Mathematically Natural Kinds (Or, Must the Fictionalist be a (Groucho) Marxist?)
By Mary Leng (York, Philosophy)
Date: Thursday, March 12, 2026
Time: 1530-1700
Room: Humanities Seminar Room (H-232)
Abstract: Pluralism about mathematical theories (according to which any consistent axiomatic theories are as good – metaphysically speaking – as any other) – is currently en vogue. Rather than defend any collection of mathematical principles as capturing the ‘true’ nature of sets, for example, the mathematical pluralist is happy to follow Groucho Marx in declaring “these are my principles, and if you don’t like them…well, I have others”. Insisting, as Kurt Gödel did, on a single objective answer to an open question about the sets (such as whether the continuum hypothesis holds), as opposed to saying ‘it’s true if you adopt these principles, but if you don’t like that, then I can offer you some other principles according to which it is false’, is thought to embroil the objectivist in inescapable epistemic difficulties. Yet reading Gödel’s paper on the continuum problem, I find my sympathies are increasingly with Gödel and objectivism. Is the combination of a fictionalist view about the nature of mathematical objects with an objectivist view about the truth of particular set theoretic principles coherent? I will argue that it is.
About the speaker: Mary Leng is Professor of Philosophy at the University of York, UK. Her work focuses on issues in the philosophy of mathematics and the philosophy of science, and in particular on mathematical realism and mathematical fictionalism. She is the author of Mathematics and Reality (2010, OUP) and has published in such journals as Mind, Philosophia Mathematica, and the Proceedings of the Aristotelian Society.
Organized by the Department of Philosophy