New poster. I love this topic. My own of view of the shortcoming of Bayesianism is as follows (speaking as a former die-hard Bayesian):
The world (multiverse) is deterministic.
Probability therefore does not describe an actual feature of the world. Probabilities only make sense as a statistical statements.
Making a statistical statement requires identifying a group of events or phenomena that are sufficiently similar that grouping makes sense. (Grouping disparate unique events makes the statistical statement meaningless, since we would have no reason to think subsequent events behave in the same way.)
Events and phenomena like balls in urns, medical tests for diseases with large sample sizes, even some human events like sports games, have sufficient regularity that grouping makes sense and statistical statements are meaningful.
Propositions about explanatory theories (are there infinite primes, is Newtonian physics “correct”) do not have sufficient regularity - a statistical statement based on any group of known propositions logically yields no predictive value about unknown propositions. (Other than where you have a good explanatory theory linking them.)
If probability statements about the correctness of an unknown explanatory proposition are therefore meaningless, priors and Bayesian updates are similarly meaningless.
Example: Newton. Before Einstein, one’s prior for the correctness of Newton would have been high. Just as one’s prior on Einstein being correct right now is presumably high. But both are meaningless, since it is not the case that there is a proportion of universes in which they are true and a proportion in which they are false.
Counterpoint: why do prediction markets seem to work? No idea! Still wrestling with this.
Would love to hear your thoughts.
New poster. I love this topic. My own of view of the shortcoming of Bayesianism is as follows (speaking as a former die-hard Bayesian):