The illustration is surely unluckily chosen; but the language in which these so-called abstract sciences are defined seems to me to be still more open to criticism. With what propriety can astronomy, or physics, or chemistry, or biology, be said to occupy themselves with the consideration of "all conceivable cases" which fall within their respective provinces? Does the astronomer occupy himself with any other system of the universe than that which is visible to him? Does he speculate upon the possible movements of bodies which may attract one another in the inverse proportion of the cube of their distances, say? Does biology, whether "abstract" or "concrete," occupy itself with any other form of life than those which exist, or have existed? And, if the abstract sciences embrace all conceivable cases of the operation of the laws with which they are concerned, would not they, necessarily, embrace the subjects of the concrete sciences, which, inasmuch as they exist, must needs be conceivable? In fact, no such distinction as that which M. Comte draws is tenable. The first stage of his classification breaks by its own weight.
But granting M. Comte his six abstract sciences, he proceeds to arrange them according to what he calls their natural order or hierarchy, their places in this hierarchy being determined by the degree of generality and simplicity of the conceptions with which they deal. Mathematics occupies the first, astronomy the second, physics the third, chemistry the fourth, biology the fifth, and sociology the sixth and last place in the series. M. Comte's arguments in favour of this classification are first—
"Sa conformité essentielle avec la co-ordination, en quelque sorte spontanée, qui se trouve en effet implicitement admise par les savants livrés à l'étude des diverse branches de la philosophie naturelle."
But I absolutely deny the existence of this conformity. If there is one thing clear about the progress of modern science, it is the tendency to reduce all scientific problems, except those which are purely mathematical, to questions of molecular physics—that is to, say, to the attractions, repulsions, motions, and co-ordination of the ultimate particles of matter. Social phænomena are the result of the interaction of the components of society, or men, with one another and the surrounding universe. But, in the language of physical science, which, by the nature of the case, is materialistic, the actions of men, so far as they are recognisable by science, are the results of molecular changes in the matter of which they are composed; and, in the long run, these must come into the hands of the physicist. A fortiori, the phænomena of biology and of chemistry are, in their ultimate analysis, questions of molecular physics. Indeed, the fact is acknowledged by all chemists and biologists who look beyond their immediate occupations. And it is to be observed, that the phænomena of biology are as directly and immediately connected with molecular physics as are those of chemistry. Molar physics, chemistry, and biology are not three successive steps in the ladder of knowledge, as M. Comte would have us believe, but three branches springing from the common stem of molecular physics.
As to astronomy, I am at a loss to understand how any one who will give a moment's attention to the nature of the science can fail to see that it consists of two parts: first, of a description of the phænomena, which is as much entitled as descriptive zoology, or botany, is, to the name of natural history; and, secondly, of an explanation of the phænomena, furnished by the laws of a force—gravitation—the study of which is as much a part of physics, as is that of heat, or electricity. It would be just as reasonable to make the study of the heat of the sun a science preliminary to the rest of thermotics, as to place the study of the attraction of the bodies, which compose the universe in general, before that of the particular terrestrial bodies, which alone we can experimentally know. Astronomy, in fact, owes its perfection to the circumstance that it is the only branch of natural history, the phænomena of which are largely expressible by mathematical conceptions, and which can be, to a great extent, explained by the application of very simple physical laws.
With regard to mathematics, it is to be observed, in the first place, that M. Comte mixes up under that head the pure relations of space and of quantity, which are properly included under the name, with rational mechanics and statics, which are mathematical developments of the most general conceptions of physics, namely, the notions of force and of motion. Relegating these to their proper place in physics, we have left pure mathematics, which can stand neither at the head, nor at the tail, of any hierarchy of the sciences, since, like logic, it is equally related to all; though the enormous practical difficulty of applying mathematics to the more complex phænomena of nature removes them, for the present, out of its sphere.
On this subject of mathematics, again, M. Comte indulges in assertions which can only be accounted for by his total ignorance of physical science practically. As for example:—
"C'est donc par l'étude des mathématiques, et seulement par elle, que l'on peut se faire une idée juste et approfondie de ce que c'est qu'une science. C'est là uniquement qu'on doit chercher à connaître avec précision la méthode générale que l'esprit humain emploie constamment dans toutes ses recherches positives, parce que nulle part ailleurs les questions ne sont résolues d'une manière aussi complète et les déductions prolongées aussi loin avec une sévérité rigoureuse. C'est là également que notre entendement a donné les plus grandes preuves de sa force, parce que les ideés qu'il y considère sont du plus haut degré d'abstraction possible dans l'ordre positif. Toute éducation scientifique qui ne commence point par une telle étude pèche donc nécessairement par sa base."[24]
That is to say, the only study which can confer "a just and comprehensive idea of what is meant by science," and, at the same time, furnish an exact conception of the general method of scientific investigation, is that which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation! And education, the whole secret of which consists in proceeding from the easy to the difficult, the concrete to the abstract, ought to be turned the other way, and pass from the abstract to the concrete.
M. Comte puts a second argument in favour of his hierarchy of the sciences thus:—