Which are the main interpretations of Aristotle's conception of nonsubstantial particulars?
There are two main interpretive contenders : a "received view" that interprets nonsubstantial particulars as individuals, i.e. as numerically distinct, non-recurring, though qualitatively identical, particular qualities, and an alternative interpretation which takes Aristotle as giving an account of nonsubstantial particulars as determinate but recurring qualities, that is some most fully determinate universals.
Introduction of terminology
In the Categories (1a20-1b9), Aristotle offers a system of classification for the things there are, that is the fundamental ontological categories, based on two fundamental relations, the SAID OF and the IN relations.
The first is understood as predication, that is if x is said of y, then x is a general term applied as a predicate to a particular entity y. But y is not necessarily a particular if it is to be a subject for something that is said of it. Namely, y itself can be said of a z. For example, color is said of red and, at the same time, red is said of a particular shade of red, say crimson. This means that the "said of " relation has the role of distinguishing general from particular in a relative way: red is particular with respect to color, but universal with respect to crimson. The same applies of course in the case of substantial entities, animal is said of man, while man is said of Socrates, and Socrates is not said of anything.
The second relation is that of inherence. It is meant to create a division line between substances and non-substances. If there is a y such that x inheres in y, then y is a substance. Inherence has to be understood as possession of an accidental property by a substance. For example, my hair being blond is an accident, while my subsumption under the predicate man is not so.
Predication and ...