(1) That an utterance of 'It might be that p' can be thought of as being correct iff the proposition p is robust with respect to a contextually relevant amount and kind of inquiry. That is, iff the proposition is not falsified by the relevant amount and kind of inquiry.
(2) Sometimes, when we assess epistemic modals, we assess whether their prejacents - the propositions p they say might obtain - meet the contextually relevant robustness requirement, but other times, we assess whether they are ultimately correct - i.e. whether they would survive all possible inquiry.
To get a feel for why you'd want something like (1), consider this phenomenon: sometimes when asked whether something might be true, we say 'I don't know'. That suggests that we don't think present evidence settles the question. Nevertheless, we might be happy after a certain amount of inquiry to say 'It turns out that p could indeed be true', and we might be happy to say this even while allowing that yet more inquiry may still falsify p. So when we were asked whether it might be that p, we took ourselves to need some more evidence than we currently have, but still not all possible evidence. Thus, we had some idea in the background of a contextually relevant amount or kind of inquiry.
To get a feel for why you'd want something like (2), consider the fact that if I'm asked whether it might be that p, and say something 'I don't know, we'd better wait for the results of the police report', and then later, once the report is in, say 'The report is in now, and yes, it might be that p', I may still, later when even more is known and we now know p is false, say 'Ah, so it turns out that our belief that p might be the case was wrong'.
My explanation for this was that the judgement made when the report came in - and perhaps the agnosticism before it - was about robustness up to a contextually relevant point, but that the later judgement once even more inquiry is done, and we know that p is false, was about ultimate correctness.
This led to the idea that, with respect to epistemic modals, expressions like 'true'/'false', 'right'/'wrong', 'correct'/'incorrect', are ambiguous. Or more carefully, that statements about epistemic modals made with these terms can be understood in different ways. (You could perhaps maintain a unified semantics for these terms by having a contextual parameter - very roughly, a view on which 'true' means something like 'cognitively good in way X'.)
Now, a forthcoming paper by Justin Khoo and Jonathan Phillips considers a version of relativism which responds to certain difficult data with a kind of ambiguity view of 'true' and 'false'. They raise a problem for this response which would also be a problem for my idea about terms like these, when epistemic modals are in play, sometimes being about contextually relevant robustness and sometimes being about ultimate correctness.
Against any such ambiguity approach - or more carefully, against any approach on which these assessment claims about epistemic modals are equivocal can be understood in different ways - Khoo and Phillips adduce the following exchange:
A: Fat Tony might be dead.And judge that what C says at the end seems 'irreparably incoherent' (p. 12 of the archived draft).
B: What A said is false.
C: #I agree with you B – what A said is false; but also, A’s claim is true since A didn’t have the evidence proving Fat Tony is alive.
I want to suggest that this is too quick. I agree that C's last utterance sounds very bad. But I don't think that is all that hard for an ambiguity approach to account for.
In service of this argument against an ambiguity approach, they consider an uncontroversially ambiguous word, 'book', and note that the following sounds fine (p. 12 of the archived draft):
D: (pointing to a bound volume with blank pages) This is a book.But this isn't a good comparison. I suggest that there's something like a rule of language which is flouted in the dialogue they complain about between A, B and C but is not flouted in the dialogue between D and E. Something like: when you use both members of a contrast pair like 'true' and 'false' then, absent explicit markers to the contrary, you're using them in the same way.
E: I agree with you D – that is a book; but it also isn’t a book since it’s not a literary work.
In support of this: if we add something like 'in a sense' and 'in another sense' to C's utterance, it begins to sound a lot better.
This has reinvigorated me - to see new considerations putting pressure on relativism to look more like the view I began to develop in 2011, which move on relativism's part then faces published (or forthcoming) objections to which I think I have a good answer.