布尔巴基结构主义与希尔伯特形式主义的比较研究  

Bourbaki's Structuralism and Hilbert's Formalism

作　　者：黄秦安[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《科学技术哲学研究》2016年第5期1-6,共6页Studies in Philosophy of Science and Technology

基　　金：2012年度陕西省社会科学基金项目"范式转换下的数学哲学研究纲领"(12C003)

摘　　要：20世纪初,为克服朴素集合论悖论,构建坚实的数学基础,形式主义者提出了宏伟的"希尔伯特纲领",哥德尔不完全性定理的发表使得形式主义的整体目标以失败告终。重建数学基础的问题再次变得迫切。布尔巴基学派应运而生,逐渐崭露头角并迅猛发展,对20世纪纯粹数学的发展产生了至深的影响。无论是从哲学还是数学的视角看,形式主义与布尔巴基结构主义之间既有着难以分割的联系,又有着许多本质上的差异。两者的共性显示了其在揭示数学知识本质上的哲学深度,而两者之间的异质差异性见证了20世纪数学知识多样恢宏的范式转换。In the early 20th century, in order to overcome a series of paradoxes arising from the naive set theory, formalists put forward the grand ＂Hlibert Programme＂ to build a firm foundation for mathematics but ended in fail- ure because of the publication of Godel＇ s incompleteness theorem. Rebuilding the foundation of mathematics be- came urgent again. It is at this moment that the school of Bourbaki emerged and developed prosperously. It has deeply influenced the progress of pure mathematics in the 20th century. Formalism and Bourbaki structuralism are both closely related and essentially different either from the philosophical or the mathematical perspective. Their common properties show their philosophical profoundity in revealing the essence of mathematical knowledge while their differences witness the splendid and diverse paradigm shift of mathematical knowledge in the 20th century.

关 键 词：布尔巴基 形式主义 结构主义 元数学 公理化 数学知识范式 

分 类 号：N02[自然科学总论—科学技术哲学]