摘要
与物理学史上5个重大物理理论相关的5个数学空间,在本体、认识与方法上也表现出有规律的哲学特征:在欧几里得空间中,本体、认识与方法之间是一种分立关系;在黎曼流形、希尔伯特空间、纤维丛与卡-丘空间中,本体、认识与方法之间分别都有交集,并且这种交集依次在增大,即从部分相交到大部分相交再到渐进融合。
Associated with five landmark theories in the history of physics, there are five mathematical spaces in mathematics, which display regular philosophical features ontologically, epistemologically and methodologically. In Euclidean space, the ontology, epistemology and methodology are discrete. In Riemann manifold, Hilbert space, fiber bundle and Calabi-Yau manifold, the ontology, epistemology and methodology overlap respectively, and their overlaps increase successively: from partly overlap to mostly overlap, and then to gradual integration.
出处
《科学技术哲学研究》
CSSCI
北大核心
2016年第4期84-95,共12页
Studies in Philosophy of Science and Technology
基金
教育部人文社科重点研究基地重大项目"数学
物理学的关系与科学理论的语境模型研究"(13JJD720012)
关键词
数学空间
哲学特征
分立关系
相交关系
融合关系
mathematical space
philosophical feature
discrete relationship
intersection relationship
gradual inte-gration