Logic: The Original Thinking Skill

We have a tendency to put academic subjects into separate and unrelated categories which have little to do with each other. We have our curriculum chart where we put things such asReadingEnglishMathScience, each one dealing with a different skill and a different body of knowledge. Logic seldom finds a place in our lists, although it may be the most important subject, since we use it in every other subject.

Why would we consider a subject we use more often than almost any other to be the least important?

Logic is a liberal art. A liberal art is a universal, generalizable intellectual skill: you use it in whatever else you do. Every academic subject requires the ability to think rationally, and logic is the science of rational thought.

There are two common schools of thought on what logic is and how it should be taught. The first is the old classical approach, which involves teaching traditional logic. The second is the newer method of modern symbolic logic. Traditional logic was articulated 2,500 years ago by Aristotle and is very language oriented; modern logic was developed by modern philosophers and is more mathematical.

While traditional logic focuses in a practical way on how human beings do in fact reason, modern logic focuses on more abstract formal relationships that are common in, for example, computer programming. The skills of traditional logic are the skills most used in argument and persuasion, and for that reason should take precedence over the modern system.

Traditional logic focuses its study on three things: words, statements, and arguments. When making arguments, it is important to understand the meaning of words since, if the meaning of a word changes in the middle of an argument, it can cause confusion and misunderstanding. It is also important to understand the different kinds of statements—affirmative and negative, universal and particular—and how statements can be opposite to each other and equivalent.

Finally, the logic student learns the different kinds of arguments and how they are structured. There are two kinds of arguments: deductive and inductive. Deductive arguments go from universal truths to particular truths. Their conclusions follow necessarily from the premises. The classic example of a deductive argument is the following:

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

An inductive argument goes from particular truths to universal truths. Its conclusions follow only probably from its premises. An example of an inductive argument is:

All three cars I have owned were Toyotas
My first car was a good car
My second car was a good car
My third car was a good car
Therefore, Toyotas are good cars

The culmination of the study of logic is in the understanding of what is called “validity”: how the conclusion of an argument follows from the premises or assumptions.

A student learns the rules of validity and how to test arguments to make sure they measure up. Then the student learns a few shortcuts that make the practical application of logic easier.

The medieval scholars were notable for their ability to systematize a subject and make it easy to teach. They took Aristotle’s treatises on logic and came up with ways in which a student could easily master just a few fundamental logical operations in a manner that allowed the student to get the most out of his language study. One great medieval scholar, William of Sherwood, came up with a simple four-line verse that taught students the nineteen valid kinds of argument and how to simplify them.

The processes involved in logic are used in every other subject. We might as well learn how to use them well. Or, as a logician would say:

All subjects that are used widely should be learned well
Logic is a subject that is used widely
Therefore, logic should be learned well

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