## 1. Matter and form introduced



Aristotle introduces his notions of matter and form in the first book
of his *Physics*, his work on natural science. Natural science
is concerned with things that change, and Aristotle divides changes
into two main types: there are accidental changes, which involve
concrete particulars, or "substances" (*ousiai*) in
Aristotle's terminology, gaining or losing a property (see
*Categories* 1-5, *Physics* i 7). For instance,
the changes whereby Socrates falls in a vat of dye and turns blue, or
puts on a few pounds from excessive feasting during the Panathenaia,
count as accidental changes (in the categories of quality and
quantity, respectively). Socrates, a substance, gains the property of
being blue, or the property of weighing twelve stone. The other main
kind of change is substantial change, whereby a substance comes into,
or passes out of, existence. For example, when Socrates dies, or is
born (or perhaps conceived, or somewhere in between conception and
birth), a substantial change has taken place.



Matter and form are required to account for this second kind of
change, if it is to conform to Aristotle's general conceptual
analysis of change. In any change, he contends, there must be three
things: (1) something which underlies and persists through the change;
(2) a "lack", which is one of a pair of opposites, the
other of which is (3) a form acquired during the course of the change
(*Physics* i 7, 190a13-191a22). Thus, for example, in an
accidental change, the underlying thing is the substance which
acquires a new accidental property. For instance, when Socrates learns
to play the flute, he transitions from a state of being unmusical (the
lack) to a state of musicality (the form). But for us to be able to
say that there is something which has changed, there must be something
which remains the same throughout the change, and in this case the
obvious candidate is Socrates, who is one and the same person
throughout his musical training.



In accidental changes there is always a substance to underlie the
change, but this is not true for substantial changes, since these
involve the coming to be or passing away of a substance (see the
amusing remark of Irving Copi, quoted at the start of the entry on
 identity over time). 
 In these cases, the thing that underlies is the matter of the
substance. When someone builds a house, it is the bricks which persist
through the change. They transition from a state of not being a house
to acquire the property of being a house. Aristotle often uses the
example of artefacts like houses, even though he does not regard them
as substances properly-speaking (*Metaphysics* vii 17,
1041b28-30), because their matter is more straightforward to
identify. Nevertheless, the same analysis holds in the case of
organisms, which are the substances proper: when an organism is
created or destroyed, when an acorn becomes an oak tree, or a human
dies, there must be some matter which persists through the change. To
say otherwise would be to say that things can come to be out of, or
vanish into, nothing, and Aristotle understandably agrees with his
predecessor Parmenides that this is impossible (*Physics* i 8,
191a23-b17). Aristotle's metaphysics takes as its starting
points observed phenomena, and seeks to preserve common sense beliefs
where possible. We never experience anything simply appearing or
disappearing at random.



The word "form" may misleadingly suggest that what is
acquired in a case of substantial generation is simply a shape, and
this impression is reinforced by some of the examples that Aristotle
uses, especially when focusing on artefacts: plausibly the form of a
bronze statue just is its shape. When we consider organisms, however,
it becomes apparent that having the right shape is not sufficient to
possess the form. A thing's form is its definition or
essence--what it is to be a human being, for example. A statue
may be human-shaped, but it is not a human, because it cannot perform
the functions characteristic of humans: thinking, perceiving, moving,
desiring, eating and growing, etc. The connection between a
thing's form and its function emerges in *Physics* ii 3,
where Aristotle distinguishes his four kinds of cause: material,
formal, efficient, and final, and suggests a special connection
between the formal and final cause.



