Incorrect comments on Open Problems Related to Solomonoff Induction - Less Wrong
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Comments (102)
I guess I failed to bridge the inferential gap here. You're right "Solomonoff Induction would not consider this a description of x as it cannot be used to compute x." The point I'm trying to make is that a correct formalization of induction/Occam's Razor ought (in order to satisfy our intuitions) to assign x some probability > 1/3^^^3 since it has a short (even if uncomputable) description, but a formalization based on this P would not, therefore it can't be a correct formalization. But this is the case no matter what P we use (with different x depending on P), hence the "unformalizability" problem.
Are you essentially saying Solomonoff Induction could be inferior to some other meta-algorithm (or whatever you call it) in uncomputable universes?
Yes. ETA: I'm also making the stronger point that any formalization of induction we can come up with would have a similar problem. (Or at least the kinds of formalizations covered by my arguments.)