Monday, March 07, 2005
Heads Hopkins Wins, Tails Summers Loses
Consider this thought experiment. Toss a coin a thousand times and note the frequency of "heads." If the result is 530 heads out of a thousand, is it reasonable to conclude that the coin is not fair? Perhaps not; the one-thousand tosses doesn't adequately account for a host of potential variables: weather, season, mood or sex of the tosser, etc. We might still have a fair coin.
Well then, have a thousand people (men and women) in a thousand places toss the coin a thousand times. If the results of these one-million tosses were gathered and it was found that "heads" in no event came up fewer than 500 times nor more than 550 times - and in fact averaged 530 - could we still say that the coin is fair?
In fact we could not. We would do what we as rational beings do when faced with empirical evidence of this type: we would say the coin is not fair, and is slightly biased towards “heads”; and further that there is a 53% chance that when tossed again the coin will yield "heads."
But this is nothing like certainty that the coin is unfair, and it may still be technically true to say that the coin is fair. The important distinction, however, is that this is a trivial logical truth; and as such it is fatuous. In spite of its abstract logical truth, we are obliged to infer the probability of heads on subsequent tosses from the frequency of heads in the large and varied sample of tosses already made.
Of course there is no controversy in making any of these statements. Further, it will be agreed that as humans we could hardly get through our days without recourse to this kind of reasoning. But if on the other hand we apply the very same logic, and suggest that women do not possess the intellectual capacity of men; and if we similarly base that observation on the intellectual performances of men and women -- over the whole of recorded history -- the response will be neither abstract nor logical; it will be swift and severe.
Such anyway was the response that greeted Larry Summers, president of Harvard University. Should Mr. Summers choose to make a stout defense of his contested statements, as opposed to buckling to the rigidities of inquisitorial campus political correctness, he could help himself greatly by an afternoon's study of David Stove. It is from Stove that I have borrowed the example of the coin toss, and on whom I rely (and excerpt) in this article. In a very compelling book of essays called Against The Idols of the Age, Stove, an Austrailian philosopher who died in 1994, is seemingly riding to Mr. Summers' aid with an essay called "The Intellectual Capacity of Women." Mr. Summers, if you can hear me, buy this book - and get a spine.
In the first words of the essay Stove, by his choice of language, makes the strongest appeal for clarity in the language we employ:
Note the distinction, critical to this line of reasoning: performance is not the same thing as capacity. Nor is inferior intellectual performance proof of inferior intellectual capacity. But not until our scientific understanding catches up to our cultural dilemma – and most certainly not until the pall of political correctness falls away from this and scores of other debates – will we have settled the issue of capacity. Until such time we are thrown back, as with the coins, on “having to infer the probabilities from the observed frequencies.”
Yet the “equality-theorists” will say that there hasn’t been enough variety in the “trials”, adding that there has always been some factor or factors that have hindered the intellectual capacity of women, thereby depressing its frequency below expected probabilities. One reasonably thinks of the burden of reproduction and nurture, a burden that falls exclusively on the female, as a significant limiting factor in the intellectual performance of women.
The recent phenomenon of fathers being present at the birth of their children, and of helping with the diapers, is but play when compared with the “deadly earnest business” which is going on at every moment between mother and infant. The performance of this earnest business is hard-wired into the female homo-sapiens; and while it is of the most vital importance, it cannot be argued that it requires much in the way of intellectual capacity. By contrast, males of the species have, for as long as we have evidence, had to rely on their wit and cunning, in constantly changing circumstances, in protecting and providing for this fledgling family. From these and other performances, repeated over thousands of years, we are obliged to infer capacities.
To conclude the essay, Stove once again asks the equality-theorists: What would convince them of the falsity of their belief? What would they even regard as being some evidence against it?
Well then, have a thousand people (men and women) in a thousand places toss the coin a thousand times. If the results of these one-million tosses were gathered and it was found that "heads" in no event came up fewer than 500 times nor more than 550 times - and in fact averaged 530 - could we still say that the coin is fair?
In fact we could not. We would do what we as rational beings do when faced with empirical evidence of this type: we would say the coin is not fair, and is slightly biased towards “heads”; and further that there is a 53% chance that when tossed again the coin will yield "heads."
But this is nothing like certainty that the coin is unfair, and it may still be technically true to say that the coin is fair. The important distinction, however, is that this is a trivial logical truth; and as such it is fatuous. In spite of its abstract logical truth, we are obliged to infer the probability of heads on subsequent tosses from the frequency of heads in the large and varied sample of tosses already made.
Of course there is no controversy in making any of these statements. Further, it will be agreed that as humans we could hardly get through our days without recourse to this kind of reasoning. But if on the other hand we apply the very same logic, and suggest that women do not possess the intellectual capacity of men; and if we similarly base that observation on the intellectual performances of men and women -- over the whole of recorded history -- the response will be neither abstract nor logical; it will be swift and severe.
