ALICE IN PUZZLE-LAND: A Carrollian Tale for Children Under Eighty

Raymond Smullyan's fast-growing reputation as a puzzler/philosopher/logician is not diminished by this latest collection, following on the heels of the exemplary The Lady or the Tiger? (p. 405). Lewis Carroll he is not, however, despite Martin Gardner's enthusiastic introduction. Instead, Smullyan has used the occasions and characters of both Wonderland and Looking Glass, along with a real-life Alice, as foils for a variety of logical, ""metalogical,"" and arithmetical puzzles and paradoxes. Characteristically, he begins with piece-of-cake samples to provide ego gratification for novices or the young, and builds to such heights as ""The King of Clubs believes that the Queen of Clubs believes that the King of Clubs believes that the Queen of Clubs is mad"" (given that mad people believe that everything false is true, and sane people are one hundred percent accurate in their beliefs). Of some philosophical interest axe Smullyan's resolutions of such well-known paradoxes as ""Epimenides the Cretan says that all Cretans are liars""--and the one about the town barber who shaves everyone who doesn't shave himself, and never shaves anyone who does shave himself. Smullyan finds them fallacious paradoxes, and then comes up with a corker that he has Humpty Dumpty propose: ""You do not know and never will know that I am a knight"" (in a kingdom where knights are always truthful, and knaves always liars). Smullyan's analysis there, and in a later chapter on looking-glass logic, has a sophistication that should please professionals. The answers and proofs, as always, are commendably lucid (and conveniently numbered for easy access by the exasperated). More tricky fun for fans.