In the previous post of this series, I explained that there is no super categories of absolutely everything that exists. The highest categories include such things as quantities, relations, substances, etc. However, I did not give any information on how to properly divide a category. All categories are properly divided by taking the right kind of attribute outside of the category, and dividing the category by how that attribute belongs to the category.
All attributes can be placed on a continuum between belonging completely and not at all. Some attributes only have two places on that continuum. For example, being a number is an attribute with only two places. Something is either a number or it is not. There is no third option. Other attributes have other options, but only have a finite number of them. The attribute of being having parts can be such an attribute. A object can have a finite number of parts. Finally, many attributes have no clear number attached to how much is there. Being white (degree of whiteness) is such an attribute. Some people are whiter than others, but there is no way to attach a number to their color that is not arbitrary.
We take such an attribute and divide the category by that attribute. How the category is divided by that attribute will depend on how the attribute can be divided. If the attribute has a finite number of options in the way it can be applied, then there are a finite number of categories generated. Otherwise, there are an infinite number of categories.
We cannot divide any category by any attribute whatsoever though. If we were to consider the category of substances, there are many possible attributes that substances have. Color, rationality, size, and composition are among these attributes. There are two rules. You cannot divide a category if the application of an attribute to that category is nonsensical. For example, middle sized objects are colored. Other objects are not colored, nor could they be. The division of a category must reflect a division in reality. This is the second rule. If we divide substances into categories, then the division we make will reflect the most fundamental level of explanation of those same substances. All further divisions of those categories will depend on the previous divisions. The first rule is really a special case of the second rule.
This second rule needs an example. Consider the case of substances. Substances can be divided into two categories. Material substances and immaterial substances. This reflects a fundamental division because material substances are capable of substantial change while immaterial substances are not. All further division of material substances depends on this division as well. Some material substances can be divided by size, color, weight, substantial causal passivity, etc. Yet none of these attributes apply to immaterial substances. By investigating the nature of material and immaterial substances further, and describing them in their various categories, we can better understand how materiality is the most fundamental division we could use to describe them.