Peer-reviewed journal articles

(Forthcoming) Barton, Neil `Forcing and the Universe of Sets: Must we lose insight?’. Forthcoming in the Journal of Philosophical Logic. Journal. PhilSci-Archive. Academia.edu.

(Forthcoming) Barton, Neil `Absence Perception and the Philosophy of Zero’. Forthcoming in Synthese. Journal. PhilSci-Archive.

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

(2019) Barton, Neil; Caicedo, Andrés Eduardo; Fuchs, Gunter; Hamkins, Joel David; Reitz, Jonas; and Schindler, Ralf `Inner-model reflection principles’. Forthcoming in Studia Logica. Journal.  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. PhilSci-Archive. Academia.edu.

(2016) Barton, Neil `Richness and Reflection’. Philosophia Mathematica, 24 (3):330-359. Journal. PhilSci-Archive. Academia.edu.

Peer-reviewed book chapters

(Forthcoming)`Structural Relativity and Informal Rigour’. In: Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics, Boston Studies in the History and Philosophy of Science. 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. PhilSci-Archive.

(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. PhilSci-Archive. Academia.edu. YouTube.

Invited/Book Reviews

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

(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. Academia.edu

Under review/In preparation

(Submitted papers with a semi-stable draft can be accessed through the relevant preprint archive. Please e-mail if you would like to request a draft of an as yet unsubmitted paper.)

`Are Large Cardinal Axioms Restrictive?’ Submitted. PhilArchive.

`Indeterminacy and `The’ Universe of Sets: Multiversism, Potentialism, and Pluralism’ Submitted. PhilPapers.

`On forms of justification in set theory’ (with Claudio Ternullo and Giorgio Venturi). Submitted. PhilSci-Archive.

`Universism and extensions of V’ (with Carolin Antos and Sy-David Friedman). Submitted. arXiv. Academia.edu.

`On Representations of Intended Structures in Foundational Theories’ (with Moritz Müller and Mihai Prunescu). Submitted. PhilArchive.

`Modality, mathematics, and time: A recurring flaw in modal arguments’.

`Algebraic Levels in Mathematical Structuralism’

`Mathematical Gettier Cases’

`Countabilism and Maximality’ (with Sy-David Friedman)

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.

(2016) 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?’ and `Countabilism and Maximality’. Since it was cited whilst under review, I have kept it available here: PhilSci-Archive.

(Unpublished) How to write a good philosophy paper (a short guide for beginning philosophy students). Paper.