Yablo's Paradox: Is the Infinite Liar Lying to Us?

Abstract

In 1993, the American logic S. Yablo was proposed an original infinitive formulation of the classical «Liar» paradox. It questioned the traditional notion of self-reference as the basic structure for semantic paradoxes. The article considers the arguments underlying two different approaches to analysis of proposals of the «Infinite Liar» and understanding of the genuine sources for semantic paradoxes. The first approach (V. Valpola, G.-H. von Wright, T. Bolander, etc.) imposes responsibility for the emergence of semantic paradoxes on the negation of the truth predicate. It deprives the «Infinite Liar» sentences of consistent truth values. The second approach is based on a modified version of anaphoric prosententialism (D. Grover, R. Brandom, etc.). The concepts of truth and falsehood are treated as special anaphoric operators. Logical constructs similar to the «Infinite Liar» do not attribute any definite truth values to sentences from which they are composed, but only state certain types of relations between the semantic content of such sentences.