论文部分内容阅读
我们可以在符号语言层面对数学对象进行认识上的考察。利用符号学理论中索绪尔和皮尔斯对符号定义的基本思想,可以提出人对数学对象的认识存在两种基本的认识结构①:“所指-能指”结构与“手段-对象”结构。只有这两种认识结构的互补,才能给出人对数学对象认识的一个整体的解释。从数学知识的产生和发展来看,“手段-对象”结构在两种结构中占主导地位,因此,人对数学对象的认识发展会表现出两个层次、三个发展阶段的具体形态。
We can make an understanding of mathematical objects at the symbolic level. Using Saussure and Pierce ’s basic idea of symbolic definition in semiotic theory, we can say that there are two basic cognitive structures of human understanding of mathematical objects: ① “” means - means “structure and ” means - the object “structure. Only by complementing these two kinds of cognitive structures can we give an overall explanation of our understanding of mathematical objects. Judging from the emergence and development of mathematical knowledge, the ”means-object" structure dominates the two structures. Therefore, people’s understanding and development of mathematical objects show two forms and three forms of development .