The Surprise Examination Paradox and the Second Incompleteness Theorem

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Notices of the AMS, Vol: 57, Issue: 11, Page: 1454-1458

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Shira Kritchman, Ran Raz
American Mathematical Society
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We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the mathematical theory in which the derivation is done; which is impossible by the second incompleteness theorem.

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Unexpected hanging paradox

The unexpected hanging paradox or hangman paradox is a paradox about a person's expectations about the timing of a future event that he or she is told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging, or a surprise school test.Despite ...

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