Suppose that coherentists can find a solution to the problem of justified inconsistent beliefs. I’ve argued that they can: the argument requires distinguishing between two kinds of necessary falsehoods and between ordinary and epistemic justification.
There’s still somewhat of a problem remaining, however. Given the distinctions above, a necessary falsehood can occur within a coherent belief system. The kinds of inconsistencies that can’t be tolerated await a solution to the question raised in the earlier post about evidence and propositions you’ve never considered. Once we determine how much of the set of logical consequences of your evidence set are evidenced by that set, then we can say exactly what kinds of inconsistent beliefs cannot be part of a coherent system and which can be. The important point, though, is that some impossibilities and perhaps some inconsistencies can be tolerated within a coherent system of beliefs.
On the whole, however, coherentists will be averse to inconsistency, and the question is why.
The usual argument, Lehrer’s, is that inconsistency makes achieving the epistemic goal of believing all and only truths impossible. But once you let in some impossibilities, that argument goes out the window. So what’s left to explain the aversion?
There are two ways to argue here that I see. The first is an “everybody’s in the same boat” argument. That is, point out that every theorist will have a similar aversion to blatant inconsistencies, so whatever explanation is given by, e.g., foundationalists can be given by coherentists. But I don’t know what foundationalists will say either, so even if this line is acceptable, it yields no insight.
The other way is to argue that the intuitive concept of coherence itself is at odds with inconsistency, though perhaps not in the strong way that requires that all inconsistencies are incoherencies. This would be a pleasing result; I just can’t see how it could be developed. That is, what might a coherentist say is involved in the ordinary concept of coherence that puts it at odds with inconsistency but not universally so?