再谈反证法的可操作性——基于对角线法在图灵论文中的应用

Introduction to the operability of reduction to absurdityagain——based on the application of diagonal process in Turing's thesis

一般观点都认为,图灵停机问题是应用康托尔对角线的一个重要成果,而很少注意到图灵的对角线实际上完全与康托尔不同。特别值得注意的是,尽管图灵最终还是落入了隐性假设的陷阱,但他对于这个问题实际上是早有警惕的。在图灵的论文中,除了图灵机这一重要的概念之外,更富启发性的其实并不是他的证明,反而是他所批判的一个谬误;只要做一些适当的改进,这个所谓的谬误就是反驳康托尔的有力证据。

General point of view,the Turing outage problem is an important achievement in cantor diagonal,and rarely notice,Turing diagonal in fact completely different from cantor. Particularly noteworthy is that although Turing eventually fall into the trap of implicit assumption,but he is actually have alert on this issue.In Turing＇s paper, in addition to an important concept of Turing machines,more inspiring wasn＇t his proving,instead is a fallacy that he criticizes;As long as we do some appropriate improvement,the so-called fallacy is the powerful evidence to refute cantor.