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.)

  • I can't really understand the question. Doxastic logic is single user, what others have to say about the same sentences is completely irrelevant. Of course, if they want to communicate/debate with others they'll have to use some interactive procedures to correlate the semantics, but before that they need to figure out for themselves what they believe, and that is what doxastic logic is for. For opinion sharing they have to use something else.
    – Conifold
    Commented Mar 6, 2023 at 21:45
  • I'm not sure how talking specifically of doxastic logic makes a difference. If two people are using different logics, then it is possible they will talk past each other. Is there some meta level at which the difference can be resolved? We can only hope so, otherwise communication would be difficult. This might amount to supposing that classical logic holds at the meta level, which we can think of as corresponding to the assumption that there is only one reality. E.g. we cannot have dialethic logic at both object and meta level without allowing that dialetheism both holds and does not hold.
    – Bumble
    Commented Mar 7, 2023 at 0:28


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