$\omega$ $\aleph$ $\infty$
Mathematical Logic at Fudan

## 2022 Annual Conference of Philosophy of Mathematics in China 2022年全国数学哲学学术研讨会

September 3 to 4, 2022

This annual conference aims to bring together philosophers of mathematics around China. The talks will range over several topics:

• Realism, scepticism and pluralism.
• Set theory, Category theory and the foundation of mathematics
• Computability theory and reverse mathematics
• Infinity

The meeting will be online and in-person. Due to the pandemic, foreign researchers can only attend remotely, but we encourage domestic researchers to participate in-person. There is no conference fee for this conference.

Please find the Zoom meeting IDs and password in the "Program" slide.

Speakers

### Invited Speakers

• Han, Linhe (韩林合), Peking University
• Hao, Zhaokuan (郝兆宽), Fudan University
• Ju, Shier (鞠实儿), Sun Yat-Sen University
• Horsten, Leon, University of Konstanz
• Linnebo, Øystein, University of Oslo

### Contributed Speakers

• Cai, Haifeng (蔡海峰)
• Kang, Xiaojun (康孝军)
• Liang, Xiaolong (梁晓龙)
• Kou, Liang (寇亮)
• Shen, Guozhen (申国桢)
• Wu, Jinyue (吴近悦)
• Xiong, Ming (熊明)
• Yang, Sen (杨森)
• Zeng, Qianli (曾千里)

Program

All times are Beijing time (GMT+8). Please come back and check if there are any changes.

#### September 3

Zoom Meeting ID for the morning: 951 1032 2232, password: 340922. Zoom Meeting ID for the afternoon: 978 9430 1882, password: 340922.

8:30 - 8:45
Opening

8:45 - 9:45

Hao, Zhaokuan (郝兆宽): Frege and Godel in Cantor's Eden
In 1885, one year’s after Frege’s Grundlagen being published, Cantor published his review of this work. The review is only one-page, but is concerned with an very important and also very interesting issue, that is the order priority of the concepts extension and cardinal numbers. Cantor’s review and Frege’s two months later response are not only of great historical interest but also closely related to a major problem in the foundation of mathematics today. In this talk, we try to argue that the essence of the problem lies in the relationship between the extension of concept and set itself. Although set theory has achieved great success since Cantor, the difficulties faced by its foundation may be related to it, and it is possible to find a mathematical solution with the help of Frege and Gödel's philosophical thinking. Slides

10:15 - 10:45

This paper provides a procedure which from any Boolean system of sentences, outputs another Boolean system called the ‘$m$-cycle unwinding’ of the original Boolean system for any positive integer $m$. We prove that for all $m > 1$, this procedure eliminates the direct self reference in the sense that the $m$-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever $m$ is relatively prime to all primary periods of a Boolean paradox, this paradox and its $m$-cycle unwinding have the same primary periods. In this way, we can always produce an indirectly self-referential Boolean paradox which has the same periodic characteristics as a known Boolean paradox.

10:45 - 11:15

Yang, Sen (杨森): Minimal degrees in generalized recursion theory
Classical recursion theory can be built on the concept of recursive functions on $\omega$ and Cohen forcing can be used in various construcitons in classical recursion theory. One can replace $\omega$ with a generalized structure and define the concept of generalized recursive functions on it. $\alpha$-recursion theory is a version of such generalized recursion theory. We attempts to explore recursion theories more general than $\alpha$-recursion, in which useful constructions can be made using Prikry-type forcings, and to apply these constructions to $\alpha$-recursion theory.

11:15 - 11:45

1918年，华沙学派的谢宾斯基（Sierpiński）提出了一个研究纲领，试图彻底弄清选择公理在每个数学定理的证明中所起的作用。我们以不依赖于选择公理的基数研究为主线，介绍百年来谢宾斯基纲领的研究进展，重点介绍报告人及其合作者在康托定理的推广的研究中的工作。

13:30 - 14:00

14:00 - 14:30

14:30 - 15:00

15:30 - 16:30

Øystein Linnebo: Potentialism in the philosophy and foundations of mathematics
Aristotle famously claimed that the only coherent form of infinity is potential, not actual. However many objects there are, it is possible for there to be yet more; but it is impossible for there in fact to be infinitely many objects. Although this view was superseded by Cantor’s transfinite set theory, even Cantor regarded the collection of all sets as “unfinished” or incapable of “being together”. In recent years, there has been a revival of interest in potentialist approaches to the philosophy and foundations of mathematics. The lecture provides a survey of such approaches, covering both technical results and associated philosophical views, as these emerge both in published work and in work in progress. Slides

16:30 - 17:30

Leon Horsten: Mathematical rationality

In this talk I discuss the question:

When is it rational for a mathematician to believe a mathematical statement?

According to the received view, a mathematician's belief in a mathematical statement A isrational if she is justified in believing A. Moreover, she is justified in believing A if she hasgood reasons for believing A. Furthermore, since Gödel, a distinction is made betweenintrinsic and extrinsic reasons for mathematical beliefs.

Against this, I defend the externalist view that rationality should be conceived of as epistemically optimal behaviour in response to epistemological challenges. In particular, I argue that a mathematician can, in certain circumstances, rationally believe certain mathematical statements (basic mathematical axioms, for instance) without having propositionally structured reasons for them. In such cases, the mathematician is epistemically entitled to relevant beliefs without having justification for these beliefs.

#### September 4

Zoom Meeting ID for the day: 956 7340 8066, password: 340922.

8:30 - 9:30

9:30 - 10:30

11:00 - 11:30

11:30 - 12:00

Organizers

• Wang, Yi (王轶)
• Yang, Ruizhi (杨睿之)

Email: ynw@xixilogic.org, yangruizhi@fudan.edu.cn