Humans know things. Matter, however, is not a thing but is a potential thing. Inasmuch as something is material, then, it contains within itself a certain degree of unintelligibility. Conversely, inasmuch as matter is actually determined to one thing, meaning inasmuch as we are speaking of something which actually is (on account of form), we are speaking of an intelligible object, an object of knowledge.
From this, we can divide human knowledge of the material world according to two criteria: the degree to which the objects of our knowledge can exist apart from matter and the degree to which the objects of our knowledge can be understood apart from matter. Here is Maritain's division:
The first degree: That which can neither exist nor be understood apart from matter. The science of these things is most properly called 'physics,' for it pertains to things which have matter within their definition. Remember in our previous post on man, animal is part of the definition. This science, then, is concerned with sensible nature.
The second degree: That which cannot exist apart from matter but can be understood apart from matter. When we abstract material quality from natural substances, we are left with quantity, and when we begin to treat of quantity as such we are engaged in the science of mathematics. We understand material substances inasmuch as they are the subject of quantity and then understand quantity as if it were a 'thing' in its own right, which it is not.
The third degree: That which can exist and be understood apart from matter. The proper object of this science is being as being, in other words, not being as it exists in material substances or being necessarily limited to the objects of our sensible experience. This science is called metaphysics and it treats of that which is most immaterial.