禁止使用自指代命题——说谎者悖论的排除和哥德尔定理的讨论
发布时间：2019-03-07 20:21
【摘要】：应把“自指代命题”从“自指命题”中区分出来,前者违反同一律,作代换还可能违反矛盾律,因此禁止使用自指代命题。对内容不明的自指命题作真假对错的评判,不可能给出确定的结论,但也不会出现矛盾。说谎者悖论是一个佯悖。它被称为悖论,是因为推理者混淆了思维的层次,构造了自指代命题并进行代换才导致矛盾。哥德尔不完全性定理所构造的自指代命题的可证性存在矛盾的双重标准,定理的证法中共用了矛盾的双重标准,其结论值得商榷。结论中的“不可判定”命题,现在有三种不同的错误解释:是非不可分辨的命题(三值)、是非可分辨但不确定的命题(二值)、除自指代命题之外的是非都不可证的其他命题,它们都不是哥德尔的证法所支持的结论。它导致“真理丧失说”和“数学丧失了确定性”缺乏依据。
[Abstract]:"self-referential propositions" should be distinguished from "self-referential propositions". The former violates the same identity and may violate the law of contradiction. Therefore, the use of self-referential propositions is prohibited. It is impossible to give a definite conclusion, but there will be no contradiction in judging the true or false right or wrong of the self-referential proposition with unknown content. The liar's paradox is a feint. It is called paradox because the reasoning person confuses the thinking level, constructs the self-referential proposition and carries on the substitution only then causes the contradiction. The proof of self-referential proposition constructed by Godel's incompleteness theorem has a double standard of contradiction. The proof of theorem is proved by the double standard of contradiction, and the conclusion is worth discussing. There are now three different misinterpretations of the "indeterminable" proposition in the conclusion: a non-indistinguishable proposition (ternary), a non-discernible but uncertain proposition (binary), Except for self-referential propositions, none of them is supported by Godel's proof. It leads to a lack of evidence for the loss of truth and the loss of certainty in mathematics.
【作者单位】： 中国人民大学现代逻辑研究所
【分类号】：B815
本文编号：2436427
[Abstract]:"self-referential propositions" should be distinguished from "self-referential propositions". The former violates the same identity and may violate the law of contradiction. Therefore, the use of self-referential propositions is prohibited. It is impossible to give a definite conclusion, but there will be no contradiction in judging the true or false right or wrong of the self-referential proposition with unknown content. The liar's paradox is a feint. It is called paradox because the reasoning person confuses the thinking level, constructs the self-referential proposition and carries on the substitution only then causes the contradiction. The proof of self-referential proposition constructed by Godel's incompleteness theorem has a double standard of contradiction. The proof of theorem is proved by the double standard of contradiction, and the conclusion is worth discussing. There are now three different misinterpretations of the "indeterminable" proposition in the conclusion: a non-indistinguishable proposition (ternary), a non-discernible but uncertain proposition (binary), Except for self-referential propositions, none of them is supported by Godel's proof. It leads to a lack of evidence for the loss of truth and the loss of certainty in mathematics.
【作者单位】： 中国人民大学现代逻辑研究所
【分类号】：B815
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