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Wei_Dai comments on Open Problems Related to Solomonoff Induction - Less Wrong
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Comments (102)
I would like to have a method of induction that for any formal language, assigns a non-zero prior to the existence of a device that can enumerate or decide all true sentences in that language, or alternatively an explanation based on reasonable principles for which such devices should have zero probabilities. Right now we do not have either, and your research program for improving SI (i.e., to base it on second-order logic) will not give us either even if it's successful. So while I'm not sure it makes sense to say I "blame" Solomonoff induction (what could that mean?), you could say that I'm not satisfied with either the status quo or any improvements to it that we can currently foresee.
Give me a set of formal languages over which you can say the phrase "for any formal language", and the truth predicate for the union of the set won't be in any language in the set. I'm still trying to understand how to deal with this inside AI, but I'm not sure that blaming it on second-order logical induction is putting the blame in the right place.
Again, I'm not sure what you mean by "blame" here. If you're saying that Tarski's result represents a problem that affects more than just attempts to generalize Solomonoff induction, then I agree.
BTW, while I have your attention, what's your evaluation of Paul Christiano's FAI design idea, which sort of tries to punt as many philosophical problems as possible (including this one)? I noticed that you didn't comment in that discussion.