Before revision: Still, this criticism only works if we assume that we can replace Lucas' reasoning with a formal system that has a Gödel sentence, but the Penrose-Lucas argument tries to prove otherwise: our ability to understand this level of arithmetic is not a formal system that can be simulated in a Turing machine.
After revision: Still, this criticism only works if we assume that we can replace Lucas' reasoning with an effective procedure that has a Gödel sentence, but the Penrose-Lucas argument tries to prove otherwise: our ability to understand this level of arithmetic is not a formal system that can be simulated in a Turing machine.