There May Be Many Arithmetical Gödel Sentences
Philosophia Mathematica 29 (2):278–287 (2021)
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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2021-02-15
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2021-02-15
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97 ( #50,850 of 69,180 )
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16 ( #45,150 of 69,180 )
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