Yablo’s Paradox and Russellian Propositions

Abstract

Is self-reference necessary for the production of Liar paradoxes? Yablo has given an argument that self-reference is not necessary. He hopes to show that the indexical apparatus of self-reference of the traditional Liar paradox can be avoided by appealing to a list, a consecutive sequence, of sentences correlated one-one with natural numbers. Yablo opens his “Paradox without Self-Reference” (Analysis, 1993) with the assumption that there is a sequence such that:

S_n : “(∀k )(k > n . → . ¬True ⌈S_k⌉)”

Each sentence on Yablo’s list is supposed to be correlated one-one with number n. Each sentence is supposed to say that for every natural number k greater than n, the k-th sentence on the list is not true. By comparing Yablo’s construction to an analogous construction with early Russellian propositions, we show that Yablo has failed to generate a paradox.