重新获得的Paradel：超越Goedel阴影的生活
Paradox regained: Life beyond Goedel's shadow
摘要：
哥德尔明确的论文是，他的不可判定公式GUS是一个良好的形式，良好定义的正式句子在任何形式化的直觉算术IA的公理和规则的推理是递归定义。他的隐含论点是，在任何这样的系统中，GUS都不是形式上不一致的。我认为，在一个建设性的，直观上无可非议的，和递归定义的形式化PP IA的GUS是一个合式公式，但不明确的正式句子，反映了“骗子”悖论PP。此外，引入“形式真理”和“可证明性”的价值观IA通过PP选择的命题导致卢卡斯的哥德尔的论点崩溃。
英文摘要：
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit thesis was that GUS is not formally inconsistent in any such system. I argue in a constructive, intuitionistically unobjectionable, and recursively definable formalisation PP of IA that GUS is a well-formed formula but an ill-defined formal sentence reflecting the "Liar" paradox in PP. Further, introducing "formal truth" and "provability" values to selected propositions of IA through PP leads to the collapse of Lucas' Goedelian argument.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
