Education

• Ph.D., Philosophy, University of Western Ontario, 1998
• M.T.M., Master in Teaching Mathematics, Concordia University, 1992
• B.A., Mathematics and Philosophy, Concordia University, 1990 (Double Major with Distinction)

About

Elaine's research area spans three broad areas: history and philosophy of mathematics, history and philosophy of science, and Plato’s philosophy of mathematics. The common thread that weaves through each is realism, both mathematical and scientific. Her research aims to build bridges between mathematics and physics, and their history and philosophy. Her most recent work towards this aim is methodolgical as-ifism; the view that the mathematician's method takes mathematical axioms as if they were true first-principles for the purpose of solving mathematical problems.

Her papers are referenced in the renowned Stanford Encyclopaedia of Philosophy (SEP), under both "Category Theory" and "Structural Realism". Two of her papers, published in 2005 and 2012 (with Jean-Pierre Marquis), have been in the top 10 of the “Top 50 Most Frequently Read Articles” for the prestigious journal Philosophia Mathematica.

She has over 30 years of teaching experience in areas ranging from mathematics to logic, to philosophy of mathematics, philosophy of physics, and history and philosophy of science more generally. She has a passion for, and strong commitment to, both teaching and learning, and most recently redeveloped (together with Rohan French) all of the Philosophy Department’s logic courses so that they now use open sources materials only and are also entirely online graded.

She is the founder and past Treasurer of the international Philosophy of Mathematics Association (PMA), she is the founder of the Philosophy of Mathematics Archive (PhilMathArchive), and she is the past President of the Canadian Society of the History and Philosophy of Mathematics (CSHPM). She also serves on the Advisory and Editorial Boards of several academic journals and presses and is a member of nine professional associations.

Research Focus

My research spans three broad areas: history and philosophy of mathematics, history and philosophy of science, and Plato’s philosophy of mathematics. The common thread that weaves through each is realism, both mathematical and scientific. Realism is the philosophical position that objects exists independently of us and they fix the truth of statements about them.

My work in philosophy of mathematics uses category-theory to frame a version of mathematical structuralism that is then used to argue that mathematical realism (typically called Platonism) is philosophically untenable in so far as it confuses the mathematician's method with the philosopher's. Against, the metaphysical position of mathematical realism we should adopt a methodological position of as-if-ism. That is, we take mathematical axioms as if they were true first principles, and so mathematical objects as if they exist, for the purpose of solving a mathematical problem.

In contrast to my stance against mathematical realism, I do believe that there are good structural realist reasons for being a scientific realist. But I also believe that this claim ought to be taken as a claim about methodology, as opposed to being taken as a claim about ontology or epistemology.

Interestingly, this methodological position finds its roots in my investigations of the writings of Plato. Indeed, my most recent research argues that even Plato himself, was not a mathematical Platonist.

My overall objective, in all three broad areas of research, is to inform current debates by showing that, from a methodological standpoint, at least in mathematics, we do not have to reify either objects or structures.

Publications

Books:

2023 Plato was Not a Mathematical Platonist, Cambridge Elements, CUP.

 

Edited Books:

2017 Categories for the Working Philosopher, Editor, OUP. (2023 paperback edition)

2015 Research in History and Philosophy of Mathematics, Proceedings of the Canadian Society for the History and Philosophy of Mathematics, Co-Editor (with Maria Zach), Birkhäuser.

2012 Structural Realism: Structure, Object and Causality, Co-Editor (with Dean Rickles), Western Ontario Series for Philosophy of Science, Reidel.

 

Papers:

2022 “Mathematics: Method Without Metaphysics”, Philosophia Mathematica.

2017 “Structural Realism and Category Theory”, in Categories for the Working Philosopher, OUP.

2015 “Mind the Gap” review of Steven French’s The Structure of the World (with Stathis Psillos, Mauro Dorato, and Steven French), Metascience, vol. 25, pp. 183-188.

2013 “The Genetic Versus the Axiomatic Method: Responding to Feferman 1977”, Review of Symbolic Logic, Volume 6 (1), Special Issue on Feferman’s 1977 Paper, pp. 24-50.

2012a “Methodological Structural Realism”, in Structural Realism: Structure, Objects and Causality, Western Ontario Series for Philosophy of Science, Reidel, Landry, E., and Rickles, D., pp. 29-59.

2012b “Recollection and the Mathematician’s Method in Plato’s Meno”, Philosophia Mathematica, Volume 20 (2), Special Issue on Plato’s Mathematical Methodology, pp. 143-169.

2011 “How to be a Structuralist All The Way Down”, Synthese 179, pp. 435-454.

2007 “Shared Structure Need Not Be Shared Set-Structure”, Synthese 158, pp. 1-17.

2006 “Scientific Structuralism: Presentation and Representation” (co-author Katherine Brading), Philosophy of Science, 73 (5), 2006, pp. 571-581.

2005 “Categories in Context: Historical, Foundational and Philosophical” (co-author Jean- Pierre Marquis), Philosophia Mathematica, Volume, 13 (1), pp. 1- 43.

Teaching

My teaching, as my research, spans three areas: history and philosophy of mathematics, history and philosophy of science, and Plato’s philosophy of mathematics. I teach undergraduate courses in logic, history and philosophy of mathematics and history and philosophy of science. My graduate seminars focus on structuralism in philosophy of mathematics and philosophy of science; with special interest on recent structural realist arguments in philosophy of physics. These courses, as do my graduate seminars on Plato’s philosophy of mathematics, consider the interplay between metaphysics and methodology.

Awards

• 2014 – 2015, FBF France-Berkeley Fund
• 2007, SSHRC International Opportunities Fund Grant, University of Calgary
• 2004 – 2010, CIHR Research Collaborator (+2 year HPS Postdoctoral Fellowship)
• 2003 – 2006, SSHRC Standard Research Grant, University of Calgary
• 2000 – 2001, SSHRC Postdoctoral Research Scholarship, Oxford University
• 1998 – 2000, FCAR Postdoctoral Research Scholarship, McGill University