IMO, most of the problems with Precise Bayesianism for humans are mostly problems with logical omnisicence not being satisfied.
Also, one the arbitrariness of the prior, this is an essential feature for a very general learner, due to the no free lunch theorems.
The no free lunch theorem prohibits 1 prior from always being universally accurate or inaccurate, so the arbitrariness of the prior is just a fact of life.
mostly problems with logical omnisicence not being satisfied
I’m not sure, given the “Indeterminate priors” section. But assuming that’s true, what implication are you drawing from that? (The indeterminacy for us doesn’t go away just because we think logically omniscient agents wouldn’t have this indeterminacy.)
the arbitrariness of the prior is just a fact of life
The arbitrariness of a precise prior is a fact of life. This doesn’t imply we shouldn’t reduce this arbitrariness by having indeterminate priors.
I’m not sure, given the “Indeterminate priors” section. But assuming that’s true, what implication are you drawing from that? (The indeterminacy for us doesn’t go away just because we think logically omniscient agents wouldn’t have this indeterminacy.)
In one sense, the implication is that for an ideal reasoner, you can always give a probability to every event.
You are correct that the indeterminancy for us wouldn’t go away.
The arbitrariness of a precise prior is a fact of life. This doesn’t imply we shouldn’t reduce this arbitrariness by having indeterminate priors.
Perhaps.
I’d expect that we can still extend a no free lunch style argument such that the choice of indeterminate prior is arbitrary if we want to learn in the maximally general case, but I admit no such theorem is known, and maybe imprecise priors do avoid such a theorem.
I’m not saying indeterminate priors are bad, but rather that they probably aren’t magical.
IMO, most of the problems with Precise Bayesianism for humans are mostly problems with logical omnisicence not being satisfied.
Also, one the arbitrariness of the prior, this is an essential feature for a very general learner, due to the no free lunch theorems.
The no free lunch theorem prohibits 1 prior from always being universally accurate or inaccurate, so the arbitrariness of the prior is just a fact of life.
I’m not sure, given the “Indeterminate priors” section. But assuming that’s true, what implication are you drawing from that? (The indeterminacy for us doesn’t go away just because we think logically omniscient agents wouldn’t have this indeterminacy.)
The arbitrariness of a precise prior is a fact of life. This doesn’t imply we shouldn’t reduce this arbitrariness by having indeterminate priors.
In one sense, the implication is that for an ideal reasoner, you can always give a probability to every event.
You are correct that the indeterminancy for us wouldn’t go away.
Perhaps.
I’d expect that we can still extend a no free lunch style argument such that the choice of indeterminate prior is arbitrary if we want to learn in the maximally general case, but I admit no such theorem is known, and maybe imprecise priors do avoid such a theorem.
I’m not saying indeterminate priors are bad, but rather that they probably aren’t magical.