Incompleteness is sometimes used to refute the existence of an [[omnipotent]] [[God]]: If God were omnipotent, he would act as an [[oracle]] (in the mathematical sense) for any mathematical theory. That is, he could decide for any statement S whether S or not-S were true, which contradicts incompleteness. This argument is a more formal version of the "Can God make a rock even He could not move" [[paradox]]. | Incompleteness is sometimes used to refute the existence of an [[omnipotent]] [[God]]: If God were omnipotent, he would act as an [[oracle]] (in the mathematical sense) for any mathematical theory. That is, he could decide for any statement S whether S or not-S were true, which contradicts incompleteness. This argument is a more formal version of the "Can God make a rock even He could not move" [[paradox]]. |