feifei-50

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Laura: Your encyclopedia is out of date.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.

哪位大牛能帮我详细讲讲为什么c对阿，还是对必要充分之类的东西很头痛，这里先多谢了

My 2 cents:

B错，因为L并没有假设：“P的品性能够决定P所作结论的正确性”

C:“理论被证明”并不能推出“P证明了定理”。是必要条件而非充分条件

请楼主参考！

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

这句话折磨死我了，太绕了，最后终于看明白了，something that is necessary for its conclusion 就是必要条件啊，something that ensures that the conclusion follows. 就是充分条件啊。

那就是说，他错在把必要条件当成充分条件了。

J说P并没有证明，所以他是骗人的。

说明P不是骗人的必要条件是P的问题可证。但是P的问题可证不代表P一定不是骗人的。也许他想骗人，结果没想到被人给证明了呢。

但是L的意思却是，因为有人证明了，所以说P不是骗人，所以J错，正是把必要当充分。

ringcheng，很久不见你了，你怎么样啊？

I still don't understand, could someone draw a logic chain to explain?

我想3楼的意思是说：J的论证过程是：理论不能被证明--> Fermat不是撒谎就是错了（原命题）

而L的反驳论证却是：理论可以被证明-->Fermat没有撒谎也没有范错误；

换句话说：原命题的否命题是否成立，“理论不能被证明”并不是原命题的必要条件（而是充分条件），所以它的逆否命题不能作为充分条件推出“Fermat没有撒谎或者范了错误”

原命题的逆否命题（等价命题）应该是：Fermat没有撒谎也没有范错误--〉理论可以被证明

我不知道我这样说搂主是不是能接受？

不过我做了feifei的题以后，发现里面有很多都是将原命题的否命题直接认为成立，所以有很多错误都是针对这种类型的：只有原命题的逆否命题才与原命题等价！

我想请问,如果这类把原命题改成了否命题,是不是就意味着作者mistakes something that is necessary for its conclusion to follow for sth that ensures that the conclusion follows?

按照楼上的讲法，我还是弄不清楚哪个充分哪个必要~~