Satan, Cantor and Infinity Mind-Boggling Puzzles

by Smullyan, Raymond M.

• ISBN13: 9780486470368
• ISBN10: 0486470369
• Format: Paperback
• Copyright: 2009-03-26
• Publisher: Dover Publications

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