Thanks to a recent visit from Jc Beall, I was reminded of a critical discussion between Jc and our colleague and friend Graham Priest in the pages of Analysis. Jc was puzzled by a claim that Graham made in his reply to Jc’s paper, concerning nonmonotonic consequence relations and failures of truth preservation. Here, I’ll explain the disagreement between Jc and Graham, and why Graham’s claim (that all nonmonotonic logics fail to preserve truth) is wrong.
In between wrapping up teaching for the end of Semester 2, and getting ready for a short trip to Scotland, I’m spending some time thinking about free logic and quantified modal logic and identity. This is difficult but exciting terrain to cover. There is no obvious way to tie together the logic of quantifiers, the modalities and identity in a way that commands broad appeal—there is no default quantified modal logic that has the same ‘market reach’ as classical first order logic.
This is a shame, because many important arguments involve quantification, identity and possibility and necessity—and claims about existence and nonexistence. Understanding the logic of these arguments better would help us gain some kind of systematic understanding of the positions in play. In the absence of a clear picture of the logic implicit in our concepts, we’re playing the dialectical game in ignorance of the rules.
Not that there’s anything wrong with that.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.