2017年4月26日 星期三

CR高分混淆選項:雙重否定因果

原文發表於Dustin部落格:http://dustingmat.blogspot.tw/2017/04/cr.html

Newspaper editorial: In an attempt to reduce the crime rate, the governor is getting tough on criminals and making prison conditions harsher. Part of this effort has been to deny inmates the access they formerly had to college-level courses. However, this action is clearly counter to the governor's ultimate goal, since after being released from prison, inmates who had taken such courses committed far fewer crimes overall than other inmates.

為了減少犯罪率,政府打算不讓囚犯上課。
但是這會跟目的牴觸,因為有上課的出獄後再犯次數較低。

Which of the following is an assumption on which the argument depends?

A. Not being able to take college-level courses while in prison is unlikely to deter anyone from a crime that he or she might otherwise have committed.


這裡是一個假設題上很常見的陷阱混淆選項。遇到帶兩個否定的因果(如這裡的be unlikely to deter表因果)的時候,要特別注意邏輯上的等價命題:若P則Q只能推到若非Q則非P(注意是逆否),反之亦然——若非Q則非P 只能推回 若P則Q。

P->Q 絕對可以推出 Q'->P' 但絕對不會等於 P'->Q'
比如若下過雨(P)則地上會濕(Q),可以推得「若地上沒濕(Q'),則一定沒下過雨(P')」
但絕對不能說「若沒下過雨(P'),則地上一定不會濕(Q')」

強化完這個觀念,我們就來看A選項要怎麼推等價命題:

Not being able to take college-level courses while in prison (Q') is unlikely to deter (P') anyone from a crime that he or she might otherwise have committed.(Q':若不能上課,則P':不太會停止犯罪)只能推得P->Q:若可以阻止這些人犯罪,則這些人是會有機會受到教育的。(很明顯的主題無關)但不能推得Q->P:若能上課則會停止犯罪。(我猜這就是很多人一開始看到A選項會覺得不錯的原因:如果能上課就不會犯罪的話,確認上課必要性,結論不就成立了嗎?)

所以請各位以後看到雙重否定因果的時候,多留意逆否命題的推法。