The Surprise Examination Paradox and the Second Incompleteness Theorem

Citation data:

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

Publication Year:
Usage 598
Downloads 337
Clicks 261
Mentions 2
References 1
Comments 1
Social Media 143
+1s 86
Shares, Likes & Comments 34
Tweets 23
Reddit 20
Repository URL:
Kritchman, Shira, Raz, Ran
American Mathematical Society
Most Recent Tweet View All Tweets
article description
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.

This article has 1 Wikipedia reference.

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 which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging, or a surprise school test.Despite sig...

Read full Article