Papers

Peer-reviewed

(Forthcoming) Barton, Neil and Friedman, Sy-David `Maximality and Ontology: how axiom context varies across philosophical frameworks’. Forthcoming in Synthese. Journal. Preprint.
(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. Preprint.
(2016) Barton, Neil `Richness and Reflection’. Philosophia Mathematica, 24 (3):330-359. Journal. Preprint.
(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. Preprint.

Invited

(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. Preprint.

In preparation

(with Carolin Antos and Sy-David Friedman) `Universism and extensions of V’. Submitted. Preprint.
(with Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, and Jonas Reitz) `Inner-model reflection principles’. Submitted. Preprint.
`Small but mighty: A defence of the countable transitive model strategy’. Submitted. Preprint.
`Modality, mathematics, and time: A recurring flaw in modal arguments’.
`Mathematics as a science of (different kinds of) patterns’.
`Structural relativity and informal rigour’.
 (with Claudio Ternullo and Giorgio Venturi) `On forms of justification in set theory’.
(with Christopher Scambler) `Realism and theoretical indeterminacy’.
(with Carolin Antos) `Forcing’. Internet Encyclopedia of Philosophy. 

Other

(2016) Executing Gödel’s Programme in Set Theory. PhD Thesis, Birkbeck College (University of London). Final version.