Claudio’s paper reminded me that there are two separate problems regarding justified inconsistent beliefs. The first problem is the problem of contingent beliefs that are jointly inconsistent, as we find in the lottery and preface paradoxes. The second problem is the problem of necessary falsehoods and the possibility of being justified in believing them.
The first problem I think I know what a coherentist can say about: distinguish between ordinary justification and epistemic justification, as I’ve written about here before (and which appears in the linked paper in the sidebar on works in progress). But what of the second problem? It appears that the distinction in question doesn’t help here, since one can be justified in thinking that one’s justification for believing a necessary falsehood would turn up only further information that is misleading. So the distinction in question doesn’t help for this issue.
I now think this appearance is misleading.
Let’s distinguish between beliefs that are inconsistent from those that are necessarily false. An inconsistent belief is one from which the falsum constant can be derived in the preferred logic. A necessarily false proposition need not be inconsistent, but may be. So the problem of justified inconsistent beliefs is only a problem for those beliefs from which this constant can be derived.
A further constraint is also in order, one regarding the question of which logic the inconsistency can be derived in. Suppose that a belief system contains an implicit, or presupposes a, theory of evidence. Such a theory of evidence will itself presuppose a preferred logic or group of logics. Coherentists will want such logics to be the ones relative to which the inconsistency can be derived.
Given this further constraint, I think the earlier distinction is adequate for this further kind of justified inconsistent belief as well. For if the governing theory of evidence for determining justificatory status is one in which a contradiction is derivable from one’s belief, then whatever evidence one has for that belief will not count as adequate evidence for the claim that gathering further evidence would reveal only misleading information. One may have some evidence for this claim about further information, but its confirming power will be defeated by the evidence one also has that this evidence confirms a claim from which the falsum constant follows.
So, it appears to me, the distinction between ordinary and epistemic justification can solve both types of justified inconsistent belief problems for coherentism. Something further may also be true: maybe inconsistent beliefs of this sort can’t even be justified in the first place. For if the theory of evidence that governs epistemic facts about you is a theory on which the falsum constant is derivable from a belief of yours, this fact itself may defeat whatever confirming power any evidence you might have in favor of this belief. But even without this claim, I think the problem of justified inconsistent beliefs in necessary falsehoods isn’t insoluble for coherentists.