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