III.
Astronomy, or at least that part of astronomy which bears the name of celestial mechanics, of all the physical sciences is the one which has been carried to the highest degree of perfection. Nowhere else have the phenomena been better reduced to a supreme law which allows us to foresee them with sufficient precision. But this result could only have been obtained by substituting the notion of a solar world to that of a universe.[123] This world is the only one which we can comprehend as a system. If the object of astronomy were the general laws of the universe, this science would be extraordinarily imperfect, not to say impossible. For what do we know about cosmic laws?[124] We do not even know whether Newton’s law applies to any or all systems of stars.
We must then distinguish between astronomy as the science of our world and sidereal astronomy. The latter is not absolutely forbidden us, but we know very little on this subject, and we shall probably never know much more. Do the innumerable suns scattered in space form a general system, or do independent systems exist? Is space limitless? Is the number of celestial bodies an infinite one? philosophers ask. In truth the consideration of our world is positive. The consideration of the universe is not.
History helps us to understand the transition which led from one to the other. Ancient philosophy made the earth the centre of the universe. Notwithstanding the diversity of their particular characteristics and of their motions, it was natural then for all the celestial bodies to be conceived as the parts of a single system. A more or less clearly expressed postulate supported this astronomical conception: the purpose of the universe was the existence of man. There was no occasion to distinguish our world from the whole world. But could this conception stand when the earth was reduced to the condition of a planet revolving round a sun so like a multitude of other suns. Suddenly the stars were carried to distances infinitely more considerable than the greatest planetary intervals. Undoubtedly the human mind could continue to regard the very small groups of which the earth forms a part as a system. But the system (if it exists) which embraces the whole of the celestial bodies ceased henceforth to be within our reach. Since then “the notion of the world has become clear and habitual, and that of the universe has become uncertain and almost unintelligible.”[125]
It matters little, moreover, for, according to one of Comte’s favourite maxims, what we have no means of knowing, neither have we any need to know; and every thing which it is our interest to learn we can also attain. Nor should we see in this any providential harmony. That which it is our interest to know must always in some way influence the conditions of our existence. By the mere fact that this action makes itself felt, it is inevitable that sooner or later, directly or indirectly, we should come to know of it. This reflection can be well applied to astronomy. The study of the laws of the solar system, of which we form a part, is of supreme interest for us: and we have reached very great precision on this point. On the contrary, the exact notion of the universe is inaccessible to us; but it is unimportant to us leaving out of the question our “insatiable curiosity.” The independence of our world is certain. The phenomena which take place within the solar system do not appear to be affected by the more general phenomena which relate to the mutual action of suns. Our tables of celestial events, drawn up long beforehand and taking into consideration no other world than our own, so far accord strictly with direct observations. Supposing the law of gravitation to extend to the entire universe, the perturbation in our world caused by a mass equal to a million times its own, and which would be situated at the distance of the nearest sun to our own, would be several thousand million times less than that which brings about our tides, that is to say practically nil.
Here, says Comte, is the only exception to the encyclopædic law according to which the more general phenomena control the more particular ones without being influenced by them.[126] From this he simply concludes that the phenomena of our system are the most general to which positive research can extend, and that the study of the universe must henceforth be excluded from natural philosophy. The encyclopædic law then remains true for the whole of positive philosophy.
