Shadows of the Mind
Penrose (Roger)
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Preface (Full Text)

  1. This book may be regarded as, in some sense, a sequel to "Penrose (Roger) - The Emperor's New Mind" (here abbreviated ENM). Indeed, I shall continue the theme that ENM initiated, but what I have to say here can be read entirely independently of that book. Part of the motivation for writing again on this subject arose originally from a need for detailed replies to a number of queries and criticisms that various people have raised in connection with arguments put forward in ENM. However, I shall be presenting a case here that stands completely on its own and which explores some new ideas going well beyond those of ENM. One of the central themes of ENM had been my contention that by use of our consciousness we are enabled to perform actions that lie beyond any kind of computational activity. However, in ENM this idea was presented as a somewhat tentative hypothesis, and there was a certain vagueness as to what types of procedure might be encompassed under the heading of 'computational activity'. The present volume provides what I believe to be a much more powerful and rigorous case for this general conclusion, and it applies to any kind of computational process whatever. Moreover, a far more plausible suggestion than could be provided in ENM is presented here, for a mechanism in brain function whereby a non-computational physical action might indeed underlie our consciously controlled behaviour.
  2. My case has two distinct strands to it. One of these is essentially negative, in that I argue strongly against the commonly held viewpoint that our conscious mentality — in all of its various manifestations — could, in principle, be fully understood in terms of computational models. The other strand to my reasoning is positive, in the sense that it represents a genuine search for a means, within the constraints of the hard facts of science, whereby a scientifically describable brain might be able to make use of subtle and largely unknown physical principles in order to perform the needed non-computational actions.
  3. In accordance with this dichotomy, the arguments in this book are presented in two separate parts. Part I provides a thorough and detailed discussion, strongly supporting my thesis that consciousness, in its particular manifestation in the human quality of ‘understanding', is doing something that mere computation cannot. I make clear that the term ‘computation' includes both ‘top-down' systems, which act according to specific well-understood algorithmic procedures, and ‘bottom-up' systems, which are more loosely programmed in ways that allow them to learn by experience. Central to the arguments of Part I, is the famous theorem of Godel, and a very thorough examination of the relevant implications of Godel's theorem is provided. This greatly extends earlier arguments provided by Godel himself, by Nagel and Newman, and by Lucas; and all the various objections that I am aware of are answered in detail. In relation to this, some thorough arguments are given against bottom-up systems (as well as top-down ones) being capable of ever achieving genuine intelligence. The conclusions are that conscious thinking must indeed involve ingredients that cannot be even simulated adequately by mere computation; still less could computation, of itself alone, evoke any conscious feelings or intentions. Accordingly, the mind must indeed be something that cannot be described in any kind of computational terms.
  4. In Part II, the arguments turn to physics and to biology. The line of reasoning, though containing portions which are decidedly more tentative than the rigorous discussion of Part I, represents a genuine attempt to understand how such non-computational action might arise within scientifically comprehensible physical laws. The basic principles of quantum mechanics1 are introduced afresh—it being not required that the reader have any prior knowledge of quantum theory2. The puzzles, paradoxes, and mysteries of that subject are analysed in some depth, using a number of new examples which graphically illustrate the important roles of non-locality and counterfactuality, and of deep issues raised by the phenomenon of quantum entanglement. I shall argue strongly for a need for a fundamental change, at a certain clearly specified level, in our present quantum-mechanical world-view. (These ideas relate closely to recent work by Ghirardi, Diosi, and others.) There are significant differences between the ideas that I shall argue for here and those promoted in ENM.
  5. I am suggesting that a physical non-computability — needed for an explanation of the non-computability in our conscious actions — enters at this level. Accordingly, I require that the level at which this physical non-computability is significant must have importance in brain action. It is here where my present proposals differ most substantially from those of ENM. I argue that whereas neuron signals may well behave as classically determinate events, the synaptic connections between neurons are controlled at a deeper level, where it is to be expected that there is important physical activity at the quantum-classical borderline. The specific proposals I am making require that there be large-scale quantum-coherent behaviour (in accordance with proposals that have been put forward by Frohlich) occurring within the microtubules in the cytoskeletons of neurons. The suggestion is that this quantum activity ought to be non-computationally linked to a computation-like action that has been argued by Hameroff and his colleagues to be taking place along microtubules.
  6. The arguments that I am presenting point to several places where our present-day pictures fall profoundly short of providing us with a scientific understanding of human mentality. Nevertheless, this does not mean that the phenomenon of consciousness must remain outside scientific explanation. I argue strongly, as I did in ENM, that there should indeed be a scientific path to the understanding of mental phenomena, and that this path should start with a deeper appreciation of the nature of physical reality itself. I feel that it is important that any dedicated reader, wishing to comprehend how such a strange phenomenon as the mind can be understood in terms of a material physical world, should gain some significant appreciation of how strange indeed are the rules that must actually govern that ‘material' of our physical world.
  7. Understanding is, after all, what science is all about — and science is a great deal more than mere mindless computation.
    Oxford, April 1994

