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> This is sort of like the absurdity in a rational agent always knowing what is best for them: it disregards computational complexity. Somewhat off-topic, but

• kmill 10y ago
  Yeah, it does seem interesting (and I've seen Tsvi around the Berkeley math department). Maybe someday I'll spend the time to understand it! When I said the thing about complexity, I was thinking about intuitionism. For an intuitionist, the only things which can be said to be true are the things you can believe with your faculties. This is where the "intuitionists don't believe in the law of the excluded middle" comes from --- just because you can see that something can't not be true doesn't mean you see it is --- or something like that. I wonder if this logical induction is a sort of Bayesian intuitionism, extending logical faculties with probabilistic ones. And, random thought, I wonder if there is a Turing-complete programming language you can design where you can prove something can be written in it, but actually finding that program is not decidable. Then, while it's true anything can be written in any language, this one would be provably infeasible to do so.