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”.
What do you think of this paper arguing that Godel’s reasoning is not constructively valid?
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: