My past research in the philosophy of mathematics mostly revolves around issues raised in Paul Benacerraf's 1973 paper "Mathematical Truth." Specifically, I have written about epistemological arguments against mathematical platonism and Quinean semantic arguments for mathematical platonism. I've also explored a neo-logicist account of these issues.
My in-progress work (not available yet) is a bit more wide-ranging. On the epistemological side, I've turned to general epistemological problems in the philosophy of mathematics, and not just problems for platonists. I've also been developing ideas about related epistemological issues in metaethics. On the metaphysics side, I've been working on abstractionist and otherwise Fregean accounts of the ontology of mathematics.
(click for papers)
2022. "The Benacerraf Problem of Mathematical Truth and Knowledge." Internet Encyclopedia of Philosophy.
2020. "Benacerraf, Field, and the Agreement of Mathematicians." Synthese 197(5): 2095--2110. (penultimate version)
2018. "Ontological Realism and Sentential Form." Synthese 195(11): 5021--36. (penultimate version)
2018. "The Limits of Reconstructive Neologicist Epistemology." The Philosophical Quarterly 68(273): 717--738. (penultimate version)
2016. "To Bridge Godel's Gap." Philosophical Studies 173(8): 2133--50. (penultimate version)
In metaphysics proper, I have a project with Ben Caplan (Kansas) and Chris Tillman (Manitoba) aimed at developing a hylomorphic account of the ontology of abstracta. We've published some of our work on propositions. That main joint project also spawned a side paper on grounding and essence, which play important roles in our account of propositions.
(click for papers)
(forthcoming). "Hylomorphic Propositions" in Chris Tillman and Adam Murray (eds.) The Routledge Handbook of Propositions. (with Ben Caplan and Chris Tillman) (penultimate version)
2018. "Constitutive Essence and Partial Grounding." Inquiry 61(2): 137--161. (with Ben Caplan and Chris Tillman) (penultimate version)