Well then, as in Astronomy we get an "exact science," because the facts and phenomena are on such a tremendous scale that we only see a minute portion of them—just a few details so to speak—and our ignorance therefore allows us to dogmatise; so at the other end of the scale in Chemistry and Physics we get quasi-exact sciences, because the facts and phenomena are on such a minute scale that we overlook all the details and see only certain general effects here and there. When a solution of cupric sulphate is treated with ammonia, a mass of flocculent green precipitate is formed. No one has the faintest notion of all the various movements and combinations of the molecules of these two fluids which accompany the appearance of the precipitate. They are no doubt very complex. But among all the changes that are taking place, one change has the advantage of being visible to the eye, and the chemist singles that out as the main phenomenon. So chemistry at large consists in a few, very few, facts taken at random as it were (or because they happen to be of such a nature as to be observable) out of the enormous mass of facts really concerned: and because of their fewness the chemist is able to arrange them, as he thinks, in some order, that is, to generalise about them. But it is certain as can be that he only has to extend the number of his facts, or his powers of observation, to get all his generalisations upset. The same may be said of magnetism, light, heat, and the other physical sciences; but it is not necessary to prove in detail what is sufficiently obvious.
But now, roughly speaking, there is a third region of human observation—a region which does not, like Astronomy (and Geology), lie so far beyond and above us that we only see a very small portion of it; nor, like Chemistry and Physics, so far below us and under such minute conditions of space and time that we can only catch its general effects; but which lies more on a level with man himself—the so-called organic world—the study of man, as an individual and in society, his history, his development, the study of the animals, the plants even, and the laws of life—the sciences of Biology, Sociology, History, Psychology, and the rest. Now this region is obviously that which man knows most of. I don't say that he generalises most about it, but he knows the facts best. For one observation that he makes of the habits and behaviour of the stars, or of chemical solutions—for one observation in the remote regions of Astronomy or Chemistry—he makes thousands and millions of the habits and behaviour of his fellowmen, and hundreds and thousands of those of the animals and plants. Is it not curious then that in this region he is least sure, least dogmatic, most doubtful whether there be a law or no? Or, rather, is it not quite in accord with our contention, namely that Science, like an uninformed boy, is most definite and dogmatic just where actual knowledge is least.
It will however be replied that the phenomena of living beings are far more complex than the phenomena of Astronomy or Physics—and that is the reason why exact science makes so little way with them. Though man knows many million times more about the habits of his fellow-men than about the habits of the stars, yet the former subject is so many million times more complicated than the latter that all his additional knowledge does not avail him. This is the plea. Yet it does not hold water. It is an entire assumption to say that the phenomena of Astronomy are less complicated than the phenomena of vitality. A moment's thought will show that the phenomena of Astronomy are in reality infinitely complex. Take the movement of the moon: even with our present acquaintance with that subject we know that it has some relation to the position and mass of the earth, including its ocean tides; also to the position and mass of the sun; also to the position and mass of every one of the planets; also of the comets, numerous and unknown as they are; also the meteoric rings; and finally of all the stars! The problem, as everyone knows, is absolutely insoluble even for the shortest period; but when the element of Time enters in, and we consider that to do anything like justice to the problem in an astronomical sense we should have to solve it for at least a million years—during which interval the earth, sun, and other bodies concerned would themselves have been changing their relative positions, it becomes obvious that the whole question is infinitely complex—and yet this is only a small fragment of Astronomy. To debate, therefore, whether the infinite complexity of the movements of the stars is greater or less than the infinite complexity of the phenomena of life, is like debating the precedence of the three persons of the Trinity, or whether the Holy Ghost was begotten or proceeding: we are talking about things which we do not understand.
Nature is one; she is not, we may guess, less profound and wonderful in one department than another; but from the fact that we live under certain conditions and limitations we see most deeply into that portion which is, as it were, on the same level with us. In humanity we look her in the face; there our glance pierces, and we see that she is profound and wonderful beyond all imagination; what we learn there is the most valuable that we can learn. In the regions where Science rejoices to disport itself we see only the skirts of her garments, so to speak, and though we measure them never so precisely, we still see them and nothing more.