Such anyway was the response that greeted Larry Summers, president of Harvard University. Should Mr. Summers choose to make a stout defense of his contested statements, as opposed to buckling to the rigidities of inquisitorial campus political correctness, he could help himself greatly by an afternoon's study of David Stove. It is from Stove that I have borrowed the example of the coin toss, and on whom I rely (and excerpt) in this article. In a very compelling book of essays called Against The Idols of the Age, Stove, an Austrailian philosopher who died in 1994, is seemingly riding to Mr. Summers' aid with an essay called "The Intellectual Capacity of Women." Mr. Summers, if you can hear me, buy this book - and get a spine.
In the first words of the essay Stove, by his choice of language, makes the strongest appeal for clarity in the language we employ:
I believe that the intellectual capacity of women is on the whole inferior to that of men. By "on the whole," I do not mean just "on the average"; though I do mean that much. My belief is that, if you take any degree of intellectual capacity which is above average for the human race as a whole, then a possessor of that degree of intellectual capacity is a good deal more likely to be a man than a woman.Observe that he is not saying that women cannot and do not reach levels of intellectual achievement as high as men. But why does Stove hold this opinion, not to mention risk opprobrium to elaborate it? I think it is because he is making a very precise (and defensible) point, and because he sees clearly what we can and can’t know. Since our understanding of the life sciences (genetics, biology, etc.) as potential explicators of the disparity is wanting, we are left with, as in the coin case, having to make inferences from the observed frequencies; that is, “on inferring the comparative intellectual capacities of men and women from their comparative intellectual performances in that large and varied sample which is past human history. .... Human intellectual capacity is a coin which has been tossed, not a million times, but very many billions of times.” [Italics mine -- ed.]
This proposition is consistent, of course, with there being women, and indeed with there being any number of women, at any level of intellectual capacity however high. But it does mean, for example, that if there is a large number of women at a given above average level of intellectual capacity, then there is an even larger number of men at that level.
Note the distinction, critical to this line of reasoning: performance is not the same thing as capacity. Nor is inferior intellectual performance proof of inferior intellectual capacity. But not until our scientific understanding catches up to our cultural dilemma – and most certainly not until the pall of political correctness falls away from this and scores of other debates – will we have settled the issue of capacity. Until such time we are thrown back, as with the coins, on “having to infer the probabilities from the observed frequencies.”
Yet the “equality-theorists” will say that there hasn’t been enough variety in the “trials”, adding that there has always been some factor or factors that have hindered the intellectual capacity of women, thereby depressing its frequency below expected probabilities. One reasonably thinks of the burden of reproduction and nurture, a burden that falls exclusively on the female, as a significant limiting factor in the intellectual performance of women.
The recent phenomenon of fathers being present at the birth of their children, and of helping with the diapers, is but play when compared with the “deadly earnest business” which is going on at every moment between mother and infant. The performance of this earnest business is hard-wired into the female homo-sapiens; and while it is of the most vital importance, it cannot be argued that it requires much in the way of intellectual capacity. By contrast, males of the species have, for as long as we have evidence, had to rely on their wit and cunning, in constantly changing circumstances, in protecting and providing for this fledgling family. From these and other performances, repeated over thousands of years, we are obliged to infer capacities.
If a species devotes a large part of its energy-budget to food-getting say, or the defense of territory, or home-making, or reproduction, or nurture of the young, then one sex takes on more of that task than the other does, and it will take on less of some other task [an organic principle known as parsimony]; and either sex will be comparatively or entirely deficient in the capacities required for the “specialisms” of the other sex. [It] is not an invariable rule, but it is the general rule: if you take any major task that a species performs, it is exceptional for the two sexes to be exactly equipped to perform it.Stove knows where you equality theorists are going right now: it is only because of our hegemonic patriarchal culture that women have been kept from attaining their true and actual capacity. Even absent the histrionics this will not do at all as an explanation. For whatever explanation is chosen it must be consistent with the equality theory. It does no good to say, “The main interfering factor has been the aggressiveness, sexual exclusiveness, and superior cunning of males."
This suggestion, considered in itself, is by no means without merit: aggressiveness, sexual exclusiveness, and superior cunning are definite and detectable things, and I at least believe that they actually do operate in males, and do impede, to some extent, the intellectual performance of women. But of course the suggestion is not one which an equality theorist can adopt, since to ascribe superior cunning to males is to contradict the very intellectual equality for which he contends.If that familiar line of defense is contradictory and off limits logically, surely there can be no argument that access to education and learning has historically been withheld from women, right up through the present day. Stove has anticipated this argument too.
