Inferences That Can Be Made from Valid Argument Form Six

Keane Xavier

Hello, all:

Just so you don't have to bring up the curriculum or your notes, argument form six is as follows:

A → B

A → C

---

B ←s→ C

I don't have a question about why we may infer "B ←s→ C" from the premises above, but rather, I have a question about the inferences we can make from the individual premises themselves, inherently.

From what I understand, without a background in formal logic (or informal logic, for that matter), it seems we assume that universally quantified statements imply the existence of their subjects on the LSAT. This is what allows us to infer "most" and "some" from "all" on the LSAT - correct? If this is the case, then can't we infer "/B -m→ /A" and "/B ←s→ /A" from "A → B" (or /B → /A) and "/C -m→ /A" and "/C ←s→ /A" from "A → C" (or /C → /A)?

I'm not sure whether we'd be tested on these inferences if we're indeed able to infer them, or if past LSATs have tested them at some point, but I thought I'd ask. Presumably, LSAC is testing our ability to see that the premises above, "A → B" and "A → C," allow us to infer "B ←s→ C."

Thank you all for your time! Best wishes to you all in your studies!

apublicdisplay

Short answer is yes, you can infer that. For the purpose of applying the contrapositive, it makes no difference if you have, for example, "R → B" or "/R → /B." That is, "R" could just as easily represent "Not raining" as "/R" as long as you're consistent in this representation. So it doesn't make a difference if you apply the contrapositive to "R → B" ("/B → /R") and then draw the inference that "/B -most-> /R." It's just that this isn't a very useful inference to make.

NotMyName

@"Cant Get Right" we can, in fact, infer all of those listed, can't we? I pasted them below as well.

"/B -m→ /A" and "/B ←s→ /A" from "A → B" (or /B → /A) and "/C -m→ /A" and "/C ←s→ /A" from "A → C" (or /C → /A)

I know we can't take the contrapositive of a most statement. But we can take the contrapositive of A-->B and infer most and some statements from that, can't we? That's what Keane's done above.

BryantFu

@"Cant Get Right"

Cant Get Right

Interesting question.

So existential fallacy aside (the LSAT does not test this, so for our purposes, this is okay), I think this is fine. Just as A most B could be derived from A --> B, we can flip it around and take the contrapositive /B --> /A and it works exactly the same from there. This shouldn't come up, but to the best of my knowledge this looks okay if we disregard the existential thing.

https://schoome.files.wordpress.com/2013/06/unicorn-cartoon.png

Keane Xavier

Thanks, @"Cant Get Right"! It just felt weird to be able to infer these things. It seems that disregarding the existential fallacy has implications of its own, which I hadn't thought of until seeing this argument form.

PS - that picture is hilarious.

Cant Get Right

Yeah, and it's definitely problematic which is why LSAT just tries to stay away from it. But if we can take a "most" statement from a conditional relationship, then we have to be able to take the contrapositive forms because the contrapositive of the original statement is logically equivalent. So anything we can do to any conditional, we can do to its contrapositive. I'd be shocked to see anything like this on a contemporary LSAT though, so let's hope this discussion is just an interesting hypothetical!

Keane Xavier

@"Cant Get Right" said:
I'd be shocked to see anything like this on a contemporary LSAT though, so let's hope this discussion is just an interesting hypothetical!

Indeed - let's hope! Thank you for your help!