Q13 - Joseph: My encyclopedia says that

[Crogati]

So I was stuck between (A) and (B). I incorrectly chose (A).

Is (A) incorrect because an assumption is something always unspoken? So a written statement never be an assumption?

Or is (A) wrong because it is not true that there is no support offered for Joseph's statement "probably this alleged theorem simply cannot be proved, since--as the article points out--no one else has been able to prove it." I suppose the support is the article he mentions?

The reason that (B) is correct seems to be much more straight forward. It essentially supports the final conclusion of Joseph's argument, and it passes the "THEREFORE" test.

[ohthatpatrick]

You were right on both counts, i.e. (A) is wrong for both reasons you mentioned.

An assumption, by definition, is unstated, so there's no way an explicit claim from someone's argument could ever correctly be called an assumption.

But, additionally, the claim IS supported. That's why we're allowed to call the claim a subsidiary conclusion.

"This alleged theorem simply cannot be proved"
Why?
since no one else has been able to prove it

Whenever you see 'since' or 'because' you're seeing a supporting idea, and the idea that it's supporting can be called a conclusion (whether or not it's the MAIN conclusion is another subject).

The overall argument core looks like:
no has been able to prove the theorem --> probably can't be proved --> Fermat was probably either lying or mistaken

Hope this helps.

[Crogati]

This was most helpful! Thank you.