An Easy Guide to Quantified Logic
- Apr 29, 2019
- Reviewed by: Matt Riley
If you’ve been studying for the LSAT for a while, you’re well acquainted with combining “all” statements, such as, “All fast food burgers are unhealthy,” or, “Doing well on the LSAT requires sacrificing your social life.” And to be honest, as long as you’re proficient with those types of statements, you’ll be A-OK on the LSAT.
However, if you’re still looking to level up your diagramming skills, there’s another type of statement you should be aware of: statements containing quantifiers such as “most” or “some.” As in, “Most characters on Game of Thrones are doomed,” or, “Some babies are unfortunate-looking.” As you can probably infer, “most” statements provide information that is true in more than half of cases, while “some” statements provide information that is true in at least one case!
But the fun doesn’t stop there, because sometimes you’ll be asked to combine statements containing quantifiers. This is where things get a little sticky, because you’ll have to remember that a valid conclusion must be supported by premises of equal or greater strength.
How it works
In the context of combining statements containing quantifiers, you can remember the golden rule by thinking of the “4 S Rule”: The Sufficient of the Stronger statement must be Shared, and the conclusion is a “Some” statement.
Here’s how it works in practice – take the following example:
1. Everyone who is studying for the LSAT is stressed.
2. Some people who are studying for the LSAT are abstaining from alcohol.
In this case, we have an “all” statement (sentence #1) and a “some” statement (sentence #2). The stronger of those two statements is the first one, the “all” statement. The sufficient condition of the stronger statement is “studying for the LSAT”; in order for us to be able to combine these statements, they must both share that condition. Fortunately, the “some” statement also references people who are studying for the LSAT, so we’re good to go.
The conclusion, as we know from our golden rule, is going to be a “some” statement — in this case, that “Some people who are stressed are abstaining from alcohol.” (Note that the conclusion does not mention people who are studying for the LSAT — we need that shared term in order to establish this conclusion, but it doesn’t actually show up in the conclusion itself.)
Let’s try another:
1. Most puppies are adorable.
2. Most puppies are not house-trained.
Here we have two “most” statements, so there isn’t a stronger statement – they are, of course, equally strong. However, as long as they share a sufficient condition, we can combine ’em. In this case, they both share the sufficient condition “puppies,” so we’re good to go. And once again, we are going to draw a “some” statement as a conclusion: “Some things that are adorable are not house-trained.”
An important caveat
These combinations work because at least one of the premises is relatively strong. However, there are two combinations that will never, EVER work, simply because the premises are too weak to support a conclusion. You can never combine a “most” statement with a “some” statement, and you can never combine two “some” statements.
For instance, consider the following example:
1. Most movies are more than two hours long.
2. Some movies are created for children.
In this case, we know that more than half of all movies are longer than two hours in length, and we know that at least one movie is created for children. But there’s not necessarily any overlap between those two things! The movies created for children could fall in the minority of movies that are less than two hours long. So we can’t conclude anything from these two statements. And the same holds true for two “some” statements, regardless of whether they share any terms.
Keep things in perspective
Questions that ask you to combine quantifiers are relatively uncommon on the LSAT; at most, it’ll only come up in one or maybe two questions on your test. So in terms of prioritizing study topics, this skill falls pretty low on the totem pole. But if you already feel pretty comfortable with most things on the LSAT, it doesn’t hurt to be aware of how combining quantifiers works, so that in the unlikely event it does come up in a question you’re prepared to handle it. Remember the golden rule and the two combinations that never work, and you’ll be good to go.
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