Between Philosophy and Mathematics

General Trends in Dissemination, Teaching, and Research on Mathematical Logic in 1930s China

Authors

  • Jan VRHOVSKI Faculty of Arts, University of Ljubljana, Slovenia

DOI:

https://doi.org/10.4312/as.2022.10.2.209-241

Keywords:

mathematical logic, mathematics, philosophy, China, Republican Period

Abstract

This article studies some central developments in the propagation and teaching of mathematical logic in 1930s China. Focusing on the emergence of a twofold disciplinary approach to mathematical logic, namely as a discipline studied and disseminated by Chinese philosophers on the one hand and mathematicians on the other, this paper explores one of the key turning points in the development of the academic notion of mathematical logic in China. Apart from casting some light on the teaching of mathematical logic in the framework of both philosophical as well as mathematical spheres of inquiry, this article also provides some preliminary insights into the circumstances surrounding the first systematic introduction of mathematical logic into the modern standardized system of education, which gradually took shape over the late-1920s and early 1930s in China.

Downloads

Download data is not yet available.

References

Bernays, Paul, and Abraham A. Fraenkel. 1958. Axiomatic Set Theory. Amsterdam: North-Holland Publishing Company.

Cheng, Minde 程民德. 1994. Zhongguo xiandai shuxuejia zhuan 中國現代數學家傳 (Biographies of Modern Chinese Mathematicians), vol. 1. Nanjing: Jiangsu jiaoyu chubanshe.

Ciaudo, Joseph. 2021. “Is ‘New Culture’ a Proper Translation of Xin Wenhua? Some Critical Remarks on a Long-Overlooked Dilemma.” Asian Studies 9 (2): 13–47. https://doi.org/10.4312/as.2021.9.2.13-47.

Creighton, James Edwin. 1919. An Introductory Logic. New York, London: Macmillan.

Dauben, Joseph W. 2002. “Internationalizing Mathematics East and West: Individuals and Institutions in the Emergence of a Modern Mathematical Community in China.” In Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited by Karen Hunger Parshall, and Adrian C. Rice, 253–85. Providence (RI): American Mathematical Society.

Editorial Committee for Elementary and Secondary School Curricular Standards of the Ministry of Education, ed. 1932. Chuji gaoji zhongxue kecheng biaozhun 初級高級中學課程標準 (Curricular Standards for Junior and Senior Middle Schools). Shanghai: Shangwu yinshuguan.

Editorial Committee for Normal School Curricular Standards of the Ministry of Education, ed. 1934. Shifan xuexiao kecheng biaozhun 師範學校課程標準 (Curricular Standards for Normal Colleges). Shanghai: Shangwu yinshuguan.

Fan, Shoukang 范壽康. 1931. Lunlixue 論理學 (Logic). Shanghai: Kaiming shudian.

Fitch, Frederic B. 1943. “Review of La Philosophie Mathématique et la Théorie des Ensembles by Tseng Ting-Ho.” Journal of Symbolic Logic 8 (2): 56–57.

Gao, Xingjian 高行健. 1936. “Shuli luoji ABC (shang) 數理邏輯ABC (上) (ABC of Mathematical Logic (Part 1)).” Kexue shijie 5 (5): 434–40.

Gödel, Kurt, and Solomon Feferman, ed. 2014. Kurt Gödel: Collected Works, volume IV: Correspondence A-G. Oxford: Oxford University Press.

Guoli Beijing daxue 國立北京大學. 1929. Beijing daxue sayi zhounian jiniankan 北京大學卅一週年紀念刊 (Commemorative Publication on the 31st Anniversary of Peking University). Beijing: National Peking University.

Guoli daxue lianhehui 國立大學聯合會. 1929. “Daxue guicheng 大學規程 (Regulations for Universities).” Guoli daxue lianhehui yuekan 2 (7): 3–7.

Guoli Wuhan daxue 國立武漢大學. 1932. Guoli Wuhan daxue yilan 國立武漢大學一覽 (National Wuhan University Guide). Wuchang: Guoli Wuhan daxue.

———. 1934. Guoli Wuhan daxue yilan 國立武漢大學一覽 (National Wuhan University Guide). Wuchang: Guoli Wuhan daxue.

———. 1936. Guoli Wuhan daxue yilan 國立武漢大學一覽 (National Wuhan University Guide). Wuchang: Guoli Wuhan daxue.

Hardy, G. H. 1932. “Wuqiongda zhi jie 無窮大之階 (Orders of Infinity).” Translated by Xiao Wencan 蕭文燦. Guoli Wuhan daxue like jikan 3 (1): 13–57.

———. 1933. “Wuqiongda zhi jie 無窮大之階 (Orders of Infinity).” Translated by Xiao Wencan 蕭文燦. Guoli Wuhan daxue like jikan 3 (3): 1–65.

