再论中国古代数学与儒学的关系——以六至七世纪学者对于礼数的不同注疏为例  

A Further Study on the Relationship Between Mathematics and Confucianism in Ancient China:The Case of Scholars' Commentaries on Ritual Numbers in the Sixth and Seventh Century China

作　　者：朱一文[1] 

机构地区：[1]中山大学哲学系暨逻辑与认知研究所,广东广州510275

出　　处：《自然辩证法通讯》2016年第5期81-87,共7页Journal of Dialectics of Nature

基　　金：欧洲学术委员会第七项目架构项目(FP7/2007-2013)"古代世界的数学科学"(项目编号:269804);教育部留学回国人员科研启动基金"唐代数学与儒学的关系研究"(教外司留[2015]311号)~~

摘　　要：本文通过分析贾公彦、孔颖达、甄鸾、李淳风等对于《仪礼·丧服》"去五分一以为带"的注疏、注释,揭示出诸家对于礼数的数理解释不尽相同。具体来说:一、贾、孔等遵循注疏儒家经典的做法,把数学知识作为儒经的一部分,他们对于礼数的理解是依据汉字结构,其算法实施不需要筹算;二、甄、李等则重新组织儒家经典以适应当时数学著作的体例,他们从数学的角度去理解礼数,其算法有一个筹算过程。从历史语境来看,这发生在甄鸾扩展数学应用范围,以及唐代政府注疏儒经和注释算经活动的背景下。本文认为我们需要拓展中国古代数学的内涵。在此基础上,数学与儒学的关系并非一成不变:据《周礼》所载,周代九数是周礼的一部分;之后,九数发展为以《九章筭术》为代表的相对独立于儒学的数学体系;另一方面,至唐代,学者们通过注疏儒经也发展出相对独立的数学体系。因此,诸家对于礼数的不同注解反映出:儒经数学是儒学天然的一部分,算经数学则是相对独立于儒学的知识体系,尽管甄鸾、李淳风等通过《五经筭术》试图重建数学与儒学的紧密联系。By analyzing commentaries on the Rites and Ceremonies by Jia Gongyan, Kong Yingda et al., Zhen Luan, and Li Chunfeng et al., this paper reveals that different scholars had different mathematical practices： on one hand, Jia and Kong et al. followed the way of doing commentary on classics, and regarded their mathematical knowledge as a part of Confucianism; moreover their understandings on ritual of numbers are on the basis of the structure of Chinese characters, and they didn＇t need counting rods for executing their mathematical procedures; on the other hand, Zhen and Li et al. reorganized classics so as to fit with the structure of mathematical books at that time; furthermore, they understood ritual of numbers in the viewpoint of mathematics, and their procedures relied on counting rods to carry out. The facts happened when Zhen Luan expanded the application of mathematics, and Tang governmental projects for commenting on Confucian and mathematical classics were undertaken. This paper suggests that we should expand the content of mathematics in ancient China. On this basis, the relationship between mathematics and Confucianism was changing with time. According to the Rites of the Zhou dynasty, Mathematics [Jiu Shu] was a part of ritual in Zhou dynasty. After that, Nine Chapters on Mathematical Procedures was produced as the result of development of mathematics [Jiu Shu]. On the other side, there was a relevant independent mathematical knowledge-system developed by scholars in Confucian classics. Therefore, different commentaries on ritual of numbers reveals that： mathematics in Confucian classics is always a part of Confucianism, while mathematics in mathematical classics is other relevant independent mathematical knowledge-system, although Zhen and Li et al. tried to rebuild the close relationship between mathematics and Confucianism through writing and commenting on the Mathematical Procedures of the Five Canons.

关 键 词：礼数 中国古代数学儒学 《五经笄术》《仪礼》 

分 类 号：N0[自然科学总论—科学技术哲学]