Never trust an unsound theory

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Theoria 88 (5):1053-1056 (2022)
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Abstract

Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in fact not Gödel sentences.

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10.1111/theo.12408

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References found in this work

Solution of a problem of Leon Henkin.M. H. Löb - 1955 - Journal of Symbolic Logic 20 (2):115-118.
There May Be Many Arithmetical Gödel Sentences.Kaave Lajevardi & Saeed Salehi - 2021 - Philosophia Mathematica 29 (2):278–287.
Aspects of Incompleteness.Per Lindström - 1999 - Studia Logica 63 (3):438-439.
On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.

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