Self-study
Professor O'Brien: Support Any of my students who heard Mercado's lecture from the beginning would have thought it was fascinating, and I know that Support some of my students did think it was fascinating, so Conclusion some of my students must have heard it from the beginning.
Argument Summary
Questions you absolutely need to diagram are rare, but sometimes a stimulus really begs for it. This stimulus begs to be diagrammed: “All thisses are thats, some doops are dips, therefore some doopity do.”
The baseline diagram you should arrive at looks like this:
Domain: O’Brien’s Students
Premise 1: Beginning → Fascinated
Premise 2: Some Fascinated
________
Conclusion: Some Beginning
The basic shape of this flawed reasoning is sufficient / necessary confusion: everyone who listened from the Beginning was Fascinated, but that doesn’t mean everyone who was Fascinated was listening from the Beginning. It’s possible that some of these Fascinated kids were from the not-Beginning group. In that world, the author’s reasoning that those kids must have been there from the beginning wouldn’t hold up.
Spoiler Alert: identifying the gap in this argument turns out to be a lot easier than understanding exactly how the correct answer exploits that gap (just look at how long the explanation for (D) is).
21.
The conclusion of Professor O'Brien's ████████ ████ ███ ██████ █████████ ████ ███ ████████ ███████ ██ ███ ███████████ ████
a
some of Professor █████████ ████████ ███ ████ ██████████ ██ █████████ ████ ███ ████ ██████ ██ ██████ ███ ███████
What if some students weren’t able to attend the lecture? That’s fine, there’s still room for the other students who did attend the lecture to have listened from the beginning.
b
many people who ███ ███ █████████ █████████ ████████ ███ ███ █████ ████ ███ ███████ ███ ████████████ ████ ██████ ████ █████ ██ ████ ███ █████████
What if some students who are not O’Brien’s students (e.g., students of a different professor) were there from the beginning and hated the lecture? That’s fine, our conclusion is about O’Brien’s students, some of whom could still have listened from the beginning.
c
some of Professor █████████ ████████ ████ █ ███ ███████ ████ ███ ███ ███████ ███ ███ ███ ████ ███ ███████ ███████████
What if some students weren’t there from the beginning and didn’t find it fascinating? That’s fine, there’s still room for other students to have arrived on time.
d
no one who █████ ███ ███████ ████ ███ █████████ ███ ███████ ████ ██ ███ ███████████ ███ ███ ██ █████████ █████████ ████████
(D) undermines the argument by presenting a strong counterexample: a possible world in which the premises are true and the conclusion cannot be true. This is best understood through a reductio ad absurdum: in the world of (D)’s counterexample, assuming the truth of the Professor’s conclusion results in a logical contradiction. Strap in:
(1) Let’s say the conclusion is true: there is at least one of O’Brien’s students who was listening from the Beginning. Let’s say that person is you. You are a Beginning kind of student.
(2) Premise 1 says if you’re a Beginning kind of student, you must also be Fascinated. So you are a Beginning+Fascinated kind of student.
(3) Now (D) comes in and says if you’re a Beginning+Fascinated kind of student, you are not one of O’Brien’s students at all.
So in a world where (D) is true, the Professor’s conclusion cannot be true, because if it were true, you would be both O’Brien’s student and not O’Brien’s student.
e
not everyone who ███████ ██ ███ ███████ ██ ████ ███ ████ ██ ████ ███ ██████ ███████ ███████ ██ ███████████ ██████ ██ █████ ███ ████ ████ ██ ████████
What if some of the those who were listening from the beginning couldn’t hear all of it? Well for starters, if any of those people were O’Brien’s students, our conclusion is proven true right then and there. But at any rate, this does nothing to suggest none of O’Brien’s students arrived on time.