what these basic principles and concepts are. But Kant does not stop there. For him there is the second task, the truly important one of demonstrating the legitimacy of these basic principles and concepts as activities of the understanding, i.e., as originally present only in the subject. That means, as Kant puts it, providing them with their “birth certificate” (B 119) on the basis of which they have objective validity, i.e., do in fact determine nature as an object.

The first task of demonstration, which consists in ascertaining the ensemble of basic principles and concepts, is the task of the metaphysical deduction of the categories. Here Kant shows the following: These basic concepts arise from the understanding and are concepts of possible unities that pertain to the ways the understanding can judge. As an act of combining, every act of judging is a function of unity; and how many concepts of unities I can produce depends on how many functions of unity I can demonstrate. These concepts of the forms of unity that are possible in the judgment are the pure concepts of the understanding, or the categories. The second task—that of the transcendental deduction—is the task of proving that these concepts of the understanding are the conditions of possibility whereby alone we can think something as an object and as a natural object. Kant’s explanation of the understanding and its action is quite analogous to the transcendental explanation of the senses, where of course Kant explains space and time both metaphysically (i.e., dogmatically) and transcendentally.

In the known of mathematical-physical knowledge—in the entities that it intends—reside space-time determinations, plus the rules that are articulated in the principles, plus determinations that express the basic concepts themselves. Does that exhaust all that always already resides beforehand in what this knowledge intends? [320] We have set out everything as regards the given except the decisive thing: that which is intended in all the principles and categories. The spatio-temporally determined is understood beforehand as the unity of nature itself. In thinking nature itself we have already priorly thought its unity, from which every statement about nature is drawn and to which it returns, whether that statement is a principle or an empirical proposition. This unity—nature—is the most prior of all that resides in the known as such. The primary a priori of unity—as the underlying ground that supports a possible togetherness of the manifold, and as the matrix within which any manifold must be together—must be concretely determinable as: nature.

Such a unity “constitutes what is essential in any knowledge of the objects [Objekte] of the senses, i.e., of experience (not merely of the intuition or sensation of the senses)” (B 218–19). “An object, however, is that in the concept of which the manifold of a given intuition is united” (B 137). In Kant’s language, that refers to a prior condition of