Year: 2025
Type: book-chapter
Abstract: I show on the basis of unpublished sources how Hilbert's conviction of the solvability of all mathematical problems originated from an engagement with Kant's philosophy of mathematics.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.
Author: Moritz Bodner
Institution: University of Vienna
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Award: G1925353595
OpenAlex ID: W4413115877