∃G (G ↔ ~Provable(G))
“there exists a proposition that is materially equivalent to a statement of its own unprovability.”
If G was Provable this contradicts its assertion: G is not Provable.
If ~G was Provable this contradicts its assertion: G is Provable
Therefore G is neither Provable nor Refutable and does not exist.
If G was false then it would be ~Provable (F ↔ T) is false
If G was true then it would be ~~Provable (T ↔ F) is false
∴ ~∃G (G ↔ ~Provable(G))
Copyright 2018 Pete Olcott