I have shown that knowledge of substance as substance is the highest form of knowledge that we can have. But we have knowledge of many subjects. Science, history and construction are all forms of knowledge. So the next subject to be discussed is how to divide knowledge.
Let’s call a subject of knowledge a science. In this understanding of science, natural science is one form of science and construction science is another form. Science is just the systematic knowledge of a particular thing. Since knowledge is unified by the subject being discussed, each science is unified by the a single subject.
Some sciences belong to other sciences because one science is a species of a thing while the other science is a genus. For example, the science of mammals belongs to the science of animals because mammal is a species of animal. This applies in general to all sciences. Construction work requires an understanding of excavation. So the science of excavation belongs to the science of construction work.
The real question is how many ultimate sciences there are. The science of substance is an ultimate science because substance has no genus that it belongs to. It is an ultimate genus itself. But although it is the highest genus, there is no reason to believe that it is the only ultimate genus. We already know that qualities and quantities are also ultimate genus as well. We also need to consider how to determine how many ultimate genus there are.
The first way to divide knowledge is by purpose. Construction work is always an action that produces a thing. It makes buildings or furniture. The science of construction work is tied up with actually making things. The science of dentistry is different. It may make something, but it does not have to do so. The science of dentistry is tied with a particular kind of action. If dentists do not actually fix teeth then they are not using the science of dentistry. Finally, the science of history is tied with knowledge. No particular actions or productions are necessary. So it seems that sciences can be divided into three categories: productive, active and theoretical. A productive science is a science that has the purpose of making something. An active science is a science that has the purpose of carrying out a particular kind of action. A theoretical science is a science that has the purpose of understanding a particular subject.
The reason why we should divide sciences by purpose is that it is the highest of the causes. If we are attempting to understand a science then we must understand it according to the highest cause of that science. Why does that science exist at all? The answer to that question is always one of purpose. Therefore, the purpose of a science will determine how that science is classified.