INTRODUCTION
The Philosophy of the Sciences is one of the leading parts of Comte’s work. No other brings out more clearly the essential differences which distinguish his doctrine from previous systems.
In Comte’s eyes the philosophy of the sciences is inseparable from the philosophy of history and from the theory of progress. For the sciences are great sociological facts and, as such, are subject, in their evolution, to invariable laws. The method of the philosophy of the sciences could therefore only be the positive method, ever like to itself.
Moreover,—and this is an immediate consequence of this first consideration,—the object of the positive philosophy of the sciences is in no way to “explain” what the sciences themselves do not explain. The sciences, as is well known, do not inquire into their data and their principles. They consider them as sufficiently established by the implicit consent of all men, or at least by the universal usage of learned men. The geometer leaves to others the care of speculating upon the essence of space, or upon the a priori character of his definitions. The physicist, if he form an idea of matter for himself, unhesitatingly adopts the one which appears to be the most immediately advantageous, that is to say, the one which is best in accordance with what he knows of its properties and of its laws. He attributes no more value than that of a simple hypothesis to this idea.
Up to the present the business of solving the questions which the scientific man does not examine has belonged to the philosopher—understand by this term the metaphysician. It is for him to seek what matter, time, movement, space, etc., may be “in themselves.” Whether he descends from metaphysics to the positive sciences, or ascends from the latter to metaphysics, he always endeavours to show that such and such a transcendental hypothesis is more in accordance than any other with what we know to-day of the laws of nature. In a word; the philosophy of the sciences has been, in general, an effort to interpret scientific knowledge metaphysically. This explanation remains in respect to such a knowledge an “extrinsic denomination.” It explains but does not touch it.
Now, according to Comte, there are not two forms of knowledge, the one positive and properly speaking scientific the other metaphysical and properly called philosophical. The whole of our real knowledge in the end bears upon special or general facts. There can therefore be no question of a philosophy which should be essentially distinct from positive knowledge. Any attempt to explain by essences, causes, principles or ends, is excluded by the positive method. Metaphysical problems can no longer be set and, in this sense, when they disappear, the philosophy of the sciences disappears with them.
But, on the other hand, as we have already seen, the positive sciences are not self-sufficient. They need to be crowned and ordered by a philosophy. If then a philosophy is indispensable, and if, at the same time, this philosophy must be positive, relative like the sciences themselves, and homogeneous with them, only one solution remains possible. The philosophy of the sciences will consist in substituting the point of view of the whole to that of the parts. It will still be a product of the positive spirit; but in it this spirit from special will have become general; from particular it will have become universal.
This universal character remains common to Comte’s philosophy and to that of his predecessors. But Comte did not understand it as they did. For metaphysicians in general, and still for Kant, universality is the distinctive sign of knowledge which does not come from experience, which is therefore necessary and a priori. Comte, who does not know of any a priori in the Kantian sense, calls that knowledge universal which remains relative, and which is founded upon induction, but which regulates the other forms of knowledge in the order of generality. Thus the principle of laws is universal. The encyclopædic laws of phenomena are universal. The point of view of humanity is universal, because from this point of view a synthesis of the whole of our knowledge is possible. And, as universality is a relative thing, we conceive universalities of different orders.
Henceforth the philosophy of the sciences is easily defined. Are we concerned with a certain science considered by itself? The philosophy of this science consists in embracing at a glance the whole, the object and the method, as opposed to the special point of view of the scientific man who follows the discovery of more or less special laws in a branch of this science, but such a philosophy necessarily remains imperfect and fragmentary. The philosophy of a science is only really established in the general philosophy of the sciences, that is to say by a view at once synthetic and single of all the sciences, in which are co-ordinated the objects which they study, the laws which they discover, the methods which they make use of, and the ends which they should pursue.
It has been said that this is not a philosophy of the sciences but simply a “synthesis of the most general results of the positive sciences.” Comte partly accepts and partly rejects the objection. If he is reproached with not having constructed a philosophy of the sciences according to the old spirit, that is to say an effort at “explanation,” which goes beyond the point of view of positive science, he grants the objection. He considers all philosophy of this kind as out of the question. Is it said that there is no difference between his point of view and that of the scientific man properly so called, unless it be that he successively goes through all the fundamental sciences? Comte calls our attention to the fact that it is not enough to place these sciences side by side to obtain their philosophy. A new point of view, truly universal, although always relative, is needed. How could Comte have distinguished otherwise, in each science, what is lasting and in conformity with the positive spirit from what is decaying and still bears the mark of the theological and metaphysical spirit? Could he especially have fixed the relations which the sciences should maintain among themselves, and could he have imposed upon them a discipline whose principle was not to be found in any one of them?
