, namely, his view that space and time are given subjective forms, and that the assertion of their independent reality must result in those contradictions to which Kant has given the title antinomy. For these reasons his intuitional theory of mathematical science has received attention out of all proportion to its importance. Its pre-Critical character has been more or less overlooked, and instead of being interpreted in the light of Critical principles, it has been allowed to obscure the sounder teaching of the Analytic. In this matter Schopenhauer is a chief culprit. He not only takes the views of mathematical science expounded in the Introduction and Aesthetic as being in line with Kant’s main teaching, but expounds them in an even more unqualified fashion than does Kant himself.

There are thus four main defects in the argument of this Introduction, regarded as representative of Critical teaching. (1) Its problems are formulated exclusively in terms of the attributive judgment; the other forms of relational judgment are ignored. (2) It maintains that judgments are either merely analytic or completely synthetic. (3) It proceeds in terms of a further division of judgments into those that are purely empirical and those that are a priori. (4) It seems to assert that the justification for mathematical judgments is intuitional. All these four positions are in some degree retained throughout the Critique, but not in the unqualified manner of this Introduction. In the Analytic, judgment in all its possible forms is shown to be a synthetic combination of a given manifold in terms of relational categories. This leads to a fourfold conclusion. In the first place, judgment must be regarded as essentially relational. Secondly, the a priori and the empirical must not be taken as two separate kinds of knowledge, but as two elements involved in all knowledge. Thirdly, analysis and synthesis must not be viewed as co-ordinate processes; synthesis is the more fundamental; it conditions all analysis. And lastly, it must be recognised that nothing is merely given; intuitional experience, whether sensuous or a priori, is conditioned by processes of conceptual interpretation. Though the consequences which follow from these conclusions, if fully developed, would carry us far beyond any point which Kant himself reached in the progressive maturing of his views, the next immediate steps would still be on the strict lines of the Critical principles, and would involve the sacrifice only of such pre-Critical doctrines as that of the intuitive character of mathematical proof. Such correction of Kant’s earlier positions is the necessary complement of his own final discovery that sense-intuition is incapable of grounding even the so-called empirical judgment.

The Introduction to the first edition bears all the signs of having been written previous to the central portions of the Analytic.[174] That it was not, however, written prior to the Aesthetic seems probable. The opening sections of the Aesthetic represent what is virtually an independent introduction which takes no account of the preceding argument, and which redefines terms and distinctions that have already been dwelt upon. The extensive additions which Kant made in recasting the Introduction for the second edition are in many respects a great improvement. In the first edition Kant had not, except when speaking of the possibility of constructing the concepts of mathematical science, referred to the synthetic character of mathematical judgments. This is now dwelt upon in adequate detail. Kant’s reason for not making the revision more radical was doubtless his unwillingness to undertake the still more extensive alterations which this would have involved. Had he expanded the opening statement of the second edition Introduction, that even our empirical knowledge is a compound of the sensuous and the a priori, an entirely new Introduction would have become necessary. The additions made are therefore only such as will not markedly conflict with the main tenor of the argument of the first edition.

How Are Synthetic a priori Judgments Possible?

Treatment of detailed points will be simplified if we now consider in systematic fashion the many difficulties that present themselves in connection with Kant’s mode of formulating his central problem: How are synthetic a priori judgments possible? This formula is less definite and precise than would at first sight appear. The central phrase ‘synthetic a priori’ is sufficiently exact (the meaning to be attached to the a priori has already been considered[175]), but ambiguities of the most various kinds lurk in the seemingly innocent and simple terms with which the formula begins and ends:

A. ‘How’ has two very different meanings:

(a) How possible = in what manner possible = wie.

(b) How possible = in how far possible, i.e. whether possible = ob.

In connection with these two meanings of the term ‘how,’ we shall have to consider the distinction between the synthetic method employed in the Critique and the analytic method employed in the Prolegomena.

B. ‘Possible’ has a still wider range of application. Vaihinger[176] distinguishes within it no less than three pairs of alternative meanings:

(a) Psychological and logical possibility.

(b) Possibility of explanation and possibility of existence.

(c) Real and ideal possibility.

A. Kant personally believed that the possibility of valid a priori synthetic judgment is proved by the existing sciences of mathematics and physics. And that being so, there were for Kant two very different methods which could be employed in accounting for their possibility, the synthetic or progressive, and the analytic or regressive. The synthetic method would start from given, ordinary experience (in its simplest form, as consciousness of time), to discover its conditions, and from them to prove the validity of knowledge that is a priori. The analytic method would start “from the sought as if it were given,” that is, from the existence of a priori synthetic judgments, and, assuming them as valid, would determine the conditions under which alone such validity can be possible. The precise formulation of these two methods, the determination of their interrelations, of their value and comparative scope, is a matter of great importance, and must therefore be considered at some length.

The synthetic method may easily be confounded with the analytic method. For in the process of its argument it makes use of analysis. By analysing ordinary experience in the form in which it is given, it determines (in the Aesthetic and in the Analytic of Concepts) the fundamental elements of which knowledge is composed, and the generating conditions from which it results. From these the validity of the a priori principles that underlie mathematics and physics can (in the Analytic of Principles) be directly deduced. The fundamental differentiating feature, therefore, of the so-called synthetic method is not its synthetic procedure, since in great part, in the solution of the most difficult portion of its task, it employs an analytic method, but only its attitude towards the one question of the validity of a priori synthetic knowledge. It does not postulate this validity as a premiss, but proves it as a consequence of conditions which are independently established. By a preliminary regress upon the conditions of our de facto consciousness it acquires data from which it is enabled to advance by a synthetic, progressive or deductive procedure to the establishment of the validity of synthetic a priori judgments. The analytic method, on the other hand, makes no attempt to prove the validity of a priori knowledge. It seeks only to discover the conditions under which such knowledge, if granted to exist, can possess validity, and in the light of which its paradoxical and apparently contradictory features can be viewed as complementary to one another. The conditions, thus revealed, will render the validity of knowledge conceivable, will account for it once it has been assumed; but they do not prove it. The validity is a premiss; the whole argument rests upon the assumption of its truth. The conditions are only postulated as conditions; and their reality becomes uncertain, if the validity, which presupposes them, is itself called in question. Immediately we attempt to reverse the procedure, and to prove validity from these conditions, our argument must necessarily adopt the synthetic form; and that, as has been indicated, involves the prior application of a very different and much more thorough process of analysis. The distinction between the two methods may therefore be stated as follows. In the synthetic method the grounds which are employed to explain a priori knowledge are such as also at the same time suffice to prove its validity. In the analytic method they are grounds of explanation, but not of proof. They are themselves proved only in so far as the assumption of validity is previously granted.

