TO MOCK A MOCKINGBIRD And Other Logic Puzzles

Few have mastered the art of writing with such deceptive simplicity about the fine points of logic, philosophy and mathematics as Smullyan. His mastery has earned him an enthusiastic horde of followers among those enamored of endless variations on the theme of truth-tellers vs. liar riddles; on the paradoxes of self-applying statements, and other such Carollian or Russelian mindplay. ""Mockingbird"" keeps their faith. The latest Smullyan collection goes beyond earlier works, however, to tackle some very tough propositions indeed. He warms up with the usual teasers designed to build confidence in the novice, e.g., what threeword question can you ask to determine if the individual you meet is John, given that he is one of three look-alike brothers and that John and James always lie while William always tells the truth? Too, there are the Smullyan trademarks: the ever-truthful knights and ever-prevaricating knaves--with some variations on day-knights and night-knights. And then, about half-way through, we reach the mockingbirds. Here novices may soon be over their heads for what the wily Smullyan has chosen to do is no less than to develop combinatorial logic--the stuff of a graduate course on logic. He puts propositions (the familiar p's and q's) into the form of birds and defines relations between them in terms of operations that allow bird A to mock the sound of bird B, etc. Those with some mathematical knowledge will see how Smullyan exploits various non-associative or non-commutative rules of operation, even elaborating a system that parallels one famous mathematician's axioms for establishing the natural number system. This is all set forth in bird talk. Perhaps the eager beaver or the toiling sparrow may follow these fancies; more likely, the artful hacker or artificial-intelligence theorist. Armchair amateurs may prefer to linger in the first half with its more accessible and always amusing mental fodder.