The verb to be
When a language has a verb 'to be' it is usually, though irregular, considered one of the simplest verb/words, so simple that other languages manage to take it as simply 'understood', much in the same way that zero was simply understood as a number before the place holder was invented. Why do you need a word or symbol to stand for nothing? Why do you need a word to stand for the basic obvious fact of existence? Well zero holds a place, enables the wonders of place value in mathematics, makes all the difference between 1, 10 and 100. A difference that can, tragically, mean the difference between life & death when applied to drug doses for example
During the Clinton impeachment almost nothing, not the stain on the dress, not the mind-boggling implications of what was going on under the desk during those phone calls, invited more universal derision than the response It all depends on what is is
Is is actually very complicated. To try & unpack this a little, let us move on to the plural version, are
Men are taller than women is a statement that would not attract much flak even from the most ardently feminist or politically correct. Not even from me, despite the fact that, at 5'10" I am taller than most men - or at least I used to be. I am now over 60, so the addition of all those giant 20-somethings & the death of all those tiny 80-somethings may mean that I am now below the average height of the British adult male
But we all understand what the statement means; we know that women rarely pair with a man shorter than they are, we know that on average women are shorter than men & that the very tallest humans are always male
For centuries, logic has taught us the essential point of the syllogism - all men are liars does not imply that all liars are men. Elementary logic does not however teach us how to cope with the less definite assertion that most men are liars. From this alone we can conclude nothing about the truth of the statement most liars are men.
This may not seem to matter much in every day life, except when it comes to statements such as Women enjoy shopping more than men or Men are better at maths than women. If you are rash enough to make one of these statements on, say, national radio, be prepared for the flak. But, just as one tall woman does not disprove the ordinary sense of the statement that men are taller than women, the existence of women who do not enjoy shopping, or of one brilliant female mathematician, does not disprove the truth of the other two statements
By the same process of reasoning, the simple statement that in some parts of London most muggers are black does not mean that most blacks are muggers, even if sometimes both police & the black community seem to think that it does, or that that is what is being implied.
In saying this last I do not wish to imply that either the black community or the police are being particularly dense; I still remember with wonder a Newsnight discussion of several years ago during which a participant seemed to argue that the existence of one young woman, the only female ever to study for a PhD under Stephen Hawkins, was enough to disprove the assertion that men are better at maths
Our problem here is language, or rather grammar; we need a different case, voice, tense of the verb to be to cope with ratio numbers. As far as the verb to be is concerned we are stuck in the time when numbers were simple counting numbers - 1,2,3,4 … The Ancient Greeks realised that these were not enough & got at least as far as understanding that ratio numbers needed to be added to the mathematical armoury. Mathematicians have since moved on to the realisation that we also need real numbers, imaginary numbers, complex numbers & heaven knows what else. But our everyday language has still not caught up
In considering the history of numbers & language we need at least to consider three aspects; the word - two; the symbol 2 or for example; and the abstract concept - the twoness of two
This might seem a bit twee or airy fairy but think about it this way. Many standard histories of mathematics make the claim that primitive man could not count beyond 3 because languages seem, almost universally, to have contained only words for one, two, three, many
But as Menninger pointed out you dont need words to count, & the fact that no words seem to exist for numbers beyond 3 does not imply that people did not understand, or comprehend the differences between, larger numbers (even just the difference between 4 & 5). In the same way, in future millennia, historians may believe that we cannot perceive subtle differences in skin colour, simply because our language seems to contain only the words black or white to describe these
There is plenty of evidence that ancient man could count; one of my favourite stories is about the use of simple clay models of sheep to keep tally of the flocks. And tally sticks were in use in the British Treasury right up to the time that they were destroyed by the fire which burned down the old Parliament building in 1834. Were the civil servants of those days any less in control of public expenditure than their modern counterparts with their digital or analogue computers?
The really odd thought is that ancient man seemed to think of twoness as a property of the particular object: two apples were different from two pears. A strange thought, unless you remember being taught in your schooldays that You cant add apples and pears. Of course you can - the answer is a number of fruit. The existence - the continuing existence - of different words for the same concept of twoness - pair, couple, double, twin … is evidence that ancient populations struggled with this notion. Do primary school children still have to learn the 'correct' words for many - a flock of sheep, a herd of cows, a clutch of eggs … ?
So it was a struggle, between the need to comprehend the abstract notion of number & the need to come up with zero as a place holder. Together these ideas mean that we can go from 0 to ∞, in the symbolism of number, with no more than the code 0,1,2,3,4,5,6,7,8,9. Did number words only follow (emerge after) this code? Probably
We have not really advanced beyond these centuries old inventions. We have words for some ratio numbers - half, quarter, third - but few that really convey the sense & complexity. Just as it took an advanced mathematician to do division or multiplication with the Roman number system, it takes a fairly advanced mathematician to work out whether 2/7 is greater than 3/8
There is some evidence of development, perhaps thanks to the metric system. The use of % - a key on the keyboard which I am using to type this - is now quite widely accepted even outside of statistical tables. When I started my career in the civil service in the 1960s the use of the symbol (rather than the words per cent) was infra dig. But we still dont understand percentages very well
Not too long ago a kind of high tech version of the rhythm method of contraception was being marketed under the promise that it was 94% effective. There were soon widespread reports that it did not work reliably; a tv programme gave a platform to young women who felt that they had been misled because they had not realised that this meant a 1 in 16 chance of becoming pregnant (6 out of 100 sounds so much less). It was however never entirely clear whether the claim meant 1 in 16 times of making love or something more complicated such as once in 16 menstrual cycles you will be making love during your fertile period. I do not think that this is just a female problem, but I am tired of pointing out that the idea that breast cancer affects 1 in 12 women means that I am 92% certain not to get it
Per cent, as a word or phrase, does at least imply the ratio, but we still have no simple means of describing what is a percentage of which. Most of the time we seem to think that this can be taken as read - there is no need to specify the period when we talk about house prices rising by 5%; we can talk about the % of women managers and somehow take it as read whether we are talking about the % of women who are managers or the % of managers who are women
Which brings us back to the beginning of these musings. Women are taller than men: we have no simple language to say whether this means simply that the average woman is shorter than the average man. But at least here we are, or think we are, talking about overall majorities
Our first past the post political system requires only that one candidate achieve the largest number of votes; in a 3-member constituency with 100 voters the one who gets 34 votes can win, even if each of the others receives 33
Children of lone parents can be said to do worse at school because only 17% of them get 3 As at A level compared with 20% of children from 2-parent families. And so on
All the above has been about the problems of is or are as a matter of proportion or majority. These problems are difficult enough if we are talking about a comparison at a fixed point in time. Consideration about 'to be' in time - I am a Mancunian, a statistician - the problems of this kind of statement, the problem of 'before' must be left for another essay
