Make Quantified Logic on the LSAT Easier By Simplifying It

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During Blueprint LSAT Prep courses, few subjects are more vexing for students than quantified logic. Shoot, it even sounds scary.

But it doesn’t have to be.

On every LSAT, there are a handful of Logical Reasoning questions that test a student’s ability to combine all, most, some, and no statements. The problem is that there are a number of combinations that the LSAT can throw in your direction, and memorizing all of these combinations is reminiscent of calculus class (also know as the reason you are going to law school in the first place).

Good news: When broken down, there are really only two principles that define the valid and invalid conclusions that can be drawn from quantified statements.

Combining a “Some” or “Most” with an “All”

Check out the following argument:

If you live in Los Angeles, then you live in California. If you live in California, you live in the United States. Thus, if you live in Los Angeles, you live in the United States.

Not exactly groundbreaking, but a valid argument, nonetheless. In the field of LSAT logic, this is called the transitive property. Students quickly grasp this method of combining conditional statements. However, the same principle drives the most common inferences using “some” and “most” statements. Now, assume we had the following two premises:

Most hippies live in California. If you live in California, you live in the United States.

Now the conclusion would be…most hippies live in the United States. The only thing that changes is the “most” from the first statement. But wait, what if we changed that first statement again? Here we go:

Some transsexuals live in California. If you live in California, you live in the United States.

The conclusion is that some transsexuals live in the United States. Note the consistency between these three statements. If you combine any quantified statement (“Some” “Most” or “All”) with an “All” statement, you can draw a valid consclusion.

Note: One thing that always confuses students is the order of premises. Remember, the order in which premises are given to you doesn’t matter.

Commonly, you will also be given two characteristics about one group and asked to decipher whether there must be some overlap between those characteristics. Here is an example:

Most NBA players are tall. Most NBA players are rich.

So do those two statements prove that there is any overlap between tall people and rich people? Must there be anyone who is both tall and rich? The answer, here, is yes.

In these situations, the question is whether the two statements you are grappling with are strong enough to prove there must be overlap. In the situation above, both statements are rather strong (most). Since over 50% of NBA players are tall and over 50% of NBA players are rich, there must be at least one tall person who is rich (otherwise, you would have a total percentage over 100%). If the percentage ever rises over 100%, there has to be some overlap between the groups, thus enabling a valid “Some” conclusion.

Consider the following:

Some country singers are from Arkansas. Most country singers wear cowboy hats.

In this one, it could be true that only 12% of country singers are from Arkansas and only 55% of country singers wear cowboy hats. Thus, because that does not exceed 100% and you can’t establish overlap, it would be fallacious to conclude that someone from Arkansas must wear a cowboy hat (despite all evidence to the contrary). One more example:

Most Hawaiians hula dance. All Hawaiians eat pineapple.

Since at least 50% of Hawaiians hula dance and 100% of Hawaiians eat pineapple, this equals well over 100% and it would be safe to conclude that some people who eat pineapple also hula dance (side note: you want to be friends with such people).

If you don’t want to do the math, let me just leave you with the combinations that work and those that do not.

Good list (leads to valid conclusions): all and all, all and most, all and some, most and most

>Bad list (no valid conclusions): most and some, some and some

Quantified logic might sound scary, but, armed with a few simple principles, it can be much more enjoyable in practice.

8 Responses

  1. Julia says:

    What is the Good list? most + most, most+all, some +all??

    • joworr@yahoo.com says:

      most+most is (over 50%+over 50%); most+all is (over 50% + 100%); some+all is (over 0%+100%)…so the good list is always over 100%, and hence a valid inference / conclusion. thx.

  2. sashafierce says:

    Wow! This was soo helpful!

  3. Marty Funkhouser says:

    ^^ditto. Just stumbled on this old article. Formerly intimidating area of logic now makes perfect sense. Thank you!

  4. Louna says:

    This is very helpful it just cleared everything for me.

    I just want to clarify if anything is from the “good list” the conclusion will be with “Some” is this correct?

    • Hi Louna,

      All the combinations from the “good list” lead to a “some” conclusion, except for one combination of an “all” and a “most” statement. If we said that “Most NBA players are over 6’4″” and “All people over 6’4″ find airplanes uncomfortable,” we could actually conclude that “Most NBA players find airplanes uncomfortable.” This is because we know that every single NBA player that is over 6’4″ would be uncomfortable on an airplane. Since those are most of the NBA players, we can validly say that most NBA players will be uncomfortable on planes. This is the exception—every other combination from the good list gives you a “some” conclusion.

      Good luck!

  5. Jamara says:

    I was able to follow your post pretty clear! But Im just curious as to how does “many” and “few” fit into the equation?

    Thanks!

    • Hi Jamara!

      “Many” should be interpreted as a “some” statement.

      It depends on how the “few” statement is phrased. For instance, “A few of my friends are coming to my party” should be interpreted as “some of my friends are coming to my party.” On the other hand, “Few of my friends are coming to my party” should be interpreted as “most of my friends are not coming to my party.”

      Good luck!

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