The analytic procedure which is involved in the complete synthetic method ought, however, for the sake of clearness, to be classed as a separate, third, method. And as such I shall henceforth regard it. It establishes by an independent line of argument the existence of a priori factors, and also their objective validity as conditions necessary to the very possibility of experience. So viewed, it is the most important and the most fundamental of the three methods. The argument which it embodies constitutes the very heart of the Critique. It is, indeed, Kant’s new transcendental method; and in the future, in order to avoid confusion with the analytic method of the Prolegomena, I shall refer to it always by this title. It is because the transcendental method is an integral part of the complete, synthetic method, but cannot be consistently made a part of the analytic method, that the synthetic method alone serves as an adequate expression of the Kantian standpoint. This new transcendental method is proof by reference to the possibility of experience. Experience is given as psychological fact. The conditions which can alone account for it, as psychological fact, also suffice to prove its objective validity; but at the same time they limit that validity to the phenomenal realm.

We have next to enquire to what extent these methods are consistently employed in the Critique. This is a problem over which there has been much controversy, but which seems to have been answered in a quite final manner by Vaihinger. It is universally recognised that the Critique professes to follow the synthetic method, and that the Prolegomena, for the sake of a simpler and more popular form of exposition, adopts the analytic method. How far these two works live up to their professions, especially the Critique in its two editions, is the only point really in question. Vaihinger found two diametrically opposed views dividing the field. Paulsen, Riehl, and Windelband maintain the view that Kant starts from the fact that mathematics, pure natural science, and metaphysics contain synthetic a priori judgments claiming to be valid. Kant’s problem is to test these claims; and his answer is that they are valid in mathematics and pure natural science, but not in metaphysics. Paulsen, and those who follow him, further contend that in the first edition this method is in the main consistently held to, but that in the second edition, owing to the occasional employment (especially in the Introduction) of the analytic method of the Prolegomena, the argument is perverted and confused: Kant assumes what he ought first to have proved. Fischer, on the other hand, and in a kindred manner also B. Erdmann, maintain that Kant never actually doubted the validity of synthetic a priori judgments; starting from their validity, in order to explain it, Kant discovers the conditions upon which it rests, and in so doing is able to show that these conditions are not of such a character as to justify the professed judgments of metaphysics.

Vaihinger[177] combines portions of both views, while completely accepting neither. Hume’s profound influence upon the development and formulation of Kant’s Critical problem can hardly be exaggerated, but it ought not to prevent us from realising that this problem, in its first form, was quite independently discovered. As the letter of 1772 to Herz clearly shows,[178] Kant was brought to the problem, how an idea in us can relate to an object, by the inner development of his own views, through reflection upon the view of thought which he had developed in the Dissertation of 1770. The conformity between thought and things is in that letter presented, not as a sceptical objection, but as an actual fact calling for explanation. He does not ask whether there is such conformity, but only how it should be possible. Even after the further complication, that thought is synthetic as well as a priori, came into view through the influence of Hume, the problem still continued to present itself to Kant in this non-sceptical light. And this largely determines the wording of his exposition, even in passages in which the demands of the synthetic method are being quite amply fulfilled. Kant, as it would seem, never himself doubted the validity of the mathematical sciences. But since their validity is not beyond possible impeachment, and since metaphysical knowledge, which is decidedly questionable, would appear to be of somewhat similar type, Kant was constrained to recognise that, from the point of view of strict proof, such assumption of validity is not really legitimate. Though, therefore, the analytic method would have resolved Kant’s own original difficulty, only the synthetic method is fully adequate to the situation.

Kant accordingly sets himself to prove that whether or not we are ready (as he himself is) to recognise the validity of scientific judgments, the correctness of this assumption can be firmly established. And being thus able to prove its correctness, he for that very reason does not hesitate to employ it in his introductory statement. The problem, he says, is that of ‘understanding’ how synthetic a priori judgments can be valid. A ‘difficulty,’ a ‘mystery,’ a ‘secret,’ lies concealed in them. How can a predicate be ascribed to a subject term which does not contain it? And even more strangely (if that be possible), how can a priori judgments legislate for objects which are independent existences? Such judgments, even if valid beyond all disputing, would still call for explanation. This is, indeed, Kant’s original and ground problem. As already indicated, no one, save only Hume, had hitherto perceived its significance. Plato, Malebranche, and Crusius may have dwelt upon it, but only to suggest explanations still stranger and more mystical than the mysterious fact itself.[179]

