Jean Lucas

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.’

Arguments have been much misunderstood. Not only has it been assumed that they must be deductive, but it has been assumed also that, although often expressed in loose and elliptical form, they must be capable, if they are valid at all, of being expressed with absolute precision, as a set of necessary and sufficient conditions for the action in question to be appropriate. Mathematical arguments are capable of being stated precisely, and it has long been a reproach to workers in other disciplines that they do not manage to achieve equal precision in their work. The assumption is made that absolute precision is in principle available, and it is only a lack of rigour by practitioners in the non-mathematical disciplines that prevents them casting their arguments in satisfactory form, and the philosopher should, therefore, reconstruct arguments to conform with these requirements, evaluating those that do, and rejecting any that do not.

Equality is one of the great issues of our age, but few people stop to wonder at its being an issue in politics at all. Yet it is surprising that a concept which has its natural habitat in the mathematical sciences should have taken root in our thinking about how we should be governed. We do not naturally think of society in terms of group theory, or rings or fields, and have long been aware of the difficulties in establishing any over-arching social or political order. But we unthinkingly assume that we can meaningfully ask, and reliably tell, whether people are, or ought to be, equal to one another even while admitting how difficult it would be to say whether they were more or less than one another. Formal logic can help. Equality is an equivalence relation, that is to say one that is transitive, symmetric and reflexive. Equivalence classes pick out classes of people or things that are the same, or similar , in some respect or other. There are many such, and we need to specify in respect of what two things are or are not equivalent before we are saying, or asking, anything definite. I can be equivalent to you in respect of age, or height, or weight, and many equivalence classes— contemporaries, co-religionists, comrades—may be of great importance socially or politically. But equality is, in its original context, more than just an expression of sameness. It suggests also a possibility of being either more than or less than. I can be the same age as you, but if I were not, I should be either older than you, or younger. This is always the case in mathematics. The law of trichotomy holds, that if two things are not equal, then one is greater, in the relevant respect, than the other, and the difference can itself be measured. With human beings, however, there are rather few respects in which we can be properly measured. Age, height and weight apart, the ascription of most numerical measures is a dubious affair. At one time psychologists were confident that they could measure intelligence, and economists still purport to measure wealth, but the ascriptions they actually make do not seem to deserve the confidence called for..

That space and time should be integrated into a single entity, spacetime, is the great insight of Einstein's special theory of relativity, and leads us to regard spacetime as a fundamental context in which to make sense of the world around us. But it is not the only one. Causality is equally important and at least as far as the special theory goes, it cannot be subsumed under a fundamentally geometrical form of explanation. In fact, the agent of propagation of causal influence is electromagnetic radiation. In this examination, the authors find support for a rationalist approach to physics, never neglecting experimentation, but rejecting a simple empiricist or positivist view of science.

Plato began it. After thinking about the nature of argument he concluded that the correct way of reasoning was the axiomatic way, and formulated the programme of axiomatization that Eudoxus and Euclid subsequently carried out. Since then the axiomatic method has been firmly established, not only as the method for mathematics, but as a paradigm to which all other disciplines should strive to be assimilated; and in this present century not only has axiomatization been carried through as completely as it can be, but the most determined efforts have been made to wish hypotheticodeductive schemata on to biology, economics, and even history.

The Norrington Table is scotched, but not killed. It still appears each year in a national daily, having been compiled by an enterprising graduate with more need for money than time. Some people argue that this shows the futility of trying to suppress the table. But that is not so. In a free society it is open to anyone to obtain information and publish his results. There are many things that people might like to know about colleges. Of greater interest to many than schools results would be the average earnings of graduates of each college five years after going down: that would enable people to pick the best college for repaying student loans, and for enjoying the fruits of worldly success. An enterprising graduate with nothing better to do might go through the university telephone directory, and work out the Ms-ratio for each college and department: no doubt the Daily Telegraph would pay good money for a list of those parts of Oxford that were entirely Ms-free. What is important is not what other people say, but what we say, or seem to endorse its being said, about us. Once the Norrington table appeared to have our imprimatur, it suggested that we set too much score by schools results, and instead of regarding final examinations as a necessary evil, bad, but less bad than any available alternative, we reckoned that getting a good result in schools was the chief..

One of the great virtues of Oxford is that most of its members are not academics, nor ever supposed that they sould be. They come to Oxford for three or four years and then go on their way to other occupations in "the service of God in Church and State". It is not that they were not good enough to become dons: it is simply that they had other fish to fry, and would rather be a barrister, a Member of Parliament, a schoolmaster or a clergyman, and would not be tempted from their chosen vocation by any offer of a Fellowship or a life of ease and scholarship. The benefits of this are great. To have left Oxford of one's own accord and not on account of having failed to get an award or a post is to part from a friend with no sense of having been rejected. The Civil Servant who goes down with a first in Greats has no sense that he did not make it at Oxford, no need to shake its dust off his shoes because Oxford did not offer him a job, and in consequence he can easily look back on four golden years of widening horizons, untarnished by some final disappointment. And in general our alumni can feel warmly to their alma mater, because their going was of their choosing, and not because they were rudely pushed out of the nest.

The ontological argument has run for a long time, regularly refuted, regularly re-appearing in a new form. Something can be learnt from its longevity. Its proponents must be on to something, or it would not have survived its many refutations. But equally, it must have been much misformulated, or it would not have seemed evidently fallacious to its many critics. Perhaps it does express a deep philosophical intimation. Certainly it has been taken to prove more than it really can establish. Like many other philosophical arguments it has suffered by being made out to be more rigorous than in the nature of the case it can be. For some philosophers addressing some questions it may have been decisive in leading them to adopt one of the few options open to them: but it is quite inconclusive for others, with different presuppositions or different problems, and cannot be reduced into a valid proof cogent for all comers and compelling them to accept the conclusion it claims to demonstrate.

Critics of Oxbridge take unkindly to our M.A. When I had to fill in one of those innumerable time-wasting forms to show how unqualified I was to hold an academic post, I was specifically instructed to describe myself as a B.A., which I was proud to do, since our B.A. is our best degree (everything in Oxford being the opposite of what it seems). But the real equivalent of a mediaeval M.A. is a modern D.Phil, with every academic wanting to call himself Doctor rather than Master, which is felt to offend our egalitarian age; and now we are going back to the mediaeval trivium followed by a post-grad quadrivium, it might seem that we should tidy up our gradations, and have simply a B.A. for the former, and a D.Phil. for the latter.

In Epiphany Term, 1942, C.S. Lewis delivered the Riddell Memorial Lectures in the Physics Lecture Theatre, King's College, Newcastle, which was then a constituent college of the University of Durham. The Riddell Memorial Lectures were founded in 1928 in memory of Sir John Buchanan Riddell of Hepple, onetime High Sheriff of Northumberland, who had died in 1924. His son, Sir Walter, was, like his father, a devout Christian, active throughout his life in public affairs. He was Fellow, and subsequently Principal, of Hertford College, Oxford, and Secretary, and subsequently Chairman, of the University Grants Committee---at a time when the interventions of the UGC in academic affairs were entirely benign. I myself have a special personal interest in the founder of the Riddell Lectures. Sir Walter and my father were contemporaries at Oxford and close friends. Owing to his untimely death I never knew him, though I am credibly assured that he must have viewed me when I was taken to Hepple in a Moses' basket at the age of six months. In being invited to give this lecture on the Riddell Lectures, I am not only honoured but enabled to discharge a debt of family..