In the last lecture, I began to describe what I think is a fairly straightforward argument. To think an object of experience is to represent it objectively, so that the concepts ascribed to it are more than merely the way it appears. To represent an object objectively one links concept and intuition in a judgment, with the copula 'is' signifying unity in the object. Any such judgment is subject to the forms of judgment. A category is a form of judgment, so far as the judgment is used to determine an object, that is, to specify its properties. So all objective representation falls under categories.
But this is not the course taken by Kant's argument, which makes central the unity of apperception. It is clear enough that the act of judgment is a synthetic act, and that synthesis must take place in one consciousness. If the subject, predicate and copula were to be found in three different consciousnesses, there would be no judgment at all. We might also grant that for judgment to be possible, the judger must be able to assign the components of the judgment to a consciousness of the self. This is the analytic proposition that stands behind all concepts of combination.
The assignment to all the representations of a judgment to myself is an act of synthesis, so the representation of the unity of self-consciousness is synthetic in a sense. Kant writes as if it is this "synthetic unity" which makes possible the unity of intuition, the representation of singular given objects. He says that "the manifold given in a sensible intuition is necessarily subject to the synthetic unity of apperception, because in no other way is the unity of intuition possible (Section 17)." In Section 17, Kant states that the conditions which make the unity of apperception possible also make the unity of intuition possible. "All my representations in any given intuition must be subject to that condition under which alone I can ascribe them to the identical self as my representations, and so can comprehend them as synthetically combined in one apperception through the general expression, 'I think'" (B138).
The unity of intuition is said to be subject to the synthetic unity of apperception because the unity of the act of combining the manifold of intuition is the unity of consciousness (B137). But what has this to do with categories? I suggest that it is categories which are the conditions of all synthesis, be it that of intuition or of self-consciousness. Categories are functions of unity, principles of combination. It may be that categories can unify intuitions only insofar as they are able to bring unity to self-consciousness.
Sometimes it seems to me that Kant's use of the notion of the unity of apperception contains a modal fallacy. That is, the ability to bring representations to the unity of consciousness is a necessary condtion of all combination. But Kant refers to this necessary condtion for unity as a "necessary unity" (B142). "I do not here assert that these representations [in the judgment 'Bodies are heavy'] necessarily belong to one another in the empirical intuition, but that they belong to one another in virtue of the necessary unity of apperception in the synthesis of intuitions, that is, according to principles of the objective determination of all representaitons, in so far as cognition can be acquired by means of these representations -- principles which are all derived from the fundamental principle of the transcendental unity of apperception" (B142). It seems as if the unity of apperception is some kind of "necessary principle" from which consequences can be derived. But it is not a principle at all, but the outcome of a process of synthesis, just as is the unity of intuition.
At any rate, by the end of Section 20, we are told that categories are conditions for the unity of all intuition. The conclusion of Section 20 seems to imply the conclusion of Section 26. If what is manifold in a given intuition is subject to the categories, it would seem that "all the objects of our senses" (B145) or "everything that can be presented to our senses" (B160) are subject to the categories, as Section 26 states. Yet Kant states that the conclusion of Section 20 only makes a "beginning" of the argument which culminates in Section 26. Kant scholars have tended not to take Kant at his word on this point. They have thought of the two arguments as different ways of reaching the same conclusion. One way of distinguishing the two is to describe the argument in Section 20 as being "from above," and that of Section 26 as being "from below." The argument from above starts with the unity of apperception and shows how it is a necessary condition for the unity of intuition, while that from below begins with intuitions and works its way up to the categories.
Another way of describing the two arguments is as "objective" and "subjective," respectively. In the argument at Section 20, Kant seeks to establish that categories are a necessary condition for an intuition's being an object for the understanding. From Sections 21 to 26, he lays out the subjective conditions required for the applicablity of the categories.
I will try construe Kant as he himself described his project, with the argument at Section 26 filling in a gap left by that of Section 20. In the Section 20 argument, Kant left us with a conditional: If a single empirical intuition is given, then it is subject to the categories. But it has not been established that such an intuition is given to us human beings. While the Transcendental Aesthetic supposed that we are given objects in space and time, appearances, the supposition was never justified. The argument of Sections 21 to 26 is designed to provide the missing justification. Empricial objects of human sensibility are represented by unified intuitions, so they are subject to categories. "In what follows (cf. Section 26) it will be shown, from the mode in which the empirical intuition is given in sensibility, that its unity is no other than that which the category (according to Section 20) prescribes to the manifold of intuition in general" (B144-5).
The synthesis by which objects are thought in general was termed by Kant an intellectual synthesis. Because of the generality of their potential application, the categories as treated in Section 20 are "mere forms of thought, through which alone no determinate object is cognized" (B150). We cannot say what it is, for example, which is a substance or which is subject to causality. For this to take place, we need to look at the specific manner in which intuition takes place.
It must be recalled that intuition has a form (space and time) and a matter (actual things that are in space and time). In the Aesthetic, it was assumed that the forms of intuitions represent objects, space and time. But now Kant states that what pure intuition provides is a manifold of pure intuition, which itself stands in need of unification. "Space, represented as object (as we are required to do in geometry), contains more than mere form of intuition; it also contains combination of the manifold, given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only a manifold, the formal intuition gives unity of representation" (B160n). To represent any spatial object, such as a triangle, combination of a manifold is required.
This act of combining is distinct from intellectual synthesis, for it does not bring an object to concepts. Rather, it produces an intuitive representation of an object. Kant calls it the figurative synthesis, which is the work of the productive imagination. A geometrical object is literally produced by the productive imagination, when it "draws" the triangle in thought. "We cannot think a line without drawing it in thought, or a circle without describing it. We cannot represent the three dimensions of space save by setting three lines at right angles to one another from the same point" (B154). The understanding produces the combinations resulting in a unified intuition. This synthesis of pure intuition makes possible a synthesis of apprehension, and it makes perception possible. "When, for instance, by apprehension of the manifold of a house, I make the empirical intuition into a perception, the necessary unity of space and outer sensible intution in general lies at the basis of my apprehension, and I draw as it were the outline of the house in corformity with this synthetic unity of the manifold in space" (B162). The intuition of the house falls under the category of quantity, to which all figurative synthesis is subject.