Page:History of Modern Philosophy (Falckenberg).djvu/578

55^ FRANCE. investigate the most general laws of nature, valid for aU phenomena, from which the particular phenomena which experience presents to us cannot be deduced, but on the basis of which an entirely different world were also possi- ble. The concrete sciences, on the other hand {e. g., botany and zoology), have to do with the actually given combina- tions of phenomena. The former follow out each separate one of the general laws through all its possible modes of operation, the latter consider only the combination of laws given in an object. Thus oaks and squirrels are the result of very many laws, inasmuch as organisms are dependent not only on biological, but also on physical, chemical, and mathematical laws. Comte enumerates six of these abstract sciences, and arranges them in such a way that each depends on the truths of the preceding, and adds to these its own special truths, while the first (the most general and simplest) pre- supposes no earlier laws whatever, but is presupposed by all the later ones. According to this principle of increas- ing particularity and complexity the following scale results: (i) Mathematics, in which the science of number, as being absolutely without presuppositions, precedes geometry and mechanics ; (2) Astronomy ; (3) Physics (with five subordi- nate divisions, in which the first place belongs to the theory of weight, and the last to electrology, while the theory of heat, acoustics, and optics are intermediate) ; (4) Chemistry; (5) Biology or physiology ; (6) Sociology or the science of society. This sequence, which is determined by the increasing complexity and increasing dependence of the objects of the sciences, is the order in which they have historically developed — before the special laws of the more complicated sciences can be ascertained, the general laws of the more simple ones must be accurately known. It is also advisable to follow this same order of increasing complexity and difficulty in the study of the sciences, for acquaintance with the methods of those which are elemen- tary is the best preparation for the pursuit of the higher ones. In arithmetic and geometry we study positivity at its source; in the sociological spirit it finds its completion. Mathematics entered on its positive stage at quite an