Naturalism in mathematics and the authority of philosophy

British Journal for the Philosophy of Science 56 (2):377-396 (2005)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,419

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Naturalism and ontology.Penelope Maddy - 1995 - Philosophia Mathematica 3 (3):248-270.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.
Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
A puzzle about naturalism.Alexander Paseau - 2010 - Metaphilosophy 41 (5):642-648.
On Naturalizing the Epistemology of Mathematics.Jeffrey W. Roland - 2009 - Pacific Philosophical Quarterly 90 (1):63-97.
Kitcher, mathematics, and naturalism.Jeffrey W. Roland - 2008 - Australasian Journal of Philosophy 86 (3):481 – 497.
Naturalizing dissension.Matthew E. Moore - 2006 - Pacific Philosophical Quarterly 87 (3):325–334.

Analytics

Added to PP
2009-01-28

Downloads
291 (#41,549)

6 months
4 (#184,953)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

A. C. Paseau
Oxford University

References found in this work

Judgement and Justification.William G. Lycan - 1988 - Cambridge University Press.
Theories and Things.W. V. O. Quine (ed.) - 1981 - Harvard University Press.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford, England and New York, NY, USA: Oxford University Prress.

View all 28 references / Add more references