Forever Undecided
āļ.āļ. 2012 · Knopf
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Forever Undecided is the most challenging yet of Raymond Smullyanâs puzzle collections. It is, at the same time, an introductionâingenious, instructive, entertainingâto GÃķdelâs famous theorems.
               With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the nativesâ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventuresâincluding journeys into the âother possible worldsâ of Kripke semanticsâeven the most illogical of us come to understand GÃķdelâs two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like GÃķdel himself, must remain Forever Undecided!
               With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the nativesâ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventuresâincluding journeys into the âother possible worldsâ of Kripke semanticsâeven the most illogical of us come to understand GÃķdelâs two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like GÃķdel himself, must remain Forever Undecided!
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RAYMOND SMULLYAN, well-known mathematician and logician, is Oscar Ewing Professor of Philosophy at Indiana University and Professor Emeritus of The City University of New YorkâLehman College and Graduate Center. His many writings include four previous volumes of recreational logic and math problems, What Is The Name of This Book?, The Lady or the Tiger?, Alice in Puzzleland, and To Mock a Mockingbird; two studies of deductive logic in chess, The Chess Mysteries of Sherlock Holmes and The Chess Mysteries of the Arabian Knights; and three collections of philosophical essays and aphorisms, The Tao Is Silent, This Book Needs No Title,  and 5000 B.C.
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