Positive logic extends to all the fundamental sciences the use of the processes at first peculiar to each one of them. Each great logical artifice, once studied in the portion of natural philosophy which shows its most spontaneous and most complete development, can afterwards be applied, with the necessary modifications, to the perfecting of the other sciences. For instance, the comparative method belongs in the first place to biology. But, when brought back to its principle and generalised, it becomes a precious instrument for sociology, for physics, and even for mathematics. In every science, the method is completed by the auxiliary use of the processes whose power and whose sphere of action have been made known by the other sciences. By these mutual loans, in each one of them, the positive method reaches its maximum of production. To be cultivated in the most rational manner possible, the sciences must then be subject to the direction of a general system of positive philosophy, “the common basis and the uniform combining element of all truly scientific labours.”[95] The scientific man must at the same time be a philosopher, since philosophy alone puts him in possession of all the resources of positive method. For instance, this philosophy will show the geometer that he must at least have a general knowledge of biology and of sociology. Biology will teach him the comparative method, of which he can make use when occasion offers, and sociology by showing him the history of his science in the general development of the human mind, will help him better to understand it. If the geometers had a more philosophical mind, their science would be better taught. The great conceptions of Descartes, of Leibnitz, of Lagrange, would be more intelligently explained and brought to light.