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

by Norman Kemp Smith

In A 178-80 = B 220-3 Kant develops a further point of difference between the mathematical and the dynamical principles, or rather explains what he means by his all too brief and consequently ambiguous reference in the first of the above accounts to “existence” (Dasein). The mathematical principles are constitutive; the dynamical are regulative. That is to say, the mathematical principles lay down the conditions for the generation or construction of appearances. The dynamical only specify rules whereby we can define the relation in which existences contingently given are connected. As existence can never be constructed a priori, we are limited to the determination of the interrelations between existences all of which must be given. Thus the principle of causality enables us to predict a priori that for every event there must exist some antecedent cause; but only through empirical investigation can we determine which of the particular given antecedents may be so described. That is to say, the principle defines conditions to which experience must conform, but does not enable us to construct it in advance. This distinction is inspired by the contrast between mathematical and physical science, and is valuable as defining the empirically regulative function of the a priori dynamical principles; but its somewhat forced character[1140] becomes apparent when we bear in mind Kant’s previous distinction between the principles of pure mathematical science and the transcendental principles which justify their application to experience. Those latter principles concern existence as apprehended through schematised categories, and are consequently, as regards certainty and method of proof, in exactly the same position as the dynamical principles. This is sufficiently evident from his own illustration of sunlight.[1141] There is as little possibility of “constructing” its intensity as of determining a priori the cause of an effect.

I. THE AXIOMS OF INTUITION

All appearances are in their intuition extensive magnitudes. Or as in the second edition: All intuitions are extensive magnitudes.

‘Extensive’ is here used in a very wide sense to include temporal as well as spatial magnitude. Kant bases this principle upon the schema of number, and the proof which he propounds in its support is therefore designed to show that apprehension of an object of perception, whether spatial or temporal, is only possible in so far as we bring that schema into play. But though this is the professed purpose of the argument, number is itself never even mentioned; and the reason for the omission is doubtless Kant’s consciousness of the obvious objections to any such position. That aspect of the argument is therefore, no doubt without explicit intention, kept in the background. But even as thus given, the argument must have left Kant with some feeling of dissatisfaction. Loyalty to his architectonic scheme prevents such doubt and disquietude from finding further expression.

The argument, in its first-edition statement, starts from the formulation of a view of space and time directly opposed to that of the Aesthetic:[1142]

“I entitle a magnitude extensive when the representation of the parts makes possible, and therefore necessarily precedes, the representation of the whole. I cannot represent to myself a line, however small, without drawing it in thought, i.e. generating from a point all its parts one after another, and thus for the first time recording this intuition.”

Similarly with even the smallest time. And as all appearances are intuited in space or time, every appearance, so far as intuited, is an extensive magnitude, that is to say, can be apprehended only through successive generation of its parts. All appearances are “aggregates, i.e. manifolds of antecedently given parts.”

This definition of extensive magnitude involves an assumption which Kant also employs elsewhere in the Critique,[1143] but which he nowhere attempts to establish by argument; namely, that it is impossible to apprehend a manifold save in succession. This assumption is, of course, entirely false (at least as applied to our empirical consciousness), as has since been amply demonstrated by experimental investigation. Kant adopted it in the earlier subjectivist stage of his teaching, before he had come to recognise that consciousness of space is involved in consciousness of time. But even after he had done so, the earlier view still tended to gain the upper hand whenever the doctrines of inner sense and of productive imagination were under consideration. For in regard to the transcendental activities of productive imagination, which are essentially synthetic, Kant continued to treat time as more fundamental than space. But, as already noted,[1144] a directly opposite view of the interrelations of space and time is expounded in passages added in the second edition.

The two central paragraphs are very externally connected with the main argument, and are probably later interpolations.[1145] In the first of these two paragraphs Kant ascribes the synthetic activity involved in the “generation of figures” to the productive imagination, and maintains that geometry is rendered possible by this faculty. In the other paragraph Kant deals with arithmetic, but makes no reference to the productive imagination. Its argument is limited to the contention that propositions expressive of numerical relation, though synthetic, are not universal. They are not axioms, but numerical formulae. This distinction has no very obvious bearing on the present argument, and serves only to indicate Kant’s recognition that no rigid parallelism can be established between geometry and arithmetic. There are, it would seem, no arithmetical axioms corresponding to the axioms of Euclid.[1146]