Forever Undecided

Forever Undecided : A Puzzle Guide to Godel

4.03 (56 ratings by Goodreads)
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Description

A challenging puzzle collection and an instructive and entertaining introduction to Kurt Godel's famous theorems, including incompleteness and undecidability. Much of the action of the book takes place on an imaginary and magical island, the Island of Knights and Knaves, where knights always make true statements, knaves always make false statements, and every inhabitant is either a knight or a knave. Here we meet an amazing array of characters, visitors to the island, seeking to determine the natives' true identities. Among them are the census-taker McGregor; a philosopher-logician in search of his flighty bird-wife Oona; and a regiment of Reasoners. 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 should come to understand Godel's theorems, some of their philosophical and mathematical implications and why we, like Godel himself, must remain forever undecided! The book is intended for puzzle fans of every age and ability - from the high-school whizz to the seasoned mathematician, logician or computer scientist.show more

Product details

  • Paperback | 272 pages
  • 129 x 196mm | 221g
  • Oxford University Press
  • Oxford Paperbacks
  • Oxford, United Kingdom
  • New edition
  • New edition
  • 0192801414
  • 9780192801418

Table of contents

Part I - You Might Be Surprized. 1: A Diabolical Puzzle. 2: Surprised?. Part II - The Logic of Lying and Truth Telling. 3: The Census Taker. 4: In Search of Oona. 5: An Interplanetary Tangle. Part III - Knights, Knaves, and Propositional Logic. 6: A Bit of Propositional Logic. 7: Knights, Knaves, and Propositional Logic. 8: Logical Closure and Consistency. Part IV - Let's Be Careful. 9: Paradoxical?. 10: The Problem Deepens. Part V - The Consistency Predicament. 11: Logicians Who Reason About Themselves. 12: The Consistency Predicament. 13: Godelian Systems. 14: More Consistency Problems. Part VI - Self-fulfilling Beliefs and Lob's Theorem. 15: Self-fulfilling beliefs. 16: The Rajah's Diamond. 17: Lob's Island. Part VII - In Deeper Waters. 18: Reasoners of Type G. 19: Modesty, Reflexivity, and Stability. Part VIII - Can't Decide!. 20: Forever Undecided. 21: More Indecisions. Part IX - Possible Worlds. 22: It Ain't Necessarily So. 23: Possible Worlds. 24: From Necessity to Provability. Part IX - Possible Worlds. 22: It Ain't Necessarily So Universe. 26: SOme Remarkable Logic Machines. 27: Modal Systems Self-Applied. Part XI - Finale. 28: Modal Systems, Machines, and Reasoners. 29: Some Strange Reasoners!. 30: In Retrospectshow more

Rating details

56 ratings
4.03 out of 5 stars
5 32% (18)
4 45% (25)
3 18% (10)
2 5% (3)
1 0% (0)
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