费费 50题

kenlilys

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Laura: Your encyclopedia is out of date.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.

50. Which one of the following most accurately describes a reasoning error in Laura’s argument?

(A) It purports to establish its conclusion by making a claim that, if true, would actually contradict that conclusion.

(B) 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.

(C) It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows.

(D) It uses the term “provable” without defining it.

(E) It fails to distinguish between a true claim that has mistakenly between believed to be false and a false claim that has mistakenly been believed to be true.



c说laura错在把必要条件当充分条件。看似有道理，而且其他答案也没有合适的，可我认为，joseph得出结论“Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.”就是基于前面“since---as the article points out---no one else has been able to prove it”，laura指出假想已经被证明，那么也就是打断了joseph的前提，这样joseph的结论也就是错的了。这样分析的话，其实laura的argument就不是必要而不充分了。

不知道思路有没有问题，欢迎讨论指正。

chriszhx

必要当充分，就算能证明也不能说明Fermat说谎或者错误，有很多种可能，也许是他随便说的但是定理凑巧被证明出来了。但是反之，则能证明就是必须的。

kenlilys

谢谢楼上的回答。
现在又想通了。。。“所有不能被证明的定理，其提出者要么说谎要么犯错误。”不能推出“所有能够被证明的定理，其提出者就没有说谎或者犯错误。”

pite82

大家的解释我明白了但是，但是我发现我并不清楚怎样是充分，怎样是必要啊？

哪位能帮忙解释下？

谢谢了

nickynicky

the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof

for a theorem that he claimed nonetheless to have proved.  这句话是什么意思。。。是说“F没有

留下任何对于某个定理的书面证明，他宣称如果他还活着，他就能证明”么？这样的话，他已经死了，就

没法判断他是否能证明了呀。。充要条件是1.定理能证明，2 P证明了定理，那不就不可能推出P没有说谎

了么。。。