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Philosophia Mathematica 2005 13(3):294-307; doi:10.1093/philmat/nki033
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Philosophia Mathematica (III), Vol. 13 No. 3 © The Author [2005]. Published by Oxford University Press. All rights reserved. For Permission, please e-mail: journals.permissions{at}oxfordjournals.org

A Nominalist's Dilemma and its Solution{dagger}

Otávio Bueno* and Edward N. Zalta**

*Department of Philosophy, University of South Carolina Columbia, S. C. 29208 U. S. A. obueno{at}sc.edu
**Center for the Study of Language and Information, Stanford University Stanford, California 94305 U. S. A. zalta{at}stanford.edu

Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with the cost of not taking mathematical theories literally. Jody Azzouni's Deflating Existential Consequence has recently challenged this conclusion by formulating a nominalist view that lacks this cost. In this paper, we argue that, as it stands, Azzouni's proposal does not yet succeed. It faces a dilemma to the effect that either the view is not nominalist or it fails to take mathematics literally. After presenting the dilemma, we suggest a possible solution for the nominalist.


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