Abstract We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about the Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.

中文翻译：

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可能有许多算术哥德尔句子†

摘要 我们认为，在服从哥德尔第一不完备定理的足够强的算术理论的通常假设下，如果没有不当之处，就不能谈论该理论的哥德尔句子。原因是，在不违反哥德尔定理的要求的情况下，如果理论不可靠，则可能存在真句和假句，每一个都可证明等同于其在理论中的不可证明性。