I don't want to harp on this point, but I was thinking again about S. Marc Cohen's claim about primary substances in connection with that passage from the Categories that I just posted on.
Remember that Cohen 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. This horse is a primary substance, and horse, the species to which it belongs, is a secondary substance. But there is no predicative complex corresponding to the fact that this is a horse in the way that there is such a complex corresponding to the fact that this horse is white.We saw that Aristotle does regard primary substances as analysable in the Categories: he is willing to analyse living things, at least, into a soul substance and a body substance (and perhaps some general form-matter distinction, as well, is either implicit or incipient).
But look again at the passage just quoted from the Categories and observe, additionally, that when Aristotle there calls a primary substance an 'atom', what he means is not that it admits of no analysis, but rather that what is referred to is not found in more than one location, 'divided' into different instances: "the thing revealed is individual (a1tomon) and numerically one."
To understand this, consider how, in contrast, something like water is divided into distinct ponds, lakes, streams, oceans, etc. The term of the mass noun, 'water', signifies a divided substance. But 'this water', mentioning a pond, signifies an undivided instance, an 'atom' of water.