An entirely non-self-referential Yabloesque paradox

Synthese 195 (11):5007-5019 (2018)
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Abstract

Graham Priest has argued that Yablo’s paradox involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve satisfaction conditions that are not recursively specifiable, and hence not recognizable in the sense required for Priest’s argument. In this paper I provide a general recipe for constructing infinitely many such noncircular Yabloesque paradoxes, and conclude by drawing some more general lessons regarding our ability to identify conditions that are necessary and sufficient for paradoxically more generally.

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Citations of this work

What Paradoxes Depend on.Ming Hsiung - 2018 - Synthese:1-27.
Unwinding Modal Paradoxes on Digraphs.Ming Hsiung - 2020 - Journal of Philosophical Logic 50 (2):319-362.

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References found in this work

The Yablo Paradox: An Essay on Circularity.Roy T. Cook - 2012 - Oxford, England: Oxford University Press.
Leitgeb,.about,. Yablo.Rafael Urbaniak - 2009 - Logique Et Analyse 52.

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