Gödel's theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met. This I attempt to do.

Gödel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then it would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula "This formula is unprovable-in-the-system" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula "This formula is unprovablein-the-system" is unprovable-in-the-system, then it is true that that formula is unprovable-in-the-system, that is, "This formula is unprovable-in-the-system" is true.

Gödel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines.

The three great problems of philosophy, according to Kant, ¹- are God, freedom, and immortality. Of these, freedom, that is, the Freedom of the Will, is the one most accessible to reason, and has continued to perplex us to the present day. We have a profound conviction of freedom. We know we are free. Yet when we think of ourselves from a scientific point of view, we do not see how we can be free. It would be a denial of science, we feel, to make man an exception to the universal laws of nature, and say that although everything else could be explained in terms of cause and effect, men were different, and were mysteriously exempt from the sway of natural laws. Men, scientifically speaking, are no different from anything else. There is no special privilege of humanity, so far as science is concerned, which makes human behaviour not susceptible of scientific enquiry and scientific explanation. There must be causes of human behaviour, as there are causes of everything else. To think otherwise is pure superstition. For there is no evidence to the contrary, and already physiologists, neurologists, and psychologists have been remarkably successful in explaining human behaviour. To maintain a doctrine of freedom in the face of these facts is mere anthropomorphic obscurantism. And yet we are reluctant to surrender our freedom without a struggle. The doctrine that we are not free runs counter to something we know to be true so surely that only the most irrefragable arguments could shake the intimations of our everyday experience. Moreover, if we did abandon our belief in freedom, we should have to abandon much else in our view of ourselves and of our moral and rational life. Nor is it clear that we ought not to think anthropomorphically. After all, we are men: we do regard men, ourselves and others, as being different from the rest of creation. Men are rational, and ought to be treated not merely as means, but always also as ends. We condemn the nazis for regarding non-Aryan men as mere animals, and treating them scientifically, as mere objects of scientific research. We are entitled at least to put the case against freedom to the test. The claim needs to be stated with precision, and the arguments expressed in full, and counter-arguments considered. Much depends on the conclusion. If it be superstition to believe in freedom, and we conclude in favour of freedom, we shall be committed to superstition. ² If, on the other hand, we conclude that man is not free, we may have to revise many of our present concepts about man and morality, responsibility and punishment, history and humanity. Kant was right in thinking freedom to be an unavoidable problem set by pure reason, though wrong in despairing of the power of reason to solve it. For the very fact that freedom is a problem for reason is itself a reason for believing that we are free. Many men have sensed this, but the argument is extremely difficult to articulate and assess. I have attempted to articulate it in Section 21, and in the following sections to reformulate it in formal terms with the aid of a profound theorem of mathematical logic discovered by Godel in 1929. It is a controversial argument, and I have tried to meet objections raised against it, for I believe it to be ultimately a decisive argument which will refute the one sort of determinism—physical determinism—which seriously worries men today. But it is not the only argument, and its bearing is difficult to assess except in the context of the whole debate; and in the first two thirds of the book I discuss, in a more orthodox fashion, the main points at issue, to which innumerable men have contributed many arguments in many forms. I have not tried to do justice to them. Exhaustive treatments are exhausting. Moreover, philosophy has to be self-thought if it is to be thought at all. It is an activity, rather than a set of propositions. Each man needs to think out the problems and their solutions for himself, and although other men's philosophizing may help him in his own, he cannot accept their conclusions, or even understand their arguments, until he has already argued a lot with himself. I have aimed to be, so far as one can be, unsophisticated. The footnotes are intended to supply the deficiency, and show the reader where he can follow up any particular line of argument in greater detail and with greater subtlety. Although I think some conclusions can be reasonably well established, I do not offer any formal proofs, but only, I hope, show how one may think one's way through to these conclusions for oneself. But only the reader, not I, can carry the programme through.

1. Critique of Pure Reason, A3/B7; A337n/B395n.

2. Compare G. J. Warnock, "Actions and Events", in D. F. Pears, ed., Freedom and the Will, London, 1963, p. 79.

Lewis has two lines of argument. One, which recurs in his novels and in his inaugural lecture at Cambridge, is that we destroy man's humanity if we treat him merely as a means, and not also as an autonomous, rational, end in himself. Emancipated from the shackles of morality, a man will treat other men merely as things, manipulating them to serve his own ends. Lewis was particularly afraid of genetic engineering, and in this, again, he was prescient. We might take issue with him on some points. Not all genetic counselling and therapy need be manipulative. And some measure of control is not the same as complete control. We always have had some measure of control over future generations---the monks of Durham were able to secure that no sons of theirs would ever sin. What frightened Lewis, and ought to frighten us, is the possibility that, by genetic engineering or social conditioning, we could program people to behave exactly as we pleased. For then they would not be people, beings other than ourselves with a mind of their own, but merely artefacts---things we could use, but not persons we could communicate with, share with, identify with, or care about.

Lewis's second argument concerns the manipulators rather than those manipulated. Emancipation for them is liberation into a vacuum. If everything is permitted, nothing is worthwhile. The Conditioners, who have no scruples to prevent them manipulating and refashioning man to their own liking, have no grounds for liking any one thing rather than any other. For a time, Lewis thinks, they may be guided by vestiges of objective values not yet completely dethroned, but in the end they can have no rational motives to guide them in deciding how to fashion subsequent generations. The same sense of human worth which ought to restrain them from manipulating other men merely as means to their own purposes provides the purposes that alone make our goals worthwhile and our decisions meaningful. In liberating ourselves from the tie of obligation to others, we diminish ourselves too, and deprive ourselves of any standards of achievement by reference to which we could hope to have done well. We are no longer rational agents, but. like other men, the playthings of heredity and environment, instinct and social conditioning.

Restoration of Man