The Motivation of Introducing Schemata

Categories are schematized in order to accommodate the idealization of empirical objects.

Two interpretations of the motivation of the schematization of categories could be brought under consideration. On the first semantic interpretation, schemata are introduced because in addition to things in themselves idealism creates a new set of objects, of which categories cannot be truly predicated. On the second metaphysical interpretation, schemata are introduced because the nature of the objects is changed so that the nature of their properties are changed.

In introducing schemata, Kant’s official line of reasoning seems to be as follows: (i) categories are only of empirical use, and therefore (ii) categories must be schematized. I will turn to them one by one. The use of categories is a question about which domain of objects categories is related. In his 1781 Critique Kant develops his argument for the empirical use of categories for the first time in Schematism-Chapter, where Kant writes:

concepts are entirely impossible, and cannot have any significance, where an object is not given either for them themselves or at least for the elements of which they consist, consequently they cannot pertain to things in themselves (without regard to how and whether they may be given to us) at all;

that, further, the modification of our sensibility is the only way in which objects are given to us; and, finally, that pure concepts a priori, in addition to the function of the understanding in the category, must also contain a priori formal conditions of sensibility (namely of the inner sense) that contain the general condition under which alone the category can be applied to any object. We will call this formal

147 and pure condition of the sensibility, to which the use of the concept of the understanding is restricted, the schema of this concept of the understanding[.] (A139/B178)

Thus the schemata of the concepts of pure understanding are the true and sole conditions for providing them with a relation to objects thus with significance, and hence the categories are in the end of none but a possible empirical use, since they merely serve to subject appearances to general rules of synthesis through grounds of an a priori necessary unity[.] (A145-146/B185)

Kant’s argument runs like this:

(1) Concepts have significance (relation to objects) only if their objects can be given to us.

(2) Sensibility is the only way in which objects are given to us.

(3) Concepts can have significance only if their objects are given in sensibility.

(4) A priori concepts of understanding can have significance only if their objects are given in sensibility.

(5) Therefore, categories are only of empirical use, not of transcendental use.

This argument neither presupposes nor entails idealism. Initially, this argument rests on the crucial premise (1), the Givenness Thesis of cognition, which Strawson calls “the principle of significance”¹⁷⁴. The Givenness Thesis should be distinguished from idealism. The Givenness Thesis by itself does not imply idealism. It merely asserts that the object’s being given in intuition is a necessary condition for the cognition of the object.

Even in conjunction with (2), it still does not commit Kant to idealism. Since an object is given to our sensibility by means of affection, the conjunction constitutes what Langton calls the Receptivity Thesis.¹⁷⁵ Receptivity Thesis is a very plausible view which is meant to acknowledge the causal nature of empirical knowledge. As the conclusion (4) shows, even the objects for categories must be given in sensibility.

Kant’s formulation often seems to suggest that it is the empirical use of categories that motivates the schematization of categories. As the following quotation from Analogies makes explicit, “these analogies have their sole significance and validity not as principles of the

174 See Strawson 1966, 3-5.

175 See Langton, 1998, 23.

148 transcendental use of the understanding but merely as principles of its empirical use, hence they can be proven only as such; consequently the appearances must not be subsumed under the categories per se, but only under their schemata.” (A180-181/B223) Taken literally, Kant claims that the schematization of categories is a consequence of his view that categories are of empirical use. In a similar passage Kant writes:

the categories in their pure significance, without any conditions of sensibility, should hold for things in general, as they are, instead of their schemata merely representing them how they appear, and they would therefore have a significance independent of all schemata and extending far beyond them.

(A147/B186)

This passage seems to suggest that Kant simply asserts a kind-correspondence between representation and object without argument. On the one hand, categories by definitions are concepts of things in general, and they are supposed to be related to things in themselves or things in general, even though we still cannot make it intelligible how categories refer to things in themselves provided things in themselves are given to us. Only if categories have the transcendental use can we say that categories per se are related to objects. On the other hand, schemata are supposed to be related to appearances. If categories are related to appearances and conditioned by sensibility, then it is schemata that are related to appearances.

On the semantic interpretation, categories are schematized because categories cannot be truly predicated of empirical objects. For instance, the concept of fish is not truly predicated of whales, because the whale is not a species of the fish. Likewise, categories per se could not generate true predication of the empirical objects, for categories per se are true of things in themselves, not of appearances. By contrast, schemata could be truly predicated of appearances. To predicate categories of appearances or representations is simply to commit a categorical mistake.

