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Cyan comments on Probabilistic Löb theorem - Less Wrong Discussion
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Do you folks at MIRI think this result is as significant an advance toward FAI as, say, Cox's theorem or Pearl-style causal inference?
I'm not at MIRI but I was at part of the workshop and my answer would be no (although I do think the result is worthwhile).
Although I would also place Cox's theorem and graphical models on pretty different standing; the latter seems much more important to me than the former.
Yes, Cox's result gives a different supporting argument for the use of probability, but didn't introduce new ways of doing probabilistic reasoning, whereas graphical models have had major applications in efficient probabilistic reasoning in practice.
This result isn't on its own (it's a possibility/impossibility result about a probability system that may not exist) - but if a variant of Paul's probability can work, then that would be significant result.