Mimesis Law
4 June 2020

Logic Games And Poor People

October 24, 2016 (Fault Lines) — Stripped to its most basic essentials, the practice of law comes down to an exercise in logic, usually in the form of Facts=>Law=>Result. For example:

  1. The defendant did X.
  2. The law says Y.
  3. Therefore, the defendant is guilty.[1]

Success as a lawyer depends on one’s ability to convince judges and juries of the validity of your logic, and the flaws in your opponent’s.

On Thursday, Admiral Greenfield leveled a rhetorical broadside against Caroline Kitchener’s article in the Atlantic. Kitchener took issue with the Analytical Reasoning section of the Law School Admissions Test, usually called the “Logic Games section.” Kitchener has a low opinion of these types of questions, claiming that

[E]very year, they stop tens of thousands of applicants from attending top law schools.

Which is correct, but trivial. Another way of phrasing that is tens of thousands of applicants are rejected from top law schools because their GPAs and LSAT scores aren’t up to snuff, and the logic games section is 25% of the LSAT score.

Kitchener goes on to say that the games section is contributing to the lack of socioeconomic diversity at top law schools, because rich students can afford to pay for prep classes to teach them how to solve the games. Which is also trivial. Rich students also have better cars, better clothes, and better accommodations, so it follows that they can afford better test prep as well.

But, our mean-ass editor misses the mark also. When he said:

Calling it the logic “games” suggests that’s just another ploy of the elites to keep the marginalized down. After all, it’s a game. It games law school admissions. And as the post URL says, the game is “rigged,” a word that’s bandied about a lot lately.

He was reading waaay too much into it. Everyone calls it the “logic games” section, in the same way that everyone calls short-sleeved, three-button knit shirts “polo shirts” or paper tissues that come from a box “Kleenex.”

Kitchener made the point that:

The section relies heavily on formal logic, a concept rarely taught outside of high-level college mathematics or philosophy courses.

Scott snapped back:

Formal logic? As opposed to, informal logic? Or what has become popularly known among humanities majors as their feelz?  After all, if you’re not taught this “concept” of formal logic, then you obviously can’t be expected to be, you know, formally logical, right?

Kitchener is actually right about this. A better name for it might be “symbolic logic,” meaning the ability to express a series of rules in mathematical or algebraic notation. Consider the following sample logic game:

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions:

If both G and S are reduced, W is also reduced.

If N is reduced, neither R nor S is reduced.

If P is reduced, L is not reduced.

Of the three areas L, M, and R, exactly two are reduced.

  1. If both M and R are reduced, which one of the following is a pair of areas neither of which could be reduced?

A) G, L

B) G, N

C) L, N

D) L, P

E) P, S

Solving this sort of game requires, among other things, knowledge of a very specific concept called the contrapositive. Take the first rule, which reduced to short hand as “G and S => not W.” Assuming you know how to derive the contrapositive, you can double the amount of information because “W=>not G or not S.” (To derive the contrapositive, you have to flip the terms, negate the terms, and reverse and/ors.)

That said, unless you’re a philosophy major, you probably didn’t learn that in college. But most people, no matter how intelligent or “logical,” aren’t going to spontaneously figure that out any more than they could independently figure out long division. So, either you have to learn that from an LSAT prep book or learn it from a prep class. Speaking as a former LSAT prep teacher, the students who plunked down the $1000 to attend my class got a better grounding on this subject than the ones who could only afford the $60 prep book.

Scott goes on to say:

This paean to ignorance is meant to demonstrate how poor students, unable to spend the time and money to take LSAT prep courses to teach them how to game the game, and thus snag the socioeconomic marginalized seat at HYS that will make society fair and just, must fail. It’s merely assumed by the patriarchally-challenged author that normal people can’t possibly be capable of logic.

It’s not that normal people aren’t capable of logic. It’s that if you’re giving a test on long division, statistically speaking the students who have had the best instruction on how to long divide are going to perform better on the test. This is not mush-headed Social Justice Warrior thinking…it’s just something that’s been true since the cavemen who lived by the better tree could afford a better spear.

[1] Or not, depending on whether you’re the prosecution or the defense.

14 Comments on this post.

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  • Joshua
    24 October 2016 at 11:20 am - Reply

    I had to stop halfway through this article to solve the logic puzzle before continuing. I wonder how many other readers did the same thing.

  • Beth
    24 October 2016 at 11:42 am - Reply

    This problem doesn’t require use of the contrapositive, a concept I used to teach in basic algebra classes. It follows clearly from the second and fourth statements – i.e. Since R is reduced, N cannot be reduced and since both M and R are reduced, L cannot be reduced. Hence, the correct answer is c) L, N.

    • Joshua Phillips
      24 October 2016 at 11:53 am - Reply

      Doesn’t the fact that N cannot be reduced follow from the contrapositive of statement 2?
      Statement 2) ~N -> (R and S)
      Contrapositive) (~R or ~S) -> N

  • DaveL
    24 October 2016 at 12:32 pm - Reply

    But most people, no matter how intelligent or “logical,” aren’t going to spontaneously figure that out any more than they could independently figure out long division.

