The author's response to the anticipated suspicion that he attaches a superstitious or fanciful importance to the number three, and forces divisions to a Procrustean bed of trichotomy.
568. I fully admit that there is a not uncommon craze for trichotomies. I do not know but the psychiatrists have provided a name for it. If not, they should. "Trichimania,« [?] unfortunately, happens to be preëmpted for a totally different passion; but it might be called triadomany. I am not so afflicted; but I find myself obliged, for truth's sake, to make such a large number of trichotomies that I could not [but] wonder if my readers, especially those of them who are in the way of knowing how common the malady is, should suspect, or even opine, that I am a victim of it. But I am now and here going to convince those who are open to conviction, that it is not so, but that there is a good reason why a thorough student of the subject of this book 2) should be led to make trichotomies, that the nature of the science is such that not only is it to be expected that it should involve real trichotomies, but furthermore, that there is a cause that tends to give this form even to faulty divisions, such as a student, thirsting for thoroughness and full of anxiety lest he omit any branch of his subject, will be liable to fall into. Were it not for this cause, the trichotomic form would, as I shall show, be a strong argument in confirmation of the reasoning whose fruit should take this form.
569. My first argument in repelling the suspicion that the prevalence of trichotomies in my system is due purely to my predilection for that form, will be that were that predilection so potent, it would inevitably have made me equally given over to the trichotomic form of classification of whatever subject I might work upon. But this is not at all the case. I once endeavored by going over the different classifications that I have made of subjects not of the special kind in which I find trichotomies to abound — a kind which I shall define below — to ascertain the relative frequency of different numbers of sub-classes in the divisions of classes generally, when the divisions were such as seemed to me undoubtedly to possess objective reality. I do not think my results of much value, on account of the great difference of the proportions in different kinds of subjects. Nevertheless, I will set them down. I found that among twenty-nine divisions of subjects not of the kind that specially abound in trichotomies, there would be eleven dichotomies, five trichotomies, and thirteen divisions into more than three parts. The fact that I got such a result, however rough it was, suffices to show that I have no marked predilection for trichotomies in general.
570. I come now to a second argument, or rather to a series of considerations not altogether foreign to what I have been saying. The warm friends who urged upon me these objections — and nothing can be more precious to a sincere student than frank and strongly put objections — were naturalists belonging to that family of minds to whom mathematics, even the simplest, seems a closed book. I would point out to them, or, to speak more accurately, I would tell them, that there is a world-wide difference between the divisions that one recognizes in classes whose essence one can comprehend, and the varieties that one observes from the outside, as one does those of objects of natural history, without being able to guess why they should be such as they seem to be, nor, except in the higher divisions, being at all sure that we have the full list of the parts, nor whether they result from a single division or from several, one succeeding another.
571. Agassiz, in his Essay on Classification, described well — I do not say perfectly, but relatively, well — what a classification of animals ought to be. But subsequent zoölogists seem to find that when he came to adjusting his idea to the facts of the animal kingdom, it did not seem to be a good fit. What wonder? It required the taxonomist to say what the idea of the Creator was, and the different manners in which the one idea was designed to be carried out. How can a creature so place himself at the point of view of his Creator?
572. Soon the zoölogists began to classify according to the course of evolution. No doubt this had the advantage of turning their minds to problems within the scope of science. But I venture upon the observation that, granting the perfect success of their investigation, what they so ascertain is precisely the genealogy of species. Now genealogy is not at all the same thing as logical division. Nothing renders this clearer than the studies of Galton and others upon the phenomena of the inheritance of characters. I mean that this is shown even to those who have no definite idea of what logical division is; while for those who know what it is, the studies of Galton gave emphasis and illustration to what they must have fully realized already.
But when my critical friends counsel me to consider the marvellous multiplicity of sub-groups into which each group of the animal kingdom is divided at each division, I accept their suggestion, and turn to Huxley's famous volume on The Anatomy of Vertebrate Animals. I find that he first divides this branch into three provinces: the Ichthyopsida, the Sauropsida,P1) and the Mammalia. He divides each Province into Classes.1)