Jean Lucas

The legend of the encounter between Wilberforce and Huxley is well established. Almost every scientist knows, and every viewer of the BBC's recent programme on Darwin was shown,* how Samuel Wilberforce, bishop of Oxford, attempted to pour scorn on Darwin's Origin of Species at a meeting of the British Association in Oxford on 30 June 1860, and had the tables turned on him by T. H. Huxley. In this memorable encounter Huxley's simple scientific sincerity humbled the prelatical insolence and clerical obscurantism of Soapy Sam; the pretension of the Church to dictate to scientists the conclusions they were allowed to reach were, for good and all, decisively defeated; the autonomy of science was established in Britain and the Western world; the claim of plain unvarnished truth on men's allegiance was vindicated, however unwelcome its implications for human vanity might be; and the flood tide of Victorian faith in all its fulsomeness was turned to an ebb, which has continued to our present day and will only end when religion and superstition have been finally eliminated from the minds of all enlightened men. Even churchmen concede that it was a disastrous defeat.1 Only Owen Chadwick strikes a note of caution, observing that the account given of the incident in Wilberforce's biography seems hardly consistent with an overwhelming defeat, and maintaining that the received account must be a largely legendary creation of a later date.

According to the legend, Bishop Wilberforce at a meeting of the British Association for the Advancement of Science in Oxford on Saturday, June 30th, 1860, turned to Thomas Huxley, and asked him ``Is it on your grandfather's or your grandmother's side that you claim descent from a monkey''; whereupon Huxley delivered a devastating rebuke, thereby establishing the primacy of scientific truth over ecclesiastical obscurantism. Although the legend is historically untrue in almost every detail, its persistence suggests that it may nonetheless be true in some deeper, mythical, sense. To explore this possibility the British Academy has invited Dr Janet Browne to be a neo-Huxley confronting Mr J.R. Lucas, as a neo-Wilberforce, with each reconsidering their earlier arguments.

I must start with an apologia. My original paper, ``Minds, Machines and Gödel'', was written in the wake of Turing's 1950 paper in Mind, and was intended to show that minds were not Turing machines. Why, then, didn't I couch the argument in terms of Turing's theorem, which is easyish to prove and applies directly to Turing machines, instead of Gödel's theorem, which is horrendously difficult to prove, and doesn't so naturally or obviously apply to machines? The reason was that Gödel's theorem gave me something more: it raises questions of truth which evidently bear on the nature of mind, whereas Turing's theorem does not; it shows not only that the Gödelian well-formed formula is unprovable-in-the-system, but that it is true. It shows something about reasoning, that it is not completely rule-bound, so that we, who are rational, can transcend the rules of any particular logistic system, and construe the Gödelian well-formed formula not just as a string of symbols but as a proposition which is true. Turing's theorem might well be applied to a computer which someone claimed to represent a human mind, but it is not so obvious that what the computer could not do, the mind could. But it is very obvious that we have a concept of truth. Even if, as was claimed in a previous paper, it is not the summum bonum, it is a bonum, and one it is characteristic of minds to value. A representation of the human mind which could take no account of truth would be inherently implausible. Turing's theorem, though making the same negative point as Gödel's theorem, that some things cannot be done by even idealised computers, does not make the further positive point that we, in as much as we are rational agents, can do that very thing that the computer cannot. I have however, sometimes wondered whether I could not construct a parallel argument based on Turing's theorem, and have toyed with the idea of a von Neumann machine. A von Neumann machine was a black box, inside which was housed John von Neumann..

It would be improper for a President to play safe. After two years of curbing my tongue and not making all sorts of observations that have sprung to my mind, in order to let you have an opportunity of having your say, I am now off the leash. And whereas mostly in academic life it is appropriate to adopt a prudential strategy, and not say anything that might be wrong, I owe it to you on this occasion to play a maximax strategy, to speak out and say what I really think, being willing to run the risk of being wrong in order not to forgo the chance of actually being right in an area of the philosophy of science which must, I think for ever, be largely a matter of metaphysical speculation.

The Unity of Science is often thought to be reductionist, but this is because we fail to distinguish questions from answers. The questions asked by different sciences are different---the biologist is interested in different topics from the physicist, and seeks different explanations---but the answers are not peculiar to each particular science, and can range over the whole of scientific knowledge. The biologist is interested in organisms--- concept unknown to physics---but explains physiological processes in terms of chemistry, not a mysterious vital force. The replacement of Laplacian determinism by quantum mechanics further erodes the tendency towards reductionism. The answers given in different explanations are not subsumed under one complete theory; and quantum mechanics does not have a concept of haecceitas, "this-i-ness" which would make its entities the fundamental constituents of everything.

