Monographs

Iterative Conceptions of Set. This mini-book is under review with Cambridge University Press as part of the Cambridge Elements series. Draft here.

Engineering Set-Theoretic Concepts. I am currently working on a book on conceptual engineering in the development of set theory. Comments are very welcome, please reach out via email or the contact form if you would like to see a draft.

Peer-reviewed journal articles

(Forthcoming) Barton, Neil. Are Large Cardinal Axioms Restrictive? To appear in Philosophia Mathematica. PhilPapers.

(2021) Barton, Neil; Müller, Moritz; and Prunescu, Mihai. On Representations of Intended Structures in Foundational Theories. Journal of Philosophical Logic, to appear. 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

(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

(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.

Under review

The following papers are under review and their semi-stable drafts can be accessed through the relevant preprint archives.

Mathematical Gettier Cases and Their Implications. PhilPapers.

Is (Un)Countabilism Restrictive?. PhilPapers.

Reflection in Apophatic Mathematics and Theology. PhilPapers.

Varieties of Class-Theoretic Potentialism (with Kameryn Williams). PhilPapers. arXiv.

Countabilism and Maximality Principles (with Sy-David Friedman). PhilPapers.

Language, Models, and Reality: Weak existence and a threefold correspondence (with Giorgio Venturi). 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.