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Hilbert's Epistemology

Published online by Cambridge University Press:  01 April 2022

Philip Kitcher
Philip Kitcher*
Affiliation:
University of Vermont
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Abstract

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.

Type
Research Article
Information
Philosophy of Science , Volume 43 , Issue 1 , March 1976 , pp. 99 - 115
Copyright
Copyright © 1976 by the Philosophy of Science Association

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