A Note on Gödel, Priest and Naïve Proof

In the 1951 Gibbs lecture, Godel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naive proof, to the effect that Godel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naive proof, in agreement with Godel’s conception, superseding the criticisms against the usual notion of naive proof used by real working mathematicians. We explore the connection between Godel’s theorem and naive proof so understood, both from a classical and a dialetheic perspective.