7.1. Generalisation
from 7. Induction — Clear Thinking by R W Jepson

Generalisation means, as its derivation implies, putting things into their genera or classes. Right from a very early age our observation and inquiries lead us to form generalisations which guide our judgments and determine our actions. For example, a child may soon learn that Matches are dangerous playthings, or that People who frown are angry, or that Dogs are faithful animals, or that Jays like peas, or that Policemen wear uniform. Each new experience, each freshly acquired piece of knowledge helps him to form new generalisations, or to strengthen or modify his old ones. It will easily be seen that without this power of generalisation, human knowledge would have never advanced, and civilisation would have been impossible. Most generalisations, at any rate in matters concerning the conduct of human affairs (i.e., as opposed to such subjects as mathematics or physics), are necessarily imperfect, because it is almost impossible to obtain sufficient data from which a universal rule can be extracted. The value of a generalisation depends on:

1. the relative number of the unobserved instances;
2. whether the instances observed form a fair and sufficient sample, and whether no exceptions are discoverable;
3. the degree of probability of the existence of such a general rule or law.

To apply these tests to our own conclusions, we shall have to ask ourselves:

1. Have our investigations covered a wide enough field?
2. Are the conditions we have observed typical of general conditions or are they special conditions prevailing only in the sphere of our investigations?
3. Is our conclusion one that could reasonably be supposed to exist?

One of the most prevalent sources of error in argument is the rash generalisation. It takes one of the following forms:

1. Generalisation from single or isolated instances.
2. Generalisation from selected instances.
3. Generalisation arising from ignorance or prejudice.

These forms roughly correspond to the conditions and tests enumerated above, and they can be detected easily enough by applying those tests.

The absurdity of forming generalisations from single or isolated instances is patent enough; but how often are people — in most respects ordinary, sensible people — guilty of it! An Englishman's casual visit to the Palais des Papes at Avignon, during which he is pushed and jostled in a crowd of French sightseers, causes him to dismiss all our neighbours across the Channel as rude and inconsiderate folk. And how often do we hear such statements as:

"Doctors are all alike. They really don't know any more than you or I do. This is the third case of faulty diagnosis I have heard of in the last month!"

Or,

" Another policeman convicted of burglary! There you are — it proves what I said — the whole police force is hopelessly corrupt."

Or again, we often hear of a self-made successful business man protesting against the raising of the school-leaving age and saying, "I left school at thirteen, and look at me!" A deputation of parents living in a rapidly growing suburban district, whose children had to attend a school over a mile away from their homes, waited upon the local education committee to request that suitable transport should be provided to convey their children to and from school. The chairman remarked:

"Why, when I was a boy, I had to walk five miles to school every day! It never did me any harm. Look at me, still hale and hearty at eighty!"

The obvious retort to the last two generalisations from single instances is the same as that of the sceptic quoted by Bacon, viz., "Yes, but where are the others?"

Members of Parliament frequently base their pronouncements on data collected from a limited field, i.e., from the conditions prevailing in their own constituencies only.

In judging some historical personage people often make the mistake of selecting a single passage from a single writer as summing up his whole character. The possible injustice of this is apparent enough even if the writer is unprejudiced; but if he happens to be prejudiced, it is even more unjust.

Vendors of panaceas and quack remedies seek to prove their efficacy by reference to the number of so-called cures they have effected; but they forbear to mention, or do not care to find out, in how many cases fatal results ensued, or no results at all.

I have already referred in the previous chapter to the human tendency to accept insufficient data as the proof of a belief, when that belief brings pleasure or comfort with it. The people who credulously accepted the story of the Russian troops on such slender testimony failed also to calculate the probability of such an occurrence or even the mechanical possibility of transporting such a vast number of men by rail across England in such a short space of time.

In politics one party frequently judges the other party by their most illogical and extreme members. Moreover, one isolated statement by one member of a party is often quoted as representing the views of the party as a whole. Mr J. R. MacDonald complained of this habit in the introduction of his little book on the Socialist Movement. He said,

"To-day the opponents of Socialism try to make Socialism itself responsible for every extravagance, every private opinion, every enthusiasm of every one of its advocates.

The logic is this: Mr Smith writes that the family is only a passing form of organisation; Mr Smith is a Socialist; therefore all Socialists think that the family is only a passing form of organisation. This method of controversy may offer for itself a shamefaced justification when it is resorted to for the purpose of a raging and tearing political fight in which the aim of the rivals is not to arrive at truth but to catch votes, but it cannot be defended on any other or higher ground."

A particularly delusive method of proof by selected instances is illustrated by the "Peace Ballot" conducted in 1936 by a popular newspaper. When the result was announced, the percentages of votes cast for and against were given, but the total number of votes cast was withheld. The use and interpretation of figures and statistics will be treated more fully later in this chapter.

An old Sussex labourer I knew was convinced that "a wet Monday meant a wet week." The inherent improbability of such a generalisation did not strike him; and I doubt if statistics ranging over a long period and proving the contrary would have altered his conviction.

