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The Surprise Examination Paradox and the Second Incompleteness Theorem

Kritchman, Shira and Raz, Ran (2010) The Surprise Examination Paradox and the Second Incompleteness Theorem. Notices of the AMS, 57 (11). pp. 1454-1458.


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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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Item Type: Published Article or Volume
Keywords: surprise examination paradox, unexpected hanging paradox, Godel, incompleteness theorem
Subjects: Specific Sciences > Mathematics
Depositing User: Prof. Ran Raz
Date Deposited: 07 Dec 2010 14:10
Last Modified: 07 Dec 2010 14:10
Item ID: 8414
Journal or Publication Title: Notices of the AMS
Publisher: American Mathematical Society
Official URL:
Subjects: Specific Sciences > Mathematics
Date: December 2010
Page Range: pp. 1454-1458
Volume: 57
Number: 11

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