Chapter X: Introduction (1)

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]