In 2009 I was elected a Fellow of the Royal Society of Canada.
My Erdös number is 3. According to the Mathematics Genealogy Project, I am one of the 30000 or so mathematical descendants of Gauss and 740 of G. H. Hardy.
My research interests and published work have been wide-ranging, embracing mathematical logic, philosophy and foundations of mathematics, classical set theory, sets and classes as many, model theory, constructive mathematics, Boolean algebras, lattice theory, category theory, topos theory, restricted second-order and infinitary languages, large cardinals, the axiom of choice, functional analysis, incompleteness, local set theory, type theory, smooth infinitesimal analysis, the development of the continuum concept, the logic of perception, quantum logic, foundations of quantum theory, causal sets in spacetime theory, the thought of Hermann Weyl, history and conceptual development of mathematics, Frege’s theorem, type-reducing correspondences, oppositions and paradoxes, mathematics and aesthetics, philosophy in literature, the nature of consciousness.
1956-57 Drew College Preparatory School, San Francisco, CA, USA
1957-58 Lick-Wilmerding High School, San Francisco, CA, USA
1958-61 Millfield School, Street, Somerset, UK
1962-65 Open Scholar, Exeter College, Oxford. B.A., Mathematics, 1965
1965-68 Senior Scholar, Christ Church, Oxford. D.Phil., Mathematics, 1969
12. Oppositions and Paradoxes: Philosophical Perplexities in Science and Mathematics, Broadview Press, 2016.
11. Intuitionistic Set Theory. College Publications, 2014.
10. Perpetual Motion: The Making of a Mathematical Logician. Llumina Press, 2010.
8. The Continuous and the Infinitesimal in Mathematics and Philosophy. Polimetrica, 2005.
7. (With D. DeVidi and G. Solomon†) Logical Options: An Introduction to Classical and Alternative Logics. Broadview Press, 2001.
3. Boolean-Valued Models and Independence Proofs in Set Theory. Clarendon Press, Oxford, 1977. 2nd edition, 1985. 3rd edition, 2005. Paperback edition, 2011.
2. (With M. Machover). A Course in Mathematical Logic. North-Holland, Amsterdam, 1977. 4th printing, 2003.
1. (With A. B. Slomson). Models and Ultraproducts: An Introduction. North-Holland, Amsterdam, 1969. Reprinted by Dover, 2006.
82. (With G. Badia) A Parametrized Axiomatization for a Large Number of Restricted Second-Order Languages. Journal of Logic and Computation, 5 August 2023. https://academic.oup.com/logcom/advance-article/doi/10.1093/logcom/exad050/7237691
80. The Continuum and the Evolution of the Concept of Real Number. Handbook of the History and Philosophy of Mathematical Practice, pp. 1-91. Springer, 2021
79. Reflections on the Notion of “Structure” and Categories, in Structures Mères: Semantics, Mathematics and Cognitve Science, A. Peruzzi and S. Zipoli, eds. Springer, 2020, pp. 1-17.
77. Categorical Logic and Model Theory, in Categories for the Working Philosopher, E. Landry, ed. Oxford University Press, 2017, pp. 113-136.
76. Contribution to Philosophy of Logic: 5 Questions, Adajian and Lupher, eds, Automatic Press, 2016.
75. Reflections on Mathematics and Aesthetics. Aisthesis. Pratiche, linguaggi e saperi dell’estetico, [S.l.], v. 8, n. 1, p. 159-179, May 2015.
74. The Axiom of Choice in an Elementary Theory of Operations and Sets, in Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos. M. Frappier, D. Brown and R. DiSalle, eds., Springer 2012
73. Types, Sets and Categories, in Sets and Extensions in the 20th Century, A.Kanamori, D. Gabbay and J. Woods, eds., Handbook of the History of Logic, Elsevier 2012.
