Papers

Peer-reviewed

(with Sy-David Friedman) `Set Theory and Structures’. Submitted. PhilSci-Archive.
(Forthcoming) Barton, Neil and Friedman, Sy-David `Maximality and Ontology: how axiom context varies across philosophical frameworks’. Forthcoming in Synthese. Journal. PhilSci-Archive. Academia.edu.
(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.
(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

(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

(with Carolin Antos and Sy-David Friedman) `Universism and extensions of V’. Submitted. arXiv. Academia.edu.
(with Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz, and Ralf Schindler) `Inner-model reflection principles’. Submitted.  arXiv.
`Absence Perception and the Philosophy of Zero’. Submitted. PhilSci-Archive.
`Forcing and the Universe of Sets: Must we lose insight?’. Submitted. PhilSci-Archive. Academia.edu.
`Large Cardinals and the Iterative Conception of Set’. Submitted. PhilSci-Archive.
`Modality, mathematics, and time: A recurring flaw in modal arguments’.
`Algebraic Levels in Mathematical Structuralism’.
`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.