Dorbear & fyhllj，还是关于费费 CR 21题--取非？

freegirl

21. Historian: We can learn about the medical history of individuals through chemical analysis of their hair. It is likely, for example, that Isaac Newton’s psychological problems were due to mercury poisoning; traces of mercury were found in his hair. Analysis is now being done on a lock of Beethoven’s hair. Although no convincing argument has shown that Beethoven ever had a venereal disease, some people hypothesize that venereal disease caused his deafness. Since mercury was commonly ingested in Beethoven’s time to treat venereal disease, if researchers find a trace of mercury in his hair, we can conclude that this hypothesis is correct.
Which one of the following is an assumption on which the historian’s argument depends?
(A) None of the mercury introduced into the body can be eliminated.
(B) Some people in Beethoven’s time did not ingest mercury.
(C) Mercury is an effective treatment for venereal disease.
(D) Mercury poisoning can cause deafness in people with venereal disease.
(E) Beethoven suffered from psychological problems of the same severity as Newton’s.

正确答案是B
------------------------from dorbear-----------------------------------------------
对(B) 的取非应该是：All people in Beethoven's time ingested Mercury. (very important! Look up some reference if any doubt.) 亦即发现 M 并不能推出一定患过venereal，因为所有人都用过M。

-------------------------from fyhllj---------------------------------------------------
some为假 ------〉all毕为假
some为真----〉推不出all为真或未假
所以，对some取反，应为none.

my confusion is: 对some取反是什么意思呀？是把原 (B) 变成假吗？
根据 fyhllj, 原 (B) 为假后，all毕为假, 所以，取反后是不是成了： “All people in Beethoven's time did not ingested Mercury” 为假？ 而这个是不是又等价于：“None in Beethoven's time ingested Mercury" 为假？ ＝〉some in Beethoven's time ingested Mercury 为真？
则与 dorbear 的不同，而且如果这样的推理，结论就依然成立呀！

不知道我哪里的分析出了毛病？我是越来越晕了！　而且，怎么样才能迅速准确地取反呢？　到底对 some 取反，应为 none 还是应为 all？ 对 some not 取反, 应为 none 还是应为 all ?  对 all/all not  取反呢？

谢谢了！

dorbear

黑体字为结论：
some为假 ------〉all毕为假
some为真----〉推不出all为真或未假
所以，对some取反，应为none.

freegirl

Dorbear gg,

please give me more detailed analysis. I'm so confused!
对some取反，应为none
So why you got : 对(B) 的取非应该是：All people in Beethoven's time ingested Mercury.
what on earth the 取非 means? add a "not" to the original statement?
God, save me!

freegirl

some为假------〉all毕为假
some为真----〉推不出all为真或未假
(B) Some people in Beethoven’s time did not ingest mercury. (为真)

取非: (B) Some people in Beethoven’s time did not ingest mercury. (为假) =>
All people  in Beethoven’s time did not ingest mercury (毕为假) == None in Beethoven’s time did ingest mercury ;
therefore, the conclusion (if his hair has the trace of mercury, he had such disease) has been strengthened rather than weaken when we 取非 the answer (B) ?????

fyhllj

freegirl,这是lsat中典型的逻辑游戏，你可能是钻入牛角尖了。

some people hypothesize that venereal disease caused his deafness. （要证明的假设）Since mercury was commonly ingested in Beethoven’s time to treat venereal disease,（证据）   if researchers find a trace of mercury in his hair, we can conclude that this hypothesis is correct. （结论）

其实，这题很简单：只需在证据和结论中间找到一个桥梁，这个强梁就是作者推论所依据的假设：即：在那个时代确实有人注射水银。
但是，those test maker不像我们正常人一样直接说：Some people in Beethoven’s time did ingest mercury. 他却说：Some people in Beethoven’s time did not ingest mercury！！很迷惑是吧。

其实两者是等价的

Some people in Beethoven’s time did ingest mercury.== Some people in Beethoven’s time did not ingest mercury

