My main research interest remains the notion of logical consequence; and extends from medieval theories in the philosophy of language, mind and logic, to the more modern concerns of relevance logic and the philosophy of logic, in particular, proof-theoretic semantics and the semantic paradoxes.
From the summer of 2017, I have been leading the Medieval Logic Research Group in the Arché Research Centre. The research of this group embraces the Leverhulme-funded project on
and Mark Thakkar's Leverhulme-funded project on John Wyclif's Logica (or Probationes Propositionum). It also hosts weekly meetings of the Medieval Logic Seminar (formerly, the Medieval Logic Reading Group). Our last workshop was on Theories of Paradox in the Middle Ages: 21-23 October 2020, held by Zoom. Recordings of many of the talks can be found at YouTube. A number of the papers will be published in due course in Studies in Logic (College Publications). Previous workshops were held on The History of Arabic Logic in May 2019, on Medieval Logic and its Contemporary Relevance in 2018 and on Proofs of Propositions (probationes propositionum) in 14th-century Logic in 2017.
The Cambridge Companion to Medieval Logic, which Catarina Dutilh Novaes and I edited, appeared in September 2016.
My new English translation with Introduction of John Buridan's Treatise on Consequences (a translation of Hubien's 1976 edition of the Latin text Tractatus de Consequentiis) appeared at the end of 2014 with Fordham UP. Sten Ebbesen reviewed it in Notre Dame Philosophical Reviews. and Sara Uckelman has recently reviewed it in Studia Logica. Here is a list of corrections and improvements.
An earlier project was an examination of Bradwardine’s discussion of insolubles and the Liar paradox. I prepared a new edition and English translation of Bradwardine’s Latin text from the thirteen known manuscripts. The work appeared in May 2010 as volume 10 in the series Dallas Medieval Texts and Translations published by Peeters. Here is a list of corrections and improvements.
In 2016, I gave some video talks on logic and paradox at Serious Science. In May 2018 I was interviewed about the modern and medieval solutions to the liar paradox by William Nava on 'Who Shaves the Barber?' In June 2020, I was invited by Bob Pasnau to organise a panel discussion, with contributions from Sara Uckelman (Durham U) and David Sanson (Illinois State U) as well as myself for the Virtual Medieval Colloquium on Theories of Paradox in the Middle Ages (recorded). In August 2020 I gave a talk to the Logic Supergroup entitled 'Everything true will be false': a sophism from Paul of Venice's Quadratura (recorded).
An interview (End Times: medieval matters) with Richard Marshall was published in 2014 in 3:AM Magazine. Another, with my former student Andrew Aberdein, is in The Reasoner vol.5 no.12 (December 2011).