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Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China

Published online by Cambridge University Press:  01 September 2003

Karine Chemla
Karine Chemla
Affiliation:
REHSEIS, CNRS University, Paris 7
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Abstract

Argument

Abstraction is commonly valued as being essential to mathematics or even consubstantial with it. In relation to this belief, mathematical texts from Antiquity – be they from Babylon, Egypt, or China –, which are composed of seemingly concrete problems and algorithms solving them, have been considered to be practice-oriented and deprived of theory. This paper offers an alternative view on both issues. Relying on evidence given by third-century commentaries on The Nine Chapters on Mathematical Procedures, a Chinese treatise composed around the beginning of the Common Era,this paper argues that, in the scholarly mathematical tradition of ancient China, generality was more valued than abstraction. In this respect, problems must be interpreted as paradigms, in the sense grammarians use the term. One of the goals of theoretical endeavor was to exhibit the most general operations possible, and this purpose can be read in quite a few specific features of mathematical practice and concepts. Moreover, it is shown that abstraction is not absent from The Nine Chapters, but that it entertains with generality a relationship that requires analysis and can by no means be taken for granted. These ancient sources hence constitute an invitation to develop a critical approach toward the relation of mathematics to abstraction and generality taken separately, as well as the relation of these two values with each other.

Type
Articles
Information
Science in Context , Volume 16 , Issue 3 , September 2003 , pp. 413 - 458
Copyright
2003 Cambridge University Press

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