Paulsen is justified in maintaining that Kant, in both editions of the Critique, recognises the validity of mathematics and pure natural science. The fact of their validity is less explicitly dwelt upon in the first edition, but is none the less taken for granted. The sections transferred from the Prolegomena to the Introduction of the second edition make no essential change, except merely in the emphasis with which Kant’s belief in the existence of valid a priori synthetic judgments is insisted upon. As has already been stated, only by virtue of this initial assumption is Kant in position to maintain that there is an alternative to the strict synthetic method. The problem from which he starts is common to both methods, and for that reason the formulation used in the Prolegomena can also be employed in the Introduction to the Critique. Only in their manner of solving the problem need they differ.[180] Kant’s Critical problem first begins with this presupposition of validity, and does not exist save through it.[181] He does not first seek to discover whether such judgments are valid, and then to explain them. He accepts them as valid, but develops a method of argument which suffices for proof as well as for explanation. The argument being directed to both points simultaneously, and establishing both with equal cogency, it may legitimately be interpreted in either way, merely as explanation, or also as proof. Kant does not profess or attempt to keep exclusively to any one line of statement. Against the dogmatists he insists upon the necessity of explaining the validity of a priori synthetic judgments, against the sceptics upon the possibility of proving their validity. And constantly he uses ambiguous terms, such as ‘justification’ (Rechtfertigung), ‘possibility,’ that may indifferently be read in either sense. But though the fundamental demand which characterises the synthetic method in its distinction from the analytic thus falls into the background, and is only occasionally insisted upon, it is none the less fulfilled. So far as regards the main argument of the Critique in either edition, the validity of synthetic a priori judgments is not required as a premiss. It is itself independently proved.

The manner in which Kant thus departs from the strict application of the synthetic method may be illustrated by an analysis of his argument in the Aesthetic.[182] Only in the arguments of the first edition in regard to space and time is the synthetic method employed in its ideal and rigorous form. For the most part, even in the first edition, instead of showing how the a priori character of pure and applied mathematics follows from conclusions independently established, he assumes both pure and applied mathematics to be given as valid, and seeks only to show how the independently established results of the Aesthetic enable him to explain and render comprehensible their recognised characteristics. This is not, indeed, any very essential modification of the synthetic method; for his independently established results suffice for deducing all that they are used to explain. The validity of mathematics is not employed as a premiss. Kant’s argument is, however, made less clear by the above procedure.

Further difficulty is caused by Kant’s occasional employment, even in the first edition, of the analytic method. He several times cites as an argument in support of his view of space the fact that it alone will account for the existing science of geometry. That is to say, he employs geometry, viewed as valid, to prove the correctness of his view of space.[183] Starting from that science as given, he enquires what are the conditions which can alone render it possible. These conditions are found to coincide with those independently established. Now this is a valid argument when employed in due subordination to the main synthetic method. It offers welcome confirmation of the results of that method. It amounts in fact to this, that having proved (by application of the transcendental method) the mathematical sciences to be valid, everything which their validity necessarily implies must be granted. Kant’s reasoning here becomes circular, but it is none the less valid on that account. This further complication of the argument is, however, dangerously apt to mislead the reader. It is in great part the cause of the above division among Kant’s commentators. The method employed in the Prolegomena is simply this form of argument systematised and cut free from all dependence upon the transcendental method of proof.[184]

The whole matter is, however, still further complicated by the distinction, which we have already noted, between real and ideal possibility. Are the given synthetic a priori judgments valid? That is one question. Can the Critical philosophy discover, completely enumerate, and prove in a manner never before done, all the possible synthetic a priori principles? That is a very different problem, and when raised brings us to the further discussion of Kant’s transcendental method. The question at issue is no longer merely whether or not certain given judgments are valid, and how, if valid, they are to be accounted for. The question is now that of discovering and of proving principles which have not been established by any of the special sciences. This shifting of the problem is concealed from Kant himself by his omission to distinguish between the undemonstrated axioms of the mathematical sciences and their derivative theorems, between the principles employed by the physicist without enquiry into their validity and the special laws based upon empirical evidence.

As regards the mathematical axioms, the problem is fairly simple. As we shall see later, in the Aesthetic, they do not require a deduction in the strict transcendental sense. They really fall outside the application of the transcendental method. They require only an “exposition.” But in regard to the fundamental principles of natural science we are presented with the problem of discovery as well as of proof. Unlike the axioms of the mathematician, they are frequently left unformulated. And many postulates, such as that there is a lex continui in natura, are current in general thought, and claim equal validity with the causal principle. Kant has thus to face the question whether in addition to those principles employed more or less explicitly by the scientist, others, such as might go to form an immanent metaphysics of nature, may not also be possible.

B. (a)[185] Psychological and logical possibility.—Both have to be recognised and accounted for. Let us consider each in order.

(1) Psychological possibility.—What are the subjective conditions of a priori synthetic judgments? Through what mental faculties are they rendered possible? Kant replies by developing what may be called a transcendental psychology. They depend upon space and time as forms of sensibility, upon the a priori concepts of understanding, and upon the synthetic activities by which the imagination schematises these concepts and reduces the given manifold to the unity of apperception. This transcendental psychology is the necessary complement of the more purely epistemological analysis.[186] But on this point Kant’s utterances are extremely misleading. His Critical enquiry has, he declares, nothing in common with psychology. In the Preface to the first edition we find the following passage: “This enquiry ... [into] the pure understanding itself, its possibility and the cognitive faculties upon which it rests ..., although of great importance for my chief purpose, does not form an essential part of it.”[187] The question, he adds, “how is the faculty of thought itself possible?... is as it were a search for the cause of a given effect, and therefore is of the nature of an hypothesis [or ‘mere opinion’], though, as I shall show elsewhere, this is not really so.” The concluding words of this passage very fairly express Kant’s hesitating and inconsistent procedure. Though he has so explicitly eliminated from the central enquiry of the Critique all psychological determination of the mental powers, statements as to their constitution are none the less implied, and are involved in his epistemological justification alike of a priori knowledge and of ordinary experience. If we bear in mind that Kant is here attempting to outline the possible causes of given effects, and that his conclusions are therefore necessarily of a more hypothetical character than those obtained by logical analysis, we shall be prepared to allow him considerable liberty in their formulation. But in certain respects his statements are precise and definite—the view, for instance, of sensations as non-spatial, of time as a form of inner sense, of the productive imagination as pre-conditioning our consciousness, of spontaneity as radically distinct from receptivity, of the pure forms of thought as not acquired through sense, etc. No interpretation which ignores or under-estimates this psychological or subjective aspect of his teaching can be admitted as adequate.[188]

(2) Logical or epistemological possibility.—How can synthetic a priori judgments be valid? This question itself involves a twofold problem. How, despite their synthetic character, can they possess truth, i.e. how can we pass from their subject terms to their predicates? And secondly, how, in view of their origin in our human reason, can they be objectively valid, i.e. legislate for the independently real? How can we pass beyond the subject-predicate relation to real things? This latter is the Critical problem in the form in which it appears in Kant’s letter of 1772 to Herz.[189] The former is the problem of synthesis which was later discovered.