Here one needs to proceed cautiously, however, since it is sometimes
said that Aristotle's word "cause" (*aitia*)
would be better translated as "explanation" (or
"explanatory factor", to avoid the implication that they
are linguistic items, as opposed to things-in-the-world). Certainly
modern philosophers tend to use "cause" in a narrower way,
which approximates to Aristotle's efficient cause.
Aristotle's idea is that there are four kinds of thing that need
to be mentioned in order to give a full account of the nature of an
object, each corresponding to a particular kind of question. We need
to know what the thing is made of, and the answer to this question is
the thing's matter--bricks, in the case of a house; bodily
organs in the case of a human being. Next we need to know what the
thing is, or how it is defined, and the answer to this is the
thing's form or essence. We also need to know what made the
thing come into existence, who or what created it, and this is the
thing's efficient or "moving" cause. Lastly, we need
to know what the thing is for, what its purpose or function
is--the final cause. Now Aristotle observes that, although these
are all distinct questions, in the case of the last three very often
the same thing will serve as the answer to all of them
(*Physics* ii 7, 198a24-27). A house is defined as a
shelter of a certain sort (*De Anima* i 1, 403b3-7;
*Metaphysics* viii 3, 1043a29-36). That is what a house
*is*, i.e., its formal cause, but it is also what a house is
*for*, its final cause, since houses, like all artefacts are
functionally defined. Similarly, a human being is defined as something
which lives a certain kind of rationally-directed life. But, on
Aristotle's view, this is also what a human being is for. The
human function is to live such a life (*Nicomachean Ethics* i
7, 1097b22-1098a20; cf. *De Anima* ii 1, 412a6-22).
As for the efficient cause, it is qualitatively, although not
numerically, identical with the formal cause, at least in the organism
case, since human beings give birth to human beings, and the same goes
for all other living things. Thus, even though Aristotle admits four
different kinds of cause, in a sense it is only really matter and form
that play any ineliminable explanatory role in his system.



In fact, Aristotle does not simply focus on the case of artefacts
because their pre-existing matter is *easier* to identify.
There is a particular issue here with the case of organisms, which
arises out of Aristotle's insistence that a human being, for
instance, is composed of a rational soul, which is the form, and an
organic body, which is the matter (for further discussion of this
problem, see Ackrill 1972/73). It is characteristic of the matter of
artefacts that numerically the same stuff which makes up one object
can later be used as the matter of another: for instance, when one
melts down a bronze statue, and then molds it into some jewelry, it is
the same bit of bronze throughout. It is crucial that a thing's
matter can survive such changes, if it is to play the role that
Aristotle needs it to play in cases of substantial generation and
destruction, as being the thing that underlies such changes. If an
artefact's matter only contingently has the form it has, the
same does not obviously seem true of organisms. Unlike in the case of
a house built from bricks, it does not seem as though one's body
predates one's existence, and so can serve as the underlying
thing in a case of substantial generation. One might think that at
least the body does exist after death, but in fact Aristotle would
disagree. Instead, he insists that a dead body is only
"homonymously" called a body--that it is only
described as "a body" by extension, because it
superficially resembles a living body (*De Anima* ii 1,
412b10-25; *Metaphysics* vii 10, 1035b9-25). It is
not a real body, because it is incapable of performing the functions
normally associated with bodies, just as a statue's eye, or an
eye in a painting, is not a real eye, because it is made of stone or
paint, and thus cannot serve the function that genuine eyes exist
for--seeing (for further discussion, see the supplement to the
entry on Aristotle's psychology on
 a fundamental problem about hylomorphism).



It might seem that Aristotle is rather going against ordinary
linguistic usage here, since we in fact regularly do refer to dead
bodies as "bodies". Whether a dead body is really a body
might seem like a trivial linguistic issue, which can simply be
decided by fiat. The obvious way to resolve the problem might seem to
be simply to drop the insistence that the body cannot exist without
being coupled to a living human soul. Allowing that a dead body
remains the same body as its living counterpart will not help the
difficulty of what to say about the matter that predates the coming to
be of the organism, when there is no apparent body, living or dead.
What is more, Aristotle is deeply committed to his position that the
human body is essentially ensouled, because of his view that things
are defined by their functions (*Meteorologica* iv 12,
390a10-15; *Generation of Animals* ii 1,734b24-31).
It seems as though he believes that a human being's matter must
be contingently alive, so that it can serve as the underlying thing
that remains when the human being comes into existence, but also that
it must be essentially alive, because it is functionally defined. If
so, he contradicts himself.



