John Lane Bell

John Lane Bell (born March 25, 1945) is Professor of Philosophy at the University of Western Ontario in Canada. He has made many contributions to mathematical logic and philosophy, and is the author of a number of influential books. His research includes such topics as set theory, model theory, lattice theory, modal logic, quantum logic, constructive mathematics, type theory, topos theory, infinitesimal analysis, spacetime theory, and the philosophy of mathematics. He is the author of more than 70 articles and of 11 books. In 2009, he was elected a Fellow of the Royal Society of Canada.

He was awarded a scholarship to Oxford University at the age of 15, and graduated with a D.Phil. in Mathematics: his dissertation supervisor was John Crossley. During 1968-89 he was Lecturer in Mathematics and Reader in Mathematical Logic at the London School of Economics.^[1]

John Bell's students include Graham Priest (Ph.D. Mathematics LSE, 1972), Michael Hallett (Ph.D. Philosophy LSE, 1979), Elaine Landry (Ph.D. Philosophy UWO, 1997), David DeVidi (Ph.D. Philosophy UWO, 1994) and Richard Feist (Ph.D. Philosophy UWO, 1999).

Bibliography

Books

• Intuitionistic Set Theory. College Publications, 2013.
• Set Theory: Boolean-Valued Models and Independence Proofs. Oxford University Press 2011.
• The Axiom of Choice. College Publications, 2009.
• The Continuous and the Infinitesimal in Mathematics and Philosophy. Polimetrica, 2005.
• (With D. DeVidi and G. Solomon†) Logical Options: An Introduction to Classical and Alternative Logics. Broadview Press, 2001.
• The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. Kluwer, 1999.
• A Primer of Infinitesimal Analysis. Cambridge University Press, 1998. Second Edition, 2008.
• Toposes & Local Set Theories: An Introduction. Clarendon Press, Oxford, 1988. Reprinted by Dover, 2008.
• Boolean-Valued Models and Independence Proofs in Set Theory. Clarendon Press, Oxford, 1977. 2nd edition, 1985. 3rd edition, 2005.
• (With M. Machover). A Course in Mathematical Logic. North-Holland, Amsterdam, 1977. 4th printing, 2003.
• (With A. B. Slomson). Models and Ultraproducts: An Introduction. North-Holland, Amsterdam, 1969. Reprinted by Dover, 2006.

