David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 7 (3):293-321 (1999)
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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Theodore Sider (2007). Neo-Fregeanism and Quantifier Variance. Aristotelian Society Supplementary Volume 81 (1):201–232.
S. Shapiro (2011). The Company Kept by Cut Abstraction (and its Relatives). Philosophia Mathematica 19 (2):107-138.
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