张行成先天数学初探——三论中国数学派

A preliminary research on ZHANG Xing-cheng's theory of primordial numbers

南宋易学家张行成是继邵雍之后的又一位数学派哲学家,在"象"与"数"的内涵和关系问题上,认为"象"为卦爻象,"数"为奇偶数;先数后象,由数生象。在"理"与"数"问题上,主张数生于理。提出"理数"的概念,以"理数"为宇宙万物的本体。通过对"太极"的阐释,进一步表明"数本论"思想。认为"太极"是兼包理气、虚实、动静之"数"。通过《易》《玄》的比较说明"先天图"为浑天象,"太玄图"为盖天象。先天图实际上反映的是先天数。由"象"而推及"数",由"数"而推及"理",由"理数"而说明天道规律和宇宙本体,是张行成象数哲学的最大特色。

ZHANG Xingcheng, an expert at Yilearning in the Southern Song Dynasty, is another philosopher of the school of numberology. For the connotations of and correlations between images and numbers, he holds that images refer to images of the hexagrams and those of the lines, numbers refer to odd or even numbers; numbers are prior to images, and the numbers produce the images. For the relationship between the (Yi) principles and numbers, ZHANG insists the latter are produced from the former. More over, he raised the concept of 'number of principle' and regards it as the noumenon of the myriad beings. By explicating Taiji, he further exhibits his thought of 'numberontology', holding that Taijisimultaneously comprise principles and Qi, solidness and emptiness, moving and stillness. By comparing Yiand Tai xuan, he concludes that the 'Primordial Diagram' reflects an image of celestial globe, but the 'Tai xuan Diagram' an image of the sky covering the earth. The 'Primordial Diagram' actually reflects the primordial numbers. ZHANG's imagenumber philosophy numbers' from 'images', inferring 'principles' is distinctively characterized with inferring 'from 'numbers', and explicating the norm of the Dao (Way) of heaven and cosmic noumenon by 'principles of number'.