Center for the Study of Language and Information, Sep 15, 2006 - Computers - 190 pages
An anthology of previously unpublished essays from some of the most outstanding scholars working in philosophy, mathematics, and computer science today, Self-Reference reexamines the latest theories of self-reference, including those that attempt to explain and resolve the semantic and set-theoretic paradoxes. With a thorough introduction that contextualizes the subject for students, this book will be important reading for anyone interested in the general area of self-reference and philosophy.
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Fixed Point Constructions
Bilattices are Nice Things
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apply arbitrary argument Berry's paradox closed term combinatory logic conflation conservative consider consistent construction contains context contradiction definable diagonal lemma dialetheic disquotational disquotationalist equivalent example exist expression extension extensionality fact Feferman finite definitions first-order arithmetic formal formula function GLF-stable valuation Godel ground model Hence hierarchy hypothesis inconsistent induction axioms inductive definition infinitary interpreted languages Kleene's strong three-valued Kripke Kripke's lambda language of arithmetic lattice least number liar paradox liar sentence mathematical means Naive Comprehension naive set theory natural number negation notion of truth Op-Ext paradoxes of denotation Peano Arithmetic Perlis positive inductive definition pre-bilattice problem proof provable prove recursively refer reflexive result revision sequence Russell set Russell's paradox schema self-reference self-referential semantic paradoxes set theory solution strong three-valued logic superdiagonalizer T-schema T)-sentences Tarski's theorem theory of truth things three-valued logic true iff truth predicate truth revision operator truth values Yablo