Satan, Cantor and Infinity Mind-Boggling Puzzles
by Smullyan, Raymond M.Format: Paperback
Pub. Date: 2009-03-26
Publisher(s): Dover Publications
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Summary
Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions.
Author Biography
Born in New York City in 1919, Raymond Smullyan is a philosopher and magician as well as a famous mathematician and logician. His career as a stage magician financed his undergraduate studies at the University of Chicago as well his doctoral work at Princeton. The author of several imaginative books on recreational mathematics, Smullyan is also a classical pianist.
Raymond Smullyan: The Merry Prankster
Raymond Smullyan (1919– ), 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
Critical Acclaim for The Lady or the Tiger:
"Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived." — Martin Gardner
Table of Contents
Preface
PART I. LOGICAL SORCERY
The Lie Detective
When I Was a Boy
The Abduction of Annabelle
How Kazir Won His Wife
A Plague of Lies
On the Other Hand
The Island of Partial Silence
PART II. PUZZLES AND METAPUZZLES
Memories of the Sorcerer's Uncle
The Planet Og
Metapuzzles
PART III. SELF-REPRODUCING ROBOTS
The Island of Robots
The Quaint System of Professor Quincy
From the Ridiculous to the Simple
PART IV. GÖDELIAN PUZZLES
Self-Reference and Cross-Reference
The Sorcerer's Miniature Gödelian Language
PART V. HOW CAN THESE THINGS BE?
Something to Think About!
Of Time and Change
PART IV. A JOURNEY INTO INFINITY
What Is Infinity?
Cantor's Fundamental Discovery
But Some Paradoxes Arise!
Resolutions
The Continuum Problem
PART VII. HYPERGAME, PARADOXES, AND A STORY
Hypergame
Paradoxical?
Satan, Cantor, and Infinity
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