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 Reading Group. We held a Workshop on Medieval Logic and its Contemporary Relevance in St Andrews from 30 April - 2 May 2018.The previous workshop was in May 2017 on the topic of Proofs of Propositions (probationes propositionum) in 14th-century Logic.
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.
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). 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?'