以标准分析和非标准分析两种微积分观点看运动论题和黑格尔的辩证法——答陈晓平教授《商榷》一文  

On the Proposition of Motion and Hegel’s Dialectics from the Views of Standard Analysis and Non-standard Analysis——an Answer to Professor Chen Xiaoping

作　　者：张华夏[1] ZHANG Huaxia(Department of Philosophy,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]中山大学哲学系

出　　处：《山东科技大学学报（社会科学版）》2019年第6期26-32,共7页Journal of Shandong University of Science and Technology(Social Sciences)

摘　　要：陈晓平教授对笔者此前发表的两篇论文提出了质疑,而陈文提出无理数(如■、■、■等)是指一个无限小区间,这是违反常识的。至于贝克莱将无穷小看作“死去了的量的鬼魂”,他的批评不是指极限论的无限的小的潜无限,而是指莱布尼茨的实无限小。用实无限小分析运动问题是当代重大课题,这就是非标准分析的运动观,可惜陈文没有从这个方面来讨论问题。笔者在此从标准分析和非标准分析两种微积分观点来探讨哲学上的运动论题和黑格尔的辩证法,并着重以非标准分析微积分的基本概念,分析矛盾辩证法和芝诺悖论的解决。Professor Chen Xiaoping has questioned my two previously published papers, which discuss dialectical proposition of Hegel and Zeno’s Paradoxes. Professor Chen argues that irrational numbers, such as■and so on, belong to infinitesimal intervals, which is against commonsense. As to the fact that George Berkeley claims infinitesimals as "the ghosts of departed quantities", what he criticizes is not potential infinity with infinitesimals in the limit theory, but the real infinitesimals proposed by W.V. Leibnitz. To analyze the proposition of motion with real infinitesimals, i.e. the non-standard analysis view of motion, is an important project in calculus nowadays. It is unfortunate that Professor Chen fails to discuss the problem from this perspective. Therefore, this paper discusses the proposition of motion and Hegel’s dialectics from the points of view of standard analysis and non-standard analysis in calculus, and focuses on the basic concepts of the non-standard analysis in calculus, and uses them to resolve the contradictory dialectics and Zeno’s Paradoxes.

关 键 词：标准分析 非标准分析 “运动”论题 矛盾辩证法 实无穷小 无限地小 

分 类 号：N031[自然科学总论—科学技术哲学]