In this article, Lucas maintains the falseness of Mechanism - the attempt to explain minds as machines - by means of Incompleteness Theorem of Gödel. Gödel’s theorem shows that in any system consistent and adequate for simple arithmetic there are formulae which cannot be proved in the system but that human minds can recognize as true; Lucas points out in his turn that Gödel’s theorem applies to machines because a machine is the concrete instantiation of a formal system: therefore, for (...) every machine consistent and able of doing simple arithmetic, there is a formula that it can’t produce as true but that we can see to be true, and so human minds and machines have to be different. Lucas considers as well in this article some possible objections to his argument: for any Gödelian formula we could, for instance, construct a machine able to produce it or we could put the Gödelian formulae that we had proved as axioms of a further machine. However - as Lucas underlines - for every of such machines we could again formulate another Gödelian formula, the Gödelian formula of these machines, that they are not able to proof but that we can recognize as true. More general arguments, such as the possibility to escape Gödelian argument by suggesting that Gödel’s theorem applies to consistent systems while we could be inconsistent ones, are moreover refuted by Lucas by maintaining that our inconsistency corresponds to occasional malfunctioning of a machine and not to his normal inconsistency; indeed, a inconsistent machine is characterized by producing any statement, on the contrary human being are selective and not disposed to assert anything. (shrink)

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. (shrink)

The application of Gödel’s theorem to the problem of minds and machines is difficult. Paul Benacerraf makes the entirely valid ‘Duhemian’ point that the argument is not, and cannot be, a purely mathematical one, but needs some philosophical premisses to be able to yield any philosophical conclusions. Moreover, the philosophical premisses are of very different kinds. Some are concerned with what is essential to being a machine—these are typically intricate, but definite, easily formalised by the mathematician, but unintelligible to the (...) layman: others attempt to capture what is essential to being a mind, a person or a self—these are typically intuitive, but vague; resistant to exact definition by the logician, but, none the less, widely used and well understood. Gödel’s theorem itself, like many other truths, can be taken either way: it can be taken as a formal proof sequence yielding certain syntactical results about a certain class of formal systems, but it can also be taken as giving us a certain type or style of argument, which we can understand, and, once having got the hang of it, adapt and apply in innumerable different circumstances. In my dispute with the mechanist, I take Gödel’s argument both ways: I first take it as an argument which the mechanist, even according to his own mechanist principles, must accept as scoring some point against his favourite machine; and then I hope that the mechanist, as a man, will see that he can do better and that this sort of argument will always apply against any form of mechanism he espouses. (shrink)

The issue is obscured by the fact that the word `space' can be used in four different ways. It can be used, first, as a term of pure mathematics, as when mathematicians talk of an `n-dimensional phase-space', an `n-dimensional vector-space', a `three-dimensional projective space' or a `twodimensional Riemannian space'. In this sense the word `space' means the totality of the abstract entities-the `points'-implicitly defined by the axioms. There is no doubt that there exist, iii this sense, non-Euclidean spaces, because all (...) that is claimed by such an assertion is that sets of non-Euclidean axioms constitute possible implicit definitions of abstract entities, that is to say that some sets of non-Euclidean axioms are consistent. If Kant or any other philosopher had denied this, he would have been wrong; but Kant himself took care not to deny it, 2 and there is little reason to suppose that any philosopher concerned about space has been using the word in this, the pure mathematician's, sense. (shrink)

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. (shrink)

Equality is the great political issue of our time. Liberty is forgotten: Fraternity never did engage our passions: the maintenance of Law and Order is at a discount: Natural Rights and Natural Justice are outmoded shibboleths. But Equality—there men have something to die for, kill for, agitate about, be miserable about. The demand for Equality obsesses all our political thought. We are not sure what it is—indeed, as I shall show later, we are necessarily not sure what it is—but we (...) are sure that whatever it is, we want it: and while we are prepared to look on frustration, injustice or violence with tolerance, as part of the natural order of things, we will work ourselves up into paroxysms of righteous indignation at the bare mention of Inequality. (shrink)