  1. Why We Need New Physics to Understand the Mind: The Non-Computability of Conscious Thought
    1. Consciousness and computation – 7
      → 1.1 Mind and science – 7
      → 1.2 Can robots save this troubled world? – 8
      → 1.3 The A, B, C, D of computation and conscious thinking – 12
      → 1.4 Physicalism vs. mentalism – 16
      → 1.5 Computation: top-down and bottom-up procedures – 17
      → 1.6 Does viewpoint C violate the Church-Turing thesis? – 20
      → 1.7 Chaos – 21
      → 1.8 Analogue computation – 24
      → 1.9 What kind of action could be non-computational? – 26
      → 1.10 What of the future? – 33
      → 1.11 Can computers have rights or responsibilities? – 35
      → 1.12 ‘Awareness', ‘understanding', ‘consciousness', ‘intelligence' – 37
      → 1.13 John Searle's argument – 40
      → 1.14 Some difficulties with the computational model – 41
      → 1.15 Do limitations of present-day AI provide a case for C? – 44
      → 1.16 The argument from Godel's theorem – 48
      → 1.17 Platonism or mysticism? – 50
      → 1.18 What is the relevance of mathematical understanding? – 51
      → 1.19 What has Godel's theorem to do with common-sense behaviour? – 53
      → 1.20 Mental visualization and virtual reality – 56
      → 1.21 Is mathematical imagination non-computational? – 59
    2. The Godelian case – 64
      → 2.1 Godel's theorem and Turing machines – 64
      → 2.2 Computations – 66
      → 2.3 Non-stopping computations – 67
      → 2.4 How do we decide that some computations do not stop? – 68
      → 2.5 Families of computations; the Godel-Turing conclusion G – 72
      → 2.6 Possible technical objections to G – 77
      → 2.7 Some deeper mathematical considerations – 88
      → 2.8 The condition of omega-consistency – 90
      → 2.9 Formal systems and algorithmic proof – 92
      → 2.10 Further possible technical objections to G – 95
      → Appendix A: An explicit Godelizing Turing machine – 117
    3. The case for non-computability in mathematical thought – 127
      → 3.1 What did Godel and Turing think? – 127
      → 3.2 Could an unsound algorithm knowably simulate mathematical understanding? – 130
      → 3.3 Could a knowable algorithm unknowably simulate mathematical understanding? – 132
      → 3.4 Do mathematicians unwittingly use an unsound algorithm? – 137
      → 3.5 Can an algorithm be unknowable? – 141
      → 3.6 Natural selection or an act of God? – 144
      → 3.7 One algorithm or many? – 145
      → 3.8 Natural selection of unworldly esoteric mathematicians – 147
      → 3.9 Learning algorithms – 150
      → 3.10 May the environment provide a non-algorithmic external factor? – 152
      → 3.11 How can a robot learn? – 154
      → 3.12 Can a robot attain ‘firm mathematical beliefs'? – 156
      → 3.13 Mechanisms underlying robot mathematics – 159
      → 3.14 The basic contradiction – 162
      → 3.15 Ways that the contradiction might be averted – 163
      → 3.16 Does the robot need to believe in M? – 164
      → 3.17 Robot errors and robot ‘meanings'? – 167
      → 3.18 How to incorporate randomness-ensembles of robot activity – 169
      → 3.19 The removal of erroneous *-assertions – 170
      → 3.20 Only finitely many *M-assertions need be considered – 173
      → 3.21 Adequacy of safeguards? – 176
      → 3.22 Can chaos save the computational model of mind? – 177
      → 3.23 Reductio ad absurdurn—a fantasy dialogue – 179