A weakness for exaggeration, a dislike for half-measures, and a desire to be thought thoroughgoing and downright lead us to make universal generalisations when a little thought would make us more chary and less sweeping in our judgments. In normal times the man who counsels caution and moderation tends to be unpopular — he is called weak and shilly-shallying and is told he does not know his own mind. In times of crisis, stress or emotional excitement his voice has even less chance of being heard. It is in times like these that sweeping generalisations about people arouse the worst barbaric passions. "A bas les aristocrates!" — with this cry French nobles, without discrimination, were hurried away in tumbrils to the guillotine.

When such sweeping statements are made about peoples as a whole, they are often dangerous and misleading. The Englishman, we are told, is phlegmatic, the Scotsman dour, the Welshman excitable, the Frenchman logical, the German ruthless, and so on. There may be some justification for these popular estimates, but it is dangerous to assume that all Englishmen are phlegmatic and all Frenchmen logical; and it is perhaps still more dangerous to take it for granted that in a particular set of circumstances an Englishman, or even most Englishmen, will betray no emotion, and that a Frenchman or the majority of Frenchmen will be guided by logical principles. Professor George Trevelyan points out that a similar assumption accounted for the British attitude to the Germans in the Franco-Prussian War of 1870. He says that when the war began it was not Germany we feared. The idea of the dreamy German being a danger to Europe was new and strange. Only a few years before, their soldiers had been drawn by our comic artists as funny little men strutting about under the weight of enormous helmets. In 1870, however, these little men had shot up into genial giants with bushy beards, singing Luther's hymns round Christmas trees in the trenches before Paris. We were too ignorant of Germany to regard her as a serious rival. This also shows how ill-judged it is to form our opinions of nations from the way they are caricatured in cartoons or on the stage.

Very often the weaker our generalisations are, the more vehemently we propound them. The degree of their weakness may perhaps be measured by the degree of obstinacy and dogmatic confidence with which we utter them. Assertiveness is frequently mistaken for strength of knowledge or the voice of authority; on the other hand, modesty and tolerance are attributed to weakness or ignorance.

The fact that we frequently make these generalisations and suppress such words as all or every, does not make them less universal in their application; it merely helps to deceive ourselves or our opponents in the course of an argument. Since, as I have said, most generalisations about human beings, their affairs and relationships, are necessarily imperfect, and may even be misleading or untrue, we should be chary of saying, or implying, all when we mean some, and of saying are when we mean tend to be, unless, of course, we can prove our statements by reference to indisputable figures.

The Generalisation, as I have remarked before in, "The Writer's Craft", Lesson XXXIII, is a good servant, but a bad master. We must not allow our desire for order and simplicity to tempt us to impose them where they do not exist. We must not attempt to force facts to square with a theory: we must modify the theory to make it account for all the available relevant facts.

When we are challenged to produce evidence for our general statements, the weakness of our case is often patent, and it is often seen to depend upon selected instances. Incidentally, it is as well to remember that selected instances can no more disprove a statement than prove it; and to remember that the common retort, when instances are quoted against our contention that "the exception proves the rule," is bad logic and a misleading translation of the Latin tag Exceptio probat regulam, which merely means that the rule covers all cases not specifically excepted.

Suppose A. in support of his statement that "All State or Municipal enterprises are extravagant, wasteful and inefficient as compared with private enterprises" refers to (1) muddles made during the war, when the State assumed control of all "key" industries, (2) a case where the attempt on the part of a certain Municipality to build houses by employing direct labour proved more expensive than entrusting the job to private contractors, (3) the inability of the Belgian State Railways to pay their way without subsidies, (4) the multitude of private, but successful, enterprises such as Ford's motors, the Imperial Chemical Industry, or Unilever. B. retorts : "What about the Post Office?" and, "Look at the number of big private concerns that have smashed recently; could the Hatry, Kreuger and Stavisky scandals have happened under State management?" A. continues: "Ah, those are the exceptions that prove the rule..."

How much further are they towards settling the question? A.'s contention may be right, but the instances he cites do not prove it; nor do B.'s instances to the contrary disprove it, much less prove it because they are exceptions. The argument, as conducted by A. and B., leads nowhere. Is it then impossible to come to a conclusion regarding the respective merits of State and Private Enterprise? By no means; given full statistics compiled by trained investigators, we should be able to formulate some generalisation that covers all the available data; but it will not be the sweeping generalisation that A. made at the outset of his argument and that was shown to be incapable of proof.