MANY thinkers deny the possibility of businessmen having responsibilities or ethical obligations. A businessman has no alternative, in view of the competition of the market-place, to do anything other than buy at the cheapest and sell at the dearest price he can. In any case, it would be irrational-if, indeed, it were possible-not to do so. Admittedly, there is a framework of law within which he has to operate, but that is all, and so long as he keeps the law (...) he is free to maximise his profits without being constrained by any moral or social considerations, or any further sense of responsibility for what he does. (shrink)

Justice has always been regarded as one of the fundamental political virtues. No association of human individuals could subsist, says Hume, “were no regard paid to the laws of equity and justice”, and nearly every thinker who has turned to consider human society, has reached the same conclusion. Yet we are not at all clear what justice is, nor why it is so important. There are many other ideals which a society may cherish, and often reformers have felt impatient of (...) having to compromise their aims merely for the sake of justice, and have not seen why the claims of justice should in any way override other political goods. I shall try to show why justice is, along with liberty, a peculiarly fundamental ideal, which is not merely co-ordinate with other ideals a society may value; but also that this notwithstanding, considerations of justice are not all-sufficient, and do not, and should not, always override all other political ideals. (shrink)

My sights in this paper are trained on facts. Most people think that they know what facts are; that while their friends often, and themselves occasionally, are ignorant of the facts, at least they know what sort of things facts are---they can recognise a fact when they see it. Facts, in the popular philosophy of today, are good, simple souls; there is no guile in them, nor any room for subjective bias, and once we have made ourselves acquainted with them, (...) we have reached the beginning and summit of all wisdom. (shrink)

Abstract Quantum mechanics has seemed to defy all attempts to construe it realistically, but antirealism, like the many?worlds hypothesis, is even more difficult to accept. In order to give a realist construal of quantum mechanics, we need first to distinguish the objective and rational aspect of reality from the paradigmatic thing?like aspects of having determinate physical properties: quantum?mechanical entities may be real in the former sense though not in the latter. Anti?realist arguments are based on the difficulty of giving an (...) account of quantum?mechanical collapse and the apparent superluminal velocities involved. Objections to superluminal velocities on the score of the special theory of relativity are found not to be conclusive, and the price?there being some preferred frame of reference?to be acceptable. A sketch of a probabilistic account of quantum?mechanical collapse is offered, which makes the difference between the macro? and the micro?world a matter of degree rather than kind. If that, or some other, account proved acceptable, we could be quantum?mechanical realists, though quantum?mechanical reality would be very different from that of material objects in hardware shops. (shrink)

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. (shrink)

J. R. Lucas; XII—Or Else, Proceedings of the Aristotelian Society, Volume 69, Issue 1, 1 June 1969, Pages 207–222, https://doi.org/10.1093/aristotelian/69.1.207.

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. (shrink)

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. (shrink)

Professor Braithwaite’s inaugural lecture, here published in book form,1 is a trial run at a Platonic definition of the concept of dianemetic justice; or, as he himself would put it, a rational reconstruction of the concept “sensible-prudent-and-fair”. Aristotle left it that dianemetic justice was an equality and a matter of ratios. A just distribution of őoα µεριστ? τoς κoινωνoσι τς πoλιτείαѕ2 was one in which each had an equitable share, no one having either more or less than he should. Professor (...) Braithwaite goes further and replaces Aristotle’s ordered scale of the-more-and-the-less in which only imprecise and unhelpful answers could be given, by a numerical scale in which he can frame the question “Exactly how much is a fair share?” and propound his s own solution. (shrink)

The problem with which I wish to deal in this paper is the problem of singular reasons in the humanities, whether they exist, or rather, whether they can exist: for it would seem that the word “reason” carried with it some idea of generality, so that the phrase “singular reason” was a contradiction in terms, a specification which could never be fulfilled. But humanists are always sensing the singularity of their studies: and the philosopher wondering about the nature of humane (...) thinking either must conclude that it is really only inadequate science, its singularity being the mark of the fact that we never really have an adequate basis for any of our generalizations, an unfortunate reminder that the whole structure is built on the shakiest of inductive foundations; or , if he is unwilling to allow that humanists are just bad, or at least amateur, scientists, he is tempted to vindicate the rationality of their reasoning by inventing a special faculty of particular ratiocination which is able to perceive particular truths—the intuition of the moralists or the insight of the Collingwoodian mode. (shrink)

