Naturalism in mathematics and the authority of philosophy

Journal article

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.

Authors: Paseau, A

• Publication status: Published
• Journal: BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE
• Volume: 56
• Issue: 2
• Pages: 377-396
• Publication date: 2005-06-01
• DOI: 10.1093/bjps/axi123
• EISSN: 1464-3537
• ISSN: 0007-0882
• Language: English