Exploiting Antitheses

I have previously identified the “some people say” principle in an LSAT logical reasoning stimulus, and have engaged in some discussion of this phenomenon at 7Sage.com.  After some further thought and research, I have decided to revise and extend my earlier remarks.

The “some people say” formulation occurs anytime an LSAT logical reasoning stimulus refers to the words, thoughts, or beliefs of persons other than the author of the stimulus. This usually takes the form of indirect discourse (i.e., “critics insist” or “paleontologists hypothesize”) but it can be more subtle. The functional test that I apply is, “Can I put somebody else’s claim in quotes?” If so, we can label it a “some people say” claim.

In my original post, I argued that every “some people say” claim is the negation of the conclusion. That goes too far. There are a handful of cases where “some people say” something that directly supports the conclusion. I think of this as “expert testimony.” There are other cases where “some people say” what they will do in the future (campaign promises, for example). Logicians distinguish “promises” from “logical statements” (for good reason). There are some other cases where “some people say” things that are not simply the negation of the conclusion–but not many.

Instead of insisting that every “some people say” statement is the negation of the conclusion, it is more accurate and helpful to say that most “some people say” statements have this characteristic. I use the term “antithesis” for such statements, and define it as follows:

An antithesis is a claim which an LSAT logical reasoning stimulus rejects.

There are significant advantages to identifying an antithesis. The first is that it makes complex stimuli simpler. “Some people say” statements can be involved, and arguments involving them can get complicated. If you extract the antithesis, what remains is often short and simple.

The second advantage is in identifying the conclusion. While this is second nature for some students, it is very hard work for others. Since an antithesis is (by definition) a claim which the stimulus rejects, it is easy to look for a part of the stimulus that says so. If there is such a statement, that is usually the conclusion.

The third advantage is in understanding the argument as a whole. If you see a “some people say” statement and suspect that it is an antithesis, you know where the argument is going before you read it. There are only so many ways to deny a  claim, and a person who is thoroughly familiar with basic argument types can anticipate them.

Thus, for example, if the antithesis is a conditional statement (“A->B”), then the simplest argument to refute it is a counterexample (“A and ~B”). If the antithesis is an affirmation (“A”), the simplest refutation is a modus tollens (“A→B, ~B, ∴ ~A”). If the antithesis is a denial (“~B”), the simplest refutation is a modus ponens (“A→B, A, ∴ B”). While these aren’t the only ways to reject such claims, they are the most common–and a person who is actively looking for such argument patterns will be able to find them faster if they really are present.

The bottom line is this: identifying an antithesis can cut a complicated stimulus in half, expose its conclusion, and reveal the argument structure quickly and accurately. While not every “some people say” statement is an antithesis, the large majority are.

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