David Corfield David Corfield

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

Personal details

I am currently an independent researcher. Email: dcorfield48ATgmailDOTcom.

Books

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

Articles and preprints

• 2024, Thomas Kuhn, Modern Mathematics and the Dynamics of Reason in Yafeng Shan (ed.) Rethinking Thomas Kuhn’s Legacy, pp. 51-76.
• 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)
• 1998 ‘Come the Revolution…’, Critical Notice on ‘The Principles of Mathematics Revisited’ by Jaacko Hintikka, Philosophical Books 39(3), 150-6.
• Smoke rings, history of knot theory

Talks

• 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)
• Philosophy and Innovation, University of Kent, 11 June 2024 (slides)
• Psychoanalysis and Mathematics, 17 August 2024 (slides)
• Charles Peirce, Inference, and Category Theory, 20 February 2025, Topos Institute Oxford
• Linear homotopy type theory: its origins and potential uses, Computer Science, Oxford, 21 February 2025 (slides)
• The Fivefold Way: Category Theory, Physics, Topology, Logic and Computation, workshop Realism and anti-realism: Paradigms and research programmes in logic and the philosophy of mathematics., 29 April 2025, (slides)

Organised conferences

• What Category Theory can do for Philosophy
• Type Theory and Philosophy
• Practical and Foundational Aspects of Type Theory
• Type theory, Category theory and Philosophy
• Graded Modalities
• Seminar on Applied Category Theory

Older talks

• ‘The Role of Analogy in Mathematical Research’, Sub-Faculty of Philosophy, University of Oxford, 1 May 1995.

• ‘The Methodology of Mathematics Research Programmes’, Centre for Philosophical Studies, King’s College London, 17 December 1996.

• ‘Towards a Philosophy of Real Mathematics’, Sigma Club, HPS Dept., Cambridge University, 21 January 1997

• ‘Argumentation and the Mathematical Process’ at a conference commemorating the 75th anniversary of the birth of Imre Lakatos, Elte University, Budapest, October 30-31 1997.

• ‘Psychoanalysis, Language and the Brain’, Girton College Cambridge, 28 March 1998.

• ‘Bayesianism and Mathematical Reasoning’, Bayesian workshop, University of Florence, 28 June 1999.

• ‘Research Programmes in Mathematics conference, 7 July 1999.

• ‘Bayesianism in Mathematics’, Philosophical Aspects of Bayesianism conference, King’s College London, 11 May 2000.

• ‘Higher dimensional algebra: ascending the category theoretic ladder’, Philosophy of Physics Group, University of Oxford, 16 Nov 2000.

• Mathematical Research Programmes;, Sigma Club, LSE, 29 January 2002.

• ‘Higher Dimensional Algebra’, History and Philosophy of Modern Mathematics Conference, Open University, 24 May 2002.

• ‘Artificial Intelligence in Mathematics’, Response to Alan Robinson, BSPS conference, University of Glasgow, 4 July 2002.

• ‘Kinds in Mathematics, or Being Kind to Mathematics’, International History and Philosophy of Mathematics Meeting, University of Seville, 18 Sept 2003.

• ‘Mathematical Laws and Mathematical Kinds’ , University of Cambridge, November 2003.

• ‘An overview of my work’, Max Planck Institute, Tüübingen, 19-21 January 2004.

• ‘n-category theory and philosophy’, IMA, University of Minnesota, 11 June 2004.

• ‘Revitalising the Special Relationship’, University of Hertfordshire, 18 November 2004.

• Blending Philosophy of Mathematics and Cognitive Science, Case Western, May 2005 (slides)

• 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)

Notes

• coterm
• LHoTT
• DisCoCat
• Brandon on modality
• modality as impure
• de dicto-de re
• jokes
• 2-D semantics
• subsentential inferentialism
• proposition
• connectives
• dependence
• ontology
• Kan
• Conor McBride
• distinguish
• first steps
• impossibilia
• Husserl
• belief
• specification type
• type-shifting
• relevance logic
• intensional conjunction
• many-sorted logic
• free logic
• 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
• 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
• What has X done for us?
• archetype

Projects

• Friedman's Dynamics of Reason (book outline, change in status of principles; Friedman's schema; cohomology; cohomology in physics; differential cohomology; objections and observations; diagnosis; Friedman and DTT; quantum physics; quantum anomalies; revolution in geometry, homotopification; supergeometry; QG predictions; Hypothesis H; Cassirer or Kuhn; Friedman's position)
• Philosophical points resolved by categorical logic
• 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
• connection
• tous
• psychoanalysis
• quantum cognition
• cybernetics
• ontology

Philosophers

• 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
• Amie Thomasson
• J. L. Austin

Mathematicians

• Misha Gromov
• William Lawvere
• Saunders Mac Lane

Cyberneticists

• Stafford Beer

Grant proposals

• Modal dependent type theory: pdf
• PACT

Café Posts

Extra

• sandbox
• Mathematics as Physics
• papers
• endorsements
• old blog
• nLab discussions
• Ros’s Etsy
• philosophy of history
• Hugh