2018. Coauthored with Sean Walsh.
With a historical appendix by Wilfrid Hodges.
Oxford University Press.

[]
[doi]
[]
[errata]
[pop-exposition]

2013.
Oxford University Press.

[]
[doi]
[]

Lieven Decock, *Notre Dame Philosophical Reviews*. [url]

Nicholas K Jones, *Analysis*. [doi] [preprint]

Drew Khlentzos, *Australasian Journal of Philosophy* [doi]

Rory Madden, *European Journal of Philosophy*. [doi] [preprint]

J.T.M. Miller, *Philosophy in Review*. [doi]

Joshua Thorpe, *Argumenta*. [doi]

Jan Westerhoff, *Mind*. [doi]

Nathan Wildman, *Zeitschrift für philosophische Forschung*. [preprint]

*draft*.
Why are all the sets all the sets?
[]
[draft]

*2024*.
Wand/Set Theories: A realization of Conway’s mathematicians’ liberation movement, with an application to Church’s set theory with a universal set.
*Journal of Symbolic Logic*.
[]
[doi]

*2025*.
The iterative conception of function and the iterative conception of set.
In N. Barton, C. Antos, and G Venturi (eds.), *Palgrave Companion to the Philosophy of Set Theory*. Palgrave.
[] [preprint]

2024. A fictionalist theory of universals.
Coauthored with Robert Trueman.
In P. Fritz and N. Jones (eds.), *Higher-Order Metaphysics*. OUP: 245–90.
[] [preprint]

2023.
Symmetric relations, symmetric theories, and Pythagrapheanism.
*Philosophy and Phenomenological Research*, 107.3: 583–612.
[] [open access
doi]

2022.
Against cumulative type theory.
Coauthored with Robert Trueman.
*Review of Symbolic Logic*, 15.4: 907–49.
[] [open access doi]

2022.
Mathematical internal realism.
In J. Conant and S. Chakraborty (eds.), *Engaging Putnam*. De Gruyter: 157–182.
[] [doi] [preprint]

2022.
Level Theory, part 3: A boolean algebra of sets arranged in well-ordered levels.
*Bulletin of Symbolic Logic*, 28.1: 1–26.
[] [doi] [preprint]

2021.
Level Theory, part 2: Axiomatizing the bare idea of a potential hierarchy.
*Bulletin of Symbolic Logic*, 27.4: 461–84.
[] [doi] [preprint]

2021.
Level Theory, part 1: Axiomatizing the bare idea of a cumulative hierarchy of sets.
*Bulletin of Symbolic Logic*, 27.4: 436–60.
[] [doi] [preprint]

2020.
Deflationary metaphysics and ordinary language.
*Synthese* 197.1: 33–57.
[] [open access doi]

2018.
Other minds and God: Russell and Stout on James and Schiller.
In M. Baghramian and S. Marchetti (eds.), *Pragmatism and the European Traditions*. Routledge: 86–109.
[] [doi] [preprint]

2018.
Wittgenstein on solipsism in the 1930s: Private pains, private languages, and two uses of ‘I’.
*Royal Institute of Philosophy Supplement* 82: 205–29.
[] [doi] [preprint]

2017.
Exclusion problems and the cardinality of logical space.
*Journal of Philosophical Logic* 46.6: 611–23.
[] [open access doi]

2017.
Grades of Discrimination: Indiscernibility, symmetry, and relativity.
*Notre Dame Journal of Formal Logic* 58.4: 527–53.
[] [open access doi]

2016. Brains in vats and model theory.
In S. Goldberg (ed.), *The Brain in a Vat*, CUP: 131–54.
[] [doi] [preprint]

2016.
Knot and Tonk: Nasty connectives on many-valued truth-tables for classical sentential logic.
*Analysis* 76.1: 7–19.
[] [doi] [preprint]

2016.
Structure and categoricity: Determinacy of reference and truth-value in the philosophy of mathematics.
Coauthored with Sean Walsh.
*Philosophia Mathematica* 24.3: 283–307.
[] [doi] [preprint]

2014.
The weight of truth: Lessons for minimalists from Russell’s Gray’s Elegy argument.
*Proceedings of the Aristotelian Society* 114.3: 261–89.
[] [doi] [preprint]

2012.
The philosophical significance of Tennenbaum’s Theorem.
Coauthored with P. Smith.
*Philosophia Mathematica*, 20.1: 114–21.
[] [doi] [preprint]

2011.
The metamathematics of Putnam’s model-theoretic arguments.
*Erkenntnis* 74.3: 321–49.
[] [doi] [preprint]

2010.
Dadaism: restrictivism as militant quietism.
*Proceedings of the Aristotelian Society* 110.3: 387–98.
[] [doi] [preprint]

2009.
Hyperloops do not threaten the notion of an effective procedure.
*Lecture Notes in Computer Science * 5635: 68–78.
[] [doi] [preprint]

2009.
SAD computers and two versions of the Church–Turing Thesis.
*British Journal for the Philosophy of Science* 60.4: 765–92.
[] [doi] [preprint]

2007.
Every now and then, no-futurism faces no sceptical problems.
*Analysis* 67.4: 325–32.
[] [doi] [preprint]

2006.
Realistic structuralism’s identity crisis: A hybrid solution.
*Analysis* 66.3: 216–22.
[] [doi] [preprint]

*draft (retired with probability ⅔)*.
Too clever by halving.
Coauthored with Daniel Rothschild and Levi Spectre.
[] [draft]

2019.
Review of: *Hilary Putnam on Logic and Mathematics*, by Geoffrey Hellman and Roy T. Cook (eds.).
*Mind*, 129.516: 1327–37.
[] [doi] [preprint]

2017.
Review of: *Naturalism, Realism, and Normativity*, by Hilary Putnam, edited by Mario de Caro.
*Philosophy* 92.2: 305–15.
[] [doi] [preprint]

2016.
Review of: *Ontology After Carnap*, by Stephan Blatti and Sandra Lapointe (eds.).
*Notre Dame Philosophical Reviews*.
[] [url] [preprint]

2014.
Review of: *Reading Putnam*, by Maria Baghramian (ed.).
*Mind* 123.490: 569–75.
[] [doi] [preprint]

2013.
The chair that is used to sit in. Review of: *The American Pragmatists*, by Cheryl Misak.
*The Times Literary Supplement* 18 October 2013.
[] [preprint]

On the other tabs, you can find my research sorted by type. Here, they are grouped by their main theme, with some repetition.

