Empirical regularities in Wittgenstein's philosophy of mathematics

Philosophia Mathematica 17 (1):1-34 (2009)
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.
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DOI 10.1093/philmat/nkn016
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Wittgenstein on Set Theory and the Enormously Big.Ryan Dawson - 2016 - Philosophical Investigations 39 (4):313-334.
Wittgenstein on Pure and Applied Mathematics.Ryan Dawson - 2014 - Synthese 191 (17):4131-4148.

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