General Research Interests

I mostly work on epistemology and philosophy of mathematics. Within philosophy of mathematics, I'm especially interested in the access/Benacerraf problem for mathematical realists, the relationship between mathematics and logic and the philosophy of set theory.

Better understanding these topics can illuminate the foundations of a priori knowledge, and metametaphysics (particularly debates about realism and knowledge by convention) and access problems in other areas,e.g., ethics.

See here for details on my book A Logical Foundation for Potentialist Set Theory .

The Access/Benacerraf Problem

• The Residual Access Problem and slideshow version presented at the 2020 Eastern APA
• Coincidence Avoidance and Formulating the Access Problem Canadian Journal of Philosophy 2020
• (Probably) Not Companions in Guilt, Philosophical Studies, September 2018
• Modal Structuralism Simplified , Canadian Journal of Philosophy 2018
• See A Logical Foundation for Potentialist Set Theory for a formal system for reasoning about logical possibility sufficient to reconstruct ZFC set theory

(Defending) Extreme Mathematical Truthvalue Realism

• Hamkins' Analogy Between Set Theory and Geometry under review
• Σ⁰₁ Soundness isn't Enough forthcoming in British Journal of Philosophy of Science
• Physical Possibility and Determinate Number Theory , now also in slideshow presented at the 2018 Joint Sessions
• Malament-Hogarth Machines and Tait's Axiomatic Conception of Mathematics Erkenntnis 2013

Ontological Knowledge By Convention

• Quantifier Variance, Mathematicians' Freedom and the Revenge of Quinean Indispensability Worries forthcoming in Erkenntnis
• Chalmers, Quantifier Variance and Mathematicians' Freedom (penultimate draft) Synthese Library Volume 373 Quantifiers, Quantifiers, Quantifiers 2015
• Gunk Mountains: A Puzzle Analysis 2019 (a puzzle that arises when trying to generalize my story about knowledge of mathematical objects).
• [Also relevant: a review of Augustin Rayo's The Construction of Logical Space Mind 2015 ]

Basic A Priori Knowledge

• External World Skepticism, Confidence and Psychologism about the Problem of Priors (penultimate draft), Southern Journal of Philosophy 2019
• Default Reasonableness and the Mathoids Synthese 2013

Quinean (and other) Indispensability Arguments

• Explanatory Indispensability Arguments and the Modal Perspective on Mathematics under review
• The Mathematical Nominalist's Real Problem With Physical Magnitudes under review
• Also see `Quantifier Variance and ...the Revenge of Quinean Indispensability' (forthcoming) above