UC San Diego

This dissertation argues for a novel interpretation of the mathematical antinomies, which concern the cosmological questions of the world’s extent in space and time and the divisibility of matter. In the resolution of the antinomies, Kant makes two striking claims. He claims (i) that the world is neither finite nor infinite in spatiotemporal extent and (ii) that spatiotemporal objects are composed neither from simples nor from infinitely many parts all of which are divided in turn. Against competing interpretations, I argue that these claims amount to a thesis of metaphysical indeterminacy for spatiotemporal phenomena. According to Kant, transcendental idealists alone can hold that spatiotemporal phenomena are metaphysically indeterminate in magnitude rather than either finite or infinite, and this commitment to indeterminacy is what allows them to escape the antinomies. Reading Kant in this way provides an interpretation of the antinomies that is more charitable than many others on offer, and it explains how the antinomies can present a dialectically effective objection to Kant’s rationalist interlocutors.Chapter 1 summarizes the arguments of the mathematical antinomies and the main interpretive positions defended in the secondary literature. Chapter 2 explains how the notions of infinity and totality relate to one another and why Kant thinks denying finitude and infinitude for spatiotemporal phenomena also implies that spatiotemporal series of conditions cannot form unconditioned totalities of conditions. With these results in hand, chapter 3 argues that the solution to the mathematical antinomies must be metaphysical rather than purely epistemic. That is, Kant’s solution is not merely that we cannot know or cognize whether spatiotemporal phenomena are finite or infinite; rather, he holds that spatiotemporal phenomena are in fact neither finite nor infinite. In chapter 4, I argue that a metaphysical indeterminacy reading is distinct from and more successful than a reading according to which the antinomies are resolved by appealing to the notion of potential infinity. Finally, in chapter 5, I show how interpreting transcendental idealism as a kind of intentional object phenomenalism can explain how metaphysical indeterminacy in spatiotemporal phenomena results from their mind-dependence.