He, Lin 賀麟. 1947. Dangdai Zhongguo zhexue 當代中國哲學 (Modern Chinese Philosophy). Nanjing: Shengli chubanshe.

He, Qingqin 何清欽. 1989. “Minguo ershiyi nian woguo zhongdeng xuexiao zhidu gaige jingguo zhi tantao 民國二十一年我國中等學校制度改革經過之探討 (A Study of the Process of Reformation of the Secondary School Education System in China, 1932).” Jiaoyu xuekan 8: 75–106.

Hilbert, David, and Wilhelm Ackermann. 1972 [1928]. Grundzüge der theoretischen Logik (Fundamentals of Theoretical Logic). Berlin, Heidelberg, New York: Springer-Verlag.

Jevons, William Stanley. 1886 [1870]. Elementary Lessons in Logc: Deductive and Inductive, with Copious Questions and Examples, and a Vocabulary of Logical Terms. London: Macmillan.

Jin, Yuelin 金岳霖. 1935. Luoji 邏輯 (Logic). Beijing: Qinghua daxue chubanshe.

Li, Mianyuan 李勉媛. 2016. “Guanyu difang zonghe daxue jiaoshi jiaoxue fazhan wenti de sikao 關於地方綜合大學教師教學發展問題的思考 (A Reflection on the Developmental Questions of Teaching at Provincial Comprehensive Universities).” Jilin shao jiaoyu xueyuan xuebao 32 (3): 31–33.

Li, Shurong 李樹榮, and Xiao Xing 蕭星. 2005. “Guizhou zhuming shuxuejia jiaoyujia Xiao Wencan 貴州著名數學家教育家蕭文燦 (Xiao Wencan—The Renowned Mathematician and Educator from Guizhou).” Guizhou wenshi congkan 2: 90–92.

Li, Weiwu 李維武. 2009. “Xiandai daxue zhexuexi de chuxian yu 20 shiji shang banye Zhongguo zhexue de kaizhan 現代大學哲學系的出現與20世紀上半葉中國哲學的開展 (Birth of Philosophical School in Modern University and Development of Chinese Philosophy in First Half of the 20th Century).” Xueshu yuebao 41 (11): 38–48.

Lin, Xiaoqing Diana. 2012. “Developing the Academic Discipline of Chinese Philosophy: The Departments of Philosophy at Peking, Tsinghua, and Yenching Universities (1910s–1930s).” In Learning to Emulate the Wise: The Genesis of Chinese Philosophy as an Academic Discipline in Twentieth-Century China, edited by John Makeham, 131–62. Hong Kong: Chinese University Press.

Ministry of Education (Jiaoyubu 教育部). 1929. “Daxue zuzhifa 大學組織法 (Organizational Law for Universities).” Fujian jiaoyu zhoukan 41: 12–13.

———. 1933. Daxue kemu caoan 大學科目草案 (Draft of the University Courses). Shanghai: Commercial Press.

———. 1940. Daxue kemu biao 大學科目表 (List of University Courses). Chongqing: Zhengzhong chubanshe.

———. 1942. Xiuzheng chu, gaoji zhongxue kecheng biaozhun 修正初、高級中學課程標準 (Revised Curricular Standards for Junior and Senior Middle Schools). Chongqing: Zhengzhong shuju.

Mou, Zongsan 牟宗三. 1940. Luoji dianfan 逻辑典范 (Logical Paradigms). Chongqing: Shangwu yinshuguan.

Pepper, Suzanne. 1996. Radicalism and Education Reform in Twentieth-Century China: The Search for an Ideal Development Model. Cambridge, New York: Cambridge University Press.

Qinghua daxue 清華大學. 1933. “Yubei toukao Qinghua de cankaoshu mulu 預備投考清華的參考 書目錄 (A Reading List for Preparations for Enrolment into Qinghua University).” Qinghua shuqi zhoukan 3/4: 87–88.

Ren, Nanheng 任南衡, and Zhang Youyu 張友余. 1994. Zhongguo shuxuehui shi­liao 中國數學會史料 (Historical Materials of Chinese Mathematical Society). Nanjing: Jiangsu jiaoyu chubanshe.

Royce, Josiah. 1913. “The Principles of Logic.” In Louis Couturat, Benedeto Croce, Federigo Enriques, Josiah Royce, Arnold Ruge, and Wilhelm Windelband. Encyclopaedia of the Philosophical Sciences: Logic, volume 1, 67–135. Translated by B. Ethel Meyer. London: Macmillan.

Russell, Bertrand. 1919. Introduction to Mathematical Philosophy. London: George Allen & Unwin Ltd.