72. (As Joel Bennhall) Inscrutable Harmonies: The Continuous and the Discrete in the Playing of Jascha Heifetz and Glenn Gould, in Vintage Enthusiasms: Essays in Honour of John L. Bell, D. Devidi, P. Clark and M. Hallett, eds., Springer 2011.
71. The Axiom of Choice in the Foundations of Mathematics, in Foundational Theories of Classical and Constructive Mathematics, Giovanni Sommaruga, ed., Springer, 2011.
70. Cohesiveness, Intellectica, 41, 2009.
69. (With H. Korté) Hermann Weyl, Stanford Encyclopedia of Philosophy, 2009
68. The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories, Mathematical Logic Quarterly, 54, no. 2, 2008.
67. The Axiom of Choice, Stanford Encyclopedia of Philosophy, 2008.
66. Contribution to Philosophy of Mathematics: 5 Questions, Hendricks and Leitgeb, eds, Automatic Press, 2007
65. Incompleteness in a General Setting. Bulletin of Symbolic Logic 13, 2007.
64. Cover Schemes, Frame-Valued Sets and Their Potential Uses in Spacetime Physics, in Spacetime Physics Research Trends, Horizons in World Physics, Volume 248, Nova Science Publishers, New York, 2007.
62. Absolute and Variable Sets in Category Theory, in What is Category Theory? Polimetrica 2006
61. Choice Principles in Intuitionistic Set Theory , in A Logical Approach to Philosophy, Essays in Honour of Graham Solomon, D. DeVidi and T. Kenyon, eds., Springer, 2006.
59. Divergent Concepts of the Continuum in 19th and Early 20th Century Mathematics and Philosophy, Axiomathes 15, 2005.
58. The Development of Categorical Logic, in Handbook of Philosophical Logic, Volume 12. Springer, 2005.
57. Continuity and Infinitesimals, Stanford Encyclopedia of Philosophy, 2005.
56. Oppositions and Paradoxes in Mathematics and Philosophy, Axiomathes 15, 2005.
55. Observations on Mathematics, in Mathematics as Story, Proceedings of 2003 Fields Institute Conference, UWO, 2004.
53. Russell’s Paradox and Diagonalization in a Constructive Context, in 100 Years of Russell’s Paradox, Munich 2001, Walter de Gruyter, 2004.
52. Hermann Weyl's Later Philosophical Views: His Divergence from Husserl, in Husserl and the Sciences, R. Feist, ed. U. of Ottawa Press, 2003.
51. Some New Intuitionistic Equivalents of Zorn’s Lemma, Archive for Mathematical Logic, 42, Number 8, 2003.
50. Time and Causation in Gödel's Universe, Transcendent Philosophy 3, 2002.
49. Observations on Category Theory, Axiomathes 12, 2001.
48. The Continuum in Smooth Infinitesimal Analysis, in Reuniting the Antipodes-Constructive and Nonstandard Views of the Continuum. Symposion Proceedings, San Servolo/Venice, Italy, 1999. U. Berger, H. Osswald and P. Schuster, eds. Kluwer, 2001.
47. Continuity and the Logic of Perception, Transcendent Philosophy 1, no. 2, 2000.
46. Hermann Weyl on Intuition and the Continuum, Philosophia Mathematica (3), 8, 2000.
45. Sets and Classes as Many, Journal of Philosophical Logic, 29, 2000.
44. Infinitary Logic, Stanford Encylopedia of Philosophy, 2000
43. Finite Sets and Frege Structures, Journal of Symbolic Logic, 64, no. 4,1999.
42. Frege's Theorem in a Constructive Setting, Journal of Symbolic Logic, 64, no. 2, 1999.
41. Boolean Algebras and Distributive Lattices Treated Constructively, Math. Logic Quarterly 45, 1999.
40. Boolean Algebras, Routledge Encyclopedia of Philosophy, 1998.
39. Zorn’s Lemma and Complete Boolean Algebras in Intuitionistic Type Theories, Journal of Symbolic Logic 62, no. 4, 1997.
