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

by Norman Kemp Smith

We are acquainted only with the rule, and not with the whole object. Any assertion, therefore, which we can make, must be dictated solely by the rule, and be an expression of it. Neither the thesis nor the antithesis of the first antinomy is valid; there is a third alternative. The sensible world is neither finite nor infinite in extent; it is infinitely extensible, in terms of the rule.

Unfortunately Kant is not content to leave his conclusion in this form. He complicates his argument, and bewilders the reader, by maintaining that this is a virtual acceptance of the antithesis, in that we assert negatively, that an absolute limit in either time or space is empirically impossible;[1571] and affirmatively, that the regress goes on in indefinitum, and consequently has no absolute quantity.

Kant also repeats the argument of the preceding section in regard to given wholes.[1572] When the problem is that of subdivision, the regress starts from a given whole, and therefore from a whole whose conditions (the parts) are given with it. The division is, therefore, in infinitum, and not merely in indefinitum. This does not, however, he argues, mean that the given whole consists of infinitely many parts. For though the parts are contained in the intuition of the whole, yet the whole division arises only through the regress that generates it. It is a quantum continuum, not a quantum discretum.[1573] This argument has been criticised above.[1574] Kant here ignores the possibility that the parts of matter, though extended, may be physically indivisible, or that they may be centres of force which control, but do not occupy, a determinate space.

REMARKS ON THE DISTINCTION BETWEEN THE MATHEMATICAL-TRANSCENDENTAL AND THE DYNAMICAL-TRANSCENDENTAL IDEAS[1575]

Statement.—Kant again[1576] introduces the distinction between the mathematical and the dynamical. The mathematical Ideas synthesise the homogeneous, the dynamical may connect the heterogeneous. In employing the former we must therefore remain within the phenomenal; through the latter we may be able to transcend it. The way is thus opened for propounding, in regard to the third and fourth antinomies, a solution in which the pretensions of Reason no less than those of understanding may find satisfaction. Whereas both the theses and the antitheses of the first and second antinomies have to be declared false, those of the third and fourth antinomies may both be true—the theses applying to the intelligible realm, and the antitheses to the world of sense.

Comment.—When the distinction between the mathematical and the dynamical is thus extended from the categories to the Ideas, its validity becomes highly doubtful. Space and time are certainly themselves homogeneous, and the categories of quality and quantity, in so far as they are mathematically employed, may perhaps be similarly described. But when the term is still further extended, to cover the pairs of correlative opposites with which the first two antinomies deal, those, namely, between the limited and the unlimited, the simple and the infinitely divisible, Kant would seem to be making a highly artificial distinction. The first two antinomies deal not with space and time as such, but with the sensible world in space and time; and within this sensible world, even in its quantitative aspects, qualitative differences have to be reckoned with. Common sense does, indeed, tend to assume that the unlimited and the simple must, like that which they condition, be in space and time, and so form with the conditioned a homogeneous series. But this assumption ordinary consciousness is equally disposed to make in regard to a first cause and to the unconditionally necessary.

Kant further attempts[1577] to distinguish between the mathematical and the dynamical by asserting that the dynamical antinomies are not concerned with the quantity of their object, but only with its existence. He admits, however, that in all four cases a series arises which is either too large or too small for the understanding; and that being so, in each case the problem arises as to the existence of an unconditioned.

The artificiality of Kant’s distinction becomes clear when we recognise that the opposed solutions, which he gives of the two sets of antinomies, can be mutually interchanged. As the sensible world rests upon intelligible grounds, both the theses and the antitheses of the first two antinomies may be true, the former in the intelligible realm and the latter in the sensuous. Similarly, both the theses and antitheses of the third and fourth antinomies may be false. In the sensible world, about which alone anything can be determined, the series of dynamical conditions forms neither a finite nor an infinite series. There is a third alternative, akin to that of the antitheses, but distinct in character from it, namely, that the series is infinitely extensible. Kant’s differential treatment of the two sets of antinomies is arbitrary, and would seem to be due to his having attempted to superimpose, with the least possible modification, a later solution of the antinomies upon one previously developed. In the earlier view, as we have already had occasion to observe, Reason has a merely empirical application. Its Ideas are taken as existing “only in the brain.” Only their empirical reference can substantiate them, or indeed give them the least significance. And as they are by their very nature incapable of empirical embodiment, all assertions which involve them must necessarily be false. Later, Kant came to regard Reason as having its own independent rights. Encouraged by his successful establishment of the objective validity of the categories, progressively more and more convinced of the importance of the distinction, which that proof reinforced, between appearances and things in themselves, and preoccupied with the problems of the spiritual life, his old-time faith in the absolute claims of pure thought reasserted itself. Through Reason we realise our kinship with noumenal realities, and through its demands the nature of the unconditioned is foreshadowed to the mind. The theses and antitheses, which throughout the entire history of philosophy have competed with one another, may both be true. Their perennial conflict demonstrates the need for some more catholic standpoint from which the two great authorities by which human life is controlled and directed, the intellectual and the moral, may be reconciled. Neither can be made to yield to the other; each is supreme in its own field. The distinction between appearances and things in themselves, recognition of which is the first step towards an adequate theory of knowledge, and without which the nature of the intellectual life remains self-contradictory and incomprehensible, itself affords the means of such a reconciliation. The understanding is the sole key to the world of appearance, the moral imperative to the realm of things in themselves. Reason with its demand for the unconditioned mediates between them, and enables us to realise our dual vocation.

This radical alteration of standpoint was bound to make the employment of manuscript representing the earlier and more sceptical attitude altogether unsatisfactory; and only Kant’s constitutional unwillingness to sacrifice what he had once committed to paper can account for his retention of the older expositions. He allows his previous treatment of the first two antinomies to remain in its sceptical form, and, by means of the distinction between the mathematical and the dynamical, develops his newer, more Idealist view exclusively in reference to the third and fourth antinomies. That it is no less applicable to the others, we have already seen.

Though the Idealist view, as here expounded, may be thus described, relatively to the sceptical view of Reason, as later, that is not to be taken as meaning that it represents the latest stage in the development of Kant’s Critical teaching. It seems to belong to the period prior to that in which the central sections of the Analytic were composed. The evidence[1578] for this consists chiefly in its subjectivist references to the nature of appearances. It would seem to be contemporary with Kant’s doctrine of the transcendental object.