LSAT
Aristotle and the LSAT
Sometimes the difference between a valid argument and a faulty one is only a single word. Replace all with most, and certainty disappears. That small shift may seem technical, but it lies at the heart of logical reasoning — and at the heart of the LSAT.
It is also the sort of shift that would have interested Aristotle.
Over the 17 years since I founded Clayborne Education, I have become increasingly interested in the history of human thought and in the ways its ideas continue to live in the work we do now. Test preparation may seem, at first glance, far removed from the ancient world. But often it is not. Again and again, the skills demanded by modern exams turn out to be part of a much older intellectual tradition. The LSAT, with its relentless attention to arguments, structure, and inference, offers a particularly good example.
Aristotle, among his many intellectual achievements, is known for formalizing the syllogism: a three-part argument in which two premises are meant to establish a conclusion with certainty, provided the premises themselves are true. One of the most familiar examples runs as follows:
Major premise: All men are mortal.
Minor premise: Socrates is a man.
Conclusion: Therefore, Socrates is mortal.
The force of the argument depends not only on the truth of the premises but on the structure of the reasoning. If all men are mortal, and Socrates is a man, the conclusion follows necessarily.
But now consider a small change:
Major premise: Most men are mortal.
Minor premise: Socrates is a man.
Conclusion: Therefore, Socrates is mortal.
The shift is slight. Only one word has changed. And yet the argument is no longer sound. The premise may still be true — if all men are mortal, then certainly most men are mortal — but the conclusion no longer follows with certainty. Socrates could, at least in principle, belong to the minority not covered by the statement. A true premise, in other words, does not guarantee a valid conclusion.
This is precisely the sort of distinction the LSAT asks students to notice. The test rarely presents arguments in the tidy form of ancient syllogisms, but it repeatedly turns on the same problem: the evidence may sound plausible, the premises may even be true, and yet the conclusion may not be justified. Often everything hinges on a small logical word — all, most, some, none.
That is one reason logical reasoning on the LSAT can feel so exacting. It is not enough to understand what a statement generally suggests. One has to understand exactly what it commits us to, and what it leaves open.
Consider the following example, written in the spirit of an LSAT stimulus:
Some members of the orchestra play the hammer dulcimer.
Most of the hammer dulcimer players also play the xylophone.
No xylophone player also plays the tuba.
At first glance, the statements seem straightforward. But once we begin asking what must be true, the terrain becomes more complicated.
For instance, we can infer that there is at least one member of the orchestra who plays the hammer dulcimer. Because most of those hammer dulcimer players also play the xylophone, there must be at least one person who plays both the hammer dulcimer and the xylophone. And because no xylophone player also plays the tuba, that person cannot play the tuba.
Already, several relationships are in place. The hammer dulcimer group overlaps at least partly with the xylophone group. The xylophone group and the tuba group do not overlap at all.
What we cannot say with certainty is just as important. We cannot conclude, for example, that some orchestra members play the tuba. We cannot conclude that most xylophone players play the hammer dulcimer. And we cannot conclude that every hammer dulcimer player also plays the xylophone, because most does not mean all.
This is one of the ideas many students initially find surprising: in logic, words such as most and some do not exclude the possibility of all. If most hammer dulcimer players also play the xylophone, it remains possible that all of them do. Likewise, if some orchestra members play the hammer dulcimer, it remains possible that every member does. The language establishes a minimum, not a maximum.
That sensitivity to quantity words — to what they guarantee, and to what they merely allow — goes a long way toward success on the LSAT. The test rewards students who can resist the temptation to read more into an argument than the words justify.
If we turned the example above into a question with answer choices, it might look like this:
Some members of the orchestra play the hammer dulcimer.
Most of the hammer dulcimer players also play the xylophone.
No xylophone player also plays the tuba.
If the statements above are true, which of the following must also be true?
- There are some members of the orchestra who play the tuba but not the hammer dulcimer.
- There are some members of the orchestra who play the hammer dulcimer but not the tuba.
- Most orchestra members who play the xylophone also play the hammer dulcimer.
- No orchestra member who plays the hammer dulcimer also plays the tuba.
- Every orchestra member who does not play the xylophone does play the tuba.
The correct answer is B. If some orchestra members play the hammer dulcimer, and most of those players also play the xylophone, then at least one orchestra member plays both the hammer dulcimer and the xylophone. Since no xylophone player also plays the tuba, that person must be a hammer dulcimer player who does not play the tuba.
I find questions like this perpetually interesting, even after more than twenty years of teaching the LSAT, because they remind us that reasoning is both exacting and strangely elegant. A single word can alter the entire shape of an argument. An apparently obvious conclusion can turn out not to follow at all. What looks simple becomes subtle.
That, to me, is part of the pleasure of this test. Beneath its difficulty lies something older and more enduring: the discipline of thinking carefully about what follows from what. Aristotle would have recognized the impulse, even if not the format.
At Clayborne, we of course want students to develop the skills that help them succeed on demanding exams. But we also hope they discover something more lasting — a sharper sense of language, argument, and the quiet satisfaction of reasoning well. Test preparation, at its best, is not just about performance. It is also about learning how to think.
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