      → 3.24 Have we been using paradoxical reasoning? – 190
      → 3.25 Complication in mathematical proofs – 193
      → 3.26 Computational breaking of loops – 195
      → 3.27 Top-down or bottom-up computational mathematics? – 199
      → 3.28 Conclusions – 201
  2. What New Physics We Need to Understand the Mind: The Quest for a Non-Computational Physics of Mind
    1. Does mind have a place in classical physics? – 213
      → 4.1 The mind and physical laws – 213
      → 4.2 Computability and chaos in the physics of today – 214
      → 4.3 Consciousness: new physics or ‘emergent phenomenon'? – 216
      → 4.4 The Einstein tilt – 217
      → 4.5 Computation and physics – 227
    2. Structure of the quantum world – 237
      → 5.1 Quantum theory3: puzzle and paradox – 237
      → 5.2 The Elitzur–Vaidman bomb-testing problem – 239
      → 5.3 Magic dodecahedra – 240
      → 5.4 Experimental status of EPR-type Z-mysteries – 246
      → 5.5 Quantum theory4's bedrock: a history extraordinary – 249
      → 5.6 The basic rules of quantum theory5 – 256
      → 5.7 Unitary evolution U – 259
      → 5.8 State-vector reduction R – 263
      → 5.9 Solution of the Elitzur–Vaidman bomb-testing problem – 268
      → 5.10 Quantum theory6 of spin; the Riemann sphere – 270
      → 5.11 Position and momentum of a particle – 277
      → 5.12 Hilbert space – 279
      → 5.13 The Hilbert-space description of R – 282
      → 5.14 Commuting measurements – 286
      → 5.15 The quantum-mechanical ‘and' – 287
      → 5.16 Orthogonality of product states – 289
      → 5.17 Quantum entanglement – 290
      → 5.18 The magic dodecahedra explained – 296
      → Appendix B: The non-colourability of the dodecahedron – 300
      → Appendix C: Orthogonality between general spin states – 301
    3. Quantum theory7 and reality – 307
      → 6.1 Is R a real process? – 307
      → 6.2 Many-worlds-type viewpoints 310
      → 6.3 Not taking |psi> seriously – 312
      → 6.4 The density matrix – 316
      → 6.5 Density matrices for EPR pairs – 321
      → 6.6 A FAPP explanation of R? – 323
      → 6.7 Does FAPP explain the squared modulus rule? – 328
      → 6.8 Is it consciousness that reduces the state vector? – 329
      → 6.9 Taking |psi> really seriously – 331
      → 6.10 Gravitationally induced state-vector reduction? – 335
      → 6.11 Absolute units – 337
      → 6.12 The new criterion – 339
    4. Quantum theory8 and the brain – 348
      → 7.1 Large-scale quantum action in brain function? – 348
      → 7.2 Neurons, synapses, and computers – 352
      → 7.3 Quantum computation – 355
      → 7.4 Cytoskeletons and microtubules – 357
      → 7.5 Quantum coherence within microtubules? – 367
      → 7.6 Microtubules and consciousness – 369
      → 7.7 A model for a mind? – 371
      → 7.8 Non-computability in quantum gravity: 1 – 377
      → 7.9 Oracle machines and physical laws – 379
      → 7.10 Non-computability in quantum gravity: 2 – 381
      → 7.11 Time and conscious perceptions – 383
      → 7.12 EPR and time: need for a new world-view – 388
    5. Implications? – 393
      → 8.1 Intelligent artificial ‘devices' – 393
      → 8.2 Things that computers do well -- or badly – 396
      → 8.3 Aesthetics, etc. – 399
      → 8.4 Some dangers inherent in computer technology – 401
      → 8.5 The puzzling election – 403
      → 8.6 The physical phenomenon of consciousness? – 406
      → 8.7 Three worlds and three mysteries – 411

