Here are three principles of varying plausibility:
1. There can’t be any justified inconsistencies: propositions which are justified for a person and which logically imply a contradiction.
2. There can’t be any justified contradictories: no instances of p being justified for a person while ~p is also justified for a person.
3. There can’t be any justified contradictions: no instance of p&~p can be justified for a person.
The question I want to ask here is whether these principles stand or fall together as a group.
The third principle looks unassailable to me, except for the possibility of different modes of presentation for each conjunct (I assume here that propositions are bearers of truth value, not theoretical devices generated to solve the problems of cognitive significance). So here I’ll just assume that we fix the other features related to cognitive significance in order to focus on the epistemological point, and if we do, I think principle 3 is about as good a principle as we can get (except perhaps for epistemological instances of non-contradiction such as ~(Jp&~Jp), but such a claim is not strictly part of the theory of justification). Principle 3 is hard to argue for, especially the more wedded we are to closure principles about justification, but let us suppose that we can’t abandon 3, whatever else we do.
But the more wedded we are to such closure principles, the harder it is to reject any of the three principles above. We should, however, be suspicious of 1, since it appears to be a datum in Lottery and Preface that the claims justified by the evidence in those cases are inconsistent. There may be some notion of justification for which 1 should be accepted, but it is hard to deny the idea from which the paradoxes begin that the statements in question are justified in some important sense. Especially, the fallibility version of the preface paradox is difficult. If we assume that we are perfectly rational and also aware of our own fallibility, it is hard to deny that it is possible to be justified in believing all of our first-order beliefs and also justified in believing that some of our first-order beliefs are false. If we accept this reasoning, then whatever closure principle we endorse for justification can’t be strong enough to take us from a denial of 1 to a denial of 3, on the assumption that 3 is unassailable.
That leaves 2, which epistemologists often accept (if anyone knows of someone who explicitly denies it, please note it in the comments–it turns out to be an essential premise, for example, in arguments for Restrictivism, the view that any attitude taken toward a proposition is either epistemically required or forbidden.) I’m not sure why they do however. Denying 1 gives some reason to expect that 2 might have to go as well, since one can’t argue for 2 on the basis of 3 without also generating an argument for 1 (as far as I can tell). But if 1 is false, that leaves me suspecting that 2 is false as well.
Here’s an argument to that effect. For 1 to be false, we need a body of evidence that can be partitioned into one part that supports one claim and another part that supports other claims that in fact are inconsistent with the first claim. (For a particular example, let the first partition support your fallibility claim that some of your first-order beliefs are false and the second partition support all of your first-order beliefs.) Moreover, these parts cannot interact in such a way that each partition defeats the support provided by the other partition (otherwise we will lose the argument against 1). But if such partitioning can occur, why can’t the partitioning still occur when the first partition supports p and the second supports ~p?
One might hope for the following kind of answer: the conflict between p and ~p is too obvious to ignore rationally. Maybe so, but the conflict between one’s first-order beliefs and one’s fallibility belief is obvious as well, but to use this conflict to undermine 1 above, we have to be able rationally to ignore the conflict.
So the question is whether it is possible to retain 2 & 3 while rejecting 1. If this can’t be done, then so much the better for coherentism (since the Foley-type attack on coherentism is just that it must reject 1). If any reason for rejecting 1 is also a reason for rejecting 2, then, I think, so much the worse for Restrictivism. And if all three claims above have to be rejected, I have no idea how to start anew in thinking about the theory of justification.