Roger Penrose and the Gödelian Argument Against AI

In my recent post of the New Yorker article by Jim Holt on what Einstein and Gödel talked about on their walks in Princeton, Holt writes about Gödel:

He believed he had shown that mathematics has a robust reality that transcends any system of logic. But logic, he was convinced, is not the only route to knowledge of this reality; we also have something like an extrasensory perception of it, which he called “mathematical intuition.” It is this faculty of intuition that allows us to see, for example, that the formula saying “I am not provable” must be true, even though it defies proof within the system where it lives. Some thinkers (like the physicist Roger Penrose) have taken this theme further, maintaining that Gödel’s incompleteness theorems have profound implications for the nature of the human mind. Our mental powers, it is argued, must outstrip those of any computer, since a computer is just a logical system running on hardware, and our minds can arrive at truths that are beyond the reach of a logical system.

Some people, like my friend Timo Hartmann, have pounced on this as proof of their conviction that computers will never be able to think like humans. Unfortunately, they are on thin ice. Penrose’s argument, set out in detail in his book Shadows of the Mind, is shaky at best, sometime’s outright bizarre, and in the end, just wrong. For a good rebuttal of Penrose, see what Hilary Putnam wrote in a review of Shadows of the Mind:

[Shadows of the Mind] will be hailed as a “controversial” book, and it will no doubt sell very well even though it includes explanations of difficult concepts from quantum mechanics and computational science. And yet this reviewer regards its appearance as a sad episode in our current intellectual life. Roger Penrose is the Rouse Ball Professor of Mathematics at Oxford University and has shared the prestigious Wolf Prize in physics with Stephen Hawking, but he is convinced by–and has produced this book as well as the earlier The Emperor’s New Mind to defend–an argument that all experts in mathematical logic have long rejected as fallacious. The fact that the experts all reject Lucas’s infamous argument counts for nothing in Penrose’s eyes. He mistakenly believes that he has a philosophical disagreement with the logical community, when in fact this is a straightforward case of a mathematical fallacy.

Read the rest of Putnam’s review here.

And here, if you need more, is a whole list of References for Criticisms of the Gödelian Argument.