本根论新探——辅以数学0的数理分析

New Exploration of the Root Theory── Mathematical Analysis Supplemented by 0

宇宙中之最究竟者,古代哲学中谓之"本根"。"本根"的称谓,各家并不统一。比如,《老子》称之为"无",道家称之为"一",《易传》称之为太极。《老子》中对于"本根"有诸多描述,相应的称谓亦有多种。周敦颐提出"无极而太极",从而导致鹅湖之辩,但是朱陆双方争而无果。关于"本根"的认知,存在诸多错误表现:误将"本根"意义上的"一"直接对应数学上的"1";误将阴爻对应数学上的"0";误将"无极"视为0维空间,将"太极"视为一维空间;误将"有"和"无"视为一对矛盾;误以为"太极本于无极"。已有认知中最根本的错误在于,以为"一""多"构成二元矛盾关系。借助数理分析可以明确两点:一是,惠施的"本根"二元论超越"一""多"二元论,即"大一""小一"才是真正的二元矛盾关系。二是,数学上的"本根"【0】是单象限空间。

The ultimate thing in the universe is called Original Root in ancient philosophy. The title of Original Root is not uniform. For example,Lao Tzu calls it None,Taoism calls it One,and Yi Zhuan calls it Tai Chi. There are many descriptions of Original Root in Lao Tzu,and there are many corresponding titles. Zhou Dun-yi proposed Wu Chi to Tai Chi,which led to the debate on the Goose Lake,but Zhu and Lu argued to no avail. There are many wrong expressions on the cognition of Original Root:mistakenly matching one in the sense of Original Root directly with"1"in mathematics;mistakenly mapping Yin with"0";Wu Chi is regarded as a 0-dimensional space,and Tai Chi is regarded as a one-dimensional space;Being and None are mistakenly regarded as a pair of contradictions;and Tai Chi is inherent to Wu Chi. The most fundamental error in the existing cognition is the idea that one and many constitute a dual contradiction relationship. With the help of mathematical analysis,two points can be clarified. One is that Hui Shi’s Original Root dualism transcends"one"and"multi"dualism,that is,the"big one"and"small one"are the true dual contradictory relationships;the other is that Original Root[0]in mathematics is a single quadrant space.