In Chapter One of the Transcendental Analytic in the Critique of Pure Reason, Kant establishes a table of the categories, or pure concepts of the understanding, according to the “leading thread” of a table of the logical forms of judgment. He proclaims that this achievement takes after and improves upon Aristotle's own endeavor in offering a list of categories, which Aristotle took to define the most general kinds of being. Kant claims that his table is superior to Aristotle's list in that it is grounded on a systematic principle. This principle is also what will eventually ground, in the Transcendental Deduction, the a priori justification of the objective validity of the categories: a justification of the claim that all objects (as long as they are objects of a possible experience) do fall under those categories.
Kant's self-proclaimed achievement is the second main step in his effort to answer the question: “How are synthetic a priori judgments possible?” The first step was the argument offered in the Transcendental Aesthetic, to the effect that space and time are a priori forms of intuition. As such, Kant argued, they make possible judgments (propositions) whose claim to truth is justified a priori by the universal features of our intuitions. Such propositions are thus both synthetic and a priori.