There is a popular belief that a boy's academical career is no index to his career in after life. This belief finds expression in a number of ways; e.g.,"You never hear of the brilliant boy after he has left school" — "I never passed an examination in my life, and look at me!" says a successful business man — "It is the dunce at school who makes his mark in after life; Mr W — C — never rose above the Third Form at H —" and so on. Suppose we desire to try to find out how much truth there is in this belief, how shall we set about it? There are certain preliminary assumptions we must make: (1) we must decide what standard of achievement, (a) at school, (b) in after life, we are going to adopt as a basis for calculation; (2) we must fix the ages at which it is possible to say that a boy and a man ought to have reached those standards of achievement, if they are to reach them at all — shall we say, for the purpose of this argument, 17 and 55? (3) we must decide from how many and what kinds of schools we are going to obtain the data that we want; (4) we must agree to accept the data when we receive them from the headmasters, who will, of course, have been fully instructed how to compile them. We are now in a position to proceed. We write to the head-masters of, say, forty schools and ask them to obtain from their records particulars of the school and after careers of 25 boys chosen at random from the 16+ to 17+ age group of the pupils in the year 1897. On the receipt of these particulars we shall have the information we want concerning 1000 boys, and we proceed to classify them as follows:

(These figures are, of course, purely imaginary.)

What can we conclude from these figures Certainly not that "All dunces at school are successful in after life " nor that "No boy with a brilliant record at school makes his mark in after life." But we can, firstly, say that the chances of a brilliant boy's ultimate success are 1 in 4; whereas the chances of success of his undistinguished schoolfellow are 1 in 8; and therefore that the brilliant boy's chance of success is twice as great as his undistinguished schoolfellow's. The point worth emphasising is that on the above figures it is as useless for anyone to try to prove any universal generalisation about either brilliant boys or dunces by merely citing all the instances in his favour, as it is useless for his opponent to prove the contrary by citing all the instances that point the other way.

It is on figures such as these that calculations of probability are based. People who hope to acquire riches by gambling would perhaps be less willing to risk their money if they were able to calculate their chances to some degree of accuracy. Many alleged contests of skill in popular newspapers are really forms of gambling under a very thin disguise — especially crosswords and picture-guessing competitions, in which, shall we say, 86 per cent of the clues or titles are so easy that no one could possibly make a mistake, while the odd 14 per cent admit of two, three or four alternative answers. Suppose there were one hundred of these pictures to guess, and of them seven admitted of two possible solutions, five of three and two of four. If the intending competitor realised that the mathematical chance of gaining first prize by guessing all the pictures "correctly" was approximately one in half a million, would he be so willing to risk his entrance fee? And perhaps he would lose any illusions he may have had regarding the generosity or disinterestedness of the proprietors of popular newspapers.

Figures, or statistics, as they are called, are of great help in enabling us to obtain a clear and comprehensive grasp of facts; by means of them we are able to sum up the results of our observations in a convenient and intelligible form. They enable us to calculate averages and ratios and proportions; to make comparisons; to detect correspondences and variations between different sets of happenings. But in interpreting statistics, i.e., in drawing conclusions from them, we must take care (1) that we understand on what assumptions they are made or on what principles they are based; (2) to see that all the relevant figures are taken into consideration; (3) not to assume that there is a causal connection between different sets of figures without further experiment or investigation.

The successful candidates of two schools at a School Certificate Examination are as follows:

Only the most foolish and ignorant observer would draw from these figures the conclusion that the results of Chart are twice as good as those of Charvel. Before we can make an adequate comparison we want to know (1) the number of pupils in each school, the age range and the number of pupils at each point in the age range; (2) the numbers of unsuccessful candidates; (3) the average age of the candidates; (4) the numbers of honours and/or distinctions gained; (5) the number of candidates taking the examination for the second time, and so on.

It is noted that at a certain "soccer" school the weather on successive Saturday afternoons, when 1st XI matches were played, began by being good, but became progressively worse, until on the last Saturday the match was played in a torrent of rain and a howling gale and on very heavy ground. The results were as follows

It is obvious that we cannot draw from this information alone the conclusion that the weather was responsible for the falling off of the performance of the team in the last two matches. We shall want to know about changes in the constitution of the team, casualties, the relative strength and weight of their opponents, and maybe other material factors, before we can say that there is even a prima facie case for our contention. But we are now trespassing on the ground to be covered in the next section dealing with cause and effect: you will be told there what tests to apply before you begin to trace causal relations between things.

The quotations of figures and statistics by opposite sides in a dispute often has inconclusive results and leaves the real issue untouched. For example, early in 1938 the Government was blamed for a rise in the cost of living. Their opponents pointed out that since 1933 the cost of living rose 11 per cent and wages only 9 per cent. The Government's case was that between 1929 and 1933 the cost of living fell 14 per cent and wages fell only 5 per cent, and that on balance therefore the workers of 1938 were 4 per cent better off than in 1929. But both the complaint and the justification were really futile and superficial over-simplifications of a complex question. The official cost of living figures were based on arbitrarily chosen items, and the rate of wages alone is not the only index to the standard of living among the workers: it takes no account of such things as social services, holidays with pay, and publicly provided amenities. In fact, the expression 'standard of living' is itself deceptive: there is a standard of satisfaction, but it would be beyond human ingenuity to express this statistically.