# 1/8. The Schematism. schema of empirical concepts, the schema of sensible concepts and the

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1 1/8 The Schematism I am going to distinguish between three types of schematism: the schema of empirical concepts, the schema of sensible concepts and the schema of pure concepts. Kant opens the discussion by addressing the question of how it is that we bring together the concept of an object with its referent and he argues that the way in which this connection is achieved is through the concept containing within it something of what it represents as belonging to the object it describes. This reference to containment should alert us however to the distinction between synthetic and analytic judgments, not least in a chapter that is the first part of a doctrine of transcendental judgment. In the Introduction to the Critique Kant initially distinguished between synthetic and analytic judgments precisely in terms of the relationship of subject and predicate in them. Kant stated there that with a synthetic judgment a third thing was necessary for the subject and predicate to connect as the predicate did not belong to the subject by definition. (A6-9/B11-13) What he now suggests with regard to empirical concepts is in fact a connection between the way in which they are thought and the conditions of their intuition: the empirical concept of a plate is homogeneous with the pure geometrical concept of a circle. The roundness which is thought in the latter can be intuited in the former (A137/B176). In other words it is because pure intuition enables there to be pure geometry that we are able to speak of the empirical concept of a plate. Hence empirical concepts contain

2 2/8 in them both elements of pure intuition and pure concepts and this is how they can describe their objects. This point is later extended to the empirical concept of dog which is said by Kant to signify a rule: according to which my imagination can delineate the figure of a four-footed animal in a general manner, without limitation to any single determinate figure such as experience, or any possible image that I can represent in concreto, actually presents (A141/B180). In stating that the empirical concept signifies the rule of imagination according to which the figure of the animal can be given to me independently of any particular example Kant is suggesting that what empirical concepts effectively do is prescribe the normative structure of objects in a pure fashion. This indicates that empirical concepts are to be always regarded as involving a referential capacity not to what the terms might be thought to naturally describe (as dog describes Rex or girl describes Alice ) but rather to the possibility of an infinite range of examples or in other terms to determine a type. However once the account of schematism is put in this form then a philosophical objection can be made to it which can even be given a Kantian pedigree. Wittgenstein famously argues that the activity of following a rule cannot be exhaustively determined by such normative considerations as we have alluded to precisely because there is always a measure implied in such rules that cannot itself be measured by them. Hence rules hit bedrock and justification has to come to an end with reference to a transcendental anthropological condition. To this objection to the characterisation as given above could be added some statements from Kant himself in the section

3 3/8 immediately prior to the chapter on schematism where he reports that judgment is a fundamental talent that cannot be taught to one who lacks it (with the person lacking in judgment identified by Kant with the stupid person who have a failing for which there is no remedy (B173n)). As Kant writes concerning the suggestion that rules of judgment be provided: to give general instruction how we are to subsume under rules, that is, to distinguish whether something does or does not come under them, that could only be by means of another rule. This in turn, for the very reason that it is a rule, again demands guidance from judgment. (A133/B172). However it is when we turn to the passage from Kant that we derive the basis of our answer to this criticism for when Kant makes the quoted remark he is speaking about the demand for a doctrine of judgment within general logic and agreeing that general logic would be incapable of being provided with such. But as he goes on to write: the situation is entirely different in transcendental logic (A135/B174) and the reason why it is, which is because it relies upon the findings of transcendental philosophy. Transcendental philosophy has however a basic task: It must formulate by means of universal but sufficient marks the conditions under which objects can be given in harmony with these concepts (A136/B175), the concepts, that is, of pure understanding. This requires that the objects be described in such a way that they can be cognised by means of the pure concepts. A last form of the objection already stated kicks in at this point and still has Wittgensteinian pedigree: if I can understand my rule, and so understand what my illustrative method is for, I have already applied the concept. i

4 4/8 For a transcendental philosopher concerned with pure concepts this objection will not work. It is plausible to isolate the notion of pure concepts (as is done in the Metaphysical Deduction) indicating that these concepts are ones we seem to possess without the possession of them determining the manner in which they can apply to objects. To take one example: the concept of causality describes something like a necessary relationship between two entities such that if A is present B will be constrained in some specifiable manner. However whilst we can state that this concept is one that we possess and indeed in indicating what the concept would involve where it to have application (and in this sense we can agree that possession of the concept indicates a rule for its use) but we cannot by this means indicate whether it does have this use as we have to be able to show what in the appearances is susceptible to description by means of this concept. What this indicates is that the fundamental question concerning schematism is not in relation to the empirical concepts with which Kant begins the chapter but with regard to pure concepts. However whilst the question of schematism is really philosophically urgent at this level it would be false to think that the schematism of empirical concepts describes nothing. With regard to the empirical concept dog for example what is indicated in the account of its schematism is that the term requires for its effective use a reference not merely to examples (such as spaniels and poodles) or to descriptions (as we first require the taxonomy to be justified as belonging to the type it does) but rather to a connection between the

