To speak of equality in education is rather like speaking of equality in love. Young men sometimes wax indignant about the unfairness of their lot, and say there ought to be arrangements whereby the available girls should be shared out equally, so that everyone should get his whack; or, more sophisticatedly, that the most desirable girls should be made to bestow their favours on egalitarian principles, so that the total female talent be fairly distributed and nobody be deprived of his rightful meed of femininity. We smile; not only at the ludicrous incongruity of bureaucrats in the Ministry of Love issuing ration cards to students giving them 2.7 date-points per week, but because the very vehemence of the young men's protestations shows that they do not understand the nature of love or what personal relations really are like. It is the same with education. Learning or teaching are like loving and friendship in being primarily a matter of personal initiatives and personal responses. I learnt because my teachers talked to me and listened to me, often told me things and often tried to see what my difficulties were and help me overcome them, and occasionally inspired me or enraged me or led me to have new insights entirely of my own. And so it is with all pupils and all teachers. In so far as anybody is educated by anyone else at all it is by personal contact and personal commitment. Institutions and syllabuses, examinations and educational authorities may have their part to play, but what makes education a reality is a personal relationship  between teacher and pupil, and with personal relationships no questions of equality can arise. Educationalists can ask whether one child has as many books or as many footballs as another child, or whether his teachers have as many `A' levels or as many Certificates or Diplomas of Education. They can also ask whether a certain selection-procedure is fair, or whether, in some specified sense, it gives all candidates equal opportunity of success. But if they become obsessed with these questions or if they make grandiloquent demands for educational equality of every sort, they raise the suspicion that they do not know what education is. For education is essentially the sort of thing to which the concept of equality does not apply.
It is easy, and proper, to counter the demand for equality in education with the question `Do you know what education really is?' It is a fair rejoinder, but an ineffective one, because those most vulnerable to this attack are least aware of their own ignorance. And whereas time often tames adolescent anger and teaches young men what love is like and why it cannot be had as of right or assigned on egalitarian principle, educationalists seldom come to know by further experience what education is really about, and continue to talk about it and apply inappropriate concepts to it with a confidence that increases with the passage of time and the distance from the class-room. And, unfortunately, they have great influence. The educational world is a grey one in which those who can, teach, and those who cannot, administrate or pontificate, and the administrators and pontificators are allowed to tell the teachers what to do. In this book, therefore, we address ourselves not to education, but to arguments, often bad arguments, about the periphery of education, not in order to elucidate the concept or give hints about its practice, but to prevent its being prevented by the mistaken pursuit of illusory and inappropriate ideals.
If we cannot usefully put questions about education, we can about equality. Equality has its original locus in the mathematical sciences. We can say that the number of children in this class is equal to the number in that, or that the two children have got an equal number of marks, or that the amount of money per pupil spent by this educational authority is equal to that spent by the neighbouring one, or that the average weight of a Lancashire lass is equal to that of a Yorkshire lad of the same age. We may go further and apply equality to variables which are not metrical but  only ordinal, as when we say that these stones are equally hard, or these two boys are equally intelligent. We mean that neither stone is harder than the other, neither boy is more intelligent than the other. Such usages may be intelligible, but may conceal hidden assumptions which may be false. In the language of the mathematicians an ordering may, or may not, be complete. In our ordinary understanding of time any event is either before some other given event, or after it, or else at the same time as it: but in relativity theory we have to contemplate events which are neither before nor after each other nor contemporaneous with each other. So too we may say of two boys that neither is more intelligent than the other without implying that they are equally intelligent, because one is better than the other at Latin and modern languages, but worse at mathematics and the natural sciences. Psychologists used to make out that there was a single factor, called intelligence, which could be measured by intelligence tests, and expressed as an intelligence quotient. We cannot rule out such a possibility a priori, but only remark that it runs counter to the facts as most people experience them, and that too often under pressure intelligence was covertly defined as the ability to do intelligence tests, which is indeed a magnitude that is completely ordered. Psychologists apart, we believe that different people have different intellectual gifts and that a boy who is worse than his fellows at some subjects may still be better at others. People who press for precise assessments of intelligence are like those who argue whether Plato was a greater philosopher than Aristotle or Kant, or the Parthenon more beautiful than Santa Sophia or the Dome of the Rock. It is not that we cannot ever make comparisons of philosophical profundity or aesthetic perfection, but that we cannot always. Plato is a greater philosopher than Plotinus or Porphyry, the Parthenon is more beautiful than the temples at Bassae or Agrigento: and by the same token it may be true that one boy is more intelligent than another. But from the fact that we can make comparisons it does not follow, although it is often believed to follow, that we tan usefully apply the concept of equality. In some cases we can, as with hardness or with age: in others we cannot, as with relativistic time, and, as I believe, intelligence.
It is the same with social equality. I habitually pay respect to the Warden, the Vice-Chancellor, the Archbishop of Canterbury, and the Queen, and undergraduates and scouts like to call me `Sir', and shop-keepers and parents listen to my opinions with deference. But if an American Congressman or a rising journalist  or a successful pop- singer were to come across me, he would be as little likely to feel respect towards me as I towards him: yet it would be an unwarranted conclusion that we were, therefore, social equals. Social equality is something much more positive than a mere absence of an ordering relation, and may, indeed, be compatible with a definitely defined order. The situation is further complicated by the fortunate fact that in most societies there is no single all-embracing hierarchy of status, but a multiplicity of conflicting ones. As a College tutor I give authoritative advice to an undergraduate on what subjects to study or books to read for our next tutorial, but down on the river as a member of the dons' eight I endeavour to manoeuvre my oar in accordance with the instructions of our undergraduate coach; and there is no incongruity in my being represented on the town council by a scout, or following the lead of a shopkeeper in Church, a boys' club, or a folk-dancing group. This is not to say that the concept of social position is useless; but except in strict status societies, like Russia or large business firms, it is a fairly imprecise concept, and one that cannot give us a useful, negative, definition of social equality.
