Another reason that some scholars have thought that Aristotle needs something like prime matter is to serve as a so-called “principle of individuation”. While the predominant view has been that this role is reserved for matter, other scholars have maintained either that Aristotle means it to be form, or that he does not see the need for a principle of individuation at all. Some of this controversy seems to have resulted from a failure to be clear about what a principle of individuation is, or what problem it is supposed to solve.
To see why this is so, one may focus on a controversy about individuation which Popper sought to dissolve, by pointing out that it derived from a false opposition. This was a controversy begotten by a disagreement between Anscombe and Lukasiewicz regarding the principle of individuation in Aristotle (see Anscombe et al. 1953). Popper points out that their disagreement is only apparent, due to the fact that they are answering different questions: Lukasiewicz insists that form should be counted as the “source of individuality” because it explains how a thing with many parts is a single individual and not a plurality, it accounts for the unity of individuals. He has in mind questions like “How do all these bricks constitute a single house?” or “What makes this collection of flesh and bones Socrates?”, and here Aristotle does indeed appear to make use of form. On the other hand, Anscombe says that it is matter which makes an individual the individual it is, numerically distinct from other individuals of the same (and other) species. Yet this is an issue about numerical distinctness rather than unity. It is perfectly consistent to say that Socrates is one man because of his form, which unifies his matter into a single whole, and he is a numerically distinct individual from Callias because his matter is numerically distinct from Callias’ matter.
It has become conventional to call an answer to Lukasiewicz’s problem a principle of unity, and an answer to Anscombe’s problem a principle of individuation. The traditional view has been that individuation is a metaphysical issue: what is it that makes one individual different from another (of the same kind)? However, some scholars have argued that Aristotle at no point addresses this issue, but is instead concerned with the epistemological question of how we tell one individual from another (see Charlton 1972).
It is worth considering why one might think that the metaphysical issue is not worth pursuing. The obvious reason is if one thought that there was no answer to the question “what makes this individual numerically distinct from that one?”—that nothing makes them distinct, they just are. An advocate of this view might point out that even if we accept that matter is what makes this individual distinct from that one, we still have no answer to the question “what makes this portion of matter numerically distinct from that one?”. There will always be certain of these numerical distinctness facts that remain unexplained on any theory. But if explanation has to stop somewhere, why not stop at the beginning? Why not just say that it is a bare fact that Socrates is numerically distinct from Callias, and leave matter out of it?
One might think that one could respond to this argument by insisting that there is an answer to the question what makes Socrates’ matter numerically distinct from Callias’ matter: it is the matter itself. If matter can explain the distinctness of individual substances, why should it not also explain its own distinctness from other matter? Whether or not this move is legitimate will depend on which facts are and which facts are not in need of explanation but may correctly be assumed to be primitive. The problem is that “this matter is distinct from that matter because it is this matter” seems to be a very similar sort of explanation to “Socrates is distinct from Callias because he is Socrates”—both are cases of x explaining its own distinctness from y. Either both should count as adequate explanations or neither should. But the advocate of matter as principle of individuation adopted this view precisely because she found this sort of explanation unsatisfactory, or not an explanation at all. Therefore this response does not seem to be open to her.
It seems that those who are committed to there being something which accounts for the numerical distinctness of individuals must say that there is nothing that accounts for the numerical distinctness of the distinctness-makers. The only alternative would be to introduce some further thing to account for their distinctness, and so on; but this results in an infinite regress, which, as well as being ontologically bloated, appears to be vicious, since we can never grasp the full account of what makes Socrates and Callias distinct. Both sides agree that explanation must stop somewhere, but they differ over where it is appropriate to stop: is it a basic, inexplicable fact that Socrates is numerically distinct from Callias, or that their matter is distinct? (See Markosian 2008, §8, for a contemporary discussion of this question.) At any rate, even if it is difficult to prove that there is an important metaphysical question here, the traditional interpretation of Aristotle is that he thinks there is.
There are two main texts which have been thought to show Aristotle advancing the view that matter is the principle of individuation: Metaphysics v 6, 1016b31–2, and vii 8, 1034a5–8. In the first of these, we are told:

اقتباس :

Moreover, some things are one in number, some in form, some in genus, some by analogy; in number those whose matter is one…

According to the traditional interpretation, here we have the claim that x and y are numerically identical (or “one in number”) if, and only if, they have the same matter (or the matter of x is “one” with the matter of y). An alternative reading takes this passage to be about unity rather than individuation: Aristotle would be saying that x is numerically one if and only if x’s matter is one, where a thing’s matter being “one” means that it is one continuous piece (of bone, for example).
The second important passage for detecting Aristotle’s views about individuation comes at vii 8, 1034a5–8:

اقتباس :

And when we have the whole, a form of such a kind in this flesh and in these bones, this is Callias or Socrates; and they are different in virtue of their matter (for that is different), but the same in form, for their form is indivisible.

