The Liar An Essay on Truth and Circularity

by Barwise, Jon; Etchemendy, John

• ISBN13: 9780195059441
• ISBN10: 0195059441
• Edition: Reprint
• Format: Paperback
• Copyright: 1989-04-06
• Publisher: Oxford University Press

Summary

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.

Author Biography

Jon Barwise is Professor of Philsophy at Stanford University and Researcher at the Center for the Study of Language and Information John Etchemendy is Associate Professor of Philosophy at Stanford University and Researcher at the Center for the Study of Language and Information

Table of Contents

Introduction	p. 1
The Liar	p. 3
Some background
Diagnosing a paradox
Some basic decisions
Plan of the book
A budget of Liar-like paradoxes
Sentences, Statements, and Propositions	p. 26
Russellian propositions
Austinian statements and propositions
A formal language
The Universe of Hypersets	p. 34
Set theory from Z to A
AFA
The consistency of ZFC/AFA
Solving equations
Inductive and coinductive definitions
Russellian Propositions and the Liar	p. 59
Modeling Russellian Propositions	p. 61
Basic definitions
A Russellian semantics for L
Truth of Russellian Propositions	p. 75
Truth and the world
The T-schema and the world
Kripke's construction and other closure conditions
Witnessing functions
Paradoxical Russellian propositions
Consequences of the Russellian Account	p. 97
Further examples analyzed
The problem with the Russellian account
Sentences and Russellian Propositions	p. 106
Some proof theory
Paradoxical sentences
Austinian Propositions and the Liar	p. 119
Modeling Austinian Propositions	p. 121
Basic definitions
Truth of Austinian propositions
Austinian Propositions and the World	p. 129
Accessible Austinian propositions
Modeling the Austinian world
The T-schema in the Austinian world
An Austinian Semantics	p. 139
The Austinian semanties for L
T-closure for expressible propositions
Further examples reanalyzed
The Austinian Completeness Theorem
Relating the Russellian and Austinian Accounts	p. 154
The Liar as a diagonal argument
The Reflection Theorem
Characterizing paradoxical sentences
Negation and Denial	p. 164
Conclusions	p. 171
The proper treatment of paradox
Lessons for the skeptic
Bibliography	p. 179
Index	p. 181
Postscript	p. 187
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