关于数学中自指可能性的一个注记
A Note on the Possibility of Self-Reference in Mathematics
摘要：
在本文中，我们提出了一个解释的自我指涉命题的“元模型”N* 的ZF。这个元模型N* 被认为是数学家在处理数论时经常使用的非正式算术模型。具体来说，我们假设在这个元模型中，公理系统ZF被应用，可以提供对句子的解释，并且可以使用自然语言。我们表明，根据建议的解释，一些类型的自指命题，被认为是合法的数学N* 变成一个不一致的模型，并检查这个结果的连接到哥德尔的第一不完全性定理的某种解释。然后讨论了从上述讨论中得出的一些一般性问题。
英文摘要：
In this paper we propose an interpretation for self-referential propositions in a "meta-model" N* of ZF. This meta-model N* is considered as an informal model of arithmetic that mathematicians often use when working with number theory. Specifically, we assume that within this meta-model, the axiom system ZF is applied, interpretations for sentences can be offered, and natural language can be used. We show that under the proposed interpretation, some types of self-referential propositions that are considered legitimate in mathematics turn N* into an inconsistent model, and examine the connection of this result to a certain interpretation of godel's first incompleteness theorem. Some general problems which follow from the above discussion are then addressed.
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