38. (With S. Gebellato) Precovers, Modalities, and Universal Closure Operators in a Topos, Math. Logic Quarterly 42, 1996.
37. Polymodal Lattices and Polymodal Logic, Math. Logic Quarterly 42, 1996.
36. (With W. Demopoulos) Elementary Propositions and Independence, Notre Dame J. of Formal Logic, 37, no. 1, 1996.
35. Logical Reflections on the Kochen-Specker Theorem, in Perspectives on Quantum Reality, R. Clifton, ed., Kluwer, 1996.
34. (With R. Clifton†) QuasiBoolean Algebras and Simultaneously Definite Properties in Quantum Mechanics. Int. J. of Throretical Physics 34, 12, 1995.
33. Infinitesimals and the Continuum, Mathematical Intelligencer , 17, no. 2, 1995.
32. Type-Reducing Correspondences and Well-Orderings: Frege's and Zermelo's Constructions Re-examined, Journal of Symbolic Logic, 60, no. 1, 1995.
31. Frege's Theorem and the Zermelo-Bourbaki Lemma. Appendix to Frege's Philosophy of Mathematics, W. Demopoulos, ed. Harvard U.P., 1995
30. Fregean Extensions of First-Order Theories, Math. Logic Quarterly, 40, 1994. (Also reprinted in W. Demopoulos, ed. Frege's Philosophy of Mathematics, Harvard U.P. 1995)
29. Hilbert's Epsilon Operator in Intuitionistic Type Theories, Math. Logic Quarterly, 39, 1993.
28. (with W. Demopoulos) Frege's Theory of Concepts and Objects and the Interpretation of Second-Order Logic, Philosophia Mathematica, (3), 1, 1993.
27. Hilbert's Epsilon-Operator and Classical Logic, Journal of Philosophical Logic, 22, 1993.
26. Some Propositions Equivalent to the Sikorski Extension Theorem for Boolean Algebras, Fundamenta Mathematicae 130, 1988.
25. Infinitesimals, Synthese, 75, 1988.
24. Logic, the Paradoxes, and the Foundations of Mathematics, LSE Quarterly Vol.I, No.3, 1987.
23. From Absolute to Local Mathematics, Synthese 69, 1986.
22. A New Approach to Quantum Logic, Brit. J. Phil. Sc., 37, 1986.
21. Orthospaces and Quantum Logic. Foundations of Physics 15, 1985.
20. Orthologic, Forcing and the Manifestation of Attributes, Proceedings of 1981 S.E. Asian Conference in Mathematical Logic. North Holland, Amsterdam, 1983.
18. (With M.F. Hallett), Logic, Quantum Logic, and Empiricism, Philosophy of Science 49, 1982.
17. Categories, Toposes and Sets, Synthese, 51, No.3, 1982.
16. Some Aspects of the Category of Subobjects of Constant Objects in a Topos, Journal of Pure and Applied Algebra 24, 1982.
15. Category Theory and the Foundations of Mathematics, Brit.J.Phil.Sci. 32, 1981.
14. Isomorphism of Structures in S-Toposes, Journal of Symbolic Logic, 46, 1981.
13. The Infinite Past Regained: A Reply to Whitrow, Brit.J.Phil.Sci. Sci, 1979
12. Boolean Extensions as Toposes, Bull. de la Soc. Francaise de Logique, Methodologie et Phil.des Sci. 6, 1979.
11. Uncountable Standard Models of ZFC + V = L, in Set Theory and Hierarchy Theory, a Memorial Tribute to Andrzej Mostowski, Springer Lecture Notes in Math. 537,1976.