5 5/8 intuition of animals of a certain type and the rule that determines them as belonging to this type. Hence whilst the empirical schema provides an account of empirical concepts it is ultimately based upon the transcendental schema. Now I am going to discuss the schema of sensible concepts. Kant s treatment of it is similar to his account of empirical concepts: No image could ever be adequate to the concept of a triangle in general. It would never attain that universality of the concept which renders it valid of all triangles, whether right-angled, obtuse-angled, or acute-angled; it would always be limited to a part only of this sphere. The schema of the triangle can exist nowhere but in thought. It is a rule of the synthesis of the imagination, in respect of pure figures in space. (A141/B180) It is clear with regard to pure sensible concepts such as triangles that Kant is of the view that there is no figure that could be given that would correspond to what is being spoken of when we construct something in accordance with the rule of them. Just as Rover and Rex as Dalmatians and bulldogs respectively are not correspondent with the purity of dog so an obtuse triangle and a rightangled one are only partially representative of what is meant by triangle. The key problem with the schema of pure concepts concerns the fact that the homogeneity that can be said to be involved in the schemas of empirical concepts and pure sensible concepts between concept and that which is described by the concept is not applicable. With the empirical concept the roundness that is involved in the notion of a plate is a determination of intuition and this determination of intuition is part of the

6 6/8 empirical concept so that this concept is not pure as it contains within it elements of intuition. With the pure sensible concept the reference to the pure intuition is embedded in the concept in question again. With pure concepts we have only a determination of thought and hence they seem to be completely different in kind to pure intuitions with the question arising as to how therefore the two can have the combination in experience that must be necessary if, as we have now discovered, even empirical concepts are to be usable. The heterogeneity between pure concept and pure intuition hence has to be somehow bridged if the pure concepts are to be applied to intuitive conditions. This is the problem of transcendental judgment and since transcendental judgments are synthetic we would expect some third thing to be at work that brings together the pure concept and the pure intuition. This third thing is what Kant terms the transcendental schema. The schema bridges the divide between pure concept and pure intuition in including universality (a condition of pure concepts) and sensibility (the basic condition of intuitions): an application of the category to appearances becomes possible by means of the transcendental determination of time, which, as the schema of the concepts of the understanding, mediates the subsumption of the appearances under the category (A139/B178). Time is referred to as the condition of all connection and hence as a universal element of sensibility and the suggestion would thus be that in temporalizing the pure concepts we will retain their universality whilst

7 7/8 sensibilizing them. So to comprehend the doctrine of schematism we need to show how the transcendental determination of time takes place. Kant suggests that the schematism of pure understanding is a product of the imagination. At this point we need to look more carefully again at how Kant describes the imagination. Whilst the fundamental and most basic description of imagination is that it is the ability to represent an object that is not present (B151) this representation does not have to take the form of an image. We saw with both empirical concepts and pure sensible concepts that an image would not be sufficient to describe the possibility of their possession. Kant now states that in fact the possession of images is dependent on the universal procedure of imagination (A140/B180) of describing concepts such that they are capable of being represented by images, or in other words, of schematising the concepts. However: the schema of a pure concept of understanding can never be brought into any image whatsoever (A142/B181). Thus whilst the concept of the triangle can be represented by an obtuse or right-angled three-sided figure and the concept of dog can be represented by a terrier the pure concept of causality cannot be represented at all. The schema of the pure concept is now given its most general determination: It is a transcendental product of imagination, a product which concerns the determination of inner sense in general according to conditions of its form (time), in respect of all representations, so far as these representations are to be connected a priori in one concept in conformity with the unity of apperception. (A142/B181)

8 8/8 So the transcendental schema would be that which would determine the temporal form of representations a priori in conformity with the transcendental unity of apperception. As such it would appear that what is described by it is virtually identical with the transcendental synthesis of imagination and Kant argues that it is at any rate effected by this synthesis (A145/B185). Subsequently Kant suggests that the transcendental schemata are a priori determinations of time in accordance with rules (A145/B184) and that these determinations will effectively give us the phenomenon, or sensible concept, of an object in agreement with the category (A146/B186). The determinations of time in accordance with rules are set out in accordance with the table of categories as four-fold relating to the time-series, the time-content, the time-order, and lastly to the scope of time (A145/B184). Finally the schematism is said to realise the categories by restricting them (A146/B186). The realisation of the categories is the demonstration of their mode of operation within experience whilst the restriction of them is the determination of them as only giving conditions of cognition through connection with intuition. i Geoffrey Warnock (1949) Concepts and Schematism Analysis 8, p. 82. In arguing that this objection is Wittgensteinian I am only suggesting it has the same basic form as the problem with rules that Wittgenstein himself adduced.

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