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Department
of |
Room TC324 |
|
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519-661-3453
(department phone) |
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University
of Western Ontario |
519-661-5750
(office) |
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London,
Ontario, N6A 3K7 |
e-mail: jbell@uwo.ca |
| Philosophy Department Web Site
| Faculty List | U.W.O. Web Site |
According to the Mathematics Genealogy Project, I am
one of the 28480 mathematical descendants of Ga
Teaching and Research Appointments
Mathematical logic, philosophy
of mathematics, set theory, Boolean algebras, lattice theory, category theory.
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At the University of
Western Ontario, 1989-present
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
Eric Snyder (Ph.D., Philosophy, 2000): The Philosophy of Mathematics of Wittgenstein’s
Tractatus Logico-Philosophicus.
Gregory Hagen (Ph.D.,
At
the
Samuel Fend
Dennis Mentzeniotis[1] (Ph.D.,
Other
For a number of years I
conducted jointly with M.
Machover of King's College a
I also taught many students in
the M.Sc. philosophy program at LSE.
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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.
|
APP. 4: THE PHILOSOPHICAL THOUGHT OF A GREAT MATHEMATICIAN:
HERMANN WEYL |
||
5. A Primer of Infinitesimal Analysis. Cambridge University Press, 1998.
4. Toposes & Local Set Theories: An
Introduction. Clarendon
Press, Oxford, 1988.
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. 2nd
printing, 1986.
1.
(With A. B. Slomson). Models and Ultraproducts: An Introduction.
North-Holland, Amsterdam, 1969.
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66.
“Cover Schemes, Frame-Valued Sets and Their Potential Uses in Spacetime
Physics”. Forthcoming, Spacetime Physics Research Trends, Horizons in World Physics, Volume 248,
64.
“Divergent Concepts of the Continuum in 19th and Early 20th
Century Mathematics and
63.
“The Development of Categorical
Logic”, Handbook of Philosophical Logic, Volume 12. Springer,
2005.
62. “Continuity and
Infinitesimals”. Stanford Encyclopedia of
61. “The
Continuum, Differential Geometry, and Spacetime in Smooth Infinitesimal
Analysis.” Forthcoming in The Continuum in Mathematics and
60.
“Choice Principles in Intuitionistic Set Theory.” Forthcoming in A
Logical Approach to
59.
“Oppositions and Paradoxes in Mathematics and
58.
“Observations on Mathematics”,
Mathematics as Story, Proceedings
of 2003 Fields Institute Conference, UWO, 2004.
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
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
46.
"Hermann Weyl on Intuition and the Continuum",
Philosophia Mathematica (3), 8, 2000.
45. "Sets and Classes as
Many",
44. "Infinitary
Logic", Stanford Encylopedia of
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
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",
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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F. W. Lawvere and R. Rosebrugh, Sets for Mathematics, Featured Review, Mathematical
Reviews, 2003.
B. Jacob, "Categorical
Logic and Type Theory",
F.
W. Lawvere and
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.
Perpetual
Motion: My First Thirty years
Philosophy in Literature.
§§§§§§§§§§§§
Answers 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.
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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“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
1956-57
Drew College Preparatory School,
1957-58
Lick-Wilmerding High School,
1958-61
Millfield School, Street,
1962-65
Exeter College, Oxford. B.A., Mathematics, 1965
1965-68
Christ Church, Oxford. D.Phil., Mathematics, 1969
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August 2005.
Department of
Comments to jbell@uwo.ca
