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"Forever Undecided" is the most challenging yet of Raymond Smullyan's puzzle collections. It is, at the same time, an introduction--ingenious, instructive, entertaining--to Godel's 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 natives' 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 adventures--including journeys into the "other possible worlds" of Kripke semantics--even the most illogical of us come to understand Godel's two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Godel himself, must remain Forever Undecided… (més)
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This book is intended for those who would enjoy understanding the Gödel incompleteness without absorbing the usual symbolic abstractions used in mathematical logic. Instead, it frames the buildup as social puzzles involving people who lie or tell the truth under various conditions, and what you can therefore believe based on what they say. This is not to say that the material does not have its challenges, but it allows a broader audience of people with the ability to understand logic problems/puzzles to grapple with the material, i.e. it makes parts of the formal theory concrete enough that someone with more mathematical talent than training could enjoy them. ( )
Informació del coneixement compartit en anglès.Modifica-la per localitzar-la a la teva llengua.
Dedicated to All Consistent Reasoners Who Can Never Know That They Are Consistent
Primeres paraules
Informació del coneixement compartit en anglès.Modifica-la per localitzar-la a la teva llengua.
Is it possible for a rational human being to be in a position in which he cannot believe that he is consistent without losing his consistency in the process?
I believe that the following puzzle may well be the most diabolical puzzle ever invented (and if it is, I proudly take credit for the invention).
Citacions
Darreres paraules
Informació del coneixement compartit en anglès.Modifica-la per localitzar-la a la teva llengua.
To which Boolos has aptly replied: "If modern modal logic was conceived in sin, then it has been redeemed through Gödliness."
"Forever Undecided" is the most challenging yet of Raymond Smullyan's puzzle collections. It is, at the same time, an introduction--ingenious, instructive, entertaining--to Godel's 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 natives' 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 adventures--including journeys into the "other possible worlds" of Kripke semantics--even the most illogical of us come to understand Godel's two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Godel himself, must remain Forever Undecided
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