The best way to resolve this apparent contradiction in
Aristotle's hylomorphism is to point out that an organism can
have more than one level of matter. Aristotle believes that all
sensible substances can be analyzed into matter and form, but such an
analysis is not restricted to the things he calls substances. Matter
can itself be divided into matter and form: for instance, bricks are
made of clay, shaped into cuboid blocks. Again, clay has its own
matter--mud, say--and so on. Eventually, if one pursues this
hierarchy of matter far enough downwards, Aristotle believes that one
will reach the four elements, earth, air, fire and water. He agrees
with Empedocles that everything in the sub-lunar world is ultimately
made up of different ratios of these four elements. Matter then should
really be understood as a relative notion--it is always the
matter *of* something. Aristotle distinguishes between a
thing's proximate matter, the stuff it is most immediately made
of, and its less proximate matter, i.e., the matter of its matter, or
even further down the hierarchy, culminating in its ultimate matter,
the elements. The organic body which is a human being's
proximate matter is essentially alive, but this need not apply to all
of the other matter further down the chain. Aristotle distinguishes
between homoiomerous and heteromerous parts (*Parts of Animals*
i 1, 640b25-30). Homoiomerous parts are stuffs, like bronze or
flesh, which Aristotle believes have no internal structure. Every part
of a homoiomerous stuff is the same as every other part, containing
the same ratio of elements. This view of homoiomerous parts is
consistent with Aristotle's denial of atomism; he believes that
matter, as well as space and time, are infinitely divisible. The
bodily organs, hands, feet, eyes, hearts, etc., are heteromerous,
since they do have internal structure, with different parts of them
made up of different stuffs. A person's hand, for instance, is
made of flesh, bones, blood and other such biological matter, which in
turn are made of earth, air, fire and water. It may be that flesh too
is functionally defined, so that dead flesh is only called
"flesh" homonymously as well. Even if nothing biological
can exist when not alive, it seems clear that the elements at least
must be able to do so. Therefore there will be some, low-level matter
to serve as the thing that underlies the coming to be and passing away
of organisms, even though an organism's proximate matter exists
for precisely as long as it does.


## 2. Prime matter



One obvious question pertains to how low such underlying levels might
go. In fact there is considerable controversy concerning how to
conceive the bottom rung of Aristotle's hierarchy of matter.
Aristotle believes that everything is made of earth, air, fire and
water. These elements are defined by their possession of one of each
of the two fundamental pairs of opposites, hot/cold and wet/dry.
Aristotle also thinks that these elements can change into one another
(*On the Heavens* iii 6, 305a14-35). If his analysis of
change is correct, when some water changes into some air, there must
be something underlying, some substrate, which persists through the
change, initially having the essential properties of water (being wet
and cold, on Aristotle's view) and then later those of air
(being wet and hot). The thing that underlies this kind of change
cannot be any of the elements, since it must be capable of possessing
the properties characteristic of each of the elements successively,
capable of being first cold and then hot, for example. The traditional
interpretation of Aristotle, which goes back as far as Augustine
(*De Genesi contra Manichaeos* i 5-7) and Simplicius
(*On Aristotle's Physics* i 7), and is accepted by
Aquinas (*De Principiis Naturae* SS13), holds that
Aristotle believes in something called "prime matter",
which is the matter of the elements, where each element is, then, a
compound of this matter and a form. This prime matter is usually
described as pure potentiality, just as, on the form side, the unmoved
movers are said by Aristotle to be pure actuality, form without any
matter (*Metaphysics* xii 6). What it means to call prime
matter "pure potentiality" is that it is capable of taking
on any form whatsoever, and thus is completely without any essential
properties of its own. It exists eternally, since, if it were capable
of being created or destroyed, there would have to be some even lower
matter to underlie those changes. Because it is the matter of the
elements, which are themselves present in all more complex bodies, it
is omnipresent, and underlies not only elemental generation and
destruction, but all physical changes. As a completely indeterminate
substratum, prime matter bears some similarities to what modern
philosophy has called a "bare particular" (see Sider
2006), although, not being a particular, it may have more in common
with so-called "gunk" (see Sider 1993).



A similar idea is to be found in Plato's *Timaeus*,
49-52, where, in addition to his Forms and the particulars which
instantiate them, he argues for the existence of a third category of
thing, "a receptacle of all coming to be" (49a5-6):




> 
> 
> it must always be called by the same term. For it does not depart from
> its own character at all. It both continually receives all things, and
> has never taken on a form similar to any of the things that enter it
> in any way. For it is laid down by nature as a recipient of
> impressions for everything, being changed and formed variously by the
> things that enter it, and because of them it appears different at
> different times. (50b6-c4) 
> 
> 
> 



Plato also motivates his receptacle by appealing to the phenomenon of
the elements changing into one another, and, although he refers to it
as "space" and not "matter", the traditional
interpretation has it that, as he often does, Aristotle has adopted an
idea first developed by his mentor.



