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.Comment: 8 page
