Journal Article

Naturalism in Mathematics and the Authority of Philosophy

Alexander Paseau

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 56, issue 2, pages 377-396
Published in print June 2005 | ISSN: 0007-0882
Published online June 2005 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axi123
Naturalism in Mathematics and the Authority of Philosophy

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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

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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