by ohthatpatrick Fri Nov 09, 2012 10:06 pm
Hey, there.
This is a "Match the Flaw" question, so our first job is to understand the flaw in the original argument.
Our second job is to think about how to express the flaw in the abstract and to characterize the type/strength/order of claims in the premise(s) and conclusion.
The argument is trying to use a statistic that says:
most bikers who are A (18+) are B (have lights on their bikes)
+
most bikers who are ~A (under 18) are ~B (don't have lights)
====
thus, most B are A
You may notice that the first premise and the conclusion make an illegal move.
Most A are B ==does not tell us that==> Most B are A
Most criminals are men, but that doesn't mean that most men are criminals.
In fact, we could run with this example even more to mimic the original argument:
Most people who are criminals are men, whereas most people who are not criminals are not men. It follows that most men are criminals.
It's true, in the real world, that most criminals are men.
It's true, in the real world, that there are more women than men, so it's true that most non-criminals are not men (women).
But obviously this conclusion is silly. The reason this is a flaw is you are not allowed to equate Most A are B with Most B are A. The 2nd premise, which says that Most ~A are ~B doesn't do anything to help prove Most B are A.
So we know our flaw (Most A are B does not prove Most B are A), and we can describe the premise and conclusion ingredients in an abstract way:
P1: Most A are B
P2: Most ~A are ~B
Conc: Most B are A
Now we just need to scan the answer choices for this structure (these three ingredients can be in a different order, as long as the conclusion is still saying the same thing).
(A) is worth considering since it has three "most" statements ("most", "almost everyone", and "fewer than half" -- which can be translated into "most")
P1: Most A (ppl in Sheldon) are B (buy gas on Mondays)
P2: Most A (ppl in Sheldon) are C (buy groceries on Tuesdays)
This already fails to match the original, so we should eliminate and move on.
(B) This is not worth analyzing. There are no "most" statements. Furthermore, there's only one premise, whereas the original argument had two.
(C) This looks promising.
P1: Most A (voted) are B (on Conservative mailing list)
P2: Most ~A (didn't vote) are ~B (not on C-list)
Conc: Most B (on C-list) are A (voted)
On a test, I would commit to this answer and move on, while circling the problem, so that if I have extra time at the end of the section I can check the two choices I didn't consider.
(D) Not worth analyzing. There are not three "most" statements. The first premise is "all", the second is "most, and the conclusion is "at least two".
(E) Not worth analyzing. There are not three "most" statements. The first premise is "all", the second is "not all", and the conclusion is just comparative "X more than Y".
Notice how the extra time I spent initially categorizing the type/strength of the premise(s)/conclusion is allowing me to not have to carefully read all the answer choices.
It's a good example of how a little extra time on the front-end can save you tons of time on the back-end.
Let me know if you have questions about any of this. Hope this helps.