I'm still having a bit of trouble understanding how the arguments presented in the stimulus and choice (B) are NOT circular reasoning, but I'm also struggling with how to symbolize the argument. I spent quite a bit of time trying to work through this, and I would appreciate it if someone could comment on my work to clear up my thought processes.
1) if some health-conscious consumers bought the cereal, the health claims printed on the box must be true. Some health-conscious consumers bought the cereal, so the claims are true.
(B[c] some HC) -> A
(B[c] some HC)
=========
A
B[c] = bought "our" cereal; HC = health-conscious consumers; A = accurate health claims on the package
2) No health conscious consumer would buy a food if the package contained health claims that were not true. But, some health conscious consumers did buy "our" cereal. So, some people who bought the cereal were really health conscious consumers.
~A -> (B[f] -> ~HC)
(HC some B[c])
=========
(B[c] some HC)
B[f] = bought food (in general); HC = health-conscious consumers; B[c] = bought "our" cereal; A = accurate health claims on the package
The circular reasoning enters into the argument when the author attempts to show that some of the people who bought the cereal are really health-conscious consumers by virtue of the fact that they bought the cereal in Argument #2, which is also the same premise that is used to show that the health claims were accurate in Argument #1.
Note that while I agree that there are two arguments here, I think that one depends on the other, with Argument #2 providing a sub-conclusion which is used to prove the claims are accurate in Argument #1.
mattsherman Wrote:So the first argument in the stimulus is valid. It says that
B --> A
B
--------
A
(Notation Key: B = bought the cereal, A = information is accurate)
I agree with the structure of the argument that you have presented here, but I think the notation leaves out a key piece of information that is used to connect the two arguments together: health-conscious consumers.
mattsherman Wrote:But the second argument in the stimulus is invalid. it says that
HC + B --> A
A + B
----------------
HC
(Notation Key: HC = health conscious, B = bought a food, A = accurate)
Clearly, this is reversed logic - and that's the flaw. We also see reversed logic in answer choice (B).
I agree that as you've notated it here, it appears to be reversed logic, but my interpretation led me to notate this part of the stimulus a little differently than what you have done.
For the answer choices, here's what I have:
(A) The second sentence appears to represent circular reasoning; however, it doesn't connect to the first sentence in the same manner that the argument in the stimulus does. This would be more correct if the second sentence were to say, "We know these people really are polite because they never fail to greet their coworkers." That said, it also does not contain the term shift that I noted in my diagram (specific case/product versus general case/product).
(B) correct answer choice. Notice the shift between "this card game" and "intellectually challenging card games" (in general). This is a direct match to the flawed logic in the stimulus, and a term shift that does not appear in (A).
(C) Not circular. The taste test represents a reasonable justification for assuming that the people really do have "highly developed taste."
(D) Not circular. Since we saw the people before they tried on the coat, we're not basing the conclusion on the fact that they were able to fit into the coat.
(E) Not circular. The second sentence provides some information that supports that the people who mistook the fake painting as the original painting actually had very poor eyesight.
Again, I would appreciate any comments; this was a very difficult question for me.