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The Liar : An Essay on Truth and Circularity - Jon Barwise

The Liar

An Essay on Truth and Circularity

Paperback Published: 6th April 1989
ISBN: 9780195059441
Number Of Pages: 208

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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.

"A splendid book. [The authors] have striking new ideas and material. These they have thought through deftly and masterfully....This is a book to seize the philosophical imagination."--Mind "We see from The Liar that the paradoxes are still a source of inspiration and logic. The book is a new, exciting contribution to the study of truth....It can be read not only as a contribution to the philosophy of language, but also as an interesting application of a theory of sets. It contains interesting theorems and in turn it will stimulate purely mathematical work."--Larry Moss, Bulletin of the American Math Society "Exploiting Peter Aczel's theory of 'hypersets'...the authors propose an interesting new solution to the liar paradox....The Liar is a significant addition to the recent best literature on the paradox."--Choice "The work grew out of research aimed at drawing up a mathematically rigorous account of language, so that computers can understand human speech....In their book the two logicians put forward a theory of language that includes explicitly some of the 'contextual parameters' so far left out of logic, but now shown to be crucial to understanding."--London Times "This delightful book is a self-contained account of the Liar paradox, complete with a formal syntax and proof theory, semantics and proofs of the theorems. It should be of interest to more than just Liar specialists, however, because of the new semantic techniques it introduces."--The Canadian Philosophical Reviews "A splendid book. [The authors] have striking new ideas and material. These they have thought through deftly and masterfully....This is a book to seize the philosophical imagination."--Mind "We see from The Liar that the paradoxes are still a source of inspiration and logic. The book is a new, exciting contribution to the study of truth....It can be read not only as a contribution to the philosophy of language, but also as an interesting application of a theory of sets. It contains interesting theorems and in turn it will stimulate purely mathematical work."--Larry Moss, Bulletin of the American Math Society "Exploiting Peter Aczel's theory of 'hypersets'...the authors propose an interesting new solution to the liar paradox....The Liar is a significant addition to the recent best literature on the paradox."--Choice "The work grew out of research aimed at drawing up a mathematically rigorous account of language, so that computers can understand human speech....In their book the two logicians put forward a theory of language that includes explicitly some of the 'contextual parameters' so far left out of logic, but now shown to be crucial to understanding."--London Times "This delightful book is a self-contained account of the Liar paradox, complete with a formal syntax and proof theory, semantics and proofs of the theorems. It should be of interest to more than just Liar specialists, however, because of the new semantic techniques it introduces."--The Canadian Philosophical Reviews "Remarkably fruitful, resulting in a theory that is deeply insightful and highly creative, both philosophically and mathematically....An interesting and valuable contribution--The Philosophical Review "B. & E. have shown great skill and inventiveness which deserves and will surely receive, expert mathematical discussion."--NOUS "Some interesting work of the Stanford based logicians Jon Barwise and John Etchemendy has thrown considerable light on to [the] vexing problem of [paradoxes]."--The Guardian "Precise and elegant. . . .The book does what it does superbly. It is very well organized, has just the right amount of detail, and is written in a style that is easy to read, even in very technical contexts. Reading it is genuinely enjoyable." --Journal of Symbolic Logic

Introductionp. 1
The Liarp. 3
Some background
Diagnosing a paradox
Some basic decisions
Plan of the book
A budget of Liar-like paradoxes
Sentences, Statements, and Propositionsp. 26
Russellian propositions
Austinian statements and propositions
A formal language
The Universe of Hypersetsp. 34
Set theory from Z to A
AFA
The consistency of ZFC/AFA
Solving equations
Inductive and coinductive definitions
Russellian Propositions and the Liarp. 59
Modeling Russellian Propositionsp. 61
Basic definitions
A Russellian semantics for L
Truth of Russellian Propositionsp. 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 Accountp. 97
Further examples analyzed
The problem with the Russellian account
Sentences and Russellian Propositionsp. 106
Some proof theory
Paradoxical sentences
Austinian Propositions and the Liarp. 119
Modeling Austinian Propositionsp. 121
Basic definitions
Truth of Austinian propositions
Austinian Propositions and the Worldp. 129
Accessible Austinian propositions
Modeling the Austinian world
The T-schema in the Austinian world
An Austinian Semanticsp. 139
The Austinian semanties for L
T-closure for expressible propositions
Further examples reanalyzed
The Austinian Completeness Theorem
Relating the Russellian and Austinian Accountsp. 154
The Liar as a diagonal argument
The Reflection Theorem
Characterizing paradoxical sentences
Negation and Denialp. 164
Conclusionsp. 171
The proper treatment of paradox
Lessons for the skeptic
Bibliographyp. 179
Indexp. 181
Postscriptp. 187
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780195059441
ISBN-10: 0195059441
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 208
Published: 6th April 1989
Country of Publication: US
Dimensions (cm): 20.83 x 13.95  x 1.42
Weight (kg): 0.25