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Logic, Mathematics, Philosophy, Vintage EnthusiasmsAbsoluteness and the Skolem Paradox

Logic, Mathematics, Philosophy, Vintage Enthusiasms: Absoluteness and the Skolem Paradox [When seen in the “correct” light, the contradictions of set theory are by no means disastrous, but instructive and fruitful. For instance, the antinomies of Russell and Burali-Forti live on in the systems of axiomatised set theory in the guise of established theorems. Zermelo used the Russell-Zermelo argument to prove that every set possesses a subset which cannot be an element of that set, and from which it follows that there can be no universal set ((Zermelo, 1908b, pp. 264–265), p. 203 of the English translation), and the essentials of the Burali-Forti argument can be used to prove that there is no ordinary set of all (von Neumann) ordinals.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Logic, Mathematics, Philosophy, Vintage EnthusiasmsAbsoluteness and the Skolem Paradox

Part of the The Western Ontario Series in Philosophy of Science Book Series (volume 75)
Editors: DeVidi, David; Hallett, Michael; Clarke, Peter
Hallett, Michael
Logic, Mathematics, Philosophy, Vintage Enthusiasms — Jan 27, 2011
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References (49)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media B.V. 2011
ISBN
978-94-007-0213-4
Pages
189 –218
DOI
10.1007/978-94-007-0214-1_10
Publisher site
See Chapter on Publisher Site

Abstract

[When seen in the “correct” light, the contradictions of set theory are by no means disastrous, but instructive and fruitful. For instance, the antinomies of Russell and Burali-Forti live on in the systems of axiomatised set theory in the guise of established theorems. Zermelo used the Russell-Zermelo argument to prove that every set possesses a subset which cannot be an element of that set, and from which it follows that there can be no universal set ((Zermelo, 1908b, pp. 264–265), p. 203 of the English translation), and the essentials of the Burali-Forti argument can be used to prove that there is no ordinary set of all (von Neumann) ordinals.]

Published: Jan 27, 2011

Keywords: English Translation; Continuum Hypothesis; Transitive Model; Propositional Connective; Uncountable Cardinal

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