The inestimable world: Kant’s resolution of the mathematical antinomies
Kant’s “antinomies” are instances of Pure Reason’s apparent conflict with itself. Kant maintains that they can be resolved if, but only if, one adopts Transcendental Idealism. This talk focuses on the ‘if’ part of this claim, and on the first two antinomies—the so-called “mathematical antinomies”. Kant’s resolution of these antinomies proceeds along two wholly distinct lines, corresponding to two traditional ways of generating apparent counterexamples to the law of excluded middle. I offer an account of what these lines are, and of why Kant pursues both of them. I briefly consider an alternative line of resolution that Kant toys with but rejects, namely, the strategy of treating the opposed claims as nonsense. I venture an explanation of why he rejects this alternative.