Articles From The Classical Teacher

How to Teach Logic
by Martin Cothran
Classical Teacher, Summer 2005

Every subject that is systematic has a certain inherent order to it that dictates how it should be approached. In some subjects this order is more explicit than others. In mathematics, for example, there is a widely acknowledged sequence in terms of what should be learned and when it should be taught. In other subjects, however, such as history, there is much less agreement on how and when certain things should be taught. Mathematics is a systematic subject, whereas history is not.

The subject of logic is, in large part, about order, and so we should not be surprised to find that there is a fairly explicit and well-defined approach that Christian educators can take to the subject.

When to Begin the Study of Logic
One of the most common questions parents and teachers interested in classical education ask about logic is: when should they start teaching it to their students?
The answer, of course, is: “When he or she is ready.” This usually happens around 7th Grade. It is at this age (about 12-13) that many children begin to seriously investigate the reasons for things. They are no longer satisfied with the concrete, but are beginning to understand and appreciate abstract ideas.

Children are not totally unfamiliar with abstract ideas even at this time. They have already encountered them in mathematics. But, whereas mathematics deals with abstraction in the realm of quantitative relationships, logic deals with abstraction in the realm of qualitative relationships. Both math and logic deal with abstraction, but math does it with quantities; logic (at least in its traditional form) does it with language.

We should point out that most modern logicians disagree with this. They view math as an extension of logic, and because of this, their logic—the system of modern logic—is very mathematical. But here we are discussing traditional logic, which is very different from modern mathematical or symbolic logic.

The Different Kinds of Logic
Let’s point out first that there are two main divisions in logic: formal logic and material logic. Formal logic studies the form of reasoning, whereas material logic deals with the content of reasoning. Formal logic is divided, in turn, between deductive reasoning and inductive reasoning. Deductive logic reasons from universal truths to particular conclusions. This is the kind of logic the student encounters when he studies arguments such as:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal

The argument begins with a universal truth, “All men are mortal,” and ends up with a particular truth: “Socrates is mortal.”

Inductive logic reasons from particular facts to universal conclusions. Here is an example:

Every mammal that has ever been examined has hair
Therefore, all mammals have hair

Here, specific instances of mammals being found with hair is said to justify the general conclusion that all mammals have hair.

Sophistical reasoning studies fallacies that really belong in the various other parts of logic but are collected together for the convenience of being able to study incorrect reasoning under one heading.

So, given this breakdown, let’s set forth several rules governing the sequence of logic study:

Rule #1: Study good reasoning first—fallacies later.
What this rule says is this: teach correct reasoning first, and incorrect reasoning only after correct reasoning is understood. An understanding of correct reasoning will enable students, in most cases, to spot bad reasoning even if they have never formally learned to identify bad reasoning. Note that we cannot say the opposite: that students will learn how to spot good reasoning by having studied examples of bad reasoning. In other words, by learning the rules of good reasoning, a student learns to spot bad reasoning as well; but learning about bad reasoning does not enable him to spot good reasoning.

This rule flies in the face of the way logic is often taught. In fact, it is not uncommon for only fallacies to be taught—to the exclusion of all else. Of course, we would not tolerate this way of doing things in any other subject. Can you imagine teaching students a list of the things that did not happen in history, expecting them to learn what actually did happen from these falsities? Or exposing them to examples of bad writing as a preparation for writing well? If a science teacher spent a whole year having his students examine great experiments that failed, we might suggest he find another line of work.

Rule #2: Study formal logic before material logic.
One reason we study formal logic before material logic has to do with the structure of these two parts of logic. Formal logic is extremely systematic in its structure, whereas material logic is less so. This is not to say that material logic does not have structure to it. Many aspects of material logic are taught under the labels of “informal logic” or “thinking skills” programs. These are often a hodgepodge of informal logic topics loosely organized and accompanied by other thinking skills that are called logic only by textbook writers and educationists who know little about the philosophical discipline of logic. The medieval discipline of material logic is a fairly well understood category of knowledge that, if not as structured as formal logic, is much less inscrutable than some educational material might make it appear.

The other reason for placing formal logic ahead of material logic in our sequence is simple pedagogical necessity. Material logic studies the content of reasoning and is best studied after students have a good grounding in what to do with this content once they have it—a skill taught in formal logic.

Rule #3: Study Deduction before Induction.
This is a fairly common procedure in most logic texts. The reason for it has to do with the fact that deduction is not only more simple and straightforward than induction, but that deduction is a more fundamental thinking skill than induction. When asked why we believe something, we are much more likely to resort to deduction (usually an incomplete one) than induction. The reason is very simple: induction, by its nature, seeks a laboratory—or maybe the assistance of a magnifying glass and a deerstalker cap. Deduction requires only a comfortable chair—and a little concentration. Induction is more the province of the expert; deduction is the right of the amateur. And, let’s face it, most of us are amateurs in most things.

In addition, as G. K. Chesterton once put it, “Every induction leads to a deduction.” Induction, in other words, requires a deduction to complete it; deduction needs no company.

While, as we have already observed, logic is not the same thing as math, it does share one important characteristic with mathematical disciplines: it is systematic and orderly. If a subject should be studied according to its inherent nature, and the inherent nature of logic is orderly, then it doesn’t take a great logician to conclude that that’s the way it should be studied.

Martin Cothran is the author of Traditional Logic, Books I and II, Material Logic, and Classical Rhetoric with Aristotle, all published by Memoria Press. He is also the managing editor of the “Classical Teacher.”