    Epilogue – 423
    Bibliography – 425
    Index – 447


Vintage Paperbacks; 1995

"Baars (Bernard) - Can Physics Provide a Theory of Consciousness? A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(8), May 1995

Introduction (Full Text)
  1. Physics is surely the most beautiful of the sciences, and it is esthetically tempting to suppose that two of the great scientific mysteries we confront today, observer effects in quantum mechanics1 and conscious experience, are in fact the same. Roger Penrose is an admirable contributor to modern physics and mathematics, and his new book, Shadows of the Mind (SOTM) offers us some brilliant intellectual fireworks --- which for me at least, faded rapidly on further examination.
  2. I felt disappointed for several reasons, but one obvious one: Is consciousness really a physics problem? Penrose writes,
      A scientific world-view which does not profoundly come to terms with the problem of conscious minds can have no serious pretensions of completeness. Consciousness is part of our universe, so any physical theory which makes no proper place for it falls fundamentally short of providing a genuine description of the world. I would maintain that there is yet no physical, biological, or computational theory that comes very close to explaining our consciousness ...
  3. Having spent 17 years of my life trying to do precisely what Penrose suggests has not and cannot be done, this point was a bit disconcerting. But even more surprising was the claim that consciousness is a problem in physics. The conscious beings we see around us are the products of billions of years of biological evolution. We interact with them --- with each other --- at a level that is best described as psychological. All of our evidence regarding consciousness depends upon reports of personal experiences, and observation of our own perception, memories, attention, imagery, and the like. The evidence therefore would seem to be exclusively psychobiological. We will come back to this question.
  4. argument in SOTM comes down to two theses and a statement of faith. The first thesis I will call the "Turing Impossibility Proof," and the second, the "Quantum Promissory Note". The statement of faith involves classical Platonism of the mathematical variety, founded in a sense of certainty and wonder at the amazing success of mathematical thought over the last 25 centuries, and the extraordinary ability of mathematical formalisms to yield deep insight into scientific questions (SOTM, p. 413). This view may be captured by Einstein's well-known saying that "the miraculous thing about the universe is that it is comprehensible." While I share Penrose's admiration for mathematics, I do not believe in the absolute nature of mathematical thought, which leads him to postulate a realm of special conscious insight requiring no empirical investigation to be understood.
  5. After considering the argument of SOTM I will briefly sketch the current scientific alternative, the emerging psychobiology of consciousness (see Baars, 1988, 1994; Edelman, 1989; Newman and Baars, 1993; Schacter, 1990; Gazzaniga, 1994). Though the large body of current evidence can be stated in purely objective terms, I will strive to demonstrate the phenomena by appealing to the reader's personal experience, such as your consciousness of the words on this page, the inner speech that often goes with the act of reading carefully, and so on. Such demonstrations help to establish the fact that we are indeed talking about consciousness as such.

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

"Chalmers (David) - Minds, machines, and mathematics. A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(9), June, 1995

Introduction (Full Text)
    In his stimulating book Shadows of the Mind, Roger Penrose presents arguments, based on Gödel's theorem, for the conclusion that human thought is uncomputable. There are actually two separate arguments in Penrose's book. The second has been widely ignored, but seems to me to be much more interesting and novel than the first. I will address both forms of the argument in some detail. Toward the end, I will also comment on Penrose's proposals for a "new science of consciousness".