Russell, Bertrand [Luosu 羅素]. 1922. Luosu shuli zhexue 羅素數理哲學 (Russell’s Mathematical Philosophy). Translated by Fu Zhongsun 傅種孫, and Zhang Bangming 張邦銘. Shanghai: Shangwu yinshuguan.

Shen, Youqian 沈有乾. Xiandai luoji 現代邏輯 (Modern Logic). Shanghai: Xinyue shudian.

Shi, Mingde 時明德, and Zeng Zhaoshi 曾昭式. 1998. “Shuli luoji zai Zhongguo fazhan zhihuan de yuanyin tanxi 數理邏輯在中國發展滯緩的原因探析 (An Exploration of Reasons of Slow Development of Mathematical Logic in China).” Xinyang shifan xueyuan xuebao 18 (2): 29–33.

Suter, Rafael. 2017. Logik und Apriori zwischen Wahrnehmung und Erkenntnis: Eine Studie zum Frühwerk Mou Zongsans (1909–1995). Berlin: Walter de Gruyter.

———. 2020. “Logic in China and Chinese Logic: The Arrival and (Re-) Discovery of Logic in China.” In Dao Companion of Chinese Philosophy of Logic, edited by Fung Yiu-ming, 465–509. Cham: Springer Nature Switzerland AG.

Tang, Zaozhen 湯璪真. 1930, trans. “Jihe lilun jihexue 集合理論幾何學 (Set-Theoretical Geometry).” Guoli Wuhan daxue like jikan 1(2): 40–48.

Tseng, Ting-ho. 1938. “La philosophie mathématique et la théorie des ensembles (Mathematical Philosophy and Set Theory).” PhD diss., University of Paris.

Tu, Xiaoshi 屠孝實. 1926. Mingxue gangyao 名學綱要 (Logic Primer). Shanghai: Shangwu yinshuguan.

Turner, J. S. 1928. Mathematical Logic. Ames (Iowa): Iowa State College.

Vrhovski, Jan. 2020. “From Mohism to the School of Names, from Pragmatism to Materialist Dialectics: Chinese Interpretations of Gongsun Longzi as a Text and Source of Chinese Logic, 1919–1937.” International Communication of Chinese Culture 7 (4): 511–38.

———. 2021a. “‘Qinghua School of Logic’: Mathematical Logic at Qinghua University in Peking, 1926–1945.” History and Philosophy of Logic 42 (2): 247–61.

———. 2021b. “Balance and Innovation: Approaches to Logic and the Teaching of Logic in the Philosophy Department of Peking University, 1916–1927.” History and Philosophy of Logic 15 (1): 1–23.

Wang, Zhenxuan 王振瑄. 1928. Lunlixue 論理學 (Logic). Shanghai: Shangwu yinshuguan.

Wolf, Abraham. 1926. Essentials of Logic. London: George Allen & Unwin Ltd.

Xiangren 湘人 [Hunanese]. 2017. Xiao Shafu pingzhuan 蕭箑父評傳 (A Critical Biography of Xiao Shafu). Kaohsiung: Duli zuojia – Xinrui wenchuang.

Xiao, Weili 肖偉例. 2010. “Zhou Gucheng yu Mao Zedong 周穀城與毛澤東 (Zhou Gucheng and Mao Zedong).” Xinxiang pinglun 10: 36–37.

Xiao, Wencan 蕭文燦. 1933. “Jihelun 集合論 (Set Theory).” Guoli Wuhan daxue like jikan 4 (2): 30–63.

———. 1939. Jihelun chubu 集合論初步 (Elementary Set Theory). Shanghai: Shangwu yinshuguan.

Xu, Yibao. 2003. “Bertrand Russell and Mathematical Logic in China.” History and Philosophy of Logic 24: 181–96.

———. “Concepts of Infinity in Chinese Mathematics.” PhD diss., The City University of New York.

Zhai, Jincheng 翟錦程. 2016. “Zhongguo jindai luojixue jiaoyu de jige wenti 中國近代邏輯學教育的幾個問題 (Several Issues of Education of Logic in Modern China).” Huabei shuili shuidian daxue xuebao (Shehui kexue ban) 32 (1): 59–63.

Zhang, Shizhao 章士釗. 1943. Luoji zhiyao 邏輯指要 (Essentials of Logic). Chongqing: Shidai jingshenshe.

Zhang, Xizhi 張希之. 1932. Lunlixue gangyao 論理學綱要 (Essentials of Logic). Beiping: Wenhua xueshe.

———. 1935. Gaozhong lunlixue 高中論理學 (Senior Secondary School Logic). Beiping: Wenhua xueshe.

Zhang, Youyu 張友余. 1991. “Sanshi niandai de Shuxue tongbao 三十年代的《數學通報》(The Bulletin of Mathematics in the 1930s).” Shuxue tongbao 8: 2–3.

