A Commentary to Kant's 'Critique of Pure Reason'

by Norman Kemp Smith

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.