和算家对中国数学思想的接受与重构  

The Acceptance and Reconstruction of Chinese Mathematical Thought by Traditional Japanese Mathematicians

作　　者：徐泽林 XU Zelin(Institute of History,College of Humanities,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学人文学院历史研究所,上海201620

出　　处：《自然科学史研究》2022年第3期364-382,共19页Studies in The History of Natural Sciences

基　　金：国家自然科学基金项目“江户时代日本学者对《授时历》的历理分析与算法改进”(项目编号:11873024);东华大学中央高校基本科研业务费专项基金项目:中华文明及其现代转型研究基地(项目编号:2232019H-02)

摘　　要：通过对和算书中序跋和理论阐述较多的《大成算经》(1711)、《缀术算经》(1722)、《方圆算经》(1739)、《自然算法》(方圆亭,1809)、《圆理算经》(1843)、《数学夜话》(1761)、《数学夜话评林》(1808)等文献的解读,聚焦于东亚传统数学思想中有关数学本体论、数学方法论、数学价值观以及无穷思想这四个侧面展开历史分析,认为江户时期和算家一方面保持对汉文化的认同,对汉文化中有关数学起源及功用的论述完整接受,另一方面又以宋明理学(特别是象数学)范畴对中国古代数学论加以重构,以理学思想建构和算的数学方法论与数学认识论,尝试以易纬象数理论建构无穷极限的理论。This paper analyzes the mathematical thought of the Edo period and its relationship with the Neo-Confucianism of the Song and Ming dynasties through a study of the prefaces and postscripts of the wasan books Daisei Sankei《大成算經》(Comprehensive Classic of Mathematics,1711),Tetsujutsu Sankei《綴術算經》(Art of Assembling,1722),Hoen Sankei《方圓算經》(Algorithms for squares and circles,1739),Shizen Sanpō《自然算法》(Natural algorithm,1809),Enri Sankei《圓理算經》(Algorithms for circles,1843),Sugaku Yawa《数学夜話》(An Evening Talk about Mathematics,1761),and Sugaku Yawa Hyorin《数学夜話評林》(Review of An Evening Talk about Mathematics,1808).The paper focuses on four aspects of traditional mathematical thought in East Asia:mathematical ontology,mathematical methodology,mathematical values and infinite limit.The author thinks that in the Edo period,against the background of Japanese national cultural consciousness,on the one hand,wasan mathematicians maintained the identity of Chinese traditional culture,integrally accepted the mathematical theories about the origin and function of mathematics in Chinese traditional culture,while on the other hand,they rebuilt the ancient Chinese mathematical theories based on the categories of Neo-Confucianism(for instance,image-numerology)in the Song and Ming dynasties.At the same time,again based on Neo-Confucianism,they constructed the mathematical methodology and epistemology of Japanese traditional mathematics,and tried to construct the theory of infinite mathematics with images.

关 键 词：和算 数学思想 理学 象数学 重构 

分 类 号：N09[自然科学总论—科学技术哲学]