The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs - Brossura

Smullyan, Raymond M.

Brossura

ISBN 10: 0486497054 ISBN 13: 9780486497051

Casa editrice: Dover Pubns, 2013

Riassunto

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.

Su questo libro

L'autore:

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

Contenuti:

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

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2013
• ISBN 10: 0486497054
• ISBN 13: 9780486497051
• Rilegatura: Copertina flessibile
• Numero di pagine: 267