Penrose's Gödelian argument. A Review of Shadows of the Mind by Roger Penrose
Feferman (Solomon)
Source: Psyche, 2(7), May 1995
Paper - Abstract

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Introduction (Full Text – “Penrose Redux”)

  1. In his book Shadows of the Mind [SOTM below], Roger Penrose has turned in another bravura performance, the kind we have come to expect ever since The Emperor's New Mind [ENM] appeared. In the service of advancing his deep convictions and daring conjectures about the nature of human thought and consciousness, Penrose has once more cut a wide swath through such topics as logic, computation, artificial intelligence1, quantum physics and the neurophysiology of the brain. Moreover, along the way, without condescension, he has done a brilliant job of explaining difficult mathematical and scientific ideas in a broadly appealing fashion <1>. While the aims and a number of the topics in SOTM are the same as in ENM, the focus here is much more on the two axes Penrose grinds in earnest. Namely, in the first part of SOTM he argues anew and at great length against computational models of the mind and more specifically against any account of mathematical thought in computational terms. Then in the second part, he argues that there must be a scientific account of consciousness but that it will require a (still to be found) non-computational extension or modification of present-day quantum physics.
  2. I am only competent to say something substantive about the first part of the new effort, resting as it does to a considerable extent on a version of Gödel's (first) incompleteness theorem. Penrose had advanced that previously in ENM, but the line of argument was much criticized, as it had been in the past when advanced by others (e.g. J.R. Newman and E. Nagel, and J.R. Lucas) <2>. So now Penrose has gone to great lengths in SOTM to lay out his Gödelian argument and to try to defend it against all possible objections. I must say that even though I think Gödel's incompleteness theorems are among the most important of modern mathematical logic and raise fundamental questions about the nature of mathematical thought, and even though I am convinced of the extreme implausibility of a computational model of the mind, Penrose's Gödelian argument does nothing for me personally to bolster that point of view, and I suspect the same will be true in general of readers with similar convictions. On the other hand, I'm sure that those whose sympathies lie in the direction of a computational model of mind will find reasons to dismiss the Gödelian argument quickly on one ground or another without wading through its painful elaboration. If I'm right, this effort -- diligent as it is -- is largely wasted. Nevertheless, since Penrose has done it, I feel obliged to address at least the more technical aspects of his argument.
  3. While I have disavowed competence concerning Part II of SOTM, I can't help registering my impression that the effort there is entirely quixotic. What Penrose aims to do is substitute one "nothing but" theory for another: in place of "the conscious mind is nothing but the action of a computer" he wishes to have "the conscious mind is nothing but the manifestation of sub-atomic physics". Can we really ever expect a completely reductive theory of one sort or another of human cognition? Surely, no one theory will serve to "explain" the myriad aspects of this phenomenon. As with any other scientific study of human beings -- inside and out -- such an enterprise will need to continue to make use of psychology, psycho-physics, physiology (neuro- and otherwise), biochemistry, molecular biology, physics (macro- and micro-) and who knows what all else (including computational models of all kinds). In my opinion Penrose's "missing science of consciousness" is a mirage.

Comment:

Review of "Penrose (Roger) - Shadows of the Mind"; Link (Defunct).

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