Paradox without satisfaction

Abstract

According to Stephen Yablo, the above list generates a liar-like paradox without circularity (see Yablo 1985 and 1993). After all, in contrast with the usual liar paradox, no sentence in the Yablo list refers to itself, and as opposed to well-known liar cycles,1 no sentence refers to sentences above it in the list. However, similarly to the (usual or cyclic) liar, a contradiction is derivable from the list. But is Yablo’s paradox really non-circular? To this question, Graham Priest gave a surprising answer. In his view, despite initial appearances, the paradox is circular (Priest 1997). After all, if the formulation of the paradox doesn’t seem to involve circularity, the argument to contradiction definitely does. As Priest argued, Yablo’s paradox has ‘a fixed point ... of exactly the same self-referential kind as in the liar paradox’. As a result, ‘the circularity is ... manifest’ (Priest 1997: 238).2 In this paper, we challenge Priest’s answer – in a new way. To the best of our knowledge, everyone in the debate has conceded the adequacy of Priest’s reconstruction of the argument to contradiction. We point out a limitation that hasn’t been noted. Priest’s argument requires the existence of a satisfaction relation that plays the role of a fixed point in Yablo’s