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.
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.