Equality can be characterised in mathematics not only negatively in terms of ordering relations, but positively in terms of equivalence relations. An ordering relation is one that is transitive and asymmetrical: if I am taller than you and you than James, then I am taller than James; and if I am taller than you, then you are not taller than me. An equivalence relation is likewise transitive, but symmetrical, not asymmetrical: if my weight is equal to yours, and yours to James', then mine is equal to James, but also if mine is equal to yours, then yours is equal to mine, not unequal. Ordering relations and equivalence relations are the two most important types of relation. Ordering relations are often expressed in English by the form `er than' (with the one exception of `other than'): equivalence relations are often expressed by some phrase using the word `same', e.g. `the same weight as'; an equivalence relation relates together all those things which have the same property. In fact, we often use equivalence relations to introduce, or even to define, properties. The concept of weight depends on our having balances, together with the facts, vindicated in experience, that if two objects exactly balance when placed in the scales, they will still balance if we interchange them, and that if two objects each exactly balance when weighed against a third, they will balance also when weighed against each other. Balancing is a symmetrical and transitive relation, which therefore enables  us to pick out all those things that balance with one another, and say that they are all in some respect the same, namely in respect of weight. Weight is just the property with the respect to which each equivalence class is the same. Frege and Russell used a similar strategy in defining the concept of number. They were able to define a `similarity relation' which could hold between classes (in the logician's sense of the word, often now called sets) and which was transitive and symmetrical: if one class is similar to another, and that other to a third, then the first class is similar to the third; and if one class is similar to another, then that other is similar to the first. All those classes which are similar to one another are said to be equinumerous, and a natural number is then defined as what a class of equinumerous classes have in common. Twelve is what the class of the apostles, the class of calendar months, the class of the sons of Jacob, the class of inches in a foot, etc., etc." all have in common. It may seem a very artificial way of defining number, and, indeed, all sorts of logical objections have been discovered. Nevertheless, the approach is a common one. When we were first introduced to the concept of a fraction at school, we were taught to cancel out, and write 9/12 as 3/4, 14/63 as 2/9 etc. More formally, we could have been told that any pair of natural numbers constituted a ratio, but that two ratios, a/b and c/d were equal to one another if ad = bc, and then that a fraction was to be defined as an equivalence class of ratios that were, according to this definition, equal to one another. Equal ratios constitute one and the same fraction. Once we have defined a relation that is an equivalence relation, we can use it to specify, define or introduce a further, higher-order, concept which is what is common to all those entities between which the given relation holds. In politics we often argue the other way, and represent the fact that a number of men all have some property in common as their being all equal in this respect. Instead of saying that we all shall die---which is true but not very grandiloquent---we talk of death being the great equaliser. Equality before the Law does not mean that the Law metes out the same sentence to us all, innocent and guilty alike, but only that we are all under the law and all answerable for our illegal acts. Many egalitarian arguments rest upon a pompous and misleading reformulation of undeniable and important truths. All men are men---nobody would deny it, and few would doubt that important consequences flow from the fact of our common humanity. But if we reformulate this truth and say that all men are equal in respect of their humanity, it is easy to forget that this is a mere tautology, misleadingly expressed, and  to take it as meaning, among other things, that all men have an equal right to go to grammar schools. That this is a fallacious argument can be best demonstrated by replacing the word `men' by the word `numbers', when we have: All numbers are numbers. therefore All numbers are equal in respect of numberhood. therefore All numbers are equal. Although fertile of fallacies and confusions, the connection between equality, sameness and unity is of fundamental importance in their applications of these concepts in social, legal and political contexts. Often we have good reasons for meting out the same treatment to different people, and often we are wanting to pick out some pervasive principle of unity, and in either case it may seem more economical or down-to-earth to talk in terms of the relevant equivalence relation. Countries are remote entities of abstract political theorising, but fellow-countrymen are real. The ideal of justice is difficult to understand, difficult to realise, but we can easily tell if others are being treated differently from ourselves, and sense that it violates our fundamental equality before the law. Hence we often express in egalitarian terms demands which are at bottom demands for unity or uniformity; and egalitarianism becomes the vehicle by means of which a large number of different, and not always compatible, aspirations are voiced. Egalitarians wax righteously indignant if any one dares to gainsay them, but the fervour of their denunciation is not matched by any corresponding clarity of discrimination. We know that there is great moral passion in the demands, but not what exactly is being demanded. And it is this latter point on which the whole question turns. Unity and uniformity are manifold, and there are many unities and many uniformities we might reasonably desire: but we cannot hope to have them all, and if we are wise we shall recognise that there are also many unities and many uniformities we ought not to, and usually do not, want. We must discriminate. Some similarities are important and ought to be taken into account, others are irrelevant and ought to be discounted. Some uniformities are desirable and ought to be encouraged or enforced, others are of no particular value or even positively unjust. Whenever equality is spoken of, we need to know in respect of what people are said to be equal, or in respect of what the treatment accorded to them is supposed to be equal. And nearly always we shall find it a great aid to clarity if we re-phrase the contention  in terms not of equality but of the underlying features and properties in respect of which the relevant sort of equality is alleged to hold.