The delimitation of the object of astronomy is one of the points where we can best follow the successive modifications of Comte’s thought. In the second volume of the Cours de philosophie positive he gave to astronomy the place which is generally conceded to it by scientific men. He even claims, as a condition for its utility, the most perfect disinterestedness of scientific research in the whole extent of its province. The example which he gives of it (the determination of longitude at sea), is borrowed from Condorcet. Undoubtedly, Comte already insists upon the distinction between the ideas of world and universe, the former only being positive. Nevertheless, he still admits that we should not give up all hope of obtaining some sidereal knowledge,[127] and that it would be very precious for us to know the relative motions of multiple stars, etc. But already in the sixth volume of the Cours he condemns entirely the “so-called sidereal astronomy, which to-day constitutes the only grave scientific aberration peculiar to celestial studies.”[128] Ten years later, in the first volume of the Politique positive, he “regenerates” astronomy from the synthetic point of view. He is no longer content to limit it to the knowledge of the solar system. He confines the particular study of our world within narrow limits. Astronomy, like the other sciences, from objective must become subjective. Instead of the vague (that is to say indefinite) study of the heavens its end must be the knowledge of the earth, and the consideration of the other celestial bodies only in their relation to the human planet. At this price alone can the unity of this science be secured.[129]
Thus Comte came back to Aristotle’s closed world with the earth as its centre. He points it out himself in showing in what way he differs from the ancient conception. “This unity,” he says, “existed for the ancients, but was of an absolute character which at that time was legitimate.” When the motion of our planet became known, the ancient constitution of celestial science might merely have been modified “by preserving in it, as subjective, the centre which was at first supposed to be objective.” That would have sufficed to change astronomy from an absolute science to a relative one. Undoubtedly the ancients were deceived in believing the earth to be the centre of the world; but, in order to correct their error, it sufficed to say, the centre of our world. The subjective synthesis “indeed concentrates the celestial studies round the earth.” The other stars only deserve our attention in so far as the knowledge of our planet requires it. Comte ends by saying in the fourth volume of the Politique positive that, strictly speaking, the study of the sun and moon would suffice. We may add to them the ancient planets, but not the “little telescopic planets.”[130]
This progressive narrowing of the astronomical domain does not indicate a radical change in Comte’s philosophical thought. It only results from the growing subordination of the scientific interest to other superior interests. To know for the sake of knowing, appears to Comte to be a wrong use of the human intellect. The Newtons and the Laplaces in the past have fulfilled a necessary function, and humanity owes them eternal gratitude. They struck a decisive blow against theological and metaphysical philosophy; and secured the victory for the positive spirit. In their time scientific speculation which tended to the discovery of the laws of phenomena, and especially of celestial phenomena, was at once the most sublime and the most useful occupation which those men of genius could set themselves. But now that their efforts have culminated in the foundation of positive philosophy, and this philosophy itself in the “final religion,” there is no longer any reason to continue researches with which henceforth humanity can dispense. We must even “cut down many idle acquisitions.”[131] In a word, from the religious point of view, Comte, in order to remedy the anarchy of science, suppresses its liberty.
These extreme, but logically deduced consequences, are part of the whole of Comte’s religious conceptions, that is to say of a distant ideal. They must not blind us to the profundity of his philosophical considerations on astronomy. His reflections upon the relation between the ideas of the world and of the universe correspond, from the positive point of view, to the first antinomy of the transcendental Dialectics in the Critique de la raison pure. Can we ever be more fully conscious of the relativity of our knowledge, that when we see that what we know of celestial phenomena is admirably precise so long as the solar system is concerned, but is reduced to almost nothing if we look beyond it?
Our world will perish, and its disappearance like its existence, will perhaps be an imperceptible incident. By the continued resistance of the general milieu, says Comte, in the end our world must be re-united to the solar mass from which it came, until, in the immensity of future ages, a fresh dilatation of this mass shall organise a new world in the same manner, destined to repeat more or less completely the former cycle. Moreover, all these immense alternatives of destruction and of renewal have to be accomplished without influencing in any way the more general phenomena due to solar interaction; so that the great revolutions in our world would only be secondary and, so to speak, local events, in relation to transformations of a really universal character.[132]
This outlook into the “immensity” of space and of duration suffices to show that Comte was not a prisoner in the little solar fatherland in which he seems to seclude himself. It may be that for moral and religious reasons he will not allow himself to go beyond it. But, like Pascal, he well knows that he inhabits “a little out of the way district of nature.”
[CHAPTER III.]
THE SCIENCES OF THE INORGANIC WORLD
If we do not separate chemistry from physics, their common object is the knowledge of the laws of the inorganic world. In this way they are clearly distinguished on one hand from astronomy which we may consider as an “emanation from mathematical science,” and on the other hand from biology. The distinction between physics and chemistry presents a greater difficulty. Nevertheless this distinction must be maintained, since the physical phenomena are more “general,” and the chemical phenomena more “special,” that is to say, the latter depend upon the former, without this dependence being for the most part reciprocal. Even if some day we succeeded in establishing that chemical phenomena are in reality physical, the distinction would none the less subsist, in this sense, that in a fact termed chemical, there is always something more than in a fact which is simply physical, namely, the characteristic alteration which the molecular composition of bodies undergoes, and which consequently affects the totality of their properties.[133]
To speak only of physics in the first place, this science presents different characteristics from those of astronomy. The speculative perfection of a science is measured by two correlative although distinct considerations, by the more or less complete co-ordination of the laws, and by the more or less accurate prevision of facts. Now, under one aspect or the other, even supposing that physics should make very important progress, it will always remain very much behind astronomy. Indeed, the celestial science presents an almost perfect unity; physics, on the contrary, is composed of several branches which are almost isolated from one another, and each one taken by itself cannot even reduce all its laws to a more general law. And, as to the second point, while a very small number of direct observations allows of rational and exact prevision of the whole of the celestial phenomena, physics only renders possible predictions which are generally founded upon experience at once immediate and within easy reach. Undoubtedly some parts of physics allow of the use of mathematical analysis (we shall see presently under what conditions). Nevertheless, the part played by experience is infinitely greater in physics than in astronomy. So it is in the former science that we first meet with the inductive method, which is afterwards used and developed in the other positive sciences. Although deduction continues to fulfil an important part, it already ceases to predominate here, because, says Comte, in it the institution of true principles begins to become more troublesome than the development of accurate consequences.[134]
The inductive method implies these essential processes; 1∘ observation properly so called, that is to say the direct examination of the phenomenon such as it appears naturally: 2∘ experimenting, which is usually defined as the examination of the phenomenon more or less modified by artificial circumstances instituted by us in order to study it better; 3∘ comparison, that is to say the gradual consideration of a succession of analogous cases, in which the phenomenon becomes more and more simple. Of these three processes astronomy only makes use of the first. Physics cannot use the third which is reserved for biology; but it avails itself of the first and institutes the second. This is a fresh confirmation of the law established by Comte: to the complexity and increasing difficulty of the sciences, corresponds an increasing development of the processes of the positive method applicable to them.
