罗素悖论的两个现代翻版——康托在集合论中的两个证明  

Two Modern Versions of Russell's Paradox——Cantor's Two Proofs in Set Theory

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》2008年第3期26-30,共5页Journal of Kashgar Teachers College

摘　　要：从经典无穷理论体系中的缺陷入手,分析了康托的实数集合不可数证明及康托定理S<P(S)证明与罗素悖论之间的本质性联系,发现它们与罗素悖论有完全相同的思路,但是康托犯了两个逻辑性错误而误用了这个悖论思路,使他这两个证明成了罗素悖论的两种畸形的翻版,并得到两个明确的结论——康托这两个证明中的思路与做法是错误的,这样的证明结果不具科学性;是现有经典无穷理论体系基础理论的致命缺陷导致这类错误的必然发生、存在与被认可.From the defects in the basic theory of present classical infinite theory, the essential relationship between Cantor＇ s proofs of the uncountability of real number set and the Cantor＇ s Theorem of S ==S 〈 ===P（S）and Russell＇s Paradox is analyzed. A mysterious error is found： the very same paradoxical idea was applied in both Russell and Cantor＇s work but Cantor made wrong use of this paradox idea with two logical mistakes. Thismade Cantor＇s above two important proofs in set theory actually became another two deformed versions of Russell＇s paradox. Two conclusions are drown the ideas and operations in Cantor＇s above two proofs are wrong and the results are not scientific at all, it is the fatal defects in the basic theory of present classical infinite theory that make such mistakes possible.

关 键 词：罗素悖论 实数集合不可数性 康托定理 无穷理论体系 认识论 逻辑 

分 类 号：O144.2[理学—数学]