自我指涉前期：自指哥德尔数研究
Self-reference Upfront: A Study of Self-referential Gödel Numberings
摘要：
在本文中，我们研究各种要求下，自我参考可以充分形式化的算术形式化的选择。特别是，我们研究了自指编号，它立即提供了一个强大的概念，即使是表达弱的语言的自指。本文的结果表明，真正的自我参考推理是否可以在算术形式化的问题是更敏感的基本编码装置比通常认为的。作为一个案例研究，我们展示了这种敏感性如何影响自我指涉真理的某些原则的正式研究。
英文摘要：
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study of certain principles of self-referential truth.
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