这是逻辑假言判断对当关系中的下反对关系，即上述两者不能同假，但可以同真。其推倒，要用到逻辑假言判断的差等关系与矛盾关系。如果你有兴趣可以参看以下面一个帖子的有关内容。
http://forum.chasedream.com/dispbbs.asp?boardID=24&ID=17023

freegirl, 千万不可沉迷于logic game中，gmat是极少考这种logic game。要说在碰到这种题如何处理：只须记住：Some people in Beethoven’s time did ingest mercury.== Some people in Beethoven’s time did not ingest mercury。 出题人只不过是拐了个弯而已。

fyhllj

[此贴子已经被作者于2003-10-2 5:09:15编辑过]

freegirl

fyhllj, 是的，偶也觉得深陷其中，不能自拔了也！
但偶还是想知道如何取非 B 呀？
如果说 Some people in Beethoven’s time did ingest mercury.== Some people in Beethoven’s time did not ingest mercury
那么， 对(B) 的取非：All people in Beethoven's time ingested Mercury 对吗？ 又是怎么通过等差来得到的这个取非结果。

dorbear

[face=Verdana]来这样看看取反的过程，希望有助于理解：
(B) Some people in Beethoven’s time did not ingest mercury.

取反：Some => None; 句子变成：
None of people in Beethoven’s time did not ingest mercury.

到这里可以理解吗? 好往下来：
句子中有一个 None, 后面有接了一个 Not; None ... Not 不就是 All 吗？所以取反会得到：
All people in Beethoven's time ingested Mercury.希望有帮助。[/face]

[此贴子已经被作者于2003-10-2 11:46:16编辑过]

fyhllj

以下是引用freegirl在2003-10-2 6:34:00的发言：
fyhllj, 是的，偶也觉得深陷其中，不能自拔了也！
但偶还是想知道如何取非 B 呀？
如果说 Some people in Beethoven’s time did ingest mercury.== Some people in Beethoven’s time did not ingest mercury
那么， 对(B) 的取非：All people in Beethoven's time ingested Mercury 对吗？ 又是怎么通过等差来得到的这个取非结果。

freegirl mm, 我想说的是此题是纯形式逻辑题，并不适合gmat中的假设取非法来处理。按照gmat中的假设取非法的理论，对假设取非将构成强销弱。但此题取非后，非但不能
削弱，反而加强！这就是你的疑惑所在，对吧。所以，此题根本不能用假设取非法来做。其做法只能如我上贴所示。不知是否说清楚了。

如还不明白，欢迎会铁，我们继续讨论。
fyhllj

[此贴子已经被作者于2003-10-2 17:03:01编辑过]

fyhllj

这两个贴类似，连在一起

http://forum.chasedream.com/dispbbs.asp?boardID=24&ID=17023

freegirl

楼上两位 gg 看过来：

我的ｃｏｎｆｕｓｉｏｎ　在于：用差等关系
some为假------〉all毕为假　
some为真----〉推不出all为真或未假
我推出来的和　ｄｏｒｂｅａｒ　的不同：
ｄｏｒｂｅａｒ：　取反：Some => None; （为什么呀，怎么得来的呀？？？）
句子变成：
None of people in Beethoven’s time did not ingest mercury. ＝＝all did, 因此削弱 （因为所有的人都吃水银， 那么即使贝多芬头发上有水银也不能确认他就是得了xx 病）

Ｍｉｎｅ：
我的取反过程是这样的：some not 本为真， 现取反为假， 则 all not 必为假 （因为差等关系：some为假------〉all毕为假） ；又因为 all not　（所有人不吃水银　为假） == none did 为假（没有人吃水银　为假） 推不出 some　did or not ( 因为差等关系：all 为假 ---〉some 真假不定), 因此得不出削弱结论，也得不出加强。

又因为 fyhllj gg 说过：some not == som did ( I agree),
如果 给 some did 取反：some did 本为真， 现取反为假, 则 all did 必为假 （因为差等关系：some为假------〉all毕为假）；   则 all did 为假 推不出 some did 为真或为假 (因为差等关系：all 为假 ---〉some 真假不定）因此， 得不出削弱结论，也得不出加强。


我的取反过程中出现什么问题？是不是取反不等于把一个真命题变成一个假命题？
如果是这样，我就只好记住　ｄｏｒｂｅａｒ＇ｓ　ｓｏｍｅ　取反成　ｎｏｎｅ　啦。

如果取反等同于把一个真命题变成一个假命题，　那么我的推理蛮像一会事的，　我就赞同ｆｙｈｌｌｊ　的结论：所以，此题根本不能用假设取非法来做， 而应该找一条在证据和结论中间找到一个桥梁，这个强梁就是作者推论所依据的假设。

还有，这几天我有一种感觉：取反加 减 not 是不太适用于这种牵涉集合类型 的。

还请 gg 们再拨开雨雾一把吧！