Varieties of Self-Reference in Metamathematics

被引：1

作者：

Grabmayr, Balthasar ^{[1
]}

Halbach, Volker ^{[2
,3
]}

Ye, Lingyuan ^{[4
]}

机构：

[1] Univ Haifa, Dept Philosophy, Haifa, Israel

[2] Univ Oxford, Oxford, England

[3] New Coll, Oxford, England

[4] Univ Amsterdam, ILLC, Amsterdam, Netherlands

来源：

JOURNAL OF PHILOSOPHICAL LOGIC | 2023年 / 52卷 / 04期

关键词：

Self-reference; Arithmetic; Intensionality; Diagonalization; Well-foundedness; Uniformity; Henkin sentence;

D O I：

10.1007/s10992-022-09696-y

中图分类号：

B81 [逻辑学（论理学）];

学科分类号：

010104 ; 010105 ;

摘要：

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 Godel's diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

引用

页码：1005 / 1052

页数：48

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