Whatever good or ill it did to Guy Fawkes, his resuscitation at the hands of Bernard Williams has, by any utilitarian reckoning, been a Good Thing. A casual glance at the literature that has accumulated over the past thirty five years leaves no doubt that the topic has been reduplicated many times over, to the great enjoyment of undergraduates, who have been able to write science fiction under the guise of essays in the Philosophy of Mind, and of dons, who in an age of cvs and Assessments, have been able to notch up page after page of counter-replies to replies to rebuttals of previous papers, not to mention an often welcome tally of references in the citation index. But the actual arguments adduced by Williams can be turned to support a much more traditional view of the self, as a necessarily unique agent whose individuality is established by his capacity for autonomous action.

The stock of natural law has risen in recent years. It is partly due to growing dissatisfaction with the elucidations offered by the legal positivists, and partly because sceptical arguments have lost their edge. In the heyday of logical positivism it was easy to say ``I don't understand what you mean by `right' . . .'' and break off discussion without more ado; but, as the bounds of unintelligibility increased and came to encompass almost the whole of human knowledge, an inability to understand became not so much a boast as a confession. Many people may still be unclear about the metaphysical foundations of the moral sciences; but we are disinclined to doubt that they are serious disciplines, or to think that they need to be, or even could be, reconstructed without any moral element. Moreover, the events of this century have begun to penetrate the academic consciousness. Having witnessed the terrible tyrannies of the Nazis, the Communists and the Third World, we find it difficult to divorce our thinking about law from our thinking about morals. Although 'duty' is still an unfashionable word, people are constantly talking about the rights that are being denied them and the wrongs being inflicted on them. And these rights claimed and wrongs resented are grounded not on some existing legal enactment or a one-time social contract, but on the nature of man and the nature of the state, and are therefore, although very different from their mediaeval articulation, arguments of natural law.

IT is ungenerous to pick holes in The Concept of Law. It is a great work. Its clarity is luminous, and its argument sustained and convincing. Hart is eminently successful in rescuing the concept of law from the Legal Realists, the Positivists, and the Formalists, who attempt to straitjacket it within schemata which are too narrow or too vague to give an adequate elucidation of it. But sometimes Hart is not carried along by his arguments as far as he should. He makes too many concessions to his opponents, and his own account of the law is, in consequence, too formalist, in spite of having himself adduced cogent considerations elsewhere for rejecting the purely formalist line of argument. The rule of recognition, although important, is not fundamental. We should, rather, see law as a social phenomenon, to be distinguished from other social phenomena, but intelligible only in a social context, and not-as lawyers are too ready to suppose-an autonomous discipline which can be explained and understood entirely in its own terms.

Plato was the first feminist. In the Republic he puts forward the view that women are just the same as men, only not quite so good. It is a view which has often been expressed in recent years, and generates strong passions. Some of these have deep biological origins, which a philosopher can only hope to recognize and not to assuage. But much of the heat engendered is due to unnecessary friction between views which are certainly compatible and probably correct. And here a philosopher can help. If we can divide the issues neatly, at the joints, then we need not quarrel with one another for saying something, probably true, because what is being maintained is misconstrued and taken to mean something else, probably false.

It is meet and right that pride and humility should be the two human characteristics on which University sermons have to be preached. Left to myself, although I might have picked on my modesty as something I should share with you, I should have given the preeminence to other among my sins than pride. My greed, my sloth, my avarice or, in this salacious age my lust, are subjects on which I could tell you much that might interest you. Pride lacks immediate appeal. We are not sure what it is, or whether it is a bad thing, when we think of it in purely individual terms. But when we consider it collectively, we can see that it is, together with humility, something Oxford is peculiarly well qualified to preach on. We all of us are proud of our university. We were proud, and our schoolmasters were proud, when we first got our places here. We are, dons and undergraduates alike, proud of our colleges, each grateful that good fortune has brought him to the best college in Oxford, and anxious that everyone else should secretly acknowledge it to be the best. Our parents were proud when we took our degrees, and although we profess to be unconcerned with classes, we are deeply content to record our firsts when occasion requires us to do so, or have our contemporaries allude to them as opportunity offers. We are studious, as dons, not to pull rank, safe in the knowledge that others will do it for us, and that we shall receive the deference due to a fellow of an Oxford college. In an age that is egalitarian in theory but elitist at heart, Oxford men have benefited greatly, as other forms of social eminence have been eroded, leaving a clear field for our own claims to public esteem, which are, if not entirely unchallenged, still generally allowed. Oxford is, as we like to be told by outsiders, a centre of excellence, and a lot of the resplendence rubs off on us, not altogether undeservedly. It is, as we corporately admit on Commemoration Sunday, largely due to our having entered into other men's labours..

