Doubting of a shadow

Beyond the doubting of a shadow

Roger Penrose


A reply to commentaries on on ‘Shadows of the Mind’ published in Psyche

This article covers Penrose’s replies to various attacks on his second consciousness book, ‘Shadows of the Mind’ in the interdisciplinary journal ‘Psyche.’

Penrose points out the apparent implausibility of the suggested ways of getting round the implications of Gödel’s theorem, such as an unknowable algorithm, or unsound mathematical reasoning. He remarks on the ‘almost religious fervour’ and often abusive manner of many of the supporters of the computationalist view, and on the fact that even more moderate commentators tend to assume, what they are supposed to be proving, that computationalism has to be right, and that the Gödelian argument cannot be serious.

This should not surprise. It is not necessary to read very much scientific literature or discussion forum material related to consciousness, to get the picture of a whole body of opinion that has an essentially metaphysical stance rooted in the obsolete assumptions of 19th century physics.

Patricia Churchland’s approach in her criticism of Penrose is interesting in this respect. She remarks that a majority of logicians reject Penrose’s view and appears to consider this a conclusive argument against the Gödelian case, apparently removing the necessity to present any actual argument. But on closer examination, a lot of this majority view comprises a fixed metaphysical stance rather than a reasoned argument.

Penrose says that most the Psyche commentator’s criticisms have been directed at the Gödelian aspect of ‘Shadows in the Mind’, rather than the discussion relative to objective reduction of the wave function or the possible instantiation of quantum coherent processes in the brain. Some critics appear to argue that there is no need to discuss these other aspects, because they have disproved the Gödelian case.

Penrose, however, says that the arguments from physics and biology could stand up even without Gödel. This appears to be reasonable. The fact that mathematical understanding was computationally based would still leave us looking for a description of consciousness, which might still be non-computational or in some way linked to fundamental physics. A non-mathematician might well have approached the whole thing differently, avoiding the fraught issue of mathematical reasoning, and going straight to the problem of deriving consciousness from matter. Similarly the arguments about the microtubules relate only to biological factors, and are not at all linked to Gödel.

Penrose first discusses the arguments of David Chalmers, the only one of his Psyche critics for whom he seems to have much patience. Chalmers argued that it was contradictory ‘to know that we are sound’ with reference here to mathematical understanding, but Penrose takes the view that the whole point of mathematical procedures is that they instil a belief in their proof procedures and their soundness.

A good part of the discussion about the Gödel theorem and its consequences is taken up with arguments about mathematicians who make errors, that is situations where mathematical understanding is not apparently sound. Penrose’s argument is that he is thinking in terms of either an idealisation or at least the development of human mathematical understanding over the medium to longer term. He is concerned with what mathematicians are able to perceive in principle by methods of mathematical proof, while short term errors of understanding are seen as correctable, and given time mathematical arguments usually become correct. Some of the critics point to longer term errors of understanding such as Kempe’s attempt to prove the four-colour theorem and Frege’s inconsistent formal set theory, but Penrose views these as correctable errors.

Penrose is particularly critical of one commentator, Drew McDermott in this respect. McDermott claimed ‘to have torn Penrose’s arguments to shreds’, but Penrose remarks that McDermott went of at a tangent, and did not actually discuss the arguments given in ‘Shadows of the Mind.’ McDermott is seen to have a problem with the concept that guaranteeable mathematical assertions may not be computable, but Penrose asserts that this is the way mathematics works. David Chalmers, to a limited extent, appears to agree with Penrose in the view that mathematicians have an underlying sound competence, even if it sometimes goes astray.

Penrose claims that many of the Psyche critics twist the argument away from his claim that the principles underlying proof procedures that are common to mathematicians might be accessible to the common understanding of the mathematical community, and towards a spurious claim that an individual mathematician has his/her own algorithm. Hans Moravec’s arguments are derided as being a travesty in this respect. Penrose also counters claims that the slightest flaw in any part of the Gödelian section of ‘Shadows of the Mind’ would demolish the argument, by saying that there is not one but several separate lines of argument.

Penrose expresses surprise at the manner in which attacks on the Gödelian argument seem to degenerate into attacks on mathematics itself, or at least on the idealised mathematical reasoning which is the basis of mathematics and also of science that is expressed in mathematical terms.

Tim Maudlin suggested that the Gödelian argument was false because the output of a human being was finite, and therefore in principle a finite computer could simulate a person’s action. Penrose claims that this would invalidate the principle of deduction from observation. Thus the solar system is finite, and its data could form the output of a computer, but without providing any of the theories by which we understand the solar system. He also points out that it is not sufficient to have a computer with pre-designed or ‘canned’ answers, because there is a complexity explosion in the number of answers that may be needed. In any cases, canned answers are said not to work in the case of the P sentences, which are sentences stating whether or not a programme halts. The trouble with a computer with such canned answers for P sentences is that according to Penrose they derive from something non-computable in the mind of the original programmer.

In answer to the question of how one would tell whether something was non-computable or not, Penrose says that this has to derive from experiment and observation. Experiments that relate to Newtonian physics reveal a deterministic structure, but this is not the case in areas of quantum physics, and a future theory that merges quantum and relativity theory may be based on experiments that reveal non-computability.

Some critics have reasonably argued that the explanatory power of a quantum theory of consciousness will be no better than classical theories of consciousness. It is not clear how consciousness arises from neurons or protein etc., but it could equally well be said that it is not clear how it would arise from atoms, electrons etc, both neurons and atoms being physical objects that give in themselves no particular indication of being conscious.

Penrose says that this is not his proposition, but rather that non-computability arises from the new physics that he proposes. Some critics, such as Bernard Baar, object to the idea of a major change in physics as being unnecessary, but it is fair to say that this reveals a lack of awareness of the problems in physics, particularly the incompatibility between quantum and relativity theory. Baars, Stanley Klein and Tim Maudlin are also both criticised for failing to grasp what is intended in the discussion of the objective reduction of the wave function.

Penrose says that he has concentrated on the issue of ‘understanding’, but feels that non-computable processes must also be essential for other aspects of conscious mentality. Consciousness is viewed as having an active and a passive side. Freewill relates to the active side, although Penrose is neutral as to whether true free will exists. The passive side relates to awareness and particularly the qualia. Anything that shed light on ‘understanding’ is also felt to shed light on qualia.

Critics have raised the issue of whether there are things that humans can in principle do better than robots. Penrose says that this applies to anything that requires understanding. He refers to a series of chess problems that were devised to be either easy for humans and hard for computers, or the other way round. The deciding factor was whether or not they required understanding of the objective of the game. This test showed an almost complete separation between human and computer aptitudes.

Penrose remarks that Daniel Dennett seems to have tried to claim that Penrose is saying that human abilities did not arise by evolution. Penrose says that he has no reason to say this if, as Penrose claims, non-computability is present in the natural world.

Only a small part of the Psyche discussions are related to biology, but Penrose does deal with one supposed refutation advanced by Grush and Churchland and also by Edelman to the effect that the drug, colchicine, used for the treatment of gout, depolymerises microtubules, but does not effect consciousness. It is pointed out that the blood-brain barrier does not allow significant amounts of the drug to enter the brain. It is true that consciousness remains even when colchicine is administered directly to the brain, but this is because the neural microtubules are much more stable than those in the rest of the body and do not undergo a polymerisation cycle in the same way.

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