Logic as a liberal art

You have already felt something follow, and you have already been taken in by something that only appeared to follow. A proof in geometry closed; a news claim did not, though it wore the shape of a proof; two people used “not” as if they had contradicted each other, when they had only disagreed. Logic begins in those recognitions. It is not a bag of puzzles, and it is not a personality trait called “being critical.” It is the art of ordering discourse toward truth.

Kearns, in the Introduction to The Principles of Discourse, already describes the movements this art has to tend. Discourse is the mind moving from one consideration to another. That happens when we go from many things of a kind to what makes the kind what it is; when we relate two concepts into something we take to be true; and when, from what we already know, the mind can move to something we did not know before. Those are not three hobbies. They are one work, taken at three depths.

R. E. Houser, using the school names that Ars Syllogistica also uses, calls them the three acts of the mind. The first is apprehension: grasping what a term means, toward a definition. The second is judgment: joining or dividing in a proposition, which can be true or false. The third is reasoning: putting propositions together so that a conclusion follows. Pierre Conway analyses the same sequence as the stages of the reasoning process: from the grasp of a nature, through the proposition, to the movement from known to unknown. This lesson takes that order as a map. It does not replace the drills.

The second act is where truth first becomes possible, and that is not a technicality. A term signifies without yet asserting: man and white, on their own, are neither true nor false. Only when the mind joins or divides — affirms this of that, or denies it — does what is said become the sort of thing that can be so or not so. That is why the first act aims at definition and not at truth, and why a student who wants to argue before he can define is trying to run the third act on the strength of neither of the first two.

Opposition belongs to the second act. Two statements may contradict, or be contrary, or sit in other relations on the square; they may also merely disagree without being logical opposites at all. Inference belongs to the second act in its immediate form — what follows from one statement alone — and to the third when a middle term carries you from premises to a conclusion. The practice application will teach the moods and the diagrams. What you need here is the question those tools serve: given what has been said, what must be said, what cannot be said, and what is still open?

Not everything that looks like an inference is one. Conway’s definition is the one to keep in view when a paragraph has the gait of an argument and none of its necessity.

The definition of a fallacy is that it is reasoning which appears to conclude but does not. The accent is on appears.

Conway then says the thing that makes this art urgent rather than decorative. The fallacies a student can name are not the ones that will take him.

The important thing to note about fallacies is that they do not seem to be fallacies. Usually when we refer to fallacies, we refer to what appear, at least to us, to be blatant examples of misreasoning. But such are mere second-rate or amateur fallacies. The perfect or expert fallacy is one which looks like, not a fallacy, but, to all but the most trained eye, the most orthodox of reasoning.

He draws the public consequence without flinching: because a known starting point may be believed without being true, “politicians can be convincing even when their premises are false… one cannot say that the truth will necessarily prevail in public discussion.” That is the case for learning this art, and it is not a case about winning debates. It is about being able to tell, in a paragraph that sounds like reasoning, whether anything has actually been concluded — when no one has labelled it for you, and when the fallacy has been built by someone competent.

Houser, presenting Aristotle, treats logic as an art rather than as a science of one subject-matter: a skill concerned with how we reason when we try to discover the truth, usable in any inquiry. That is why this course will not begin from symbolic calculi. Those have their use. They are not the first form of an art that already lives in the language you speak. Formal logic, in Houser’s map, studies the structure of the three acts; material logic asks how certain the conclusion is, given the matter of the premises — demonstration when the conclusion is necessary, dialectic when it is probable, sophistry when it only seems to be either.

Demonstration and persuasion must be kept distinct. A conclusion can follow necessarily from true premises and still fail to move a hearer. A speech can move a hearer and still not have shown the thing. Kearns puts the second fact without dressing it.

Much human discourse also involves persuasion, since even if we express the truth to someone they may not be persuaded then we have not shown them the relevant truth.

Rhetoric will take up how a hearer is actually shown. Logic keeps the first question from being confused with it. If you want to “win” before you can tell whether anything follows, you are asking rhetoric to do logic’s work. Look ahead at the rhetoric pages if that is already your trouble — then come back. If your terms have gone muddy, if you cannot tell what is being said of what, return to grammar and to Ars Grammatica. Logic cannot order what has not yet been said as a saying.

The order of word, concept, and thing that this art presupposes was set out in the foundation pages: words signify concepts immediately and things through them, and the logician works on words precisely insofar as they signify things through thoughts. Those pages also gave the first act its vocabulary — universal and singular, comprehension and extension, univocal and equivocal naming — which the practice application drills.

Continue to Into Ars Syllogistica.