Kant's Theory of Knowledge

by H. A. Prichard

THE SCHEMATISM OF THE CATEGORIES

As has already been pointed out,[1] the Analytic is divided into two parts, the Analytic of Conceptions, of which the aim is to discover and vindicate the validity of the categories, and the Analytic of Principles, of which the aim is to determine the use of the categories in judgement. The latter part, which has now to be considered, is subdivided into two. It has, according to Kant, firstly to determine the sensuous conditions under which the categories are used, and secondly to discover the a priori principles involved in the categories, as exercised under these sensuous conditions, such, for instance, as the law that all changes take place according to the law of cause and effect. The first problem is dealt with in the chapter on the 'schematism of the pure conceptions of the understanding', the second in the chapter on the 'system of all principles of the pure understanding'.

We naturally feel a preliminary difficulty with respect to the existence of this second part of the Analytic at all. It seems clear that if the first part is successful, the second must be unnecessary. For if Kant is in a position to lay down that the categories must apply to objects, no special conditions of their application need be subsequently determined. If, for instance, it can be laid down that the category of quantity must apply to objects, it is implied either that there are no special conditions of its application, or that they have already been discovered and shown to exist. Again, to assert the applicability of the categories is really to assert the existence of principles, and in fact of just those principles which it is the aim of the System of Principles to prove. Thus to assert the applicability of the categories of quantity and of cause and effect is to assert respectively the principles that all objects of perception are extensive quantities, and that all changes take place according to the law of cause and effect. The Deduction of the Categories therefore, if successful, must have already proved the principles now to be vindicated; and it is a matter for legitimate surprise that we find Kant in the System of Principles giving proofs of these principles which make no appeal to the Deduction of the Categories.[2] On the other hand, for the existence of the account of the schematism of the categories Kant has a better show of reason. For the conceptions derived in the Metaphysical Deduction from the nature of formal judgement are in themselves too abstract to be the conceptions which are to be shown applicable to the sensible world, since all the latter involve the thought of time. Thus, the conception of cause and effect derived from the nature of the hypothetical judgement includes no thought of time, while the conception of which he wishes to show the validity is that of necessary succession in time. Hence the conceptions discovered by analysis of formal judgement have in some way to be rendered more concrete in respect of time. The account of the schematism, therefore, is an attempt to get out of the false position reached by appealing to Formal Logic for the list of categories. Nevertheless, the mention of a sensuous condition under which alone the categories can be employed[3] should have suggested to Kant that the transcendental deduction was defective, and, in fact, in the second version of the transcendental deduction two paragraphs[4] are inserted which take account of this sensuous condition.

The beginning of Kant's account of schematism may be summarized thus: 'Whenever we subsume an individual object of a certain kind, e. g. a plate, under a conception, e. g. a circle, the object and the conception must be homogeneous, that is to say, the individual must possess the characteristic which constitutes the conception, or, in other words, must be an instance of it. Pure conceptions, however, and empirical perceptions, i. e. objects of empirical perception, are quite heterogeneous. We do not, for instance, perceive cases of cause and effect. Hence the problem arises, 'How is it possible to subsume objects of empirical perception under pure conceptions?' The possibility of this subsumption presupposes a tertium quid, which is homogeneous both with the object of empirical perception and with the conception, and so makes the subsumption mediately possible. This tertium quid must be, on the one side, intellectual and, on the other side, sensuous. It is to be found in a 'transcendental determination of time', i. e. a conception involving time and involved in experience. For in the first place this is on the one side intellectual and on the other sensuous, and in the second place it is so far homogeneous with the category which constitutes its unity that it is universal and rests on an a priori rule, and so far homogeneous with the phenomenon that all phenomena are in time[5]. Such transcendental determinations of time are the schemata of the pure conceptions of the understanding.' Kant continues as follows:

"The schema is in itself always a mere product of the imagination. But since the synthesis of the imagination has for its aim no single perception, but merely unity in the determination of the sensibility, the schema should be distinguished from the image. Thus, if I place five points one after another, . . . . . this is an image of the number five. On the other hand, if I only just think a number in general—no matter what it may be, five or a hundred—this thinking is rather the representation of a method of representing in an image a group (e. g. a thousand), in conformity with a certain conception, than the image itself, an image which, in the instance given, I should find difficulty in surveying and comparing with the conception. Now this representation of a general procedure of the imagination to supply its image to a conception, I call the schema of this conception."

"The fact is that it is not images of objects, but schemata, which lie at the foundation of our pure sensuous conceptions. No image could ever be adequate to our conception of a triangle in general. For it would not attain the generality of the conception which makes it valid for all triangles, whether right-angled, acute-angled, &c., but would always be limited to one part only of this sphere. The schema of the triangle can exist nowhere else than in thought, and signifies a rule of the synthesis of the imagination in regard to pure figures in space. An object of experience or an image of it always falls short of the empirical conception to a far greater degree than does the schema; the empirical conception always relates immediately to the schema of the imagination as a rule for the determination of our perception in conformity with a certain general conception. The conception of 'dog' signifies a rule according to which my imagination can draw the general outline of the figure of a four-footed animal, without being limited to any particular single form which experience presents to me, or indeed to any possible image that I can represent to myself in concreto. This schematism of our understanding in regard to phenomena and their mere form is an art hidden in the depths of the human soul, whose true modes of action we are not likely ever to discover from Nature and unveil. Thus much only can we say: the image is a product of the empirical faculty of the productive imagination, while the schema of sensuous conceptions (such as of figures in space) is a product and, as it were, a monogram of the pure a priori imagination, through which, and according to which, images first become possible, though the images must be connected with the conception only by means of the schema which they express, and are in themselves not fully adequate to it. On the other hand, the schema of a pure conception of the understanding is something which cannot be brought to an image; on the contrary, it is only the pure synthesis in accordance with a rule of unity according to conceptions in general, a rule of unity which the category expresses, and it is a transcendental product of the imagination which concerns the determination of the inner sense in general according to conditions of its form (time) with reference to all representations, so far as these are to be connected a priori in one conception according to the unity of apperception."[6]

