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Naturalism in Mathematics and the Authority of Philosophy

Alexander Paseau
The British Journal for the Philosophy of Science
Vol. 56, No. 2 (Jun., 2005), pp. 377-396
Stable URL: http://www.jstor.org/stable/3541708
Page Count: 20
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Naturalism in Mathematics and the Authority of Philosophy
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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.

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