There is another point, however, of which much is often made as a plea for the substantial accuracy of the scientific laws and generalisations, namely that they enable us to predict events. But this need not detain us long. J. S. Mill in his "Logic" has pointed out—and a little thought makes it obvious—that the success of a prediction does not prove the truth of the theory on which it is founded. It only proves the theory was good enough for that prediction.
There was a time when the sun was a god going forth in his chariot every morning, and there was a time when the earth was the centre of the universe, and the sun a ball of fire revolving round it. In those times men could predict with certainty that the sun would rise next morning, and could even name the hour of its appearance; but we do not therefore think that their theories were true. When Adams and Leverrier foretold the appearance of Neptune in a certain part of the sky, they made a brief prediction to an unknown planet from the observed relations of the movements of the known planets; that does not show, however, that the grand generalisation of these movements, called the "law of gravitation," is correct. It merely shows that it did well enough for this very brief step—brief indeed compared with the real problems of Astronomy, for which latter it is probably quite inadequate.
Tycho Brahé, excellent astronomer as he was, kept as we saw to the epicycle theory. He imagined that the moon's path round the earth was a fixed combination of cycle and epicycle. Kepler introduced the conception of the ellipse. Later on the motion of the perigee and other deviations compelled the abandonment of the ellipse and the supposition of an endless curve, similar to an ellipse at any one point, and maintaining a fixed mean distance from the earth, but never returning on itself or making a definite closed figure of any kind. Finally the researches of Mr. George Darwin have destroyed the conception of the fixed mean distance, and introduced that of a continually enlarging spiral. Certainly no four theories could well be more distinct from each other than these; yet if an eclipse had to be calculated for next year it would scarcely matter which theory was used. The truth is that the actual problem is so vast that a prediction of a few years in advance only touches the fringe of it so to speak; yet if the fulfilment of the prediction were taken as a proof of the theory in each of these different cases, it would lead in the end to the most hopelessly contradictory results.
The success of a prediction therefore only shows that the theory on which it is founded has had practical value so far as a working hypothesis. As working hypotheses, and as long as they are kept down to brief steps which can be verified, the scientific theories are very valuable—indeed we could not do without them; but when they are treated as objective facts—when, for instance, the "law of gravitation"—derived as it is from a brief study of the heavenly bodies—has a universal truth ascribed to it, and is made to apply to phenomena extending over millions of years, and to warrant unverifiable prophecies about the planetary orbits, or statements about the age of the earth and the duration of the solar system—all one can say is that those who argue so are flying off at a tangent from actual facts. For as the tangent represents the direction of a curve over a small arc, so these theories represent the bearing of facts well enough over a small region of observation; but as following the tangent we soon lose the curve, so following these theories for any distance beyond the region of actual observation we speedily part company with facts.[22]
To proceed with a few more words about the general method of Science. Science passes from phenomena to laws, from individual details which can be seen and felt to large generalisations of an intangible and phantom-like character. That is to say, that for convenience of thought we classify objects. How is this classification effected? It is effected through the perception of identity amid difference. Among a lot of objects I perceive certain attributes in common; this group of common attributes serves, so to speak, as a band to tie these objects together with—into a bundle convenient for thought. I give a name to the band, and that serves to denote any unit of the bundle by. Thus perceiving common attributes among a lot of dogs—as in an example already given—I give the name foxhound to this group of attributes, and thenceforth use the name foxhound to connect these objects by in my mind; again perceiving other common attributes among other similar objects, I invent the word greyhound to denote these latter by. The concept foxhound differs from the objects which it denotes, in this respect that these latter are (as we say) real dogs with thousands and thousands of attributes each: one of them has a broken tooth, another is nearly all white, another answers to the name "Sally," and so on; while the concept is only an imaginary form in my mind, with only a few attributes and no individual peculiarities—a kind of tiny G.C.M. arising from the contemplation of a long row of big figures.