My research employs the methods of model theory and proof theory in order to study a number of different types of explanation. In particular, I am concerned with: constitutive explanatory terms such as ‘necessary for’, ‘sufficient for’, ‘what it is for’, ‘just is for’; causal explanatory terms such as ’caused’ and ‘makes’; and normative explanatory terms such as ‘reason for’. I am also interested in counterfactual and modal logics. My aim has been to understand how these common elements of human reasoning function in order to shed light on how we learn and think about the world, as well as informing scientific methodology. I am particularly interested in the application of these resources in machine learning and am concerned to evaluate the risks that these applications raise.

You can find my PhilPapers here.

Papers

• “Identity and Aboutness” JPL, 50, p. 1471-1503 (2021). This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (Journal of Philosophical Logic, 4545, 199–226  13, 14, 15) introduces. I will then move to compare the resulting logic of propositional identity (PI¹) with Correia’s (The Review of Symbolic Logic, 9, 103–122  9) logic of generalised identity (GI), as well as the first degree fragment of Angell’s (2) logic of analytic containment (AC). The paper concludes by extending PI¹ to include axioms and rules for a subject-matter operator, providing a much broader theory of subject-matter than the principles with which I will begin.
• “A Complete Logic of Ground I: Unilateral Propositions” RSL (R&R)  A proposition is specific just in case there is exactly one way for that proposition to obtain, and one proposition grounds another just in case every way for the former to obtain is a way for the latter to obtain. This paper provides a proof system for a unilateral logic of ground with a specificity operator, establishing soundness and completeness over a state semantics in which propositions are sets of states closed under finite fusion.
• “A Complete Logic of Ground II: Bilateral Propositions” RSL (R&R)  Having established soundness and completeness for a unilateral logic of ground with a specificity operator in a previous paper, this paper extends these results to a bilateral logic where propositions are closed under infinite fusion. By contrast with the Boolean lattices described by extensional and intensional logics, the space of bilateral propositions forms a non-interlaced bilattice. I will conclude by defining the bilateral notions of essence and ground in terms of unilateral ground.

In Progress

• “The Varieties of Constitutive Explanation” Constitutive explanations play important roles throughout many domains of inquiry. What is necessary for an atom to be gold? What is sufficient for an action to be wrong? What is it for a number to be prime? These are good question with good answers. This paper provides an account of constitutive explanatory readings of `necessary for’, `sufficient for’, and `what it is for’, arguing that modal regimentations of these locutions fail to track the explanatory relationships that these locutions are typically intended to express. Rather, I present a logic for constitutive explanation which includes operators for essence and ground in addition to the modal operators and the truth-functions. In support of these developments, the majority of the paper is devoted to clarifying the theoretical roles which the different forms of constitutive explanation are intended to play, as well as contrasting the present treatment to related accounts in the literature.