This chapter provides a novel reading of Immanuel Kant’s critique of “the second part of metaphysics,” a critique that takes place in the Transcendental Dialectic of the Critique of Pure Reason. Kant offers a number of complex and difficult arguments in support of his verdict, most of which depend on what he takes himself to have established in the first part of the Critique. The chapter shows that at least some of the purported proofs of speculative metaphysics are formally invalid, and that their invalidity can be traced back to shortcomings in their logic of negation. The distinction between negative and infinite judgement is crucially involved in Kant’s resolution of the antinomies and his concomitant dismissal of the apagogic method in metaphysics, i.e., the use of indirect proofs by assuming the opposite or reductio ad absurdum. According to Kant the apagogic method, i.e., the application of reductio ad absurdum is illicit in metaphysics.