More recently, opponents of attributing a doctrine of prime matter to
Aristotle have complained that there is insufficient evidence for his
holding this kind of view, and that it is so philosophically
unappealing that principles of charity militate against it as an
interpretation. Such scholars point out that Aristotle actually
criticizes Plato's account from the *Timaeus*, in *On
Generation and Corruption* ii 1: 



> 
> 
> what Plato has written in the *Timaeus* is not based on any
> precisely-articulated conception. For he has not stated clearly
> whether his "Omnirecipient" exists in separation from the
> elements; nor does he make any use of it. (329a13-15) 
> 
> 
> 



Although Aristotle is clearly criticizing Plato here, it may be that
his point is simply that Plato was not sufficiently clear that prime
matter is never to be found existing apart from the elements, and that
he did not give good enough reasons for its introduction, not that he
was wrong to believe in it.



In this connection it is appropriate to note that Aristotle does in
fact use the expressions "prime matter"
(*prote hule*) and "primary underlying
thing" (*proton hupokeimenon*) several times:
*Physics* i 9, 192a31, ii 1, 193a10 and 193a29;
*Metaphysics* v 4, 1014b32 and 1015a7-10, v 6,
1017a5-6, viii 4, 1044a23, ix 7, 1049a24-7; *Generation
of Animals* i 20, 729a32. The mere fact that he uses the phrase is
inconclusive, however, since, he makes it explicit that "prime
matter" can refer either to a thing's proximate matter or
to whatever ultimately makes it up: 



> 
> 
> Nature is prime matter (and this in two ways, either prime in relation
> to the thing or prime in general; for example, in the case of bronze
> works the bronze is prime in relation to them, but prime in general
> would be perhaps water, if everything that can be melted is water).
> (1015a7-10) 
> 
> 
> 



Here Aristotle is referring to his predecessor Thales' view that
everything is ultimately made of water, which he in fact rejects.



In other passages too Aristotle seems to leave the question of whether
or not there is prime matter deliberately open. In
*Metaphysics* ix 7, he uses a conditional to talk about the
possibility: 



> 
> 
> it seems that what we call not this, but that-en--for example, we
> call the box not wood, but wooden, nor do we call the wood earth, but
> earthen, and again earth, if it is this way, we do not call something
> else, but that-en--that is always potentially without
> qualification the next thing...But *if* there is something
> primary, which is no longer called that-en with respect to something
> else, this is prime matter. For example, if earth is airy, and air is
> not fire but firey, fire is prime matter, being a this.
> (1049a18-22...24-27) 
> 
> 
> 



Here Aristotle uses the generic adjective "that-en"
(*ekeininon*), a word that he coins, to mean made of
*that* material. If a material could not be so described, it
would be prime matter. Again, he shows himself aware of prime matter
as a possibility, without wanting to commit to it here.



Another key passage where Aristotle has been thought to commit himself
more decisively to prime matter is *Metaphysics* vii 3. Here we
are told: 



> 
> 
> By "matter" I mean that which in itself is not called a
> substance nor a quantity nor anything else by which being is
> categorized. For it is something of which each of these things is
> predicated, whose being is different from each of its predicates (for
> the others are predicated of substance, and substance is predicated of
> matter). Therefore this last is in itself neither substance nor
> quantity nor anything else. Nor is it the denials of any of these; for
> even denials belong to things accidentally. (1029a20-26) 
> 
> 
> 



Although the word "prime" does not occur here, Aristotle
is evidently talking about prime matter. A natural way to read this
passage is that he is saying there is a wholly indeterminate
underlying thing, which he calls "matter", and it is not a
substance. Those who wish to avoid attributing a doctrine of prime
matter to Aristotle must offer a different interpretation: that if we
were to make the mistake of regarding matter, as opposed to form, as
substance, we would be committed (absurdly) to the existence of a
wholly indeterminate underlying thing.



