Classification of disciplines has been a staple of philosophy since the time of Aristotle, and Comte’s studies make no exception. Of course, there have been plenty of classifications presented as the correct one, so it is reasonable to ask what is so special in Comte’s. Comte himself has a clear answer: earlier classifications derive from a time when all fields of science had not reached the status of positivism.
Before introducing his classification of sciences, Comte considers the question of what he should actually be classifying. He first distinguishes theoretical sciences from practical arts and delineates between these two extremes the field of engineering, which aims at applying results of theoretical sciences to practical questions. He notes that arts and engineering are essentially dependent on theoretical sciences. Indeed, he adds, one art can depend on various sciences, for instance, agriculture requires theoretical knowledge of plants, of chemicals and even of sun, moon and stars. Thus, he concludes that the basic classification should be made at the level of theoretical sciences, not on the level of their practical applications.
Another distinction Comte makes is that between general or abstract sciences and particular or concrete sciences. Abstract sciences, he explains, deal with what is possible, for instance, according to known physical and chemical laws. Concrete sciences then deal with actual instances of such laws: examples include natural history and mineralogy. Comte also points out that just like practical arts depend on theoretical sciences, concrete sciences depend on abstract sciences, being their specifications. Thus, the disciplines good for classification are abstract theoretical sciences.
Comte goes on to speak about the method one should use in the classification. He points out that while we strive for what could be called a natural classification, we can approach such classification only through various artificial classifications. Indeed, he notes, we often begin classification of a new science historically, that is, by noting new ideas and discoveries in the order in which they were found. The more a science is developed, Comte notes, less and less possible it becomes to use the historical approach, because the number of theorems involved becomes too unwieldy. Historical classification is then replaced by a dogmatic approach, where the ideas in question should form a systematic whole. This dogmatic approach abbreviates the historical approach. In the particular case of classifying all sciences, there is the further link that the most abstract disciplines, from which the dogmatic approach begins, are also historically the earliest to reach a more complete stage.
Comte’s classification is meant to be a basis for a complete reform of the educational system. His idea is simple: if we can organise general theoretical sciences into a hierarchical system, in accordance with the dogmatic approach, we then know the ideal order of science education - the education must always start with the most abstract science and move towards more concrete ones. That way, researches working with problems of the more concrete sort would have the necessary tools for understanding more abstract field, on which the more concrete questions depend.
The actual classification Comte suggests seems somewhat problematic - this is just to be expected, since the development of science has been explosive in the last two centuries. Comte’s main dividing line between sciences of inorganic and organic nature seems acceptable, but subdivisions of the two feel less successful. For instance, Comte divides study of inorganic nature into study of stellar phenomena or astronomy and study of terrestrial phenomena, which he then divides into study of more mechanical phenomena or physics and chemistry. Considering that Comte clearly states that zoology and botany are not divisions of the abstract study of organic nature, being more like concrete applications of the study of organisms for two actual species of organisms, one might protest that astronomy is also just application of the same physical laws into stellar objects. Indeed, this is even more evident nowadays, when we know that chemistry could also be used to describe elements of the stellar objects.
Comte’s division of the study of organisms is also problematic. He suggests dividing this whole into a study of individual organisms or physiology and a study of interactions of organisms or sociology. One has to wonder if this is just a circumspect way to distinguish study of humans from study of plants and animals, trying to avoid the same criticism that Comte himself leveled against distinguishing zoology and botany, or if he truly will accept study of all populations of organisms as application of sociology. Even if the latter would be true, it is still doubtful whether we really can meaningfully separate study of an individual organism from study of the interactions of organisms in the same species.
There’s one very conspicuous absence in Comte’s classification - mathematics. This is simply because mathematics plays a very special role for Comte. In a sense it is a part of the classification, the most abstract science there is. In another sense it is for Comte a general methodology for all concrete sciences. Because of this role, mathematics is tightly linked to things it is used for, although it also has a part that is pure of all applications - but this is a discussion I’ll be entering later.
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