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Philosophia Mathematica 2005 13(1):78-90; doi:10.1093/philmat/nki001
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Philosophia Mathematica (III), Vol. 13 No. 1 © Oxford University Press, 2005, all rights reserved

Book Review

Charles S. Chihara. A Structural Account of Mathematics. Oxford: Oxford University Press, 2004. Pp. xiv + 380. ISBN 0-19-926753-7

John P. Burgess*

* Department of Philosophy, Princeton University Princeton, New Jersey 08544-1006, U. S. A. jburgess@princeton.edu

The first 150 words of the full text of this article appear below.

There are now four books by Charles Chihara. I learned a great deal from Chihara when I was his student, learned more from each of his first three books, and have found yet more to be learned in this new one. Like its predecessors it is a combination of criticism of other philosophers of mathematics with exposition of a positive program. On the positive side, Chihara now merges the nominalism of his earlier works with a form of structuralism. On the critical side, the philosophers attacked range from the reviewer and his co-author Gideon Rosen, who are neither nominalists nor structuralists, to Geoffrey Hellman, who is both but combines the two 'isms in a way not to Chihara's liking. Two structuralists who are not nominalists, Michael Resnik and Stewart Shapiro, come in for especially heavy criticism. Given the wide range of views and topics considered, any review of tolerable length . . . [Full Text of this Article]


   1. Structuralism without Nominalism
 

   2. Nominalism without Structuralism
 

   3. Chihara's Commitments
 

   4. Combining the 'Isms
 

   5. The Van Inwagen Problem
 

   6. The Benacerraf Problem
 

   7. What Science Teaches Us
 

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