Authors
Alexander Paseau
Oxford University
Abstract
Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the only available argument for it. I argue that this argument, the so-called Failure Argument, itself fails. My overall conclusion is that although there is no self-refutation argument against reinterpretation naturalism, there are as yet no good reasons to accept it. Naturalism in mathematics The consistency of mathematical naturalism The failure argument Objections to the failure argument Philosophy as the default.
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DOI 10.1093/bjps/axi123
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References found in this work BETA

The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Judgement and Justification.William G. Lycan - 1988 - Cambridge University Press.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.
Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.

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Citations of this work BETA

Deferentialism.Chris Daly & David Liggins - 2011 - Philosophical Studies 156 (3):321-337.
Maddy and Mathematics: Naturalism or Not.Jeffrey W. Roland - 2007 - British Journal for the Philosophy of Science 58 (3):423-450.

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