The many faces of the Liar Paradox

Abstract

The Liar Paradox is a classic argument that creates a contradiction by reflection on a sentence that attributes falsity to itself: ‘this sentence is false’. In our paper we will discuss the ways in which the Liar sentence (and its paradoxical argument) can be represented in first-order logic. The key to the representation is to use first-order logic to model a self-referential language. We will also discuss several related sentences, like the Liar cycles, the empirical versions of the Liar and the Truth teller sentences.