Is G true by Gödel's theorem?
Is G true by Gödel's theorem?

Summary/Abstract: Two philosophical arguments, e.g. that the meaning of an expression transcends its use and that the human arithmetical thinking is not entirely algorithmic (the argument Lucas/Penrose) base their theses on Gödel's first incompleteness theorem. But both in these arguments and in some of their criticisms the word "true" is often used ambiguous: it swings between a licit metamathematical use and an illicit transfer of it in a formal system. The aim of this paper is to show the way these arguments are connected, via G-type sentences (sect 2), and how do we argue that the sentence G, albeit unprovable in PA, is true, by using non-conservative extensions of PA with reflections (sect 3). And this without any illicit use of “true”.

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