PrepTest 112, Section 4, Question 13
Joseph: My encyclopedia says that the mathematician Pierre(89 more words not shown)
Joseph's statement that "this alleged(15 more words not shown)
- Aan assumption for(5 more words not shown)
- Ba subsidiary conclusion(8 more words not shown)
- Ca potential objection(12 more words not shown)
- Dthe principal claim(7 more words not shown)
- Ebackground information that(7 more words not shown)
Reading the argument
Not leaving a written proof isn't the same as never having found one. Perhaps Fermat worked it out without writing it down, or the written version was lost. We don't know that either happened, but the absence of a surviving proof leaves room for those possibilities.
Joseph adds that nobody else has managed to prove the theorem. That makes him suspect it cannot be proved, and he uses that suspicion to conclude Fermat was probably lying or mistaken. I can follow the steps without treating the absence of success as proof of impossibility.
Laura's new information does damage Joseph's reasoning: a successful proof defeats his claim that the theorem cannot be proved. But it doesn't settle whether Fermat personally proved it centuries earlier. Someone else could later succeed even if his own claim had been false.
What we’re looking for
The question focuses on Joseph's statement that the theorem probably cannot be proved. Start from his final claim about Fermat. The disputed statement gives a reason for that claim: if the theorem couldn't be proved, Fermat couldn't truthfully have proved it. I'd initially describe it as support for the conclusion. Now we need to see which answer accurately captures its place in the whole argument.
Working the answers
- A
It does help support the final claim, but it isn't left without support of its own. Joseph cites the encyclopedia's report that nobody else has been able to prove the theorem. He offers that as a reason to think proof is impossible. Whether that reason is persuasive is separate from whether he gives one.
- BCorrect
The statement does two jobs. It receives support from the reported failure of others to find a proof, and it provides support for the claim that Fermat was lying or mistaken. A subsidiary conclusion is a conclusion along the way to the main one.
Trace the sequence: others haven't proved it, so it probably cannot be proved; if it cannot be proved, Fermat's claim to have proved it was probably false. The middle claim is what the question names. Recognizing that it supports the final conclusion is useful, but B also captures the support Joseph offers for it.
- C
Joseph isn't anticipating an objection from someone else and trying to answer it. The impossibility claim is part of his own case. Laura later challenges that claim, but being challenged by another speaker doesn't turn it into an objection Joseph raised against himself.
- D
Joseph uses the statement to support his position; he doesn't structure the argument to refute it. Laura is the one who rejects the impossibility claim. D assigns Joseph the other speaker's attitude toward it and misses its supporting role in his argument.
- E
The claim matters directly to the conclusion about Fermat's honesty or accuracy. If the theorem were impossible to prove, that would be a reason to reject his claim to have proved it. Joseph therefore uses the statement as support, rather than merely supplying background about the subject.
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