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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. ████████ ████ ███████ ███████ ██████ ██████ ██ ███████ ██████████ ███ ███████ ██████ ████████ ███ ████ ███ ████ ████ ██ █████ ███ █████████ ██ ██ ██████ ████ ██████ ███ ██████ █████ ██ ████ ████████ ████ ██ ████ ███ ██████
██████ ████ ████████████ ██ ███ ██ █████ ████████ ███████ ███ ██ ████ ██████ ████████ ████████ ███ █████ ███ ███████ ██ █████████ ████ ████████████ ██████ ███ █████ ██ ██████████████████ ██ ██████
Summarize Argument: Counter-Position
Laura concludes that Fermat was not lying or mistaken when he claimed to have proven his theorem. She supports this by saying that someone recently proved the theorem, so it is provable.
Identify and Describe Flaw
Laura concludes that, because the theorem is provable, Fermat wasn’t lying or mistaken when he claimed to have proven it. That is, she concludes that Fermat really did prove the theorem. If Fermat proved the theorem, it is necessary that the theorem is in fact provable. But Laura mistakenly assumes that the theorem being provable ensures that Fermat proved it.
In other words, it’s possible that even though the theorem is provable, Fermat himself never proved it, so he was either lying or mistaken when he said that he did.
14.
Which one of the following ████ ██████████ █████████ █ █████████ █████ ██ ███████ █████████
a
It purports to █████████ ███ ██████████ ██ ██████ █ █████ █████ ██ █████ █████ ████████ ██████████ ████ ███████████
b
It mistakenly assumes ████ ███ ███████ ██ █ ████████ █████████ ███ ████████████ ██ █████ ██ █████████ ███ ████████ ██ ███ ██████ ████ ██████ ███ █████
c
It mistakes something ████ ██ █████████ ███ ███ ██████████ ██ ██████ ███ █████████ ████ ███████ ████ ███ ██████████ ████████
d
It uses the ████ ██████████ ███████ ████████ ███
e
It fails to ███████████ ███████ █ ████ █████ ████ ███ ██████████ ████ ████████ ██ ██ █████ ███ █ █████ █████ ████ ███ ██████████ ████ ████████ ██ ██ █████