Research
My research is in logic, philosophy of mathematics, and metaphysics and epistemology. I am interested both in technical problems in these areas and in more traditionally philosophical questions, and I have an appreciation for the ways these two types of questions often interact. You'll find information about my publications and other works in progress below.
Publications
"A Hierarchy of Relevance Properties," forthcoming in New Directions in Relevant Logic.
"What is Forcing Potentialism?" forthcoming in The Palgrave Companion to the Philosophy of Set Theory.
"Coarsening Natural Deduction Proofs II: Finding Gaunt Proofs," (2024) Journal of Logic and Computation. Published version available here.
"Coarsening Natural Deduction Proofs I: Finding Perfect Proofs," (2023) Journal of Logic and Computation. Published version available here.
"A Classical Modal Theory of Lawless Sequences," (2023) Bulletin of Symbolic Logic. Published version available here.
"Disagreement, the Independence Thesis, and the Value of Repeated Reasoning," (2023) Pacific Philosophical Quarterly. Published version available here.
"In Defense of the Implicit Commitment Thesis," (2023) in Ergo.
"Metaphysical Nihilism and Modal Logic," (2022) Philosophical Studies. Published version available here.
with Øystein Linnebo and Stewart Shapiro, "Divergent Potentialism: A Modal Analysis with an Application to Choice Sequences," (2022) Philosophia Mathematica. Published version available here.
"The Modal Logic of Potential Infinity: Convergent versus Branching Possibilities," (2022). Erkenntnis. The published version available here.
with Neil Tennant, "Transmission of Verification," (2021). Review of Symbolic Logic. Published version available here.
"The Dependence of Computability on Numerical Notations," (2021) Synthese. Published version available here.
"Mirroring Theorems in Free Logic," (2020) Notre Dame Journal of Formal Logic. Published version available here.
"Relevance for the Classical Logician," (2020) Review of Symbolic Logic. Published version available here.
"Second-order Logic and the Power Set", (2018) Journal of Philosophical Logic . Published version available here.
Ongoing Projects
A brief overview of some current work.
In a pair of papers on the nature of certainty, I argue that we can identify different types of certainty according to the type of epistemic reasons that justify a belief. This view on certainty then suggests a way of rehabilitating the notion of mathematical certainty. These papers develop some ideas I initially proposed in the paper "In Defense of the Implicit Commitment Thesis."
I am in the early stages of a new project on predicative mathematics, studying both its historical roots in Weyl, Russell, and Poincare, and subsequent metamathematical work on the topic. My approach to the topic is informed by the connections between predicativity, constructivism, and potential infinity.
I continue to pursue the proof-theoretic project that I initially proposed in "Relevance for the Classical Logician". This includes work in various stages of progress (some under review, some early drafts of papers, and some mere ideas to follow up on later). Several of my publications above fall under this project, including "Coarsening Natural Deduction Proofs I & II" and "A Hierarchy of Relevance Properties."