The distinction between things in themselves and appearances is a consequence of Kant’s commitment to idealism. It seems that the distinction between categories per se and schemata is in turn a consequence of the distinction between things in themselves and appearances. The line of reasoning might be as follows:

(1) If categories are truly predicated of something, then they are truly predicated of things in themselves. (Uniqueness Claim)

149 (2) According to idealism, things in themselves are not only distinct from appearances, they also do not overlap with them. (Idealism)

(3) Categories are not truly predicated of appearances as the objects of intuition.

(4) In fact, there are concepts that are true predications of appearances as the objects of intuition.

(5) The concepts must be numerically distinct from categories.

(6) These representations that are truly predicated of appearances are nothing but schemata.

This argument outlines a story of how schemata are introduced to save the true predication of empirical objects before our sense. These true predications are nothing but the synthetic a priori propositions in pure physics, as Kant acknowledges in the Introduction to 1787 Critique.

One might think that the premise (2) is crucial for the introduction of schemata. If (2) were changed from idealism to realism, then we would have the following argument: (1) If categories are truly predicated of something, then they are truly predicated of things in themselves.

(Uniqueness Claim) (2*) If transcendental realism is true, then things in themselves are identical with appearances. (3*) As a result, for transcendental realism categories are applied to appearances as well as to things in themselves.

On my view, however, this line of reasoning is misguided. As for (2), it is important to bear in mind that idealism does not make appearances a different set of things. Therefore, the correspondent introduction of schemata is dubious. As has been shown in the previous section 5.3, idealism is merely committed to a reductive metaphysics of appearances. This implies that in extensional context one sentence could be paraphrased into another sentence in virtue of reductive analysis without changing the truth value of the original sentence. Take the following example for illustration: if the sentence that I touch the table is true, then the sentence that I touch the motion of electrons is also true. Therefore, we could nonetheless perfectly say that categories per se are truly predicated of appearances, even if idealism holds. As a result, the introduction of schemata is independently from whether idealism is true or realism is true. Nevertheless, it remains undetermined whether it is categories or schemata that are truly predicated of appearances to generate the acknowledged synthetic a priori propositions. Therefore, it cannot explain the motivation of the introduction of schemata.¹⁷⁶

176 One could pose a further question on the premise (1): why categories are designed for being applicable of things in themselves. To say that it is so by definition does not solve the problem.

150 5.5.3 A New Justification: Schemata as Determinations

According to the metaphysical interpretation, schemata are introduced as the instantiation of categories, since categories per se cannot be the instances of categories in empirical objects. As we will see, on the second interpretation, the Copernican move and the accompanied ontological degeneration do motivate the schematization of categories, but in a quite different way.

Initially, this new interpretation appears to be puzzling. One might object that true predication is equivalent to instantiation: when we say that F is truly predicated of x, we are saying that F is instantiated in x. However, in this formula the instantiated F is left out. Schemata are introduced to play the role of the necessary property of objects.

The simple point Kant makes is that categories themselves and the instances of categories are numerically distinct. It brings another consequence of generality: the distinction is also independently from whether idealism or realism is true. Even appearances are identified with things in themselves, categories per se are still numerically distinct from their instantiation.

However, this does not suggest again that idealism does not play any role in motivating the introduction of schemata. The way in which categories are instantiated does depend on whether idealism is true or false. Schematization is precisely the particular mode of the instantiation of categories when idealism is true. Consider the following account. As we have seen, to say that something a priori determines objects is to say that something adds new determinations or properties to the otherwise undetermined empirical objects and that these determinations or properties must be necessarily instantiated. As Kant makes clear, “in accordance with [the principles], everything (that can even come before us as an object) necessarily stands under rules” (A159/B198).

Now the question is how it is possible for the determinations to be necessarily instantiated.

The answer is nothing but Kant’s idea of ontological degeneration. Empirical objects do not suffice for necessary instantiation, for empirical objects can still be things in themselves, the robust reality of which leaves no room for a priori determination. It is at this point where idealism steps in.

According to Kant’s idealism, physical objects are reduced to representations. What is more important is that for Kant physical objects are representations in virtue of being in space and time which are ideal forms of sensibility. In this light, spatial and temporal properties are necessarily instantiated by physical objects. Without space and time, physical objects are not only deprived of spatial and temporal properties; they are also deprived of all the necessary properties that they can have.

Therefore, to say that empirical objects are subsumed under schemata is to say that empirical

151 objects are subsumed under space and time, rather than to say that empirical objects are subsumed under empirical concepts.The theoretical benefit of this interpretation is that it could explain away the worry that the introduction of schemata undermines the project of Transcendental Deduction by making categories irrelevant to the empirical objects.