CAJ | 학술논문

数学结构主义的兴起，为数学基础这一传统问题注入了新的活力。尤其是范畴论能否取代集合论在数学基础问题中的统治地位，已成为数学基础问题研究的主要争论之一。文章以范畴论为基本立场，首先分析集合论基础所面临的困境，系统阐述范畴结构主义的基本内容，最后通过模态结构主义与范畴结构主义之间的论争，为作为数学基础的范畴论做辩护。
수학결구주의적흥기，위수학기출저일전통문제주입료신적활력。우기시범주론능부취대집합론재수학기출문제중적통치지위，이성위수학기출문제연구적주요쟁론지일。문장이범주론위기본립장，수선분석집합론기출소면림적곤경，계통천술범주결구주의적기본내용，최후통과모태결구주의여범주결구주의지간적논쟁，위작위수학기출적범주론주변호。
The rise of mathematical structuralism has injected new vitality to studies on mathematical foundation. It has become one of the main topics whether or not category theory can replace the dominance of set theory as founda- tion of mathematics. Based on category theory, this paper analyzes the dilemmas the set theory is faced with, articu- lates the basic ideas of categorical structuralism and justifies the category theory by illuminating the argument between modal structuralism and categorical structuralism.