So far, Bayesian probability has been extended to infinite sets only as a limit of continuous transfinite functions. So I’m not quite sure of the official answer to that question.
On the other hand, what I know is that even common measure theory cannot talk about the probability of a singleton if the support is continuous: no sigma-algebra on 2ℵ0 supports the atomic elements.
And if you’re willing to bite the bullet, and define such an algebra through the use of a measurable cardinal, you end up with an ultrafilter that allows you to define infinitesimal quantities
I don’t know enough math to understand your response. However, from the bits I can understand, it seems leave open the epistemic issue of needing an account of demostrative knowledge that is not dependent on Bayesian probability.
So far, Bayesian probability has been extended to infinite sets only as a limit of continuous transfinite functions. So I’m not quite sure of the official answer to that question.
On the other hand, what I know is that even common measure theory cannot talk about the probability of a singleton if the support is continuous: no sigma-algebra on 2ℵ0 supports the atomic elements.
And if you’re willing to bite the bullet, and define such an algebra through the use of a measurable cardinal, you end up with an ultrafilter that allows you to define infinitesimal quantities
I don’t know enough math to understand your response. However, from the bits I can understand, it seems leave open the epistemic issue of needing an account of demostrative knowledge that is not dependent on Bayesian probability.