Final answer:
Comte's hierarchy of the natural sciences is in the order of Mathematics, Astronomy, Physics, Chemistry, and Biology. This hierarchy comes from his belief in a progression from the abstract to the specific and is tied to his law of three stages and the development of sociology.
Step-by-step explanation:
Auguste Comte arranged the natural and social sciences into a hierarchy, placing the sciences in order from the most abstract and general to the most concrete and specific. According to Comte, the hierarchy of the natural sciences is as follows: Mathematics, Astronomy, Physics, Chemistry, and Biology. This arrangement reflects Comte's belief in a progression of complexity, with mathematics being the most abstract and far-reaching in terms of application across the sciences, while biology is the most complex, focusing on living organisms which can be more difficult to predict and understand than inanimate objects.
Comte's law of three stages also underlies his hierarchical view, with the scientific study of the natural world amongst other fields evolving through theological, metaphysical, and positive (empirical) phases, leading to the final positivist stage where empirical sciences are paramount. This framework influenced the development of sociology, the 'science of society', which Comte believed could lead to human progress through empirical study, much like the natural sciences.