Is there something to the proposed limitations of Bayes’ theorem they present?
Pretty much, no. The questions they are trying to answer, of “how does a system deal with a lack of exact numbers” and such, are approached with tools like replacing discrete probabilities with probability distributions and using maximum ignorance or Kolgomorov complexity-approximating priors.
More broadly, be skeptical of any weakenings. Going from quantitative posterior probabilities to qualitative “probably or approximately yes” judgments is suspicious (especially because posterior probabilities are about “probably or appoximately” yes or no answers). Similarly, moving from cardinal probabilities (posteriors that are a decimal between 0 and 1 representing how likely a thing is to happen) to ordinal probabilities as Richard Carrier (see quote below) does is likely bad.
you can at least say that something wouldn’t be less likely than X or more likely than Y
Thanks for the comment. This lines up with my [basic-level] thinking on this. It struck me as similar to EY’s point in Reductionism with his friend insisting that there was a difference between predictions resulting from Newtonian calculations and those found using relativity.
In a similar vein, they seem to insist that this area isn’t governed by Bayes’ theorem.
Lastly, I might have not credited Carrier well enough. He does assign cardinal values to his predictions. He simply makes the point that when we don’t know, we can use a “fringe” number that everyone agrees is at the low or high end. For example, he’s making a case against the resurrection and needs a value for the possibility that the Centurion didn’t properly verify Jesus’ death. Carrier says:
As it is, we must grant at least a 0.1% chance that the centurion mistook him for dead...
All I was pointing out is that Carrier, though making a case to those who disagree with him, tries to present some reasons why a person in that day and time might mistake a living (but wounded) person for being dead when they weren’t. Then he brings in a cardinal number, in essence saying, “You’ll grant me that there’s a 1 in 1000 chance that this guy made a mistake, right?”, and then he proceeds to use the value itself, not a qualitative embodiment.
Eh, yes.
Pretty much, no. The questions they are trying to answer, of “how does a system deal with a lack of exact numbers” and such, are approached with tools like replacing discrete probabilities with probability distributions and using maximum ignorance or Kolgomorov complexity-approximating priors.
More broadly, be skeptical of any weakenings. Going from quantitative posterior probabilities to qualitative “probably or approximately yes” judgments is suspicious (especially because posterior probabilities are about “probably or appoximately” yes or no answers). Similarly, moving from cardinal probabilities (posteriors that are a decimal between 0 and 1 representing how likely a thing is to happen) to ordinal probabilities as Richard Carrier (see quote below) does is likely bad.
Thanks for the comment. This lines up with my [basic-level] thinking on this. It struck me as similar to EY’s point in Reductionism with his friend insisting that there was a difference between predictions resulting from Newtonian calculations and those found using relativity.
In a similar vein, they seem to insist that this area isn’t governed by Bayes’ theorem.
Lastly, I might have not credited Carrier well enough. He does assign cardinal values to his predictions. He simply makes the point that when we don’t know, we can use a “fringe” number that everyone agrees is at the low or high end. For example, he’s making a case against the resurrection and needs a value for the possibility that the Centurion didn’t properly verify Jesus’ death. Carrier says:
All I was pointing out is that Carrier, though making a case to those who disagree with him, tries to present some reasons why a person in that day and time might mistake a living (but wounded) person for being dead when they weren’t. Then he brings in a cardinal number, in essence saying, “You’ll grant me that there’s a 1 in 1000 chance that this guy made a mistake, right?”, and then he proceeds to use the value itself, not a qualitative embodiment.
Is that any clearer re. Carrier?