I think it is worth pointing out that the Lucas-Penrose argument goes beyond Gödel's disjunction: apparently Gödel himself could not rule out both sides of his

I think it is worth pointing out that the Lucas-Penrose argument goes beyond Gödel's disjunction: apparently Gödel himself could not rule out both sides of his disjunction being true, but Penrose, expanding Lucas's argument[1] to book length, thinks he can. It seems, however, that most experts now find their arguments inadequate[2], and the speaker in this video is prominent among them. Wikipedia has a short summary of some of the objections[3], and I think Minsky's is particularly to the point: as humans can believe false ideas to be true, human mathematical understanding need not be consistent and consciousness may easily have a deterministic basis. [1] http://cogprints.org/356/1/lucas.html http://cogprints.org/356/1/lucas.html [2] https://www.maa.org/press/maa-reviews/g-dels-disjunction https://www.maa.org/press/maa-reviews/g-dels-disjunction [3] https://en.wikipedia.org/wiki/Penrose%E2%80%93Lucas_argument#Criticism https://en.wikipedia.org/wiki/Penrose%E2%80%93Lucas_argument...