*draft*.
Why are all the sets all the sets?
[] [draft]

*2024*.
Wand/Set Theories: A realization of Conway’s mathematicians’ liberation movement, with an application to Church’s set theory with a universal set.
*Journal of Symbolic Logic*.
[]
[doi]

*2025*.
The iterative conception of function and the iterative conception of set.
In N. Barton, C. Antos, and G Venturi (eds.), *Palgrave Companion to the Philosophy of Set Theory*. Palgrave.
[] [preprint]

*Bulletin of Symbolic Logic*, 28.1: 1–26.
[] [doi] [preprint]

*Bulletin of Symbolic Logic*, 27.4: 461–84.
[] [doi] [preprint]

*Bulletin of Symbolic Logic*, 27.4: 436–60.
[]
[doi]
[preprint]

*Review of Symbolic Logic*, 15.4: 907–49.
[]
[open access doi]

2018.
*Philosophy and Model Theory*.
Coauthored with Sean Walsh.
OUP.
[]
[doi]
[errata]

*Philosophia Mathematica* 24.3: 283–307.
[]
[doi]
[preprint]

2013.
*The Limits of Realism*, chapters 1–7. OUP.
[]
[doi]

*Philosophia Mathematica*, 20.1: 114–21.
[]
[doi]
[preprint]

*Erkenntnis* 74.3: 321–49.
[] [doi] [preprint]

*Higher-Order Metaphysics*. OUP: 245–90.
[] [preprint]

*Review of Symbolic Logic*, 15.4: 907–49.
[] [open access doi]

See also: the papers on Sets & levels.

*Philosophy and Phenomenological Research*, 107.3: 583–612.
[] [open access doi]

2018.
*Philosophy and Model Theory*, chapter 5.
Coauthored with Sean Walsh.
OUP.
[] [doi] [errata]

2013.
*The Limits of Realism*, chapters 18–19. OUP.
[] [doi]

See also: the publications on Model Theory.

*Engaging Putnam*. De Gruyter: 157–182.
[] [doi] [preprint]

2018.
*Philosophy and Model Theory*, chapters 9–13.
Coauthored with Sean Walsh.
OUP.
[] [doi] [errata]

*The Brain in a Vat*, CUP: 131–54.
[] [doi] [preprint]

*Analysis* 76.1: 7–19.
[] [doi] [preprint]

2013. *The Limits of Realism*. OUP.
[] [ doi]

*Proceedings of the Aristotelian Society* 110.3: 387–98.
[] [doi] [preprint]

*2025*.
The iterative conception of function and the iterative conception of set.
In N. Barton, C. Antos, and G Venturi (eds.), *Palgrave Companion to the Philosophy of Set Theory*. Palgrave.
[] [draft]

*Higher-Order Metaphysics*. OUP: 245–90.
[] [preprint]

*Philosophy and Phenomenological Research*, 107.3: 583–612.
[] [open access doi]

2020.
Deflationary metaphysics and ordinary language.
*Synthese* 197.1: 33–57.
[] [open access doi]

*Journal of Philosophical Logic* 46.6: 611–23.
[] [open access doi]

*Naturalism, Realism, and Normativity*, by Hilary Putnam, edited by Mario de Caro.
*Philosophy* 92.2: 305–15.
[] [doi] [preprint]

*Ontology After Carnap*, by Stephan Blatti and Sandra Lapointe (eds.).
*Notre Dame Philosophical Reviews*.
[] [url] [preprint]

*Reading Putnam*, by Maria Baghramian (ed.).
*Mind* 123.490: 569–75.
[] [doi] [preprint]

*Analysis* 67.4: 325–32.
[] [doi] [preprint]

*Analysis* 66.3: 216–22.
[] [doi] [preprint]

*Royal Institute of Philosophy Supplement* 82: 205–29.
[] [doi] [preprint]

*Pragmatism and the European Traditions*. Routledge: 86–109.
[] [doi] [preprint]

*Lecture Notes in Computer Science * 5635: 68–78.
[] [doi] [preprint]

*British Journal for the Philosophy of Science* 60.4: 765–92.
[] [doi] [preprint]

*Hilary Putnam on Logic and Mathematics*, by Geoffrey Hellman and Roy T. Cook (eds.).
*Mind*, 129.516: 1327–37.
[] [doi] [preprint]

*Notre Dame Journal of Formal Logic* 58.4: 527–53.
[] [open access doi]

*Proceedings of the Aristotelian Society* 114.3: 261–89.
[] [doi] [preprint]

*The American Pragmatists*, by Cheryl Misak.
*The Times Literary Supplement* 18 October 2013.
[] [preprint]

2013.
Review of: *Truth by Analysis: Games, Names, and Philosophy*, by Colin McGinn.
*Analysis* 73.3: 577–80.
[] [doi] [preprint]

*draft (retired with probability ⅔)*.
Too clever by halving.
Coauthored with Daniel Rothschild and Levi Spectre.
[] [draft]