The Liar An Essay on Truth and Circularity

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct
conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the Russellian conception of the relation between sentences, propositions, and truth is
crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of
model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics.

This monograph purports to provide a solution to semantical paradoxes like the Liar. The authors base this solution on J. L. Austin's idea of truth, which is fundamental to situation semantics. They compare two models of language, propositions and truth, one based on Russell and the other on Austin, as they bear on the Liar Paradox. In Russell's view, a sentence expresses a proposition, which is true or not. According to Austin, however, there is always a contextual parameter - the situation the sentence is about - that comes between the sentence and proposition. The Austinian perspective proves to have fruitful applications to the analysis of semantic paradox. The authors show that, on this account, the liar is a genuine diagonal argument. This argument can be shown to have profound consequences for our understanding of some of the most basic semantical mechanisms at work in our language. Jon Barwise is, with John Perry, a co-founder of the Centre for the Study of Language and Information at Stanford.

INTRODUCTION: The Liar; Sentences, statements, and Propositions; The universe of hypersets; RUSSELLIAN PROPOSITIONS AND THE LIAR: Modeling Russellian propositions; Truth of Russellian propositions; Consequences of the Russellian account; Sentences and Russellian propositions; AUSTINIAN PROPOSITIONS AND THE LIAR: Modeling Austinian propositions; Austinian propositions and the world; An Austinian semantics; Relating the Russellian and Austinian accounts; Negation and denial; Conclusions; Bibliography; Index.