PrepTest 30, Section 3, Question 14
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. Probably this alleged theorem simply cannot be proved, since�as the article points out�no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.
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. Probably this alleged theorem simply cannot be proved, since�as the article points out�no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.
Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat's theorem. And since the theorem is provable, your claim�that Fermat was lying or mistaken�clearly is wrong.
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. Probably this alleged theorem simply cannot be proved, since�as the article points out�no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.
Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat's theorem. And since the theorem is provable, your claim�that Fermat was lying or mistaken�clearly is wrong.
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. Probably this alleged theorem simply cannot be proved, since�as the article points out�no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.
Which one of the following most accurately describes a reasoning error in Laura's argument?
It purports to establish its conclusion by making a claim that, if true, would actually contradict that conclusion.
It mistakenly assumes that the quality of a person's character can legitimately be taken to guarantee the accuracy of the claims that person has made.
It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows.
It uses the term "provable" without defining it.
It fails to distinguish between a true claim that has mistakenly been believed to be false and a false claim that has mistakenly been believed to be true.
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