Joseph:  My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written...

Naz June 5, 2014

Make sure to pay close attention to the question stem. The question stem asks: "Joseph's statement that 'this alleged theorem simply cannot be proved' plays which one of the following roles in HIS argument?"

We know that Joseph's conclusion is: "it is likely that Fermat was either lying or else mistaken when he made his claim." Why? His encyclopedia says that Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed to have proved. He said that since no one else has been able to prove it, the theorem probably "cannot be proved." Thus, the statement "this alleged theorem simply cannot be proved" is a subsidiary conclusion in Joseph's argument, which his argument's main conclusion is based on. Therefore, answer choice (B) is the answer.

Hope that helped! Let us know if you have any more questions.

KimJongUn May 6, 2018

Can you please explain why answer choice A is not correct? I understand why B is the correct answer, but I do not understand why A can not be.

Mehran May 7, 2018

Hi @KimJongUn, thanks for your post.

An assumption is an *unstated* premise. The statement "this alleged theorem simply cannot be proved" is explicit (stated), and thus not an assumption.

Hope this helps! Please let us know if you have any additional questions.

Courtnee-Green July 17, 2018

@Mehran, can you explain why B is the correct answer?

Mehran July 19, 2018

@Courtnee-Green of course!

Let's breakdown Joseph's argument.

His conclusion is, "Therefore it is likely that Fermat was either lying or else mistaken when he made his claim."

What was his claim? That he had proved the theorem.

And why does Joseph claim he was either lying or else mistaken?

Because (1) he died without leaving behind any written proof and (2) it cannot be proved, since no one else has been able to prove it.

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.

This is an Argument Structure question that points us to the statement, "this alleged theorem simply cannot be proved".

We have identified that this is Joseph's subsidiary conclusion so (B) would be the correct answer, i.e. "a subsidiary conclusion on which his argument's main conclusion is based."

Hope that helps! Please let us know if you have any other questions.