10. A Note on Generic Ultrafilters, Zeitschr. f. Math.Logik und Grund.der Math. 22, 1976.
9. Universal Complete Boolean Algebras and Cardinal Collapsing, Zeitsch. f. Math.Logik und Grund. der Math. 22, 1976.
8. A Characterization of Universal Complete Boolean Algebras, J. London Math.Soc. (2), 12, 1975.
7. On Compact Cardinals, Zeitschr.f.Math.Logik und Grund.der Math. 20.1974.
6. (With D.H. Fremlin) A Geometric Form of the Axiom of Choice, Fund. Math. 77, 1972.
5. (With D.H. Fremlin), The Maximal Ideal Theorem for Lattices of Sets, Bull. London Math. Soc., 4, 1972.
4. On the Relationship between Weak Compactness and Restricted Second- Order Languages, Arch. Math. Logik 15, 1972.
3. Some Remarks on Current Mathematical Practice, in Proceedings of the Bertrand Russell Memorial Logic Conference, Denmark, 1971. Reprinted with commentary, Philosophy of Mathematics Education Journal, No. 38, Dec. 2021
2. (With F. Jellett). On the Relationship between the Boolean Prime Ideal Theorem and Two Principles of Functional Analysis, Bull. de l'Acad. Pol. des Sci., XIX, No.3, 1971.
1. Weak Compactness in Restricted Second-Order Languages, Bull. de l'Acad. Pol. des Sci., No.3, 1970.
Gregory H. Moore. Zermelo’s Axiom of Choice: Its Origins, Development, and Influence. Mineola, N.Y.: Dover Publications, 2013. ISBN 978-0-48648841-7 (pbk). Pp. 448 Philosophia Mathematica (2014) 22 (1): 131-134 doi:10.1093/philmat/nkt038
Mark van Atten, Pascal Boldini, Michel Bourdeau, and Gerhard Heinzmann, eds., One Hundred Years of Intuitionism (1907–2007): The Cerisy Conference. Basel, Boston, Berlin: Birkhäuser, 2008. ISBN 978-3-7643-8652-8. Pp. xiii + 422 Philosophia Mathematica (2013) 21 (3): 392-399 first published online March 19, 2013 doi:10.1093/philmat/nkt004
By: KAO, MOLLY; FILLION, NICOLAS; BELL, JOHN. Philosophia Mathematica, Jun 2010, Vol. 18 Issue 2.
A. Kock, Synthetic Differential Geometry, 2nd edition, Bulletin of Symbolic Logic 13, 2, 2007.
P. Rusnock, Bolzano’s Philosophy and the Emergence of Modern Mathematics, Philosophia Mathematica 14, 3, 2006.
F. W. Lawvere and R. Rosebrugh, Sets for Mathematics, Featured Review, Mathematical Reviews, 2003.
B. Jacob, Categorical Logic and Type Theory, Studia Logica, 69, 2001.
F. W. Lawvere and S. Schanuel, Conceptual Mathematics: A First Introduction to Categories, Minds and Machines, 5, 1995.
B. Rotman, Ad Infinitum: The Ghost in Turing's Machine, Philosophia Mathematica, 3, 1995.
C. McLarty, Elementary Categories, Elementary Toposes, Journal of Symbolic Logic, 58, 1993.
J. Chapman and F. Rowbottom, Relative Category Theory and Geometric Morphisms, Bull. London Math. Soc., 25, 1993.
J. Lambek and P.J. Scott, Introduction to Higher-Order Categorical Logic ,Journal of Symbolic Logic, 54, 1989.
Hao Wang, Reflections on Kurt Gödel, Philosophical Quarterly, 39, 1989.
P. Gibbins, The Limits of Quantum Logic, Philosophical Quarterly, 38, 1988.
Kurt Gödel, Collected Works I, Philosophical Quarterly, 37, 1987.
