这个考试悖论还真是引出很多非常有意思的话题!



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送交者: 自如 于 2005-4-19, 12:38:02:

林壑虽然有那两处令人不快的发挥,实在也通告了大家可以看什么书。正准备去借那本Unexpected Hanging,nothing的帖子让我知道了悖论还是源于“预先知道”的理解上。

(预先知道明天考试=>明天不能考试)=>预先知道明天不会考试
But 明天真的考试了=>预先没有知道

这似乎与“This is a lie”的味道有些相似。MathWorld上说它与bottle imp paradox类似,我倒没有想明白为什么。大概还是要看看Gardner的书。

abada的帖子涉及到一个我曾经认真想过很久的问题:假如自由意志只是假象,我的努力奋斗有否意义?最后我的结论是,先把它放一边,“想”干嘛干嘛。说不定“自由意志只是假象”并非事实,或者我的理解有误呢?

量子现象存在于微观层次上,而人的行为是体现在宏观层次上的。测不准原理是否能为自由意志留出空间,赵南元的“认知科学和广义进化论”里有一个很有意思的讨论,他并且从社会责任的角度给自由意志这一概念的存在提出了他自己的解法。复杂的确定性系统的混沌现象可以为自由意志提出另一种理解:一个人的行为也许在“客观世界”里是已经确定的了,但从认识论的角度来讲,别人无法精确预测其长期行为,因此表现出“自由意志”的假象。

D. Dennett的新书“Freedom Evolved”则是从进化的角度讨论这个问题。由他的书名可以看出,他认为自由意志的概念是人的意识在进化过程中逐渐发展起来的结果,是一种“useful illusion”。不过我还未有时间细读全书。

abada说的股票预测又是一个很有意思的问题:假如有人真的发现了一种预测方法,可以准确的估计股票长期的升跌,他也只能将之藏诸名山。因为如果大家都知道了这一方法,大家都运用这种方法去投资,股票价格的规律将被改变,而这种方法也就不再灵验。也就是说,从某种意义上说,我们对社会规律的“认识”将改变社会的规律本身。我们要认识我们的“认识”本身,在认识过程中认识不可避免的会遭到改变。这似乎是另一种层面上的“测不准原理”,也是某种意义上的“考试悖论”。

=== Unexpected Hanging @ Mathworld
http://mathworld.wolfram.com/UnexpectedHangingParadox.html

A paradox also known as the surprise examination paradox or prediction paradox.

A prisoner is told that he will be hanged on some day between Monday and Friday, but that he will not know on which day the hanging will occur before it happens. He cannot be hanged on Friday, because if he were still alive on Thursday, he would know that the hanging will occur on Friday, but he has been told he will not know the day of his hanging in advance. He cannot be hanged Thursday for the same reason, and the same argument shows that he cannot be hanged on any other day. Nevertheless, the executioner unexpectedly arrives on some day other than Friday, surprising the prisoner.

This paradox is similar to that in Robert Louis Stevenson's "bottle imp paradox," in which you are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every desire. The only catch is that the bottle must thereafter be resold for a price smaller than what you paid for it, or you will be condemned to live out the rest of your days in excruciating torment. Obviously, no one would buy the bottle for 1¢ since he would have to give the bottle away, but no one would accept the bottle knowing he would be unable to get rid of it. Similarly, no one would buy it for 2¢, and so on. However, for some reasonably large amount, it will always be possible to find a next buyer, so the bottle will be bought (Paulos 1995).




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