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

by Norman Kemp Smith

Antithesis.—(a) The world has no beginning in time; (b) has no limits in space. In both these respects the world is infinite.

In these antitheses Kant assumes that space and time are actually infinite, and from that assumption advances to the proof that this is likewise true of the world in its spatial and temporal aspects. This, by itself, ought to be sufficient evidence that Kant does not regard the actual infinite as an inherently impossible conception. As the antinomies are avowedly formulated from the realist, dogmatic standpoint of ordinary consciousness, Kant is also enabled to assume that if the world begins to be, it must have an antecedent cause determining it to exist at that moment rather than at another.

Antithesis a. Proof.—Let us assume the opposite, namely, that the world has a beginning. It will then be preceded by an empty time in which it was not. But in an empty time no becoming is possible, since in such a time no part possesses over any other any distinguishing condition of existence rather than of non-existence. The world must therefore be infinite as regards past time.

Criticism.—In this argument everything depends upon what is to be meant by the term ‘world.’ If Kant means by it merely the material world, the assumption of its non-existence does not leave only empty time and space. Other kinds of existence may be possible, and in these a sufficient cause of its first beginning may be found. The nature of creative action will remain mysterious and incomprehensible, but that is no sufficient reason for denying its possibility. If, on the other hand, Kant means by the world ‘all that is,’ the assumption of its non-existence is likewise the assumption of the non-existence of all its possible causes. That, however, is for ordinary consciousness a quite impossible assumption, since it runs counter to the causal principle which is taken as universally valid. From this point of view the argument consists in making an impossible assumption, and in then pointing out the impossible consequence which must follow. By such a mode of argument no conclusion can be reached. Kant’s decision ought rather to have been that, as time is actually infinite, the world may be so likewise, but that though reality must in some form be eternally existent, the material world cannot be proved to be so by any a priori proof of the kind here given.

Antithesis b. Proof.—Let us assume the opposite, namely, that the world is finite, existing in an empty limitless space. There will then be not only a relation of things in space, but also of things to space. But as the world is a totality outside of which no object of intuition can be found, the relation of the world to empty space is a relation to no object. Such a relation is nothing. Consequently the opposite holds; the world must be infinitely extended.

Criticism.—That Kant himself felt the inadequacy of this argument, when taken from the dogmatic standpoint, is indicated by the lengthy note which he has appended to it, and which develops his own Critical view of space as not a real independent object, but merely the form of external intuition. From the standpoint of ordinary consciousness space is a self-existent entity, and there is no insuperable difficulty in conceiving a relation as holding between it and its contents. The introduction of the opposed standpoint of the Aesthetic therefore runs directly counter to Kant’s own intention of expounding the antinomies from the dogmatic standpoint which involves this realist view of space, and of showing that they afford, in independence of the arguments of the Aesthetic, an indirect proof of the untenableness of that belief.[1512] The conclusion which ought to have been drawn is analogous to that above suggested for thesis a. As space is actually infinite, the material world may be so likewise; but that it actually is so, cannot be established by an a priori argument of the kind here attempted.

SECOND ANTINOMY

Thesis.—Every composite substance in the world consists of simple parts, and nothing anywhere exists save the simple or what is composed of it.

Proof.—Let us assume the opposite, namely, that substances do not consist of simple parts. If all composition be then removed in thought, no composite part, and (as there are no simple parts) also no simple part, and therefore nothing whatsoever, will remain. Consequently no substance will be given. Either, therefore, it is impossible to remove in thought all composition, or after its removal something that exists without composition, i.e. the simple, must remain. In the former case the composite would not itself consist of substances (with them composition is a merely accidental relation, and they must, as self-persisting beings, be able to exist independently of it). As this contradicts our assumption, only the latter alternative remains, namely, that the substantial compounds in the world consist of simple parts.

Criticism.—Kant here assumes, by his definition of terms, the point which he professes to establish by argument. The substance referred to, though never itself mentioned by name, is extended matter. Kant identifies it with ‘composite substance.’ Substance, he further dogmatically decides, is that which is capable of independent existence, and to which all relations of composition are therefore merely accidental. If these assumptions be granted, it at once follows that composition cannot be essential to matter, and that when all composition is thought away, its reality will be disclosed as consisting in simple parts. Kant, however, makes no attempt to prove that extended matter can be defined in any such terms. From the dogmatic point of view of ordinary consciousness, though not from the sophisticated standpoint of Leibniz, extension is of the very essence of matter; and, as Kant himself believed,[1513] the continuity of extension is such as to exclude all possibility of elimination of the composite. For he maintains that, however far division be carried, the parts remain no less composite than the whole from which the regress has started. On any such view the extended and the composite are not equivalent terms. The opposite of the composite is the simple; the opposite of the extended is the non-extended. Kant is here surreptitiously substituting a Leibnizian metaphysics in place of the empirical reality which is supposed to necessitate the argument.