“数学研究纲领方法论”何以可能?——拉卡托斯之后数学哲学研究的新发展

Establishment of “methodology of mathematics research programs” :is it possible

拉卡托斯有意把他的科学研究纲领方法论推广应用到他的拟经验的数学哲学中去,建立起“数学研究纲领法论”.拉卡托斯的“科学研究纲领方法论”赖以建立的两个前提是自然科学的经验性和可证伪性,那么对于数学,其是否也有与经验科学一样的完全的经验性质呢?数学能象经验科学一样被证伪吗?这是建立“数学研究纲领方法论”必须首先解决的问题.本文正是围绕这一问题,对拉卡托斯后继者在这一方向上的数学哲学研究作了简要的介绍和分析,以期引起对“‘数学研究纲领方法论’何以可能?”这一问题的深入讨论和研究.

Lakatos based'his methodology of scientific research programs on the premises of empiricism and fallibilitism. Does mathematics have the same empirical features as science? Does mathematics show fallibilitism as well? These are questions Lakatos had to answer when he tried to build his methodology of mathematics research programs. The present paper discusses the above problems and attempts a brief introduction and analysis of the study of mathematical philosophy by Lakatos' followers, with the hope that the problem of the possible establishment of methodology of mathematics research programs will arouse much discussion and an interest in further study.