Equiparadoxicality of Yablo's Paradox and the Liar

Authors
Ming Hsiung
Zhongshan University
Abstract
It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition
Keywords Circularity  Equiparadoxical  Liar paradox  T-schema  Yablo’s paradox
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DOI 10.1007/s10849-012-9166-0
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References found in this work BETA

Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
What Truth Depends On.Hannes Leitgeb - 2004 - Journal of Philosophical Logic 34 (2):155-192.
Yablo’s Paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.
Patterns of Paradox.Roy T. Cook - 2004 - Journal of Symbolic Logic 69 (3):767-774.
Yablo's Paradox and Ω-Inconsistency.Jeffrey Ketland - 2005 - Synthese 145 (3):295-302.

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Citations of this work BETA

Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - forthcoming - Journal of Philosophical Logic:1-9.
Tarski's Theorem and Liar-Like Paradoxes.Ming Hsiung - 2014 - Logic Journal of the IGPL 22 (1):24-38.

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