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

by Norman Kemp Smith

(a) Kant’s own words require no comment:

“Space and time are quanta continua because no part of them can be given, save as enclosed between limits (points or moments), and therefore as being itself a space or a time. Space therefore consists only of spaces, time only of times. Points and moments are only limits, i.e. mere positions that limit space and time. But positions always presuppose the intuitions which they limit or are intended to limit; and out of mere positions, viewed as constituents capable of being given prior to space and time, neither space nor time can be constructed. Such magnitudes may also be called flowing, since the synthesis of productive imagination involved in their production is a progression in time, and the continuity of time is ordinarily denoted by the expression flowing.”[1155]

(b) When Kant proceeds to apply the principle of continuity to intensive magnitude, his conclusion rests upon a somewhat different basis. He argues that appearances must be continuous owing to the fact that they are apprehended in space and time.[1156] So far as they are extended in space and enduring in time that may perhaps be true; but Kant’s assertion has a wider sweep. It implies that sensations and the physical conditions of sensation, as for instance the sensation of red or the force of gravity, are capable of existing in every possible degree between zero and any given intensity. This affords the key to his method of formulating his second and third proofs of the principle of Anticipations of Perception, which, in the form in which he interprets it, contains this further implication of continuity. These proofs are inspired by the desire to make all apprehension, even that of simple sensation, a temporal process, and by that indirect means to establish for sensuous intensity and its objective conditions a continuity similar to that of space and time. The proof is, however, as we have seen, inconclusive. This application of continuity must be regarded as more in the nature of a mere hypothesis than Kant is willing to recognise. As regards sensations, it would seem to have been positively disproved by the results of experimental psychology.

From his supposed proof of the continuity of all intensive magnitudes Kant draws two further conclusions: first, that experience can never be made to yield proof of the void in either space or time. For if all reality can exist in innumerable degrees, and if each sense has a determinate degree of receptivity, the complete absence of reality can never be itself experienced. Inference to such absence is also impossible for a second reason, namely, that one and the same extensive magnitude may be completely occupied by an infinite number of different intensive degrees, indefinitely approximating to, and yet also indefinitely differing from, zero. Kant is here referring to the dynamical theory of matter which he had long held,[1157] and which he expounds in opposition to the current mechanistic view.[1158] The mechanistic theory rests, he contends, upon an assumption purely metaphysical and therefore wholly dogmatic, that the real in space has no internal differences, but is uniform like the empty space in which it exists.[1159] In accordance with this assumption physicists infer that all qualitative differences in our sensations must be due to merely quantitative differences in their material causes, and ultimately to differences in the number and distribution of the constituent parts of material bodies. If two bodies of the same volume differ in weight or in inertia, the variation must be traced to differences in the amount of matter, or, otherwise stated, to differences in the amount of unoccupied space, in the two bodies. To this view Kant opposes his own hypothesis—for it is in this more modest form that it is presented in these paragraphs—namely, that matter occupies space by intensity and not by mere bulk, and that it may therefore be diminished indefinitely in degree without for that reason ceasing completely to fill the same extensive area. Thus an expanded force such as heat, filling space without leaving the smallest part of it empty, may be indefinitely diminished in degree, and yet may still with these lesser degrees continue to occupy that space as completely as before. This may not, Kant admits, be the true explanation of physical differences, but it at least has the merit of freeing the understanding from metaphysical preconceptions, and of demonstrating the possibility of an alternative to the current view. If matter has intensity as well as extensity, and so can vary in quality as well as in quantity, physical science may perhaps be fruitfully developed on dynamical lines.

3. THE ANALOGIES OF EXPERIENCE

The principle of the Analogies is: Experience is possible only through the representation of a necessary connection of perceptions.[1160]

Kant introduces the three analogies with the statement of an underlying principle, which corresponds to the central thesis of the transcendental deduction. In the second edition this general principle is reformulated, and a new proof is added. These alterations do not seem, however, to be of any special significance. The two proofs repeat the main argument of the transcendental deduction, but with special emphasis upon the temporal aspect of experience. The categories of relation, as schematised, yield the Analogies, which acquire objective validity in so far as they render experience possible. The first proof (given in the second paragraph of the first edition) maintains that they are indispensable for apperception, and the second proof (that of the second edition) that they are indispensable for knowledge of objects. The references to time in the second proof are too condensed to be intelligible save in the light of the more explicit arguments given in support of the three Analogies.

The first paragraph in the first edition must be a later interpolation, as its assertion that simultaneity is a mode of time conflicts with the proof given of the first Analogy, but agrees with what must be regarded as a later interpolated passage introductory to that proof.[1161] This paragraph is also peculiar in another respect. Hitherto Kant has traced the existence of the three analogies to the three categories of relation, each of which conditions a separate schema. But in this paragraph he bases their threefold form on the fact that time has three modes, duration, sequence,[1162] and coexistence, and that there is therefore a threefold problem: first, what is involved in consciousness of duration; secondly, what is involved in consciousness of succession; and thirdly, what is involved in consciousness of coexistence. This is not, however, a satisfactory mode of stating the matter, for it might seem to imply that the three aspects of time can be separately apprehended, and that each has its own independent conditions. What Kant really proves is that all three involve one another. We can only be conscious of duration in contrast to succession, and of succession in contrast to the permanent, while both involve consciousness of coexistence. The three analogies thus treat of three aspects of the same problem, the first connecting with the category of substance, the second with that of causality, and the third with that of reciprocity.

The only point that calls for further comment[1163] concerns Kant’s adoption of the term Analogy as a title for the three principles of “relation.” The term is employed in contra-distinction to constitutive principle or axiom; and Kant points out that this usage of the term must be carefully distinguished from the other or mathematical. “In philosophy analogy is not the likeness of two quantitative but of two qualitative relations.” In mathematical analogy a fourth term can be discovered from three given terms; but in an ‘analogy of experience’ we possess a rule that suffices only for the determination of the relation to a term not given, never for knowledge of this term itself. Thus if we are informed that 15 is to x as 5 is to 10, the value of x can be determined as 30. But if it be stated that a given event stands to an antecedent event as effect to cause, only the relation holding between the events can be specified, not the actual cause itself. The principle of causality thus serves only as a regulative principle, directing us to search for the cause of an event among its antecedents.

Riehl has suggested a very different explanation of the term, namely, as signifying that the categories of relation are employed only on the analogy of the corresponding, pure logical forms.