Preface to Festschrift *Vintage Enthusiasms*

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*.

Translation of Grothendieck’s
*The** New Universal Church*

**Podcast**: *Philosophy of Mathematics, the Axiom of
Choice, Continuum and Consciousness. *2 September 2024

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.**

**9. The Axiom of Choice. Front Matter. 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. Review by W.A. J.
Luxemburg.

**4**. **Toposes
& Local Set Theories: An Introduction. **Clarendon Press, Oxford, 1988. Reprinted by Dover,
2008. Reviews
(?) thereof.

**3.** **Boolean-Valued
Models and Independence Proofs in Set Theory. **Clarendon Press, Oxford,
1977. 2^{nd} edition, 1985. 3^{rd} 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.

Unpublished
books:

**The Exploits of Joel Bennhall, Chrononaut and Scholar**

**Philosophy in Literature: A
Survey of the Novel of Ideas.**

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 19 ^{th} and Early 20^{th} Century Mathematics and
Philosophy,*

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 Theor*y, __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,

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.

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

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*

Jean-Pierre Marquis. *From a Geometrical Point of View: A Study of the History and Philosophy
of Category Theory*. By:
KAO, MOLLY; FILLION, NICOLAS; BELL, JOHN*. *__Philosophia Mathematica__,
Jun 2010, Vol. 18 Issue 2.

A. Kock, *Synthetic Differential Geometry*, 2^{nd}
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*

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.

Commutative Rings as
Algebras of Intensive Quantities

What is the Source of the
Commutativity of the Basic Arithmetical Operations?

Quantum Incompatibility and
Noncommutativity

The Bibliography Paradox
Revisited

Googol Plus One: A Reminiscence

My Collaboration with Bill
Demopoulos

Answers to a
Mathematical Questionnaire

The Consolations of Zorn’s
Lemma and the Escape into Maximality

Thoughts on the Incipient Loss
of Sight through Macular Hole

Fred Hoyle: Cosmologist Extraordinaire Under “Recollections” may be found
a reproduction of my handwritten notes on Hoyle’s cosmology lectures, Cambridge
1962.

Nuclear Weapons and Climate
Change

"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.

https://www.flickr.com/photos/152639850@N05/

Newton and Einstein as Musicians

University of Colorado Lecture
Poster

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:

*Mathematics
and Aesthetics. *World
Logic Day, Jan i2, 2024

*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 17^{th} 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 19^{th} and Early 20^{th}
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.

**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:
- 1989 -2019
Professor of Philosophy. Now Emeritus.
- Adjunct
Professor, Department of Mathematics

·
École
Polytechnique, Paris, 2007: Visiting Directeur de Recherche, CNRS.

**At
the University of Western Ontario, 1989-2019**

*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
mathematical logic, set theory, analysis, algebra, topology. Lecture courses in
model theory, Boolean algebras, set theory.

**THESIS SUPERVISION:**

__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 [1]__ (Ph.D., Philosophy,
2013):

__Nicolas Fillion [2]__ (Ph.D., Philosophy, 2013):

__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__[3] (Ph.D., Philosophy,
1986): *Continuity and Infinitesimals*

__Enrique Hernandez__[4] (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*.