As I'm clearing out material I keep meaning to write about, I came across an excellent post about Bayesianism and 21st century intellectualism:
Popperian falsification is just a special case of the Bayesian view: if the likelihood P(data|model) is zero (indicating that the data is impossible given the model), P(model|data) is zero, regardless of the prior [and the model is falsified]. But the Bayesian approach offers some sort of a weighted preference among all the models that haven't been refuted yet, balancing the Ockhamist preference for simplicity through the prior and the desire for accuracy through the likelihood.
This is very true, and a powerful insight into where Popperian demarcation will wind up. Science would encompass those ideas which can have their posterior probabilities modified by new data. The supernatural predicts anything, and applying any likelihood to data given the supernatural is impossible as well (without knowing the mind of God).
This approach also gives the possibility of more certainty in knowledge than Popper would seem to allow. While nothing is provably true, our estimate of its probability can be raised so high as to justify great certainty.