David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophy of Science 43 (1):99-115 (1976)
Hilbert's program attempts to show that our mathematical knowledge can be certain because we are able to know for certain the truths of elementary arithmetic. I argue that, in the absence of a theory of mathematical truth, Hilbert does not have a complete theory of our arithmetical knowledge. Further, while his deployment of a Kantian notion of intuition seems to promise an answer to scepticism, there is no way to complete Hilbert's epistemology which would answer to his avowed aims
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Alexander Paseau (2011). Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence. Studies in History and Philosophy of Science Part A 42 (1):140-149.
Sören Stenlund (2012). Different Senses of Finitude: An Inquiry Into Hilbert's Finitism. Synthese 185 (3):335-363.
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