Opportunity, like Equality, is a treacherous concept, and Equality of Opportunity doubly so. To have an opportunity of doing something is not to be able to do it, but to be able to try, though without any certainty of success. As I consider what course to take, I have to recognise that many courses are not open to me and that I had better put them out of my mind at once. I have no opportunity of becoming President of the United States or Pope; these doors are closed to me, and I cannot set about making my way in the direction of those goals; but I do have the opportunity of becorhing a city councillor or a member of the diocesan synod; if I wanted to, I could set about getting myself elected. I might not be successful, but for all I know now I might be successful, and at least I could try. The door is open---the relevant door that I can see from my present situation---although if I go through it, I may find other doors which are barred, or may lose my way in the maze of rooms and passages beyond. But for all I know, I may succeed. And therefore if I do not decide to make the attempt, it is because I do not want to, not because I cannot.
It follows that whether I have an opportunity or not depends very much on the context in which I am speaking. Although I have no opportunity of being President of the United States or Pope, I do, in a sense, have an opportunity of being Prime Minister. I am eligible, in the sense of not being disqualified on the score of nationality or religion, as I am disqualified from being President or Pope. But although I am eligible in this sense, I am not eligible in another. I am not a Member of Parliament, and therefore the Queen could not even consider sending for me. And although in one sense I should have an opportunity of becoming an MP next time there is an election---I am not a peer or a lunatic, and so can stand---in another sense I have no opportunity at all-nobody will vote for me on the strength of my personal characteristics, and I cannot get a party to put me forward as their candidate. Thus whether I have an opportunity or not depends on how I see the situation in which I am making the choice. So far as formal eligibility goes, I have an opportunity---I am not formally disqualified: but so far as practical politics go, I am entirely out of the running. If I were a citizen of Boston, Massachusetts, but a  Protestant, I should have an opportunity in the formal sense of being Mayor, but not in any substantial sense. One of Scott Fitzgerald's heroes worked out that undergraduates at Princeton invariably elected blond men with blue eyes as their leader; in which case 1, whatever formal opportunities I might possess, would never have any real opportunity of leading Princeton's youth. Although the formal door is open, yet if I look through it I can see that the next door, one of the practical ones, is shut, and so I reckon that that way is effectively closed to me. It depends on how far I can see ahead and how far I look, what opportunities I can reasonably reckon I have.
Equality of opportunity implies comparison. My opportunities are being compared with yours. We must therefore be aiming at the same sort of goals, or our opportunities would clearly be non-comparable---how could we compare my opportunity of getting on the town council with yours of making friends? We must also be assessing the situation from the same vantage point, or again we shall be talking at cross-purposes---had I the same opportunity of getting to the University in the 1940s as you in the 1970s? I may say that I had less of an opportunity because far fewer places were available, but you may say I had far more of an opportunity because there were fewer people trying for them. Unless we define the situations in which our respective opportunities are being assessed, comparisons become impossible. Hence equality of opportunity tends to be applicable only in the context of a competition where a number of people are competing for the same goal in accordance with rules, which can be assessed as being equal or unequal. We can say of bridge or football or monopoly that the players have all an equal opportunity of winning. This does not mean that they all will win; nor necessarily that they all have the same chance of winning---skilled bridgeplayers or footballers tend to win more often than their opponents; but it does mean that the rules of the game do not themselves favour any one competitor rather than any other. And where the rules do introduce some asymmetry-as between the Surrey and Middlesex banks in the Oxford and Cambridge boatrace, or the choice between batting and fielding in cricket, or having the first turn in Monopoly, it is felt to be a blemish, requiring a preliminary toss of the coin or shake of the dice to allocate advantageous asymmetries impartially. Games lose their point if the outcome is a foregone conclusion, and if from the mere rules of the game it is clear that one competitor has a significant advantage, we do not think much of it as a game. We require of  games that they shall, so far as their rules are concerned, give each competitor an equal opportunity of winning.
The distinction between rules and other factors is difficult to maintain. However they start, games (other than cricket) tend to end in victory for one competitor and defeat for the rivals. And in so far as we can account for the outcome it will be in terms of some antecedent asymmetry between the players which may in turn be stigmatised as unequal and unfair. Even in games of chance it depends very much on how we describe the situation whether we assign equal or unequal chances to the players: given the disposition of the cards or the dice, I have no chance whatever of winning; it is only under another, and not obviously more applicable, description that I can be said to have an equal chance; and considerable philosophical argument is required to assure us that the latter is both applicable and relevant.1 The difficulty strikes us more forcibly in games of skill, and often we arrange the competitors in `leagues' where they will be more or less evenly matched, or impose handicaps on the stronger, in order that the result may still be open.
Games are played only for fun, and there is no very strong reason why one set of rules should be preferred to another. We may think that the result of the boat-race should depend on the muscles of the oarsmen and not on skilful coxing, but we may not; just as some people think that players should not handle the ball in football, and different people have different conventions for playing bridge. But life is not a game, and when we assess competitive situations in which real goods are at stake, we can criticise the rules not merely for formal inequalities but substantial ones. We often decide disputes by some form of competition-as when we put a public contract out to tender, or award scholarships by an examination, or hold an election---and essentially we require the parties to the dispute to conduct a rule- governed exercise on the basis of which the dispute will be decided. We can therefore criticise either the exercise or the rules whereby it is interpreted, as being irrelevant to the dispute in issue. Ordeal by combat has fallen into desuetude because ability to fight is irrelevant to the justice of one's case. If we are going to award contracts by competitive tender, we must advertise the fact, so that contractors have an opportunity of tendering, and should take into account not only theprice they ask but the quality of their workmanship. if we are going to have an examination, we should not tell  some candidates but not others what questions are going to be asked.
