态射的建构与发展:发生认识论的一种动态形式化

发生认识论主要研究认识的心理发生及其形式化。对于后者的研究,上个世纪30年代皮亚杰建构了“群集”结构来解释儿童前运算阶段的思维方式,70年代又引入了数学范畴论来解释形式运算阶段的认知发展,再一次对儿童思维的发展与科学发展两者间的连续性给出了明证。数学范畴论是对数学对象的结构间变换进行形式化的一个数学分支,建构的思想以及对所建构结构进行转换是范畴论的本质,而其中作为范畴对象的态射与态射组合体现了其建构本质,且能最为妥贴地描述认识的动态发生与发展。新的理论建模将对应与转换揉合在一起更好地阐释认知发展过程中每一转换过程的机制与结构发展。本文试图通过介绍认识发生过程中对应、转换的发展,以及所引入数学范畴论中态射的概念,来阐释认识发生中认知生成工具———态射———的建构与发展,以及认知结构的系统发展,从而对皮亚杰晚年这一形式化工作予以简单说明与评价。

The Construction and Development of Morphism: A Kind of Dynamic Formalization on Piaget's Genetic Epistemology

Genetic Epistemology focus on the psychogenetic and its formalization. In 1930s,Piaget explained the development of children's thinking on their preoperational stages by means of constructing "groupment";and reinterpreted their formal stage with the theory of categories in 1970s,which provided the evidence on the continuum between the development of children and science again.As a branch of mathematic,the theory of category aims at formalizing transformation on the mathematical structure.As its object,Morphism is fit for describing the dynamic genetic and development.The new theory construction is characterized by mechanism of the process and structural development by integrating the correspondence and transformation which are introduced in this paper.Moreover,we describe morphism and its construction and development during the course of psychogenetic and therefore estimate the work in Piaget late year.