Thus, until Auguste Comte’s time, the philosophy of the sciences had been a metaphysical conception, joined more or less closely to the whole of positive knowledge. Comte endeavoured to form a conception of this whole, which should be philosophical while remaining positive. It is this conception which is especially set forth in the three first volumes of the Cours de philosophie positive. From the static point of view it is founded upon the hierarchy of the sciences, the unity of the method, and the homogeneity of knowledge. From the dynamic point of view, it endeavours to show the progressive convergence of all the sciences towards sociology, the final and universal science. With this “guiding thread,” Comte will be able to establish in turn the philosophy of each fundamental science, without ever losing sight of the relation which it bears to the whole of the others.
[CHAPTER I]
MATHEMATICS
In the eyes of philosophers, mathematics has always occupied a privileged place among the sciences. Plato located their object in an intermediate region between the world of sensible phenomena and that of intelligible realities. On the one hand mathematical objects, and in particular the geometrical figures, appeal to the imagination as sensible things; on the other hand, mathematical truths like ideas and the relations between ideas, are characterised by immutable and eternal fixity. This is why the study of mathematics is an excellent preparation for philosophy, which is the science of ideas. While still leaving to the mind the help of direct sensible perception, it accustoms it to permanent truth. During the whole of antiquity the science of mathematics, as the name indicates, was pre-eminently the science. The science of physics, less sure of its object and of its method, was hardly distinguished from philosophical speculation, and lent itself with difficulty to the purely scientific form.
For Plato then, and for those who followed him, mathematics has characteristics which distinguish it from the study of phenomena. In a certain measure, it partakes of the nature of science, conceived as bearing upon what is, upon the absolute reality which is neither subject to change nor to motion. It is true that they start from definitions and hypotheses. But, once the principles are established, they are developed a priori by a succession of necessary demonstrations like the dialectics of ideas.
This conception offers a mixture of metaphysical and positive elements. It implies that the object of science is reality such as it is in itself; but, at the same time, it sees in the demonstration the essential character of science. A long evolution, which culminates in Comte’s doctrine, has driven the metaphysical elements out of science while the other elements subsist in it still. Far from saying with Plato or with his successors that there is no science of the phenomenon or of that which passes away, Comte thinks on the contrary, that the only object of science is phenomenal reality so far as it is subject to laws. Science has not to search for causes or substances; it suffices for it to determine invariable relations.
If the mathematical sciences have long been the only sciences properly so called, and if to-day they are still more advanced than any others, it is because the geometrical and mechanical phenomena are indeed the simplest of all, and those which are most naturally connected among themselves. The period during which they could be studied by observation could therefore be very short, so short that it is even not absurd to maintain that it never existed, and that, in this case, rational knowledge was not preceded by the empirical establishment of facts. But the difference between mathematics and the other sciences none the less remains one of degree and not of kind. The Science of Mathematics is in advance of the other sciences; but all work on common ground. In a word, like all other sciences it is a natural science.
This endeavour to present the whole of the sciences as homogeneous, that is to say, to avoid two distinct classes being formed of mathematics on the one hand, and of the sciences of nature on the other, had already been attempted before Comte. This endeavour imposed itself, so to speak, upon modern philosophers, from the time when Descartes sought for a universal method for science conceived as a whole. Comte, who saw very well the defect in the Cartesian conception, in which the ascendency of mathematics was still too much felt, did not, however, deny that his own conception proceeded from that of Descartes. In another form, the idea of the homogeneity of the sciences is also found in Leibnitz and even in Kant. Does not the Critique de la raison pure show that mathematics on the one hand, and physics on the other, equally rest upon principles which are synthetic a priori? In the Prolégomenes à toute métaphysique future just as the chapter corresponding to l’esthétique transcendentale is entitled “How are pure mathematics possible a priori?” so the chapter corresponding to the Logique transcendentale bears as its title “How are pure physics possible a priori?” On another plan Comte’s theory is parallel to Kant’s. Here as there mathematics as well as physics rests upon synthetic principles—“superior to experience,” says Kant—proceeding from experience, says Comte. The latter, it is true, did not know Kant’s theory, and, had he known it he would not have accepted it. But the analogy of tendency subsists none the less beneath the diversity of doctrines.
The immediate antecedent of Comte’s theory is found in d’Alembert. The author of the Discours préliminaire had said, “We will divide the science of nature into physics and mathematics.”