What are the smallest and/or simplest domains which aren’t amenable to Bayesian analysis?
Notice that you’re talking domains already, you’ve accepted it, more or less.
I’d like to ask the opposite question—are there any non-finite domains where perfect Bayesian analysis makes sense?
On any domain where you can have even extremely limited local rules you can specify as conditions, and unbounded size of the world, you can use perfect Bayesian analysis to say if any Turing machine stops, or to prove any statement about natural number arithmetics.
The only difficulty is bridging language of Bayesian analysis and language of computational incompleteness. Because nobody seems to be really using Bayes like that, I cannot even give a convincing example how it fails. Nobody tried other than in handwaves.
Notice that you’re talking domains already, you’ve accepted it, more or less.
I’d like to ask the opposite question—are there any non-finite domains where perfect Bayesian analysis makes sense?
On any domain where you can have even extremely limited local rules you can specify as conditions, and unbounded size of the world, you can use perfect Bayesian analysis to say if any Turing machine stops, or to prove any statement about natural number arithmetics.
The only difficulty is bridging language of Bayesian analysis and language of computational incompleteness. Because nobody seems to be really using Bayes like that, I cannot even give a convincing example how it fails. Nobody tried other than in handwaves.
Check things from Goedel incompleteness theorem and Turing completeness lists.
It seems that mainstream philosophy have figured it out long time ago. Contrarians turn out to be wrong once again. It’s not new stuff, we just never bothered checking.