My questions arose when reading an article about artificial intelligence, and the argument of Penrose that says that humans can see the truthfulness of statements that machines cannot. But it doesn't say what those "Godel sentences" are. http://en.wikipedia.org/wiki/Philosophy_of_artificial_intelligence#Lucas.2C_Penrose_and_G.C3.B6del "Roger Penrose expanded on this argument in his 1989 book The Emperor's New Mind and his 1994 book Shadows of the Mind. He presents a complex argument, and there are many details that need to be considered carefully. However the essence of it is that It is impossible for a Turing machine to enumerate all possible Godel sentences. Such a program will always have a Godel sentence derivable from its program which it can never discover Humans have no problem discovering these sentences and seeing the truth of them"