P. T. Johnstone, Stone Spaces, Bull. London Math. Soc., 19, 1987.
A. P. Morse, A Theory of Sets, Bull. London Math. Soc., 19, 1987.
E. Bishop and D. Bridges, Constructive Analysis, Bull. London Math. Soc., 18, 1986.
A. G. Hamilton, Numbers, Sets, and Axioms, Times Higher Ed. Supp.,13 May 1983.
G. Moore, Zermelo's Axiom of Choice, Bull. London Math. Soc. ,15, 1983.
R. Goldblatt, Topoi: The Categorial Analysis of Logic, Brit. J. Phil. Sci., 38, 1982.
J. Barwise (ed.), Handbook of Mathematical Logic , Brit. J. Phil. Sci., 30, 1979.
Gone to the Dogs, Times Lit. Supp., 8 July 1977.
F. Drake, Set Theory and T. Jech, The Axiom of Choice, Brit. J. Phil. Sci., 27, 1975.
A. Fraenkel, Y. Bar-Hillel and A. Levy, Foundations of Set Theory, Brit. J. Phil. Sci., 26, 1975.
S. W. P. Steen, Mathematical Logic, Brit. J. Phil. Sci., 23, 1972.
J. B. Rosser, Simplified Independence Proofs: Boolean-Valued Models of Set Theory, Bull. London Math. Soc., 3, 1971.
Fred Hoyle: Cosmologist Extraordinaire Under “Recollections” may be found a reproduction of my handwritten notes on Hoyle’s cosmology lectures, Cambridge 1962.
"Edward Hubert Linfoot" (Obituary) Bull. London Math. Soc., 16, 1984.
"Iterated Boolean Extensions and the Consistency of Souslin's Hypothesis, Lecture Notes No. 10, Dept. of Mathematics, National University of Singapore, 1982.
English translation of "Groupes Algebriques", by M. Demazure and P. Gabriel as "Introduction to Algebraic Geometry and Algebraic Groups", North-Holland, Amsterdam, 1980.
Editor (with J. Cole, G. Priest, and A. Slomson) "Proceedings of the Bertrand Russell Memorial logic Conference", Uldum, Denmark, 1971, published in Leeds, 1972.
English translation of "La Geometrie dans le Monde Sensible" in "Geometry and Induction", by J. Nicod, Routledge and Kegan Paul, London, 1969.
"Model-Theoretic Axiomatization Results for Certain Restricted Second-Order Languages", Doctoral Dissertation, Oxford 1969.
"Infinitary Languages", Diploma Dissertation, Oxford 1966.
(With A. B. Slomson) "Introduction to Model Theory", Mathematical Institute, Oxford, 1965
"A Short Survey of Phrase-Structure Grammars", Elliott Computers Technical Report 65/122, 1965.
Before emigrating to Canada in 1989, I gave invited lectures at seminars and conferences in (select listing only) Oxford, Cambridge, London, Bristol, Sussex, Leeds, Manchester, Open University, York, St. Andrews, Glasgow, Paris, Florence, Warsaw, Singapore, Montreal, Milano, and Chicago.
Since emigrating to Canada I have given the following invited lectures:
The Labyrinth of the Continuum and the Concept of the Infinitely Small. Bard College, April 2023.
Infinitesimals and the Labyrinth of the Continuum. 2018 William Reinhardt Memorial Lecture, Philosophy Department, University of Colorado at Boulder, Oct. 2018.
Reflections on the Axiomatic Approach to Continuity. Conference on Axiomatic Thinking: One Hundred Years since Hilbert’s Address in Zurich. University of Zurich, Oct. 2017.
Reflections on Bourbaki’s Notion of Structure and Categories. Conference on Structures Méres in Semantics, Mathematics and Cognition. University of Florence, May 2017.
Challenging the Presuppositions of Classical Set Theory. CUNY Graduate Center, Oct. 2016.
Hermann Weyl and Constructivism, PhilMath Intersem 6, University of Paris 7-Diderot, June 2015.
Challenging the Logical Presuppositions of Classical Set Theory. Mathematics Department, University of Georgia, Feb. 2015.
