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smoofra comments on Reflection in Probabilistic Logic - Less Wrong
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So you are assuming that it will be wanting to prove the soundness of any successors? Even though it can't even prove the soundness of itself? But it can believe in it's own soundness in a Bayesian sense without being able to prove it. There is not (as far as I know) any Godelian obstacle to that. I guess that was your point in the first place.