Thursday, October 29, 2015

A weakly-fallibilist evidentialist can't be an evidential Bayesian

The title is provocative, but the thesis is less provocative (and in essence well-known: Hawthorne's work on the deeply contingent a priori is relevant) once I spell out what I stipulatively mean by the terms. By evidential Bayesianism, I mean the view that evidence should only impact our credences by conditionalization. By evidentialism, I mean the view that high credence in contingent matters should not be had except by evidence (most evidentialists make a stronger claims). By weak fallibilism, I mean that sometimes a correctly functioning epistemic agent appropriately would have high credence on the basis of non-entailing evidence. These three theses cannot all be true.

For suppose that they are all true, and I am a correctly functioning epistemic agent who has appropriate high credence in a contingent matter H, and yet my total evidence E does not entail H. By evidentialism, my credence comes from the evidence. By evidential Bayesianism, if P measures my prior probabilities, then P(H|E) is high. But it is a theorem that P(H|E) is less than or equal to P(EH), where the arrow is a material conditional. So the prior probability of EH is high. This conditional is not necessary as E does not etnail H. Hence, I have high prior credence in a contingent matter. Prior probabilities are by definition independent of my total evidence. So evidentialism is violated.


Heath White said...


Suppose I start out with no views about the color of ravens (my prior probability that H, all ravens are black, is arbitrarily low) but I have by now seen some millions of black ravens and none of any other color. I have been conditionalizing on this evidence E and now my P(H|E) is very high. Your argument is that P(H|E) <= P(E  H), so my prior probability that “if millions of observed ravens are all black and none are of any other color, then all ravens are black” (read as a material conditional) must have been quite high. But that, you say, violates evidentialism.

This kind of evidentialism is going to face a regress problem no matter what. For any evidence to be of use, I have to already believe “E is evidence for H.” (Or at least: such a belief has to be justifiable for me.) That belief is either contingent, or not. If contingent, evidentialism says it has to be backed by evidence, so in order for it to be justifiable I’ll have to have other evidence E’, and believe “E’ is evidence for (E is evidence for H)”, and so on. We could bottom out in either (i) rationalism: some of these evidential relations are apriori knowable because necessary; or (ii) foundationalism: some of these evidential relations are justifiably believed without evidence, albeit contingent.

Consider the evidence rule schema, “That observed Fs are G is evidence that unobserved Fs are G.” If the observed Fs are a representative sample, this is I think a mathematical (statistical) truth, hence knowable apriori. But in any case, it seems like a foundational belief, by which I mean a belief one is justified in holding, without evidence, unless there are good reasons to the contrary. Maybe this is tantamount to the claim that “observed Fs are a representative sample of Fs” is a foundationally justified belief.

Since defeating the regress argument for skepticism requires foundationally justified beliefs anyway, that doesn’t seem so bad to me. This is an interesting place they show up, though.

Brian Cutter said...

Isn't there already a conflict between evidentialism (as you've defined it) and Bayesianism, even without mention of weak fallibilism or a specifically *evidential* version of Bayesianism? Assume (quite reasonably) that the relevant space of epistemic possibilities has more than 2 or 3 epistemically possible worlds in it. My prior probability function will correspond to some measure on this space. Since *every* measure on the space has to assign a high measure to some proper subset of the probability space (if there are n points in the space, there is guaranteed to be some proper subset of the space with a measure of at least 1 - 1/n), there is guaranteed to be some proper subset S of the probability space to which my prior probability function assigns a high probability. Since S is a proper subset of the space, it's going to correspond to a contingent proposition. So I have a high prior probability in a contingent proposition, and prior probabilities are by definition independent of my evidence.

Alexander R Pruss said...


Yeah, that's much simpler.

Alexander R Pruss said...


While your example is exactly right, my example may generalize more easily to settings where prior probabilities are interval-valued. For we could imagine that all priors are intervals with a very broad range (say, [0.0001,0.9999]). But when H has a definitely high posterior (i.e., posteriors which are intervals whose lower bound is close to 1), there must (I haven't checked details, but I am pretty confident) be a definitely high prior for a conditional probability, and hence there must be a definitely high prior for a material conditional.