(Forthcoming) Reflection in Apophatic Mathematics and Theology. To appear in Ontology of Divinity (ed. Mirosław Szatkowski), De Gruyter. 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.
(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.
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.
Countabilism and Maximality Principles (with Sy-David Friedman). PhilPapers.
Language, Models, and Reality: Weak existence and a threefold correspondence (with Giorgio Venturi). PhilPapers.
(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(Unpublished) Large Cardinals and the Iterative Conception of Set. This paper has been superseded by `Are Large Cardinal Axioms Restrictive?’, `Is (Un)Countabilism Restritive?’, and `Countabilism and Maximality Principles’.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.