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Philosophia Mathematica Advance Access published online on July 1, 2006
Philosophia Mathematica, doi:10.1093/philmat/nkl005
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© The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Article

Burgess's ‘Scientific’ Arguments for the Existence of Mathematical Objects{dagger}

Charles Chihara 1 *

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

* To whom correspondence should be addressed.
Charles Chihara, E-mail: charles1{at}berkeley.edu


  Abstract

This paper addresses John Burgess's answer to the ‘Benacerraf Problem’: How could we come justifiably to believe anything implying that there are numbers, given that it does not make sense to ascribe location or causal powers to numbers? Burgess responds that we should look at how mathematicians come to accept:

There are prime numbers greater than 1010

That, according to Burgess, is how one can come justifiably to believe something implying that there are numbers. This paper investigates what lies behind Burgess's answer and ends up as a rebuttal to Burgess's reasoning.

{dagger} Versions of this paper were presented at the Logic Colloquium of the University of California, Berkeley, on December 2, 2005, at the Workshop entitled ‘Philosophy of Mathematics Today’ held from January 23-27, 2006, at the De Giorgi Center in Pisa, and at the Séminaire de Philosophie des Mathématiques et de l'Informatique which took place on January 30, 2006, at the Institut d'Histoire et de Philosophie des Sciences et des Techniques in Paris. I am grateful for many helpful comments I received at these presentations. Thanks also go to two referees for this journal for their useful suggestions and criticisms.
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The Burgess-Rosen critique of nominalistic reconstructions{dagger}
Philosophia Mathematica, February 1, 2007; 15(1): 54 - 78.
[Abstract] [Full Text] [PDF]


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