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 an effective procedure that can be simulated in a Turing machine.
After revision: Still, this criticism only works if we assume that Lucas is attaining the truth of the sentence using a logical proof , but the Penrose-Lucas argument tries to prove otherwise: our ability to understand this level of arithmetic is not an effective procedure whichbased on the classical idea of provability nor is it can be simulated in a Turing machine.