Abstract

Our previous research showed that the semantic tableau deductive methodology of Fitting and Smullyan permits boundary-case exceptions to the second incompleteness theorem, if multiplication is viewed as a 3-way relation (rather than as a total function). It is known that tableau methodologies prove a schema of theorems verifying all instances of the law of the excluded middle. But if one promotes this schema of theorems into formalized logical axioms, then the meaning of the pronoun of ‘I’, used by our self-referencing engine, changes quite sharply. Our partial evasions of the second incompleteness theorem shall then come to a complete halt.

中文翻译：

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关于细线的刻画，该细线将语义表推论下的第二个不完全性定理的推广和边界情况例外分开

摘要

我们以前的研究表明，如果将乘法视为三向关系（而不是总函数），则Fitting和Smullyan的语义表演绎方法允许第二种不完全性定理有边界情况例外。众所周知，Tableau方法论证明了一个定理的方案，该定理验证了排除中间律的所有实例。但是，如果有人将这种定理模式提升为形式化的逻辑公理，那么我们的自引用引擎所使用的“ I”代词的含义就会发生急剧变化。然后，我们对第二个不完全性定理的部分逃避将完全停止。