莱布尼茨二进制形成中的概念变化分析

An Analysis of the Conceptual Evolution throughout the Formation of Leibniz's Binary System

有关莱布尼茨二进制与中国古代典籍《易经》关系问题的讨论涉及到如何看待近代中西文化的各自特质以及它们之间的相互作用问题。虽然二进制只是一种算术记数法和计数法,但它实际上是特定文化(包括数学、语言、符号、逻辑和哲学等)的产物。现有观点中的一个明显不足是把与二进制相关的概念、理论(原理、符号等)的形成与发展看作是单因素的、一次性完成的结果,又把二进制与《易经》哲学和卦图的相互作用关系看作是"全或无"的关系,从而忽视了概念、理论的形成和变化过程,也容易导致两种极端的判断。因此,立足于近代中西文化交流的大背景,从概念与认知分析入手,能够把莱布尼茨二进制思想的形成过程置于近代中西文化交流所编织的概念网络系统之中,进而梳理出莱布尼茨在秉承西方近代数学概念的同时,如何通过获取和吸纳《易经》概念资源而实现概念的创造性转换的脉络。我们看到,除了莱布尼茨个人的独创性的伟大贡献外,近代意义上的二进制实际上是"中西合璧"的产物。

Discussions on the relationship between Leibniz's binary system and ancient Chinese document Yi jing(Classic of Changes)involve how to view the respective unique qualities of Western and Chinese cultures and the interplay between them.Although the binary system is no more than a system of numeration and method of counting,it was actually aproduct of a specific culture(including mathematics,language,symbols,logic,and philosophy).An obvious defect of current points of view is they consider formation and evolution of the concepts and theories[i.e.,principle,symbols,and so on]related to the binary system to be a single element and the result of one time accomplishment,and that they view the binary system either as completely derived from or as having nothing to do with Yi jing philosophy including diagrams of the trigrams and hexagrams,neglecting the process of the formation and evolution of the concept and theory.This defect can easily lead to two extremely different judgments.Therefore,on the basis of the broad background of Chinese-Western cultural exchanges,and through conceptual and cognitive analysis,the process of formation of Leibniz's binary system can be placed in the conceptual web woven in Chinese and Western cultural communications in premodern times,and the context in which how Leibniz hadrealized the creative change of the concept through obtaining and adopting the conceptual resources of the Yi jing when he was handling Western mathematical concepts can further be clarified.It can be seen that besides Leibniz's personal ingenious contributions,the binary system in modern sense was actually aproduct of the combination of Chinese and Western elements.