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

by Norman Kemp Smith

Third Paragraph.—The third and fourth paragraphs of this section ought to have had a separate heading. They summarise the total argument of the Aesthetic in regard to space as well as time, distinguish its tenets from those of Newton and of Leibniz, and draw a general conclusion. The summary follows the strict synthetic method. The opening sentences illustrate Kant’s failure to distinguish between the problems of pure and of applied mathematics, and also show how completely he tends to conceive mathematics as typified by geometry. The criticism of alternative views traverses the ground of the famous controversy between Leibniz and Clarke. Their Streitschriften were, as we have good circumstantial grounds for believing,[554] a chief influence in the development of Kant’s own views. Kant, who originally held the Leibnizian position, was by 1768[555] more or less converted to the Newtonian teaching, and in the Dissertation of 1770 developed his subjectivist standpoint with the conscious intention of retaining the advantages while remedying the defects of both alternatives.[556] For convenience we may limit the discussion to space. (a) The view propounded by Newton, and defended by Clarke, is that space has an existence in and by itself, independent alike of the mind which apprehends it and of the objects with which it is filled. (b) The view held by Leibniz is that space is an empirical concept abstracted from our confused sense-experience of the relations of real things.[557]

The criticism of (a) is twofold. First, it involves belief in an eternal and infinite Unding. Secondly, it leads to metaphysical difficulties, especially in regard to the existence of God. If space is absolutely real, how is it to be reconciled with the omnipresence of God? Newton’s view of space as the sensorium Dei can hardly be regarded as satisfactory.

The objection to (b) is that it cannot account for the apodictic certainty of geometry, nor guarantee its application to experience. The concept of space, when regarded as of sensuous origin, is something that may distort (and according to the Leibnizian teaching does actually distort) what it professes to represent, and is something from which restrictions that hold in the natural world have been omitted.[558] As empirical, it cannot serve as basis for the universal and necessary judgments of mathematical science.[559]

The first view has, however, the advantage of keeping the sphere of appearances open for mathematical science. As space is infinite and all-comprehensive, its laws hold universally. The second view has the advantage of not subjecting reality to space conditions. These advantages are retained, while the objections are removed, by the teaching of the Aesthetic.

Kant further criticises the former view in A 46 ff. = B 64 ff. There is no possibility of accounting for the a priori synthetic judgments of geometry save by assuming that space is the pure form of outer intuition. For though the Newtonian view will justify the assertion that the laws of space hold universally, it cannot explain how we come to know them a priori. And assuming, as Kant constantly does, that space cannot be both an a priori form of intuition and also independently real, he concludes that it is the former only.

In B 71 Kant also restates the metaphysical difficulties to which the Newtonian view lies open. In natural theology we deal with an existence which can never be the object of sensuous intuition, and which has to be freed from all conditions of space and time. This is impossible if space is so absolutely real that it would remain though all created things were annihilated.

Fourth Paragraph.—Space and time are the only two forms of sensibility; all other concepts belonging to the senses, such as motion and change, are empirical.[560] As Kant has himself stated, no reason can be given why space and time are the sole forms of our possible intuition:

“Other forms of intuition than space and time, ... even if they were possible, we cannot render in any way conceivable and comprehensible to ourselves, and even assuming that we could do so, they still would not belong to experience, the only kind of knowledge in which objects are given to us.”[561]

The further statement,[562] frequently repeated in the Critique, that time itself does not change, but only what is in time,[563] indicates the extent to which Kant has been influenced by the Newtonian receptacle view. As Bergson very justly points out, time, thus viewed as a homogeneous medium, is really being conceived on the analogy of space. “It is merely the phantom of space obsessing the reflective consciousness.”[564]