Notre Dame Journal of Formal Logic

A Topological Approach to Yablo's Paradox

Claudio Bernardi


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.

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Notre Dame J. Formal Logic, Volume 50, Number 3 (2009), 331-338.

First available in Project Euclid: 10 November 2009

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Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 03F45: Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25] 54D30: Compactness

fixed point of a continuous function ungrounded sentence


Bernardi, Claudio. A Topological Approach to Yablo's Paradox. Notre Dame J. Formal Logic 50 (2009), no. 3, 331--338. doi:10.1215/00294527-2009-014.

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