Every subject that is systematic has a certain inherent order to it that dictates its approach. For some subjects, this order is more explicit than in others. In mathematics, for example, there is a widely acknowledged sequence of what should be learned and when it should be taught. When working in other subjects, 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. Although logic is a language art, it is more like math in this respect than history.
When to Begin to Teach Logic
When should students begin to learn logic? The answer, of course, is: “When they are ready.” This can happen as early as seventh grade. It is at this age (about 12-13) that many children begin to seriously think about the reasons for things. They are no longer satisfied with the concrete but are beginning to understand and appreciate abstract ideas.
Most students have already encountered abstract ideas in mathematics. But, whereas mathematics deals with abstraction in the realm of quantitative relationships, logic deals with abstraction in the realm of qualitative relationships. We should point out that most modern logicians disagree with this. They view logic as an extension of math, and because of this, their logic—the system of modern logic—is very mathematical. But in this article, we are discussing traditional logic, which is very different from modern mathematical or symbolic logic.
Different Kinds of Logic
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 ever examined has hair
Therefore, all mammals have hair
Here, specific instances of mammals found with hair justify the general conclusion that all mammals have hair.
Sophistical reasoning, a branch of material logic, 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.
Let’s set forth several rules governing the sequence of logic study:
RULE 1: Study good reasoning first—fallacies later.
An understanding of correct reasoning will enable students to spot bad reasoning (called “fallacious reasoning”) even if they have never formally learned to identify bad reasoning, but learning about bad reasoning does not enable them to spot good reasoning.
We would not tolerate this reverse approach in any other subject. 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.
Bank tellers learn how to detect counterfeit cash by becoming intimately accustomed to the real thing.
RULE 2: Study formal logic before material logic.
Formal logic is extremely systematic in its structure, whereas material logic is less so. This makes it easier to study in an organized manner and helps students who are still struggling with abstract thinking to get a handle on logical thinking.
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. When asked why we believe something, we are much more likely to resort to deduction 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.
Logic 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.