![]() There is a very naive "resolution" to this paradox using backward induction. In it, they take the classic example of an exam that will be given next week, but you won't be able to know the day of the exam ahead of time (it's also often re-phrased in terms of an execution next week, but you won't know the day of the execution this is how it is described at Wikipedia). NP idea and what its ramifications would be on human mathematics if P happened to actually be equal to NP.Īnother recent paper that uses Godel's theorems in a very technical way to address a philosophical problem is "The Surprise Examination Paradox and the Second Incompleteness Theorem" by Kritchman and Raz. In particular there is a great (but not well-known) letter mentioned in it from Godel to Von Neumann in which Godel essentially anticipates the whole P vs. ![]() ![]() ![]() It covers a wide range of topics in philosophy that have been dramatically changed not just by computability but also by complexity theory. ![]() I think you might like to read a great recent paper by Scott Aaronson called "Why Philosophers Should Care About Computational Complexity". ![]()
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