Immanuel Kant
Transcendental deduction of the categories of the understanding

The "Analytic of Concepts" argues for the universal and necessary validity of the pure concepts of the understanding, or the categories, for instance, the concepts of substance and causation. These twelve basic categories define what it is to be a thing in general — that is, they articulate the necessary conditions according to which something is a possible object of experience. These, in conjunction with the a priori forms of intuition, are the basis of all synthetic a priori cognition. According to Guyer and Wood, "Kant's idea is that just as there are certain essential features of all judgments, so there must be certain corresponding ways in which we form the concepts of objects so that judgments may be about objects."

Kant provides two central lines of argumentation in support of his claims about the categories. The first, known as the "metaphysical deduction", proceeds analytically from a table of the Aristotelian logical functions of judgment. As Kant was aware, this assumes precisely what the skeptic rejects, namely, the existence of synthetic a priori cognition. For this reason, Kant also supplies a synthetic argument that does not depend upon the assumption in dispute.

This argument, provided under the heading "Transcendental Deduction of the Pure Concepts of the Understanding", is widely considered to be both the most important and the most difficult of Kant's arguments in the Critique. Kant himself said that it is the one that cost him the most labor. Frustrated by its confused reception in the first edition of his book, he rewrote it entirely for the second edition.

The "Transcendental Deduction" gives Kant's argument that these pure concepts apply universally and necessarily to the objects that are given in experience. According to Guyer and Wood, "He centers his argument on the premise that our experience can be ascribed to a single identical subject, via what he calls the 'transcendental unity of apperception,' only if the elements of experience given in intuition are synthetically combined so as to present us with objects that are thought through the categories."

Kant's principle of apperception is that "The I think must be able to accompany all my representations; for otherwise something would be represented in me that could not be thought at all, which is as much as to say that the representation would either be impossible or else at least would be nothing for me." The necessary possibility of the self-ascription of the representations of self-consciousness, identical to itself through time, is an a priori conceptual truth that cannot be based on experience. This is only a bare sketch of one of the arguments that Kant presents.
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