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. If you think all mathematical infinities add up to the same, or have the same properties, you'd be wrong. But how can this be proved?
Smullyan ends the book with a story of one of Cantor's students outsmarting Satan, relying on language and set theory to confuse the naming of a set in a clever bargain.
The book is a wonderful romp through logic, set theory, and rational thinking. It is not a simple book -- there are a number of places where equations and symbol logic methods are used; having at least a basic knowledge of algebra and elementary logic will make this book much more fun and accessible. However, many of the puzzles rely on common sense kinds of logic.
It is quite fun. Don't be a knave; read this book.
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