QUESTION TEXT: Which one of the following most accurately…
QUESTION TYPE: Flawed Reasoning
CONCLUSION: Laura concludes that Fermat was neither lying nor mistaken when he claimed to have proven the theorem.
REASONING: Someone else did prove the theorem (therefore it was possible to prove the theorem.)
ANALYSIS: Laura makes the mistake of assuming that since it was possible for Fermat to have proven the theorem then Fermat must have proven the theorem.
It is possible that Fermat didn’t actually prove the theorem, even though someone else did later.
- The fact that someone did prove the theorem does not contradict the idea that Fermat did. In fact it shows its is possible that Fermat did prove it. It doesn’t make it certain that Fermat proved the theorem, of course.
- Laura hasn’t said anything about the quality of Fermat’s character.
- CORRECT. For Fermat to have proven the theorem it is necessary that it was possible. But the mere fact that it was possible doesn’t mean that Fermat actually did prove the theorem.
- Everyone can figure out what provable means: possible to prove true.
- Laura doesn’t mention either of these two phenomena. Joseph made the mistake of thinking that a true claim (the theorem can be proven) was false, but that doesn’t have much to do with Laura’s reasoning.
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