American Scientist

Logic Made Easy: How to Know When Language Deceives You. Deborah J. Bennett. 256 pp. W. W. Norton, 2004. $24.95.

You enter the voting booth and there is a local measure to repeal term limits. You vote yes. Does this mean you favor term limits?

A mother says to her son, "If you finish your vegetables, you can have dessert.“ Does this mean that the child must eat all of his vegetables in order to get dessert?

The answer to the first question is no. If you said otherwise, then you just voted the wrong way! The answer to the second question: It all depends. Formal logic (sometimes called classical logic) says the answer is no. Strictly speaking, the sentence says nothing about what happens if the child does not finish his vegetables. Consequently, it is possible for the son to get dessert without finishing his vegetables. But every parent and child in the world knows the correct answer is yes: No vegetables, no dessert. Period. Only grandparents may follow the rules of classical logic in this situation. Everyone else must follow natural logic, the logic that underlies the normal, everyday use of language within a society.

These are just two of the many examples Deborah J. Bennett discusses in her superb little book Logic Made Easy. Some of the problems she presents will challenge even experts. In particular, a very clear head is required for the well-known Wason Selection Task and for the THOG problem, both of which were devised by cognitive psychologist Peter C. Wason. Many of the other examples Bennett gives come from the Law School Admission Test (LSAT).

If I were giving a university-level course on logical reasoning, this would be my textbook, and I would demand that the students read it from cover to cover. The only caution I would give them would be to ignore the book's title. In fact, one thing Bennett makes crystal clear is that logic is anything but easy. Her subtitle, How to Know When Language Deceives You, is more to the point, and I suspect that the main title is a product of those in charge of marketing the book, rather than an attempt by the author to describe the content. An accurate, but perhaps less salesworthy, title would be "Logic explained in an entertaining and intelligent fashion,“ or perhaps "The best introduction to logic currently available." You get my drift.

By and large, Bennett sticks to the classical propositional logic that we inherited from the ancient Greeks—and, or, not, implies, if and only if—barely mentioning quantification and not covering the work of Kurt Gödel and Alfred Tarski at all. These are entirely the right choices, given that this is a book aimed at helping people from all walks of life to become better reasoners, not a textbook in logic for mathematics students.

The underlying material is for the most part standard and has been covered many times by a great many authors. What Bennett brings to the table are a superb compact history of the subject and a broad view of the relationship between formal logic and everyday human reasoning (both features that are sorely lacking in many other books on logic), backed up by research results from cognitive psychology and supported by a collection of excellent examples.

In the latter part of the book, Bennett touches on some extensions of classical Greek propositional logic—such as Venn diagrams, truth tables, modal logic and fuzzy logic—that bear upon everyday reasoning. But here, and throughout, for the most part she stays well clear of mathematical formalisms, and the closest she gets to mathematical logic is a brief mention of George Boole's algebra of logic.

In a blurb on the front cover, veteran mathematics writer Martin Gardner calls the book "The best and the most lucid introduction to logic you will find." I can't argue with his logic.—Keith Devlin, Department of Mathematics and Center for the Study of Language and Information, Stanford University