Although the structure of any real-life competition is inherently open to criticism, it is inherent also in the nature of a competition that not all such criticisms be accepted. For competitions are artifices whereby we deem one exercise, fairly easy to evaluate, to be the decision also of another more difficult dispute. Hence it is bound to be somewhat crude, placing a premium on some features that are irrelevant and neglecting other relevant ones. The large well-known firm that can undercut its rivals has an advantage in securing public contracts. The undergraduate with a quick facile mind does better in university examinations than one with a more profound but slower-moving intellect. The scion of an ancient family has a better chance of achieving public office than his opponent whose name is entirely unknown. We should be always prepared to admit the force of such criticisms, and sometimes to alter the rules so as to meet them---as when one consulship at Rome was reserved for plebeians, or when some places in the Civil Service were given without a written examination: but we cannot meet them all, or we shall no longer be having a rulegoverned way of deciding the dispute at all. In this, as in many other aspects of political life, we have to forgo the best in order to ensure that we do not end up with the worst. Examinations, we should concede, are often an evil. But they are less of an evil than any alternative might become. If we have an examination, there are certain rules, not totally irrelevant to the awards in issue, and everyone has an equal opportunity under those rules of winning the awards in question. It does not give everyone everything he wants: in particular, it does not and cannot give everyone a guarantee of success, or even an equal chance of success. But it does mean that nobody starts off at a formal disadvantage by reason of the rules. And this is something.
We can make sense of Equality of Opportunity in particular games or particular competitions, but life is not a game, nor should it be viewed as a continuing race. Convention can determine what counts as a goal in soccer but not what should be regarded as the goals in life, and therefore we cannot lay down what factors should be relevant, and what ought not to be allowed to count. We are equally uncertain when the race begins and where the finishing post is. Every contest ends in some contender winning and others not. But if every contest is succeeded by another contest, the strict egalitarian may object to the result of the first contest being allowed to have any influence on the outcome of the  second. Those who pass the eleven-plus have an advantage over those who fail, when they come to compete for places at the university. So egalitarians, who were loudest in their support of the eleven-plus in the 1940s, on the ground that it gave children equality of opportunity, clamour for its abolition, on the ground that it denies children equality of opportunity. 2 Even at the outset of their school career, the children of middle-class parents have an advantage by reason of their home environment, and equality of opportunity seems to require that all children should from birth be brought up in state crèches in order to ensure that none should obtain any adventitious advantage over his peers. But even birth is too late. Ability is partly inherited, and genetic inheritance is fixed from the moment of conception. And therefore the egalitarian finds himself unwillingly toying with the unwelcome conclusion that only in a Brave New World where we are all clones shall we have secured true equality of opportunity. 3
It is clear what has gone wrong. As we have generalised from a game or an isolated competition to the whole of life, both the purposes and the temporal limits of the competitive situation have become indefinite, and therefore the crucial distinction between asymmetries in the rules---which are open to objection as denying equality of opportunity---and differences in skill and luck is obliterated, and it becomes easy to argue the toss. Every competition must result in some being successful and others not: and therefore, if the competition proceeds on a rational basis, it not only creates a new inequality, but reveals an antecedent one. A competition in which there is equality of opportunity is one in which the best man wins, and therefore one in which the winner is deemed to have been the best man, and in that crucial respect, unequal. Many educational statisticians have laboriously amassed figures to show that children of professional people obtain proportionately more places at the university than children from the working classes, and have concluded that this shows up the unfairness of the system. But what these figures reveal is not that children from the working classes have less opportunity of getting into the university, but only that they are less likely to. We can say that there is a smaller probability of a child of working-class  parents getting into the university than of a child of middle-class or upper-class parents; and it is tempting, but fallacious to rephrase this as that a child of working-class parents has a smaller chance of getting into the university, and then construe that as meaning that he has less opportunity, or that there is discrimination against working-class children. For although the low proportion of children from the working classes could be due to their not having had the same opportunities, it could also be due to their not having wanted to go to the university or to their not having been as academically gifted as their competitors, and therefore having been quite fairly turned down in a competitive examination. Only if we make the two assumptions that all people want to go to the university and that all people are equally gifted academically can we infer any unfairness from the figures. And these assumptions are not only unwarranted but are contrary to all that we know about young people's motivation and about human heredity.
But even so the egalitarian will not be content. Even if there is equality of opportunity, it only serves to reveal and to emphasise other inequalities. If there is any selection at all, there is, in some sense, discrimination, to which the egalitarian, shifting his ground, still takes exception, and demands that it too be eliminated. `Discrimination against working-class children does not meet the most elementary requirement of justice. The objective should be equality, not equality of opportunity. 4 This change of front reflects neither dishonesty nor outstanding stupidity on the part of egalitarians, but the ambiguity of the concept of opportunity and the internal inconsistency of that of absolute equality. Whenever we talk of opportunities we should remember that what we are talking about is whether it is worth trying, not whether we can be sure of success: and whenever we talk of equality we need both to be able to say in respect of what people are being compared, and to remember that although we can secure equality in certain respects between members of certain classes for certain purposes and under certain conditions, we could not conceivably secure equality in all respects between all men for all purposes and under all conditions. 
