Revenge of the liar

Revenge of the liar: New essays on the paradox. Ed. by JC Beall. Oxford: Oxford University Press, 2007. Pp. 296. ISBN 9780199233908. $49.95.

Reviewed by Caroline Gagné, Université Laval

Are sentences spoken by a liar true or false? One suggestion would be to consider them to be a part of a category beyond truth and falsity; however, this beckons the revenge of the liar: dealing with a liar creates another one. The liar paradox also raises questions about logic, language, truth, and semantics. In this volume, fourteen experts focus on the nature of liar paradox from a logical perspective.

In Ch. 1, JC Beall presents the background of the liar and his revenge, focusing on the truth, the liar and the revenge phenomenon, and the revengers’ revenge. In Ch. 2, Roy T. Cook asserts that the concept of language is indefinitely extendable because of the revenge phenomenon. In this perspective, the semantic values of language should be indefinitely extendable as well.

In Ch. 3, Matti Eklund studies general theses that are related to the liar phenomenon, focusing primarily on inexpressibility and weak universality. In Ch. 4, Hartry Field presents his theory of truth, which concerns received wisdoms about revenge. Thomas Hofweber, in Ch. 5, advances the idea that strict reading and generic reading are both valid senses of an inference rule ‘just if truth-preserving’ (15). This distinction may resolve the revenge phenomenon by viewing the rules as generically valid.

In Ch. 6, Hannes Leitgeb discusses Field’s theory (presented in Ch. 4) and proposes two metatheories—one classical and one nonclassical—to explore Field’s theory of truth. Leitgeb’s theory shares Field’s logic. In Ch. 7, Tim Maudlin maintains that normative principles of assertion can be learned from the revenge phenomenon. He argues for three semantic categories: truth, falsity, and ungroundedness.

In Ch. 8, Douglas Patterson proposes an inconsistency view of the semantic paradoxes in English. For Patterson, understanding a language is a relation to a false theory. Graham Priest (Ch. 9) focuses on a characterization of the liar’s revenge, a discussion of Field’s theory, and the background of Zermelo-Frankel set theory, which meets a revenge-like situation.

Agustin Rayo and P. D. Welch (Ch. 10) advance that Field’s theory of truth is not really revenge-free. In Ch. 11, Stephen Read discusses Thomas Bradwardine’s (a physicist and theologian in the 1300s) theory of truth. Greg Restall (Ch. 12) examines the costs of using nonclassical solutions to solve the paradoxes of self-reference.

In Ch. 13, Kevin Scharp argues that the liar’s revenge shows that truth is an inconsistent concept. In Ch. 14, Stewart Shapiro maintains that the Burali-Forti’s paradox has its own revenge issues and discusses the ways to deal with them. In Ch. 15, Keith Simmons demonstrates the difference between direct revenge and second-order revenge and presents his theory that may resolve second-order revenge.

This book will be useful to anyone working in truth studies, philosophical logic, and philosophy of language, or for those interested in formal semantics and metaphysics.