David Corfield

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

- 2020, Modal Homotopy Type Theory, OUP
- 2007, Why Do People Get Ill?, Hamish Hamilton
- 2003, Towards a Philosophy of Real Mathematics, CUP

- 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.
- 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, (Scholarship online)
- 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, pdf
- 2002, Argumentation and the mathematical process, in G. Kampis et al. (eds.)
*Appraising Lakatos*, Kluwer, 115-138. - 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.

- What Category Theory can do for Philosophy
- Type Theory and Philosophy
- Practical and Foundational Aspects of Type Theory
- Type theory, Category theory and Philosophy

- stuff
- negative facts
- logic-mathematics
- univocal-equivocal
- inferences
- n-theory
- explanation, evidence, cause
- coercion
- Set theory, higher-order logic, dependent type theory
- relation between category theory and type theory
- concrete universal
- intermodality
- old tools
- dependency
- elements
- fact
- seems
- quotient types
- proposition
- thick concept
- mathematical landscape
- Event types
- Brandom and material inference
- All types
- graded modality
- hyperintensionality
- probability
- judgments
- deduction, induction, abduction
- polarity
- modality
- invariance
- type, object, monad, process
- temporal type theory
- knowledge
- inferentialism
- space - cohesion, etc.
- continuous logic, probability, quantum
- history
- counterfactual
- least action
- types in philosophical literature
- condensed
- questions

- Friedman's Dynamics of Reason (change in status of principles; Friedman's schema; cohomology; differential cohomology; objections and observations; diagnosis; Friedman and DTT; quantum physics; paradigm shift)
- A Dialogue on Infinity
- Klein 2-Geometry
- Two Cultures
- Mathematics and Co-Mathematics
- Physics of the observer
- Motifs and Phantoms
- realism
- Philosophy as Normative or Descriptive
- Homotopy type theory
- Dialectic and Eristic
- Bayesianism in Mathematics
- Shaperean Philosophy of Mathematics
- 1-2-3
- Langlands
- HoTT for Physics
- Historical Motivation
- MHTT2

- Albert Lautman
- Imre Lakatos
- Ernst Cassirer
- Colin McLarty
- R G Collingwood
- Michael Polanyi
- David Carr
- Dudley Shapere
- Rudolf Carnap
- Robert Brandom
- Gilbert Ryle
- Peter Strawson
- Hasok Chang

Last revised on April 15, 2021 at 10:13:16. See the history of this page for a list of all contributions to it.