Penrose–Lucas argument

The Penrose–Lucas argument is a logical argument partially based on Kurt Gödel's first incompleteness theorem. In 1931, Gödel proved that every effectively generated theory capable of proving basic arithmetic either fails to be consistent or fails to be complete. John Lucas and Roger Penrose postulate that this incompleteness does not apply to humans, and conclude that humans can have mathematical insights that Turing machines can't. Penrose and Stuart Hameroff proposed a quantum explanation, and used it to provide the basis of their theory of consciousness: orchestrated objective reduction. The argument is rejected by most scholars.

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