Material phenomena must be defined in material terms. My argument is that piors, beliefs and value functions are not ultimately defined in material terms. Immaterial phenomena is beyond the realm of scientific analysis.
I don’t even know what this means. It sounds like a ‘separate magisteria’ type argument.
Here’s my response, arguing for objective priors as a solution to some of the problems you raise.
(I haven’t read all the other responding comments so I may be repeating stuff.)
I will attempt to refrain from “jumping ahead” and guessing your replies to these points, because that would require me to guess your motivation (IE, why you think the four ‘problems’ are indeed problematic). I will instead take your statements at face value, as if you think these things are problems-in-themselves (which, if addressed, cease to be problems).
I do this in the spirit of hoping to draw out better statements of what you think the real problems are (things which, if addressed, would actually change your mind, as opposed to just changing your argument).
Bayesian Probability has the following problems.
The answer to “Why do you believe x?” is always reducible to priors, which are non-falsifiable. Evidence has no effect on priors.
With description-length priors, claims about prior value are verifiable. Scientists can objectively demonstrate the ‘elegance’ of their theory by displaying a short description. (IE, elegance has been operationalized.)
Rational agents with wildly differing priors are (usually) unable to come into even approximate agreement when provided with scarce evidence.
Selecting a shared prior obviously addresses this.
Rational agents who disagree about unconditional priors P(A) but who agree about evidence likelihood P(Bi) and conditional priors P(A|Bi) should be able to come into agreement. Instead, Bayesians who disagree about unconditional priors P(A) while agreeing about evidence likelihood P(Bi) and conditional priors P(A|Bi) are provably unable to ever reach exact agreement if they use Bayes’ Theorem. This is the opposite of how empiricism should work.
Selecting a shared prior obviously addresses this.
Identifying someone else’s beliefs requires you to separate a person’s value function from their beliefs, which is impossible.
Selecting a shared prior doesn’t address this fully, but does allow one to infer beliefs by combining the (agreed-upon) prior with the evidence which that person has encountered.
(I haven’t read all the other responding comments so I may be repeating stuff.)
I do not think you are repeating stuff. If you are repeating stuff, you are not doing so in an annoying way. Your comment is unequivocally constructive.
I don’t even know what this means. It sounds like a ‘separate magisteria’ type argument.
Here’s my response, arguing for objective priors as a solution to some of the problems you raise.
(I haven’t read all the other responding comments so I may be repeating stuff.)
I will attempt to refrain from “jumping ahead” and guessing your replies to these points, because that would require me to guess your motivation (IE, why you think the four ‘problems’ are indeed problematic). I will instead take your statements at face value, as if you think these things are problems-in-themselves (which, if addressed, cease to be problems).
I do this in the spirit of hoping to draw out better statements of what you think the real problems are (things which, if addressed, would actually change your mind, as opposed to just changing your argument).
With description-length priors, claims about prior value are verifiable. Scientists can objectively demonstrate the ‘elegance’ of their theory by displaying a short description. (IE, elegance has been operationalized.)
Selecting a shared prior obviously addresses this.
Selecting a shared prior obviously addresses this.
Selecting a shared prior doesn’t address this fully, but does allow one to infer beliefs by combining the (agreed-upon) prior with the evidence which that person has encountered.
I do not think you are repeating stuff. If you are repeating stuff, you are not doing so in an annoying way. Your comment is unequivocally constructive.