A deflationary account of the truth of the Gödel sentence $$mathcal{g}$$
pp. 71-90
in: Gabriele Lolli, Marco Panza, Giorgio Venturi (eds), From logic to practice, Berlin, Springer, 2015Abstrakt
We give a negative answer to the question of whether our conviction about the truth of the Gödel sentence (mathcal{G}) involves a theory of truth beyond the deflationary theories (Shapiro, J Philos 95:493–521, 1998; Ketland, Mind 108:69–94, 1999; Tennant, Mind 111:551–582, 2002; Ketland, Mind 114:75–88, 2005; Tennant, Mind 114:89–96, 2005; Cieśliński, Mind 119:409–422, 2010). After discussing and dismissing Neil Tennant's deflationary account of incompleteness, we show how a new deflationary construal of the incompletability of formal systems can be framed in the setting of Peano Arithmetic augmented to include a constructive version of the ω-rule based on Herbrand's notion of prototype proof.