“ Ich liebe dich 3 ” the swains in mountain valleys of Austria inscribe on their presents to those to whom they plight their troth. The pun is a rare one in German. Only in remote valleys does the word for ‘three’ rhyme with joy; and the word for ‘true’ is usually ‘ wahr ’ not ‘ treu ’ ‘ Wahr ’ is more propositional, less evaluative than our ‘true’. So too in Latin and the romance languages ‘ verum ’, (...) ‘ Vrai ’ ‘ vera ’ ‘ verdadero ’ carry a lighter load of feeling. Only the Hebrews resembled us in giving their word for ‘true’ strong moral overtones, and using the same or some cognate word to praise him who had used no deceitfulness to his neighbour as to recommend some statement as being meet to be believed. (shrink)

South. So we have agreed to bury intuitionism. Well, I dare say it is right. But we ought to bury some of the grave-diggers too. Some of the things that Ross said are no doubt wrong, or at least misleading: but they are a lot less wrong than most of the things said since the war.

Equality in the present age has become an idol, in much the same way as property was in the age of Locke. Many people worship it, and think that it provides the key to the proper understanding of politics, and that on it alone can a genuinely just society be reconstructed. This is a mistake. Although, like property, it is a useful concept, and although, like property, there are occasions when we want to have it in practice, it is not (...) a fundamental concept any more than property is, nor can having it vouchsafe to us the good life. In an earlier paper I argued against equality by showing that the concept of equality was confused and that many of the arguments i egalitarians adduced were either invalid or else supported conclusions I which were not really egalitarian at all. Many egalitarians, however, have complained that my arguments were not fair, because I had failed to elucidate the concept adequately, or because the position I attacked was not one that any egalitarian really wished to maintain, or because I had overlooked other arguments which were effective in establishing egalitarian conclusions, or because the positive counter-arguments of my own I put forward more as a matter of taste than of serious political commitment. In this paper, therefore, I want to elucidate the concept more fully, concede what I should to my critics, point out that, even so, their conclusions do not follow, and give further reasons not only for supposing that egalitarian arguments are invalid but for discerning positive merits in some forms of inequality. (shrink)

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. (shrink)

The experimental and highly regarded Gifford Lectures at Edinburgh University was endowed in the late nineteenth century. Over the years, participants have including many leading representatives of religion, science, and philosophy. This series has as its subject, The Development of Mind. First published in 1972, the series continues to attract widespread interest. In this volume, contributors argue about the mind from diverse analytical standpoints. The focus of the series remains the relationship between religion, science, and philosophy. This volume attempts to (...) achieve a comprehensive view of the subject of mind. The mental development of children in the light of modern psychology is discussed, and the distinction between "how" and "why" questions is put forward with clarity. The development of mind is further contrasted with the evolution of embryos in the young. The mind is considered as a capacity for intellectual activity, and as a multi-purpose program. Goal-directed behavior and language development are given importance, and issues of cosmic purpose, and the how and why of evolution, are never far from the surface of the argument. The lecturers know their opposition and their positions, and the cut-and-thrust of the discussion has much acumen and wit to it. Issues ranging from the impact of mind on theories of religion, causation, and rational will are examined in an informal, yet compelling, manner. (shrink)

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. (shrink)

Plato was politically incorrect---gloriously incorrect: hard to ignore and difficult to refute. Read An Engagement with Plato's Republic to argue with him or against him, for contemporary orthodoxies or against them. ``Plato was the first feminist. Women were the same as men, only not so good.''.

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. (shrink)

Of course I have an axe to grind. I am one of the old school of tutors, generally regarded as outmoded and amateurish by our more up-to-date successors, who are anxious to introduce more professionalism into Oxford's academic life. I probably shan't be replaced, but if I am, it will be by somebody competent, capable of looking the twenty-first century in the face, who knows what he is about, and adopts effective means to bringing it about.

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.