, Volume 22, Issue 1, pp 23-31
Date: 05 Oct 2012

Equiparadoxicality of Yablo’s Paradox and the Liar

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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.