When faced with "global, recursive" epistemic problems one arrives at an extremely power-law asymmetric distribution where the "bayesian value" of almost all evidence is near zero.
We live our entire lives in this "nero zero" range, and i'd suppose, this makes a "pure bayesian" solution to the problem of knowledge deficient. Since we succeed in knowing, so we succeed in making hyperfine determinations.
This sort of "hyperfine epistemology" works globally to allow us to "know at all", but as you're sensing here -- it's pretty much useless for any local problem.
Perhaps this is just the single up-side of the bayesian approach to the drake eqn: it shows how impossible it is to state such an eqn, let alone evaluate it. We cannot, a priori, make such hyperfine determiniations on such circumstantial matters.