표준해석학과 비표준해석학의 패러다임 관점에서 본 ‘제논의 역설’

Abstract

This study has analyzed the phenomenon that Zeno’s paradox is still not completely resolved despite the explanation of a geometric series from the perspectives of the ‘spontaneous’ meaning of ‘everyday language’ as well as ‘standard analysis and non-standard analysis’. As a result of analyzing the philosophers’s arguments, the ‘arriving moment’ on the continuum of time expressed in Zeno’s paradox contained a meaning of non-standard analysis. Kant says that time and space are human transcendental forms of intuition. In Zeno's paradox and its dissolution, time is expressed in terms of non-standard analysis, and space is expressed by the limit of a geometric series in terms of standard analysis. Since the two types of intuition of human beings are expressed in different mathematical theories, Zeno’s paradox is not completely solved by the geometric series. This study suggests that the difficulty of mathematical understanding can be attributed to the use of different mathematical structures or paradigms.