The Department of Philosophy at Columbia University will be hosting an event, Ultrafinitism: Physics, Mathematics, & Philosophy, on April 11-13, 2025.
A summary, tentative schedule, and registration information follows.
There are established doubts about the real numbers, and even the natural numbers, understood as a 'completed' infinite set, in Aristotle's sense. What, though, about enormous finite numbers, like (10^(10^(10+1)+1)+1)? In what sense are these more real, clear, or tangible than infinite ones? Is there a fact of the matter about whether the aforementioned number is prime, even if no human or physical computer could ever find out? What if the universe contains fewer than (10^(10^(10+1)+1)+1) things? Although the idea that even large numbers "do not exist" -- or, alternatively, that certain questions about them lack determinate answers -- has been periodically advanced, it is usually dismissed as untenably radical. At this conference, experts from philosophy, mathematics, physics, computer science, and linguistics will clarify what ultrafinitism is, or could be, and whether it is true. Peer reviewed presentations will appear in a two volume special issue of Philosophia Mathematica.
Friday, April 11th (at the East Gallery, Buell, Hall, Maison Francaise)
10:30–10:45: Arrival and greetings
10:45–11:00: Opening remarks, Justin Clarke Doane (Columbia University)
11:00–11:30: Rohit Parikh (CUNY)
11:30–11:50: Q&A
11:50–12:20: Walter Dean (Warwick)
12:20–12:40: Q&A
12:40–2:10: Lunch
2:10–2:40: Doron Zeilberger (Rutgers)
2:40–3:00: Q&A
3:00–3:30: Sean Carroll (JHU)
3:30–3:50: Q&A
3:50–4:20: Sam Buss (UCSD)
4:20–4:40: Q&A
4:40–5:10: Break
5:10–5:40: Tim Maudlin (NYU)
5:40–6:00: Q&A
6:30: Dinner
Saturday, April 12th (at the Lynn Chu Classroom MLC LL002 in the Milstein Center and Sulzberger Parlor in Barnard Hall)
10:30–10:45: Arrival and greetings
10:45–11:15: Crispin Wright (NYU, Stirling), from Zoom
11:15–11:35: Q&A
11:35–12:05: Andras Kornai (Budapest Institute of Technology)
12:05–12:25: Q&A
12:25–1:45: Lunch
1:45–2:15: Pavel Pudlak (Czech Academy of Sciences)
2:15–2:35: Q&A
2:35–3:05: Toby Meadows and James Weatherall (UCI), (James Weatherall will be
speaking from Zoom)
3:05–3:25: Q&A
3:25–3:55: Vladimir Sazonov (University of Liverpool)
3:55–4:15: Q&A
4:15–4:45: Break
4:45–5:15: Joel David Hamkins (Notre Dame)
5:15–5:35: Q&A
5:35–6:30: Reception
Sunday, April 13th (at the Lynn Chu Classroom MLC LL002 in the Milstein Center and Sulzberger Parlor in Barnard Hall)
9:30–9:45: Arrival and greetings
9:45–10:15: Jean Paul Van Bendegem (Vrije Universiteit Brussel), from Zoom
10:15–10:35: Q&A
10:35–11:05: Lee Smolin (Perimeter Institute)
11:05–11:25: Q&A
11:25–11:55: Zuzana Hanikova (Czech Academy of Sciences)
11:55–12:15: Q&A
You may register to attend here.
For administrative questions, please contact Zimu Zhang ([email protected]).