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The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs

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The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic is necessary.

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

Product Details

ISBN:
9780486497051
Author:
Smullyan, Raymond M.
Publisher:
Dover Publications
Subject:
Recreations & Games
Subject:
recreational math
Subject:
Logic puzzles
Subject:
Paradoxes
Subject:
Mathematics-Games and Puzzles
Copyright:
Edition Description:
Trade Paper
Publication Date:
20130931
Binding:
TRADE PAPER
Language:
English
Pages:
288
Dimensions:
8.5 x 5.38 in

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Related Subjects

Health and Self-Help » Self-Help » General
Hobbies, Crafts, and Leisure » Games » General
Hobbies, Crafts, and Leisure » Games » General Puzzles
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Games and Puzzles
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Popular Surveys and Recreational

The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs New Trade Paper
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Product details 288 pages Dover Publications - English 9780486497051 Reviews:
"Synopsis" by ,
These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic is necessary.
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