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Does matter consist of simple substances, or is it infinitely divisible? This is the question in the second antinomy in the Critique of Pure Reason. This first comprehensive systematic study of the antinomy of divisibility analyses its derivation, the proofs of the thesis and antithesis, and their resolution. The developmental and historical dimensions are also discussed, taking present-day problems in the philosophy of nature into account. The study demonstrates that the antinomy of divisibility is on the one hand a critique of metaphysics, but at the same time gains a positive result for Kant's transcendental philosophy. The resolution of the antinomy presents firstly a conceptual sharpening of realism and idealism and of the transcendental concept of phenomena. Secondly it shows that the structure of matter is dependent on a priori determinations by reason and understanding. These insights are highly relevant not only for Kant's project of establishing an a priori foundation for the natural sciences but also for the problem of the soul.