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Gödel’s Theorem and Direct Self-Reference
Review of Symbolic Logic 16 (2):650-654 (2023)
Abstract
In his paper on the incompleteness theorems, Gödel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that ‘direct’ self-reference can actually be used to prove his result.Author's Profile
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Citations of this work
Self-Reference Upfront: A Study of Self-Referential Gödel Numberings.Balthasar Grabmayr & Albert Visser - 2023 - Review of Symbolic Logic 16 (2):385-424.
A Step Towards Absolute Versions of Metamathematical Results.Balthasar Grabmayr - 2024 - Journal of Philosophical Logic 53 (1):247-291.
Essential hereditary undecidability.Albert Visser - forthcoming - Archive for Mathematical Logic:1-34.
HYPER-REF: A General Model of Reference for First-Order Logic and First-Order Arithmetic.Pablo Rivas-Robledo - 2022 - Kriterion – Journal of Philosophy 36 (2):179-205.
References found in this work
Self-reference in arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
Self-Reference Upfront: A Study of Self-Referential Gödel Numberings.Balthasar Grabmayr & Albert Visser - 2023 - Review of Symbolic Logic 16 (2):385-424.
Self-reference and the languages of arithmetic.Richard Heck - 2007 - Philosophia Mathematica 15 (1):1-29.
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