How Metaphysical is “Deepening the Foundations”?: Hahn and Frank on Hilbert’s Axiomatic Method

Abstract
Only recently has David Hilbert’s program to axiomatize the sciences according to the pattern of geometry left the shade of his formalist program in the foundations of mathematics.1 This relative neglect — which is surprising in view of the enormous efforts Hilbert himself had devoted to it — was certainly influenced by Logical Empiricists’ almost exclusively focusing on his contributions to the foundational debates. Ulrich Majer puts part of the blame for this neglect on Hilbert himself because “he failed to make his position sufficiently clear, and he did not take much effort to promote his views beyond the narrow circle of mathematical physics in Göttingen.”
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