Penrose's theory of Objective Reduction predicts the relationship between quantum mechanics and general relativity. For this reason, the argument is sometimes called the Penrose-Lucas argument). An earlier version of the argument was given by J. (The argument was first given by Penrose in The Emperor's New Mind (1989) and is developed further in Shadows of The Mind. He takes this disparity to mean that human mathematicians are not describable as formal proof systems and are not running an algorithm, so that the computational theory of mind is false, and computational approaches to artificial general intelligence are unfounded. The essence of Penrose's argument is that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Gödel-type results are provable by human mathematicians. Further to that, for any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory. In 1931, the mathematician and logician Kurt Gödel proved his incompleteness theorems, showing that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Main article: Orch-OR § The Penrose–Lucas argument The human mind has abilities that no Turing machine could possess because of this mechanism of non-computable physics.Īrgument Mathematical thought.
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