三谈反证法的可操作性——基于蕴涵怪论与哥德尔不完全性定理  

Introduction to the operability of reduction to absurditythirdly——based onparadoxes of implication and Godel's incompleteness theorem

作　　者：黄汝广 

机构地区：[1]深圳南天电力有限公司,广东深圳518040

出　　处：《大众科技》2017年第5期132-134,146,共4页Popular Science & Technology

摘　　要：文章认为,蕴涵关系"P→Q"基于命题P与Q的真值约定是不可取的,而应该将其定义为有效推理,这样不但可以解决通常所谓的蕴涵怪论,更可以使我们对反证法有新的认识。实际上,由于"已知事实"的被忽略,反证法的两种常见模式——"~P→P,所以P"与"~P→Q,~P→~Q,所以P"——都是存在问题的;为此,在所谓的标准模式中,笔者特别强调了"已知事实"的重要性。最后,通过梳理哥德尔不完全性定理的整个证明过程,发现了三个导致其证明无效的重要因素:(1)根据"定理Ⅴ"推导的式(15)(16)有误,并且两式的"或"关系,被误当作了"与"关系;(2)使用了反证法的不当模式,也即"~P→Q,~P→~Q,所以P";(3)在肯定前件式的假言推理中,由于概念混淆造成了前件被肯定的假象。This paper argues that the appointed true value of implication relationship ＂P→Q＂ based on P and Q is not desirable,and should be defined as the effective reasoning,such not only can solve the so-called usually paradoxes of implication,more can make us have new understanding of reduction to absurdity.Actually, because of the known facts neglected,two kinds of common mode of reduction to absurdity-＂-P→P, so P＂and＂-P→Q,-P→-Q,so P＂-is wrong;Therefore,in the so-called standard model,the author particular emphasis on the importance of the known facts.Finally, by combing the proof process of godel＇s incompleteness theorem,found three important factor which causes theproof is invalid：（1）the derived formulas（15）（16）according to the ＂theorem V＂ are wrong,and then the ＂or＂ relationship of two formulas has been mistaken for the ＂and＂ relationship;（2） using the error model of reduction to absurdity, namely ＂- P→Q, P→- Q,so P＂;（3） in modus Ponens ,the precondition is mistakenly identified due to confusion of concepts.

关 键 词：蕴涵怪论 有效推理 反证法 事实 哥德尔不完全性定理 

分 类 号：B81[哲学宗教—逻辑学]