Activities
MAA Mathfest
August 6-9, 2025
Sacramento, CA
POMSIGMAA Business Meeting, Reception, and Guest Lecture
Speaker: Jared Warren, Stanford University
Title: Conventionalism and Mathematical Truth
Thursday, August 7, 6:00 p.m. to 8:00 p.m.
Location TBA
Abstract: Mathematics consists of various truths – two plus two equals four, there are infinitely many prime numbers, every set has a power set – yet mathematical truth is puzzling. Mathematical truths seem to describe various abstract objects – numbers, sets, functions – while also seeming objective, eternal, and necessary. But it is very difficult to understand how human beings could ever discover objective, eternal, and necessary truths about abstract objects. It is so difficult to understand that many historical philosophers and mathematicians gave up on trying to understand it. Despite this, all of the puzzling features of mathematical truth get demystified once we embrace conventionalism about mathematics. According to mathematical conventionalism, mathematics is a byproduct of our linguistic conventions and conceptual choices. Conventionalism was historically popular among scientists and empiricist philosophers but fell out of favor during the resurgence of metaphysical speculations in the late twentieth century. Whether fashionable or not, I will explain conventionalism and argue that it is the only way to correctly understand and demystify mathematical truth.
Organizer: Bonnie Gold
Invited Paper Session
Philosophy of Mathematics: The View from Paradox
Friday August 8, 2025, 8:00 a.m.-11:00 a.m.
Location TBA
Session description:
Logicians, it is said, abhor ambiguity but love paradox. This opening sentence of 'The Liar' by Barwise and Etchemendy captures some of the appeal of the notion of paradox, and there is no denying that paradoxes have had an influence on philosophy of mathematics over the millennia. From Zeno and the Liar through Gilbert and Sullivan to Russell and Yablo, paradoxes have been partners with which philosophers and theories have sparred. They have had an effect on mathematics as well. What is the status of a paradox like the set of all sets? At what stage does a paradox like Lowenheim-Skolem become a theorem? This session will be devoted to the role of paradoxes in the philosophy of mathematics and logic. There will be room for other topics in the philosophy of mathematics as time allows.
| Time | Presenter | Title |
|---|---|---|
| 8:00 a.m. | Martin Flashman | Mathematical Paradoxes and the Evolution of Philosophical Commitments |
| Cal Poly Humboldt (Emeritus) | ||
| 9:00 a.m. | Daniel Sloughter | Algorithms and Neoplatonism in an Old Norse Algorismus |
| Furman University (Emeritus) | ||
| 9:30 a.m. | Amy Ackerberg-Hastings | The Paradoxical Philosophy of American Mathematics Education, 1790–1840 |
| MAA Convergence | ||
| 10:00 a.m. | Paul Zorn | An Ample Budget of Paradoxes |
| St. Olaf College (Emeritus) | ||
| 10:30 a.m. | Thomas Drucker | Truth Standing On Its Head |
| University of Wisconsin-Whitewater (Emeritus) |
Organizers: Steve Deckleman, Thomas Drucker, Bonnie Gold