According to the traditional interpretation, these lines are saying that Socrates and Callias are numerically distinct because of their matter, not their form, and on the face of it this is the clearest example of Aristotle affirming that matter is the principle of individuation. We can adopt an alternative reading, however, if we suppose that “different” means not numerically distinct, but qualitatively different. In that case, the passage could be making an epistemological claim about how we discern Socrates and Callias: suppose Callias is pale and Socrates dark; they are different, but not different in form; they differ because of their matter, since pallor and darkness primarily qualify their skin, i.e., part of their body.
There is a difficulty for the idea that matter can act as the principle of individuation, which arises out of the following problem that can be raised for Aristotle’s hylomorphism (see Fine 1994). It seems that two substances, e.g., Socrates and Callias, may have numerically the same matter at different times; that it is possible (however unlikely) for all and only the particular elements that now compose Socrates to end up composing Callias at some later date. In such a case, Socrates and Callias would have the same matter, albeit at different times. Moreover, both being human beings, they would have the same form. But they themselves are compounds of matter and form, so if their matter and form are numerically the same, they must themselves be numerically the same.
Put schematically, the argument looks like this:

1. It is possible that Socrates and Callias be composed of numerically the same matter (albeit at different times).
   
   
2. Socrates and Callias have the same form.
   
   
3. Socrates and Callias are compounds of matter and form.
   
   
4. Therefore, it is possible that Socrates and Callias are numerically the same.
   
   