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

"Feferman (Solomon) - Penrose's Gödelian argument. A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(7), May 1995

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 intelligence, 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).

"Klein (Stanley A.) - Is quantum mechanics relevant to understanding consciousness? A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(3), April 1995

Introduction (Full Text)
  1. The present essay explores three issues raised by Penrose in Shadows of the Mind (abbreviated Shadows from here on):
    1. Is classical (non-quantum) science incapable of understanding brain operation?;
    2. Are long-range quantum effects able to produce measurable changes in neural activity?;
    3. Why have so many researchers proposed a strong connection between quantum mechanics1 and consciousness2?
  2. In connection with this third topic, I will argue that although Penrose is probably wrong about the physics of quantum mechanics3 being relevant to the (third person) neural correlates of awareness, the metaphysics of quantum mechanics4 may be essential to understanding the (first person) subjective nature of consciousness. In Penrose's approach these two aspects become inseparably intertwined, adding confusion to an already murky area.

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

"Maudlin (Tim) - Between the motion and the act.... A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(2), April 1995

Introduction (Full Text)
  1. In these comments I want to leave aside entirely whether human mathematical understanding is achieved solely through the manipulation of linguistic symbols by syntactically specifiable rules, i.e. whether it is solely a matter of humans performing a computation. I also want to leave aside the problems that arise in interpreting quantum theory1, in particular the measurement problem. Those problems stand on their own quite independent of Gödel's theorem. Rather, I want to focus explicitly on how Gödel's theorem, together with facts about human mathematical understanding, could conceivably have any bearing on physics, that is, on how the first part of Shadows of the Mind is related to the second. I want chiefly to argue the reflections arising from Gödel's theorem and human cognitive capacities do not, and could not, have any bearing on physics.
  2. That there might be any connection at all would be surprising for the following reason. Ultimately, the empirical data of physics resolve themselves into claims about the positions of material bodies. Any physical theory that correctly predicts or accounts for the positions of bodies -- including the positions of needles on complicated scientific instruments, the positions of ink particles on computer printouts, and the positions of dots on photographic plates -- cannot be objected to on empirical grounds. One might object on aesthetic or other grounds (e.g. one might object in principle to a theory that postulates unmediated action at a distance) but this would not be an empirical failure of the theory. So if Professor Penrose's argument somehow shows that classical physics or quantum physics cannot be complete and correct accounts of physical reality, then Gödel's theorem must somehow have implications about how material bodies can move.
  3. The overall strategy for connecting Gödel's result to physics would have to be to show that some actual motion of bodies cannot in principle be accommodated within a physical theory of a certain kind. Just as analysis can show that the physical behavior of planets whose orbits precess cannot be accounted for by Newtonian gravitational theory, so Penrose seems to claim that all of classical and quantum physics (as well as a large class of possible extensions or emendations of those theories) cannot account for the physical motions of some known physical bodies: those of human mathematicians. How, in detail, could this connection between a mathematical theorem and physical action possibly be made?

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

"McCarthy (John) - Awareness and understanding in computer programs. A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(11), July 1995

Introduction (Full Text)
  1. This book and its predecessor The Emperor's New Mind argue that natural minds cannot be understood and artificial minds cannot be constructed without new physics, about which the book gives some ideas. We have no objection to new physics but don't see it as necessary for artificial intelligence. We see artificial intelligence research as making definite progress on difficult scientific problems. I take it that students of natural intelligence also see present physics as adequate for understanding mind.
  2. This review concerns only some problems with the first part of the book. Considerations in my review (McCarthy, 1990a) of the earlier book are not repeated here.