Equality of opportunity is a treacherous concept, but has seemed a natural one with which to express a certain requirement of justice we wish to maintain in our society. We believe in justice, and one of the tenets of distributive justice is that benefits at the disposal of the state should be apportioned fairly. And therefore education, which is generally reckoned to be a good, and which is largely financed by public funds, should be made available according to some just principle of distribution. But justice is many-faceted, and may, as Aristotle observed, be taken as requiring that each be given an equal share or that each be given a share proportional to his deserts. Much of the present debate is a re-play of that which went on in Athens in the fourth century BC; in particular, the egalitarian feeling which is current now is to be seen historically as a natural reaction against the meritocratic argument fashionable in the forties and fifties of this century, and shares with it the mistaken assumptions that education is a good that can be distributed according to formula and that life is a competitive exercise in which those competitors who have a good education, have an advantage over those who do not. These are both profound untruths, but contain enough truth to be very plausible and widely believed. Education is not a good to be doled out by civil servants like petrol rations: but since it is institutionalised in schools and universities, admission to these is naturally regarded as a good for which people may reasonably compete. Again, although education should be aimed at enabling each individual to fulfil himself, fulfilment depends on his relations with society as well as with himself, and for some people depends very much on being successful according to various external, public criteria. Since the Middle Ages England has been a country in which clever boys `get on' by climbing the educational ladder. Education has been for them a way up to the top, and has been represented in this light to many others. One source of our present discontents has been the over-extension of this concept. So long as only a few schoolboys regarded education as a race, no great harm was done. Their own view of themselves and their potentialities may have been needlessly narrowed, but other people were free to develop their abilities uncompetitively, and those who failed to get full marks were under no pressure to regard themselves as failures for life. The meritocrats thought this wrong. In the name of equality of opportunity, they made every one compete, and made out that the only way of doing well in life was to  go from school to University and thence into the higher reaches of the Civil Service or some other suitable setting for Top People. Most people, however, do not want to wear bowler hats or read The Times. They feel that although life has its competitive aspects, it is not to be construed itself as a competition; and if other people insist on so construing it, those who can would rather not compete, and those who cannot, feel themselves unfairly done by. There are great virtues in learning Latin---to have read Catullus will forewarn a young man and enable him to know in advance what love can be like---and in order to overcome individual idleness we may add the argument that only by learning Latin will some necessary examination be passed. But if the overarching justification for learning Latin, or anything else, is solely in terms of clearing examination hurdles in order to stay in the field for a further examination still, the whole activity is, and is seen to be, a pointless exercise. The meritocratic view of education, like the meritocratic view of life, is tolerable only so long as it is not generally accepted. A generation ago, reactionary schoolmasters and dons were being criticised by educationalists for not showing adequate enthusiasm for competitive examinations, intelligence tests and the like. Now that our educational system has been strait-jacketed by competitive examinations, it is being discovered, as a new truth, that examinations are not everything, and that competition is not necessarily the criterion of justice.
It is too easy, however, simply to say that competition is bad. Education is a good, both in itself and as a means to other ends, and although it largely depends on one's own attitude and efforts, it does depend on other things too, some of which can be assessed in a reasonably impersonal way. Some schools are better than others, and although often it is no kindness to a boy to send him to a school where the pace is too hot for him, nevertheless there are many boys who would benefit but who cannot all go. The meritocrats recognised the problem, and offered a solution: good things in education were to be assigned not on the basis of parental pull or wealth but by innate merit as measured by intelligence test or examination. The egalitarians think this is a bad solution, and would rather that there were no problem, and seek to achieve this by ensuring that there are no good things in short supply. In each case, the negative argument seems stronger than the positive. It seems right that facts about the child rather than facts about his parents should be the basis of decisions about him: but the belief that each child has an innate ability which is the sole criterion of educational merit is itself open to serious criticism. For  one thing, as we have seen, the concept of intelligence as a single factor which can be assessed by intelligence tests, is based on dubious assumptions and runs counter to the facts of everyday life. More seriously, even granted that we can make some crude comparisons of intellectual ability, it would be wrong to make this the sole grounds on which to allot the good things of life. Justice is many-faceted, and we fail to do justice to our ideal of justice if we altogether overlook the claims not only of promise but of actual performance, or altogether discount claims based on parental or childhood choice, or on need. Schoolmasters and dons are entitled to devise examinations to show up natural ability rather than industriously acquired knowledge, but they are unfair (as well as extremely unwise) if they make it a rule always to prefer the man who is intelligent but idle to the virtuous but unbrilliant slogger. A willingness actually to work does constitute a claim on scarce educational resources as strong as imputed, but as yet unrealised, potentiality. So too the fact of being willing to forgo other goods in order to devote time or money to scholarly pursuits. Nor are we entitled to rule out the willingness of parents to pay as absolutely irrelevant to whether a child should go to a particular school or not: no man is an island, and no child ought to be regarded as a mere atom in complete isolation from his parents. For better or worse we are our parents' children, and our parents' attitudes are, as much as their genes, deeply relevant facts about us. This is not to say that we are merely our parents' children, and that their inability or unwillingness to pay should be an absolute bar to their children's being educated; but from the fact that a child is not merely its parents' offspring, it does not follow that it is not their child at all, and the valid insight that it was wrong to deny schooling to the children of the poor needs to be distinguished from the fashionable illiberalism which would forbid parents to spend any money whatever on their children's education. If we deny people the right to do the best they can for their children, not only do we infringe one of the fundamental freedoms of family life, but we are being unfair to both parents and children in failing to accord to them that liberty which is their due of deciding their priorities for themselves.
