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Quinn comments on [LINK] Cantor's theorem, the prisoner's dilemma, and the halting problem - Less Wrong
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Of course, when you ignore the payoff matrix, the argument is no longer really about the Prisoner's Dilemma (and so I don't know that it's fair to accuse the barber paradox of having a lot of extra cruft not present in the PD formulation).
But I agree that this is a cute presentation of diagonal arguments in culturally relevant terms. A fun read.