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.

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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