In defending the teaching of Formal Logic, Dorothy Sayers notes, “Another cause for the disfavor into which Logic has fallen is the belief that it is entirely based upon universal assumptions that are either unprovable or tautological. This is not true. Not all universal propositions are of this kind.”

I want to make two comments. First, it appears that Sayers is committing the fallacy of apriorism here. The discreditors of Logic attack it by arguing that the universal assumptions upon which Logic is based are unprovable or tautological (and are thus worthless). She implies, in what appears to be a hasty generalization, that they are attacking all universal propositions (when she argues that not all universal propositions are of this kind), when in fact they are only attacking some of them. Maybe I am missing something here, but it seems that the universal propositions she defends may not be the same ones the discreditors are attacking.

Second, if I were to respond to the discreditors given her assumption, I would argue this way: “Do you really believe that all universal propositions are unprovable or tautological? Then how about that claim? Is it unprovable, or tautological?” All universal propositions are unprovable or tautological is itself a universal proposition, and is thus open to the same refutation. Thus this attack on universals lays itself wide open to a classic reductio.

It would be an instructive exercise to take Logic or Rhetoric students through a defense of Sayers claim that not all universal propositions are unprovable or tautological. Ask your students, “How do we know the truth of universal propositions?” Discuss the value of an inductive defense of universals. Discuss also the proving of universals by authority, by definition, and by deduction from other universals.

In her essay “The Lost Tools of Learning,” Dorothy Sayers has identified for many classical Christian schools of our day an outline for a modern education following the medieval Trivium: Grammar, Logic, and Rhetoric. I am interested in what she says about Logic and the Dialectic Stage, and plan to occasionally post some thoughts about these and related topics. I will start my posts with a comment she makes that I have found helpful in my own teaching of Logic.

In describing a student of the medieval Trivium, Sayers writes, “Secondly, he learned how to use language; how to define his terms and make accurate statements; how to construct an argument and how to detect fallacies in argument.” This short statement gives us what I have come to believe are the four primary lessons to be learned in a Logic class, and in the proper order.

First, the logic student learns about terms, which are the building blocks of statements. They learn what a term is, how terms differ from words, the methods and rules of defining terms, and how to use the tools that relate terms to one another, such as genus and species charts.

Second, the logic student learns about statements. They learn what a statement is, how to identify the different types of statements, how to relate statements to one another, and how to determine the truth of a given statement.

Third, the student learns “how to construct an argument.” Logical arguments are built out of statements, which are connected as premises to make conclusions. Students learn how to distinguish between valid and invalid arguments, what validity means, and why it differs from truth. Once they are able to identify valid arguments given to them, they learn how to construct valid arguments of their own.

Fourth, the logic student learns “how to detect fallacies in argument.” A fallacy is an invalid form of argument. They learn to identify not only the formal fallacies discovered by the rules of validity, but also informal fallacies such as ad hominem and post hoc.

Thus, Sayers has given us the outline of a complete introductory logic curriculum. I would only add that we should not limit our learning of the above to categorical logic, but include the tools of propositional (or symbolic) logic as well. Students should be given the powerful tools of relating symbolic propositions, determining the validity of propositional arguments, and learning how to construct propositional proofs.

In our doctrine class we discuss classical arguments for and against the existence of God. One such argument is the Problem of Evil and goes something like this: “If God exists, then he is both perfectly good and infinitely powerful. If he is perfectly good, then he is willing to prevent evil. If he is infinitely powerful, then he is able to prevent evil. But if evil exists, then God is neither unwilling or unable to prevent it. Evil does exist. Therefore God does not exist.” We use a shorter truth table to show that this argument is indeed valid (or perhaps we write a proof for it). The students who have taken logic know that if an argument is valid, but the conclusion is false (as this obviously is), then at least one of the premises must be false. This leads to a fruitful discussion about which premise is false, and why. Is God infinitely powerful but not able to prevent evil because he cannot interfere with the free will of men? This is the choice of many modern evangelicals. Does God’s perfect goodness require that He is always willing to prevent evil? Reformed scholars would say no, and give counterexamples such as the crucifixion.

How do you take formal logic and apply it to real life during the dialectic stage? In other words, how do you move from the theory into practical application of what has been learned?

First, the obvious. We must teach logic-it’s definitions, theories and techniques-so that the students fully grasp these concepts. By its very nature logic is immediately applicable; every area of study in which conclusions are drawn from premises employ the techniques of logic. So students who fully understand these techniques will make their own application, just as students who understand mathematics, grammar, or the sciences naturally find applications of those subjects in their daily lives.

Second, we must teach tools of logic. These include techniques such as determining assumed premises in enthymemes, applying immediate inferences, identifying formal and informal fallacies, defining terms, developing and answering dilemmas, and using truth tables. The teacher must, for the students’ sake, distinguish all these tools from those lessons which are merely the means to an end, such as mood and figure, Venn diagrams, formal proofs, and so on. These latter lessons are helpful in their place, but everyone should honestly recognize their limited applicability outside of the classroom.

Third, we must give students examples of logic being applied. The teacher should not immerse the student in too many highly-symbolic lessons without occasionally surfacing for a breath of application in ordinary language. To be sure, as a symbolic language, logic, like mathematics, has a certain elegance or even beauty. But God has given us logic in order to apply it to the world around us, and we must lead students in showing how this is done. Point out to your students examples of informal fallacies in the newspaper, analyze enthymemes in the Bible to uncover the assumptions, show how Jesus uses and gets out of dilemmas, analyze Aquinas’s arguments with shorter truth tables.

Fourth, we must review and apply the tools of logic throughout the secondary curriculum. The students should see some of these being applied in different way in all their other classes. Certainly, courses like Geometry and Rhetoric will overtly re-teach many of the techniques learned in the logic class, but every subject will use some of the tools. Do not all teachers define terms for their students? Do not all draw premises form conclusions? All secondary teachers should learn enough logic to use the tools appropriate to their particular subjects.