(b) (1) Possibility of explanation and (2) possibility of existence.—(1) How can synthetic a priori judgments be accounted for? How, despite their seemingly inconsistent and apparently paradoxical aspects, can their validity (their validity as well as their actuality being taken for granted) be rendered comprehensible? (2) The validity of such judgments has been called in question by the empiricists, and is likewise inexplicable even from the dogmatic standpoint of the rationalists. How, then, can these judgments be possible at all? These two meanings of the term ‘possible’ connect with the ambiguity, above noted, in the term ‘how.’ The former problem can be solved by an analytic method; the latter demands the application of the more radical method of synthetic reconstruction.

(c) Real and ideal possibility.[190]—We have to distinguish between the possible validity of those propositions which the mathematical and physical sciences profess to have established and the possible validity of those principles such as that of causality, which are postulated by the sciences, but which the sciences do not attempt to prove, and which in certain cases they do not even formulate. The former constitute an actually existent body of scientific knowledge, demonstrated in accordance with the demands of scientific method. The latter are employed by the scientist, but are not investigated by him. The science into which they can be fitted has still to be created; and though some of the principles composing it may be known, others remain to be discovered. All of them demand such proof and demonstration as they have never yet received.[191] This new and ideal science is the scientific metaphysics which Kant professes to inaugurate by means of the Critique. In reference to the special sciences, possibility means the conditions of the actually given. In reference to the new and ideal metaphysics, possibility signifies the conditions of the realisation of that which is sought. In view of this distinction, the formula—How are synthetic a priori judgments possible?—will thus acquire two very different meanings. (1) How are the existing a priori synthetic judgments to be accounted for? (2) How may all the really fundamental judgments of that type be exhaustively discovered and proved? Even in regard to immanent metaphysics Kant interprets the formula in both ways. This is due to his frequent confusion of immanent metaphysics with the principles of natural science. Its propositions are then regarded as given, and only their general validity calls for proof. It is, however, in the problem of ideal possibility that the essential problem of the Critique lies; and that is a further reason why it cannot be adequately dealt with, save by means of the synthetic method.

Experience.—Throughout the Introduction the term experience[192] has (even at times in one and the same sentence) two quite distinct meanings, (1) as product of sense and understanding acting co-operatively, and (2) as the raw material (the impressions) of sense. Considerable confusion is thereby caused.

Understanding and reason[193] are here, as often elsewhere in the Critique, used as equivalent terms. Throughout the entire two first sections of the Introduction to the second edition the term reason does not occur even once. As first mentioned,[194] it is taken as the source of metaphysical judgments.

General (a priori) truths have an inner necessity and must be clear and certain by themselves.[195]—These statements are not in accordance with Kant’s new Critical teaching.[196] They have remained uncorrected from a previous way of thinking. This must be one reason for the recasting of this paragraph in the second edition.

Even with (unter) our experiences there is mingled knowledge which must be of a priori origin.[197]—Kant is here distinguishing the immanent a priori, such as that involved in any causal judgment, from the transcendent a priori dwelt upon in the next paragraph. The latter is expressed through metaphysical judgments, such as ‘God exists,’ ‘the soul is immortal.’

Original concepts and judgments derived from them.[198]—Cf. B 5-6.

Pure.—In the title of the section the term pure[199] (rein) is, as the subsequent argument shows, taken as exactly equivalent to a priori. As Vaihinger notes, the adjective apriorisch had not yet been invented. The opposite of pure is here empirical (empirisch).[200]

All our knowledge begins with experience.[201]—This is a stronger statement than any in the corresponding paragraphs of the first edition. Had Kant proceeded to develop its consequences, he would have had to recast the entire Introduction, setting the problem of empirical knowledge alongside that of the a priori.[202] As it is, he is forced[203] to subdivide the absolutely a priori into the pure and the mixed.[204]

By objects which affect (rühren) our senses. The raw material of sensuous impressions.[205]—These incidental statements call for discussion. Cf. below, pp. 80-8, 120-1, 274 ff.

A knowledge of objects which we call experience.[206]—Kant does not keep to this definition. The term experience is still used in its other and narrower sense, as in the very next paragraph, when Kant states that knowledge does not, perhaps, arise solely from experience (= sense impressions).

In respect of time.[207]—This statement, taken as an account of Kant’s teaching in the Critique, is subject to two reservations. In the Aesthetic[208] Kant sometimes claims a temporal antecedence for the a priori. And secondly, the a priori is not for Kant merely logical. It also possesses a dynamical priority.[209]

Even experience itself is a compound.[210]—The “even” seems to refer to the distinction drawn in A 2 between the immanent and the transcendent a priori.[211]

It is therefore a question whether there exists such knowledge independent of experience.[212]—This question was not raised in the first edition.[213] The alternative methods, analytic and synthetic, are discussed above, p. 44 ff.

Such knowledge is called a priori and is distinguished from empirical knowledge.[214]—Throughout the Introduction, in both editions equally, Kant fails to state the problems of the Critique in a sufficiently comprehensive manner. He speaks as if the Critique dealt only with the absolutely a priori, in its two forms, as immanent scientific knowledge and as transcendent speculation. It also deals with the equally important and still more fundamental problem of accounting for the possibility of experience.[215] Our empirical knowledge involves an a priori element, and may not therefore be opposed to a priori knowledge in the manner of the passage before us.