Hermann Weyl's Views on the Foundations of Mathematics and Physics as Informed by his Philosophical Outlook, International Conference on Hermann Weyl and the New Physics, Université Paris-Diderot, Dec. 2014.
Reflections on Mathematics and Aesthetics, International Conference on Aesthetics in Mathematics, University of East Anglia, Dec. 2014.
Causal Sets and Frame-Valued Set Theory, Perimeter Institute, May 2012.
On the Cohesiveness of the Continuum, Philosophy Department, McMaster University, November 2011.
The Continuous and the Infinitesimal, Keynote Address, Western Canadian Philosophical Association Conference, U. of Lethbridge, October 2011.
ETHOS: An Elementary Theory of Operations and Sets, Mathematics Department, University of Padova, June 2011.
“The Axiom of Choice in a Constructive Setting”, Philosophy Department, McGill University, April 2010; Mathematics Department, University of Cambridge, May 2010; Mathematics Department, University of Oxford, May 2010; Philosophy Department, University of Florence, June 2010.
“Incompleteness in a General Setting”, Mathematics Department, University of Manchester, May 2010.
“On the Cohesiveness of the Continuum”, Philosophy Department, University of Bristol, May 2010.
“Continuity and Infinitesimals”, Mathematics Department, London School of Economics, May 2010.
“Russell’s Paradox and Diagonalization in a Constructive Setting” Philmath Intersem 2010, Foundations of Mathematics: What and Why?, University of Paris, June 2010.
“What is Categorical Logic?”, International Conference on Philosophy and Model Theory, University of Paris, June 2010.
“Intuitionistic Logic, Frame-Valued Sets and Evolving Spacetime.” New Directions in Foundations of Physics Conference, Washington D. C., May 2009.
“Cosmic Origins”. Philosophy Department, University of Ohio, October 2008
“Cohesiveness”. Philosophy Department, University of Bucharest, July 2008
“Infinitesimals and the Continuum in the 17th Century”. Bucharest Colloquium in Early Modern Philosophy, July 2008.
“Infinitesimals and the Continuum in Smooth Infinitesimal Analysis”. Congress for the Humanities and Social Science, Vancouver, June 2008.
“Dissenting Voices: Divergent Conceptions of the Continuum in 19th and Early 20th Century Mathematics and Philosophy”, Ramifications of Category Theory, International Conference, University of Florence, November 2003.
“Synthetic Differential Geometry as a Framework for Spacetime”, Workshop on Sheaves and Topoi in Theoretical Physics, Imperial College, London, July 2003.
“Russell’s Paradox and Cantor’s Diagonalization in a Constructive Setting”, A Logical Approach to Philosophy, A Workshop in Philosophical Logic in Memory of Graham Solomon, University of Waterloo, May 2003.
“Causal Sets and Frame-Valued Set Theory”, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, March 2003.
“Oppositions and Paradoxes in Mathematics”, Distinguished Guest Lecture, Ontario Philosophical Society Meeting, University of Waterloo, November 2002.
“Infinitesimals and the Continuum”, Philosophy Department, University of Minnesota, October 2002.
8 lectures delivered at Mini-Workshop on Foundational Theories in Mathematics, Mathematics Department, University of Trento, September 2002.
"Comparing the Smooth and Dedekind Reals in Smooth Infinitesimal Analysis", Conference on Nonstandard Methods and Applications in Mathematics, Pisa, June 2002
"Cosmological Theories and the Question of the Existence of a Creator", Symposium on Science, Religion, and Philosophy, University of Toronto, May 2002
"Infinitesimals and the Continuum", Department of Philosophy, University of Lethbridge, March 2002
"Sets and Classes as Many", Departments of Philosophy, Mathematics and Computer Science, University of Calgary, March 2002
"Infinitesimals and the Continuum", Department of Philosophy, University of Alberta, March 2002
"Russell's Paradox and Diagonalization in a Constructive Context", 100 Years of Russell's Paradox, International Conference, Munich, June 2001.
