错用罗素悖论——康托在集合论中的两个逻辑性错误  

Misusing Russell's Paradox——Cantor's Two Logical Errors in Set Theory

作　　者：欧阳耿[1] 

机构地区：[1]漳州师范学院数学系,漳州363000

出　　处：《数学理论与应用》2008年第3期44-49,共6页Mathematical Theory and Applications

摘　　要：分析了罗素悖论与康托的实数集合不可数证明及康托定理■<■证明之间的本质性联系,发现康托的这两个非构造性证明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使他误用了这个悖论思路。得到明确的结论:康托在集合论中如上两个证明里的核心部分实际上是罗素悖论的翻版,这两个证明中的思路与做法是错误的,这样的证明结果没有科学性。Through a new analysis on the essential relationship betwen Russell＇s Paradox and Cantor＇s proof on the uncountability of real number set and the proof on the Cantor＇ s Theorem of S〈P（S）, two mysterious errors were found： The very same idea was applied in both Russell and Cantor＇s work,but Cantor made wrong use of it with two logical mlstakes.A conclusion is drown： The core of Cantor＇ s ahove two important proofs in set theory are acturally another version of Russell＇s paradox,the ideas and operations in the two Cantor＇ s proof are wrong and the results are not scientific at all.

关 键 词：康托定理S〈P(S) 实数集合不可数性 罗素悖论 无穷理论体系 部分 全体 认识论 逻辑 

分 类 号：O144.2[理学—数学]