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Satan, Cantor and Infinity: Mind-Boggling Puzzlesby Raymond M. Smullyan
Synopses & Reviews
A clear-headed command of logic can make the mind powerful enough to outmaneuver the devil himself, according to these intriguing stories. More than 200 puzzles, problems, and paradoxes await within these pages, woven together by a wizard's captivating narrative. The Sorcerer — so skilled in the art of logic that his reasoning seems like magic — takes a puzzle-based perspective on the principles underlying the works of mathematician Georg Cantor. His fascinating riddles involve probability, certainty, time, and infinity, and they unfold amid a landscape populated by honorable knights, lying knaves, quick-witted robots, and other fanciful characters.
Amusing and enlightening, the Sorcerer's guided tour of infinity is geared toward the most dedicated puzzle-solvers. Although many of the solutions require only common sense, equations appear in several of the stories, and a familiarity with algebra is essential. The author of several imaginative books on recreational mathematics, Raymond Smullyan is a well-known mathematician and logician. He provides solutions within text, rather than at the end or in footnotes, offering readers a natural progression on a puzzle-filled path through the wonders of logic.
A renowned mathematician tells stories of knights and knaves in an entertaining look at the logical precepts behind infinity, probability, time, and change. Complete solutions appear within the narrative of the text.
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 teach readers to apply logical precepts to issues of infinity, probability, time, and change. Complete solutions appear within the narrative of the text.
About the Author
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
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
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!
The Continuum Problem
PART VII. HYPERGAME, PARADOXES, AND A STORY
Satan, Cantor, and Infinity
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