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

by Norman Kemp Smith

But though Kant’s method of introducing and expounding the argument of this chapter is thus misleading, the contents themselves are of intrinsic value, and have a threefold bearing: (a) on the doctrine of productive imagination; (b) on the relation holding between image and concept; and (c) on the nature of the categories in their distinction from the pure forms of understanding.

(a) Kant gives definite and precise expression to the two chief characteristics of the productive imagination, namely, that it deals with an a priori manifold of pure intuition[1110] and that it exercises a “hidden art in the depths of the human soul.”[1111] Kant’s description of the schema as “a third thing,” at once intellectual and sensuous, seems to be in large part due to the transference to it of predicates already applied to the faculty which is supposed to be its source. The distinction between the transcendental schema and the particularised image is also given as analogous to that between the pure and the empirical faculties of imagination. In A 141-2 = B 180-1, Kant speaks of the empirical faculty of productive imagination, and so is led, to the great confusion of his exposition, though also to the enrichment of his teaching, to allow of empirical as well as of transcendental schemata, and thus contrary to his own real position to recognise schemata of such empirical objects as dog or horse—a view which empirical psychology has since adopted in its doctrine of the schematic image. This passage was doubtless written at the time when he was inclining to the view that the empirical processes run parallel with the transcendental.[1112] Kant’s final view is that empirical imagination is always reproductive. This brings us, however, to our second main point.

(b) Kant makes a statement which serves as a valuable corrective of his looser assertions in other parts of the Critique.[1113] Five points set after one another, thus,....., form an image of the number five. The schema of the number five is, however, of very different nature, and must not be identified with any such image. It is

“...rather the representation of a method whereby a multiplicity [in this case five] may be represented in an image in accordance with a certain concept, than this image itself....”[1114]

This becomes more evident in the case of large numbers, such as a thousand. The thought or schema of the number remains just as clear and definite as in the case of smaller numbers, but cannot be so adequately embodied and surveyed in a concrete image.

“This representation of a general procedure of imagination in providing its image for a concept, I name the schema to this concept.”[1115]

But even in the simplest cases an image can never be completely adequate to the concept. The image of a triangle, for instance, is always some particular triangle, and therefore represents only a part of the total connotation. As the schema represents a universal rule of production in accordance with a concept, it resembles the concept in its incapacity to subsist in an objective form. Images become possible only through and in accordance with schemata, but can never themselves be identified with them. Schemata, therefore, and not images—such is the implied conclusion—form the true subject-matter of the mathematical sciences. Images are always particular; schemata are always universal. Images represent existences; schemata represent methods of construction.

There are three criticisms which must be passed upon this position. In the first place, the selection of the triangle as an illustration tends to obscure the main point of Kant’s argument. As there are three very different species of triangle, the concept triangle is a class concept in a degree and manner which is not to be found in the concepts, say, of the circle or of the number five. So that while Kant may seem to be chiefly insisting upon the inadequacy[1116] of the image to represent more than a part of the connotation of the corresponding concept, his real intention is to emphasise that the schema expresses the conceptual rule whereby, even in images that cover the whole connotation, the true meaning of the image can alone be determined.

Secondly, the above definition of the schema as being “the representation of a general procedure of imagination in providing an image for a concept” is obviously bound up with Kant’s view of it as “a third thing,” additional to the concept, and as intermediate between it and the image.[1117] But as we have already found occasion to note, in discussing Kant’s doctrine of the “construction” of mathematical concepts,[1118] this threefold distinction is out of harmony with his Critical principles. It results from his retention of the traditional view of the concept as in all cases a mere concept, i.e. an abstracted or class concept. In defining the schema Kant is defining the true nature of the concept as against the false interpretation of it in the traditional class-theory; he misrepresents the logic of his own standpoint when he interpolates a third kind of representation intermediate between the concept and the image. The concept ‘triangle,’ as a concept, is (to employ Kant’s own not very satisfactory terms) the representation of the method of constructing a certain type of object; and the only other mode of representing this kind of object is the image. There may, indeed, as Kant has himself suggested, be a species of image that may be entitled schematic; but if that be identified with a blurred or indeterminate or merely symbolic form of representation, it can have nothing in common with the transcendental or conceptual schema, save the name.