The Gödelian Puzzle Book Puzzles, Paradoxes and Proofs

by Smullyan, Raymond M.

• ISBN13: 9780486497051
• ISBN10: 0486497054
• Format: Paperback
• Copyright: 2013-09-19
• Publisher: Dover Publications

Summary

These recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Written by a distinguished mathematician and creator of numerous popular puzzle books, this volume requires no background in formal logic and will delight readers of all ages.

Author Biography

Raymond Smullyan received his PhD from Princeton University and taught at Dartmouth, Princeton, Indiana University, and New York's Lehman College. Best known for his mathematical and creative logic puzzles and games, he was also a concert pianist and a magician. He wrote over a dozen books of logic puzzles and texts on mathematical logic.

 

Raymond Smullyan: The Merry Prankster
Raymond Smullyan (1919–2017), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was First-Order Logic (1995). Recent years have brought a number of his magical books of logic and math puzzles: The Lady or the Tiger (2009); Satan, Cantor and Infinity (2009); an original, never-before-published collection, King Arthur in Search of His Dog and Other Curious Puzzles (2010); and Set Theory and the Continuum Problem (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years.

In the Author's Own Words:
"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini."

"Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.'" — Raymond Smullyan

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