CANON AND COMMENTARY:<br />AN OUTLOOK BASED ON MATHEMATICAL SOURCES

Le document est la version de l'article distribuée au colloque "Critical Problems in the History of East Asian Science", organisé par Prof. KIM Yung Sik au Dibner Institute, les 16-18 novembre 2001. La version définitive est à paraître dans les ActesChina's written traditions distinguished a subset of the texts produced in the Middle Kingdom from the others, by granting them the status of “Canons (jing)”. This does not hold true only for the most conspicuous of them all, the “Confucian Canons”, on which the examination system was based. In many domains of inquiry too, scholars designated some earlier texts as “Canons”. What did it mean for a text to be considered a “Canon”? Which specific attitudes and modes of reading did this fact entail? These are some of the questions to the understanding of which this paper aims at contributing. <br />John Henderson already examined such questions in his Scripture, Canon and Commentary. A Comparison of Confucian and Western Exegesis (Princeton University Press, 1991). However, as far as I know and as J. Henderson himself stressed, the discussion on these matters has until today mainly concentrated on the case of the “Confucian canons” and has not yet benefited from investigating the writings considered as “Canons” by the practitioners of fields of inquiry like medicine or mathematics.<br />In contrast to these earlier studies, I focus on the book that, for centuries, has been deemed to be the most important Canon for mathematics: The nine chapters on mathematical procedures (Jiuzhang suanshu). A Han composition of problems and general procedures to solve them, this book constitutes the earliest mathematical source handed down to us by the written tradition and was granted the status of canon soon after its completion. My aim is to examine what the case of mathematics can contribute to the description of a “Canon” as text. <br />Indeed, there is evidence showing that actors themselves felt that these texts belonged to the same category. For example, one can quote the 13th century commentator, Yang Hui, who is himself quoting the preface composed by Rong Qi when he had Jia Xian (11th c.)'s commentary printed in 1148. He states: “When the government instituted the examinations in mathematics to select officials, they chose The nine chapters to be the most important of the mathematical Canons, since, indeed, it is like the six Canons of the Confucians, the (Canon of) difficulties and the (Grand) Simplicity of the medical schools, the Book of Master Sun of military art!” It is hence legitimate to inquire into the nature of such books by relying on the case of mathematics.<br />I approach the questions raised above by observing the earliest readers of the Canon whose testimony came down to us, namely: the commentators. Indeed, as any Canon, The nine chapters on mathematical procedures gave rise to commentaries, two of which were selected by the written tradition to be handed down with the text of the Canon itself. These are the commentaries by Liu Hui, completed in 263, and those written by a group of scholars under the supervision of Li Chunfeng and finished in 656 —let us call the latter, for the sake of simplicity, Li Chunfeng's comments. Moreover, until the Song-Yuan era, scholars went on composing comments on it, two of which came down to us: Jia Xian's (11th century) and Yang Hui's (13th century), mentioned above.<br />These commentators operated at very different time periods. However, they share a same expectation towards the Canon: they all consider that it should encompass the whole of mathematics. However strange this belief may seem, it takes us to the heart of the matter, since such an expectation is regularly met with in commentaries to canons. When looked upon from the point of view of contemporary mathematics, it may be considered as meaningless, an attitude that some contemporary scholars were tempted to adopt. However, when examining this expectation from the perspective of the category of texts to which The nine chapters belong, it seems to only translate the fact that The nine chapters were deemed a Canon.<br />My paper attempts to elucidate, in the case of mathematics, which kinds of reading and exegesis the commentators performed that led them to conceive of the Canon as exhaustive. This may help us understand this statement more generally, as regards any canon. Moreover, I discuss the conception of mathematics that went along with such an expectation