From Free Life No 24, December 1995

For something like a quarter of a century I have maintained - and declaimed to listeners willing or unwilling - that most of the evils of mankind would be avoided if only logic were taught in high schools.

One obvious difficulty with my panacea is that since logic has traditionally been seen as a university level subject, suitable high school textbooks don't exist. Many fine introductions to logic have indeed been written; varying in density from H.W.B. Joseph's weighty An Introduction to Logic (1916), to W.A. Sinclair's slimline classic The Traditional Formal Logic (1937); with, in between, plenty of good undergraduate level overviews such as those by Irving Copi or Lionel Ruby. But no introductory work I have seen has seemed appropriate for teenagers in the increasingly undemanding classrooms of the later 20th Century.

Today, I am pleased to announce that help is at hand. I do not think I have ever come across a better book for beginners in any field than David Kelley's The Art of Reasoning. For in setting out to write a book about "how to think" (p.1) Dr Kelley evidently adopted a single governing principle, clarity, and then adhered to it throughout with the religious devotion of an Ignatius Loyola. The book is so clear that even the apprentice butchers in Tom Sharpe's Wilt could understand it. I defy anybody to show me a subject more clearly presented than logic in the hands of Dr Kelley.

But clarity is just the beginning. The Art of Reasoning is also a very student-friendly book. It is devoid of any trace of patronising. No talking down, oversimplification, or dazzling with superior wisdom here. Dr Kelley merely wishes to convey important information in an effective manner. So the style is pleasantly light, with just the right amount of humour, analogy, and illustration to keep the information flowing, the attention fixed, and comprehension occurring naturally and easily.

The arrangement of the work is traditional; i.e., the traditional syllabus is covered in the traditional order, and modern innovations (such as an obsession with symbols - which converts logic into algebra) are ignored entirely. However, good use is made throughout of simple diagrams which help the student to `see' the bare bones of an argument and thus more quickly assess its strength or weakness.

Unlike some logic textbooks, The Art of Reasoning begins with a detailed analysis of concepts and their classification. This is followed by a thorough presentation of the principles of definition, along Aristotelian lines, which leads into the discussion of propositions to complete Part One.

Modernists might protest (Popper most certainly would have) that reverting to Aristotelian techniques of definition is a retrograde step. If so, I suggest they read Dr Kelley's analysis of Wittgenstein's discussion of the word `game' (pp. 47-51). Although young students probably won't realise it, at least not at the time, they will learn from this amiable and unassuming presentation that Wittgenstein's language games were no better founded than his earlier picture theory and thus that much of modern linguistic philosophy appears to have arisen from a single error of definition. If only logic had been taught in high schools ...

Part Two of The Art of Reasoning analyses arguments in general, including bad ones - there is an extensive presentation of the common fallacies - and it is not until Page 170 that the student reaches the meat and fish courses of logic, deductive and inductive reasoning, which are dealt with in Parts Three and Four. The result of this slow build-up is that the young reader will have acquired a considerable familiarity with reasoning, and some skill at it, before he or she starts to tuck into syllogisms, hypothetical and disjunctive reasoning, Mill's Methods, etc.

Although clarity and excellence of explanation make the book stand out, the Art of Reasoning has several other virtues as a teaching aid. These include brilliantly concise introductions to, and summaries of, each chapter; the breaking down of every topic into easily digestible chunks; the conclusion of each section by a practice quiz (with answers provided at the back of the book); and a comprehensive glossary defining all the technical terms used in the book.

To illustrate Dr Kelley's light touch, here are some samples from a practice quiz (p. 63). The student is asked to determine whether a dozen pairs of sentences express the same proposition. Interspersed with `straight' pairs such as

"a) Stealing is a sin. b) Stealing is a crime", one finds:

a) Kim is not very bright.

b) Kim is not dealing from a full deck.

a) George is a mellow individual.

b) George is an unmotivated slob.

a) I am angry at him.

b) I'm so mad I could push a bead up his nose.

A second good illustration of Dr Kelley's gentle humour can be found later in the same chapter (p. 73), where the student is asked to identify propositions in accident reports that drivers have filed with insurance companies, viz:

"I pulled away from the side of the road, glanced at my mother-in-law, and headed over the embankment."

"The pedestrian had no idea which way to go, so I ran over him."

