P: Y–most–BP: ?D: B–some–D

Mehran May 27, 2016

@Spring of course! If more than half of Ys are Cs and more than half of Ys are Ds, there is bound to be an overlap between C and D.

A simple numerical example will make this very clear.

Let's pretend we have five Ys.

If more than half of the Ys are Cs, this means at least 3 of the Ys are Cs.

Similarly, if more than half of the Ys are Ds, the means at least 3 of the Ys are Ds.

Since both C and D make up more than half of the Ys, there is bound to be some overlap between C and D.

CCC
YYYYY
DDD

Hope this helps! Please let us know if you have any other questions.

SRuffner February 19, 2022

But this is comparing Y, B and D. Where are you getting C's?

Emil-Kunkin March 30, 2022

Hi @sruffner, this may have been a typo. It looks like the Cs should be Bs.

Mazen June 6, 2022

Hi

Should there be premise establishing the existence of at least one Y?

Emil-Kunkin June 7, 2022

Hi Mazen,

I think there should be if we are thinking about this in terms of a real argument- that is one with words instead of just symbols.The way these are written is intended to just focus on understanding the quantifiers.

On the other hand, perhaps this could be an argument about some abstract idea, or categories/concepts. We could say "most frameworks are useless, and most useless things are stupid, so some frameworks are stupid." I think this argument holds regardless of whether there exists an actual thing called a framework

Mazen June 9, 2022

Hi Emil,

Thank you for your input. Regarding the example you offer in the second paragraph, "most frameworks are useless, and most useless things are stupid," I believe that you meant to say: "most frameworks are useless, and most frameworks [not useless things] are stupid, so some useless things are stupid (or some stupid things are useless)."

The raw method is that to make an inference from two "most" premises, the variables to the right of the quantifier "most" out to be identical, and the inference/conclusion is a "some" quantifier relating the two variables to the left of the "most" quantifier.

The logic behind the raw method is that "most" means "more than half" and refers to the variable of which "most" things are the subject, e.g. "most of A" means "more than half of A."

And so when we have the same variable investing more than half of itself in two other variables, logic dictates that "at least one" of the former/same variable's investments overlaps/combines the other two. And since "at least one" means "some," we can then make the "some" inference combining the other two variables.

I have not doubt that it's a typo on your part, I just felt compelled to clarify the example in your post so future students don't get puzzled by it.

Having said that, I want to say that I sincerely appreciate your constant attention and followups to my posts. You are very helpful and I hope you continue to guide me with your expertise.

Again Thank you Emil

Emil-Kunkin June 10, 2022

Hi Mazen,

Good catch! Looks like I committed an illegal reversal of a most statement there. I think there is a broader lesson here- that if you find it useful to make an example/analogous argument in order to further your understanding of an argument presented, make sure you take the time to ensure that it is correct, and proofread. Thanks again!

Mazen June 11, 2022

Hi Emil

You're welcome, and your instruction is duly noted.

Thank You

nattyfitz March 10, 2024

@mehran another way to arrive at the correct answer is D.