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The surprise examination or unexpected hanging paradox

By Timothy Y. Chow


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 so-called “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 Gödel’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. In this article, I describe some of this work, emphasizing the ideas that are particularly interesting mathematically. I also try to dispel some of the confusion that surrounds the paradox and plagues even the published literature. However, I do not try to correct every error or explain every idea that has ever appeared in print. Readers who want more comprehensive surveys should see [30, chapters 7 and 8], [20], and [16]

Year: 1998
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