The argument from need is less unfashionable, but no less cogent. The Plowden Report maintained that the country should devote extra resources to depressed areas, and even ardent egalitarians seldom complain at additional attention being given to backward pupils. But remedial teaching for the dull is as clear a breach of the principle of equality as streaming or setting or any  sort of special attention for the clever. But justice is not equality, and what justice requires is not that we treat all children the same, but that we give proper regard to their many and various claims, claims not only of need but of desert, not only of ability but of justice. Justice is not a one- dimensional concept, as both the meritocrats and the egalitarians have wrongly assumed, and is not to be identified either with merit or with equality, or with any of the strands of which it is composed, but rather is to be seen as a web of different guide-lines, each affording some indication of what ought in some circumstances to be done, but none constituting a sole and sufficient criterion for all cases. It is an untidy concept, and can never be completely realised in any actual society. Aristotle realised this, but educational idealists are unwilling to recognise any limitation to their idealism, and, rather than balance the claims of one sort of justice against another, seek to redefine justice in terms of only one aspect of it, and to the neglect of all its other facets; and having reconstructed justice, have little compunction in strait- jacketing education to fit. But if we are wise, and if we value justice and education for their own sakes, we shall take a humbler view of our powers, and see our duty not as that of aspiring to an ideal best, but of avoiding the many actual injustices to which all educational systems---like all other systems---are prone. We cannot hope to have an educational system that is absolutely just, because we cannot hope to have any system that is; and if we delude ourselves by too much talk about ideals, we shall probably overlook glaring injustices under our eyes. What we should do in our concern for education is to take care not to neglect the many different claims based on many different aspects of justice---on merit, on need, on promise, on freedom of choice---and to ensure that, while they cannot all be entirely satisfied, none of them is altogether ignored.
The argument for equality in education is not only founded on a claim for justice. It is often now contended that any difference of schooling is in itself divisive, and that if we want to have a society that is at one with itself and united by strong bonds of fellowfeeling, we must abolish all separation and apartheid between different sorts of school, and educate our young in one homogenised mass.
Fellow-feeling is a powerful sentiment. We could not use the first person plural at all unless we had something in common  whereby we all could be referred to by the one word `we', and we could not do things together unless we shared some understanding whereby we could concert our activities. Even barely to communicate requires, as the word witnesses, that we have something in common, a common language and all the subtle, tacit presuppositions of mutual talk. Not only are we bound to admit a common humanity, but often we want to. Shylock speaks to us all when he says
`I am a Jew! Hath not a Jew eyes? hath not a Jew hands, organs, dimensions, senses, affections, passions? fed with the same food, hurt with the same weapons, subject to the same diseases, healed by the same means, warmed and cooled by the same winter and summer as a Christian is? If you prick us, do we not bleed? if you tickle us, do we not laugh? if you poison us, do we not die? and if you wrong us, shall we not revenge? If we are like you in the rest, we will resemble you in that.'
If we did not share at least these values in common, and did not all eschew pain and seek ease, we could hardly understand one another, or discuss our other values, at all. Yet it is scarcely enough to recognise in another a bare sentient being, and although some great religions and philosophies have proclaimed the common humanity of man, the sympathies that have moved us most have been more limited ones, restricted to one's countrymen, co-religionists, members of the family, or wearers of the old school tie. Not only are such sentiments of social solidarity often intense, but often too they are exquisitely delectable. Middle-aged men look back nostalgically to the days of Dunkirk, because then we all were equal in the face of Hitler's threat, and even Britons talked to one another in trains, knowing that we were all in it together, and that defeat could be averted only if we sank all our differences, and all strained our utmost to preserve everything we held most dear. Family sorrows are often also occasions of great happiness, because in the face of great sorrow members of the family are drawn together, and rediscover how close they are to one another. Friends hark back to hard times they have been through together, and the best days of an undergraduate's life often appear in retrospect to be those when with his contemporaries he walked in the shadow of their final examinations. These moments of stress seem moments of truth, in which we strip away the adventitious artificialities of our normal existence, and know ourselves as we really are, and how much we are at one with one another. We lose the normal sense of alienation from our  fellows, of isolation in private little insulated cells, of insincerity and mauvaise foi, and realise ourselves as part of a whole, which is greater than our puny insignificant efforts can ever be, as a manifestation of an objective fact which is of serious moral worth, in contradistinction to our subjective whims and selfish efforts to have everything just as we happen to please. And so it is that students start demonstrations, and existentialists write books about the moral purity of mob rule.
Plato was the first to be disenchanted with individual autonomy, and seek to replace it by selfless absorption in the pursuit of the common good. In his Republic we read of an ideal society in which individuals no longer seek to maximise their own separate goods, but believing that they all are of one common blood and fashioned from the same clay as their fellow-citizens, are so much of one mind with them that they no longer have any use for the possessive pronouns `mine' and `yours', and even have their wives and children in common. We feel the fascination of Plato's dream. It strikes a chord, especially with those newly come to man's estate, who are finding the burden of making their own decisions heavy, and are yearning for the support that total membership of a group seems to offer. But although drawn, we are also repelled. It is unrealistic to suppose that we could be as selfless as Plato would require us to be, and undesirable that we should be. To be totally of one mind with someone else is to be the same person as he. Of all the different marks of personal identity, the crucial one is the ability to make up one's mind for oneself. Unless one has a mind of one's own, and can take decisions which are at variance with those of other people, one is not a person at all, but only a cypher or a robot. We are conscious of ourselves as autonomous agents, and unless we are free to think for ourselves and form our own intentions, we should not use the first person of ourselves, but only an impersonal third; and our fundamental complaint with Plato is that in his effort to replace `I' by `we', he has succeeded in only replacing it by `one'. True though it is that each one of us can discover his identity only as a member of a group, it is likewise true that each can be himself only also in contrast to everybody else. We need individuality as well as solidarity, liberty as well as equality, the right to be different as well as the recognition that we all are, in some respects, the same.
