serial order in which the various sciences entered the positive stage. Mathematics comes first, which had even become positive already among the Greeks, then successively Astronomy, Physics, Chemistry, Biology and Sociology (theory of society). But this serial order likewise presents a successive passage from the simplicity of the objects considered to their complexity: the simpler the objects of a given science, the sooner it will become positive. The serial order furthermore reveals a constant passage from universality to particularity: the laws of mathematics are valid of all phenomena, whilst the astronomical, physical, chemical and biological laws apply to an increasingly smaller group, and those of sociology to the most circumscribed group of all. Finally we likewise find in this serial order a gradual passage from the predominance of the deductive method to the predominance of induction.—These four principles of classification, as may be readily observed, are closely related.
The various departments of experience corresponding to the different sciences are not connected in a single continuum. Discontinuity manifests itself even within one and the same department, as e. g., between the various physical energies, between the organic species, etc.,—Comte was not acquainted with the law of the conservation of energy, which however did not receive general recognition during his lifetime, and he did not survive the appearance of Darwin.
His classification omits logic and psychology, of which the former should be placed before mathematics and the latter between biology and sociology.—In his later years Comte himself added ethics as a seventh science. According to his conception, ethics is more specialized than
