Self-study
Merle: Support Usually when I insert a dollar bill into the change machine at the office it makes a squeaking sound before it produces change. ███ ███ ███████ ███ ████ ███ █████ ████ ████ ███ ████████ ██████ ██ ██ ███████ ████ ██ ██████ ███ ██████████ ██ ████ ██ ████ ███ ████████ ██████ ███████ ██ ██████ ███
tldr
The flaw in the argument is that the conclusion is about all moments in time whereas the first premise was only about those moments in time when I insert a dollar bill into the machine. So sure, most of the time when I insert a dollar bill, the outlet is turned on (which would have been the valid conclusion). But that doesn't mean that most of the time the outlet is turned on. What, am I like just standing next to the machine 24/7 nonstop inserting dollar bills into it?
Shallow Dip: Getting to (D) and (E)
Before explaining this argument’s flaw, which requires a full breakdown of its structure, I want to emphasize a fundamental element of Parallel (and Parallel Flaw) questions: the correct answer’s claims must match the logical strength of the stimulus’ claims.
For this question, the spectrum of quantifiers – from some to most to all – is the relevant measure of logical strength: if a Parallel question’s stimulus features 2 some claims and a most conclusion, an answer choice that features 2 all claims and a some conclusion is wrong. Straight up.
In this stimulus,
This logic alone should narrow the field down to (D) and (E) during your shallow dip. Explanations for (A), (B), and (C) are below each answer – take a moment to identify their quantifier mismatches before revealing them.
Deep Dive: Argument Structure and (D) vs. (E)
Let’s talk about the argument’s actual structure. On a first read in English, the argument might seem completely fine:
Premise 1: When I insert a bill, most of the time there’s a squeak.
Premise 2: If there’s a squeak, the outlet must be on.*
________
Conclusion: The outlet is on most of the time.
*In Premise 2, “
A completely fine argument is no good, though. This is a Parallel Flaw question. The flaw gets easier to see if you try to think in formal logic. Diagramming the conclusion is a bit ridiculous:
Premise 1: Insert Bill –most→ Squeak
Premise 2: Squeak → Outlet ON
________
Conclusion: ??? –most→ Outlet ON
Perhaps you want to write “Outlet –most→ ON,” but you can’t just go around splitting up individual terms willy nilly. Like you can’t say “Insert –most→ Bill” and make formal logic moves around that.
Spoiler Alert: You don’t actually need to figure out what the conclusion’s deal is to distinguish between (D) and (E). You just need to pick the answer that makes you confused in the same way. You can diagram (E)’s conclusion like normal – it just links two terms from its premises. (D)’s is weirder.
Here’s what’s actually going on. There’s a subtle domain shift between Premise 1 and the Conclusion. Premise 1 applies to [moments in time when I am inserting a dollar bill]. The Conclusion applies to [all moments in time]:
Premise 1: If we consider all the moments in time when I am inserting a dollar bill, most of those moments involve some squeaking.
Conclusion: If we consider all the moments in time, most of those moments involve the outlet being on.
For another lens on the domain shift, the stimulus’ conclusion would be valid if it said:
Valid Conclusion: The electric outlet usually is turned on when I am inserting a dollar bill.
Here’s the argument again in formal logic emphasizing the domain shift:
Premise 1: [Moments in time when I am inserting a bill] –most→ Squeak
Premise 2: Squeak → Outlet ON
________
Conclusion: [Moments in time] –most→ Outlet ON
So yeah, that’s the template (D) will match. (B) matches the domain shift, too, by the way! It’s just wrong for other reasons.
22.
Which one of the following █████████ ████████ ██████ █████████ ████ ███████ ██ ███ ██████ █████████ █████████ ██ ███████ █████████
a
Everyone who has ████ ███ ███ ██████ █████ █████ ███ ████ ███████████ ███████ ███ ████ █████ ███████ ██████ ████ █ █████ ████████████ ██████████ ████████ ███ ███ ████ ███ █████ ████ ████ █ █████ ████████████
(A) is wrong because it features 3 all claims instead of one most premise, one all premise, and a most conclusion. That mismatch suffices.
There are other reasons too, but they’re much harder to identify and describe. Hit me up in the comments if you’d like a full breakdown just for fun, but if you dove any deeper than “3 all claims BOOO!” you need to take this as a lesson on the importance of matching quantifiers.
b
Some people who ████ ████ ███ ███ ██████ █████ █████ ███ ████ ███████████ ███ ███ ████ █████ ███ ██ ██████████ ██ ██████ ███ ████ █████ █████████████ ██████████ ████ ██████ ████ ████ █████ █████████████
(B) is wrong because it replaces the stimulus’ most claims with some claims. That mismatch suffices.
Good thing, too, because (B) also mirrors the stimulus’ domain shift – it jumps from [people who have read the novel] to just [people]. For advanced reasons I could describe but won’t, it turns out that pulling a domain shift like this with some claims is actually fine – (B) is a valid argument.
Hit me up in the comments if you’d like a full breakdown just for fun, but all you need to eliminate (B) is “2 some claims BOOO!”
c
Many people who ████ ████ ███ ███ ██████ █████ █████ ███ ████ ███████████ ████████████ ████████ ███ █████ ███ ████ ██████████ ███ █ █████ ████████████ ██████████ ████ ██ ███ ██████ ███ ████ ████ ███ █████ ████ ████ █████ █████████████
(C) is wrong because it replaces the stimulus’ most claims with some claims. “But wait!” you might protest, “Those claims you’re talking about in (C) are many claims!” Indeed they are. And many means some.
(C) also lacks the stimulus’ domain shift, and demonstrates valid some before all reasoning. Hit me up in the comments if you’d like a full breakdown just for fun, but you don’t need any of that to eliminate (C). All you need is “2 some claims BOOO!”
d
Most people who ████ ████ ███ ███ ██████ █████ █████ ███ ████ ███████████ ███ ███ ████ ██████ ███████ ██████ ███ █████ █ █████ ████████████ ██████████ ████ ██████ ████ ████ █████ █████████████
(D) should pass your shallow dip because it matches the stimulus’ quantifiers with one most premise, one all premise, and a most conclusion.
On a deep dive, it also preserves the stimulus’ domain shift – it jumps from [people who have read the novel] to just [people]. Here’s (D)’s full structure:
Premise 1: [People who have read the novel] –most→ Disturbing
Premise 2: Disturbing → Vivid Imagination
________
Conclusion: [People] –most→ Vivid Imagination
e
Most people who ████ ████ ███ ███ ██████ █████ █████ ███ ████ ███████████ ███ ███ ████ ██████ ███████ ██████ ███ ████ █████ █████████████ ██████████ ████ ██████ ████ █████ ████████████ ████ ████ ███ ████ ███████████
(E) should pass your shallow dip because it matches the stimulus’ quantifiers with one most premise, one all premise, and a most conclusion.
On a deep dive, though, it doesn’t preserve the stimulus’ domain shift. (E)’s conclusion is just Premise 2 flipped left-to-right and turned into a most claim:
Premise 2: Disturbing → Vivid Imagination
Conclusion: Vivid Imagination –most→ Disturbing
(D) and (E) have the exact same premises, so look at (D)’s explanation to see the conclusion (E) should have drawn.