David Corfield David Corfield



This is the personal area of David Corfield within the nLab.

Personal details

I am currently Senior Lecturer in Philosophy at the University of Kent. Email: dcorfield48ATgmailDOTcom.


Articles and preprints

  • 2023, Thomas Kuhn, Modern Mathematics and the Dynamics of Reason
  • 2021, with Hisham Sati, Urs Schreiber, Fundamental weight systems are quantum states, arXiv:2105.02871
  • 2017, Expressing 'The Structure of' in Homotopy Type Theory, Synthese.
  • 2017, Homotopy type theory and the vertical unity of concepts in mathematics, (link to draft) in What is a Mathematical Concept?, CUP. pp. 125-142.
  • 2017, Reviving the philosophy of geometry, (link) in Elaine Landry (ed.) Categories for the Working Philosopher, OUP.
  • 2017, Duality as a category-theoretic concept, Studies in History and Philosophy of Modern Physics, Volume 59, August 2017, Pages 55-61, (pdf, link).
  • 2014, with Ralf Krömer, The Form and Function of Duality in Modern Mathematics, Philosophia Scientiae, 18-3 (link)
  • 2012, Narrative and the Rationality of Mathematical Practice, In: Doxiadis, Apostolos and Mazur, Barry, eds. Circles Disturbed: The Interplay of Mathematics and Narrative. Princeton University Press, Princeton, pp. 244-280. (Scholarship online).
  • 2011, Understanding the Infinite II - Coalgebra, Studies in History and Philosophy of Science, Part A, Volume 42, Issue 4, December 2011, pp. 571-579, (pdf, link)
  • 2010, Understanding the Infinite I: Niceness, Robustness, and Realism, Philosophia Mathematica, 18 (3). pp. 253-275, (pdf, link)
  • 2010, Lautman and the Reality of Mathematics, published in French as ‘Lautman et la réalité des mathématiques’, Philosophiques 37(1), 2010, 95-109.
  • 2010, Varieties of justification in machine learning, Minds and Machines 20 (2), 291-301, (doi:10.1007/s11023-010-9191-1)
  • 2010, Nominalism versus Realism, EMS Newsletter March, pdf
  • 2009, Falsificationism and statistical learning theory: Comparing the Popper and Vapnik-Chervonenkis dimensions, (with B Schölkopf, V Vapnik), Journal for General Philosophy of Science 40 (1), 51-58.
  • 2008, Projection and Projectability In J. Quiñonero-Candela, M. Sugiyama, A. Schwaighofer, & N. Lawrence (Eds.), Dataset Shift in Machine Learning (pp. 29-38).
  • 2006, Review of Omnès’ ‘Converging Realities’, Metascience 15: 363–366, pdf, original draft (makes better sense before it was edited).
  • 2006, Some Implications of the Adoption of Category Theory for Philosophy, in Giandomenico Sica (ed.), What is Category Theory?, Polimetrica s.a.s., 75-94, Sica.doc Final draft
  • 2005, Categorification as a Heuristic Device, in Carlo Cellucci and Donald Gillies (eds.), Mathematical Reasoning and Heuristics, College Publications, doc
  • 2005, Review of Martin Krieger’s ‘Doing Mathematics’, Philosophia Mathematica, Volume 13, Issue 1, February 2005, Pages 106–111, doi
  • 2004, Mathematical Kinds, or Being Kind to Mathematics, Philosophica, 74, 30–54, article * 2002, Argumentation and the mathematical process, in G. Kampis et al. (eds.) Appraising Lakatos, Kluwer, 115-138, (pdf)
  • 2002, Review of ‘Conceptual Mathematics’ by F. W. Lawvere and S. Schanuel and ‘A Primer of Infinitesimal Analysis’ by J. Bell, Studies in History and Philosophy of Modern Physics, 33B(2), 359–366, (pdf).
  • 2002, From mathematics to psychology: Lacan’s missed encounters, in J. Glynos and Y. Stravrakakis (eds.) ‘Lacan and Science’, Routledge, 179-206, (pdf)
  • Smoke rings, history of knot theory


  • Modal Homotopy type theory, Bristol, Sept 16, slides
  • Homotopy type theory: A revolution in the foundations of mathematics?, Canterbury, March 17, slides
  • And, Kent, Feb 18, slides
  • Modal Homotopy type theory: the new new logic, Beijing, Aug 18, slides
  • The ubiquity of modal types, Birmingham, Sept 18, slides
  • How we use monads without ever realising it, Kent, Mar 19, slides
  • Health methodology and the psychosomatic approach to medicine, Kent, June 19, slides
  • The narratives category theorists live by, LSE, Sept 19, slides
  • Vienna, Dec 19
  • Evidence seminar, Kent, Nov 20, slides
  • Philosophy of Mathematics Seminar, Oxford, Jan 21, slides.
  • Analogy in Mathematics, May 21, Centre for Reasoning. slides.
  • Modal types, LMU, Autumn school Proof and Computation, Sept 21, slides.
  • Dynamics of Reason Revisited, Kent, Oct 21, (slides), developments in the Friedman project.
  • Graded modalities and dependent type theory, Kent, June 22 (slides)
  • Modal and graded modal types, Prague, July 22 (slides)
  • Kuhn and modern mathematics, Canterbury, July 22 (slides)
  • Category Theory as a Heuristic Tool in Logic and Mathematics, Rome, Feb 23 (slides).
  • Philosophical perspective on category theory, Mar 23 (recording, slides)
  • (see later slides below) Type-theoretic Expressivism, Logica 2023, Tepla, Czechia, Jun 23 (slides)
  • Modal and Linear HoTT in Physics, Computation and Quantum Gravity conference, Sydney, Australia, September 23 (slides)
  • How to Apply Category Theory: from Physics to Epidemiology, Collège de France, Paris, October 23 (slides)
  • Methodological reflections, online to CFAR, 4 November 23 (slides)
  • Mind in Medicine, University of Kent, 15 November 23 (slides)
  • Type-theoretic Expressivism, University of Bristol, February 24 (slides)
  • Homotopy type theory and its modal variants, Sheffield, 1 May 2024 (slides)
  • Philosophy and Innovation, Northeastern university London, 4 May 2024 (slides)

Organised conferences

Older talks

  • NIPS 2006

  • Between the Philosophy of Science and Machine Learning, NIPS 2011, Philosophy and Machine Learning Workshop, Sierra Nevada, Spain - 17 December 2011 (workshop site)






Grant proposals

  • Modal dependent type theory: pdf
  • PACT

Café Posts


Last revised on May 20, 2024 at 10:29:33. See the history of this page for a list of all contributions to it.