扩展Cantor Partial
Extending Cantor Paradox
摘要：
在集合论的基础上所涉及的不一致性总是由无穷大和自指引起的;只有通过适当的公理限制才能消除它们。纵观历史，这两个概念已被证明是一个取之不尽的矛盾和矛盾的来源。因此，似乎有理由对其形式上的一致性提出一些问题。这正是本文的目的所在。本文从康托悖论的一种延伸--实无穷的不一致性出发，简要回顾了康托悖论的争议历史，并提出了一种基于w-序的新的批评方法。本文还从句法和语义的角度对自指进行了分析。这一批评影响了哥德尔第一不完全性定理的形式化句子及其日常语言解释。
英文摘要：
The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to be an exhaustible source of paradoxes and contradictions. It seems therefore legitimate to pose some questions concerning their formal consistency. This is just the objective of this paper. Starting from an extension of Cantor's paradox that suggests the inconsistency of the actual infinity, the paper makes a short review of its controversial history and proposes a new way of criticism based on w-order. Self-reference is also examined from a critique perspective which includes syntactic and semantic considerations. The critique affects the formal sentence involved in Godel's first incompleteness theorem and its ordinary language interpretation.
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。
