It seems to me that in science, there is always an implicit agreement that the current theory could be revised in light of new contradictory evidence. As far as I can tell, the Bayesian approach seems to lack this feature, since we have to assume a fixed model of the world to do the probability updates.
For example, what's the probability that the sun will rise tomorrow? How do you even calculate it? (To keep things simple, suppose you have seen the sun rise N times).
More abstractly, suppose every day you get a bit of information from some source, and the first N bits are all one. What's the probability that the next bit is one? How would the perfect Bayesian mind answer that?
An interesting way to avoid all this is to simply look at behavior (rather than beliefs) and apply an evolutionary argument which goes like this:
Finding and exploiting patterns is useful for survival, so evolution favored organisms that could do so. No "laws" required. The universe just needs to be orderly enough for life to survive. It need not make sense all the way down. I don't believe it, but it's interesting nevertheless.