There’s a lot more going on in that paper than an occasional reference to Penrose:
In this paper I argue that, contrary to Gödel’s assertion, his argument for the existence of “formally undecidable but intuitively true propositions” in the formal system of standard PA [Peano Arithmetic] (and other “systems” that are symbolically sufficient to formalise Intuitive Arithmetic recursively) is not clearly “constructive and intuitionistically unobjectionable”.
It says: “I argue that [the author’s material] leads to the collapse of the Gödelian argument advanced by J.R.Lucas, Roger Penrose and others.”
Well, duh! Fail—for taking Penrose’s nonsense seriously.
There’s a lot more going on in that paper than an occasional reference to Penrose: