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Models for Compatibility

11 February 2016

This morning I received an email from Rachael Briggs, asking me some questions about the notion of compatibility as it appears in my paper “Negation in Relevant Logics.” These questions got me to thinking that there were some ideas in that paper and a much-less-read paper of mine “Modelling Truthmaking”, which might be worth reflecting on some more. So I’ll try to do that here. Here’s the background you need to get up to speed.

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I’ve been away from home in Auckland at a conference over the last couple of days, so I’m a bit behind on the news, but tonight I’ve finally found a few moments to write something in honour of my friend and mentor, Bruce French, who was—three days ago—named an Officer of the Order of Australia in the 2016 Australia Day Honour’s list. Bruce was awarded this honour because of his many decades of work, learning about tropical food plants throughout the Pacific, Asia and Africa, cataloguing that knowledge and making it freely available to anyone who can use it.

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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.

Update on March 9, 2016: I submitted a version of this note to the journal Thought, and it has been accepted for publication. The prepublication version of the paper is archived here.

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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.

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I’ve been at the University of Melbourne since 2002, and the Logic Group has been meeting regularly since my arrival there. While it’s changed significantly in its membership over the last 13 years, one thing has remained constant—we’ve been an informal, friendly bunch of people, so hard at work in teaching and research that we’ve not had time to make a website for the group. Well, thanks to the hardworking Shawn Standefer, that’s changed. Point your browsers to http://blogs.unimelb.edu.au/logic/ to keep up with Logic at Melbourne.


Recent Writing

  • “Fixed Point Models for Theories of Properties and Classes,” article under submission. Abstract  pdf
  • “On Priest on Nonmonotonic and Inductive Logic,” to appear in Thought. Abstract  pdf
  • “Three Cultures—or: what place for logic in the humanities?” unpublished essay. Abstract  pdf
  • “Generality and Existence I: Quantification and Free Logic,” article in progress. Abstract  pdf
  • “Assertion, Denial, Accepting, Rejecting, Symmetry and Paradox,” pages 310-321 in Foundations of Logical Consequence, edited by Colin R. Caret and Ole T. Hjortland, Oxford University Press, 2015 Abstract  pdf

Recent & Upcoming Presentations

Recent & Upcoming Classes


about

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.

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