摘要
数学可应用性问题一直未能被很好的解释,近期一种结构主义进路的"映射"理论被提出,认为可以仅仅通过诉诸数学与其所应用的领域之间的结构相似性来解释数学的可应用性。但该理论无法解释在某些数学应用的情况中,为何一些数学解无物理对应物。从认知的角度引入一种与映射理论相容的数学认知理论,通过解释数学与其所应用的领域之间结构相似性的认知来源,可以解释映射理论无法说明的问题。通过分析一个具体的自由落体方程负数解的案例可以展现从认知进路解释数学可应用性的可行性。
The applicability of mathematics has always not been explained well. A mapping account wanted to explain it by appealing to structural similarity between mathematical structure and structure of the world. But this mapping account couldn＇t explain why some mathematical solution have not physical counterpart. I try to explain the applicability of mathematics by explaining where structural similarity comes from by a cognitive theory of mathematics. And I will analyze a case about free failing body which have a negative mathematical solution with no physical counterpart.
出处
《自然辩证法研究》
CSSCI
北大核心
2014年第4期35-40,共6页
Studies in Dialectics of Nature
关键词
数学可应用性
数学认知
自由落体
applicability of mathematics
mathematical cognition
free falling body
