Professor John L. Bell


                                                                                   

INDEX


I was the first (2006-7) Graham and Gail Wright Faculty of Arts Distinguished Scholar at the University of Western Ontario.

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.

Teaching and Research Appointments

  • London School of Economics, University of London:
    • 1968-71 Assistant Lecturer in Mathematics
    • 1971-75 Lecturer in Mathematics 
    • 1975-80 Senior Lecturer in Mathematics
    • 1980-89 Reader in Mathematical Logic
  • Polish Academy of Sciences, 1975: Visiting Fellow
  • National University of Singapore, 1980, 1982: Visiting Fellow
  • Department of Mathematics, University of Padova, 1991: Visiting Professor
  • University Of Western Ontario:
    • Since July, 1989: Professor of Philosophy
    • Adjunct Professor, Department of Mathematics
  • École Polytechnique, Paris, 2007: Visiting Directeur de Recherche, CNRS.

Research Interests

Mathematical logic, philosophy of mathematics, set theory, Boolean algebras, lattice theory, category theory.

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Courses Taught

At the University of Western Ontario, 1989-present

  • Graduate
    • Philosophy of mathematics
    • Set theory
    • Model Theory
    • Lattices and Boolean algebras
    • Types and toposes 
    • Constructivity in Mathematics
    • Weyl’s Das Kontinuum
    • Foundations of Mathematics
    • The Continuous and the Discrete
  • Undergraduate
    • Philosophy in Literature
    • Conceptual Development of Mathematics
    • Mathematics and the Arts
    • Introduction to Logic
    • Introduction to Logical Theory
    • Mathematical Logic
    • Introduction to Modal and Intuitionistic logic
    • Set theory
    • Philosophy of Mathematics
    • Problems in Metaphysics

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 math. logic, set theory, analysis, algebra, topology.

Lecture courses in model theory, Boolean algebra, set theory.

 

THESIS SUPERVISION:

 

At the University of Western Ontario

 

Nicolas Fillion[1]  (Ph.D., Philosophy, 2012): The Reasonable Effectiveness of Mathematics.

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[2] (Ph.D., Philosophy, 1986): Continuity and Infinitesimals

Enrique Hernandez[3] (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.

 

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Publications


Books


10. Perpetual Motion: The Making of a Mathematical Logician.  Llumina Press, 2010.

9. The Axiom of Choice. College Publications, 2009.

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.

6. The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. Kluwer, 1999.

5. A Primer of Infinitesimal Analysis.  Cambridge University Press, 1998. Second Edition, 2008.

4. Toposes & Local Set Theories: An Introduction. Clarendon Press,  Oxford, 1988. Reprinted by Dover, 2008. 3. Boolean-Valued Models and Independence Proofs in Set Theory. Clarendon Press, Oxford, 1977. 2nd edition, 1985. 3rd edition, 2005.

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.



Articles

76. 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

 

75. (As J. Bennhall). Inscrutable Harmonies: The Continuous and the Discrete as Reflected 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.

 

74. The Axiom of Choice in the Foundations of Mathematics, in Foundational

Theories of Classical and Constructive Mathematics, Giovanni Sommaruga, ed., Springer, 2011.

 

72. Types, Sets and Categories, Sets and Extensions in the 20th Century,  A.Kanamori, D. Gabbay and J. Woods, eds., Handbook of the History of Logic, Elsevier 2012.

 

71. Cohesiveness, Intellectica, 41, 2009.

 

70. Hermann Weyl, Stanford Encyclopedia of Philosophy, 2009

69. ‘The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories”, Mathematical Logic Quarterly, 54, no. 2, 2008.

68. “The Axiom of Choice”, Stanford Encyclopedia of Philosophy, 2008.

67. Contribution to “Philosophy of Mathematics: 5 Questions”, V. Hendricks and H. Leitgeb, eds., Automatic Press, 2007.

66. “Incompleteness in a General Setting”. Bulletin of Symbolic Logic 13, 2007. Click here for corrected version online.

65. “Cover Schemes, Frame-Valued Sets and Their Potential Uses in Spacetime Physics”. Spacetime Physics Research Trends, Horizons in World Physics, Volume 248, Nova Science Publishers, New York, 2007.        

64. “Cosmological Theories and the Question of the Existence of a Creator”. Religion and the Challenges of Science, Ashgate Publishers, 2007.

63. “Abstract and Variable Sets in Category Theory”. In What is Category Theory?, Polimetrica, 2006.

62. “Divergent Concepts of the Continuum in 19th and Early 20th Century Mathematics and Philosophy”. Axiomathes 15, 2005.

61. “Continuity and Infinitesimals”. Stanford Encyclopedia of Philosophy, 2005.

