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.
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: 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.
"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
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