Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T09:53:19.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Hilbert's Epistemology

Published online by Cambridge University Press:  01 April 2022

Philip Kitcher
Philip Kitcher*
Affiliation:
University of Vermont
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benacerraf, P. “Mathematical Truth.” Journal of Philosophy 70 (1973): 661–679.CrossRefGoogle Scholar
Benacerraf, P. and Putnam, H. (eds.) Philosophy of Mathematics. Englewood Cliffs, New Jersey: Prentice-Hall, 1964.Google Scholar
Dedekind, J. W. R. Essays on the Theory of Numbers. Translated by Beman, W. W. New York: Dover.Google Scholar
Frege, G. The Foundations of Arithmetic. Translated by Austin, J. L. Oxford: Blackwell, 1959.Google Scholar
Hilbert, D. “On the Infinite.” Translation by S. Bauer-Mengelberg. Printed in [12], pp. 369–392.Google Scholar
Hilbert, D. “On the Foundations of Mathematics.” Translated by S. Bauer-Mengelberg and D. Follesdal. Printed in [12], pp. 464–479.Google Scholar
Hilbert, D. Gesammelte Abhandlungen. Volume 3. Berlin: Springer, 1935.Google Scholar
Hilbert, D. and Bernays, P. Grundlagen der Mathematik. Volume 1. Berlin: Springer, 1934.Google Scholar
Kreisel, G. “Hilbert's Programme.” In [2], pp. 157–180.Google Scholar
Poincaré, H. Science and Method. Translated by Maitland, F. New York: Dover, 1952.Google Scholar
Resnik, M. “On the Philosophical Significance of Consistency Proofs.” Journal of Philosophical Logic 3 (1974): 133–147.CrossRefGoogle Scholar
van Heijenoort, J. From Frege to Gödel: A Source Book in Mathematical Logic 1879–1931. Cambridge, Massachusetts: Harvard University, 1967.Google Scholar