算學、儒學與制度化－初唐數學的多樣性及其與儒學的關係

唐因隋制，國子監設算學館，李淳風等注釋的十部算經被立於學官，其後更是在科舉中設明算科。毫無疑問，初唐數學獲得了巨大的制度化成就。但是，前人對這些史實背後的歷史動力討論不多。透過《儀禮注疏》、《禮記正義》與《五經筭術》，本文分析了六至七世紀學者賈公彥、孔穎達、甄鸞、李淳風等對《儀禮》〈喪服〉的同例注疏，從而揭示出諸家對儒經的數理解釋在計算思路、方法、工具等多方面的差異，是兩種不同的數學實作。而且，本例中賈、孔等人的算法特點亦體現在唐代其他儒經的注疏中，並且延續至清中葉，因此形成了具有一般性的儒家自身的計算文化傳統。本文進而再透過分析諸家對數學的相關論述，揭示初唐時期學者們對於數學的功能與作用存在不同觀點。一方面，賈公彥、孔穎達等認為其自身的計算文化傳統應用於儒經，而傳統籌算數學應用於算經；另一方面，李淳風等則認為傳統籌算數學可以廣泛地應用於音律、度量衡、曆法、儒學等諸多領域，甚至將之視為一切知識的基礎。這兩種數學實作與對數學觀的差異，恰好可以印證初唐算學館的數次置廢，以及算學與儒學在制度安排上的差別。由此，初唐數學的高度制度化發展實際上是李淳風等在算學與儒學張力之中努力的結果。

關鍵字

算學；儒學；制度化；《儀禮》；《五經筭術》

並列摘要

The Tang dynasty (618-907), like the Sui dynasty (581-618) that preceded it, established a School of Mathematics in the Imperial University. The Shibu suanjing (十部算經Ten Mathematical Canonical Texts) edited and commented by Li Chunfeng and his colleagues became the School’s designated textbooks, and mathematics later became an imperial examination subject. The dynamics of these undoubtedly great institutional achievements in early Tang dynasty, however, has not received much attention in the scholarly community. By examining the Yili zhushu (儀禮注疏Commentaries and Subcommentaries on the Ceremonies and Rites), Liji zhengyi (禮記正義The Proper Meaning on the Records of Rites) and Wujing suanshu (五經筭術Mathematical Procedures of the Five Canonical Texts), this paper analyzes commentaries and subcommentaries written by the 6^(th) and 7^(th) century scholars Jia Gongyan 賈公彥 (fl. 650), Kong Yinda 孔穎達 (574-648), Zhen Luan 甄鸞 (fl. 570) and Li Chunfeng 李淳風 (602-670) on an excerpt from the Yili (儀禮Ceremonies and Rites). This analysis reveals that differences in these scholars’ computational thinking, methods, tools, etc., are due to the employment of two different mathematical practices embodied in early Tang commentaries and subcommentaries on other Confucian canonical literature and on the mathematical texts. These continued until the mid-Qing dynasty (1644-1911), thus forming Confucianism’s own general mathematical culture tradition. Furthermore, this paper discovers scholars’ different arguments regarding the role and the function of mathematics. On one hand, Jia and Kong believe the mathematics in Confucian canonical literature and the mathematical texts are applied in different domains; on the other hand, Li Chunfeng argues that the mathematics in mathematical canonical texts is the fundamental basis for all knowledge. Two mathematical practices and two viewpoints on the role of mathematics are evidenced to explain the abolishment of the School of Mathematics several times in early Tang dynasty, and the huge difference between mathematics and Confucianism with respect to institutionalization. This paper therefore argues that the highly institutionalized development of mathematics during the early Tang dynasty was a result of the endeavors of Li Chunfeng and his colleagues amidst the dynamic tension between Confucianism and mathematics.