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AustinLorenz comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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Actually, "not proving a falsehood" is not the same as being consistent; assuming that PA is consistent, the theory PA+~Con(PA) is also consistent, but proves the false statement ~Con(PA). Consistency is the weaker condition of not proving both a formula and its negation.
I should have said "contradiction"; edited. I intended "falsehood" to mean "false in all models," not "false in the standard model."