Not really. To the extent that we limit attention to theories of the form:
Always(Everywhere(Forall x (P(x)) ) )
we Bayesians can never “cash in” on a bet that the theory is true—at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.
However, both Bayesians and Popper fans can become pretty certain that such a theory is false—even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.
Do you have an answer to that point-that-should-have-been?
Not really. To the extent that we limit attention to theories of the form:
we Bayesians can never “cash in” on a bet that the theory is true—at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.
However, both Bayesians and Popper fans can become pretty certain that such a theory is false—even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.