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

The Access/Benacerraf Problem

(Defending) Extreme Mathematical Truthvalue Realism

Ontological Knowledge By Convention

Basic A Priori Knowledge

Quinean (and other) Indispensability Arguments

- 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
- Σ
^{0}_{1}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