This term a priori is not yet definite enough.[216]—It is frequently employed in a merely relative sense. Thus we can say of a person who undermines the foundations of his house that he might have known a priori that it would collapse, that is, that he need not wait for the experience of its actual fall. But still he could not know this entirely a priori; he had first to learn from experience that bodies are heavy, and will fall when their supports are taken away. But as dealt with in the Critique the term a priori is used in an absolute sense, to signify that knowledge which is independent, not of this or that experience only, but of all impressions of the senses. Thus far Kant’s position is comparatively clear; but he proceeds to distinguish two forms within the absolutely a priori, namely, mixed and pure. The absolutely a priori is mixed when it contains an empirical element, pure when it does not. (“Pure” is no longer taken in the meaning which it has in the title of the section.[217] It signifies not the a priori as such, but only one subdivision of it.) Thus after defining absolutely a priori knowledge as independent of all experience, Kant takes it in one of its forms as involving empirical elements. The example which he gives of an absolutely a priori judgment, which yet is not pure, is the principle: every change has its cause. “Change” is an empirical concept, but the synthetic relation asserted is absolutely a priori. In the next section[218] this same proposition is cited as a pure judgment a priori—“pure” being again used in its more general meaning as synonymous with a priori. This confusion results from Kant’s exclusive preoccupation with the a priori, and consequent failure to give due recognition to the correlative problem of the empirical judgment. The omitted factor retaliates by thus forcing its way into Kant’s otherwise clean-cut divisions. Also, it is not true that the relative a priori falls outside the sphere of the Critical enquiry. Such judgment expresses necessity or objectivity, and for that reason demands a transcendental justification no less urgently than the absolutely a priori. The finding of such justification is, indeed, the central problem of the Analytic.[219]

The subdivisions of the a priori may be tabulated thus:

A priori knowledge— Relative, e.g. every unsupported house must fall.

Absolute—Mixed, e.g. every change has its cause. Pure, e.g. a straight line is the shortest distance between two points.

The term pure (rein) thus acquires a second meaning distinct from that defined above.[220] It is no longer employed as identical with a priori, but as a subdivision of it, meaning unmixed. Its opposite is no longer the empirical, but the impure or mixed. Owing, however, to the fact that “pure” (in its first meaning) is identical with the a priori, it shares in all the different connotations of the latter, and accordingly is also employed to denote that which is not relative. But “pure” has yet another meaning peculiar to itself. The phrase “independent of experience” has in reference to “pure” an ambiguity from which it does not suffer in its connection with “a priori” (since mathematical knowledge, whether pure or applied, is always regarded by Kant as a priori). It may signify either independence as regards content and validity, or independence as regards scope. The latter meaning is narrower than the former. By the former meaning it denotes that which originates, and can possess truth, independently of experience. By the latter it signifies that which is not only independent of sense but also applies to the non-sensuous. In this latter meaning pure knowledge therefore signifies transcendent knowledge. Its opposite is the immanent. The various meanings of “pure” (four in number) may be tabulated as follows:

(a) (1) A priori: independent of experience as regards origin and validity. (Its opposite = empirical.)

(2) Absolutely independent of experience. (Its opposite = relative.)

(3) Unmixed with experience. (Its opposite = impure or mixed.)

(b) (4) Independent of experience as regards scope = transcendent. (Its opposite = immanent.)

All these varied meanings contribute to the ambiguity of the title of the Critique. Kant himself employs the title in all of the following senses:

1. Critique of absolutely pure a priori knowledge, determination of its sources, conditions, scope and limits.

2. Critique of all a priori knowledge, relative as well as absolute, in so far as it depends upon a priori principles, determination, etc.

3. Critique of all knowledge, whether a priori or empirical, determination, etc.

4. Critique of transcendent knowledge, its sources and limits.

Further meanings could also be enumerated but can be formulated by the reader for himself in the light of the ambiguities just noted.[221] The special context in each case can alone decide how the title is to be understood. If a really adequate definition of the purpose and scope of the Critique is sought by the reader, he must construct it for himself. The following may perhaps serve. The Critique is an enquiry into the sources, conditions, scope and limits of our knowledge, both a priori and empirical, resulting in the construction of a new system of immanent metaphysics; in the light of the conclusions thus reached, it also yields an analysis and explanation of the transcendental illusion to which transcendent metaphysics, both as a natural disposition and as a professed science, is due.

Kant further complicates matters by offering a second division of the absolutely a priori,[222] viz. into the original and the derivative. Also, by implication, he classes relative a priori judgments among the propositions to be reckoned with by the Critique; and yet in B 4 he speaks of the proposition, all bodies are heavy, as merely empirical.[223]

A criterion.[224]—Necessity and universality are valid criteria of the a priori (= the non-empirical). This follows from Kant’s view[225] of the empirical as synonymous with the contingent (zufällig). Experience gives only the actual; the a priori alone yields that which cannot be otherwise.

“Necessity and strict universality are thus safe criteria of a priori knowledge, and are inseparable from one another. But since in the employment of these criteria the empirical limitation of judgments is sometimes more easily shown than their contingency, or since, as frequently happens, their unlimited universality can be more convincingly proved than their necessity, it is advisable to use the two criteria separately, each being by itself infallible.”[226]

Now Kant is here, of course, assuming the main point to be established, namely, that experience is incapable of accounting for such universality and necessity as are required for our knowledge, both ordinary and scientific. We have already considered this assumption,[227] and have also anticipated misunderstanding by noting the important qualifications to which, from Kant’s new Critical standpoint, the terms ‘necessity’ and ‘universality’ become subject.[228] The very specific meaning in which Kant employs the term a priori must likewise be borne in mind. Though negatively the a priori is independent of experience, positively it originates in our human reason. The necessity and universality which differentiate the a priori distinguish it only from the humanly accidental. The a priori has no absolute validity. From a metaphysical standpoint, it is itself contingent. As already stated,[229] all truth is for Kant merely de facto. The necessary is not that which cannot be conceived to be otherwise, nor is it the unconditioned. Our reason legislates only for the world of appearance. But as yet Kant gives no hint of this revolutionary reinterpretation of the rationalist criteria. One of the chief unfortunate consequences of the employment in this Introduction of the analytic method of the Prolegomena is that it tends to mislead the reader by seeming to commit Kant to a logical a priori of the Leibnizian type.

