Hilbert’s problems, Kant, and decidability

Abstract

I show on the basis of unpublished sources how Hilbert’s conviction of the solvability of all mathematical problems originated from an engagement with Kant’s philosophy of mathematics. Furthermore, I consider other sense of the “solvability” or “decidability” of mathematical problems which Hilbert thought about later: decidability in finitely many steps, which is an issue Hilbert inherited from Kronecker, “finitistic decidability” which Hilbert develops by reflecting on Kronecker’s methodological strictures, and finally the decision-problem as raised by Behmann in the 1920s. I argue that these different preoccupations have different historical and biographical roots, and should also be kept conceptually distinct.