Ultrafinitism: Physics, Mathematics, and Philosophy

There are established doubts about the real numbers, and even the natural numbers, understood as a 'completed' infinite set.  What, though, about enormous finite numbers, like the floor of the first Skewes's number?  In what sense are these more real, clear or tangible than infinite ones?  Could not the universe be finite?  Might it be physically impossible to compute this number?  Although the idea that even large natural numbers "do not exist" -- or, perhaps better, that certain questions about them lack determinate answers -- is periodically advanced, it is usually dismissed as untenably radical.  For example, A. S. Troelstra disregards such an idea in his Constructivism in Mathematics on the ground that "no satisfactory development exists at present."  At this conference, experts from philosophy, mathematics, physics, and linguistics will clarify what ultrafinitism is and whether it is true. Peer reviewed contributions will appear in a two volume special edition of Philospohia Mathematica.

Friday, April 11th (at the 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 Sulzberger Parlor in Barnard Hall)

9:30–9:45: Arrival and greetings

9:45–10:15: Crispin Wright (NYU + University of Stirling)

10:15–10:35: Q&A

10:35–11:05: Fay Dowker (Imperial College London)

11:05–11:25: Q&A

11:25–11:55: Andras Kornai (Budapest Institute of Technology)

11:55–12:15: Q&A

12:15–1:35: Lunch

1:35–2:05: Pavel Pudlak (Czech Academy of Sciences)

2:05–2:25: Q&A

2:25–2:55: Toby Meadows and James Weatherall (UCI)

2:55–3:15: Q&A

3:15–3:45: Break

3:45–4:15: Vladimir Sazanov (University of Liverpool)

4:15–4:35: Q&A

4:35–5:05: Joel David Hamkins (Notre Dame)

5:05–5:25: Q&A

5:25–6:30: Reception

Sunday, April 13th (at the Sulzberger Parlor in Barnard Hall)

9:30–9:45: Arrival and greetings

9:45–10:15: Jean Paul Van Bendegem (Vrije Universiteit Brussel)

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