To show that, if experience is to be possible, [pure a priori propositions] are indispensable, and so to prove their existence a priori.[230]—At first sight Kant would seem to be here referring to the alternative synthetic method of procedure, i.e. to the transcendental proof of the a priori. The next sentence shows, however, that neither in intention nor in fact is that really so. He argues only that a priori principles, such as the principle of causality, are necessary in order to give “certainty” to our experience; such a principle must be postulated if inductive inference is to be valid. Experience could have no [scientific] certainty, “if all rules according to which it proceeds were themselves in turn empirical, and therefore contingent. They could hardly be regarded as first principles.” There is no attempt here to prove that empirical knowledge as such necessarily involves the a priori. Also the method of argument, though it seeks to establish the necessity of the a priori, is not transcendental or Critical in character. It is merely a repetition of the kind of argument which both Hume and Leibniz had already directed against the sensationalist position.[231] Very strangely, considering that these sentences have been added in the second edition, and therefore subsequent to the writing of the objective deduction, Kant gives no indication of the deeper problem to which he finally penetrated. The explanation is, probably, that to do so would have involved the recasting of the entire Introduction. Even on the briefest reference, the hard-and-fast distinction between the a priori and the empirical, as two distinct and separate classes of judgment, would have been undermined, and the reader would have been made to feel the insufficiency of the analysis upon which it is based.[232] The existence of the deeper view is betrayed only through careless employment of the familiar phrase “possibility of experience.” For, as here used, it is not really meant. “Certainty of experience”—a very different matter—is the meaning that alone will properly fit the context.

Reason and understanding.[233]—They are here distinguished, having been hitherto, in A 1-2, employed as synonymous. The former carries us beyond the field of all possible experience; the latter is limited to the world of sense. Thus both Reason and understanding are here used in their narrowest meaning.

These inevitable problems of pure Reason itself are God, freedom, and immortality. The science which, with all its methods, is in its final intention directed solely to the solution of these problems, is called metaphysics.[234]—These sentences are characteristic of the second edition with its increased emphasis upon the positive results of the Critique on the one hand, and with its attitude of increased favour towards transcendent metaphysics on the other. The one change would seem to be occasioned by the nature of the criticisms passed upon the first edition, as, for instance, by Moses Mendelssohn who describes Kant as “the all-destroyer” (der alles zermalmende). The other is due to Kant’s preoccupation with the problems of ethics and of teleology. The above statements are repeated with even greater emphasis in B 395 n.[235] The definition here given of metaphysics is not strictly kept to by Kant. As above noted,[236] Kant really distinguishes within it two forms, immanent and transcendent. In so doing, however, he still[237] regards transcendent metaphysics as the more important. Immanent metaphysics is chiefly of value as contributing to the solution of the “inevitable problems of pure Reason.”

A 3-4 = B 7-8.—The reasons, here cited by Kant, for the failure of philosophical thinking to recognise the difference between immanent and transcendent judgments are: (1) the misunderstood character, and consequent misleading influence, of a priori mathematical judgments; (2) the fact that once we are beyond the sensible sphere, experience can never contradict us; (3) natural delight in the apparent enlargement of our knowledge; (4) the ease with which logical contradictions can be avoided; (5) neglect of the distinction between analytic and synthetic a priori judgments. Vaihinger points out[238] that in the Fortschritte[239] Kant adds a sixth reason—confusion of the concepts of understanding with the Ideas of Reason. Upon the first of the above reasons the best comment is that of the Methodology.[240] But the reader must likewise bear in mind that in B xvi Kant develops his new philosophical method on the analogy of the mathematical method. The latter is, he claims, mutatis mutandis, the true method of legitimate speculation, i.e. of immanent metaphysics. The one essential difference (as noted by Kant[241]), which has been overlooked by the dogmatists, is that philosophy gains its knowledge from concepts, mathematics from the construction of concepts.

Remain investigations only.[242]—Cf. Prolegomena, § 35.

The analysis of our concepts of objects.[243]—Vaihinger’s interpretation, that the concepts here referred to are those which we “form a priori of things,”[244] seems correct.[245] The rationalists sought to deduce the whole body of rational psychology from the a priori conception of the soul as a simple substance, and of rational theology from the a priori conception of God as the all-perfect Being.

Analytic and synthetic judgments.[246]—“All analytic judgments depend wholly on the law of contradiction, and are in their nature a priori cognitions, whether the concepts that supply them with matter be empirical or not. For the predicate of an affirmative analytic judgment is already contained in the concept of the subject, of which it cannot be denied without contradiction. In the same way its opposite is necessarily denied of the subject in an analytic, but negative, judgment by the same law of contradiction.... For this very reason all analytic judgments are a priori even when the concepts are empirical, as, for example, gold is a yellow metal; for to know this I require no experience beyond my concept of gold as a yellow metal: it is, in fact, the very concept, and I need only analyse it, without looking beyond it elsewhere.... [Synthetic judgments, a posteriori and a priori] agree in this, that they cannot possibly spring solely from the principle of analysis, the law of contradiction. They require a quite different principle. From whatever they may be deduced, the deduction must, it is true, always be in accordance with the principle of contradiction. For that principle must never be violated. But at the same time everything cannot be deduced from it.”[247]

In A 594 = B 622 analytic judgments are also spoken of as identical; but in the Fortschritte[248] this use of terms is criticised:

“Judgments are analytic if their predicate only represents clearly (explicite) what was thought obscurely (implicite) in the concept of the subject, e.g. all bodies are extended. Were we to call such judgments identical only confusion would result. For identical judgments contribute nothing to the clearness of the concept, and that must be the purpose of all judging. Identical judgments are therefore empty, e.g. all bodies are bodily (or to use another term material) beings. Analytic judgments do, indeed, ground themselves upon identity and can be resolved into it; but they are not identical. For they demand analysis and serve for the explanation of the concept. In identical judgments, on the other hand, idem is defined per idem, and nothing at all is explained.”