    I question this claim. They may not formalize the idea in the terms you used, but I’d argue that intelligent, “logical” people understand the reasoning without even consciously putting a name to it. Beth would be such an example, having implicitly derived (R -> ~N) from (N -> ~(R | S)).

    • Neal Zupancic
      25 October 2016 at 3:46 am - Reply

      “But most people, no matter how intelligent or “logical,” aren’t going to spontaneously figure that out any more than they could independently figure out long division.”

      There is actual evidence to support this claim. The method used in Beth’s “implicit” deduction is the same method (modus tollens) required to complete the Wason selection task – https://en.wikipedia.org/wiki/Wason_selection_task – which fewer than 10% of respondents can complete correctly in an abstract reasoning context.

      • DaveL
        25 October 2016 at 6:58 am - Reply

        That supports the “most people” part, but not the “no matter how intelligent or logical” part which, if you think about it, rather contradicts the first.

        • Neal Zupancic
          25 October 2016 at 11:49 am - Reply

          Well I think that “intelligent” and “logical” are under-defined for the purpose of this argument. The Wason task results show that this is specifically a problem with abstract reasoning, meaning that a person could be highly intelligent and very good at applying logic to concrete problems in concrete or relatively familiar contexts but simultaneously not very good at applying logic to abstract problems presented with algebraic notation.

  • PVanderwaart
    24 October 2016 at 1:08 pm - Reply

    Any student with a few courses in math or computer programming is not going to have trouble with a contrapositive. And there is plenty of time in one semester in the philosophy department to cover the basics of symbolic logic and to also cover the classic errors in argument: ad hominem, appeal to authority, etc.

    If this is a known barrier to doing well on the LSAT, why aren’t the students prepared?

  • Jason K.
    24 October 2016 at 1:53 pm - Reply

    I have never had a formal logic course, nor have I ever taken the LSAT, nor any prep course, and I was able to derive the correct answer in about 20 seconds. While it is true that practice and training will make almost anyone perform better on almost anything, I’m with Scott on this one. If you’ve got the chops, you shouldn’t need a prep course. If you need a prep course to get a decent score, it is a sign that you are marginally qualified at best.

    The more beneficial change would be to go after the practice of rating law schools by how much money they spend. That is what really keeps the socioeconomically marginalized out of the good schools.

  • Jonathan
    24 October 2016 at 4:29 pm - Reply

    There are a few things in this article that aren’t quite right.

    (1) “Success as a lawyer depends on one’s ability to convince judges and juries of the validity of your logic”

    It’s a minority of lawyers who litigate, and a minority of them who try cases.*

    (2) The thing about the logic games is they test for pattern recognition more than logic. (At least if you’ve read a prep book.) The questions fall into a limited number of types and recognizing the type is most of the battle.

    (3) Kirschner didn’t really critique the logic games, her solution wasn’t to abandon them but to extol free prep materials/classes that are coming on line.

    Incidentally, if one really wanted to attack the logic games from an exclusionary perspective, the thing to ask would be if they test for what they purport to test for.

    *And the folks who are best at it didn’t necessarily go to top law schools.

  • Brian
    24 October 2016 at 5:06 pm - Reply

    Speaking strictly as a mathematician…if that’s the level of the logic games on the LSAT, maybe I could take up the law if a future career at NASA doesn’t pan out! Okay, kidding aside, that actually took me longer to read than solve, and I read *fast*.

    PVanderwaart has the right of it. Symbolic logic is taught as part of the introductory courses in philosophy (at least up here in New England it is). More than that, a mechanical engineer friend of mine took the same course at a non-flagship (sometimes read as: for poor people) state university. They exist. If the kids know this is going to be a problem, then it’s incumbent on them to spend the time and learn the basics, not on the test designers to lower standards just so they can pass anyway.

  • Anon
    24 October 2016 at 6:32 pm - Reply

    The life of the law is experience not logic.

    Of course Holmes didn’t have to sit for the LSAT. If he had, would he still have gone to Harvard. We can only wonder.

  • C Streak
    25 October 2016 at 12:57 am - Reply

    … unless you’re a philosophy major, you probably didn’t learn [that a statement is equivalent to its contrapositive] in college.

    In Indiana, at least, you get the opportunity to learn that in high school geometry (and between high school geometry and sitting the LSAT, you get the opportunity to forget it).

  • Neal Zupancic
    25 October 2016 at 3:40 am - Reply

    I learned symbolic logic starting in 8th and 9th grade in NYC public schools in the 90’s. Wikipedia suggests that it’s been taken out of the curriculum, which is disappointing if true. I don’t see how a student can reasonably approach topics like computer science or discrete mathematics (probability theory, set theory, etc.) without a solid grounding in symbolic logic.

    About the contrapositive: if you’ve studied logic explicitly you can skip the contrapositive entirely and just use modus tollens (a logical method of inference derived from the contrapositive) on the second condition.

    By the way, you seem to have a transcription error with this statement “G and S => not W” – shouldn’t that be “G and S => W”?