Page:Popular Science Monthly Volume 15.djvu/555

Rh tables out of which averages are deduced. There can not be a more perfect example than they afford, of what the metaphysicians mean by generalizations, when the objects generalized are objects of vision, and when they belong to the same typical group, one important characteristic of which is that medium characteristics should be far more frequent than divergent ones. It is strange to notice how commonly this conception has been overlooked by metaphysicians, and how positive are their statements that generalizations are impossible, and that the very idea of them is absurd. I will quote the lucid writing of Sir W. Hamilton to this effect, where he epitomizes the opinions of other leading metaphysicians. I do so the more readily because I fully concede that there is perfect truth in what he says, when the objects to be generalized are not what a cautious statistician would understand by the word generic.

Sir W. Hamilton says:

Take, for example, the term man. Here we can call up no notion, no idea, corresponding to the universality of the class, or term. This is manifestly impossible. For as man involves contradictory attributes and as contradictions can not exist in one representation, an idea or notion adequate to man can not be realized in thought. The class man includes individuals, male and female, white and black and copper-colored, tall and short, fat and thin, straight and crooked, whole and mutilated, etc., and the notion of the class must therefore at once represent all and none of these. It is therefore evident, though the absurdity was maintained by Locke, that we can not accomplish this; and, this being impossible, we can not represent to ourselves the class man by any equivalent notion, or idea. All that we can do is to call up some individual image and consider it as representing, though inadequately representing, the generality. This we can easily do, for as we can call into imagination any individual, so we can make that individual image stand for any or for every other which it resembles, in those essential points which constitute the identity of the class. This opinion, which, after Hobbes, has been in this country maintained among others by Berkeley, Hume, Adam Smith, Campbell, and Stewart, appears to me not only true but self-evident.

If Sir W. Hamilton could have seen and examined these composite portraits, and had borne in mind the well-known elements of statistical science, he would certainly have written very differently. No doubt, if what we are supposed to mean by the word man is to include women and children and is to relate only to their external features and measurements, then the subject is not suitable for a generic picture, other than of a very blurred kind, such as a child might daub with a paintbrush. If, however, we take any one of the principal races of man and confine our portraiture to adult males, or adult females, or to children whose ages lie between moderate limits, we ought to produce a good generic representation.

It will, I trust, be quite understood that, although for the sake of