Mini workshop on Philosophy of Math

Time: Dec. 23rd 2017 9:30 am to 18:00 pm

Location: Room 106, Department of Philosophy, Peking University

Confirmed participants: Kun Gao, Fengkui Ju, Shihui Kang, Jie Liu, Colin McLarty, Xianghui Shi, Yanjing Wang, Taotao Xing, Difei Xu, Feng Ye, Yue Yang

Tentative topics and questions to be discussed (not exclusive):
  1. Is logic the basis of mathematics, or is mathematics the basis of logic (as Pierce and Brouwer said)?
  2. Why does infinitary mathematics seem more popular among mathematicians than finitary mathematics?
  3. Is mathematics truly cumulative? Or do we just make it seem that way, by constantly changing the ideas of Euclid or Newton or even Dedekind, then pretending that is what they meant themselves?
  4. Why is current science (such as string theory or the extended genome in biology) so much more widely studied in philosophy of science than the latest math is in philosophy of math?
  5. Should philosophers of mathematics think more about how children actually learn basic arithmetic and geometry?
  6. Can we do research in math without mathematical intuition (and what it is)?
  7. Should there be a single foundation of math or different foundations for different branches of math?
  8. How to compare synthetic math vs. analytic math in general? How to compare the univalent foundations with existing approaches?

We focus on discussions rather than standard talks. Please try to be
concise (and to the point) when expressing your thoughts (try to do it within 5 mins each time).

Preliminary programme:

9: 30 - 10:00 Colin McLarty: Introduction to the background of the selected topics

10:10 - 11:00 Topic 1: Logic and mathematics (Question 1)

11:10 - 12:00 Topic 2: Foundations of mathematics (Questions 7, 8)

12:00 - 13:30 Lunch

13:30 - 14:20 Topic 3: Infinitary vs. finitary (Question 2)

14:30 - 15:20 Topic 4: Epistemology of mathematics (Question 3, 5)

15:30 - 16:20 Topic 5: Mathematical intuition and explanation (Question 6)

16:30 - 17:30 Other related questions (Question 4 and others)

18:00 - 20:00 Dinner

20:00 - 23:00 Evening discussion