In addition to disputing the correct interpretation of these passages
where Aristotle explicitly mentions prime matter, much of the debate
has centered around, on the one hand, whether what he says about
change really commits him to it, on the other, whether the idea is
really absurd. Some opponents of prime matter have argued that
Aristotle does not, after all, wish to insist that there is always
something which persists through a change (see Charlton 1970,
Appendix, and 1983). In particular, when one of the elements changes
into another, there is an underlying thing--the initial
element--but in this case it does not persist. They point out
that in the key passage of *Physics* i 7, where Aristotle gives
his account of change in general, he uses the expressions
"underlying thing" and "thing that remains".
While readers have usually supposed that these terms are used
interchangeably to refer to the substance, in cases of accidental
change, and the matter in substantial changes, this assumption can be
challenged. In the elemental generation case, perhaps there is no
thing that remains, just an initial elements that underlies. The worry
about this interpretation is whether it is consistent with
Aristotle's belief that nothing can come to be out of nothing.
If there is no "thing that remains" in a case of elemental
generation, how is an instance of water changing into air to be
distinguished from the supposedly impossible sort of change whereby
some water vanishes into nothing, and is instantly replaced by some
air which has materialized out of nothing?



The main philosophical objections to prime matter are that it is, at
best, a mysterious entity that we cannot know anything about, since we
never perceive it directly, but only the things it underlies. Of
course, there can be good theoretical reasons for believing in things
that we never actually see. No one has ever seen a quark, but we can
still know things about them, based on the kind of theoretical work
that they are required to perform. Still, Aristotle's theory
will be more parsimonious, if he can manage without positing such
theoretical entities. At worst, prime matter is said to be outright
contradictory. It is supposed to be capable of taking on any form
whatsoever, and thus to have no essential properties of its own. The
idea that it has no essential properties of its own seems to make it
difficult for us to characterize it positively in any way: how can it
be invisible, or eternal, or the ultimate bearer of properties, if
these are not properties that belong to it essentially? Moreover, if
it is what ultimately underlies all properties, it seems that it must
be able to take on properties that are inconsistent with what we would
like to be able to think of as its own nature: when Socrates turns
blue, there is also some prime matter that underlies him, which also
turns blue. But how can prime matter be simultaneous invisible and
blue? To get around these problems, it looks as though proponents of
prime matter will have to distinguish between two different kinds of
property that prime matter has, or perhaps two different ways in which
it has properties. There are its essential properties, which define
the kind of entity that it is, and which it has permanently, and then
there are its accidental properties, which it gains and loses as it
underlies different sorts of thing. A worry about this solution is, if
one can distinguish between the prime matter and its essential
properties, this might suggest that there is a need for a further
entity to act as the underlying thing for those properties, and then
this further entity would need to have its own nature, and something
to underlie that nature, and so on. It seems best to try to avoid such
an infinite regress by insisting that prime matter can underlie its
own essential properties, without being a compound of those properties
and some further matter.


## 3. The principle of individuation



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, SS8, 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: 



> 
> 
> 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: 



> 
> 
> 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 some
*proximate* 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's
*proximate* 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: \(X = F(m\_1, m\_2, \ldots m\_n)\), where
\(m\_1\ldots m\_n\) are \(X\)'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).



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. \(X = F\_t(m)\), where *m* is the
proximate matter of *X* at *t*; or, combining this idea with
the previous one, \(X = F\_t(m\_1\ldots m\_n)\), where t is the period of
time for which *X* exists, and \(m\_1\ldots m\_n\) 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.



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 *Metaphysics* viii
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.


## 4. Matter-involving forms



As we have seen, Aristotle introduces matter and form as contrasting
notions, distinct causes, which together make up every ordinary
object. It may come as a surprise, then, to find that he makes
comments which suggest that matter and form are more intimately
intertwined than is obviously required by the manner of their
introduction. It is worth noting in this regard that he is eager to
distance himself from Plato's theory of Forms, which exist quite
apart from the material world. He does so in part by insisting that
his own forms are somehow enmeshed in matter (*Metaphysics* vi
1 and vii 11, and *De Anima* i 1). He also maintains that all
natural forms are like something which is snub, where something is
snub only if it is concavity-realized-in-a-nose (*Physics* ii
2; cf. *Sophistical Refutations* 13 and 31). The purport seems
to be that all natural forms are such that they are themselves somehow
material beings, or at least that one must mention matter in their
specification. Consequently, some scholars have been inclined to
suppose that a thing's form itself contains a specification of
the matter which anything with that form has to have (see Balme 1984,
Charles 2008, Peramatzis 2011). If so, rather than being contrasted
with matter, forms will be themselves somehow intrinsically material.
Other scholars have been disinclined to draw this inference, not least
because it seems to result in an unhappy conflation of the separate
roles that matter and form are meant to play in Aristotle's
metaphysics (see Frede 1990).



