Feifei50

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Laura: Your encyclopedia is out of date.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.
      

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

Laura: Your encyclopedia is out of date.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.
      

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.

So what is "something that is necessary for its conclusion to follow "and " something that ensures that the conclusion follows. " in this argument ?I am always confused with this kind of question. Please tell me!!!!!

誤以為 "something that is necessary for its conclusion to follow " (必要条件)

 is

 " something that ensures that the conclusion follows." (充要条件)

Hope you get it now.

thank you . but what is the (必要条件)and (充要条件)in this argument?thank you

conclusion:  the theorem is provable ---> Fermat was not lying or mistaken.

the theorem is provable is only a 必要条件, but Laura takes it as a 充要条件.

In other words, Fermat may still be lying or mistaken even if the theorem is provable to us.