This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

中文翻译：

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元数学中自我参照的多样性

本文研究了在哪些条件下可以采用对角线句子来构成自我参照的范例。我们对对角运算符和编码设备提出了动机良好的约束，这些约束将范式自指句子（例如通过哥德尔的对角化方法获得）与偶然的对角句子分开。特别是，我们表明这些约束成功地排除了 Kreisel 构造的可反驳的 Henkin 句子。