The passage in the *Metaphysics* where Aristotle most obviously
addresses this question is vii 11. He begins the chapter by asking
"what sorts of thing are parts of the form, and which are not,
but are parts of the compound" (1036a26-7). He first
discusses the case of things which are realized in multiple different
sorts of matter: a circle may be realized in bronze or stone; so it is
clear that its matter, bronze or stone, is not part of the form of the
circle, since it is separate from them (1036a33-4). We are then
told that, in the case of things which are not seen to be separate,
nothing prevents the same considerations from applying to them,
"even if all the circles that had been seen were bronze"
(1036b1).



Having considered the case of circles, Aristotle moves on to consider
the form of a man, and to ask of flesh and bones, "Are these too
parts of the form and definition?" (1036b5). Some interpreters
understand the next sentence to contain Aristotle's answer: 



> 
> 
> In truth no, they are the matter; but, because <the
> form> is not also in other <sorts of matter>, we
> are unable to separate them. (1036b5-7) 
> 
> 
> 



Rendered thus, the text suggests that, as in the circle case, flesh
and bones are not part of the form of man. However, other editors,
especially those friendly to matter-involving forms, print this
sentence as a question, so that it reads 



> 
> 
> Or are they rather matter; but because <the form> is not
> also in other <sorts of matter>, we are unable to
> separate them? 
> 
> 
> 



This second way of understanding the sentence, though it does not
require it, leaves open the possibility that Aristotle's answer
will be that, unlike in the circle case, flesh and bones are indeed
part of the form of a man. Since punctuation marks are a later
invention, it is impossible to be certain which reading Aristotle
intended. The sentence, as it stands, is inconclusive.



We might hope that Aristotle's view about whether flesh and
bones are part of the form of man will become clearer later in the
chapter. Unfortunately, the relevant passage is also open to multiple
interpretations. The chapter goes on to describe how 



> 
> 
> some people are in doubt even in the case of the circle and the
> triangle, on the grounds that it is not right to define them in terms
> of lines and continuity, but that these too should all be spoken of in
> the same way as flesh and bones of man and bronze and stone of statue.
> (1036b8-12) 
> 
> 
> 



Presumably these thinkers object to lines and continuity being parts
of the definitions of circle and triangle on the grounds that they are
matter, comparing them to other sorts of matter that are obviously
inadmissible in definitions. Aristotle criticizes this line of
thought, which suggests that maybe he does think that certain sorts of
matter or at least matter-like concepts are admissible in definitions.
However, the fact that he groups flesh and bones with bronze and stone
as the sort of matter that is obviously inadmissible suggests that he
does not think that they are parts of the form of man.



The impression so far is seemingly contradicted a bit later, when we
are told: 



> 
> 
> And therefore to reduce everything in this way and to take away the
> matter is futile: for surely some things are this <form>
> in this <matter> or these things is this state; and the
> comparison in the case of animal, which Socrates the Younger used to
> make, is not a good one; for it leads away from the truth, and makes
> one think that it is possible for man to exist without his parts, as
> the circle can without bronze. (1036b22-8) 
> 
> 
> 



Here Aristotle would seem to be referring back to the earlier
comparison between the flesh and bones of a man and the bronze or
stone of a statue at 1036b11, and claiming that the comparison
misleadingly suggests that flesh and bones are not part of the form of
a man, when in fact they are.



That anyway is how those in favour of matter-involving forms take this
passage, but there is another possible reading. Instead of failing to
realize that human beings, unlike circles, are essentially realized in
flesh and bones, and as such these must be included in their form,
Socrates the Younger's mistake might have been his paying
insufficient attention to the fact that circles, being mathematical
objects, need not be instantiated in any specific kind of matter at
all, whereas human beings always are. If this is the mistake that
Aristotle is identifying, this passage would not support any sort of
matter-involving forms, but only the view that natural forms, like the
form of a man, are always instantiated in matter of certain sorts.
Even if the forms were necessarily so instantiated, this would not
require that the matter be included in the specification of the
thing's form.



