There is something interesting about Aristotle’s primary substances — they can never predicate to anything else. Secondary substances, on the other hand, can. What Aristotle did not notice however is that there is a substance which cannot be predicated to. There is no name for it. I will call it the ultimate substance.
The name is not very intuitive because the term “substance” is a misnomer. This is especially true of secondary substances, which are descriptions of qualities, and in that sense do not have substance as such. Primary and ultimate substance are real objects or are composed of real objects. Primary substances are the individual particulars. Ultimate substance is the complete set of particulars.