Naturalism and Mathematics

In Kelly James Clark (ed.), The Blackwell Companion to Naturalism. Hoboken, NJ: Wiley. pp. 289–304 (2016)
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Abstract

In this chapter, I consider some problems with naturalizing mathematics. More specifically, I consider how the two leading kinds of approach to naturalizing mathematics, to wit, Quinean indispensability‐based approaches and Maddy's Second Philosophical approach, seem to run afoul of constraints that any satisfactory naturalistic mathematics must meet. I then suggest that the failure of these kinds of approach to meet the relevant constraints indicates a general problem with naturalistic mathematics meeting these constraints, and thus with the project of naturalizing mathematics itself.

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Jeffrey W. Roland
Louisiana State University

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References found in this work

Philosophy of Logic.Hilary Putnam - 1971 - New York, NY, USA: Routledge.
Carnap and logical truth.Willard van Orman Quine - 1954 - Synthese 12 (4):350--74.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.

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