Zhu, Yanjun 朱言鈞. 1928a. “Bo shiyan zhuyi 駁實驗主義 (A Refutation of Experimentalism).” Minduo zazhi 9 (4): 1–8.

———. 1928b. “Zai bo zhiyan zhuyi 再駁實驗主義 (A Further Refutation of Experimentalism).” Minduo zazhi 9 (4): 1–5.

———. 1928c. Lixing piping pai de zhexuejia Naersong (ta de shengping yu xueshuo) 理性批評派的哲學家納爾松 (他的生平與學説) (Nelson—A Philosopher of Critical Rationalism (His Life and Teaching)). Shanghai: Shangwu yinshuguan.

———. 1929a. “Xin jihexue yu zhexue 新幾何學與哲學 (New Geometry and Philosophy).” Guanghua qikan 5: 1–4.

———. 1929b. “Zuijin suanxue jie zhong de liang da chaoliu 最近算學界中的兩大潮流 (Two Major Currents in Mathematical Circles of the Recent Years).” Guanghua qikan 5: 1–7.

———. 1929c. “Cong renshilun dao pipinglun 從認識論到批評論 (From Theory of Knowledge to Critical Theory). Zhexue pinglun 2 (4): 1–12.

———. 1929d. “Xuanxue yu ziran kexue de guanxi 玄學與自然科學的關係 (On the Relationship between Metaphysics and Natural Science). Zhinan 100: 28–37.

———. 1929e. “Sugeladi yu Na’ersong 蘇格臘底與納爾松 (Socrates and Leonard Nelson).” Zhexue pinglun 2 (4): 13–18.

———. 1932. “Hebaide Hilbert Jiaoshou zhi shenshi jiqi yuanli shuo 赫百德 Hilbert 教授之身世及其原理說 (Professor Hilbert’s Life Experience and his Theory of Axiomatics).” Guanghua daxue banyuekan 1: 2–8.

———. 1933. “Shuli luoji gangyao 數理邏輯綱要 (Essentials of Mathematical Logic).” Zhexue pinglun 4 (3–4): 51–76.

———. 1934a. “Cong gaodeng shuxue de guandian tantan chudeng shuxue 從高等數學的觀點談談初等數學 (Speaking About Elementary Mathematics from the Point of View of Advanced Mathematics).” Guanghua daxue banyuekan, 3 (2): 8–14; 3 (3): 21–26; 3 (4): 26–31.

———. 1934b. “Shuli luoji gangyao 數理邏輯綱要 (Essentials of Mathematical Logic).” Guoli Wuhan daxue like jikan 5 (2): 179–205.

———. 1935a. “Jinnian lai suanxue zhong zhi liang da sichao 近年來算學中之兩大思潮 (Two Major Tides of Thought in Mathematics in the Past Few Years).” Guanghua daxue banyuekan 3 (9/10): 244–56.

———. 1935b. “Shuxue zhong zhi tuili fangfa 數學中之推理方法 (Methods of Inference in Mathematics).” Guanghua daxue banyuekan 4 (1): 31–36.

———. 1935c. “Dingxing jihexue yu wuren zhi kongjian guan 定性幾何學與 吾人之空間觀 (Topological Geometry and Our Views on Space).” Xueshu shijie 1 (2): 31–33.

———. 1936a. “Shuxue renshi zhi benyuan 數學認識之本源 (The Origins of Mathematical Knowledge).” Shuxue zazhi 1 (1): 6–19.

———. 1936b. “Shuli luoji daolun 數理邏輯導論 (An Introduction to Mathematical Logic).” Shuxue zazhi 1 (1): 80–94.

———. 1936c. “Jilun xiaotan 集論小談 (Casual Conversations on Set Theory).” Guanghua dauxe banyuekan 4 (9): 28–35.

———. 1937a. “Shuxue yuanlixue zhi piping 數學原理學之批評 (Critiques of Mathematical Axiomatics).” Tushu zhanwang 2 (9–10): 49–53.

———. 1937b. “Jilun xiaotan 集論小談 (Casual Conversations on Set Theory).” Guanghua dauxe banyuekan 5 (9): 24–26.

———. 1947. Shuli congtan 數理叢談 (Mathematical Discussions). Shanghai: Shangwu yinshuguan.

Zhu, Zhangbao 朱章寳. 1940. Xinbian gaozhong lunlixue 新編高中論理學 (New Edition Senior Secondary School Logic). Chongqing: Zhonghua shuju.

Downloads

Published

09.05.2022

How to Cite

Vrhovski, J. (2022). Between Philosophy and Mathematics: General Trends in Dissemination, Teaching, and Research on Mathematical Logic in 1930s China. Asian Studies, 10(2), 209–241. https://doi.org/10.4312/as.2022.10.2.209-241

Issue

Section

A Century of Mathematical Logic in China