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Equiparadoxicality of Yablo’s Paradox and the Liar

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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.

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Correspondence to Ming Hsiung.

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This work was supported by the National Social Science Foundation of China (project number 10CZX036) and the Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (project number WYM08064).

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Hsiung, M. Equiparadoxicality of Yablo’s Paradox and the Liar. J of Log Lang and Inf 22, 23–31 (2013). https://doi.org/10.1007/s10849-012-9166-0

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