Forever Undecided - Softcover

Raymond Smullyan

Softcover

ISBN 10: 0192801414 ISBN 13: 9780192801418

Publisher: Oxford University Press, 2000

Synopsis

A challenging puzzle collection and an instructive and entertaining introduction to Kurt Godel's famous theorems, including incompleteness and undecidability. Much of the action of the book takes place on an imaginary and magical island, the Island of Knights and Knaves, where knights always make true statements, knaves always make false statements, and every inhabitant is either a knight or a knave. Here we meet an amazing array of characters, visitors to the island, seeking to determine the natives' true identities. Among them are the census-taker McGregor; a philosopher-logician in search of his flighty bird-wife Oona; and a regiment of Reasoners. By following the Reasoners through brain-tingling exercises and adventures - including journeys into the "other possible worlds" of Kripke semantics - even the most illogical of us should come to understand Godel's theorems, some of their philosophical and mathematical implications and why we, like Godel himself, must remain forever undecided! The book is intended for puzzle fans of every age and ability - from the high-school whizz to the seasoned mathematician, logician or computer scientist.

About this title

From Publishers Weekly

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.
Copyright 1987 Reed Business Information, Inc.

From Library Journal

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,
Copyright 1987 Reed Business Information, Inc.

Edition details

• Publisher: Oxford University Press
• Publication date: 2000
• Language: English
• ISBN 10: 0192801414
• ISBN 13: 9780192801418
• Binding: Paperback
• Number of pages: 272