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Philosophia Mathematica Advance Access originally published online on July 12, 2008
Philosophia Mathematica 2009 17(1):1-34; doi:10.1093/philmat/nkn016
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© The Author [2008]. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Empirical Regularities in Wittgenstein's Philosophy of Mathematics{dagger}

Mark Steiner*

* The Hebrew University of Jerusalem, Jerusalem, Israel. marksa{at}vms.huji.ac.il

During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e., that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assigns to empirical regularities had profound implications for all of his later philosophy; some of these implications (particularly to rule following) are addressed in the essay.

{dagger} I am indebted to the Israel Science Foundation for support, under Grants no. 949/02 and 251/06, of this research. For invaluable criticisms of earlier versions of this work, I thank Hilary Putnam, Carl Posy, Gilead Bar-Elli, Juliet Floyd, and reviewers for Philosophia Mathematica.


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