Logic defines the way things relate to each other. In a classical school, students begin every subject by memorizing facts. The facts are the subject’s grammar. When a student has learned them well enough, the next thing is to learn the subject’s logic. How are the facts related? How can they be distinguished or combined?
Logic can also be generalized more abstractly. The rules that govern how things relate to each other may be described in a symbolic way, similar to mathematics. Logic is often learned this way in connection with subjects like geometry or computer programming. The more traditional way for classical schools is to study logic as a part of language. At Columbia, we can become acquainted with using logic in fifth and sixth grade through computer exercises and puzzles, but we begin to study categorical logic in earnest at the seventh and eighth grade levels by learning to recognize the forms of valid reasoning.
The aim of learning logic in a classical school is to develop the ability to craft a coherent essay or present a speech for some purpose. This is the art of rhetoric, and the application of logic in such a presentation is called dialectic. More generally, the knowledge of logic gives scholars the ability to think correctly about their observations and what they read or hear from others. This has wide application to science and every kind of art.
It may seem that everyone already knows how to think correctly, but that’s not so. Logic allows the thinker to say something more useful than, “I disagree with what that person has said” or “I feel like the truth is….” Instead of simply expressing an opinion or a feeling, the logic student can express reasoning by giving statements that are supported in valid, objective ways. Instead of saying, “I disagree with that,” logic allows the student to say something like, “Your statement is based on an unsupported premise. You haven’t made the case for what you are saying.” Or, “Your reasoning is not valid, because your premises do not lead to the conclusion you are making.” Or on the other hand, “I accept your conclusion because you have supported it with true premises and valid reasoning.”
Parents and schools ought to teach the logic of every subject because it allows students to understand the relationship between basic facts. They ought to teach logic as its own subject when students are ready to think more abstractly, because the study of logic allows students to recognize the difference between a coherently-supported statement and an unsupported opinion or statement of feeling, and also to support their own statements when writing or speaking.