Vaihinger[249] cites the following contrasted examples of analytic and synthetic judgments:

Analytic.—(a) Substance is that which exists only as subject in which qualities inhere.[250] (b) Every effect has a cause.[5] (c) Everything conditioned presupposes a condition.

Synthetic.—(a) Substance is permanent. (b) Every event has a cause.[251] (c) Everything conditioned presupposes an unconditioned.

B 11-12.—The first half of this paragraph is transcribed practically word for word from the Prolegomena.[252] The second half is a close restatement of an omitted paragraph of the first edition. The chief addition lies in the concluding statement, that “experience is itself a synthetic connection of intuitions.” This is in keeping with statements made in the deduction of the categories in the second edition,[253] and in the paragraph inserted in the proof of the second analogy in the second edition.[254] The x has strangely been omitted in the second edition in reference to empirical judgments, though retained in reference to synthetic a priori judgments.

The proposition: everything which happens has its cause.[255]—As we have already observed,[256] Hume influenced Kant at two distinct periods in his philosophical development—in 1756-1763, and again at some time (not quite definitely datable) after February 1772. The first influence concerned the character of concrete causal judgments; the second related to the causal axiom. Though there are few distinctions which are more important for understanding the Critique than that of the difference between these two questions, it has nowhere been properly emphasised by Kant, and in several of the references to Hume, which occur in the Critique and in the Prolegomena, the two problems are confounded in a most unfortunate manner. The passages in the Introduction[257] are clear and unambiguous; the influence exercised by Hume subsequent to February 1772 is quite adequately stated. The causal axiom claims to be a priori, and is, as Hume asserts, likewise synthetic. Consequently there are only two alternatives, each decisive and far-reaching. Either valid a priori synthesis must, contrary to all previous philosophical belief, be possible, or “everything which we call metaphysics must turn out to be a mere delusion of reason.” The solution of this problem is “a question of life and death to metaphysics.” To this appreciation of Hume, Kant adds criticism. Hume did not sufficiently universalise his problem. Had he done so, he would have recognised that pure mathematics involves a priori synthesis no less necessarily than do the metaphysical disciplines. From denying the possibility of mathematical science “his good sense would probably have saved him.” Hume’s problem, thus viewed, finds its final and complete expression in the formula: How are synthetic a priori judgments possible?

In A 760 = B 788 the account differs in two respects: first, it discusses the metaphysical validity of the causal axiom as well as its intrinsic possibility as a judgment; and secondly, reference is made to the conception of causality as well as to the axiom. The implied criticism of Hume is correspondingly modified. Otherwise, it entirely harmonises with the passages in the Introduction.

“Hume dwelt especially upon the principle of causality, and quite rightly observed that its truth, and even the objective validity of the concept of efficient cause in general, is based on no insight, i.e. on no a priori knowledge, and that its authority cannot therefore be ascribed to its necessity, but merely to its general utility in the course of experience and to a certain subjective necessity which it thereby acquires, and which he entitles custom. From the incapacity of our reason to make use of this principle in any manner that transcends experience he inferred the nullity of all pretensions of reason to advance beyond the empirical.”

Now so far, in these references to Hume, Kant has had in view only the problems of mathematical and physical science and of metaphysics. The problems involved in the possibility of empirical knowledge are left entirely aside. His account of Hume’s position and of his relation to Hume suffers change immediately these latter problems are raised. And unfortunately it is a change for the worse. The various problems treated by Hume are then confounded together, and the issues are somewhat blurred. Let us take the chief passages in which this occurs. In A 764 = B 792 ff. Kant gives the following account of Hume’s argument. Hume, recognising the impossibility of predicting an effect by analysis of the concept of the cause, or of discovering a cause from the concept of the effect, viewed all concrete causal judgments as merely contingent, and therefrom inferred the contingency of the causal axiom. In so doing Hume, Kant argues, confuses the legitimate and purely a priori inference from a given event to some antecedent with the very different inference, possible only through special experience, to a specific cause. Now this is an entire misrepresentation of Hume’s real achievement, and may perhaps be explained, at least in part, as being due to the fact that Kant was acquainted with Hume’s Treatise only through the indirect medium of Beattie’s quotations. Hume committed no such blunder. He clearly recognised the distinction between the problem of the validity of the causal axiom and the problem of the validity of concrete causal judgments. He does not argue from the contingency of concrete causal laws to the contingency of the universal principle, but shows, as Kant himself recognises,[258] that the principle is neither self-evident nor demonstrable a priori. And as necessity cannot be revealed by experience, neither is the principle derivable from that source. Consequently, Hume concludes, it cannot be regarded as objectively valid. It must be due to a subjective instinct or natural belief. (The two problems are similarly confounded by Kant in A 217 = B 264.)

In the Introduction to the Prolegomena there is no such confusion of the two problems, but matters are made even worse by the omission of all reference to Hume’s analysis of the causal axiom. Only Hume’s treatment of the concept of causality is dwelt upon. This is the more unfortunate, and has proved the more misleading, in that it is here that Kant makes his most explicit acknowledgment of his indebtedness to Hume. In §§ 27 ff. of the Prolegomena both problems reappear, but are again confounded. The section is preceded by sentences in which the problem of experience is emphasised; and in keeping with these prefatory remarks, Kant represents “Hume’s crux metaphysicorum” as concerning only the concept of causality (viewed as a synthetic, and professedly a priori, connection between concrete existences). Yet in § 30 the causal axiom is also referred to, and together they are taken as constituting “Hume’s problem.”

