摘要
欧几里得几何是第一个公理化体系,非欧几何的出现促使人们对它的基础作了严格审视,其中希尔伯特公理化方法最为成功;但它的相容性问题一直没有解决,集合论悖论使得这个问题更加尖锐。虽然集合论的公理化一度时期曾化解了悖论给公理化方法所带来的危机,但不久哥德尔不完全性定理就深刻地揭露了公理化方法不可避免的局限性。尽管后来的布尔巴基学派的结构数学使公理化方法更上一层楼,但仍然无法克服公理化方法本身的局限性。
Euclid geometry is the first system of Axiomatizing and non-Euclid geometry causes the strict examination to Euclid geometry. In the try to build a new base of geometry, Hilbert＇s axiomatizing is the best one. But there is an important problem that its consistence can＇t be proved. The appearance of paradox of set theory makes this problem more poignant. Although the axiomatize of set theory dispels the crisis of axiomatizing in some time. Theory of incompletion of Godel drastically exposes the limitation of axiomatizing itself. The method of structure of 13ourbakian can＇t conquer this limitation.
出处
《太原理工大学学报（社会科学版）》
2006年第2期34-38,共5页
Journal of Taiyuan University of Technology(Social Science Edition)
关键词
欧几里得几何
公理化
相容性
历史发展
局限性
Euclid geometry
Axiomatizing
consistence
historical development
limitation
