Chapter

Wittgenstein and Intuitionism

Robert J. Fogelin

in Philosophical Interpretations

Published in print April 1992 | ISBN: 9780195071627
Published online November 2003 | e-ISBN: 9780199833221 | DOI: http://dx.doi.org/10.1093/019507162X.003.0015
Wittgenstein and Intuitionism

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This essay explores one important strain that runs through Wittgenstein's Remarks on the Foundations of Mathematics: his commitment to themes characteristic of the intuitionist movement in logic and mathematics. Chief among them are his attacks on the unrestricted use of the Law of Excluded Middle, his distrust of nonconstructive proofs, and his impatience with the idea that mathematics stands in need of a foundation. The central idea of the essay is that these aspects of Wittgenstein's position can be explained by attributing to him the view that mathematical and logical propositions are tacitly governed by the modal operator “it is a rule that.”

Keywords: foundations; intuitionism; Law of Excluded Middle; mathematics; modal operator; nonconstructive proofs; Remarks on the Foundations of Mathematics; Wittgenstein

Chapter.  5690 words.  Illustrated.

Subjects: Philosophy

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