There are other texts, which have been used to argue directly for the
view that Aristotle embraces matter-involving forms: *De Anima*
i 1, where Aristotle describes anger as desire for retaliation
manifested in boiling of the blood around the heart; or
*Physics* ii 2, where he says that natural forms are analogous
to snubness, i.e., concavity realized in a nose. Defenders of pure
forms can attempt to deal with these passages by distinguishing
between a pure form, and a broader "definition"
(*logos*, *horos*, *horismos*) which brings in
other causes.



As well as purely textual arguments, several more philosophical
motivations have been proffered in favour of matter-involving forms.
One such argument relies on the fact that natural things, unlike
mathematical ones, are subject to change. Only things with matter are
capable of change, and, if natural forms are to account for the
characteristic changes undergone by natural compounds, the claim is
that they must themselves be matter-involving. For example, the
property of falling downwards when unsupported is one had by all human
beings. Aristotle would explain this propensity as being due to their
being made of a preponderance of the heavier elements, earth and
water. If the form of a human being is to account for this fact,
plausibly it will have to make mention of the material constitution of
human beings that results in this sort of characteristic
behaviour.



In assessing this argument, a lot seems to depend on how extensive an
explanatory role can be assigned to hypothetical necessity (cf.
*Physics* ii 9). All human beings have a tendency to fall,
necessarily, at least in a world with laws of physics like ours.
However, it is not so clear whether this characteristic sort of change
is one which must be explained by the form or essence of a human
being, as opposed to his matter. After all, there are lots of other
sorts of thing, both living and inanimate, which share this particular
characteristic. Supposing there was a characteristic sort of change
peculiar to all and only human beings, even then it is not obvious (a)
that this fact has to be explained by the essence of a human being,
and (b) that its explanation will require the essence to be
matter-involving. To be sure, we would like some explanation of why
this sort of change is peculiar to this sort of creature, but it might
simply be a fact about the world that anything with an essence of this
sort has to change in this sort of way, without that change being
something that is specified within the essence itself.



In this connection it is important to notice that Aristotle recognizes
the existence of *idia*, that is of properties that apply to
all and only instances of a given species, which an instance of that
species has necessarily, but which are not part of its essence: e.g.,
all and only human beings are capable of laughter (cf.
*Categories* 5, 3a21, 4a10; *Topics* i 5,
102a18-30, and v 5, 134a5-135b6). The essence of a human
being is rationality, and the fact that we all (apparently) have a
sense of humour follows from the essence together with how the world
is. Many characteristic changes of organisms may be best explained in
a similar way: all ducks waddle, but waddling is not part of their
function. Rather anything that fulfils the functional requirements of
a duck must (in a world like ours) walk inelegantly.



The question of whether or not Aristotelian forms are
"essentially matter-involving" is further complicated by
some unclarity about what this description precisely amounts to. In
particular, it is unclear whether it is supposed to be a thing's
form, which is also its essence, which is matter-involving, or the
essence of the form (or both). Aristotle identifies a thing's
form with its essence at *Metaphysics* vii 7, 1032b1-2:
"by form I mean the essence of each thing and
<its> primary substance". (He makes the same
identity claim at vii 10, 1035b32, cf. also viii 4, 1044a36.) With
this in mind, we can divide the possible views about matter-involving
forms into the following four positions, with ascending degrees of
matter-involvement:


1. Pure forms: natural compounds (and their forms) have forms or
essences that are not matter-involving.
2. Compounds have forms or essences that involve matter, i.e., matter
is part of the compound's essence or form. The form that is part
of the compound's form, however, itself has a *further*
form or essence that is not matter-involving.
3. As in (2), compounds have forms or essences that involve matter;
but forms themselves have no essences or forms.
4. As in (2) and (3), compounds have forms or essences that involve
matter; and so do forms, i.e., not only are the forms or essences of
compounds themselves in some sense compounds of matter and form, as in
(2) and (3), but they themselves have *further* essences or
forms that are compounds of matter and form.



A serious objection to position (4) is that it apparently leads to a
vicious infinite regress: if a compound's essence or form is
itself a compound of matter and form, and this second form has an
essence or form which is also a hylomorphic compound, etc., every
compound will have an infinite series of essences or forms associated
with it. Socrates is (essentially) a compound of matter and form, so
is his form, so is its form, etc. Note that this regress only applies
if all forms are held to be matter-involving. It does not afflict the
more moderate matter-involving position, (2), since it holds that the
form of the compound is matter-involving, and hence has both material
and formal parts, but that this second form, the form of the form, is
pure, and has itself as a form, e.g., the form of a computer may be
computing functions in certain suitable matter, but the formal part of
that form (computing functions) would be pure. The regress is not
merely unattractively bloated and otiose. If a full explanation of
what something is requires one to list an infinite series of forms,
such explanations will not be viable for finite beings like us.



