**Personal****Education****Teaching and Research Appointments****Research Interests****Courses Taught****Publications and Writings**- Books
- Articles
- Book Reviews
- Expositions, Course Notes, Etc.
- Other Writings
**Paintings and****Images****Invited Lectures**

**Photographs** **(1) (2) (3) Denmark 1982 (1) (2) With Sandra **

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*.

1956-57 Drew College
Preparatory School,

1957-58 Lick-Wilmerding
High School,

1958-61 Millfield
School, Street,

1962-65 Open Scholar, Exeter College,
Oxford. B.A., Mathematics, 1965

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

**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.

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.

**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 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*.

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Survey of the Novel of Ideas, Unpublished.**

**13**. The Continuous,
the Discrete, and the Infinitesimal in Philosophy and Mathematics (New and
Revised Edition of **8**), Springer, 2019.

**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. **

**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.

79. *Reflections on Bourbaki’s Notion of
“Structure” and Categories, *__Structures ____Mères____:
Semantics, Mathematics and Cognitve Science__, A.
Peruzzi and S. Zipoli, eds. Springer, 2020, pp. 1-17.

77.
*Categorical Logic and Model Theory, *__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.* __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 J. 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”. __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”. __Axiomathes____
__15, 2005.

58.
*“The Development of Categorical Logic*”,
__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”*,
*__Mathematics as Story__**, **Proceedings
of 2003 Fields Institute Conference, UWO, 2004.

53.
“Russell’s Paradox
and Diagonalization in a Constructive Context”, __100 Years of
Russell’s Paradox, Munich 2001__, Walter de Gruyter, 2004.

52.
"Hermann Weyl's Later
Philosophical Views: His Divergence from Husserl", __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 __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.

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. 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.

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.

Back to INDEX . . . Back to TOP

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.

*Synthetic Differential Geometry*, 2^{nd} edition, __Bulletin
of Symbolic Logic__ 13, 2, 2007.

P. Rusnock, *Bolzano’s Philosophy
and the Emergence of Modern Mathematics, *

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 __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.

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

**Joel Bennhall: Scholar,
Musician, Mathematician: An Unfinished Portrait**

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

Translation of Grothendieck’s *The
New Universal Church*

"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:

*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.