My point is that perfect Bayesians can only deal with finite domains. Gold standard of rationality—basically something that would assign some probabilities to every outcome within some fairly regular countable domain, and they would merely be self-consistent and follow basic rules of probability—it turns that even the simplest such assignment of probabilities is not possible, even in theory.
What are the smallest and/or simplest domains which aren’t amenable to Bayesian analysis?
I’m not sure you’re doing either me or Taleb justice (though he may well be having too much fun going on about how much smarter he than just about everyone else) -- I don’t think he’s just talking about completely unknown unknowns, or implying that people could get things completely right—just that people could do a great deal better than they generally do.
For example, Taleb talks about a casino which had the probability and gaming part of its business completely nailed down. The biggest threats to the casino turned out to be a strike, embezzlement (I think), and one of its performers being mauled by his tiger. None of these are singularity-level game changers.
In any case, I would be quite interested in more about the limits of Bayesian analysis and how that affects the more theoretical side of LW, and I doubt you’d be downvoted into oblivion for posting about it.
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.
What are the smallest and/or simplest domains which aren’t amenable to Bayesian analysis?
I’m not sure you’re doing either me or Taleb justice (though he may well be having too much fun going on about how much smarter he than just about everyone else) -- I don’t think he’s just talking about completely unknown unknowns, or implying that people could get things completely right—just that people could do a great deal better than they generally do.
For example, Taleb talks about a casino which had the probability and gaming part of its business completely nailed down. The biggest threats to the casino turned out to be a strike, embezzlement (I think), and one of its performers being mauled by his tiger. None of these are singularity-level game changers.
In any case, I would be quite interested in more about the limits of Bayesian analysis and how that affects the more theoretical side of LW, and I doubt you’d be downvoted into oblivion for posting about it.
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.