Of course two different people cannot be numerically the same. So, if the argument is valid, at least one of its premises must be false.
One possible rejoinder to this argument is that it turns on an equivocation in the meaning of “matter”. As we have seen, for Aristotle matter comes in different levels. In the situation envisaged Socrates and Callias would have the same remote or low-level matter (the same elements) but they might still have different proximate matter, since the proximate matter of a human being is his body. Since a substance is a compound of a substantial form and someproximate matter, we are not entitled to conclude that Socrates and Callias are the same. Although this may be an effective way of dealing with the initial problem, it can be restated so as to avoid this objection that the argument equivocates on “matter”. Each level of matter is a compound of the matter at the level immediately below it and a form. If the proximate matter of two things is to be different, despite their lower-level matter being the same, the reason must be that the forms of the proximate matters are different. We can redescribe the situation so that not only are Socrates’ and Callias’ forms the same, but the forms of their bodies are also the same, and the forms of the matter of their bodies, and so on all the way down. Although it is unclear what in general is required for the matter of two things of the same form to have the same form, e.g., for Socrates’ and Callias’ bodies to have the same form, it seems reasonable to suppose that it is sufficient for two things to have the same form that they be qualitatively the same. So we can ensure that Socrates’ and Callias’ matters have the same form, if we suppose that they are qualitatively the same. One might insist that no two things are qualitatively the same, but there is little reason to think that Aristotle is committed to Leibniz’s doctrine of the identity of indiscernibles. What is more, although strict qualitative identity, i.e., having all the same non-relational and relational properties, may require demanding metaphysical assumptions such as an eternally cyclic universe, probably all that is required is that there be no relevant qualitative difference between Socrates and Callias, where “relevant” means such as to result in them or their matter having different forms. While one might insist that two things must be qualitatively the same to have the same form, this also does not seem to be Aristotle’s view. So if we tailor our example to this requirement, we can thwart the charge of equivocation. The argument then is valid, so we must choose one of its premises to reject.
One might try to reject the first premise of the argument, on the grounds that a person’s matter is essential to them. We have seen that Aristotle plausibly does believe this about a person’sproximate matter—their body—since a dead body is only homonymously a “body”. Nevertheless, he is committed to their more remote matter—the elements that make them up, for instance—being capable of existing independently of them. He needs there to be something to underlie the change whereby a substance comes into or goes out of existence, to make it consistent with his account of change in general in Physics i 7. There seems to be no reason to deny that, when a tree, for instance, dies, the earth, air, fire and water that constituted it still exist in the dead stump. But, if so, there seems no reason to think they could not leave the stump, and end up becoming the matter of some new tree. This is all that is needed for the problem to arise. Prime matter, if it exists, will not help: if the elements are allowed to escape the substances that they underlie, it seems that the prime matter that underlies them should also be capable of doing so. It is supposed to be capable of underlying anything; so insisting that it is confined to being the prime matter of a particular sort of thing makes no sense.
A more promising option is to reject the second premise of the argument, that co-specific or relevantly similar things like Socrates and Callias must have a common form. This one might reject if one were a believer in particular forms. The question of whether Aristotle’s forms are particular or universal has garnered a huge amount of scholarly attention (those in favour of particular forms include Sellars 1957, Frede 1978, and Irwin 1988; those in favour of universal forms include Albritton 1957, Lewis 1991, and Loux 1991). If Aristotle believed in universal forms, he could have constructed particular forms out of some kind of indexed version of the universal (e.g., an ordered pair of the universal form and the thing which had it); but that would make the identity of the particular form dependent on that of the substance that had it. Since it is the substance’s form which is acting as principle of individuation, if the common form premise is rejected, particular forms cannot be individuated by the substances that have them, on pain of circularity: what makes Socrates different from Callias is that they have different forms; and what makes their forms different is that one belongs to Socrates, the other to Callias. To play this role, particular forms would have to be defined independently of the things that have them. It would be a particular form which combines with a thing’s matter to make it the thing that it is. Some scholars find this conception of particular forms problematic.
A final reaction to the argument would be to reject the third premise, the idea that anything enmattered is a compound of its matter and form at a given time. Certainly the most straightforward way of understanding hylomorphism is that the compound is compounded of the thing’s matter and form at a particular time, and the relation between the compound and the thing is identity. This way of understanding composition is not only problematic because it leads to the problem currently under discussion: assuming that things can change their matter, we might well also wonder (a) how just one of the matters, which it has at a particular time, can yield the whole thing, and (b) how different matters at different times can yield the same thing. An alternative way to understand compounding would be to say that a thing is the compound of its form and all the various matters that it has at different times: [ltr]X=F(m[size=13]1,m2,…mn)X=F(m1,m2,…mn)[/ltr], where [ltr]m1…mnm1…mn[/ltr] are [ltr]XX[/ltr]’s proximate matters in order of temporal occurrence. This would solve worries (a) and (b) above, since now all the different matter-slices are incorporated into the one object. It does not obviously help with the problem at hand, however, since, if it is possible for Socrates and Callias to have the same matter at a time, there seems to be no barrier to them having exactly the same sequence of matter-slices throughout their lives (provided that they are not born at the same time, and live to exactly the same age).[/size]
Finally, one could relativize the concept of a compound to a time: enmattered objects are absolutely identical to compounds, but a compound is not absolutely a compound of matter and form, but only relative to a particular time. [ltr]X=F[size=13]t(m)X=Ft(m)[/ltr], where m is the proximate matter of X att; or, combining this idea with the previous one, [ltr]X=Ft(m1…mn)X=Ft(m1…mn)[/ltr], where t is the period of time for which X exists, and [ltr]m1…mnm1…mn[/ltr] are its matters in order of occurrence. This solution does deal with the problem directly, since Socrates and Callias can have the same form and matter, and yet be different compounds because the times are different. There may also be a modal version of the puzzle: Socrates is such that his matter and form could be identical with those of Callias at a certain time. This puzzle might be solved by also relativizing compounds to worlds.[/size]
There is an exegetical problem with ascribing this final way of understanding composition to Aristotle, and that is that it apparently conflicts with the view that he expresses in Metaphysicsviii 6, 1045a7–10, and vii 17, 1041a26, that a form is what unifies a compound. The problem is how to understand the role of the time in the unification of the compound by the form: it cannot be just another element to be unified, for the time at which the matter exists does not figure as a part of the resulting unity. If we try to make the form unify a given portion of matter into many different things, depending on what time the unifying takes place at, we also run into the difficulty that such a process no longer seems worthy of the title “unification”, since the result is many objects, not just one. Indeed we can reformulate the problem without mentioning composition at all: if a common form must unify common matter into one and the same thing, and Socrates and Callias have the same form and the same matter, they are one and the same. Since Aristotle (and many neo-Aristotelians) would surely be unwilling to give up the unifying role of form, this does not look like a viable solution.
We have seen that there are some textual reasons to think Aristotle makes matter his principle of individuation; but in fact particular forms are better suited to play this role. We need to distinguish between two different questions, one about unification, the other about individuation: (i) what makes this giraffe (or this giraffe-matter) one and the same giraffe (over time)? (ii) what makes this giraffe distinct from that one? The first question seems to be the one which Aristotle addresses in Metaphysics vii 17, and does not obviously require an answer that is unique to the giraffe in question. Giraffeness in general may well suffice. The answer to the second question, however, cannot be the universal species, since it is common to both giraffes, nor can it be their matter, since they could (albeit improbably) be composed of the numerically same stuff at different times. It is not so obvious that Aristotle sees the need to address the second question, but, if his forms are particular, not universal, he is in a good position to do so.