数学认识活动中的主客体关系

The Relation between Subject and Object in Mathematical Knowledge Pursuits

本文通过讨论数学认识活动中的主客体关系,首先引入数学认识客体的三个层次:即现实世界的量及其关系可以看作外在于人的较原始的认识客体;作为思想事物的纯的数学研究对象是内在于人的较高层次的认识客体;界于这两个层次之间中间层次的认识客体是在人们头脑中形成相应的数学的生理——心理结构。接着在分析皮亚杰关于发生认识论的研究的基础上,通过继承与发展,阐述了在数学认识活动中,主体和客体是怎样相互作用的。最后以上述的思想观点为指导,分析了数学哲学中争议较多的一些问题。

In this paper, through the relation between subject and object in mathematical knowledge pursuits, firstly, we introduce the three stratifications on mathematical knowledge object: Namely, the quantities in real world and their relation may be regard as more primitive knowledge object out of man; as target of purely mathematical studies of ideological things is the knowledge object of higher stratification in man; the knowledge object of intermediate stratification between two stratifications is corresponding mathematical physiology formed by man's brains-psychological structure. On the basis of analysing Peajie's study about happening theory of knowledge, through interitance and development, we go on to expound that subject and object are how to act on each other in mathematical knowledge pursuits. Lastly, by above-mentioned thinking and viewpoint as guidance we analyse more disputed problems in mathematical philosophy.