x8.1 `Real' The word `real' has many senses, and has been much misunderstood in consequence. It was, along with other philosophical terms, such as quality, quantity, entity, identity, essence and substance, coined by the Schoolmen in the Middle Ages|realis, reale from the Latin res, a thing|to mark the distinction between what really existed and what mere existed in intellectu, in the mind; and the word still carries connotations of thinginess, which can confuse our thinking about reality in the present age.

Elijah foretold evil for Ahab in the name of the Lord. ‘I will bring evil upon you; I will utterly sweep you away, and will cut off from Ahab every male, bond or free in Israel’ … but when he heard those words, he rent his clothes, and put sackcloth upon his flesh, and fasted and lay in the sackcloth, and went about dejectedly. And the word of the Lord came to Elijah saying ‘Have you seen how Ahab has humbled himself before me? Because he has humbled himself before me, I will not bring the evil in his days, but in his son's days I will bring evil upon his house.’

Some of my best friends are women, but I would not want my sister to marry one of them. Modern-minded persons criticize me for manifesting such out-dated prejudices, and would like to send me to Coventry for a compulsory course of reindoctrination. They may be right. It could conceivably be the case that in due course the Sex Discrimination Act will be tightened up, even to the extent of our recognizing that there are no ‘good reasons why the State should not recognize contracts which are in all respects like marriage, except for the sex of the parties concerned’. We can envisage a society so enlightened that the relations between men and women will be purely platonic and it will be a matter of no concern whether two people are members of the opposite sex or not: or, alternatively, our feelings could be so completely homogenized, that it will make no difference to an emotional relationship whether Leslie and Julian have only one Y-chromosome between them, or two, or none at all. In that event I shall be shown to be wrong, and my critics entitled to erect a monument to female equality on my grave. But I have doubts, and suspect that long after I am dead men will go on falling in love with women and women will continue to find their hearts wooed and won by men. And this fact, if it is a fact, makes a profound difference to our social institutions. I want to follow out the logic of social differentiation, relying as little as I can on putative facts about the differences between the sexes. Scientifically attested knowledge is scarce in this field. Many academics take refuge in a safe suspension of judgment, but this is a craven dereliction of duty. We have yet to develop an adequate theory of knowledge in social matters, and only by thrashing out the apparently telling arguments on this and similar issues can we clear our minds about the nature of social knowledge. Moreover, if those who might argue rationally draw back from doing so, they leave the field clear for others who suffer from fewer inhibitions and fewer scruples. And finally, serious social consequences can follow from public confusion about the logic of a situation, and what things are possible and what desirable. There is a danger that in our attempts to remedy the real wrongs done to women we shall only succeed, as with much modern legislation, in making a bad case worse

After a brief and informal explanation of the Gödel’s theorem as a version of the Epimenides’ paradox applied to Elementary Number Theory formulated in first-order logic, Lucas shows some of the most relevant consequences of this theorem, such as the impossibility to define truth in terms of provability and so the failure of Verificationist and Intuitionist arguments. He shows moreover how Gödel’s theorem proves that first-order arithmetic admits non-standard models, that Hilbert’s programme is untenable and that second-order logic is not mechanical. There are furthermore some more general consequences: the difference between being reasonable and following a rule and the possibility that one man’s insight differs from another’s without being wrong. Finally some consequences concerning moral and political philosophy can arise from Gödel’s theorem, because it suggests that – instead of some fundamental principle from which all else follows deductively – we can seek for different arguments in different situations

We were discussing the retirement age. Many of my colleagues said that of course existing interests must be preserved, but they had noticed that some of their colleagues had been past their prime by the time they reached 67, and that it would be a good thing if in future dons were retired at 65. I agreed, but pointed out that the argument went further. Quite a few of us were already deteriorating before they were 65. Nor was it clear that 60 was the watershed. One could think of people who had finished their creative work by the time they were 55, indeed, by the time they were fifty. In fact some of us were already bores in our forties, and in so far as a large part of our raison d'etre was to teach the young, our ability to relate to them began to diminish in our thirties. The temperature dropped five degree with each five years, and in chilly silence the College moved on to Next Business.