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

共 50 条

[31] Program Self-Reference in Constructive Scott Subdomains
John Case
Samuel E. Moelius
Theory of Computing Systems, 2012, 51 : 22 - 49
[32] Program Self-reference in Constructive Scott Subdomains
Case, John
Moelius, Samuel E., III
MATHEMATICAL THEORY AND COMPUTATIONAL PRACTICE, 2009, 5635 : 89 - 98
[33] Four Paradoxes of Self-Reference: The Being of the Universal
Moss, Gregory S.
JOURNAL OF SPECULATIVE PHILOSOPHY, 2014, 28 (02) : 169 - 189
[34] SELF-REFERENCE AND THE DIVORCE BETWEEN MEANING AND TRUTH
Tsohatzidis, Savas L.
LOGIC AND LOGICAL PHILOSOPHY, 2013, 22 (04) : 445 - 452
[35] Finding relevance in the news: The scale of self-reference
Barchas-Lichtenstein, Jena
Voiklis, John
Glasser, Darcey B.
Fraser, John
JOURNAL OF PRAGMATICS, 2021, 171 : 49 - 61
[36] Cantor Diagrams: A Unifying Discussion of Self-Reference
G. M. Germano
S. Mazzanti
Applied Categorical Structures, 2003, 11 : 313 - 336
[37] Depressive cognition: Self-reference and depth of processing
Wisco, Blair E.
CLINICAL PSYCHOLOGY REVIEW, 2009, 29 (04) : 382 - 392
[38] Self-reference modulates the perception of visual apparent motion
Huang, Jianrui
Chen, Lihan
Zhou, Xiaolin
ATTENTION PERCEPTION & PSYCHOPHYSICS, 2023, 85 (01) : 188 - 195
[39] Self-reference in psychosis and depression: a language marker of illness
Fineberg, S. K.
Leavitt, J.
Deutsch-Link, S.
Dealy, S.
Landry, C. D.
Pirruccio, K.
Shea, S.
Trent, S.
Cecchi, G.
Corlett, P. R.
PSYCHOLOGICAL MEDICINE, 2016, 46 (12) : 2605 - 2615
[40] Characterizing Programming Systems Allowing Program Self-Reference
John Case
Samuel E. Moelius
Theory of Computing Systems, 2009, 45 : 756 - 772

← 1 2 3 4 5 →