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Satan, Cantor, And Infinity and Other Mind-Boggling Puzzles Hardcover – November 24, 1992

by
Raymond M. Smullyan (Author)
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Raymond M. Smullyan (Author)
5 out of 5 stars 6 customer reviews
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Product Details

  • Hardcover: 270 pages
  • Publisher: Knopf (November 24, 1992)
  • Language: English
  • ISBN-10: 0679406883
  • ISBN-13: 978-0679406884
  • Product Dimensions: 1 x 6 x 8.5 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #1,394,699 in Books (See Top 100 in Books)

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10 of 10 people found the following review helpful
To tell the truth...
By FrKurt Messick HALL OF FAMEVINE VOICE on July 17, 2004
Format: Hardcover
Raymond Smullyan has been described (by Martin Gardner, no less) as the most entertaining logician ever (lets leave aside the lack of competition here -- after all, Kurt Godel wasn't known to be a bundle of laughs, etc. ...). One of the points of logic is to figure out what lines of reasoning make sense, and what can be considered true and false, given the proper rules of rational thought and the right information.
This can be done by means of equations, symbolic expressions and linguistic tools, but this can be rather dry. A much more enjoyable means of learning to apply logical principles is through the kinds of puzzles presented by Smullyan. It is somewhat ironic -- story problems are the point of greatest dread among many mathematics students, yet the logic-equivalent of story problems are the most fun!
Smullyan has written several books on logic puzzles, and often starts with the device of puzzles with figuring out who is telling the truth and who is lying -- here it starts on the island of Knights and Knaves, where Knights always tell the truth, and Knaves always tell lies. However, apart from this distinction, it is impossible to tell them apart. Smullyan presents the problems, and then presents the solutions, not in the back of the book or in a footnote, but as part of the narrative. It is a very natural and logical progression.
In this logic-puzzle-story, Smullyan introduces the Sorcerer, not really a magician, but someone so skilled in logical thought that he is considered a magical figure. He leads the path across the novel, including what Smullyan describes as a 'guided tour of infinity' -- it is here that Cantor (from the title, the mathematician George Cantor) is brought up. If you think all infinities are equal, guess again.Read more ›
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5 of 5 people found the following review helpful
Satan, Cantor, and Infinity - a novel about set theory
By A Customer on December 6, 2001
Format: Hardcover
Professor Smullyan's book Satan, Cantor, and Infinity, is an excellent mathematical novel, extremely readable for everybody from elementary schoolboys(girls) to first class college (university) students. The story concerns three major personalities - The Sorcerer living in the Knight-Knave Island and Princess Annabelle with her suitor. As in many books of professor Smullyan the first half of the story is devoted to various puzzles about knights (truth-tellers) and knaves (liars). The third chapter takes place on the island of robots. The puzzles of self-constructive and self-destructive robots throw light on problem of languages, which allow self-reference, and the famous Gödel's theorems. This chapter may be harder to catch and the reader is recommended to consult another professor Smullyan's book, Forever Undecided. In the rest of the book are introduced Zeno's paradoxes concerning the problem of continuity and change (with these paradoxes are discussed the most elementary ideas of infinitesimal calculus), envelope paradox (a kind of paradox of rationality), ant the set-theoretic paradoxes (Burry's paradox, Mannoury's paradox, Russell's paradox and Cantor's paradox). The basic ideas of set theory are introduced in the form of problems of a prisoner in the Hell - Satan gives the prisoner opportunity to save himself(herself) if he(she) puzzles out an integer which Satan wrote on the paper closed in an envelope. Story also introduces the famous Continuum problem - the set theoretic problem formulated by the founder of set theory Georg Cantor in the 19th century and unsolved to our times (or at least unsolved by the more modest set theoretic principles not using some hypotheses concerning large cardinals).Read more ›
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4 of 4 people found the following review helpful
Perhaps Smullyan's best
By A Customer on April 22, 2002
Format: Hardcover
A highly enjoyable book of mathematical puzzles and ideas. Overall I think this is the best of the books by Smullyan I have seen, as the narrative (hardly a story, but a narrative of discussions which introduce and explain ideas) is very readable. Smullyan uses this technique in several other books but often one gets a sense that there is only a little narrative to connect much hard stuff - here the maths is interwoven into the narrative in a way that makes it much easier to follow (for example, the characters make various comments and objections which the central character, the Sorcerer, responds to as if engaged in an informal tutorial).
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