Hi @A.A., thanks for your post. Let's first assess the stimulus carefully.
Joseph is making an argument. His conclusion is introduced by the structural indicator "therefore": "it is likely that Fermat was either lying or else mistaken when he made his claim." What support is given for this claim? (1) Joseph's encyclopedia says that Fermat died in 1665 without leaving behind any written proof for a theorem he claimed to have proved; (2) no one else has been able to prove it so (3) probably it cannot be proved.
The third piece - the statement that "this alleged theorem simply cannot be proved" - is a subsidiary conclusion. It is supported by at least one premise (here, Joseph's claim that "no one else has been able to prove it") and it in turn supports the main conclusion (that Fermat was likely either lying or else mistaken). This is why answer choice (B) is correct.
Answer choice (C) is incorrect because this statement does not play the role of an "objection" to Joseph's conclusion. Indeed, Joseph's paragraph has no objections of any kind.
Hope this helps. Please let us know if you have any additional questions.
Michael_NwaNovember 15, 2018
I'm unsure why you all are saying the below is a subsidiary conclusion instead of the main conclusion:
Notice that (2) is a subsidiary conclusion, i.e. the conclusion is it cannot be proved and the premise is because no one else has been able to prove it.
MehranNovember 20, 2018
Hi there. A subsidiary conclusion supports another conclusion (the main conclusion). The subsidiary conclusion we identified here is a statement that is itself supported by a premise, and which in turn supports the overall conclusion of the stimulus. Does that help to clarify?
