What Did They Mean by “Calculation Principles”?: Revisiting Argumentative Styles in Late Ming to Mid-Qing Chinese Mathematics = What Did They Mean by “Calculation Principles”?: Revisiting Argumentative Styles in Late Ming to Mid-Qing Chinese Mathematics

다국어 초록 (Multilingual Abstract)

This article discusses the influence that two versions of the Elements had in Ming and Qing China as well as Chinese scholars` efforts to “integrate” (huitong 會通) Western and Chinese mathematics into a unified system in terms of argumentative styles in mathematics. Although much high praise was given to the axiomatic-de-ductive system of Euclid`s Elements, numerical arguments and problem-solving re-main important traits in the works of Chinese scholars. The compilation of the Shuli jingyun 數理精蘊 and the inclusion of another version of the Elements in it again prompted East Asian mathematicians to reflect more upon their methods of argu-mentation, and later scholars began to write texts whose arguments are more abstract than numerical. This paper presents examples taken from the works of several rep-resentative scholars from the late Ming to the mid-Qing periods to argue that their efforts of huitong produced argumentative styles that are a combination of both Chi-nese and Western approaches, and that there was a trend of moving from concrete calculations to general arguments in mathematical texts throughout the course of history. Finally, the authors conclude that what 17^th and 18^th century Chinese math-ematicians meant by “calculation principles” (suanli 算理) was never the kind of pure deduction in the Euclidean manner, but a combination of induction and deduc-tion, with the help of intuition, for the purpose of problem-solving.

참고문헌 (Reference)

1 洪萬生, "談天三友" Mingwen shuju 144-, 1993

2 程和欽, "清代算學家杜知耕及其《數學鑰》之研究" National Taiwan Normal University 2006

3 李儼, "海島算経新注" Shanghai kexue jishu chubanshe 1963

4 Mei Rongzhao, "歐幾里德原本的傳入和對我國明清數學的影響" Ming-Qing shuxueshi lunwenji 53-83,

5 梅榮照, "明清數學史論文集" Jiansu jiaoyu chubanshe 1-20, 1990

6 Wang Yusheng, "中國科學技術典籍通匯: 數學篇" Henan Education Press 1145-1150, 1993

7 田淼, "中國數學的西化歷程" Shandong Education Press 26-38, 2003

8 洪萬生, "中國史新論: 科技與中國分冊" Lianjing chubanshe 353-421, 2010

9 Catherine Jami, "“European Science in China” or “Western Learning”?: Representations of Cross-Cultural Transmission, 1600-1800" 12 (12): 413-434, 1999

10 Suan shu shu, "‘Writings on Reckoning’: A Translation of a Chinese Mathematical Collection of the Second Century BC, with Explanatory Commentary, and an Edition of the Chinese Text" Needham Research Institute 2004

11 L. Burton, "Why Is Intuition So Important to Mathematicians but Missing from Mathematics Education?" 19 (19): 27-32, 1999

12 Catherine Jami, "Western Influence and Chinese Tradition in an Eighteenth-Century Chinese Mathematical Work" 15 : 311-331, 1988

13 Catherine Jami, "Western Humanistic Culture Presented to China by Jesuit Missionaries (XVII-XVIII centuries)" Institutum Historicum S. I 175-199, 1996

14 Reviel Netz, "The Shaping of Deduc-tion in Greek Mathematics : A Study in Cognitive History" Cambridge University Press 1999

15 Catherine Jami, "The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662-1722)" Oxford University Press 173-176, 2012

16 Judith V. Grabiner, "The Centrality of Mathematics in the History of Western Thought" 61 (61): 220-230, 1988

17 Hashimoto Keizo, "Statecraft and Intellec-tual Renewal in Late Ming China: The Cross-Cultural Synthesis of Xu Guangqi (1562-1633)" Brill 263-278, 2001

18 Chu Pingyi, "Scientific Dispute in the Imperial Court: The 1664 Calendar Case" 14 : 7-34, 1997

19 Morris Kline, "Mathematics in Western Culture" Oxford University Press 1953

20 James Hawthorne, "Inductive Logic"

21 Karine Chemla, "Generality above Abstraction: The General Expressed in Terms of the Paradig-matic in Mathematics in Ancient China" 16 (16): 413-458, 2003

22 Jami, "From Clavius to Pardies"

23 Peter Engelfriet, "Euclid in China : The Genesis of the First Chinese Translation of Euclid's Ele-ments in 1607 and Its Reception up to 1723" Brill 1998

24 Joshua Schechter, "Deductive Reasoning"

25 Huang Yi-Long, "Court Divination and Christianity in the K’ang-hsi Era" 10 : 1-20, 1991

26 Li Yan, "Chinese Mathematics: A Concise History" Clarendon Press 226-230, 1987

27 Christopher Cullen, "Astronomy and Mathematics in Ancient China : The Zhou Bi Suan Jing" Cambridge University Press 77-80, 1996

28 Donald B. Wagner, "An Early Chinese Derivation of the Volume of a Pyramid" 6 : 164-188, 1979

29 Jean-Claude Martzloff, "A History of Chinese Mathematics" Springer 105-106, 2006