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Philosophia Mathematica Advance Access originally published online on May 23, 2007
Philosophia Mathematica 2007 15(3):397-399; doi:10.1093/philmat/nkm022
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Copyright © The Author 2007. Published by Oxford University Press.

Book Review

GRAHAM OPPY. Philosophical Perspectives on Infinity

Elliott Mendelson*

* Queens College (CUNY), Flushing, N.Y. 11367, U.S.A., and City University of New York Graduate Center, New York, N.Y. 10016, U.S.A.

Correspondence: emenqc@msn.com

Graham Oppy. Philosophical Perspectives on Infinity. Cambridge: Cambridge University Press, 2006. ISBN 0-521-86067-9. Pp. xvii + 316

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The author tells us that this book was originally intended to be part of a larger work, with the provisional title God and Infinity, but that he opted instead for a separate and independent treatment of the notion of infinity in philosophy and related areas. The original purpose is very well-hidden, showing itself clearly only in the Preface and a few other places. The book begins with a chapter describing some known alleged difficulties having to do with the infinitely large and infinitely small (for example, Al-Ghazali's problem, Hilbert's hotel, Craig's library, and Thomson's lamp). This is followed by a chapter on some basic mathematical notions and facts, including sketchy references to Zermelo-Fraenkel set theory (ZF), ordinal and cardinal numbers, Cantor's diagonal method, some special set-theoretic . . . [Full Text of this Article]


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