If I imagine having a compiler that translates back-and-forth between intuitionistic and classical logic as in the post, and I want to stop the accumulation of round-trip ‘cruft’, I think the easiest thing to do would be to add provenance information that let me figure out whether a provability predicate, say, was “original” or “translational”. But frustratingly that’s not really possible in the case where I’m trying to translate between people with pretty different ontologies (who might not be able to parse their interlocutors statements natively).
I dunno whether you’re thinking more about the case of differing ontologies or more about the case of preferred framings (but fluency with both), so not sure how relevant to your inquiries.
I’m interested in concrete advice about how to resolve this problem in a real argument (which I think you don’t quite provide), but I’m also quite interested in the abstract question of how two people with different ontologies can communicate. Normally I think of the problem as one of constructing a third reference frame (a common language) by which they can communicate, but your proposal is also interesting, and escapes the common-language idea.
If I imagine having a compiler that translates back-and-forth between intuitionistic and classical logic as in the post, and I want to stop the accumulation of round-trip ‘cruft’, I think the easiest thing to do would be to add provenance information that let me figure out whether a provability predicate, say, was “original” or “translational”. But frustratingly that’s not really possible in the case where I’m trying to translate between people with pretty different ontologies (who might not be able to parse their interlocutors statements natively).
I dunno whether you’re thinking more about the case of differing ontologies or more about the case of preferred framings (but fluency with both), so not sure how relevant to your inquiries.
I’m interested in concrete advice about how to resolve this problem in a real argument (which I think you don’t quite provide), but I’m also quite interested in the abstract question of how two people with different ontologies can communicate. Normally I think of the problem as one of constructing a third reference frame (a common language) by which they can communicate, but your proposal is also interesting, and escapes the common-language idea.