建部贤弘的数学认识论--论《大成算经》中的"三要"

“象形”、“满干”和“数”,是日本江户时代数学家建部贤弘在《大成算经》中所讨论的三个范畴 ,也是该书的纲纪 ,谓之“三要”。这些范畴来源于中国传统文化中的术数 ,语言晦涩 ,一直为日本数学史界所忽视。文章从中国数学文化传统出发 ,重新解读这些文字 ,提出一些全新的观点。认为在汉字文化圈数学家中 ,建部贤弘在中国象数学文化背景下 ,首次系统地阐述了数学科学的本质 ,讨论了数学研究对象及其存在性问题 ,并已接触到数学变量的讨论 ,同时对实数系给出了一种分类。其“三要”数理观是汉字文化圈数学认识论的突出反映 ,具有数学哲学意义。

Takebe Katahiro's Epistemology of Mathematics

xiang xing,man gan and shu are three categories discussed in Daisei Sankei,written by the Japanese mathematician Takebe Katahiro of the Edo era. They are also disciplines in Daisei Sankei,and are called sanyao(three main points).Stemming from shushu in traditional Chinese culture,these categories are hard to understand, and are ignored in the history of Japanese mathematics all the time. This paper, which proceeds from the cultural tradition of Chinese mathematics, interprets these words again, and puts forward some completely new viewpoints. The paper considers that among the mathematicians of Using Chinese Characters, Takebe Katahiro was the first to state systematically the essence of mathematics science,discussed an object of mathematics and its existence,involved the discussion to mathematics variable, and categorized the real number system under the cultural sphere of Chinese xiangshu xue.His mathematical standpoint of sanyao is a reflection of epistemology of mathematics of Using Chinese Characters, and has mathematics philosophy significance.