"Julio Di Egidio" <email@example.com> wrote in message news:firstname.lastname@example.org... > "Peter Percival" <email@example.com> wrote in message > news:firstname.lastname@example.org... > >> Gödel's first published proof of his incompleteness theorem was entirely >> syntactical. It described a formula, which I'll call G, such that >> neither G nor ~G is a theorem of a theory he called P, just so long as P >> is omega consistent. > > Just so long as P is true:
Sorry, I meant of course G.
> indeed the proof is purely syntactical only under a strictly formal > paradigm, where the importance of a pre-formal (or meta-theoretical) > recognition of truth is simply overlooked.