Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

After what has been said in the deduction of the categories, we hope that nobody will hesitate in answering the question whether these pure concepts of the understanding allow only of an empirical or also of a transcendental application, that is, whether, as conditions of a possible experience, they refer a priori to phenomena only, or whether, as conditions of the possibility of things in general, they may be extended to objects by themselves (without restriction to our sensibility). For there we saw that concepts are quite impossible, and cannot have any meaning unless there be an object given either to them or, at least, to some of the elements of which they consist, and that they can never refer to things by themselves (without regard as to whether and how things may be given to us). We likewise saw that the only way in which objects can be given to us, consists in a modification of our sensibility, and lastly, that pure concepts a priori must contain, besides the function of the understanding in the category itself, formal conditions a priori of sensibility (particu- [p. 140] larly of the internal sense) which form the general condition under which alone the category may be applied to any object. We shall call this formal and pure condition of sensibility, to which the concept of the understanding is restricted in its application, its schema ; and the function of the understanding in these schemata, the schematism of the pure iinderstaiiding.

The schema by itself is no doubt a product of the imagiTranscendental Analytic 115 nation only, but as the synthesis of the imagination does not aim at a single intuition, but at some kind of unity alone in the determination of sensibility, the schema ought to be distinguished from the image. Thus, if I place five 2points, one after the other , this is an image of the number five. If, on the contrary, I think of a number in general, whether it be five or a hundred, this thinking is rather the representation of a method of representing in one image a certain quantity (for instance a thousand) according to a certain concept, than the image itself, which, in the case of a thousand, I could hardly take in and compare with the concept. This representation of a general procedure of the imagination by which a concept receives its image, I call the schema of such concept.

The fact is that our pure sensuous concepts do not depend on images of objects, but on schemata, [p. 141] No image of a triangle in general could ever be adequate to its concept. It would never attain to that generality of the concept, which makes it applicable to all triangles, whether right-angled, or acute-angled, or anything else, but would always be restricted to one portion only of the sphere of the concept. The schema of the triangle can exist nowhere but in thought, and is in fact a rule for the synthesis of imagination with respect to pure forms in space. Still less does an object of experience or its image ever cover the empirical concept, which always refers directly to the schema of imagination as a rule for the determination of our intuitions, according to a certain general concept. The concept of dog means a rule according to which my imagination can always draw a general outline of the figure of a four-footed animal, without being restricted to any particular figure supplied

1 1 6 TraiLScendental Analytic 3by experience or to any possible image which I may draw in the concrete. This schematism of our understanding appHed to phenomena and their mere form is an art hidden in the depth of the human soul, the true secrets of which we shall hardly ever be able to guess and reveal. So much only we can say, that the image is a product of the empirical faculty of the productive imagination, while the schema of sensuous concepts (such as of figures in space) is a product and so to say a monogram of [p. 142] the pure imagination a priori, through which and according to which images themselves become possible, though they are never fully adequate to the concept, and can be connected with it by means of their schema only. The schema of a pure concept of the understanding, on the contrary, is something which can never be made into an image ; for it is nothing but the pure synthesis determined by a rule of unity, according to concepts, a synthesis as expressed by the category, and represents a transcendental product of the imagination, a product which concerns the determination of the internal sense in general, under the conditions of its form (time), with reference to all representations, so far as these are meant to be joined a priori in one concept, according to the unity of apperception.

Without dwelling any longer on a dry and tedious determination of all that is required for the transcendental schemata of the pure concepts of the understanding in general, we shall proceed at once to represent them according to the order of the categories, and in connection with them.

The pure image of all quantities {quanta^ before the external sense, is space ; that of all objects of the senses in general, time. The pure schema of quantity {(juajtTranscendental Analytic 117