The Shadows of the Mind
by Roger Penrose
(A). All thinking is computation;in particular,feelings of conscious awareness are evoked merely by the carrying out of appropriate computations.
(B). Awareness is a feature of the brain's physical action;and whereas any physical action can be simulated computationally,computational simulation cannot by itself evoke awareness.
(C). Appropriate physical action of the brain evokes awareness,but this physical action cannot be properly simulated computationally.
(D).Awareness cannot be explained by physical,computational,or any other scientific terms.
Some critics may argue, however, that by seeming to force us into either viewpoint (C) or viewpoint (D) , the Gödel argument has implications that must be regarded as being 'mystical' , and certainly no more palatable to them than any such let-out from the Gödel argument. With regard to (D) , I am in effect agreeing with them. My own reasons for rejecting (D) - the viewpoint which asserts the incompetence of the power of science when it comes to matters of the mind-spring from an appreciation of the fact that it has only been through use of the methods of science and mathematics that any real progress in understanding the behaviour of the world has been achieved. Moreover, the only minds of which we have direct knowledge are those intimately associated with particular physical objects - brains and differences in states of mind seem to be clearly associated with differences in the physical states of brains.
Even the mental states of consciousness seems to be associated with certain specific types of physical activity taking place within the brain.If it were not for the puzzling aspects of consciousness that relate to the presence of 'awareness' and perhaps of our feelings of 'free will', which as yet seem to elude physical description, we should not need to feel tempted to look beyond the standard methods of science for explanation of minds as a feature of the physical behaviour of brains.
On the other hand, it should be made clear that science and mathematics have themselves revealed a world full of mystery. The deeper that our scientific understanding becomes, the more profound the mystery that is revealed. It is perhaps noteworthy that the physicists, who are the more directly familiar with the puzzling and mysterious ways in which matter actually behaves, tend to take a less classically mechanistic view of the world than do the biologists.
In Chapter 5, I shall be explaining some of the more mysterious aspects of quantum behaviour, a few of which have been only fairly recently uncovered.
It may well be that in order to accommodate the mystery of mind, we shall need a broadening of what we presently mean by 'science' , but I see no reason to make any clean break with those methods that have served us so extraordinarily well. If, as I believe, the Gödel argument is consequently forcing us into an acceptance of some form of viewpoint (C) , then we shall also have to come to terms with some of its other implications. We shall find ourselves driven towards a Platonic viewpoint of things.According to Plato, mathematical concepts and mathematical truths inhabit an actual world their own that is timeless and without physical location. Plato's world is an ideal world of perfect forms, distinct from the physical world, but in terms of which the physical world must be understood. It also lies beyond our imperfect mental constructions; yet, our minds do have some direct access to this Platonic realm through an 'awareness' of mathematical forms, and our ability to reason about them. We shall find that whilst our Platonic perceptions can be aided on occasion by computation, they are not limited by computation.It is this potential for the 'awareness' of mathematical concepts involved in this Platonic access that gives the mind a power beyond what can ever be achieved by a device dependent solely upon computation for its action.
Such airy-fairy stuff may (or may not ) be all very well, some readers will doubtless complain. What serious relevance do sophisticated issues of mathematics and of mathematical philosophy have for most of the matters of direct interest to artificial intelligence, for example? Indeed, many philosophers and proponents of AI are quite reasonably of the opinion that although Gödel 's theorem is undoubtedly important in its original context of mathematical logic, it can have very limited implications, at best, for AI or for the philosophy of mind. Very little of human mental activity is directed, after all,at issues relating to Gödel 's original context : the axiomatic foundations of mathematics. My answer is that a great deal of human mental activity involves, on the other hand, the application of human consciousness and understanding. My use of the Gödel argument is to show that human understanding cannot be an algorithmic activity. If we can show this in some specific context, this will suffice. Once it is shown that certain types of mathematical understanding must elude computational description, then it is established that we can do something non-computational with our minds. This being accepted, it is a natural step to conclude that non-computational action must be present in many other aspects of mental activity. The floodgates will indeed be open!
The mathematical argument establishing the needed form of Gödel 's theorem, as given in Chapter 2, may well seem to have very little direct bearing on most aspects of consciousness. Indeed, a demonstration that certain kinds mathematical understanding must involve something beyond computation do not appear to have much relevance to what is involved in our perception of the colour red, for example, nor does there seem to be any manifest role for mathematical desiderata in most other aspects of consciousness. For example, even mathematicians do not normally think of mathematics when they are dreaming! Dogs appear to dream, and are presumably also aware, to some extent,when they dream; and I would certainly think that they can be aware at other times. But they do not do mathematics. Undoubtedly, contemplating mathematics is very far from being the only animal activity requiring consciousness ! It is a highly specialized and peculiarly human activity (Indeed,some cynics might even say that it is an activity confined to certain peculiar humans). The phenomenon of consciousness, on the other hand, is ubiquitous, being likely to be present in much non-human as well as human mental activity , and certainly in non-mathematical humans, as well as in mathematical humans when they are not actually doing mathematics (which is most of the time). Mathematical thinking is a very tiny area of consciousness activity that is indulged in by a tiny minority of conscious beings for a limited fraction of their conscious lives.
Why then do I choose to address the question of consciousness here in a mathematical context first? The reason is that it is only within mathematics that we can expect to find anything approaching a rigorous demonstration that some, at least, of conscious activity must be non-computational .The issue of computation, by its very nature, is indeed a mathematical one .We cannot expect to be able to provide anything like a 'proof' that some activity is not computational unless we turn to mathematics I shall try to persuade the reader that whatever we do with our brains or minds when we understand mathematics is indeed different from anything that we can achieve by use of a computer; then the reader should be more readily prepared to accept an important role for non-computational activity in conscious thinking generally.
Nevertheless, as many might argue, it is surely just obvious that the sensation of 'red' can in no way be evoked merely by the carrying out some computation. Why bother at all with attempting some unnecessary mathematical demonstration when it is perfectly obvious that 'qualia' - ie subjective experiences-have nothing to do with computation? One answer is that this argument from 'obviousness' (with which I do have a considerable sympathy) refers only to the passive aspects of consciousness. Like Searle's Chinese Room, it may be presented as an argument against viewpoint (A),but it does not distinguish (C) from (B).
Moreover , I must attack the functionalist's computational model (ie viewpoint (A)) on its home ground, so to speak; for it is the contention of the functionalists that all qualia must indeed be somehow evoked by merely carrying out the appropriate computations, no matter how improbable such a picture may at first sight seem. For, they argue, what else can we indeed be usefully doing with our brains unless it is performing computations of some kind? What is the brain for, if not just some kind of-albeit highly sophisticated - computational control system? Whatever 'feelings of awareness' the brain's action somehow evokes must, they would claim, be the result of this computational action. They often maintain that if one refuses to accept the computational model for all mental activity , including consciousness, then one must be resorting to mysticism. (This is to suggest that the only alternative to viewpoint (A) is viewpoint (D)! ) It is my intention, in Part II of this book,to provide some partial suggestions as to what else a scientifically describable brain might actually be doing. I shall not deny that some of the 'constructive' parts of my argument are speculative. Yet I believe that the case for some kind of non-computational action is compelling, and it is in order to demonstrate the compelling nature of this case that I must turn to mathematical thinking.