There May Be Many Arithmetical Gödel Sentences

Philosophia Mathematica 29 (2):278–287 (2021)
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Abstract
We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.
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First archival date: 2021-02-20
Latest version: 2 (2022-01-26)
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