Topics in Philosophical Logic

2505/29178         Topics in Philosophical Logic           Room 1001-B CL
Dunn, J. Michael

Thursday 9:30-12:00

Please note that this is a Special Lecture that will meet Thursday & Friday mornings every two weeks, beginning the second week of the Spring term.

I was a grad student in Philosophy at Pitt in the mid 1960’s when Pittsburgh was not just the home to the steel industry, but also to relevance logic. Alan Ross Anderson, Nuel Belnap and some of their students (I mention in reverse alphabetical order, Alasdair Urquhart, Robert K. Meyer, and J. Michael Dunn) made Pitt the home of relevance logics, at least until these were off-shored to Australia and New Zealand (where they were pronounced “relevant” logics). I consider it a privilege to be able to offer this seminar and pass down both the published and oral history. We will review the semantics (model theory) of modal logics initiated by Kripke and others in the 1950s using a binary (2-placed) accessibility relation of "relative possibility" between "possible worlds." The adaptation of this approach to other non-classical logics took decades, and involved the realization that the third place is the charm. In the early 1970’s an explosion occurred using the ternary accessibility relation, featuring most famously the Routley-Meyer semantics, but also similar inventions by Alasdair Urquhart, Kit Fine, Larisa Maksimova, and Dov Gabby (the exact details varied). And a decade or so later independent creations were gone by Jean-Yves Girard (linear logic), Johan van Benthem and Yde Venema (arrow logic), Jon Barwise (channel theory). The goal of this course is to investigate the connections and interactions between different approaches to the semantics of relevance and related logics. The emphasis will be on implication, but we will also consider various approaches to negation. Through this comparative study, we will achieve a better understanding of the logics themselves, and hopefully be able to define superior semantics for them with various applications. We will also study the development of the ideas behind these approaches -- sort of an analytical history.

Prerequisite(s): A good familiarity with first-order classical logic and basic set theory. Graduate standing.

This is a kind of combination of a "Background" and "Research" seminar.  It is intended to introduce students to the semantics of modal and relevance logic (and some related logics). But the course will reflect on-going research by the instructor and Katalin Bimbó (University of Alberta) on both the historical development and refining interpretations of the ternary relational semantics for relevance logic. The general idea is that the class will meet every two weeks, with a lecture/discussion on Thursday and student presentations and/ or discussion on Friday.  We will start with some introductory material, especially on lattices and the Kripke semantics for modal logic.  I expect to have an exam over this material but the most important grading component will be a term paper (which could emphasize mathematical, philosophical, or historical content).