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.
I have been awarded a Leverhulme Project Grant for a project on Theories of Paradox in Fourteenth-Century Logic: Edition and Translation of Key Texts. The aim is to produce critical editions from the medieval manuscripts of the texts on insolubles by Paul of Venice, Walter Segrave, John Dumbleton, with English translations and commentary.
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 Theories of Paradox in Fourteenth-Century Logic, and Mark Thakkar's Leverhulme-funded project on John Wyclif's Logica. It also hosts weekly meetings of the Medieval Logic Reading Group. We are organising a Workshop on Medieval Logic and its Contemporary Relevance in St Andrews from 30 April - 2 May 2018.
The Cambridge Companion to Medieval Logic, which Catarina Dutilh Novaes and I edited, appeared in September 2016.
Recently, I led the Arché research group in History and Philosophy of Logic and Mathematics, formerly, the MMM group (Models, Modality and Meaning, 2012-15). The most recent HPLM workshop was in May 2017 on the topic of Proofs of Propositions (probationes propositionum) in 14th-century Logic.
I was the Principal Investigator in an Arché research project, funded by the Arts and Humanities Research Council (AHRC) on the Foundations of Logical Consequence. This project started in January 2009 and concluded in June 2012.
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.