Now if we bear in mind that Hume awakened Kant to both problems—how a priori knowledge is possible, and how experience is possible—this confusion can easily be understood. Kant had already in the early ‘sixties studied Hume with profound admiration and respect.[259] In the period subsequent to 1772 this admiration had only deepened; and constantly, as we may believe, Kant had returned with fresh relish to Hume’s masterly analyses of causality and of inductive inference. It is not, therefore, surprising that as the years passed, and as the other elements in Hume’s teaching revealed to him, through the inner growth of his own views, their full worth and significance, he should allow the contribution that had more specifically awakened him to fall into the background, and should, in vague fashion, ascribe to Hume’s teaching as a whole the specific influence which was really due to one particular part. By 1783, the date of the Prolegomena, Kant’s first enthusiasm over the discovery of the fundamental problem of a priori synthesis had somewhat abated, and the problem of experience had more or less taken its place. This would seem to be the reason why in the Prolegomena he thus deals with both aspects of Hume’s problem, and why in so doing he gives a subordinate place to Hume’s treatment of the causal axiom. But though the misunderstanding may be thus accounted for, it must none the less be deplored. For the reader is seriously misled, and much that is central to the Critical philosophy is rendered obscure. The influence which Kant in the Prolegomena thus ascribes to Hume was not that which really awakened him from his dogmatic slumber, but is in part that which he had assimilated at least as early as 1763, and in part that which acted upon him with renewed force when he was struggling (probably between 1778 and 1780) with the problems involved in the deduction of the categories. It was Hume’s treatment of the causal axiom, and that alone, which, at some time subsequent to February 1772, was the really effective influence in producing the Copernican change.[260]

Purely a priori and out of mere concepts.[261]—Vaihinger’s comment seems correct: Kant means only that neither actual experience nor pure intuition can be resorted to. This does not contradict the complementary assertion,[262] that the principle, everything which happens has its cause, can be known a priori, not immediately from the concepts involved in it, but only indirectly[263] through the relation of these concepts to possible experience. “Possible experience,” even though it stands for “something purely contingent,” is itself a concept. Vaihinger[264] quotes Apelt upon this “mysterious” type of judgment.

“Metaphysics is synthetic knowledge from mere concepts, not like mathematics from their construction in intuition, and yet these synthetic propositions cannot be known from bare concepts, i.e. not analytically. The necessity of the connection in those propositions is to be apprehended through thought alone, and yet is not to rest upon the form of thought, the principle of contradiction. The conception of a kind of knowledge which arises from bare concepts, and yet is synthetic, eludes our grasp. The problem is: How can one concept be necessarily connected with another, without also at the same time being contained in it?”

The paragraphs in B 14 to B 17 are almost verbal transcripts from Prolegomena, § 2 c, 2 ff.

Mathematical judgments are one and all (insgesammt) synthetic.[265]—This assertion is carelessly made, and does not represent Kant’s real view. In B 16 he himself recognises the existence of analytic mathematical judgments, but unduly minimises their number and importance.

All mathematical conclusions proceed according to the principle of contradiction.[266]—To the objection made by Paulsen that Kant, in admitting that mathematical judgments can be deduced from others by means of the principle of contradiction, ought consistently to have recognised as synthetic only axioms and principles, Vaihinger replies as follows:[267]

“The proposition—the angles of a triangle are together equal to two right angles—Kant regards as synthetic. It is indeed deduced from the axiom of parallels (with the aid of auxiliary lines), and to that extent is understood in accordance with the principle of contradiction.... The angles in the triangle constitute a special case of the angles in the parallel lines which are intersected by other lines. The principle of contradiction thus serves as vehicle in the deduction, because once the identity of A and A´ is recognised, the predicate b, which belongs to A, must also be ascribed to A´. But the proposition is not for that reason itself analytic in the Kantian sense. In the analytic proposition the predicate is derived from the analysis of the subject concept. But that does not happen in this case. The synthetic proposition can never be derived in and by itself from the principle of contradiction; ... but only with the aid of that principle from other propositions. Besides, in this deduction intuition must always be resorted to; and that makes an essential difference. Without it the identity of A and A´ cannot become known.”

Pure mathematics.[268]—“Pure,” as thus currently used, is opposed only to applied, not to empirical. Kant here arbitrarily reads the latter opposition into it. Under this guise he begs the point in dispute.

7 + 5 = 12.[269]—Though 7 + 5 = 12 expresses an identity or equality, it is an equality of the objects or magnitudes, 7 + 5 and 12, not of the concepts through which we think them.[270] Analysis of the concepts can never reveal this equality. Only by constructing the concepts in intuition can it be recognised by the mind. This example has been already cited in the first edition.[271] It is further elaborated in the Prolegomena, § 2 c, and is here transcribed. Kant’s mode of stating his position is somewhat uncertain. He alternates between “the representation of 7 and 5,” “the representation of the combination of 7 and 5,”[272] and “the concepts 7 and 5.”[273] His view would seem to be that there are three concepts involved. For the concept of 7 we must substitute the intuition of 7 points, for the concept of 5 the intuition of 5 points, and for the concept of their sum the intuitive operation of addition.

Call in the assistance of intuition, for instance our five fingers.[274]—This statement, repeated from the Prolegomena,[275] does not represent Kant’s real position. The views which he has expressed upon the nature of arithmetical science are of the most contradictory character,[276] but to one point he definitely commits himself, namely, that, like geometrical science, it rests, not (as here asserted) upon empirical, but upon pure intuition.[277] Except indirectly, by the reference to larger numbers, Kant here ignores his own important distinction between image and schema.[278] The above statement would also make arithmetic dependent upon space.

Segner: Anfangsgründe der Arithmetik,[279] translated from the Latin, second edition, Halle, 1773.