Logic in a Time of Confusion

The pundits say—well, the pundits say a lot of things, and too often it can be difficult to figure out the truth in public discourse, whether political, commercial, or social. We have learned as a culture to carve out rivers of words, and when we have to brave those torrents, as we all have to every day, we risk being carried away to conclusions we only feel must be true because others assert them so assertively—and because we don’t feel confident calling on authorities, as we see them, to explain themselves.

Those mentally menacing circumstances, which are all around us now, call for the tempering strength of some critical thinking, a discipline which includes the traditional science of logic. If there is any one word that is likely to cause us to shudder a bit, as if locked out in the cold on a dreary winter night, logic will do it. The term, though, is much homelier than the reputation it evokes. It derives from the simple classical Greek noun for a word (logos), and because it is with words that we assemble speech, and with speech we converse and think, the term logic has been taken to name what is the science of rational discourse.

Not all thinking, of course, is rational. We feel some realities, intuit others, and rely often and rightly on our basic, inexplicable common sense in many a situation. Thinking rationally, though, means understanding the reasons behind our thoughts and conclusions, and logic is the science, the organized body of knowledge and techniques, that discovers and tests the necessary connection between things. For logic, the world is made up, oddly perhaps, of things, and anything we can identify or name in language is considered a thing. That’s what is meant by rational thinking: a ration is a portion, and a portion of the world we are dealing with at any given time is a thing to the science of logic.

All of which is to say that language, which names and relates things, can be a double-edged sword. In studying logic, one learns about conceptions and terms and propositions, what makes for a sound argument and what makes for one that only sounds like it’s true. And it’s the last of these topics, called fallacies, that makes the study of logic, though arduous at times, so rewarding: for seeing through nonsense and knowing why it’s nonsensical is deeply and naturally satisfying to all of us. There is no set number of fallacies, but all textbooks of logic will treat the ones we are more likely to encounter in our daily rounds (an excellent handlist of which, and an excellent introduction to the study as well, can be found in D. Q. McInerny’s Being Logical, Random House, 2004). One such fallacy is called equivocation, and with an illustration of it, we can see how the science of logic joins up with the art of estimating the value of what someone else is saying—a not entirely useless habit these days.

Suppose, for example, you happened to overhear this exchange between a manager at a factory of some sort and an assistant: “We’ve got to create a specialized position for this new project, but experts think they’re worth a lot of money, so I’ve got to be careful.” “Yeah, and everybody’s an expert.” “Don’t say that, or everybody will start believing they’re worth a lot of money.” Although we can’t see or hear it right away, there is an argument presented here, and the techniques of logic would explain to us exactly how to reduce all that conversational verbiage to these three distinct but connected propositions: Since every expert thinks they’re worth a lot of money, and since everybody is an expert, everybody, therefore, thinks they’re worth a lot of money.

But does that conclusion necessarily follow in this context? It sure sounds like it at first, but something’s going on with the noun expert. The first time it is used, the manager means someone trained with special skill and knowledge for a particular task. The next time the same noun is used, however, the assistant is not referring to someone with special skill and knowledge, but to anyone who thinks they may possess such talents; the assistant means to say sarcastically (and the manager seems to take it seriously) that We all think we know something others don’t and we all believe that our opinions are the right ones. The same noun expert, therefore, has been used in two different ways, a logical fallacy called equivocation, using the same word for two different things.

But how do we ever learn to recognize mistakes like that in reasoning? The practical side of a science comprises techniques, and one technique of the science of logic—the science of things, remember—requires that we can only talk about three ideas at a time when we’re making an inference, that is, when we’re drawing a conclusion on the basis of earlier assumptions. And on that specific rule—or on the violation of it, I should say—we can confidently recognize that the slight, subtle, quick change in the way the assistant used the noun expert effectively introduced a fourth term, thereby causing the seemingly reasonable statement to come logically crashing down.

And as it should have, no matter how good and reasonable it may have sounded at first. There, really, is the pressing importance of logic in matters much more consequential than this likely intentional equivocation on the assistant’s part. The study would give us a habit, ready to be used when needed, to push away from the emotional rocks in a river of truthful-sounding words and gain breadth to test what we may otherwise so very much wish to believe unjustifiably. We do not enjoy a fully human life without emotion, but we can have too much of a good thing at times, and come to rely on unreliable ways of thinking when some hard thinking is in order. Logic can go far in helping us regain the center of the stream and sail along in more control of things.

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