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    “考试悖论”的思考

    作者：vale

    该被牛人们笑话了——我从中学开始就浪费了很多时间在这个垃圾题目上，
始终没绕清楚。最近在xys上重逢，本想此方高人不少，应有所启示，但发现真正
思考的人没有几个，更没人能给出令人信服的解答。倒是林壑、子牛二位给了出
处，倒更有用。

    量子先生在其"反证法"中说：如果到周五还不考试，不论周六考不考，老
师都要违背自定的游戏规则。我不知"游戏规则"为何，老师没说（也没有隐含的
说）"无论哪天考试"，只是说：1.要考试；2.学生无法事先预知。他将考试放在
周三，请问违背上述哪一条？

    关于"考试悖论"一篇很有价值的文章是
T. Y. Chow，The Surprise Examination or Unexpected Hanging Paradox 
（http://arxiv.org/PS_cache/math/pdf/9903/9903160.pdf）。我只读过此文的缩
减版（http://rec-puzzles.org/new/sol.pl/logic/unexpected），因为逻辑基础差，
后半部分没太明白。作者是搞数学的，大家可以看看文后所列的参考文献数量和
作者对其的评述，就可知道什么才算在"在科学圈子内"。

    
在xys上讨论最多的就是科学的态度，何谓科学的态度，子牛先生的文章可参考，
有调研，有思考，虽然没有答案。而某些文章，价值为零。

    最后引用该Chow文中的第一段：

    Many mathematicians have a dismissive attitude towards paradoxes. 
This is unfortunate, because many paradoxes are rich in content, having 
connections with serious mathematical ideas as well as having pedagogical 
value in teaching elementary logical reasoning. An excellent example is the 
socalled"surprise examination paradox" (described below), which is an 
argument that seems at first to be too silly to deserve much attention. 
However, it has inspired an amazing variety of philosophical and mathematical
investigations that have in turn uncovered links to Godel's incompleteness 
theorems, game theory, and several other logical paradoxes (e.g., the liar 
paradox and the sorites paradox). Unfortunately, most mathematicians are 
unaware of this because most of the literature has been published in 
philosophy journals. 

(XYS20050421)

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