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《Studies In The History of Natural Sciences》 2002-03
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Takebe Katahiro's Epistemology of Mathematics

XU Zelin(Department of Mathematics,Tianjin Normal University,Tianjin 300074; Institute of Mathematics,Academy of Mathematics and System Science,CAS ,Beijing 100080,China)  
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.
【CateGory Index】: O113.13
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【References】
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