"'What is support?' (This is not asking for its essential nature or a perfect definition, just to explain clearly and precisely what the support idea actually says) and 'What is the difference between "X supports Y" and "X is consistent with Y"?' If anyone has the answer, please tell me."

Bayesians appear to have answers to these questions. Moreovoer, far from wishing to refute Popper, they can actually incorporate a fomr of Popperianism.

"On the other hand, Popper's idea that there is only falsification and no such thing as confirmation turns out to be incorrect. Bayes' Theorem shows that falsification is very strong evidence compared to confirmation, but falsification is still probabilistic in nature; it is not governed by fundamentally different rules from confirmation, as Popper argued."

But of course Popper was a falliblist as well as a falsificationist, so his falsifications aren't absolute and certain anyway. Bayes just brings out that where you don't have absolute falsification, you can't have absolute lack of positive support. Falsification of T has to support not-T. But the support gets spread thinly...