The Liar:An Essay on Truth and CircularityBringing 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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actual situation Aczel's atomic sentences Austinian account Austinian propositions axiom of foundation basic Chapter circular claims Claire Coalgebra coherence conditions coherent conception consider constituent containing define depicted determinate truth values dom(w equations example Exercise expressible propositions F-closure falsity fixed point hypersets indeterminates intuitions involved Kripke Kripke's language least fixed point Liar cycle Liar paradox Liar proposition Liar sentence logic maximal models node nonwellfounded normal form sentences notion numbers p₁ parameter Peter Aczel PrePROP proof proof theory PROP proper class propo proposition expressed real situations refer Reflection Theorem relation Russellian account Russellian model Russellian propositions satisfying semantical facts semantically closed sentences express set theory set-theoretic simply sition Solution Lemma statement subset T-closed T-schema Tarski's tences three of clubs tions transitive closure treatment true proposition True(this truth value Truth-teller wellfounded ZFC/AFA