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Philosophia Mathematica Advance Access originally published online on January 19, 2007
Philosophia Mathematica 2007 15(1):54-78; doi:10.1093/philmat/nkl023
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Copyright © The Author 2007. Published by Oxford University Press.

The Burgess-Rosen critique of nominalistic reconstructions{dagger}

Charles Chihara

Department of Philosophy, University of California Berkeley, Berkeley, California 94720-2390 U. S. A.

Correspondence: charles1{at}berkeley.edu

In the final chapter of their book A Subject With No Object, John Burgess and Gideon Rosen raise the question of the value of the nominalistic reconstructions of mathematics that have been put forward in recent years, asking specifically what this body of work is good for. The authors conclude that these reconstructions are all inferior to current versions of mathematics (or science) and make no advances in science. This paper investigates the reasoning that led to such a negative appraisal, and it produces a rebuttal to this reasoning.

I am grateful to the following mathematicians who were kind enough to provide me with their thoughts about nonstandard analysis: Martin Davis, Laura Chihara, Ted Chihara, Steve Galovich, Bonnie Gold, and especially Roger Simons, whose comments about an earlier version of this paper were very helpful. Thanks also go to two referees for their useful suggestions and criticisms of an earlier version of this paper.


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