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本文作者是美国纽约州立大学数学系教授。他从客观性原则出发,认为数学是一门客观的科学,并对数学哲学中的形式主义、直觉主义、逻辑主义和柏拉图主义作了分析和评论,引起数学界一些人的重视。例如S.M.莱恩说:“数学哲学中的这些学派或理论没有一个对数学的本质作出令人满意的分析。N.D.古德曼最近写的一篇文章《数学是一门客观的科学》,对这种缺陷作了令人信服的分析。最近发表的数学哲学方面的一些著作,从普特兰、奎因到王浩,都很少提出新的见解,很少从数学输入新的东西”(《数学译林》1989年第2期第136—144页)。为了使读者了解古德曼的工作,我把它翻译出来,供读者参考。
The writer is a professor of mathematics at New York State University in the United States. Starting from the principle of objectivity, he considered mathematics as an objective science and analyzed and commented on formalism, intuitionism, logicism and Platonism in mathematical philosophy, arousing the attention of some people in mathematics. For example, SM Lane said: “None of these schools or theories in mathematical philosophy offers a satisfactory analysis of the nature of mathematics.” Goodman, a recent article written by Goodman, “Mathematics is an objective science” Defects have been convincingly analyzed.Many published works on philosophy of mathematics, from Putland, Quinn to Wang Hao, rarely put forward new ideas, rarely enter new things from mathematics “(” Mathematics Yilin "1989 the second issue 136-144). In order for the reader to understand Goodman’s work, I translated it for readers’ reference.