 While philosophers of science have always recognized the place of Comte in the history of their discipline, the philosophy of science presented in the Course, and a fortiori the one in the System, have hardly been studied (Laudan 1981, Brenner 2021). Comte’s philosophy of science is based on a systematic difference between method and doctrine. These are, to use Comtean terminology, opposed to one another, as the logical point of view and the scientific point of view. Method is presented as superior to doctrine: scientific doctrines change (that is what “progress” means), but the value of science lies in its methods. At the level of doctrine, mathematics has a status of its own, well indicated in the second lesson, where it is presented last, and as if to make up for something forgotten. As much as it is itself a body of knowledge, it is an instrument of discovery in the other sciences, an ‘organon’ in the Aristotelian sense. Among the remaining sciences, leaving sociology aside for the moment, two occupy a pre-eminent place: