意外考试悖论：一个语义学悖论，亦称“考试悖论”或“预告悖论”。一个老师预告，下星期将有一次意外的考试。这时，有位学生断言，这样的考试不能发生。考试不能在星期五（即该星期的最后一个工作日），因此若在此时，完全不是意外的事情。它也不能在星期四，因为如果星期三还没有进行既定的考试，我们将知道，它会在星期四或星期五来临。但是，既然星期五已被排除，星期四就称了所剩的唯一一天，那么，考试也就不意外了。以同样的方式，也能逐一排除其他几天。因此，下星期能有一次毫无意外的考试。有些批评家认为，如果这位学生推算出意外的考试不能在星期五（或给定的另外某天）发生，那么，假如它在那时发生了，就会是意外的。所以，它能在下周的某一天发生。这个悖论最初是由一次世界大战期间斯德哥尔摩的一位数学老师发现的。当时，他听到官方发布的一则告示，声称：作为演习，下星期的某一天将有一次意外的防空警报，在警报期间，人们应该躲到防空所里去。
“这类论证分成两个部分：”一部分用于是否能有一次意料不到的考试发生在最后一天，即星期五；另一部分提出关于这个争论的否定结论，并意欲将其扩展到其余各天。“
——赛斯伯里：《悖论》，1988年，第94页
surprise examination paradox：Logic A semantic paradox, also called theexamination paradox or prediction paradox. A teacher announces that there willbe a surprise examination next week. Then a student claims that such an examinationcan not occur. The examination can not be on Friday (the last working day ofthe week), for at that time it would not be a surprise. It can not be onThursday. For if there is no examination given on Wednesday, we will know thatit will come either on Thursday or Friday, but since Friday has been ruled out,Thursday will be the only day left, and then the examination will not be asurprise. The other days can be eliminated in the same manner. Hence there canbe no surprise examination next week. Some critics argue that if the student calculatesthat the surprise examination can not take place on Friday (or any other givenday), it would be a surprise if it were to take place then and that ittherefore could take place on any day of the week. The paradox was originallyobserved by a mathematics teacher in Stockholm during the Second World War,when he heard a declaration from the authorities that, as an exercise, there wouldbe a surprise air-raid alarm some day during the next week, during which peopleshould go to an air-raid shelter.
“The class’s argument falls into two parts: one applies to whether there can be an unexpected examination on the last day, Friday; the other takes forward the negative conclusion on this issue, and purports to extend it to the other days.”
—— Sainsbury, Paradoxes
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