The use of statistics in argument is essentially deduction from insufficient premises, and though the mass of men who are getting more and more exasperated with the results of such argument are not yet conscious of the flaw in their oppressors' reasoning, they only know instinctively that it is bad reasoning--and they are right.
The whole argument against the abuse of statistics is summed up in the story of the man who explained what an average was. "If you were struck dead by lightning at my side and I remained safe and sound, we should both be on the average half dead."
But there is a deeper final cause for the suspicion of numbers on which one must touch very carefully, because though it has led to the wildest extravagance in philosophy, and has weakened the use of the human reason in modern times, it none the less has a basis of truth.
Numbers, absolute though they be, and the expression of the human mind's divine capacity for measure, escape us in their ultimate use. The science of numbers, when you have pursued it far enough, lands you where every human analysis lands you--in a contradiction or a mystery. On this account it is that men have been tempted of late to a monstrous denial of mathematical truth, and that as a part of their general revolt against reason. But it is true that you approach regions beyond which what had hitherto been the necessary laws of number cease to stand. You have it wherever there is a sudden passage from an indefinitely increasing number to an indefinitely small one; a sudden passage through what we call "the infinite" to "Zero." And you get it in the "limit" of any mathematical process.
For instance, as you stretch out an ellipse it ought to get more and more like a parabola, at any rate at the business end, if I may so express myself; and it ought gradually at the end of the process to merge into a parabola. Then, as you go on tilting your plane, you ought logically to be able to follow the process of the parabola turning into an hyperbola. Well, the thing does not happen that way. The ellipse remains an ellipse though its foci get farther and farther apart. It remains an ellipse right up to the critical moment, when the distant focus vanishes into infinity, and, then, suddenly, the curve becomes a parabola, and then in a flash, it turns inside out, splits into two, and is an hyperbola. And no one will ever be able to tell you what happened out in the infinities, where the transmogrification took place.