Social equality obtains its emotional appeal from our sense of social solidarity. I like the company of my equals because I feel at one with them, and can feel at ease and speak my mind freely in their presence. I do not have to mind my step, as when I am  among my social superiors, or to maintain my position, as among my social inferiors; nor am I shy, as among strangers. I am accepted as one of them, and am at home among them, and can be myself, naturally and without strain. We are quite right to value this relationship, and to be anxious to foster it: our only error is in our analysis of its essential nature, and of the conditions under which it can flourish. Although it requires that we be the same in some respects, it cannot, as we have seen, require that we be the same in all respects, nor does it, in fact, require that we be the same in many respects to which egalitarians attach importance. We congregate naturally with those who speak the same language, are the same age, share the same genes, have the same intellectual, aesthetic or athletic interests: but any one of these bonds granted, we do not demand that all the others should be too, but positively welcome some sorts of diversity: young people feel kinship with other young people of different lands, and can communicate in spite of a diversity of tongues; members of the same family have different hobbies and different interests; the rowing fraternity links Old Blues and young oars irrespective of age, nationality or economic status. Although every group presupposes something held in common by its members, it presupposes differences between them too. With large groups we boast that they transcend the barriers of religion, race and residence, and that people are welcome `irrespective of creed, colour or nationality', whereas with small groups we reckon that each member is enabled to make his own individual contribution, and is accepted and valued for himself alone.
The interplay between uniformity and diversity is complex, and may be resolved in a number of different ways. The two paradigm examples are found in marriage and the peer-group. In marriage the different contributions of the two partners are emphasised, in the peer-group the similar backgrounds, tastes and interests. Husband and wife are essentially different, as the etymology of the word `sex' shows, but it is because they are different and lack what the other has, that the bond is so strong, and enables the individuality of each to find its most intimate expression. It is because husband and wife complement each other that it matters intensely exactly what sort of person each of them is, so much so that each is to the other irreplaceable and unique. It is in love and in marriage that most people discover their individuality most fully: it is no accident that as Plato works out his programme of total collectivism, it is his treatment of sex and family life that we most immediately find repugnant. Women and children are subversive  of communal life, as the monasteries realised and the kibbutzim have discovered. Although there is intense togetherness between husband and wife, and they have more things in common than any other two people, the relationship is exclusive, and its effect individualistic, and if we want always to be using the first person plural rather than the first person dual, we must have our main institution not marriage but the peer-group---as in the gang, the club, the college, the regiment, the union, the old comrades' associations, the pub and perhaps the Women's Institute and Mothers' Union. The obsessive concern with sex in Anglo-Saxon countries since the War has led to a general neglect of institutions based on the peer-group, and this may, in turn, be responsible for the yearning for group solidarity that many people now feel. It is a less demanding relationship than marriage, and emotionally at a lower temperature. It is not exclusive, and one is not indispensable. Whereas my girl-friend's boy-friend is very much not my friend but my rival, my 'good friend's good friend' (to borrow a useful American phrase) is for that very reason my good friend. It is easy to enter a circle of friends on the introduction of any one of them, and correspondingly easy to move away without repine or recrimination. Particularly when growing up, we need this relationship, as an easy one not too demanding or constricting, in which we can try out different possible personalities and develop the one that is going to be our own. But, just as marriages although founded on the principle of difference need also a large measure of similarity in outlook, assumptions and interests, so peer- groups, although founded on the principle of similarity, need also to admit many differences in attitude, circumstance and aspiration. If a peer-group becomes too demanding in its requirements of conformity, it loses its liberating effect and is felt as a tyranny. We are happy to wear the same clothes as our fellows, have our hair the same length, and rave about the same pop-stars: but cannot long abide having all our thoughts and all our likes dictated by theirs. If we value social equality because we value peer- groups, we shall need to act very sensitively in establishing similarities of circumstance. It is quite possible to have a strong sense of solidarity even though there is an established hierarchy according to which orders are given and taken---as in an Officers' Mess: and it is quite possible to have no sense of community in spite of the fact that no orders are given or obeyed---as in a railway waiting-room. If we throw people together by virtue of some comirion circumstance we may succeed in establishing a peer- group; or we may not. It is often assumed by educationalists  that by sending everybody to the same school, they will get to know one another and all feel equal. But knowledge does not always breed respect. It can breed informed dislike, and will if the wrong similarities are too much insisted upon. An age-group will not mean much to those who believe athletic prowess more important than age, or truth more important than youth, and if in the name of social equality we force them to congregate with uncongenial contemporaries, we shall only find them asserting their superiority with their fists, or by opting out and saying Odi profanum vulgus et arceo. Comprehensive schools could be far more divisive than public or grammar schools were ever even alleged to be, because enforced juxtaposition in accordance with an egalitarian ideology which denies the right of people to be different is liable to breed in those who are or who want to be different a far more intense resentment than an enforced difrerentiatio'n among those who want to be the same. If we go to different schools, we can still do things together in the evenings, at the week-ends or in the holidays: but if I am subject to pressure to be like everybody else at school in every respect, to dislike Latin and to like boxing, to dislike art and to like television, I am likely to become very rebellious indeed. A peer-group will be an effective focus of loyalty only if it is not too demanding, and allows individuals to be themselves, and only if it is based on similarities that are felt to be relevant. It is difficult to fashion institutions which will unite men by the bonds of a common love. Some schools have done it---often because of the love that certain school-masters have poured into their work---but larger groups (age-groups or nationality groups) are united less easily by love than by hate or fear or hardship, and in the absence of sweet uses of adversity, are likely to generate an adventitious antagonism merely as a means of mass unification. The final result of forcing equality on the young could be that they found a sort of unity in a universal hostility to the middle-aged who had, in the name of equality, insisted on treating them not as individuals but as units.
