Forever Undecided

Forever Undecided : Puzzle Guide to Godel

4.06 (63 ratings by Goodreads)
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Description

This book provides an introduction to Kurt Godel's theorems through a collection of puzzles interspersed with an account of symbolic logic. Godel's argument has been transferred from the formal domain of mathematical systems in an attempt to make its essential ideas more accessible to the general reader. The primary emphasis is on belief systems and how they are related to systems of mathematics. This leads to the subject of possible world semantics which plays a role in computer science and artificial intelligence.show more

Product details

  • Paperback | 272 pages
  • 127 x 195.58 x 20.32mm | 181.44g
  • Oxford University Press
  • Oxford Paperbacks
  • Oxford, United Kingdom
  • English
  • 0192821962
  • 9780192821966

Table of contents

Part 1 You might be surprised: a diabolical puzzle; surprised. Part 2 The logic of lying and truth telling: the census taker; in search of Oona; an interplanetary tangle. Part 3 Knights, knaves and propositional logic: a bit of propositional logic; logical closure and consistency. Part 4 Let's be careful: paradoxical; the problem deepens. Part 5 The consistency predicament: logicians who reason about themselves; the conistency predicament; Godelian systems; more consistency predicaments. Part 6 Self-fulfilling beliefs and Lob's theorem: self-fulfilling beliefs; the Rajah's diamond; Lob's island. Part 7 In deeper waters: reasoners of type G; modesty, reflexivity and stability. Part 8 Can't decide: forever undecided; more indecisions. Part 9 Possible worlds: it ain't necessarily so; from necessity to provability. Part 10 The heart of the matter: a Godelized universe; some remarkable logic machines; modal systems self-applied. Part 11 Finale: modal systems, machines and reasoners; some strange reasoners; in retrospect.show more

Rating details

63 ratings
4.06 out of 5 stars
5 33% (21)
4 44% (28)
3 17% (11)
2 5% (3)
1 0% (0)
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