Philosophia Mathematica 7 (3):293-321 (1999)

Authors
Stewart Shapiro
Ohio State University
Alan Weir
University of Glasgow
Abstract
We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory.
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DOI 10.1093/philmat/7.3.293
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References found in this work BETA

Science Without Numbers.Hartry Field - 1980 - Princeton University Press.
Die Grundlagen der Arithmetik.Gottlob Frege - 1988 - Felix Meiner Verlag.
The Limits of Abstraction.Kit Fine - 2002 - Oxford University Press.
Science Without Numbers.Hartry Field - 1980 - Synthese 51 (2):283-291.

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Citations of this work BETA

Neo-Fregean Ontology.Matti Eklund - 2006 - Philosophical Perspectives 20 (1):95-121.
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Neo-Fregeanism and Quantifier Variance.Theodore Sider - 2007 - Aristotelian Society Supplementary Volume 81 (1):201–232.
Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.

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