Self-study
Support Each of the candidates in this year's mayoral election is a small-business owner. ████ ██████████████ ██████ ███ █████████ █████████ █████████ ██ █████████ ███████ █████ ███ ██████ █████████ ██ ██ █ ████ ██████ ███ ████ ██ ███ ██████████ ██ ████ ██████ ███████ ████████ ████ ███ ██████ █████████ ██ ██ █ ████ ██████
Method of Reasoning
The premises in this argument create a conditional chain, as shown below. Because all candidates are small business-owners, and most small-business owners are competent managers, and all competent managers have the necessary skills, the author concludes that most candidates have the necessary skills.
Identify and Describe Flaw
This argument rests on a misunderstanding of the quantifier “most.” Imagine there are 10 candidates for mayor, and there are 1,000 small-business owners. Let’s say 501 of the small-business owners are competent managers and therefore possess the necessary skills. That means there are 499 small-business owners who don’t possess the necessary skills. But remember, there are only 10 candidates for mayor! All 10 of those candidates could fall into the group of 499 small-business owners who lack the necessary skills.
21.
The pattern of flawed reasoning ██ █████ ███ ██ ███ █████████ ██ ████ ███████ ██ ████ ██ ███ ████████ ██████
a
Anyone who has ██████ ██ █████ ██ ████ ███████ ███ ████ ██ ███ ██ █████ █ █████ ████ ██ ████ █████████ ██████████ ███ ██████ ██ ███ █████ ███████████ ███ █████ ██ ███ ███ ███ ██████ ██ ███ █████ ██████████ ███ ████ ████ █ ████ █████ ██ ██████████ ██████████ ████ ██ ████ █████████ █████ ██████████ ███████████ ██████████
No flaw. This is a valid argument! If most of upper management has done sales for at least 1 year, and everyone who has done sales for at least 1 year understands marketing, then we can validly conclude that most of upper management understands marketing.
b
Everything on the ████ ██ ███████ █████ ████ ██ █████████ ████ ████████ █████ ███ ██████ ███ ███████████ ███ ███ ██████████ █████ ███ ██████ ███ ███ ██ █████████ ██████ ████ █████ ██ ███ ████ ██ ███████ ███ ███ ██ █████████
The premises in this argument create a conditional chain, as shown below. Because everything at Maddy’s is fat-free, and most fat-free things are sugar-free, and all sugar-free things are low calorie, the author concludes that most things at Maddy’s are low calorie. This is the same misunderstanding of the quantifier “most” from the stimulus: just because everything at Maddy’s is fat-free and most fat-free things in the world are low calorie does not mean that most things at Maddy’s are low calorie!
c
All the books ██ ████ █████████ ███ █████████ ██████ ████ █████████ █████ ███ ████ ████ ███ █████ █████ ██ ███ █████ ████ █ ████ ██████ ████ ███ █████ ██ ███ ████████ ██ ████ ████ █ ██████ ███ ██ ███ █████ ████ ███ ██ ███ █████ ██ ███ ████████ ██ ████ ████ █ ██████
Wrong flaw. Like the stimulus, this relies on a misunderstanding of the quantifier “most”: just because Ed’s books are all hardcover and most hardcovers in the world are 100+ pages, doesn’t mean that all of Ed’s books are 100+ pages! But the conclusion here is not in the same form as the stimulus’ conclusion—the stimulus concludes a “most” relationship, while (C) concludes a simple statement (Ed hasn’t read his books in under 3 hours).
d
Each of the ███████████ █████ ██ ████ ██████ ████ ████████ ██ ████ ████ ██ ████ █████ ████ █████ ████ ████ ██ ████ ████ ██ ███ ██████ ████████████ ███████████ ███ █████ ██ █████ ████ ████ ██ ████ ████ ███ ██ █████████████ ██ ███████ ████ ████ ██ ███ ██████ ██ ████ ██████ ████ ████████ ██ ███ ████ ██ █████████████
Wrong flaw. While (D) does describe a “most” relationship, that relationship isn’t actually utilized by the conclusion—it’s an offshoot of the conditional chain. Therefore, (D)’s flaw isn’t a misunderstanding of the “most” quantifier like we saw in the stimulus. Rather, (D) is flawed because its premises refer only to the avant-garde films at this year’s festival and its conclusion makes a claim about most of the films at the festival overall. We have no idea how many of those films were avant-garde!
e
All of the ███████ ███████ ████ ██ ████ █████ ████ ████ ███████ ██ █████ ████ ██ ███ ███████ ███████ ████ ██ ████ █████ ████ ████ ██████ ██ █████ ███ █████ ██ ███████ ████ ████ ██████ ██ ████ ██ ███ ████ ████ ███████ ██ █████ ██ ███████ ████ ████ ██ ███ ███████ ██ ████ █████ ████ ████ ███████ ██ ████ ████ ██████ ██ █████
Wrong flaw. Unlike the stimulus, this sets up a series of conditional statements that relate back to the same term (”helmet”): if it’s a helmet, it has plastic; most helmets have rubber, and all helmets with rubber have plastic. The argument then erroneously links the terms “plastic” and “rubber” using a “most” quantifier—a statement the premises do not support. But this is a different flaw and argument structure than the stimulus’!