Reading Brand Blanchard's Reason and Analysis, I've realized that the core problem with Popper's philosophy of science is that it is merely the negative image of positivism. Positivism held that scientific statements had to be verifiable. Popper saw that, per positivist strictures, that would never occur. He suggested that instead they need only be falsifiable. But falsification is only the flip side of verification -- if I falsify a, I verify ~a. And, per Popper, verification is impossible! I can never verify the result R that supposedly falsifies theory T. Only whim can lead me to decide that I should believe R and cease believing T.
Falsificationists typically answer, "Well, you have no reason to doubt R." That won't work, because:
1) Per Popper, I certainly do have such a reason: There is 0 probability that any of my current theories are true. (Given an infinity of possible theories, what are the odds I've hit on the correct one?)
2) I have no reason to doubt T except R, so the choice to stick with one is arbitrary.
3) Repeated demonstrations of R are irrelevant on Popper's own terms -- that would imply a degree of verification!
OK, I promise to stop obsessing about Popper!