摘要
"什么是数"是一个重要的哲学议题,数学哲学与数学史的实作转向使得从历史的角度解答该议题成为可能。宋代是中国传统数学的高峰,学科间的兼并与重组导致了数学内容的扩大和数的多种分类,并在数的表达与其所运用的领域间形成对应。故南宋杨辉用多种方式表达数在运算中的不同位置和功能,反映出运算位置也被认为与数的本质相关。因此,探究"什么是数"不应局限于印度-阿拉伯数码,应将该议题作为一个开放的研究纲领,会产生更有力的科学史研究实践。
"What is number"is an important philosophical issue. The practical turn in the philosophy and history of mathematics makes it possible to solve this problem from the perspective of history. Song Dynasty was the peak of Chinese mathematics. The continuous annexation and reorganization of disciplines led to the expansion of mathematical content. Scholars produced a variety of classifications of numbers, and gradually formed a correspondence between the representations of numbers and the fields they used. Therefore, Yang in the Southern Song Dynasty used many ways to express the different positions and functions of numbers in operations. This reflects the positions in operations are also considered to be related to the essence of numbers. As a result, the study of the nature of numbers should not be limited to the Hindu-Arabic numerals;taking it as an open research program will lead to a powerful practice in the study of the history of science.
作者
朱一文
ZHU Yi-wen(Department of Philosophy&Institute of Logic and Cognition,Sun Yat-sen University,Guangzhou 510275,China)
出处
《自然辩证法研究》
CSSCI
北大核心
2020年第12期98-102,共5页
Studies in Dialectics of Nature
基金
国家社会科学基金重大项目“桐城方氏学派文献整理与研究”(19ZDA030)。
关键词
宋代
杨辉
数学实作
数的表达
数的用法
Song Dynasty
Yang Hui
mathematical practice
representations of numbers
uses of numbers
