David Corfield David Corfield



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


Articles and preprints

  • 2023, Thomas Kuhn, Modern Mathematics and the Dynamics of Reason
  • 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, (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, (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 (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 Dataset Shift in Machine Learning, MIT Press.
  • 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).
  • 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
  • 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)

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 March 28, 2023 at 15:14:40. See the history of this page for a list of all contributions to it.