Journal articles

• The Axiom of Choice in the Foundations of Mathematics, forthcoming in volume on Foundations of Mathematics, Giovanni Sommaruga, ed., University of Western Ontario Series, Springer
• Cohesiveness, Intellectica, 41, 2009.
• Types, Sets and Categories, Handbook of the History of Logic (Elsevier), forthcoming.
• Hermann Weyl, Stanford Encyclopedia of Philosophy, 2009
• "The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories", Mathematical Logic Quarterly, 54, no. 2, 2008.
• "The Axiom of Choice", Stanford Encyclopedia of Philosophy, 2008.
• Contribution to "Philosophy of Mathematics: 5 Questions", V. Hendricks and H. Leitgeb, eds., Automatic Press, 2007.
• "Incompleteness in a General Setting". Bulletin of Symbolic Logic 13, 2007.
• "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.
• "Cosmological Theories and the Question of the Existence of a Creator". Religion and the Challenges of Science, Ashgate Publishers, 2007.
• "Abstract and Variable Sets in Category Theory". In What is Category Theory?, Polimetrica, 2006.
• "Divergent Concepts of the Continuum in 19th and Early 20th Century Mathematics and Philosophy". Axiomathes 15, 2005.
• "The Development of Categorical Logic", Handbook of Philosophical Logic, Volume 12. Springer, 2005.
• "Continuity and Infinitesimals". Stanford Encyclopedia of Philosophy, 2005.
• "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.
• "Oppositions and Paradoxes in Mathematics and Philosophy." Axiomathes 15, 2005.
• "Observations on Mathematics", Mathematics as Story, Proceedings of 2003 Fields Institute Conference, UWO, 2004.
• Whole and Part in Mathematics. Axiomathes 14, 2004.
• (With Geoffrey Hellman) "Pluralism and the Foundations of Mathematics". Proceedings of Workshop on Scientific Pluralism, University of Minnesota, 2002. Minnesota University Press, 2006.
• "Some New Intuitionistic Equivalents of Zorn's Lemma", Archive for Mathematical Logic, 42, Number 8, 2003.
• "Russell's Paradox and Diagonalization in a Constructive Context", 100 Years of Russell's Paradox, Munich 2001, Walter de Gruyter, 2004.
• "Hermann Weyl's Later Philosophical Views: His Divergence from Husserl", Husserl and the Sciences, R. Feist, ed. U. of Ottawa Press, 2003.
• "The Development of Categorical Logic", Handbook of Philosophical Logic, Volume 12. Springer, 2005.
• "Time and Causation in Gödel's Universe", Transcendent Philosophy 3, 2002.
• "Observations on Category Theory", Axiomathes 12, 2001
• "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.
• "Continuity and the Logic of Perception", Transcendent Philosophy 1, no. 2, 2000.
• "Hermann Weyl on Intuition and the Continuum", Philosophia Mathematica (3), 8, 2000.
• "Sets and Classes as Many", Journal of Philosophical Logic, 29, 2000.
• "Infinitary Logic", Stanford Encyclopedia of Philosophy, 2000
• "Finite Sets and Frege Structures", Journal of Symbolic Logic, 64, no. 4,1999.
• "Frege's Theorem in a Constructive Setting", Journal of Symbolic Logic, 64, no. 2, 1999.
• "Boolean Algebras and Distributive Lattices Treated Constructively", Math. Logic Quarterly 45, 1999.
• "Boolean Algebras", Routledge Encyclopedia of Philosophy, 1998.
• "Zorn's Lemma and Complete Boolean Algebras in Intuitionistic Type Theories", Journal of Symbolic Logic 62, no. 4, 1997.
• (With S. Gebellato) "Precovers, Modalities, and Universal Closure Operators in a Topos", Math. Logic Quarterly 42, 1996.
• "Polymodal Lattices and Polymodal Logic", Math. Logic Quarterly 42, 1996.
• (With W. Demopoulos) "Elementary Propositions and Independence", Notre Dame J. of Formal Logic, 37, no. 1, 1996.
• "Logical Reflections on the Kochen-Specker Theorem", in Perspectives on Quantum Reality, R. Clifton, ed., Kluwer, 1996.
• (With R.Clifton†) "Quasi Boolean Algebras and Simultaneously Definite Properties in Quantum Mechanics", Int. Journal of Theoretical Physics, 34, 12, 1995.
• "Infinitesimals and the Continuum", Mathematical Intelligencer, 17, no. 2, 1995.
• "Type-Reducing Correspondences and Well-Orderings: Frege's and Zermelo's Constructions Re-examined", Journal of Symbolic Logic, 60, no. 1, 1995.
• "Frege's Theorem and the Zermelo-Bourbaki Lemma". Appendix to Frege's Philosophy of Mathematics, W. Demopoulos, ed. Harvard U.P., 1995
• "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)
• "Hilbert's Epsilon Operator in Intuitionistic Type Theories", Math. Logic Quarterly, 39, 1993.
• (with W. Demopoulos) "Frege's Theory of Concepts and Objects and the Interpretation of Second-Order Logic", Philosophia Mathematica, (3), 1, 1993.
• "Hilbert's Epsilon-Operator and Classical Logic", Journal of Philosophical Logic, 22, 1993.
• "Some Propositions Equivalent to the Sikorski Extension Theorem for Boolean Algebras", Fundamenta Mathematicae, 130, 1988.
• "Infinitesimals", Synthese, 75, 1988.
• "Logic, the Paradoxes, and the Foundations of Mathematics", LSE Quarterly Vol.I, No.3, 1987.
• "From Absolute to Local Mathematics", Synthese 69, 1986.
• "A New Approach to Quantum Logic", Brit. J. Phil. Sc., 37, 1986.
• "Orthospaces and Quantum Logic", Foundations of Physics 15, 1985.
• "Orthologic, Forcing and the Manifestation of Attributes", Proceedings of 1981 S.E. Asian Conference in Mathematical Logic. North Holland, Amsterdam, 1983.
• "The Strength of the Sikorski Extension Theorem for Boolean Algebras", Journal of Symbolic Logic 48, 1983.
• (With M.F. Hallett), "Logic, Quantum Logic, and Empiricism", Philosophy of Science 49, 1982.
• "Categories, Toposes and Sets", Synthese, 51, No.3, 1982.
• "Some Aspects of the Category of Subobjects of Constant Objects in a Topos", Journal of Pure and Applied Algebra 24, 1982.
• "Category Theory and the Foundations of Mathematics", Brit.J.Phil.Sci. 32, 1981.
• "Isomorphism of Structures in S-Toposes", Journal of Symbolic Logic, 46, 1981.
• "The Infinite Past Regained: A Reply to Whitrow", Brit.J.Phil.Sci. Sci, 1979
• "Boolean Extensions as Toposes", Bull. de la Soc. Francaise de Logique, Methodologie et Phil.des Sci. 6, 1979.
• "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.
• "A Note on Generic Ultrafilters", Zeitschr. f. Math.Logik und Grund.der Math. 22, 1976.
• "Universal Complete Boolean Algebras and Cardinal Collapsing", Zeitsch. f. Math.Logik und Grund. der Math. 22, 1976.
• "A Characterization of Universal Complete Boolean Algebras", J. London Math.Soc. (2), 12, 1975.
• "On Compact Cardinals", Zeitschr.f. Math.Logik und Grund.der Math. 20.1974.
• (With D.H. Fremlin), "A Geometric Form of the Axiom of Choice", Fund. Math. LXXVII, 1972.
• (With D.H. Fremlin), "The Maximal Ideal Theorem for Lattices of Sets", Bull. London Math. Soc., 4, 1972.
• "On the Relationship between Weak Compactness and Restricted Second- Order Languages", Arch. Math. Logik 15, 1972.
• "Some Remarks on Current Mathematical Practice", in Proceedings of the Bertrand Russell Memorial Logic Conference, Denmark, 1971.
• (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.
• "Weak Compactness in Restricted Second-Order Languages", Bull. de l'Acad. Pol. des Sci., No.3, 1970.

References

External links

• John Bell's webpage
• John Bell at the Mathematics Genealogy Project