Forever Undecided

March 1, 1987
In these mathematical and logic puzzles, truth-telling knights battle lying knaves; a philosopher-logician named George falls in love with Oona, flighty bird-girl of the South Pacific; Inspector Craig and timid, conceited or modest reasoners match wits. Using such fictional enticements, the author of What Is the Name of This Book? and To Mock a Mockingbird steers us through the logical thickets of Kurt Godel's famous Incompleteness Theorem, which holds that mathematical systems can never prove their own consistency. Readers who make it halfway through this book will learn more symbolic logic than a college freshman stuffed with "new math.'' In the second half, the deeper waters of modal logic are navigated. This field, which dates back to Aristotle, impinges on current debates in computer science and artificial intelligence. Smullyan's gift is to make complex ideas both accessible and enjoyable to the persevering reader.

February 1, 1987
Godel's incompleteness theorem is generally considered to have shown that formal number systems cannot prove their own consistency. Through a series of problems and solutions ("On the Island of Knights and Knaves, knights always make true statements and knaves always make false statements, and every inhabitant is either a knight or a knave . . . ") that are converted to symbolic logic, Smullyan progresses from an elementary to an advanced consideration of Godel's theorem. Apart from a few remarks at book's end, Smullyan makes no attempt to show what bearing Godel's results might have on more general, particularly epistemological, problems. Serious students of logic, computer theory, and artificial intelligence should find this entertaining and instructive, but it cannot be recommended for a larger audience. Leon H. Brody, U.S. Office of Personnel Management Lib., Washington, D.C.

Copyright 1987 Library Journal, LLC Used with permission.