Now, in order to determine whether schemata can constitute the desired link between the pure conceptions or categories and the manifold of sense, it is necessary to follow closely this account of a schema. Kant unquestionably in this passage treats as a mental image related to a conception what really is, and what on his own theory ought to have been, an individual object related to a conception, i. e. an instance of it. In other words, he takes a mental image of an individual for the individual itself.[7] On the one hand, he treats a schema of a conception throughout as the thought of a procedure of the imagination to present to the conception its image, and he opposes schemata not to objects but to images; on the other hand, his problem concerns subsumption under a conception, and what is subsumed must be an instance of the conception, i. e. an individual object of the kind in question.[8] Again, in asserting that if I place five points one after another, . . . . . this is an image of the number five, he is actually saying that an individual group of five points is an image of a group of five in general.[9] Further, if the process of schematizing is to enter—as it must—into knowledge of the phenomenal world, what Kant here speaks of as the images related to a conception must be taken to be individual instances of the conception, whatever his language may be. For, in order to enter into knowledge, the process referred to must be that by which objects of experience are constructed. Hence the passage should be interpreted as if throughout there had been written for 'image' 'individual instance' or more simply 'instance'. Again, the process of schematizing, although introduced simply as a process by which an individual is to be subsumed indirectly under a conception, is assumed in the passage quoted to be a process of synthesis. Hence we may say that the process of schematizing is a process by which we combine the manifold of perception into an individual whole in accordance with a conception, and that the schema of a conception is the thought of the rule of procedure on our part by which we combine the manifold in accordance with the conception, and so bring the manifold under the conception. Thus the schema of the conception of 100 is the thought of a process of synthesis by which we combine say 10 groups of 10 units into 100, and the schematizing of the conception of 100 is the process by which we do so. Here it is essential to notice three points. In the first place, the schema is a conception which relates not to the reality apprehended but to us. It is the thought of a rule of procedure on our part by which an instance of a conception is constructed, and not the thought of a characteristic of the reality constructed. For instance, the thought of a rule by which we can combine points to make 100 is a thought which concerns us and not the points; it is only the conception corresponding to this schema, viz. the thought of 100, which concerns the points. In the second place, although the thought of time is involved in the schema, the succession in question lies not in the object, but in our act of construction or apprehension. In the third place, the schema presupposes the corresponding conception and the process of schematizing directly brings the manifold of perception under the conception. Thus the thought of combining 10 groups of 10 units to make 100 presupposes the thought of 100, and the process of combination brings the units under the conception of 100.

If, however, we go on to ask what is required of schemata and of the process of schematizing, if they are to enable the manifold to be subsumed under the categories, we see that each of these three characteristics makes it impossible for them to fulfil this purpose. For firstly, an individual manifold A has to be brought under a category B. Since ex hypothesi this cannot be effected directly, there is needed a mediating conception C. C, therefore, it would seem, must be at once a species of B and a conception of which A is an instance. In any case C must be a conception relating to the reality to be known, and not to any process of knowing on our part, and, again, it must be more concrete than B. This is borne out by the list of the schemata of the categories. But, although a schema may be said to be more concrete than the corresponding conception, in that it presupposes the conception, it neither is nor involves a more concrete conception of an object and in fact, as has been pointed out, relates not to the reality to be known but to the process on our part by which we construct or apprehend it.[10] In the second place, the time in respect of which the category B has to be made more concrete must relate to the object, and not to the successive process by which we apprehend it, whereas the time involved in a schema concerns the latter and not the former. In the third place, from the point of view of the categories, the process of schematizing should be a process whereby we combine the manifold into a whole A in accordance with the conception C, and thereby render possible the subsumption of A under the category B. If it be a process which actually subsumes the manifold under B, it will actually perform that, the very impossibility of which has made it necessary to postulate such a process at all. For, according to Kant, it is just the fact that the manifold cannot be subsumed directly under the categories that renders schematism necessary. Yet, on Kant's general account of a schema, the schematizing must actually bring a manifold under the corresponding conception. If we present to ourselves an individual triangle by successively joining three lines according to the conception of a triangle, i. e. so that they enclose a space, we are directly bringing the manifold, i. e. the lines, under the conception of a triangle. Again, if we present to ourselves an instance of a group of 100 by combining 10 groups of 10 units of any kind, we are directly bringing the units under the conception of 100. If this consideration be applied to the schematism of a category, we see that the process said to be necessary because a certain other process is impossible is the very process said to be impossible.

If, therefore, Kant succeeds in finding schemata of the categories in detail in the sense in which they are required for the solution of his problem, i. e. in the sense of more concrete conceptions involving the thought of time and relating to objects, we should expect either that he ignores his general account of a schema, or that if he appeals to it, the appeal is irrelevant. This we find to be the case. His account of the first two transcendental schemata makes a wholly irrelevant appeal to the temporal process of synthesis on our part, while his account of the remaining schemata makes no attempt to appeal to it at all.

"The pure schema of quantity, as a conception of the understanding, is number, a representation which comprises the successive addition of one to one (homogeneous elements). Accordingly, number is nothing else than the unity of the synthesis of the manifold of a homogeneous perception in general, in that I generate time itself in the apprehension of the perception."[11]