It seems like you’re saying that, pragmatically speaking, it’s not a problem if we all settle on the same set of formalisms. But I don’t see how that’s relevant to my point, which is that there’s no real objective constraints on the formalism we use, and what’s more, any given formalism could lead to virtually any prior between 0 and 1 for any proposition. So, as I said earlier, Solomonoff doesn’t help very much in objectively guiding our priors. We could just dispense with this Solomonoff business entirely and say, “The problem of priors isn’t an issue if we all just arbitrarily choose the same priors!”
Sure there are. Use a sufficiently far out reference machine and things go haywire, and you no-longer get a useful implementaion of Occam’s razor.
Key word there being “useful.” “Useful” doesn’t translate to “objectively correct.” Lots of totally arbitrarily set priors are useful, I’m sure, so if that’s your standard, then this whole discussion is again redundant. Anyway, the fact that Occam’s razor-as-we-intuit-it falls out of one arbitrary configuration of the paramaters (reference machine, language and orthography) of the theory isn’t in itself evidence that the theory is amazingly useful, or even particularly true. It could just be evidence that the theory is particularly vulnerable to gerrymandering, and could theoretically be configured to support virtually anything. There is, I believe, a certain polynomial inequality that characterizes the set of primes. But that turns out not to be so interesting, since every set of integers corresponds to a similar such equation.
It seems like you’re saying that, pragmatically speaking, it’s not a problem if we all settle on the same set of formalisms. But I don’t see how that’s relevant to my point, which is that there’s no real objective constraints on the formalism we use, and what’s more, any given formalism could lead to virtually any prior between 0 and 1 for any proposition. So, as I said earlier, Solomonoff doesn’t help very much in objectively guiding our priors. We could just dispense with this Solomonoff business entirely and say, “The problem of priors isn’t an issue if we all just arbitrarily choose the same priors!”
Sure there are. Use a sufficiently far out reference machine and things go haywire, and you no-longer get a useful implementaion of Occam’s razor.
Not really: in many cases, if the proposition and language are selected, everyone agrees on the result.
Solomonoff induction is just a formalisation of Occam’s razor, which IMO, is very useful for selecting priors.
Key word there being “useful.” “Useful” doesn’t translate to “objectively correct.” Lots of totally arbitrarily set priors are useful, I’m sure, so if that’s your standard, then this whole discussion is again redundant. Anyway, the fact that Occam’s razor-as-we-intuit-it falls out of one arbitrary configuration of the paramaters (reference machine, language and orthography) of the theory isn’t in itself evidence that the theory is amazingly useful, or even particularly true. It could just be evidence that the theory is particularly vulnerable to gerrymandering, and could theoretically be configured to support virtually anything. There is, I believe, a certain polynomial inequality that characterizes the set of primes. But that turns out not to be so interesting, since every set of integers corresponds to a similar such equation.