Is Yablo's paradox Liar-like?

Abstract

The most obvious difference between Yablo's paradox and traditional versions of the Liar is that Yablo's paradox is generated by considering an infinite collection of sentences (So, S1, and for each n, Sn). If we restrict ourselves to a finite collection of the Sn, then no paradox arises. The upshot of this is that there is no first-order derivation of a contradiction from Yablo's premisses and the Tarski biconditionals. The second difference is that Yablo's paradox requires an infinite number of instances of the T-schema. With traditional versions of the Liar we only need to appeal to a finite number of instances of the T-schema. Yablo's paradox will not go through if we limit ourselves to only a finite number of such instances. Suppose otherwise, then there is a proof of a contradiction from the Yablo sentences and some finite subset of the Tbiconditionals for the Yablo sentences. Call this proof P.2 Since P mentions only a finite number of the T-biconditionals, there is a greatest number m such that P mentions the T-biconditional for Sm. Now consider a model in which for all n> m, the T-biconditional for Sn does not hold. (Note that in