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.
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Book Description
Editorial Reviews
Review
"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
--This text refers to the Paperback edition.
About the Author
Jon Barwise is at Indiana University. John Etchemendy is at Stanford University.
--This text refers to the
Paperback
edition.
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1 of 12 people found the following review helpful:
4.0 out of 5 stars
Very good read.,
By GangstaLawya (TimBuckToo) - See all my reviews
This review is from: The Liar: An Essay on Truth and Circularity (Paperback)
Anyone at all familiar with epistemology will note the frustrating fact all of our categorical statements are subject to the self referential fallacy. For example, the relativist who asserts "All truth is relative" has just asserted a self defeating statement since he obviously wishes this statement to be the one exception. Afterall, if all truth is relative, so is the truth value of this statement, which henceforth is not true according to its own critieria. Of course, this isn't limited to formal statements which we assign as saying something about the world. Kurt Godel has shown that even statements whose extension is purely formal, and not empirical, contain paradox and pitfalls. The authors take their own knowledge in Symbolic Logic and attempt to look at these issues from a new angle. They don't merely repeat the same theses you see in other books and so the book is valuable for this reason. Merleau-Ponty, who was a follower of Heidegger, presented these issues in all their perplexity in his book "The Visible and the Invisible." In comparison, I prefer the analytic philosophical approach of the former over the phenomenological approach of the latter. However, both schools of thought are capable of giving profound insight on this topic of language and epistemological conundrums. Underlying all of these types of works, including this one, seems to be those continual debates that see no merits in the contravening philosophical position. Most noteworthy is the authors' failure to consider bibical theology as an intellecutal contribution to insights about the condition of human intelligence in a fallen world. For this reason, the book loses one star.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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reflection theorem, assertive liar, denial liar, tagged graph, propositional demonstratives, normal form sentences, semantical facts, witnessing function, expressible propositions, maximal models, circular propositions, weak model, coinductive definition, wellfounded sets, pretheoretic intuitions, very same proposition, descriptive conventions, determinate truth values, classical propositions, cumulative hierarchy, paradoxical propositions, sentence negation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Claire Has, Solution Lemma, The Universe of Hypersets, Truth of Russellian Propositions, Strengthened Liar, Modeling Russellian Propositions, Gupta's Puzzle, Closure Theorem, Gupta Puzzle, Consequences of the Russellian Account, Modeling Austinian Propositions, Strong Kleene, Open Problem, Contingent Liar, Sentential Model Existence Theorem, Löb's Paradox, Russellian Liar, Witnessing Condition Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
reflection theorem, assertive liar, denial liar, tagged graph, propositional demonstratives, normal form sentences, semantical facts, witnessing function, expressible propositions, maximal models, circular propositions, weak model, coinductive definition, wellfounded sets, pretheoretic intuitions, very same proposition, descriptive conventions, determinate truth values, classical propositions, cumulative hierarchy, paradoxical propositions, sentence negation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Claire Has, Solution Lemma, The Universe of Hypersets, Truth of Russellian Propositions, Strengthened Liar, Modeling Russellian Propositions, Gupta's Puzzle, Closure Theorem, Gupta Puzzle, Consequences of the Russellian Account, Modeling Austinian Propositions, Strong Kleene, Open Problem, Contingent Liar, Sentential Model Existence Theorem, Löb's Paradox, Russellian Liar, Witnessing Condition Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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