"As I approached the intersection, a stop sign suddenly appeared in a place where no stop sign had ever appeared before."

"An invisible car came out of nowhere, struck my vehicle, and vanished."

"Coming home, I drove into the wrong house and collided with a tree I don't have."

Obviously, we're not looking at great moments of comedy, but this is exactly the sort of comic relief that helps young people to learn. It is a good example of the old precept, "when speaking to the people use the people's language". Dr Kelley's straightforward yet eloquent prose, coupled with well-pitched humour, crosses the generation gap in a single fluent stride.

The exercises which conclude each chapter comprise another signal virtue of The Art of Reasoning. In fact, fully a third of the book is devoted to exercises. The literary sources of these are amazingly diverse, and they are chosen not merely to stretch the student, but to make the lesson memorable. Besides humour - controversy, emotion, current affairs, curious facts and figures, and incidents from daily life, are all enlisted to spark interest and sustain attention.

For example, Chapter 11 (pp. 236-61), "Syllogisms in Ordinary Reasoning", ends with over 50 exercises, organised in seven groups, with samplings taken from sources as varied as old English proverbs, "Pride goeth before a fall", to the sayings of baseball star Yogi Berra: "You can't think and hit at the same time". In between, quotations from Blackstone, Samuel Johnson, Machiavelli, Benjamin Franklin, Conan Doyle, Oscar Wilde, Isaac Asimov, F.A. Hayek, Ernst Mayr, Shakespeare, Leibniz, Locke, La Rochefoucauld, and many others - plus a sprinkling from the New York Times, Wall Street Journal and Harpers magazine - show how integral reasoning, both good and bad, is to human life.

All chapters have similar, and uniformly excellent, selections of exercises; and the main lesson - the number of reasoning errors to be found in newspapers, in politics, in law, in science, in textbooks, in fact everywhere - is driven home in the most thorough fashion. Some may find the prevalence of logical error, even among experienced and intelligent writers, to be quite astounding. I suppose it is. But then, if only logic were taught in high schools ...

One particularly commendable chapter is on statistical reasoning (pp. 307-43). Disraeli's famous dictum that there are three kinds of lie - lies, damned lies and statistics - is amply illustrated. Yet, at the same time, Dr Kelley shows how enormously valuable statistics can be if we understand them and use them properly.

Although my own interest is in reaching pre-university teenagers, The Art of Reasoning has proved to be an ideal text for the college undergraduates for whom it was designed. Although only seven years on the market, it is already used by some two hundred philosophy departments across North America.

The book can also serve as the basis for more advanced study. It has two companion works: Readings for Logical Analysis, a 300-page selection of fully developed, "real world" philosophical arguments, edited by Dr Kelley and Stephen Hicks; and LogicTutor Software, a 900-exercise, interactive computer programme. Two instructors' manuals (for the 1st and 2nd editions of The Art of Reasoning) complete the set. These contain chapter outlines, teaching suggestions and (phew!) solutions to all the exercises.

As to criticisms, I can think of a few, but none are that significant. For instance, some modern logicians may resent the lack of so much as a nod in their direction, so perhaps there ought to be a chapter on those interminable TF equations etc. (Perhaps there is in the Second Edition?) Another small point is that while standard terms are used throughout, enthymeme's old friend and partner `sorites' is missing for some reason; replaced by the term `extended argument'. A less friendly critic might also demand more exercises from philosophical works rather than from the New York Times, although in so doing he would miss the point of the book. As to typography, I did notice one or two small (and obvious) errors, but in hundreds of otherwise flawless pages, so what? Finally, some suggestions for further reading might have been helpful but, at this level, they're not essential.

While I have praised The Art of Reasoning as so clear that it should easily be understood at Sixth and possibly Fifth Form levels, the book is more than just a textbook, it can be read with pleasure and profit by anybody. Clarity, excellence of explanation, an easy unassuming style, a leaven of wit, and a wealth of entertaining exercises, make the book a charming stroll through what is always intriguing, if for some readers, familiar territory.

Nor does it ever hurt, in my view, to test one's skill in logic. With the kind of exercises chosen by Dr Kelley, it can also be a thoroughly enjoyable passtime. I mean, can you identify the fallacy in the following exchange? (p.135)

He: "C'mon, spend the night with me."

She: "Why should I?"

He: "Why shouldn't you?"

Nicholas Dykes.