I find that in discussions of the Categories there tends to be a lack of clarity about what Aristotle means by a primary substance. I shall therefore draw a distinction and then, by way of illustration, give a few texts in which this distinction seems to be fudged. I shall refer to the distinction as that between 'commonsense' and 'theoretical' primary substance.
A commonsense primary substance is what we would call a 'thing'. It is a particular to which we might give a proper name. E.g. this particular horse ('Secretariat') or this particular human ('Socrates').It makes sense that, on Aristotelian terms, there should be such entities as theoretical primary substances. After all, the category of substance is distinct from that of quality, quantity, relation, and so on. Therefore, the entity which is a substance would be distinct from the entities which are qualities, quantities, relations, and so on, inhering in that substance. The substance, then, would presumably be something that existed distinct from these other things.
A theoretical primary substance is a notion we arrive at by beginning with a commonsense primary substance, but then conceiving of it (somehow) in abstraction from any of the accidents that might belong to it. E.g. this instance of horse nature; this instance of human nature.
Of course, one might wonder how there can be an instance of human nature which was not, however, determined yet in accordance with the other categories.
Now which of these does Aristotle mean when he talks of 'primary substances' in the Categories? The language he uses is indeterminate as between them. ho tis anthropos can mean either "The particular human" (in the ordinary sense of the term) or "The instance, man" (in the theoretical sense).
Now, as I said, I find unclarity when scholars refer to the primary substances of the Categories. Dan Devereux, for instance, refers to them as 'concrete particulars' and says such things as the following:
Although the species 'horse' has two substance-making features while the individual horse has only one, the individual horse (and not the species) is a primary substance because it is more of an underlying subject (162).It looks as though by 'individual horse' he means a commonsense thing, such as Secretariat; and yet his language, I suppose, could be taken in the other way (although, admittedly, 'concrete particular' definitely suggests the commonsense notion).
S. Marc Cohen seems to go back and forth between both notions in his SEP article on Aristotle's Metaphysics. When he says:
The concepts of matter and form, as we noted, are absent from the Categories. Individual substances — this man or that horse — apart from their accidental characteristics — the qualities, etc., that inhere in them — are viewed in that work as essentially simple, unanalyzable atoms. Although there is metaphysical structure to the fact that, e.g., this horse is white (a certain quality inheres in a certain substance), the fact that this is a horse is a kind of brute fact, devoid of metaphysical structure.He seems to be understanding primary substances as theoretical. And yet when he says, in the same article:
At the top (or trunk) of the tree are the most generic items in that category (e.g., in the case of the category of substance, the genus plant and the genus animal); branching below them are universals at the next highest level, and branching below these are found lower levels of universals, and so on, down to the lowest level universals (e.g., such infimae species as man and horse); at the lowest level — the leaves of the tree — are found the individual substances, e.g., this man, that horse, etc.He seems to be understanding them as commonsensical. Surely 'this man' is something like Socrates, and 'this horse' is something like Secretariat.
Which is Aristotle's notion? This much, at least, is clear: if Aristotle's notion is of a 'theoretical' substance, then it would be natural for him to speak of 'the substance of' a thing (as he does, without explanation, in the Metaphysics)--because the substance of Secretariat would be the horse nature that Secretariat has; the substance of Socrates would be the human nature that Socrates has; etc.
I believe the most common view is that by 'primary substances' in the Categories Aristotle means the commonsensical sort. But that view has a big problem--doesn't it?--namely that a commonsensical substance is not only a substance: it has lots of accidents thrown in with it.