关于极限论对Berkeley悖论之解释方法的分析与研究  

Analysis of and Research on the Method Interperation of the Limit Theory for Berkeley Paradox

作　　者：黄秀琴[1] 朱梧槚[2] 

机构地区：[1]南京晓庄学院行知学院,江苏南京211171 [2]南京航空航天大学信息科学与技术学院,江苏南京210016

出　　处：《南京晓庄学院学报》2011年第6期13-17,共5页Journal of Nanjing Xiaozhuang University

摘　　要：该文是文献[5]的续篇,由于文献[1]之2.5论证指出:当代极限论没有给Berkeley悖论留下任何有关0/0一类悖论生成余地或隙缝.(文献[1]P26),文献[5]在确认潜无限(poi)与实无限(aci)在ZFC框架内是无中介矛盾对立面(p,-p)前提下,论证结论是当代极限论所留给Berkeley悖论有关0/0一类悖论的,远不止一个隙缝,而是一个大窟窿.但文献[1]之2.5与2.6还有诸多针对文献[2]之6.7.3的质疑,本文旨在质疑文献[1]对文献[2]的每一条质疑,结论是文献[1]针对文献[2]之任何一条相关的质疑都是没有根据的.并在逻辑数学层面上对文献[1]中所谓"双相无限"概念略作评论.This paper is the sequel of Reference [ 5 ] . As demonstrated in 2.5 of Reference [ 1 ] that there is no any room for a class of 0/0 paradoxes generated or apertured, such as the Berkeley Paradox in the limit theory, Reference [ 5 ] recognizes that there is no intermediary conflicts （p, -p） between the potential infinity （poi） and the actual infinity （aci） in ZFC. On this premise, it has proved there are more paradoxes, such as 0/0 in the limit theory. However, there are a lot of doubts proposed in 2.5 and 2.6 of Reference [ 1 ] concerning 6.7.3 of Reference [ 2 ] . This paper is to question each doubt proposed in Reference [ 1 ] for questioning Reference [ 2 ]. It is concluded that there is no basis for any of the questions of Reference [ 1 ] for Reference [ 2 ]. Meanwhile, the paper makes some comments on the concept of ＂two-phase infinity＂ in Reference [ 1 ] at the Mathematical logic level.

关 键 词：潜无限 实无限 极限论 近代公理集合论 中介逻辑 

分 类 号：O211.4[理学—概率论与数理统计]