Naturalism in Mathematics and the Authority of Philosophy

Author: Paseau, Alexander

Source: British Journal for the Philosophy of Science, Volume 56, Number 2, June 2005 , pp. 377-396(20)

Buy & download fulltext article:

Price: $44.11 plus tax (Refund Policy)

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</ITEM><ITEM>

The consistency of mathematical naturalism</ITEM><ITEM>

The failure argument</ITEM><ITEM>

Objections to the failure argument</ITEM><ITEM>

Philosophy as the default</ITEM></LIST>

Document Type: Research article

DOI: http://dx.doi.org/10.1093/bjps/axi123

Publication date: 2005-06-01

More about this publication?

For over fifty years The British Journal for the Philosophy of Science has published the best international work in the philosophy of science under a distinguished list of editors including A. C. Crombie, Mary Hesse, Imre Lakatos, D. H. Mellor and David Papineau.