Modes of Reasoning

Abstract

For anyone claiming to write the history of a science of which reasoning forms the very essence the question of the logic is of paramount importance. However, despite this obvious fact, general histories of Chinese mathematics rarely show concern for this question. They insist above all on presenting results, the initial raison d’etre of which is unclear, even though they incidentally provide the reader with hypothetical reconstitutions of proofs. While this approach to the history of mathematics is naturally a result of various causes, one which probably plays an essential role is the fact that most Chinese mathematical works contain no justifications. However, there is one major exception, namely a set of Chinese argumentative discourses which has been handed down to us from the first millennium AD. We are essentially referring to the commentaries and sub-commentaries of the Jiuzhang Suanshu, the key work which inaugurated Chinese mathematics and served as a reference for it over a long period of its history. This fact, which was long unrecognised, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia or India.