60. “Choice Principles in Intuitionistic Set Theory.”, A Logical Approach to Philosophy, Essays in Honour of Graham Solomon, D. DeVidi and T. Kenyon, eds., Springer, 2006.

59. “Oppositions and Paradoxes in Mathematics and Philosophy.” Axiomathes 15, 2005.

58. “Observations on Mathematics”, Mathematics as Story, Proceedings of 2003 Fields Institute Conference, UWO, 2004.

57. Whole and Part in Mathematics. Axiomathes 14, 2004.

56. (With Geoffrey Hellman) “Pluralism and the Foundations of Mathematics”. Proceedings of Workshop on Scientific Pluralism, University of Minnesota,  2002. Minnesota University Press, 2006.

55. “Some New Intuitionistic Equivalents of Zorn’s Lemma”, Archive for Mathematical Logic, 42, Number 8, 2003.

54. “Russell’s Paradox and Diagonalization in a Constructive Context”, 100 Years of Russell’s Paradox, Munich 2001, Walter de Gruyter, 2004.

53. "Hermann Weyl's Later Philosophical Views: His Divergence from Husserl", Husserl and the Sciences, R. Feist, ed.  U. of Ottawa Press, 2003.

52. "The Development of Categorical Logic", Handbook of Philosophical Logic, Volume 12. Springer, 2005.

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) "Quasi Boolean Algebras and Simultaneously Definite Properties in Quantum Mechanics", Int. Journal of Theoretical 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.

19. "The Strength of the Sikorski Extension Theorem for Boolean Algebras", Journal of Symbolic Logic 48, 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. LXXVII, 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.

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.

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Book Reviews

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

 

Expositions and Course Notes

Measurable Cardinals

Philosophy of Mathematics    Reading List

Notes on Toposes and Local Set Theories

 

 


Other Writings

Philosophy in Literature

Responses to a Mathematical Questionnaire

Unpublished Encyclopaedia Articles: 1. Boolean Algebra  2. The Axiom of Choice  3. Continuity  4. Heyting Algebras  5. Infinitesimals

"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.

"Completeness and Axiomatization Results for Weak 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.


Miscellanea

Newton,  Einstein, and the Diatonic Scale.

Excerpts from Reviews of Tractatus Logico-Toposphicus         

 

Current Projects

Current research: Infinitesimals and divergent conceptions of the continuum. Philosophy of Hermann Weyl.  Maximal principles in local set theories and toposes. Sets and classes as many. Variability and logic. Evolution of categorical logic. Oppositions and paradoxes in mathematics.

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Invited Lectures

"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.

“The Axiom of Choice” and “On the Indecomposability of the Continuum”. Canadian Mathematical Society Winter Meeting, London, Ontario, December 2007.

“Oppositions and Paradoxes in Mathematics and Philosophy”, Mathematics Department, London School of Economics, May 2007.

“The Axiom of Choice” and “On the Indecomposability of the Continuum” CREA, École Polytechnique, Paris, May 2007.

“Frame-Valued Sets and Evolving Space-Time” and “The Natural Numbers in Toposes and Local Set Theories”, École Normale Superieure, Paris, May 2007.

“Continuity and Infinitesimals”, Philosophy Department, University of Georgia, April 2007.

“Smooth Infinitesimal Analysis in Physics”, Nonstandard Methods in Mathematics, International Conference, University of Pisa, May-June 2006.

“Hermann Weyl: Mathematician-Philosopher”, Colloquium on Hermann Weyl, University of Aix-en-Provence, December 2005.

“Dissenting Voices” and “The Continuum in Synthetic Differential  Geometry”, two lectures delivered at The Continuum in Mathematics and Philosophy, International Conference, The Carlsberg Academy, Copenhagen, November 2004.

“Choice Principles in Intuitionistic Set Theory”, Philosophy Department, Carnegie-Mellon University, March 2004.

Dissenting Voices: Divergent Conceptions of the Continuum in 19th and Early 20th Century Mathematics and Philosophy”. Center for History and Philosophy of Science, University of Pittsburgh, March 2004.

“The Axiom of Choice, Zorn’s Lemma, and their Applications in Algebra and Logic”. Department of Mathematics, University of Western Ontario, February 2004.

“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.

Before my emigration to Canada in 1989, I gave invited lectures at seminars and conferences in Oxford, Cambridge, London, Bristol, Sussex, Manchester, Leeds, Open University, York, St. Andrews, Glasgow, Paris, Florence, Wroclaw, Warsaw, Singapore, Montreal, Milan,...

 


Education

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 Exeter College, Oxford. B.A., Mathematics, 1965

1965-68 Christ Church, Oxford. D.Phil., Mathematics, 1969

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September 2012.
Department of Philosophy,, University of Western Ontario
Comments to jbell@uwo.ca

 



[1] Joint supervisor

[2] Joint supervisor

[3] Joint supervisor