Philosophy and Model Theory. Co-authored with Tim Button, with a historical appendix by Wilfrid Hodges. Oxford University Press, 2018.

The Prehistory of the Subsystems of Second-Order Arithmetic. Co-authored with Walter Dean. The Review of Symbolic Logic, 10(2):357–396, 2017. [doi]

Definability Aspects of the Denjoy IntegralFundamenta Mathematicae, 237:1–29, 2017. [doi]

Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics. Co-authored with Tim Button. Philosophia Mathematica, 24(3):283–307, 2016. [doi]

Realizability Semantics for Quantified Modal Logic: Generalizing Flagg’s 1985 Construction. Co-authored with Benjamin G. Rin. The Review of Symbolic Logic, 9(4): 752–809, 2016. [doi]

The Strength of Abstraction with Predicative ComprehensionThe Bulletin of Symbolic Logic, 22(1):105–120, 2016. [doi]

Fragments of Frege’s Grundgesetze and Gödel’s Constructible Universe. The Journal of Symbolic Logic, 81(2):605–628, 2016. [doi]

Predicativity, the Russell-Myhill Paradox, and Church’s Intensional LogicThe Journal of Philosophical Logic, 45(3):277–326, 2016. [doi]

Relative Categoricity and Abstraction Principles. Co-authored with Sean Ebels-Duggan. The Review of Symbolic Logic, 8(3):572–606, 2015. [doi]

Empiricism, Probability, and Knowledge of Arithmetic: A Preliminary DefenseJournal of Applied Logic, 12(3):319–348, 2014. [doi]

Logicism, Interpretability, and Knowledge of ArithmeticThe Review of Symbolic Logic, 7(1):84–119, 2014. [doi]

Comparing Peano Arithmetic, Basic Law V, and Hume’s PrincipleAnnals of Pure and Applied Logic, 163:1679–1709, 2012. [doi]

Incongruent Counterparts and Causality. Kant-Studien 98(4): 418–430, 2007. [doi]


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Slides from recent talks

Infinitesimals and classification. Pacific APA, Book Symposium. April 18, 2019.

Infinitesimals, valued fields, and the orders of infinite smallnessClaremont History and Philosophy of Mathematics Seminar. April 22, 2019.