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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References found in this work BETA

Skolem and the Skeptic.Paul Benacerraf & Crispin Wright - 1985 - Proceedings of the Aristotelian Society, Supplementary Volumes( 59:85-137.
Skolem's Promises and Paradoxes.W. D. Hart - 1970 - Journal of Philosophy 67 (4):98-109.
Skolem's Paradox and Constructivism.Charles McCarty & Neil Tennant - 1987 - Journal of Philosophical Logic 16 (2):165 - 202.

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Citations of this work BETA

Non-Ontological Structuralism†.Michael Resnik - 2019 - Philosophia Mathematica 27 (3):303-315.
On Arbitrary Sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.

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