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

"McCullough (Daryl) - Can humans escape Gödel? A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(4), April 1995

Introduction (Full Text – “Gödel's Theorem And The Mind”)
  1. In the first part of Shadows of the Mind, Penrose gives an argument that human reasoning must go beyond what is computable. Therefore, no computer program can ever hope to be as intelligent as a human being. Penrose doesn't give a direct argument for his thesis. He doesn't for instance, show that there is some task that humans can perform which no computer can. (Although he suggests without offering a proof that certain kinds of geometric visualization may allow us to deduce facts in an inherently noncomputable way.) Instead, Penrose uses an indirect proof-he assumes that there exists a computer program that is every bit as intelligent as a human, and shows that that leads to a contradiction.

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

"McDermott (Drew) - Penrose is Wrong. A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(17), October, 1995

Introduction (Full Text – “Penrose vs AI - Again”)
  1. Roger Penrose's new book, Shadows of the Mind, is strongly reminiscent of his previous work in the same vein, The Emperor's New Mind. This book restates the author's central line of argument about the place of consciousness in the material world. He has no sympathy at all for attempts to work out a computationalist theory of mind, and instead pins his hopes on a future theory that would allow large-scale quantum-mechanical effects in the brain to play a central role.
  2. A broad outline of his argument goes like this:
    • Because of Gödel's Incompleteness Theorem, mathematical insight cannot be mechanized.
    • Mathematical insight depends on consciousness, and so it is doubtful that any part of consciousness can be mechanized.
    • But then a physical system can be conscious only if it can't be simulated by a computer.
    • That would be very strange; fortunately, the world as imagined in modern physics is very strange.
    • The interaction between quantum mechanics1 and the general theory of relativity is poorly understood. Fundamental questions about time and causality2 seem to depend on how that interaction gets worked out.
    • Perhaps the brain exploits some large-scale quantum coherence to achieve consciousness. Perhaps the site of this effect is in the cytoskeletons of neurons.
  3. This argument, when put down in black and white, seems extraordinarily weak. The least speculative step is the first, but that's also the easiest to show is fallacious, as I will do shortly. But before I do, I want to raise the question, Why is Penrose bothering?
  4. A clue might be this sentence on p. 373: "It is only the arrogance of our present age that leads so many to believe that we now know all the basic principles that can underlie all the subtleties of biological action." Penrose wants to do battle against the arrogance he perceives, especially in the AI community, regarding the problem of consciousness. It is true that AI has, from its inception, had the ambition to explain everything about the mind, including consciousness. But is this arrogance? Or merely the sincere adoption of a working hypothesis? If someone wants to work on the problem of mind, it seems to me that he must choose among three options: treat the brain as a computer, and study which parts compute what; study neurons, on the assumption that they might be doing something noncomputational; or work in a seemingly unrelated field, like physics, on the off chance that something relevant will turn up. In any case, no matter which tack is taken, one gets mighty few occasions to feel arrogant about one's success. Neuroscience and AI have made definite progress, and so has physics, for that matter, but their successes haven't resulted in a general theory of mind. If anything, AI seemed closer to such a theory thirty years ago than it seems now.
  5. So if someone wants to believe that AI will never explain the mind, he might as well. The burden of proof is on whoever claims it ultimately will. Penrose isn't satisfied with this state of affairs, however, and wants to exhibit a proof that a computationalist theory of mind is impossible. I suppose he sees himself fighting for the hearts and minds of neutral parties, who are in danger of being fooled into thinking that AI is on the verge of such a theory by the breathless stories they read in the papers. I don't know; perhaps an argument like Penrose's will, once it has been filtered through the distorting lens of the TV camera, be a sort of homeopathic antidote to those breathless stories. But, I regret to say, the argument would still be wrong. And so those of us in a position to point out the flaws in it must sheepishly rise to do so, in the full knowledge that AI can't win the debate if it degenerates into Mutual Assured Destruction ("You can't prove AI is possible," "Oh yeah? Well, you can't prove it's not").

