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2009 A Topological Approach to Yablo's Paradox
Claudio Bernardi
Notre Dame J. Formal Logic 50(3): 331-338 (2009). DOI: 10.1215/00294527-2009-014

Abstract

Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. Consider an infinite sequence of sentences, where any sentence refers to the truth values of the subsequent sentences: if the corresponding function is continuous, no paradox arises.

Citation

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Claudio Bernardi. "A Topological Approach to Yablo's Paradox." Notre Dame J. Formal Logic 50 (3) 331 - 338, 2009. https://doi.org/10.1215/00294527-2009-014

Information

Published: 2009
First available in Project Euclid: 10 November 2009

zbMATH: 1190.03003
MathSciNet: MR2572977
Digital Object Identifier: 10.1215/00294527-2009-014

Subjects:
Primary: 03A05
Secondary: 03F45, 54D30

Rights: Copyright © 2009 University of Notre Dame

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Vol.50 • No. 3 • 2009
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