哥德尔不完全性定理
Goedel's Incompleteness Theorem
摘要：
我以直观的方式提出了哥德尔第一不完全性定理的证明，同时涵盖了所有技术上具有挑战性的步骤。我提出的推广哥德尔的不动点引理两句和多句的版本，允许证明不完整性，通过循环版本的骗子的悖论。我讨论的关系，哥德尔的第一和第二不完备性定理哥德尔的完备性定理，并结束与评论的影响，这些结果的数学，计算，理论的心理和人工智能。
英文摘要：
I present the proof of Goedel's First Incompleteness theorem in an intuitive manner, while covering all technically challenging steps. I present generalizations of Goedel's fixed point lemma to two-sentence and multi-sentence versions, which allow proof of incompleteness through circular versions of the liar's paradox. I discuss the relation of Goedel's First and Second Incompletneness theorems to Goedel's Completeness theorems, and conclude with remarks on implications of these results for mathematics, computation, theory of mind and AI.
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。
