Self-paced
Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. ████████ ████ ███████ ███████ ██████ ██████ ██ ███████ ██████████ ███ ███████ ██████ ████████ ███ ████ ███ ████ ████ ██ █████ ███ █████████ ██ ██ ██████ ████ ██████ ███ ██████ █████ ██ ████ ████████ ████ ██ ████ ███ ██████
██████ ████ ████████████ ██ ███ ██ █████ ████████ ███████ ███ ██ ████ ██████ ████████ ████████ ███ █████ ███ ███████ ██ █████████ ████ ████████████ ██████ ███ █████ ██ ██████████████████ ██ ██████
Stimulus Summary
Joseph's argument has three layers. His encyclopedia says Fermat claimed to have proved a theorem but died without leaving any written proof. Since no one else has been able to prove it either, Joseph concludes the theorem probably can't be proved. And if it can't be proved, then Fermat was probably lying or mistaken when he said he proved it.
Laura responds by updating the facts. Someone has recently proved Fermat's theorem, so the encyclopedia is out of date. Since the theorem is provable, she concludes that Joseph is wrong to say Fermat was lying or mistaken.
It's worth translating Laura's conclusion into what it actually means. If Fermat wasn't lying and wasn't mistaken when he said he proved the theorem, then he proved it. That's what Laura is claiming: Fermat proved the theorem. Her evidence for this is that someone else recently proved it, which shows the theorem is provable. But provable and "proved by Fermat" are different things. Someone proving the theorem today shows it can be done. It doesn't show that Fermat, specifically, did it back in 1665. He could still have been wrong about his own proof even though the theorem itself turned out to be provable.
14.
Which one of the following ████ ██████████ █████████ █ █████████ █████ ██ ███████ █████████
a
It purports to █████████ ███ ██████████ ██ ██████ █ █████ █████ ██ █████ █████ ████████ ██████████ ████ ███████████
Laura’s premise doesn't support her conclusion well, but it doesn’t contradict her conclusion.
b
It mistakenly assumes ████ ███ ███████ ██ █ ████████ █████████ ███ ████████████ ██ █████ ██ █████████ ███ ████████ ██ ███ ██████ ████ ██████ ███ █████
Laura doesn’t make any claims or assumptions about the quality of Fermat’s character or how his character affects the accuracy of his claims.
c
It mistakes something ████ ██ █████████ ███ ███ ██████████ ██ ██████ ███ █████████ ████ ███████ ████ ███ ██████████ ████████
In order for Laura’s conclusion— that Fermat was neither lying nor mistaken about proving the theorem— to follow, it is necessary that the theorem is actually provable. But the theorem being provable does not ensure that this conclusion follows.
d
It uses the ████ ██████████ ███████ ████████ ███
It’s true that Laura never defines the term “provable,” but this isn’t an error in her argument. She doesn’t need to define the term.
e
It fails to ███████████ ███████ █ ████ █████ ████ ███ ██████████ ████ ████████ ██ ██ █████ ███ █ █████ █████ ████ ███ ██████████ ████ ████████ ██ ██ █████
Laura doesn’t mention either of these kinds of claims, nor does she fail to distinguish between them. Joseph mistakenly believes a true claim— that the theorem is provable— to be false, but this doesn’t describe an error in Laura’s argument.