Proceedings of the XXIII World Congress of Philosophy

Volume 55, 2018

Philosophy of Logic

Is G True by Gödel’s Theorem?

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 Lucas/Penrose argument) base their theses on Gödel’s first incompleteness theorem. But in both these arguments and in some of their criticisms the word “true” is often used ambiguously: 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 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”.