If person M has a concept of belief, and a logic for that concept, B1, but some other person N has concept B2, with different inference rules over the operator, then on the first-order level, does M mean to say anything such as B1(S) (for some statement), in such a way that N can be said to say B2(~S)? Or by having different concepts of belief, do M and N not really agree or disagree about S?
Offhand, I'd guess that higher-order doxastic logic, metabeliefs say, could mediate something more than "talking past each other." Or by dissolving the basis for disagreement (as well as agreement, though), maybe the logical pluralist, with respect to doxastic logic, simply carries through the theme of logical pluralism to its hoped-for conclusion (its practical conclusion, that is: to circumvent the social-conflict model of abstract knowledge acquisition (i.e. to counteract the tradition of "disputation")).
Does doxastic logical pluralism undermine the standpoint of disagreement, but by doing so (if it does), does it undermine itself too, by eliding the distinction-by-illocutionary-force between different, potentially conflicting beliefs? (So to say, if disagreement doesn't actually exist, then there aren't a plurality of logics for people to variously agree or disagree with, and though we would not go back to the land of some magical One True Logic, we would venture off instead into a very alien territory even so, it would seem, where everything gets churned together in the end, spread out like a mass of water with logical currents demarcating the zones theretofore conceived of as separate and contentious beliefs about logic.)