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

by Norman Kemp Smith

CHAPTER II
SYSTEM OF ALL PRINCIPLES OF PURE UNDERSTANDING

The introductory remarks to this important chapter are again dictated by Kant’s architectonic, and set its actual contents in an extremely false light. Kant would seem to imply that as the Analytic of Concepts has determined all the various conceptual elements constitutive of experience, and has proved that they serve as predicates of possible judgments, it now remains to show in an Analytic of Principles what a priori synthetic judgments, or in other words what principles, can actually be based upon them. Though this is a quite misleading account of the relation holding between the two books of the Analytic, it has been accepted by many commentators.[1128] For several reasons it must be rejected. The pure forms of understanding are not predicates for possible judgments. They underlie judgment as a whole, expressing the relation through which its total contents are organised. Thus in the proposition “cinnabar is heavy” the category of substance and attribute is not in any sense the predicate; it articulates the entire judgment, interpreting the experienced contents in terms of the dual relation of substance and attribute. Judgment, its nature and conditions, is the real problem of the misnamed Analytic of Concepts. As already indicated,[1129] the two main divisions of the Analytic deal with one and the same problem. But while doing so, they differ in two respects. In the first place, as above noted, the Analytic of Concepts supplies no proof of the validity of particular categories, but only a quite general demonstration that forms of unity, such as are involved in all judgment, are demanded for the possibility of apperception. The proofs of the indispensableness of specific categories are first given in the Analytic of Principles. Secondly, in the Analytic of Concepts the temporal aspect of experience falls somewhat into the background, whereas in the Analytic of Principles it is emphasised.

From these two fundamental points of difference there arises a third distinguishing feature. When the categories, or rather schemata, are explicitly defined, and receive individual proof, they are found to be just those principles that are demanded for the possibility of the positive sciences. This is, from Kant’s point of view, no mere coincidence. Scientific knowledge is possible only in so far as experience is grounded on a priori conditions; and the conditions of sense-experience are also the conditions of its conceptual interpretation. But while the Analytic of Concepts deals almost exclusively with ordinary experience, in the Analytic of Principles the physical sciences receive their due share of consideration.

First and Second Sections. The Highest Principles of Analytic and Synthetic Judgments.—These two sections contain nothing not already developed earlier in the Critique. Though the principle of non-contradiction is a merely negative test of truth, it can serve as a universal and completely adequate criterion in the case of all judgments that are analytic of given concepts. The principle of synthetic judgments, on the other hand, is the principle whereby we are enabled to advance beyond a given concept so as to attach a predicate which does not stand to it in the relation either of identity or of contradiction. This principle is the principle of the possibility of experience. Though a priori synthetic judgments cannot be logically demonstrated as following from higher and more universal propositions,[1130] they are capable of a transcendental proof, that is, as being conditions of sense-experience.

“The possibility of experience is what gives objective reality to all our a priori knowledge.”[1131] “Although we know a priori in synthetic judgments a great deal regarding space in general and the figures which productive imagination describes in it, and can obtain such judgments without actually requiring any experience; yet even this knowledge would be nothing but a playing with a mere figment of the brain, were it not that space has to be regarded as a condition of the appearances which constitute the material for outer experience....”[1132]

In the first part of the last sentence, as in the page which precedes it, Kant would seem to be inculcating his doctrine of a pure a priori manifold, but the latter part of the statement would not be affected by the admission that space is not an independent intuition but only the form of outer sense.

Third Section. Systematic Representation of all the Synthetic Principles of Understanding.—Kant is not concerned in this section with the fundamental propositions of mathematical science, since, on his view, they rest upon the evidence of intuition. He claims, however, that their objective validity depends upon two principles, which, though not themselves mathematical in the strict sense, may conveniently be so described from the transcendental standpoint—the principle of the “axioms of intuition,” and the principle of the “anticipations of experience.” The physicist, who takes the legitimacy of applied mathematics for granted, has no occasion to formulate these principles. That he none the less presupposes them is shown, however, by his unquestioning assumption that nature conforms to the strict requirements of pure mathematics. And since the principles involve pure concepts, the one embodying the schema of number, and the other the schema of quality, they fall outside the scope of the Transcendental Aesthetic, and call for a deduction similar to that of the other categories.

As already indicated, Kant’s procedure is extremely arbitrary, and is due to the perverting influence of his architectonic. Proof of the validity of applied mathematics has already been given in the Aesthetic[1133] of the first edition—a proof which is further developed in the Prolegomena,[1134] and recast in the second edition so as to constitute a separate “transcendental exposition.”[1135] As Kant teaches in these passages, the objective validity of applied mathematics rests upon proof that space and time are the a priori forms of outer and inner sense. The new deductions of the schemata of number and quality, which he now proceeds to formulate, are quite unnecessary, and also are by no means conclusive in the manner of their proof. This, however, is more than compensated by the extremely valuable proofs of the schematised categories of relation which he gives in the section on the Analogies of Experience. The section on the Postulates of Empirical Experience, which deals with the principles of modality, also contains matter of very real importance.

The principles with which this chapter has to deal can thus be arranged according to the fourfold division of the table of categories: (1) Axioms of Intuition, (2) Anticipations of Perception, (3) Analogies of Experience, (4) Postulates of Empirical Thought. And following the distinction already drawn in the Analytic of Concepts,[1136] Kant distinguishes between the Axioms and Anticipations on the one hand, and the Analogies and Postulates on the other. The former determine the conditions of intuition in space and time, and may therefore be called mathematical and constitutive. They express what is necessarily involved in every intuition as such. The latter are dynamical. They are principles according to which we must think the existence of an object as determined in its relation to others. While, therefore, the first set of principles can be intuitively verified, the second set have only an indirect relation to the objects experienced. Whereas a relation of causality can never be intuited as holding between two events, but only thought into them, spatial and temporal relations are direct objects of the mind. Similarly, the relation of substance and attribute cannot be intuited; it can only be thought into what is intuited. The mathematical principles thus acquire an immediate (though, be it remembered, merely de facto) evidence; the a priori certainty, equally complete, of the dynamical principles can be verified only through the circuitous channel of transcendental proof.

The composite constitution of these sections finds striking illustration in the duplicated account of this distinction which precedes and follows the table of principles. The two accounts can hardly have been written in immediate succession to one another. The earlier in location[1137] is probably the later in date. It would seem to rest upon some such uncritical distinction as that drawn in the Prolegomena between judgments of perception and judgments of experience.[1138] The second and briefer account[1139] is not open to this objection.