数学基础理论中的千古悬案——科学哲学——芝诺悖论、贝克莱悖论和罗素悖论新解  

The Suspending Critical Defects in the Foundation of Mathematics——the Philosophy of Science——A New Exploration on Zeno's Paradox,Berkeley's Paradox and Russell's Paradox

作　　者：欧阳耿[1] 

机构地区：[1]漳州师范学院数学系,福建漳州363000

出　　处：《喀什师范学院学报》2009年第6期30-36,共7页Journal of Kashgar Teachers College

摘　　要：结合新发现的经典无穷观和与之相关的经典数量体系中所存在的缺陷,从基础理论学的新思路,分析、揭示了悬而未决的芝诺悖论、贝克莱悖论和罗素悖论这三大悖论家族所暴露的自古以来就存在于数学基础理论中与"有穷-无穷"概念相关内容的缺陷,并认为,自古以来由于受"重形式-轻本体"这种错误思路的影响,数学与科学哲学基础理论中与"有穷-无穷"概念相关的那部分内容非常薄弱,导致了三大悖论家族的产生与不断繁荣壮大,使人们无法真正认清这三大悖论的本质,从而决定了由它们所揭示的问题在现有科学理论体系中一直无法得到解决.Connecting with the newly discovered defects in the classical infinite theory and its relating number system, the long being fundamental defects relating to the ＂finite-infinite＂ concepts in the basic theories of mathematics exposed by the three suspending paradox families of Zeno＇s Paradox, Berkeley＇s Paradox and Russell＇s Paradox are further analyzed and disclosed with the new ideas and thinking ways of basitheoryology. Two conclusions are drawn： the contents relating to the ＂finite-infinite＂ concepts in the basic theories of mathematics and the philosophy of science are very weak due to the wrong thinking and working way of ＂form superior to thing-in-itself＂ and this is the main reason for the birth and the continuously developing of the three paradox families. It is also the very reason that makes people failed to understand clearly the natures of these three paradoxes and makes those defects exposed by the three suspending paradox families unsolvable in present science. In this article, the natures of these three paradoxes are further explored and the new ways to solve the problems disclosed by the three paradoxes are sought.

关 键 词：新无穷观 新数量体系 芝诺悖论 贝克莱悖论 罗素悖论 数学基础 基础理论学 科学哲学 

分 类 号：O143[理学—数学] B028[理学—基础数学]