Some attempts have been made at finding a priori probabilities, i.e. probability distributions in some sense logically required by the nature of one’s state of uncertainty; these are a subject of philosophical controversy, with Bayesians being roughly divided into two schools: “objective Bayesians”, who believe such priors exist in many useful situations, and “subjective Bayesians” who believe that in practice priors usually represent subjective judgements of opinion that cannot be rigorously justified (Williamson 2010). Perhaps the strongest arguments for objective Bayesianism were given by Edwin T. Jaynes.
Critical rationalism explicitly proposes a third decision rule for rational belief formation: it is rational to believe a hypothesis if it has so far withstood serious criticism better than its competitors.
I’ll add that a decent summary of the position espoused in Where recursive justification hits bottom (linked in the grandparent) is that critical rationalism (or something like it) entails objective Bayesianism. It both entails the use of Baye’s rule to update on information and it entails a set of correct priors.
FYI that is a misleading statement of Critical Rationalism.
For one thing, Popper was not a “belief philosopher” so he wouldn’t have stated it quite like that.
There are a lot of misleading statements about CR floating around. Most come from its opponents trying to make sense of it on their own terms. In trying to formulate it in a way that makes sense given their anti-CR premises, they change it. It’s best to read primary sources for this.
For people like me who have no clue, if you scroll down a bit here there is a comparison (so you get a vague idea):
Subjective Bayesians emphasize the relative lack of rational constraints on prior probabilities.
Objective Bayesians (e.g., Jaynes and Rosenkrantz) emphasize the extent to which prior probabilities are rationally constrained.
More here:
And of course Critical rationalism:
Critical rationalism explicitly proposes a third decision rule for rational belief formation: it is rational to believe a hypothesis if it has so far withstood serious criticism better than its competitors.
I’ll add that a decent summary of the position espoused in Where recursive justification hits bottom (linked in the grandparent) is that critical rationalism (or something like it) entails objective Bayesianism. It both entails the use of Baye’s rule to update on information and it entails a set of correct priors.
Thanks for helping me realize that Critical Rationalism and Bayesianism can be compliments rather than substitutes.
FYI that is a misleading statement of Critical Rationalism.
For one thing, Popper was not a “belief philosopher” so he wouldn’t have stated it quite like that.
There are a lot of misleading statements about CR floating around. Most come from its opponents trying to make sense of it on their own terms. In trying to formulate it in a way that makes sense given their anti-CR premises, they change it. It’s best to read primary sources for this.