The Mathematics of Skolem's Paradox

In Dale Jacquette (ed.), Philosophy of Logic. North Holland. pp. 615--648 (2006)

Abstract

Over the years, Skolem’s Paradox has generated a fairly steady stream of philosophical discussion; nonetheless, the overwhelming consensus among philosophers and logicians is that the paradox doesn’t constitute a mathematical problem (i.e., it doesn’t constitute a real contradiction). Further, there’s general agreement as to why the paradox doesn’t constitute a mathematical problem. By looking at the way firstorder structures interpret quantifiers—and, in particular, by looking at how this interpretation changes as we move from structure to structure—we can give a technically adequate “solution” to Skolem’s Paradox. So, whatever the philosophical upshot of Skolem’s Paradox may be, the mathematical side of Skolem’s Paradox seems to be relatively straightforward.

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Timothy Bays
University of Notre Dame

References found in this work

Models and Reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Skolem and the Skeptic.Paul Benacerraf & Crispin Wright - 1985 - Proceedings of the Aristotelian Society, Supplementary Volumes 59:85-137.
Intended Models and the Löwenheim-Skolem Theorem.Virginia Klenk - 1976 - Journal of Philosophical Logic 5 (4):475-489.

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