| I believe you can actually get Popperian falsification out of Bayesianism if you squint right. Consider an falsification experiment. It disproves some theories while not changing our relative beliefs in other theories. this would be basically for all i in S1 p(evidence | theory i) = 0 for all i in S2 p(evidence | theory i) = k * p(evidence) I would say that most scientific evidence is of this sort, except that the probabilities for the "falsified" theories can also be a little bit above 0 to account for measurement error. Edit: Actually it may be fruitful to introduce a distinction similar to the one probability theory has... In probability theory there is a difference between sample and event. An event is a set of samples. In our case, I believe we want a distinction between a theory... and a lets call it micro-theory. To pick a funny and memorable example a theory could be something like "there is a Loch Ness monster". Now a micro-theory could be something like "there is a Loch Ness monster, that is invisble, and makes no sounds, but it can be detected by radar... and... and...". So it would include all these additional constraints. So the theory it's composed of a lot of these micro theories right. Now if we take photos of every inch of Loch Ness, and we don't find any Loch Ness monster, we make it less likely that there is a monster right. We may say "oh we were careless, and just missed it" but if we keep looking eventually that becomes an impossibility. So we disprove a bunch of micro theories, but some will remain. Our previous micro theory that among other thing says that the monster is invisible remains. And whats worse the relative likelyhood of them is unchanged compared to the no monster. p(cant get monster on photo | no monster) = k p (cant get monster on photo) and p(cant get monster on photo | invisible monster) = k p (cant get monster on photo) Now if we want to further increase our belief in "no monster" we would have to go after these wacky micro-theories and disprove them, using e.g. radar. But given that a sensible person assigns those micro-theories low prior likelyhood we may be satisfied with the situation and not bother. So basically these was just Popperianism in Bayesianism clothing right? Almost... Notice the very last point. We allowed ourselves not to bother with theories of invisible monsters. Because of our prior likelyhood. |