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Philosophia Mathematica Advance Access originally published online on January 27, 2007
Philosophia Mathematica 2007 15(1):79-93; doi:10.1093/philmat/nkl029
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Copyright © The Author 2007. Published by Oxford University Press.

Book Review

Burgess on Plural Logic and Set Theory{dagger}

Øystein Linnebo

Department of Philosophy, University of Bristol, Bristol BS8 1TB United Kingdom

Correspondence: Oystein.Linnebo{at}bristol.ac.uk

John Burgess in a 2004 paper combined plural logic and a new version of the idea of limitation of size to give an elegant motivation of the axioms of ZFC set theory. His proposal is meant to improve on earlier work by Paul Bernays in two ways. I argue that both attempted improvements fail.

I am grateful to Philip Welch, two anonymous referees, and especially Ignacio Jané for written comments on earlier versions of this paper, which have led to substantial improvements. Thanks also to the participants in a discussion group at the University of Bristol, where an earlier version was presented.


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