"An Invitation to Smooth Infinitesimal Analysis", Mathematics Department, Instituto Superiore Tecnico, Lisbon, May 2001.
"Boolean Algebras and Distributive Lattices Treated Constructively", Logic Group, Instituto Superiore Tecnico, Lisbon, May 2001.
"Time and Causation in Gödel's Universe", 2nd International Conference on Mulla Sadra and Comparative Philosophy, School of Oriental and African Studies, University of London, May 2001.
"The Status of Some Principles and Theorems of Classical Mathematics in Constructive Set Theory", Department of Philosophy, Indiana University, March 2001.
"Hermann Weyl's Later Philosophical Views: His Divergence from Husserl", Conference on Husserl and the Sciences, University of Ottawa, October 2000.
"The Natural Numbers in Constructive Set Theories", Department of Philosophy, University of Glasgow, May 2000.
"Smooth Infinitesimal Analysis: An Introduction", Department of Mathematics, University of Manchester, May 2000.
"Continuity and the Logic of Perception", International Conference on Perception according to Mulla Sadra and Western Schools of Philosophy, Birkbeck College, University of London, May 2000.
"Boolean Algebras and Distributive Lattices Treated Constructively", Department of Mathematics, University of Munich, May 2000.
"The Natural Numbers in Constructive Set Theories", 2nd PvView Conference on Logic and Formal Topology, Department of Mathematics, University of Padova, April 2000.
"Boolean Algebras and Distributive Lattices Treated Constructively", Department of Mathematics, University of Paris VII, April 2000.
"The Incredible Shrinking Manifold: Spacetime from the Synthetic Point of View", Conference on Spacetime, University of Western Ontario, April 2000.
"Smooth Infinitesimal Analysis: An Introduction", Conference on Infinitesimals: Concepts and Applications, University of Western Ontario, October 1999.
"Hermann Weyl on Intuition and the Continuum", Conference on Intuition in Mathematics and Physics, McGill University, September 1999.
"The Continuum in Smooth Infinitesimal Analysis", Symposium on Constructive and Nonstandard Views of the Continuum, Venice international University, May 1999
"Elementary Toposes", four lectures, Mathematics Department, UWO, November 1998.
"Boolean Algebras and Distributive Lattices Treated Constructively", Mathematics Department, University of Siena, June 1998.
"Boolean Algebras and Distributive Lattices in a Constructive Setting", Mathematics Department, University of Padova, June 1998.
"Whole and Part in Mathematics", Bolzano Conference on Whole and Part, June 1998.
"Mathematics and Physics in the Smooth World", UC Irvine Philosophy Dept. Conference on Philosophy of Math. in Physics, March 1998.
"The Rehabilitation of Infinitesimals", Philosophy Department, University of St. Andrews, November 1997.
"The Rehabilitation of Infinitesimals in Mathematics and Physics", Philosophy Department, University of Pittsburgh, July 1997.
"Remarks on Category Theory", CSHPM meeting on Ontological Issues in Category Theory, Brock University, May 1996.
"The Rehabilitation of Infinitesimals", Philosophy Department, University of Toronto, December 1995.
"The Rehabilitation of Infinitesimals", Philosophy Department, University of Waterloo, November 1995.
"The Philosophical Thought of Hermann Weyl", Canadian Philosophical Association Annual Meeting, Calgary, July 1994.
"Type Reducing Correspondences", Philosophy Department, Universityof Padova, June 1994.
"How to Make Intuitionistic Set Theory Classical", Math Department, University of Padova, June 1994.
"Frege's and Zermelo's Constructions Re-Examined", Philosophy Department, University of Florence, June 1994.
"Category Theory and Philosophy of Mathematics", Panel Discussion, Joint ASL/APS Meeting, Kansas City, May 1994.
"Modalized Distributive Lattices", Math. Department, McMaster University, March 1994.
