"It seems that separateness and a this belong most of all to substance
(τὸ χωριστὸν καὶ τὸ τόδε τι ὑπάρχειν δοκεῖ μάλιστα τῇ οὐσίᾳ)"
"It is evident that nothing belonging as a universal is a
substance, as nothing predicated in common signifies a
(φανερὸν ὅτι οὐδὲν τῶν καθόλου ὑπαρχόντων οὐσία ἐστί, καὶ ὅτι οὐδὲν σημαίνει τῶν κοινῇ κατηγορουμένων τόδε τι)"
The Development of Aristotle's Thought
In the Categories, general objects exist. In addition to individual men, man exists. Man is a general object. Man, however, is a secondary substance, not a primary substance. General objects exist, but they are substances only with qualification. Aristotle, in this way, takes a significant step away from the ontology Plato presents in the Timaeus.
In the Metaphysics, Aristotle takes a much more significant step away from Platonism. In the Metaphysics, general objects do not exist. Man and other such general objects are not only not secondary substances, they are not part of reality. Natural bodies fall into kinds. Socrates is a man, but the natural kind man itself does not exist.
In this way, Aristotle has become a nominalist about universals. What is said in predicating the term 'man' is general. The term is said of all the particulars, but only particulars exist. The term 'man' is significant. It is meaningful and can be used to express truths, but man does not refer to anything. There is no object that is the reference of the term 'man.'
"It is a basic nontrivial fact about the world that things come with forms that are exactly alike, and not just sufficiently similar to class them together in one kind. The reality of kinds amounts to no more than this: that the specification of the form of particular objects turns out to be exactly the same for a variety of objects. But for this to be true, there is no need for a universal form or a universal kind, either a species or a genus. And, in fact, the import of [Metaphysics] Z 13 seems to be that there are no substantial genera or species in the ontology of the Metaphysics" (Michael Frede, "Substance in Aristotle's Metaphysics," 78).
Aristotle's New Solution to an Old Problem
"Those who speak of the forms in one way speak rightly that they are separate, if they are substances, but in another way wrongly, in that they say the form is one over many (οἱ τὰ εἴδη λέγοντες τῇ μὲν ὀρθῶς λέγουσι χωρίζοντες αὐτά, εἴπερ οὐσίαι εἰσί, τῇ δ᾽ οὐκ ὀρθῶς, ὅτι τὸ ἓν ἐπὶ πολλῶν εἶδος λέγουσιν)" (Metaphysics VII.16.1040b27-30).
For Aristotle, in his mature thought in the Metaphysics, general truths do not require the forms of natural bodies to be separate from matter.
It might seem that if general truths about the natural bodies (for example, that all men are rational animals) were not ground in forms that existed separately from matter, there would only be the various subjective and different viewpoints of human beings. This idea seems to be part of what motivated Plato in his Theory of Forms. For Aristotle, however, at least in the Metaphysics, the separateness in account that belongs to the forms of natural bodies is enough to make what it is to be the species of a given natural body is a possible object of knowledge.
"The philosophies described above were succeeded by the system of Plato, which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians. In his youth Plato first became acquainted with Cratylus and the Heraclitean doctrines--that the whole sensible world is always in a state of flux, and that there is no knowledge (ἐπιστήμης) of it--and in after years he still held these opinions. And when Socrates, disregarding the physical universe (τῆς ὅλης φύσεως) and confining his study to ethical (ἠθικὰ) questions, sought in this sphere for the universal (καθόλου) and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing. These entities he called Ideas (ἰδέας), and held that all sensible things are named after them sensible and in virtue of their r elation to them; for the plurality of things which bear the same name as the Forms exist by participation in them" (Metaphysics I.6.987a-b).
"The theory of forms (εἰδῶν) occurred to those who enunciated it because they were convinced as to the true nature of reality by the doctrine of Heraclitus, that all sensible things are always in a state of flux; so that if there is to be any knowledge (ἐπιστήμη) or thought (φρόνησις) about anything, there must be certain other entities, besides sensible ones, which persist. For there can be no knowledge of that which is in flux. Now Socrates devoted his attention to the virtues of character (ἠθικὰς ἀρετὰς), and was the first to seek a general definition of these. ... and he naturally inquired into the essence of things; for he was trying to reason logically, and the starting-point of all logical reasoning is the essence. ... But whereas Socrates regarded neither universals nor definitions as existing in separation (χωριστὰ), they gave them a separate existence, and to these universals and definitions of existing things they gave the name of Ideas" (Metaphysics XIII.4.1078b).