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Philosophical Interpretations$
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Robert J. Fogelin

Print publication date: 1992

Print ISBN-13: 9780195071627

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/019507162X.001.0001

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Wittgenstein and Intuitionism

Wittgenstein and Intuitionism

Chapter:
(p.196) 13 Wittgenstein and Intuitionism
Source:
Philosophical Interpretations
Author(s):

Robert J. Fogelin (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/019507162X.003.0015

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

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