Equiparadoxicality of Yablo’s Paradox and the Liar

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.