Research by way of experiment, which is impossible in Astronomy, appears in Physics. It is therefore here where it originates that we must study it. It is also here that it is most successful, and gives the greatest number of results. Indeed, to experiment successfully we must be able to compare two cases “which present no other difference direct or indirect, than that which relates to the course of the phenomenon under analysis.”[135] By experimenting, Comte here clearly designates what John Stuart Mill will call the method of difference, that is to say the most powerful of his methods for the investigation of phenomena.
Now, experimenting, so understood, is extremely difficult when very complicated phenomena are concerned. In physiology, for instance, the experiments must be combined in such a way as to maintain the subjects in the living state, and even, as far as possible, in the normal state. But any modification of one part of the organism immediately affects the other parts. The living being reacts instantly, and adapts itself as best it can to the new conditions in which it has been placed by the experimentalist. We can therefore hardly ever establish in physiology what is so easily obtained in physics: two cases exactly similar in all respects, except in the one which we want to analyse. In chemistry, it is true, experimenting would seem to be even easier than in physics, since in it, as a rule, we merely consider facts resulting from circumstances which are produced by man’s intervention. But this is to mistake the nature of the experimental method. The essence of this process does not consist in man’s institution of the circumstances surrounding the phenomena; it lies in the “freest possible choice of the case best suited to show the law of the phenomenon,” whether this case be, moreover, natural or artificial. Now, this choice is nearly always easier in physics than in chemistry. For the chemical phenomena more complex in themselves, in general can only be brought about by the co-operation of a great number of different influences; for this reason in chemistry, it is more difficult to modify the circumstances under which phenomena are produced, and still more difficult to isolate as completely as in physics the various conditions by which phenomena are determined.
To the use of the experimental method, physics can often join that of mathematical analysis. But in the employment of the latter it must be extremely cautious, and we must only have recourse to this application of mathematics after having “carefully considered the reality of the starting point,” which alone can guarantee the solidity of the deductions. In a word, the spirit proper to physical investigation, must constantly direct the use of this powerful instrument. Now, this condition has not always been fulfilled. Too often the preponderance of mathematical analysis has been the cause of the neglect of experimental studies. Not only has mathematical analysis in this way retarded the progress of physics but it has even tended to vitiate the conception of that science, and to bring it back to a state of obscurity and uncertainty which, says Comte, notwithstanding the apparent severity of the forms differs little, at bottom, from its old metaphysical state.[136]
For this reason, the application of analysis to physics must not be left to geometers who are chiefly concerned with the instrument. It must belong to the physicists who before all things consider the use to be made of it. Mathematicians have often encumbered physics with a quantity of analytical labour founded upon very doubtful hypothesis; they must give way to physicists trained in experimental studies, and, nevertheless, with sufficient knowledge of mathematics to make use of the analysis whenever it is possible. Within these limits mathematical analysis will render the greatest service to the science of physics. Would optics, acoustics, the theories of heat and of electricity have reached the point where we see them to-day without the powerful help of analysis? Yet even here, physical researches are almost always so complex that, in order to assume a mathematical form, they demand the setting aside of a more or less essential portion of the conditions of the problem. Indeed we are here in presence of the general problem of the translation of the concrete into the abstract. This problem, which is admirably solved in mathematics, and sufficiently in astronomy, is only imperfectly solved in physics. The art of closely combining experience and analysis, says Comte, is still almost unknown. It constitutes the final progress of the method proper to the deeper study of physics.[137] We may add, and this is in Comte’s mind, that conversely the progress made by this art would be useful to analysis itself.