Monographs

(2024) Iterative Conceptions of Set. Cambridge University Press. Publisher. PhilPapers.

Collections

(2025) Antos, Carolin; Barton, Neil; and Venturi, Giorgio (eds.) The Palgrave Companion to the Philosophy of Set Theory. Palgrave Macmillan. Book.

(2020) Carolin Antos , Neil Barton, Sy-David Friedman, Claudio Ternullo and John Wigglesworth. Synthese Special Issue on Foundations of Mathematics. Journal issue.

Peer-reviewed journal articles

(Forthcoming) Mathematical Gettier Cases and Their Implications. To appear in the Australasian Journal of Philosophy. Journal. PhilPapers.

(Forthcoming) Countabilism and Maximality Principles (with Sy-David Friedman). To appear in the Notre Dame Journal of Formal Logic. PhilPapers.

(2025) Barton, N. Is (Un)Countabilism Restrictive?. Journal of Philosophical Logic 54, 1061–1077 (2025). Journal. Philpapers.

(2024) Barton, Neil and Williams, Kameryn J. Varieties of Class-Theoretic Potentialism. The Review of Symbolic Logic , Volume 17 , Issue 1 , March 2024 , pp. 272 – 304. Journal. PhilPapers. arXiv.

(2023) Barton, Neil. Are Large Cardinal Axioms Restrictive? Philosophia Mathematica, Volume 31, Issue 3, October 2023, Pages 372–407. Journal. PhilPapers.

(2022) Barton, Neil; Müller, Moritz; and Prunescu, Mihai. On Representations of Intended Structures in Foundational Theories. Journal of Philosophical Logic, Vol 51, pp. 283–296. Journal. PhilPapers.

(2021) Antos, Carolin; Barton, Neil; and Friedman, Sy-David, Universism and Extensions of V. The Review of Symbolic Logic , Vol. 14(1), pp. 112–154. Journal. PhilPapers.

(2020) Barton, Neil. Forcing and the Universe of Sets: Must we lose insight? Journal of Philosophical Logic, Vol. 49, pp. 575–612. Journal. PhilPapers.

(2020) Barton, Neil. Absence Perception and the Philosophy of Zero. Synthese, Vol. 197, pp. 3823–3850. Journal. PhilPapers.

(2020) Barton, Neil; Ternullo Claudio; and Venturi, Giorgio. On Forms of Justification in Set Theory. The Australasian Journal of Logic. Vol. 17(4), pp. 158–200. Journal. PhilPapers.

(2020) Barton, Neil and Friedman, Sy-David. Maximality and Ontology: how axiom context varies across philosophical frameworks. Synthese, Vol. 197, pp. 623–649. Journal. PhilPapers.

(2020) Barton, Neil; Caicedo, Andrés Eduardo; Fuchs, Gunter; Hamkins, Joel David; Reitz, Jonas; and Schindler, Ralf. Inner-model reflection principles. Studia Logica, Vol. 108, pp. 573–595,. Journal. PhilPapers. arXiv.

(2017) Barton, Neil. Independence and Ignorance: How agnotology informs set-theoretic pluralism. Journal of Indian Council of Philosophical Research, Volume 34, Issue 2, pp. 399–413. Journal. PhilPapers.

(2016) Barton, Neil. Richness and Reflection. Philosophia Mathematica, 24 (3):330-359. Journal. PhilPapers.

Peer-reviewed book chapters

(2025) Language, Models, and Reality: Weak existence and a threefold correspondence (with Giorgio Venturi). In: Antos, C., Barton, N., Venturi, G. (eds) The Palgrave Companion to the Philosophy of Set Theory. Palgrave Companions. Palgrave Macmillan, Cham. Chapter. PhilPapers.

(2024) Reflection in Apophatic Mathematics and Theology. In Miroslaw Szatkowski (ed.), Ontology of Divinity, De Gruyter. pp. 583-612. Chapter. PhilPapers.

(2022) Barton, Neil. Structural Relativity and Informal Rigour. In: Oliveri G., Ternullo C., Boscolo S. (eds) Objects, Structures, and Logics, Boston Studies in the History and Philosophy of Science, vol 339, pp 133-174, Springer, Cham. Book. PhilPapers.

(2021) Barton, Neil. Indeterminateness and `The’ Universe of Sets: Multiversism, Potentialism, and Pluralism. In M. Fitting (ed) Research Trends in Contemporary Logic (Landscapes in Logic), pp. 105–182. College Publications. Book. PhilPapers.

(2019) Barton, Neil and Friedman, Sy-David. Set Theory and Structures.  In: Centrone S., Kant D., Sarikaya D. (eds) Reflections on the Foundations of Mathematics. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science), pp. 223–253 vol 407. Springer, Cham. Book. PhilPapers.

(2016) Barton, Neil. Multiversism and Concepts of Set: How much Relativism is acceptable?. In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Springer. pp. 189-209. Book. PhilPapers. YouTube.

Invited/Book Reviews

(2025) Barton, Neil. Review: Level Theory Parts 1-3 (Tim Button).(2025) Bulletin of Symbolic Logic 31 (4): 686-689. 2025. DOI: 10.1017/bsl.2024.58. Journal. Philpapers.

(2020) Barton, Neil. Review: Categories for the Working Philosopher (Elaine Landry ed.). Philosophia Mathematica, Volume 28, Issue 1, February 2020, Pages 95–108, Journal. PhilPapers.

(2015) Barton, Neil. Review: Pluralism in Mathematics: A New Position in Philosophy of Mathematics. By Michèle Friend. Logic, Epistemology and the Unity of Science, Springer, 2014.’ Philosophy, 90(4), pp.685-691. Journal. PhilPapers.

Submitted/under review

The following papers have been submitted; their semi-stable drafts can be accessed through the relevant preprint archives.

On the Aims and Norms of Inquiry in Mathematics. PhilPapers.

Metasemantics and the Continuum Hypothesis. PhilPapers.

What makes a `good’ modal theory of sets? PhilPapers.

Forcing and indeterminate names. PhilPapers.

Make It So: Imperatival Foundations for Mathematics (with Ethan Russo and Chris Scambler). PhilPapers.

Other

(2020) Antos, C., Barton, N., Friedman, S. et al. Introduction to Synthese special issue on the Foundations of Mathematics. Synthese 197, 469–475.  Journal.

(2017) Executing Gödel’s Programme in Set Theory. PhD Thesis, Birkbeck College (University of London). Final version.

(Unpublished) Large Cardinals and the Iterative Conception of Set. This paper has been superseded by `Are Large Cardinal Axioms Restrictive?’, `Is (Un)Countabilism Restritive?’, and `Countabilism and Maximality Principles’. Since the draft was cited, I have kept it available here: PhilSci-Archive.