Nothing belong as a Universal is a Substance
Aristotle's conception of reality becomes less Platonic from the Categories to the Metaphysics.
Nominalism about Universals
In the Categories, general objects exist. Man exists in addition to the individual men. Man is a general object. Man, however, is not a primary substance. It is a secondary substance.
"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 this (φανερὸν ὅτι οὐδὲν τῶν καθόλου ὑπαρχόντων οὐσία ἐστί, καὶ ὅτι οὐδὲν σημαίνει τῶν κοινῇ κατηγορουμένων τόδε τι)" (Metaphysics VII.1038b).
"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 (Metaphysics VII.16.1040b27-30). In the Metaphysics, Aristotle's conception of reality becomes even less Platonic. In the Categories general objects exist but are not primary substances. In the Metaphysics, general others are nothing at all. Natural bodies fall into kinds. Socrates is a man, but man does not exist.
Aristotle, in this way, becomes 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, but it does not refer to an object. Man does not exist.
A New Solution to an Old Problem
"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 (ἀεὶ ῥεόντων), and that there is no knowledge 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 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, as they are always changing (ἀεί γε μεταβαλλόντων). These entities he called Ideas (ἰδέας), and held that all sensible things are named after them and in virtue of their relation to them; for the plurality of things which bear the same name as the forms exist by participation in them" (Metaphysics I.6.987a).
"For things that are seen to be induced in specifically different materials, as, e.g., a circle is in bronze and stone and wood, it seems clear that neither the bronze and the stone belong at all to the substance of the circle, because it is separate (χωρίζεσθαι) from them. As for things which are not seen separated, there is no reason why the same should not apply to them; e.g., if all the circles that had ever been seen were bronze; for the bronze would be none the less no part of the form, but it is difficult to separate it in thought For example, the form of man is always manifested in flesh and bones and parts of this kind; then are these actually parts of the form and account, or are they not so, but matter, though since the form is not induced in other materials, we cannot separate it? Now since this seems to be possible, but it is not clear when, some thinkers are doubtful even in the case of the circle and the triangle, considering that it is not proper to define them by lines and the continuous, but that all these are to the circle or triangle as flesh or bone is to man, and bronze or stone to the statue; and they reduce everything to numbers" (Metaphysics VII.11.1036a31). Plato, as Aristotle understands him, thought that the things Socrates asked about existed separately from the sensible objects. Just why Plato thought this is not completely clear, but Aristotle seems to say that Plato thought that for there to be universal and necessary truths (for example, that all men are rational animals), there must be unchanging general objects. Further, because nothing unchanging exists among the sensible objects, Plato "gave [these objects] a separate existence."
"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 (ἀεὶ ῥεόντων); so that if there is to be any knowledge..., 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, and was the first to seek a general definition of these. ... and he naturally inquired into the essence of things (τὸ τί ἐστιν); 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 [Plato and the Platonists] gave them a separate existence, and to these universals and definitions of existing things they gave the name of Ideas (ἰδέας)" (Metaphysics XIII.4.1078b).
Aristotle, in the Metaphysics, thinks that natural bodies have forms but that these forms are particular objects. These forms are the organizations of the material into objects of the natural kind. These organizations are the starting-points for change in the natural bodies, but these organizations themselves do not change. Further, these organizations are such that natural bodies of a given kind are organized in the same general way. Human beings, for example, are all rational animals.
These forms are unchanging because although they are in matter, they have no material parts. The form of a human being always exists in flesh and blood, but flesh and blood is not part of what the form is. The form is in matter and separate in account. This, for Aristotle, is separateness enough for there to be universal and necessary truths and hence for the possibility of knowledge.
"[W]e have shown that the material parts of a thing cannot be present in the account of the substance (since they are not parts of that substance, but of the composite substance; and of this in one way there is an account, and in another there is not. There is no account involving the matter, for this is indefinite; but there is an account in accordance with the primary substance, e.g., in the case of a man, the account of the soul; because the substance is the form within, of which and of the matter the composite substance is said to be" (Metaphysics VII.11.1037a24).
Perseus Digital Library:
Henry George Liddell, Robert Scott, A Greek-English Lexicon:
καθόλου (= καθ᾽ ὅλου), katholou, adverb, "on the whole, in general,"
τι, ti, indefinite prounoun, (τόδε τι = "a this," "some this," "a something"),
τόδε, tode, demonstrative pronoun, "this,"
χωριστός, chōristos, adjective, "separable"
"Traditionally it has been assumed that forms are universal. But it is of the very nature of ultimate subjects that they cannot be predicated and, hence, cannot be universal. Therefore, if substantial forms are the ultimate subjects, they must be particular. A moment's reflection, though, shows that this is a view that Aristotle is committed to anyway. For in [Metaphysics] Z 13 he argues at length that no universal can be a substance. But since he also wants forms to be substances, he has to deny that forms are universal. And, in fact, we do find him claiming that the form of a particular object is peculiar to that object, just as its matter is; Socrates' form, i.e., his soul, is different from Plato's form, i.e., Plato's soul (Met. Δ 1, 1071a 24-29)" (Michael Frede, "Substance in Aristotle's Metaphysics," 77. Essays in Ancient Philosophy, Michael Frede (University of Minnesota Press, 1987), 72-80).
"We even find Aristotle claiming that the form is a particular this (a tode ti [= a τόδε τι]; 8, 1017b 25; H I, 1042a 29; Δ 7, 1049a 28-29; De gen. et corr. 318 b 32). And, of course, he has to claim that a form is a particular this, if he wants forms to be substances, since he assumes that a substance has to be a particular this. It was for this reason that Aristotle rejected the claim of matter to be substance [(Metaphysics VII.3.1029a)]; matter is only potentially a particular this" (Michael Frede, "Substance in Aristotle's Metaphysics," 77. Essays in Ancient Philosophy, Michael Frede (University of Minnesota Press, 1987), 72-80).
"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. Essays in Ancient Philosophy, Michael Frede (University of Minnesota Press, 1987), 72-80).