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’ in claims like, “The rainy weather is a *reason for* John to take an umbrella.” I am also interested in theories of subject-matter, relevance, counterfactual and indicative conditionals, as well as logics for tense and modality.

In addition to understanding how these common elements of human reasoning function, I am interested in applications of my work on causal, normative, and conditional reasoning in AI safety in order to assist efforts to maintain oversight of AI-assisted decision-making in socially and morally sensitive sectors. Separately, I am working to construct modern analogues of ancient Indian philosophies of the self which are often stated in constitutive explanatory terms.

## 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 (PI^{1}) 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 PI^{1}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 proposition is*“A Complete Logic of Ground I: Unilateral Propositions” RSL (R&R)**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.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.*“A Complete Logic of Ground II: Bilateral Propositions” RSL (R&R)*

## In Progress

Standard intensional semantic theories take possible worlds to be complete histories of everything. Insofar as the same sentence may be true at some times and false at others, evaluating a sentence at a possible world does not fix its truth-value. However, if possible worlds are taken to be primitive, including a time in the point of evaluation introduces a degree of freedom that invalidates the perpetuity principle (PP) that what is necessarily the case is always the case. Instead of excluding countermodels by fiat, this paper will construct possible worlds from moments, where a moment is a maximal possible way for things to be at an instant. Since sentences are assigned truth-values at moments, times are exogenous to the interpretation of the language, eliminating unnecessary degrees of freedom in the definition of a model. Accordingly, sentences may be evaluated at world-time pairs where the resulting semantic theory validates a natural bimodal logic for tense and modality in which (PP) is a theorem. The paper concludes by reviewing objections and extensions to the framework.**“Counterfactual Worlds”**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.*“The Varieties of Constitutive Explanation”*This paper develops a hyperintensional semantic theory for past tense causal claims such as ‘Throwing the stone caused the window to break’ and ‘The fuse blowing caused the fire to start’. Consideration of where David Lewis’ (1973, 1986, 2000) accounts fail to capture common usage will motivate an extension of Kit Fine’s (2017a,b,c) state semantics that is better able to encode the explanatory relationships between events. After employing the resulting semantic theory to analyse a number of important causal scenarios, the paper concludes by presenting objections and possible extensions to the framework.*“Hyperintensional Causation”*Given a constitutive explanatory reading of ‘sufficient for’ which I will refer to as*“Relevant Implication and Ground”**ground*— or in symbols ‘≤’— it is natural to assume that A ≤ B entails: (1) A strictly implies B; and (2) A is wholly relevant to B. For instance, although A ≤ A ∨ B holds in general, A ∧ B ≤ A does not since B may be unrelated to A. By contrast, relevance logics accept the principle that A ∧ B relevantly implies A. This paper conducts a study of the conceptual targets that guided the development of relevance logics, comparing the results to a logic of ground which is designed to regiment constitutive explanatory readings of ‘sufficient for’. The paper concludes by presenting a unified logic and semantic theory for ground, relevance, and modality.This paper investigates the nature of the self. In particular, I will seek to regiment the Upanishadic claim, ‘sa esa neti netyatma’ (NA), which Olivelle (1998, p. 101) translates as, ‘About this self (atman), one can only say ‘not—, not—’.’ After presenting the context of the ´Sakalya Dialogue from the Brihadaranyaka Upanishad in which this claim first occurs, I will regiment NA by means of the following second-order principle: For any way of being, being that way does not strictly ground what it is to be the self (atman). It follows that the self is fundamental on account of failing to have any strict grounds. I will conclude by examining the relationship between the fundamentality of the self and the nature of the absolute (brahman). In particular, given the assumptions that the self (atman) is the absolute (brahman) and that every way of being is to be weakly grounded in the way that the absolute is, it follows that the self is fundamental.*“Fundamentality and the Self”*