Journal of Logic, Language and Information

, Volume 22, Issue 1, pp 23–31

Equiparadoxicality of Yablo’s Paradox and the Liar

Authors

    • School of Politics and AdministrationSouth China Normal University
Article

DOI: 10.1007/s10849-012-9166-0

Cite this article as:
Hsiung, M. J of Log Lang and Inf (2013) 22: 23. doi:10.1007/s10849-012-9166-0

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

CircularityEquiparadoxicalLiar paradoxT-schemaYablo’s paradox
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Copyright information

© Springer Science+Business Media Dordrecht 2012