On the Limits of Artificial Intelligence

In The Emperor's New Mind, and in the later Shadows of the Mind, Sir Roger Penrose argues that human intelligence is not purely computational by appeal to Godel's Theorem. Basically the argument is this: given that every minimally complex and consistent system of proof (such as that constituted by the average PC) contains sentences that are true but unprovable in that system, there are truths comprehensible to the human mind that cannot be programmed into a computer, from which it follows that the human intelligence is not purely computational. Penrose' argument -sometimes known as the "Penrose-Lucus argument" - has been heavily criticized by mainstream academia, and its conclusion rejected. In this note the argument is defended by identifying Godel's Theorem as a member of a broader class of statements whose incomprehensibility by any artificial computational device is unambiguous. Moreover, it is argued that natural quantum computers are not subject to the limit that puts these statements beyond the reach of artificial computational devices, and so that Penrose' proposal that the human mind has a quantum computer at its disposal is the appropriate explanation of why human mathematicians succeed where man-made computers are bound to fail.