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 East Gallery, 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 (University of Warwick)

12:20–12:40: Q&A

12:40–2:10: Lunch

2:10–2:40: Doron Zeilberger (Rutgers University)

2:40–3:00: Q&A

3:00–3:30: Sean Carroll (Johns Hopkins University, Sante Fe Institute)

3:30–3:50: Q&A

3:50–4:20: Sam Buss (University of California, San Diego)

4:20–4:40: Q&A

4:40–5:10: Break

5:10–5:40: Tim Maudlin (New York University)

5:40–6:00: Q&A

6:30: Dinner

Saturday, April 12th (Talks will be in the Lynn Chu Classroom MLC LL002 at the Milstein Center, reception at Sulzberger Parlor in Barnard Hall)

10:30–10:45: Arrival and greetings

10:45–11:15: Crispin Wright (New York University, University of Stirling), from Zoom

11:15–11:35: Q&A

11:35–12:05: András Kornai (Budapest Institute of Technology)

12:05–12:25: Q&A

12:25–1:45: Lunch

1:45–2:15: Pavel Pudlák (Czech Academy of Sciences)

2:15–2:35: Q&A

2:35–3:05: Toby Meadows and James Weatherall (University of California, Irvine), (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 (University of Notre Dame)

5:15–5:35: Q&A

5:35–6:30: Reception

Sunday, April 13th (Talks will be in the Lynn Chu Classroom MLC LL002 in the Milstein Center)

10:30–10:45: Arrival and greetings

10:45–11:15: Lee Smolin (Perimeter Institute), from Zoom

11:15–11:35: Q&A

11:35–12:05: Zuzana Haniková (Czech Academy of Sciences)

12:05–12:25: Q&A