Self-Reference Upfront: A Study of Self-Referential Gödel Numberings

Review of Symbolic Logic 16 (2):385-424 (2023)
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Abstract

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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Citations of this work

Gödel’s Theorem and Direct Self-Reference.Saul A. Kripke - 2023 - Review of Symbolic Logic 16 (2):650-654.
There May Be Many Arithmetical Gödel Sentences.Kaave Lajevardi & Saeed Salehi - 2021 - Philosophia Mathematica 29 (2):278–287.
Essential hereditary undecidability.Albert Visser - 2024 - Archive for Mathematical Logic 63 (5):529-562.
Varieties of Self-Reference in Metamathematics.Balthasar Grabmayr, Volker Halbach & Lingyuan Ye - 2023 - Journal of Philosophical Logic 52 (4):1005-1052.
A Step Towards Absolute Versions of Metamathematical Results.Balthasar Grabmayr - 2024 - Journal of Philosophical Logic 53 (1):247-291.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Toward useful type-free theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.
Gödel’s Theorem and Direct Self-Reference.Saul A. Kripke - 2023 - Review of Symbolic Logic 16 (2):650-654.

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