"Fregean Extensions of 1st Order Theories", One-day conference on Frege, St. Andrews University, June 1993.
"Infinitesimals and the Continuum", Philosophy Department, London School of Economics, June 1993.
"Infinitesimals and the Continuum", 19th Annual Meeting of the CSHPM, Carleton University, Ottawa, May 1993.
"Hilbert's epsilon-Calculus and Classical Logic", Philosophy Department, University of Toronto, January 1993.
"How to Make Intuitionistic Set Theory Classical". Mathematics Department, University of Michigan, Ann Arbor, December 1992.
"Infinitesimals", Physics Department, UWO, September 1992.
"How to Make Intuitionistic Set Theory Classical", Mathematics Department, McMaster University, February 1992.
"Variability and Logic", Philosophy Department, University of Padova, June 1991.
"Local Set Theories", Mathematics Department, University of Siena, May 1991.
"Hilbert's epsilon-Calculus and Classical Logic", Philosophy Dept., University of Florence, May 1991.
"Toposes and Local Set Theories” (a series of 15 lectures), Mathematics Department, University of Padova, May-June, 1991.
"Hilbert's epsilon-Calculus and Classical Logic", Logic Colloquium, SUNY at Buffalo, April 1991.
"Infinitesimals", Mathematics Department, UWO, March 1991.
"The Sikorski Extension Theorem for Boolean Algebras", Mathematics Department, McMaster University, February 1991.
· École Polytechnique, Paris, 2007: Visiting Directeur de Recherche, CNRS.
At the University of Western Ontario, 1989-2019
At the London School of Economics 1968-89
Undergraduate lecture courses on: algebra, multivariable calculus, analysis, mathematical logic, set theory, history and philosophy of mathematics.
Advanced lecture courses on: set theory, model theory, Boolean algebras, functional analysis, category theory.
At Oxford, 1965-68
Tutorials in mathematical logic, set theory, analysis, algebra, topology. Lecture courses in model theory, Boolean algebras, set theory.
At the University of Western Ontario
Emerson Doyle (Ph.D., Philosophy, 2013): The Methodological Roles of Tolerance and Conventionalism in the Philosophy of Mathematics: Reconsidering Carnap’s Logic of Science.
Robert Moir (Ph.D., Philosophy, 2013): Structures in Real Theory Application: A Study in Feasible Epistemology.
Darren McDonald (Ph.D., Philosophy, 2012): Anti-Foundational Categorical Structuralism.
Leo Jordao (Ph.D., Philosophy, 2010): Elements of a New Constructional System.
Greg Andres (Ph,D,. Philosophy, 2007): The Metaphysical Basis of Logic
Eric Snyder (Ph.D., Philosophy, 2000): The Philosophy of Mathematics of Wittgenstein’s Tractatus Logico-Philosophicus.
Richard Feist (Ph.D., Philosophy, 1999): The Mathematical Intuitionism of Hermann Weyl
Elaine Landry (Ph.D., Philosophy, 1997): Category -Theoretic Realism: A Linguistic Approach to the Philosophy of Mathematics
Gregory Hagen (Ph.D., Philosophy, 1996): Leibniz’s Puzzle and the Smooth Continuum
David DeVidi (Ph.D., Philosophy, 1994): Term-Forming Operators in First-Order Logic
At the University of London
Samuel Fendrich (Ph.D., Philosophy, 1987): From Axiomatization to Generalization of Set Theory
Dennis Mentzeniotis (Ph.D., Philosophy, 1986): Continuity and Infinitesimals
Enrique Hernandez (Ph.D., Mathematics, 1984): Automorphisms of Models of Set Theory
Michael Hallett (Ph.D., Philosophy, 1979): Cantorian Set Theory and Limitation of Size.
Graham Priest (Ph.D., Mathematics, 1972): Type Theory in which Variables Range over Predicates.
John Lake (Ph.D., Mathematics, 1972): Ackermann Set Theory.