A different way to avoid the regress which plagues (4) would be to
deny the assumption that anything that is matter-involving must be a
compound of matter and form. Form is matter-involving, but that is not
to say that it has its own form or essence and its own matter. Form
and matter are introduced to explain certain facts about ordinary
objects of perception, such as this man or this horse. Once those
facts have been accounted for, there is no need to look for the same
explanations of the theoretical entities which have been introduced to
provide the original explanation. This way out of the regress involves
denying that forms have essences, i.e., it reverts to position (3).
This position faces a number of textual obstacles. For instance, at
the beginning of *De Anima* i 1, Aristotle announces that
"our aim is to grasp and understand [the soul's] nature
and essence, and secondly its properties" (402a7-8). In
*Metaphysics* vii 11, he refers to the account (*logos*)
of the essence (1037a22-3), and claims that "the account
of the soul is [the account] of the man" (1037a28-9) (cf.
also *Physics* ii 2, 194a13). For these textual reasons it
would be preferable for a proponent of (3) to be able to say that
forms do have essences or definitions in a sense, but they are
identical with these (as snubness = concavity in a nose). Their
essences are not some further thing, distinct from them.



The difficulty with this is that it is not clear that the defender of
(3) can claim that forms have definitions of any sort and still
maintain a doctrine that is distinct from both (2), on the one hand,
and (4) on the other. Given that forms are definitions, they must have
a structure that approximates to that of a linguistic entity. Whatever
else one says about them then, it seems clear that they must be
divisible (in thought) into component parts, as complex predicates are
divisible into words. We may ask of these component parts whether or
not they are matter-involving, i.e., the question which the proponent
of (3) answers in the affirmative with respect to the form or essence
of the compound--does it have parts which correspond to material
terms like "flesh" or "hand" or
"matter"? If some parts of the form's definition are
matter-involving, and others are not, this seems to make the
definition in some sense a compound of material and formal parts. We
can then identify the formal parts, and ask if there is a definition
of them, and, if the answer is "yes, a matter-involving
one", we are stuck once again with the regress which afflicted
(4). On the other hand, if no part of the form's definition is
matter-involving, the proponent of (3) must hold that, while compounds
have essences which are matter-involving, these essences have
definitions which are not, and this seems to make his view intolerably
similar to (2).



It might seem as though it does not make much difference whether
Aristotle subscribes to position (1) or (2). According to (2), every
physical object has two forms associated with it: a matter-involving
one, which combines with the proximate matter to make up the compound,
and a second form or essence of this matter-involving form, which is
not matter-involving. On position (1), a thing has only one form,
which is "pure" in the sense that it contains no matter.
However, the defender of pure forms must admit that there is also a
broader definition of a thing, which does include its matter, as well
as its other causes. Superficially, the only difference seems to be
whether or not this "definition" gets to be classified as
a form, and this might appear to be a merely verbal disagreement. In
fact, more is at stake here: although, "definition",
"form" and "essence" are often treated as
though they were interchangeable, a definition is strictly-speaking
something linguistic, whereas an essence or form may have a structure
that corresponds to something linguistic, but it is still a thing in
the world. For example, the essence or form of a human being is a
soul. A commitment to two essences or forms per compound substance is
an additional metaphysical commitment in a way that a broader
linguistic definition of a thing that mentions both its form and its
matter need not be. If important theoretical work cannot be found for
matter-involving forms, then, pure forms are the more ontologically
parsimonious choice.



In any event, one can see that Aristotle's initial contrast
between matter and form grows quickly complex once hylomorphism leaves
the domain of change. Although introduced as contrastive notions
suited to explicate change and substantial generation in the absence
of generation *ex nihilo*, any easy contrast between form and
matter turns out to be difficult to sustain once it finds employment
in its further applications. Even so, as Aristotle implies, and as
many of his followers have affirmed, hylomorphism proves no less
elastic than explanatorily powerful across a wide range of explanatory
roles.