Chapter

Numbers

Penelope Maddy

in Realism in Mathematics

Published in print September 1992 | ISBN: 9780198240358
Published online November 2003 | e-ISBN: 9780191597978 | DOI: http://dx.doi.org/10.1093/019824035X.003.0003

Series: Clarendon Paperbacks

 Numbers

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Begins with a review of Benacerraf's metaphysical challenge to mathematical realism based on sets: how, for example, can number theory be the study of particular sets when other sets with the same structural relations would seem to do just as well? The set theoretic realist gives the straightforward response that numbers are not particular sets, but properties of sets. I close with a digression on the prospects for ‘Frege numbers’—i.e. numbers construed as proper classes.

Keywords: Benacerraf; Frege numbers; numbers; proper classes; set theoretic realism

Chapter.  11099 words. 

Subjects: Philosophy of Mathematics and Logic

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