Mark Nelson has a paper on this issue in Mind which I tried reading today, but I was waiting in Jiffy Lube and Ellen was on (not that I wanted to watch, but I can't read when a TV is on). I'll take a look at that later. Here's an argument on the general issue. (Andrew, this is for you.)
I'm interested in the issue of positive epistemic obligations in part because the following strikes me as a plausible argument against the view that the rational and the justified amount to the same thing:
1. If the rational and the justified were the same thing, then if there were only one rational option available, it would be obligatory.
2. There are situations in which it would be irrational to withhold judgment as to whether p and irrational to disbelieve p.
3. (Therefore) If the rational and the justified were the same status, you would be obligated to believe p.
4. There are no positive epistemic obligations.
C. (Therefore) the rational and the justified are distinct statuses and the former does not make for the latter.
In support of (2), think about situations in which you are in the same non-factive mental states as someone who is trying to settle the question as to whether p and then hits upon evidence they know is conclusive evidence for p. To withhold judgment or to judge that ~p in such a situation does seem irrational. Nevertheless, I think we should not say that this is a situation in which you are epistemically obligated to believe p. If so, then we have our conclusion.
What is wrong with the idea of positive epistemic obligations? First, intuitively, I just do not see what wrong you could be guilty of if you do not bother to draw conclusions from the evidence you have. If you believe p and fail to believe p’s obvious logical consequences, what of it? Not forming the obvious logical consequences of what you believe is not like not bothering to help those less fortunate than you.
Second, I have a hard time seeing any plausible account of positive epistemic obligation. If there were positive epistemic obligations, there should be some principle that identifies a condition, C, such that if your belief meets C, you ought to have that belief. Suppose that condition is truth. Since we cannot believe all the true propositions, much less all the true propositions we can grasp, we have a violation of ‘ought’ implies ‘can’. The same problem arises for the view that you ought to believe all the known consequences of your evidence.
What if instead the principle said that you ought to form as many beliefs as you can that satisfy C? This still seems problematic. You have two options. You can head to the library or you can head to the laboratory. In the library it is easy to learn new truths. It takes more work to form beliefs that satisfy C in the lab, which means that the number of beliefs you could form that meets C in the library is greater than the number of beliefs you could form that meets C in the lab. Suppose further that the beliefs that you would form in the lab and the library differ in content. Now, suppose you head to the lab. The beliefs you form there constitute knowledge, but forming those beliefs means that you cannot form the beliefs you would have formed in the library. You would not satisfy the principle, but certainly you meet your epistemic obligations if all of your beliefs constitute knowledge. Discovering that p rather than learning that q and that r is not like deciding not to save the greater number.
One way of getting around the problem is to specify the obligation in such a way that it is relative to interests (or something like that). Then the principle might be something like this:
(HPO) If you're interested in whether p, you ought to believe p if your belief satisfies C.
Two problems. First, the rationality of withholding doesn't depend upon whether you're interested in settling a question. So, if this is what we're forced to, the problem that I think arises for the view that rationality just is justification doesn't go away. Second, I don't think this is a positive epistemic obligation. If there are positive epistemic obligations, shouldn't they apply to you even if you don't really care to settle questions?