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

"Moravec (Hans) - Roger Penrose's gravitonic brains. A Review of Shadows of the Mind by Roger Penrose"

Source: Psyche, 2(6), May 1995

Introduction (Full Text)
  1. Summarizing a surrounding 200 pages, pages 179 to 190 of Shadows of the Mind contain a future dialog between a human identified as "Albert Imperator" and an advanced robot, the "Mathematically Justified Cybersystem", allegedly Albert's creation. The two have been discussing a Gödel sentence for an algorithm by which a robot society named SMIRC certifies mathematical proofs. The sentence, referred to in mathematical notation as Omega(Q*), is to be precisely constructed from on a definition of SMIRC's algorithm. It can be interpreted as stating "SMIRC's algorithm cannot certify this statement." The robot has asserted that SMIRC never makes mistakes. If so, SMIRC's algorithm cannot certify the Goedel sentence, for that would make the statement false. But, if they can't certify it, what is says is true! Humans can understand it is true, but mighty SMIRC cannot certify it. The dialog ends melodramatically as the robot, apparently unhinged by this revelation, claims to be a messenger of god, and the human shuts it down with a secret control.
  2. Severe incongruities in the dialog's logic and characterization suggest the following continuation:

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

"Penrose (Roger) - Beyond the Doubting of a Shadow"

Source: Psyche, 2(23), January 1996

Introduction (Full Text)

Replies To:
  1. Bernard J. Baars1: Can physics provide a theory of consciousness?
  2. David J. Chalmers2: Minds, machines, and mathematics
  3. Solomon Feferman3: Penrose's Gödelian argument
  4. Stanley A. Klein4: Is quantum mechanics5 relevant to understanding consciousness?
  5. Tim Maudlin6: Between the motion and the act….
  6. John McCarthy7: Awareness and understanding in computer programs
  7. Daryl McCullough8: Can humans escape Gödel?
  8. Drew McDermot9t: Penrose is wrong
  9. Hans Moravec10: Roger Penrose's gravitonic brains

  1. General remarks
  2. Some technical slips in Shadows
  3. The central new argument of Shadows
  4. The "bare" Gödelian case
  5. Gödel's "theorem-proving machine"
  6. The issue of errors
  7. The "unknowability" issue
  8. AI and MJC
  9. Mathematical Platonism
  10. What has Gödel's theorem to do with physics?
  11. How could physics actually help?
  12. State-vector reduction
  13. Free will
  14. Some remarks on biology
  15. What is consciousness?

COMMENT: Response to reviews of "Penrose (Roger) - Shadows of the Mind"; Link (Defunct).

In-Page Footnotes ("Penrose (Roger) - Beyond the Doubting of a Shadow")

Footnote 1: See "Baars (Bernard) - Can Physics Provide a Theory of Consciousness? A Review of Shadows of the Mind by Roger Penrose".

Footnote 2: See "Chalmers (David) - Minds, machines, and mathematics. A Review of Shadows of the Mind by Roger Penrose".

Footnote 3: See "Feferman (Solomon) - Penrose's Gödelian argument. A Review of Shadows of the Mind by Roger Penrose".

Footnote 4: See "Klein (Stanley A.) - Is quantum mechanics relevant to understanding consciousness? A Review of Shadows of the Mind by Roger Penrose".

Footnote 6: See "Maudlin (Tim) - Between the motion and the act.... A Review of Shadows of the Mind by Roger Penrose".

Footnote 7: See "McCarthy (John) - Awareness and understanding in computer programs. A Review of Shadows of the Mind by Roger Penrose".

Footnote 8: See "McCullough (Daryl) - Can humans escape Gödel? A Review of Shadows of the Mind by Roger Penrose".

Footnote 9: See "McDermott (Drew) - Penrose is Wrong. A Review of Shadows of the Mind by Roger Penrose".

Footnote 10: See "Moravec (Hans) - Roger Penrose's gravitonic brains. A Review of Shadows of the Mind by Roger Penrose".

"Penrose (Roger) - Shadows of the Mind"

Source: Penrose - Shadows of the Mind

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