In the proof of Gödel's incompleteness theorem the Diagonalization Lemma is applied to the negated provability predicate $¬Prov_F(x)$: this gives a sentence $G_F$ such that
$F ⊢ G_F ↔ ¬Prov_F(⌈G_F⌉) $,
where F is the formal system and $⌈G_F⌉$ the Gödel number of $G_F$. To rest of the proof is a fairly straightforward task.
What I'm concerned about is the interpretation of $G_F$: Many sources interpret the assertion of it to be 'This sentence is unprovable'. I know, $¬Prov_F(⌈G_F⌉)$ seems to suggest this but strictly speaking the Diagonalization lemma purports $¬Prov_F(⌈G_F⌉) $ follows from $G_F$ and vice versa, nothing more.
So what does it mean for a sentence to assert its own unprovability? A proposition saying 'This sentence is unprovable' seems to have no content since 'This sentence' is not specified. What sentence is unprovable?
Just to stress, I've no problem with the proof of Gödel's incompleteness theorem. I just don't understand the expression in the metalanguage.