The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs

Overview

These brand-new recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.
The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious ...
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The The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs Gödelian Puzzle Book

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Overview

These brand-new recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.
The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.
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Product Details

  • ISBN-13: 9780486497051
  • Publisher: Dover Publications
  • Publication date: 8/21/2013
  • Pages: 240
  • Sales rank: 310,882
  • Product dimensions: 5.30 (w) x 8.40 (h) x 0.70 (d)

Table of Contents


Part I Puzzles, Paradoxes, Infinity and other Curiosities
I A Chatty Personal Introduction
II Some Curious Adventures
III The Strange Island of Musica
IV Four Metapuzzles
V Certified Knights and Knaves
VI Paradoxical?
VII Infinity and Induction
VIII Introducing Self-Reference
IX Fixed Point Puzzles
X Some Curious Systems
XI How to Stump a Decision Machine
XII Some Additional Godelian Puzzles
 
Part II
XIII Truth and Provability
XIV Syntactic Incompleteness Theorems
XV Provability in Stages
XVI Formal Systems and Recursion
XVII Incompleteness and Undecidability
XVIII First-Order Arithmetic
XIX Arithmetic Truth is Not Formalizable 
XX The Incompleteness of Peano Arithmetic
References
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