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. 2025;79(1):12.
doi: 10.1007/s00407-025-00350-y. Epub 2025 Aug 11.

Hilbert's problems, Kant, and decidability

Moritz Bodner  1
Affiliations

Hilbert's problems, Kant, and decidability

Moritz Bodner. Arch Hist Exact Sci. 2025.

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I show on the basis of unpublished sources how Hilbert's conviction of the solvability of all mathematical problems originated from an engagement with Kant's philosophy of mathematics.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.

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Conflict of interest statement

Conflict of interestI have no stake or interest, financial or otherwise, in anything on which the work presented here has any bearing. There are thus no conflict of interest to declare.

References

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