Gödel's Incompleteness Theorem And Its Implications For Artificial Intelligence - deep ideas

McCullough also addresses the fact that Penrose's argument rests on the assumption that human reasoning is consistent and that human beings can be sure of their own consistency. He argues that this assumption is not beyond doubt and presents a thought experiment in order to show how inconsistencies could turn up even during careful and justified reasoning. He proposes to imagine an interrogator asking questions that can be answered by yes or no, and an experimental subject that can answer these questions by pressing a'yes' button or a'no' button. If the interrogator asks the question "Will you push the'no' button", then this question cannot be answered truthfully. The subject knows that the true answer is'no', but he cannot communicate this answer by pressing the'no' button.