Is Yablo's Paradox Self-Referential?

The article addresses the question whether Yablo's paradox is self-referential or not. Yablo himself claimed that the paradox is free from self-reference. Priest challenged this claim by showing that a self-referential predicate must be used both in the description of paradoxical sentences and in deriving contradiction from them. Some objected to Priest. Bueno and Colyvan suggested a derivation of contradiction that allegedly makes no use of Priest's self-referential predicate. Yablo modified paradoxical sentences intending to preclude the circular reading thereof. The author examines those replies and argues that they are both erroneous, since (a) Bueno and Colyvan's derivation is incomplete, and (b) Yablo's modification of his paradox remains subject to the circular reading. He concludes that, from the formal point of view, the paradox is self-referential in the sense that there is no way to present paradoxical sentences and to derive contradiction from them without using circular devices like Priest's predicate. The author also examines Sorensen's informal argument advocating the view that Yablo's paradox is free of self-reference and Beall's informal argument in favor of the opposite view. The result is that none of these arguments achieves its goal but they jointly show that there is no definitive informal solution to the problem.

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