One might think that there is some connection between low (or inscrutable) probability and defeat. Plantinga, for example, rests an entire argument against evolutionary naturalism on this point, and the argument is generally viewed to fail on this point. Tom Crisp and I were talking about this issue at a conference this past weekend, and I was skeptical of the connection.
Here’s the concern. Let’s say defeaters are either rebutters or undercutters. For low probability to be a rebutter, you’d have to have some information e such that the probability of the target claim p was low or inscrutable on e. But, of course, we almost always have some such information for our beliefs, even when rational and known to be true. Tom’s idea was to focus on undercutters instead, where we have information e (he talked in terms of states of mind, but I think it won’t matter) such that the (conditional) probability that our belief-forming process concerning the target claim p is reliable is low given e. (He also has an additional clause to rule out overriders, but that isn’t my concern here.)
But, once again, I think we almost always have such information, even for fully rational beliefs and beliefs known to be true. Let p be a perceptual belief: it is raining outside. Let e be completely irrelevant, unrelated information: the moon is not made of green cheese. The conditional probability that perception is reliable, given that the moon is not made of green cheese, is really low. But that conditional probability isn’t a defeater of my belief that it is raining.
That’s where our conversation stopped on this point, but since then I’ve thought of further possible moves to try to link low conditional probabilities with defeat. I’m more interested in whether others think there is a good way to link the two, so I won’t list the various ways I thought of and how they fail. Any ideas?