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i think one problem with the webster definition is that it doesn't address the question of who gets to set the truth conditions.
i dont think it is the case that faith cannot be subject to demonstration...at least not necessarily.
that's a reformation thing, so among the criteria that protestantism initially advanced to differentiate itself from catholicism. and in a way the wars of religion were about the about a fight over truth conditions. well, they were more about the political realignments that protestantism enabled, but that's another matter.
i say this because it's not like aquinas or the whole scholastic tradition didn't happen. and one thing that unifies scholasticism is the idea that faith and reason are not incompatible and that the structured exercise of reason can result in an approximate knowledge of the god character. the structured exercise of reason proceeded by way of proofs--so premises, variables and rules for combination and/or derivation.
so i guess the first point would be that there is no single definition of faith.
secondly there is no *necessary* contradiction between faith and the exercise of reason (here in the form of proofs, you know?)
i think i'm writing like this because of my reaction to the term "truth criteria"--which formally is a pretty simple matter: a statement is true that is produced through the use of procedures in a way that does not violate the rules that shape the proof.
the problem is that any proof is subject to the characteristics of the axioms that enable it.
and axioms cannot be demonstrated from within a proof that presupposes them.
one way of thinking about the source of the differend (talking past each other) is that the difference between believers and others plays out over the question of axioms, over what counts as axiomatic, and not over the procedures that shape proof (now a metaphor for the exercise of reason) that are structured by those axioms.
so if you want a dialogue between those who believe in something like a god-character and those who don't and you want to imagine it being either enabled or disallowed by agreements over "truth criteria" you're talking about the wrong thing, working at the wrong level.
what you're talking about is a dialogue about axioms (in the case of a proof, which really isnt much of a dialogue).
what that would require in principle is the construction of a meta-game that would result in the production of acceptable axioms (again, the language of proofs) or that would result in assumptions and rules that would then shape the space within which a dialogue could happen.
of course there could be squabbles about the rules that shape the meta-game, which may require the construction of a meta-meta game for adjudicating problems that may arise within the meta-game.
and there's nothing to prevent the same thing from happening inside the meta-meta game.
so good luck with that.
but if i assume that the technical language you use in the op isn't being used in anything like a technical sense and read the op as asking what are the conditions of possibility for a dialogue between members of communities that operate with basically different language games (sorry...wittgenstein is clanging around in my brain) so basically different assumptions about what constitutes a "legitimate" argument or--more to the point--"legitimate" data...basically that's pretty simple. good will. the desire to have such a dialogue.
there's a tendency here for folk who do not believe in some god to assume that belief is a defect of some kind, and a counter-assumption (which you see less often here because of the demographic we happen to have playing the game of posting stuff) that the lack of belief constitutes a defect of some kind. it's hard to get to a space of good will through that.
the reason this is a problem is, i think anyway, that the basic problem with dialogue across this divide is whether and on what basis a god-function can get introduced into a discussion.
across conflict/discussion about that, i suppose the main question that comes up, sooner or later, is really: why do you believe?
i can imagine more and less constructive conversations happening about that as a function of who happens to participate and, frankly, the mood that they're in across the duration it requires to make a post.
but there's no formal way to adjust for that.
differends aren't necessarily bad things.
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a gramophone its corrugated trumpet silver handle
spinning dog. such faithfulness it hear
it make you sick.
-kamau brathwaite
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