We have distinguished two I senses of social equality which may be the concern of education. Education is concerned, among other things, to promote the unity of a country, of a culture, or of mankind, and in so far as it succeeds, we may be said to be recognising one another as equals. But the sense of solidarity which we feel with other men does not require that we should have received exactly the same education, any more than it requires that we should have the same tastes or the same hobbies. Rather, especially in England, there is built into our fellow- feeling for our  fellow-countrymen a considerable measure of `live and let live': differences, provided they are not felt to be unfair, are acceptable, and strengthen rather than weaken the sense of unity. Liberty and justice, rather than equality, are what bind the different members of society together, and there is no overriding need for education to be the same for every one without regard to individual needs and capacities. Education is also concerned with social equality in a second sense in that each person needs to have the experience of being a social equal, not necessarily with every one, but at least with some other people. In order to secure this we may need to establish suitable institutions or lay down certain rules--- school uniforms have sometimes been defended on the grounds that they prevent rich children having visibly better clothes than poor ones can afford. Exactly what rules are required will depend very much on time and circumstance, and is a matter for practical judgement on the part of schoolmasters rather than abstract theorising on the part of educationalists. Schoolmasters have a strong sense of the importance of corporate activities at school, and seldom fail to convey to their pupils the importance of getting on with their equals.
It is difficult to fight equality. Egalitarianism is not so much a doctrine as a temper of mind, which is ready to wax indignant at particular inequalities it dislikes, but is not prepared to think through the alternative and submit it for rational assessment and criticism. In so far as any articulate doctrine is propounded, it is expressed in terms of such cloudy indeterminacy that it is difficult to know what is being maintained. Under attack, it withdraws into a set of morally innocuous truisms, but in application it is extended to make highly questionable claims. Under attack, equality collapses into some principle of similarity or uniformity, treat like cases alike, or some principle of solidarity or unity, e.g. that we all should recognise one another as our fellows and live on a basis of reciprocity with them. These are valid principles, which can scarcely be gainsaid. But they are not the only principles, nor is their application automatic. I should treat like cases alike---true: but it does not at all follow that we should therefore send all children, who are all alike inasmuch as they are children, to the same school, or that the mere existence of direct grant schools is a flagrant violation of natural justice. I should, within limits, encourage patriotism and ésprit de corps---true: but it does  not at all follow that this is best done by enabling children to learn at close quarters how unlovable their fellow-countrymen are, or by making social solidarity seem a suffocating ideal from which any sensitive individual will be seeking to escape. We must balance different ends against one another, and choose those ways and means that will achieve them with the least encroachment on other ideals we ought also to cherish. But this is just what the doctrinaire egalitarian will not do. Acutely aware of some sorts of inequality, he is quite oblivious of the many other differences and difficulties which are relevant to the schoolmaster's job. If only his eyes could be opened and he could be enabled to see the complexities of the considerations which have to be borne in mind, we could discuss his points, and see how far they could be met without sacrificing other goods we value. If only.... It is difficult to be patient, difficult to listen, to appreciate, and then to point out the W'oolliness and the non sequiturs without betraying irritation. It is easy to lose one's temper, and to match the shrill stupidity of egalitarian propaganda by equally shrill counterblasts, and if less stupid, equally unattractive. It is tempting, but both wrong and ineffective: wrong, because although egalitarians are in error, the points they are expressing in a muddled and confused fashion often have some validity, and in trying to preserve education from their procrustean propensities, we should not say that we have no regard for justice or the other concerns of society; and ineffective, because silliness is seldom silenced by denunciation. We shall not succeed in saving our schools by shouting down the egalitarians, but by arguing with them, understanding what they say, and why it is wrong, and being able to show them where their terms are equivocal, where their arguments are invalid, or where relevant factors have been overlooked; not by decrying the fashionable feeling for equality in education, but by educating our educationalists and teaching even egalitarians to think.
1. For a fuller account, see J.R.Lucas,
The Concept of Probability (Oxford), 1970, Chs.VI and
2. ``The central and irresistible argument against the eleven-plus lies in the denial of social justice and equal opportunity which this implies.''-- -Mr Crosland at Harrogate, 7 January 1966.
3. See, for example, B.A.0.Williams, ``The Idea of Equality'' in Peter Laslett and W. G. Runciman (Eds.), Philosophy, Politics and Society (Oxford), 1962, pp. 125-9.
4. Mr Brian Simon, Reader in Education, in Leicester University, addressing the Confederation for the Advancement of State Education, as reported in The Times, 27 September 1965.
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