Wherever some defect has been found or imagined in existing arrangements for the education of females, energetic and ingenious people have always been busy setting up a form of education free from that real or supposed defect. Novel schemes of education, intended among other things to remove obstacles to the exercise of the intellectual capacity of women, are at least as old as Plato, and hundreds of them have been put into more or less widespread practice. Yet despite all this variety in the supposed causes of female intellectual performance, the effects have been singularly invariant. I do not mean that these schemes of education have never had any effect at all on female intellectual performance. I do not know, but it is in any case indifferent to my thesis, whether they have or not. My thesis only requires, what is the case, that educational innovations have never shown any significant tendency to bridge the gap between male and female intellectual performance.We are left to wonder what change in the frequency and variety of our observations of these disparities would constitute a fair trial in the minds of the equality defenders. If in fact we were to observe, for the next one thousand years and in the widest variety of circumstances, that the intellectual performance of women was on a par with that of men, we would still be none the wiser about how the intellectual capacities of the two sexes compare. This is because certainty is out of reach (for now) on such a question; the only guide we have to intellectual capacity is intellectual performance. Think again of the coins.
Is not this virtually unlimited variety, variety enough? Has it not constituted a fair trial of the intellectual capacity of women? “No,” says the equality-theorist. But this theory now begins to remind us of a supremely silly thing which G. K. Chesterton once said: that Christianity has not been tried and found wanting, but was found difficult, and never properly tried. Now, I ask you: Christianity has not had a fair trial!?! Why, at this rate, nothing has ever had a fair trial, and we can know, or even rationally believe, nothing whatever about the capacities of anything. But this is just an even stronger version of that silly skepticism…that human history can never constitute a fair trial. In fact we know, or near enough know, that Christianity does not have the capacity, which it claims to have, to satisfy indefinitely the religious aspirations of all human beings. And such a case proves, let us notice, that an historical sample of performance can be varied enough, and large enough, to be the basis of a rational inference to capacity, or rather to the lack of capacity.Stove admits to having been asked what it would take for him to be convinced that the intellectual capacity of women is equal to that of men. After recourse to the study of historical performance differentials, he believes the question is more fairly turned around: “What would convince you (the equality-theorist) of the inferior intellectual capacity of women?” Owing to the religious quality of the theorist's attachment to their theory, an easy answer would not be forthcoming.
A comparison between Christianity, and the supposedly equal intellectual capacity of women, is in fact worth pausing over. Equality-theorists are never tired of reminding us of the obstacles which have been put in the way of the exercise of the intellectual capacity of women, at such-and-such a period, in that society or the other; and of course there are countless such cases. Those obstacles, however, have never been more than trifles when compared with the obstacles which, in countless cases, have been put in the way of the practice of the Christian religion. It is a mere abuse of words to speak, as some do, of “martyrs” and “persecution” in the one case as in the other. In both cases, for every instance in which some obstacle was put in the way, there is another instance in which that obstacle was not put in the way. Now, Christianity has sometimes made its way, sometimes without obstacles, sometimes even with obstacles; whereas the supposed equal intellectual capacity of women has never made its way, with or even without obstacles. Yet female intellectual capacity has obviously been tried in a far greater number of cases, and in a far wider variety of circumstances, than Christianity.
This is a sad state of affairs, but it is, of course, the equality-theorists who are chiefly to blame for bringing it about. For they have created in recent years a climate of feeling in which many men are afraid to deny the equality-theory openly, and even ashamed to doubt it inwardly. Hence the phenomena which are now so observable, of hypocrisy, self-deception, and pious fraud: those inevitable concomitants of a militant religion.We must pause to admire Stove’s prescience in describing precisely the situation that exists today at Harvard. But surely even he could not have guessed that Summers, for the “thought crime” of speculating that there might be genetic reasons that women are underrepresented in the fields of mathematics and science, would in the year 2005 be facing a virtual auto da fe. Given his wit though, I think there can be little doubt that Stove would be having a sardonic laugh at the prospect of an MIT biologist admitting to this reaction to Summers’ remarks: "I felt I was going to be sick. . . . My heart was pounding and my breath was shallow", as one Nancy Hopkins did.
To conclude the essay, Stove once again asks the equality-theorists: What would convince them of the falsity of their belief? What would they even regard as being some evidence against it?
Any serious answers to these questions would be instructive, but I do not really expect to receive any such answer. The evidence for the inferior intellectual capacity of women is so obvious and overwhelming, that anyone who can lightly set it aside must be defective in their attitude to evidence; and our contemporary equality-theorists are in fact (as I have hinted several times) religious rather than rational in their attitude to evidence. As providing some further indication of this, the following thought-experiment may be of use. Suppose that the historical evidence had been the exact reverse of what has usually been: that is, suppose that the intellectual performance of men had been uniformly inferior, under the widest variety of circumstances, to that of women. Rational people would in that case be as confident of the superior intellectual capacity of women as they now are of the reverse. But would those people who are at present equality-theorists be as confident then as they are now of the equal intellectual capacity of the two sexes? To ask this question is to answer it. The fact is, our egalitarians treat evidence on a basis of heads-I-win-tails-you-lose; indeed, to say so is putting it mildly at that.Please refrain from giving further proof to Stove’s analogy of the “militant religious” nature of the believers, by stoning the messenger, i.e., me. Be careful to understand Stove’s thesis and the precise language he employs. And remember that outside the cloistered halls of the institutions which have prostrated themselves in the church of political correctness, there are many who will and do support this proposition.
# posted by mds : 3:57 PM
