Blackwell Reference Online

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A teacher announces that there will be a surprise examination next week. A clever student argues that this is impossible. ‘The test cannot be on Friday, the last day of the week, because it wouldn't be a surprise. We would know the day of the test on Thursday evening. This means we can also rule out Thursday. For after we learn that no test has been given by Wednesday, we would know the test is on Thursday or Friday – and would already know that it is not on Friday by the previous reasoning. The remaining days can be eliminated in the same manner.’ This puzzle has over a dozen variants. The first was probably invented by the Swedish mathematician Lennart Ekbom in 1943. Although the first few commentators regarded the reverse elimination argument as cogent, every writer on the subject since 1950 agrees that the argument is unsound. The controversy has been over the proper diagnosis of the flaw. Initial analyses of the student's argument tried to lay the blame on a simple equivocation. Their failure led to more sophisticated diagnoses. The general format has been an assimilation to better known paradoxes. One tradition casts the surprise examination paradox as a self-referential problem, as fundamentally akin to the Liar, the paradox of the knower , or Gödel's incompleteness theorem. The original talk of a surprise is read as a reflexive claim about unprovability. That is, the teacher's ... log in or subscribe to read full text