Abstract
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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References found in this work BETA

The Incompleteness Theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.
The Incompleteness Theorems After 70 Years.Henryk Kotlarski - 2004 - Annals of Pure and Applied Logic 126 (1-3):125-138.
Computational Complexity and Godel's Incompleteness Theorem.Gregory J. Chaitin - 1970 - [Rio De Janeiro, Centro Técnico Científico, Pontifícia Universidade Católica Do Rio De Janeiro.
A Goedelized Formulation of the Prediction Paradox.Frederic B. Fitch - 1964 - American Philosophical Quarterly 1 (2):161 - 164.
Kolmogorov Complexity and the Second Incompleteness Theorem.Makoto Kikuchi - 1997 - Archive for Mathematical Logic 36 (6):437-443.

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Citations of this work BETA

Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.
On the Diagonal Lemma of Gödel and Carnap.Saeed Salehi - 2020 - Bulletin of Symbolic Logic 26 (1):80-88.
Paradoxes and Contemporary Logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.
Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.

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