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

by Norman Kemp Smith

”[Antithetic] is the conflict between two apparently dogmatic judgments [Erkenntnisse] to neither of which can we ascribe any superior claim to acceptance over the other, i.e. by Antithetic I mean a thesis, together with an antithesis.” “Transcendental Antithetic is an investigation of the antinomy of pure Reason, its causes and outcome.”

The very existence of such antinomy presupposes a twofold condition: first, that it does not refer to a gratuitous but to an inevitable problem of human Reason, “one which it must necessarily encounter in its natural progress”; and secondly, that the thesis and the antithesis together generate a “natural and inevitable illusion,” which continues to persist even after its deceptive power has been clearly disclosed. Such conflict is caused by the fact that Reason seeks a unity which transcends the understanding, and which nevertheless is meant to conform to the conditions of the understanding. If the unity is adequate to the demands of Reason, it is too great for the understanding; if it is commensurate with the understanding, it is too small for Reason.[1504] The theses express the higher unity at which Reason aims; the antitheses are the judgments to which the understanding is constrained by the nature of the appearances with which both it and Reason profess to deal. If we hold to Reason, we make assertions contradictory of the appearances; while if we place reliance on the understanding, Reason condemns our conclusions.

This conflict is limited to those few problems above enumerated in which we are called upon to complete a given series.[1505] Since totality, whether in the form of a first beginning of the series or as an actual infinity of the whole series, can never itself be experienced, these are problems in regard to which experience can be of no assistance to us. It can neither confirm nor refute any particular solution. The only possible method of deciding between the competing claims is to watch or even to provoke the conflict, in the hope that we may finally be able to detect some misunderstanding, and so to resolve the conflict to the satisfaction of both the litigants. Such is Kant’s description of what he entitles his “sceptical method.”[1506]

Without here attempting a full discussion of the subject, it seems advisable to point out at the very start what Kant’s exposition seriously obscures, namely, the real character of the evidence upon which the theses and the antitheses respectively rest. The latter are not correctly stated as transcending experience, and as therefore incapable of confirmation by it. The proofs which Kant offers of them are, indeed, of a non-empirical a priori character. They are formulated in terms of the dogmatic rationalism of the Leibnizian position, with a constant appeal to abstract principles. But, as a matter of fact, they can be much more adequately established—in so far as they can be established at all—through analysis of the spatial and temporal conditions of material existence. As space and time are continuous and homogeneous, any assertion which is true of a space or time however small is likewise true of a space or time however large. Any space consists of spaces, and must be regarded as itself part of a larger whole.[1507] Any time consists of parts which are themselves times, and is apprehensible only as following upon preceding times. It is by such considerations as these that we are led to regard the material world as unlimited, as infinitely divisible, and as having no first state.

Kant’s method of demonstrating the theses—that the world is limited, is finitely divisible, and has a first state—is no less misleading. Here again his rationalistic arguments conceal the basis upon which the various theses really rest. Their true determining ground is the demand of Reason for some more satisfactory form of unconditionedness than that which is found in the actual infinite. It is this demand which has led philosophers to look around for proofs in support of the theses, and to elaborate those rationalistic arguments which Kant here reproduces. Thus the grounds of the antitheses are altogether different from those of the theses; and in neither case are they properly represented by the arguments which Kant employs.[1508]

The reasons why Kant in his detailed statement of the antinomies has omitted, or at least subordinated, the above considerations, are complex and various. In the first place, this doctrine of antinomy was in several of its main features already formulated prior to his development of the Critical philosophy. It forms part of his Dissertation of 1770; and at that time Kant was still largely in fundamental sympathy with the Leibnizian ontology. Secondly, Kant is here professing to criticise the science of rational cosmology, and is therefore bound to expound it in more or less current form. And in the third place, he teaches that the antinomies exist as antinomies only when viewed from the false standpoint of dogmatic rationalism. Had he eliminated the rationalistic proofs, the conflict of the antinomies, in its strictly logical form, as the conflict of direct contradictories, would at once have vanished. The general framework of this division of the Dialectic demanded a rationalistic treatment of both theses and antitheses, and Kant believed that the rationalistic proofs which he propounds in their support are unanswerable, so long as the dogmatic standpoint of ordinary consciousness and of Leibnizian ontology is preserved. But even when that important limitation is kept in view, Kant fails to justify this interpretation of the conflict, and we must therefore be prepared to find that his proofs, whether of theses or of antitheses, are in all cases inconclusive. I shall append to each of his arguments a statement of the reasons which constrain us to reject them as unsound. We shall then be in a position to consider his whole doctrine of antinomy in its broader aspects, and in its connection with the teaching of the other main divisions of the Dialectic.

FIRST ANTINOMY

Thesis.—(a) The world has a beginning in time, and (b) is also limited in regard to space.

Thesis a. Proof.—If we assume the opposite, namely, that the world has no beginning in time, and if we define the infinite as that which can never be completed by means of a successive synthesis, we must conclude that the world-series can never complete itself. But the entire series of past events elapses, i.e. completes itself at each moment. It cannot therefore be infinite.

Criticism.—This argument gains its plausibility from the illegitimate use of the term ‘elapse’ (verfliessen) as equivalent to ‘complete itself.’ If it be really correct to define the infinite as that which can never be completed, the conclusion to be drawn is that the temporal series is always actually infinite, and that no point or event in it is nearer to or further from either its beginning or its end.[1509] We may select any point in the series as that from which we propose to begin a regress to the earlier members of the series, but if the series is actually infinite, it will be a regress without possibility of completion, and one therefore which removes all justification for asserting that at the point chosen a series has completed itself. It has no beginning, and has no completion. What it has done at each moment of the past it is still doing at each present moment, namely, coming out of an inexhaustible past and passing into an equally inexhaustible future. Time is by its given nature capable of being interpreted only as actually infinite, alike in its past and in its future. It cannot complete itself any more than it can begin itself. The one would be as gross a violation of its nature as would the other. The present exists only as a species of transition, unique in itself, but analogous in nature to the innumerable other times that constitute time past. It is a transition from the infinite through the infinite to the infinite. That we cannot comprehend how, from an infinitude that has no beginning, the present should ever have been reached, is no sufficient reason for denying what by the very nature of time we are compelled to accept as a correct description of the situation which is being analysed. The actual nature of time is such as to rule out from among the possibilities the thesis which Kant is here professing to be able to establish; time, being such as it actually is, can have no beginning.