Reflections on Skolem's relativity of set-theoretical concepts

Philosophia Mathematica 9 (2):129-153 (2001)

In this paper an attempt is made to present Skolem's argument, for the relativity of some set-theoretical notions as a sensible one. Skolem's critique of set theory is seen as part of a larger argument to the effect that no conclusive evidence has been given for the existence of uncountable sets. Some replies to Skolem are discussed and are shown not to affect Skolem's position, since they all presuppose the existence of uncountable sets. The paper ends with an assessment of the assumptions on which Skolem's argument rests from a present-day perspective.
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DOI 10.1093/philmat/9.2.129
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Skolem and the Skeptic.Paul Benacerraf - 1985 - Proceedings of the Aristotelian Society 59:85-115.
Skolem and the Skeptic.Paul Benacerraf & Crispin Wright - 1985 - Proceedings of the Aristotelian Society, Supplementary Volumes( 59:85-137.

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On Arbitrary Sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.

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