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International Studies in Phenomenology and Philosophy

Book | Chapter

176845

A deflationary account of the truth of the Gödel sentence $$mathcal{g}$$

Mario Piazza Gabriele Pulcini

pp. 71-90

Abstract

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.

Publication details

Published in:

Lolli Gabriele, Panza Marco, Venturi Giorgio (2015) From logic to practice: Italian studies in the philosophy of mathematics. Dordrecht, Springer.

Pages: 71-90

DOI: 10.1007/978-3-319-10434-8_5

Full citation:

Piazza Mario, Pulcini Gabriele (2015) „A deflationary account of the truth of the Gödel sentence $$mathcal{g}$$“, In: G. Lolli, M. Panza & G. Venturi (eds.), From logic to practice, Dordrecht, Springer, 71–90.