How popular is Bayes' theorem among philosophers? As a physicist, it has had a profound effect on my thinking, and seems to reflect the way we intuitively deal with new evidence presented to us.
As a reminder, Bayes' theorem states:
Probability(A given B) = Probability(B given A)*Probability(A)/Probability(B)
For example, if A is "A revolutionary new theory" and B is "Data from my experiment", then Bayes' theorem tells us that we have to take into account our initial (prior) belief in the theory P(A), given our background knowledge, before even looking at our data.