Proper Relations of Association (Zheng 正) vs. Logical Validity of Syllogism: A Case Study of Shared Practices of Matteo Ricci, S. J and Chinese Mathematicians in Seventeenth Century

Abstract

The discourse between Jesuits and Chinese scholars in seventeenth century China brings some significant progress in building a mutual understanding between the West and the East at a level of logical practices. This chapter studies the shared practices of Matteo Ricci and Chinese mathematicians in seventeenth century when they translate Euclid’s Elements into Jihe yuanben, and introduces how they make it possible to introduce Aristotelian logic to Chinese people through geometry. The author claims that the gap between concepts proper relations of associations (zheng 正) in Chinese logic and logical validity in Aristotelian logic cause some major difficulties in introducing Aristotelian logic to Chinese people. In a Chinese language-game, there is no concept of logical validity. Practicing the rule Ostensive Definitions, Ricci and Chinese mathematicians, together, demonstrate for Chinese learners how to understand syllogistic patterns through particular cases. The conclusion of this paper is that Chinese logic and Aristotelian logic are very different. The effort of seeking for proper relations of associations (zheng 正) has no comparison to seeking for logical validity. However, attempts to understand the unfamiliar and the novel are common to all human beings. Whether a mutual understanding is possible, the effort must be made from both sides.