(Waking up.) Sure, if I thought I had evidence (how) of P&~P, that would be pretty good reason to believe a paraconsistent logic was true (except what does true mean in this context? not just about logics, but about paraconsistent ones!!)
But if that ever happened, if we went there, the rules for being rational would be so radically changed that there wouldn’t necessarily be good reason to believe that one has to update one’s probabilities in that way. (Perhaps one could say the probability of the law of non-contradiction being true is both 1 and 0? Who knows?)
I think the problem with taking a high probability that logic is paraconsistent is that all other beliefs stop working. I don’t know how to think in a paraconsistent logic. And I doubt anyone else does either. (Can you get Bayes Rule out of a paraconsistent logic? I doubt it. I mean, maybe… who knows?)
(Waking up.) Sure, if I thought I had evidence (how) of P&~P, that would be pretty good reason to believe a paraconsistent logic was true (except what does true mean in this context? not just about logics, but about paraconsistent ones!!)
But if that ever happened, if we went there, the rules for being rational would be so radically changed that there wouldn’t necessarily be good reason to believe that one has to update one’s probabilities in that way. (Perhaps one could say the probability of the law of non-contradiction being true is both 1 and 0? Who knows?)
I think the problem with taking a high probability that logic is paraconsistent is that all other beliefs stop working. I don’t know how to think in a paraconsistent logic. And I doubt anyone else does either. (Can you get Bayes Rule out of a paraconsistent logic? I doubt it. I mean, maybe… who knows?)