Volume II (2015)
Identity Through Change in Aristotle:
How Hylomorphism Solved the Parmenidean Puzzle
Alejandro Naranjo
Cornell University
Abstract
Influential commentators have argued that Aristotle’s discussions regarding change are
inconsistent. Against this thesis, the present paper looks at various discussions concerning
change in Aristotle’s texts in order to demonstrate that a feature that unifies them does in fact
exist. I argue that this unifying feature is that the accidental form of a substance changes while its
essential form and matter remain constant. Thus, I claim that this gives us reason to believe that
Aristotle always held a hylomorphic theory of substance, i.e., the theory that substances are a
complex of matter and form. Moreover, I contend that Aristotle uses this unifying feature to
solve the puzzle that Parmenides raised with his argument for the impossibility of change
without having to postulate the existence of Platonic Forms.
I.
Introduction
Throughout his texts, Aristotle gives several accounts of change that challenge the opinions of
previous philosophers such as Plato, Parmenides, and Heraclitus and his followers, to name a
few. Significantly, in Physics I he rejects Plato’s explanation of change through the Forms and
claims to have solved the puzzle that Parmenides posed with his argument regarding the
impossibility of change. However, there are many other passages in which Aristotle explicitly
analyses change in (at least) one of what he takes to be its four possible forms: alteration,
growth, locomotion, and coming-to-be or passing-away. It is far from clear that his views on
change remained the same through all of his discussions. In fact, many commentators charge
Aristotle with inconsistency in this matter. For example, Daniel Graham claims that Aristotle’s
ideas on substantiality change too radically from text to text to provide a unique Aristotelian
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account of change.1 In the present essay, I argue contra these commentators that there is a unique
feature that all of these accounts of change share and that this feature is what constitutes
Aristotle’s main innovation with respect to the philosophers that preceded him. In particular, I
discuss several analyses that Aristotle presents concerning growth with the purpose of
confirming the presence of this unifying feature.
II.
Aristotle’s notion of substantiality: What Remains Constant Through Change.
First, we must introduce Aristotle’s views on substantiality since his innovations on change
depend on them. In the Categories, Aristotle defines substances2 in the following way: “a
substance … is that which is neither said of a subject nor in a subject” (2a11), where ‘P’ is said
of ‘x’ just in case ‘P’ is predicated of ‘x’ (e.g., the musical is said of man just in case he is
musical); and ‘y’ is in a subject ‘x’ just in case ‘y’ is not a part of ‘x’ but the existence of ‘y’
depends on the existence of ‘x’ (1a21).3 He then argues that all other things, in a broad sense of
the term that includes all other nine categories (quantity, relatives, etc.), are said of substances or
are in them as subjects (2a35). Since substances are fundamental with respect to predication, they
are the basic building blocks of reality on which everything supervenes. As he explains: if
“substances did not exist it would be impossible for any of the other things to exist” (2b5). In
particular, Aristotle claims that individual objects4 are substances, “e.g. the individual man or the
individual horse” (2a15).
Aristotle argues that any substance is able to receive contraries at different times while
preserving its numerical identity, e.g., the same individual man is said to be not-musical at one
time and musical at another time. Moreover, it is only substances that have this capacity: “in no
[case other than substance] could one bring forward anything, numerically one, which is able to
receive contraries” (4a10). Now, Aristotle understands change as receiving different predicates at
1
Daniel Graham, Aristotle’s Two Systems (New York: Oxford University Press, 1988).
In this paper, ‘substance’ is short for ‘primary substance’, since we will not discuss Aristotle’s notion of secondary
substances.
3
All translations are taken from The Complete Works of Aristotle, ed. Jonathan Barnes (Princeton: Princeton
University Press, 1984).
4
The notion of individuality at play is outside of the scope of this paper, but maybe logical independence will
suffice, i.e., a pack of wolves does not qualify as a substance, since its existence logically depends on the existence
of at least two of the individual wolves (unless one trivially counts a lonely wolf as a pack).
2
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different times. This explains why he uses both notions interchangeably. E.g., “what has become
cold instead of hot, or dark instead of pale, or good instead of bad, has changed” (4a31). More
formally, an object changes if and only if at some time the set of predicates that are said of the
object is different from the set of predicates that are said of it at another time. Hence, we have
that only substances can be the subject of any change and be numerically one and the same
through it. Here, by the subject of change I mean what undergoes change. I will use the term
agent of change to refer to the cause of the change.
However, we cannot say without qualification that only substances can be the subject of
change and remain numerically identical through it. Some will object that “statements and beliefs
are like this. For the same statement seems to be both true and false” (4a23), and we do not want
to count statements and beliefs as substances. With this, the opponent means that, e.g., the
statement ‘it is raining in Ithaca’ is the same throughout the year, but its truth-value changes. It is
true when it is in fact raining in Ithaca, and it is false otherwise. At this point, Aristotle argues
that substances remain identical through change by themselves, while statements do not. In our
example, the truth-value of our statement changes because the actual things the statement refers
to have changed. In contrast, the not-musical man becomes musical by performing an activity
himself—by playing an instrument, or learning how to play one. In Aristotle’s words, “in the
case of substances it is by themselves changing that they are able to receive contraries […].
Statements and beliefs, on the other hand, themselves remain completely unchangeable in every
way” (4a30). For short, I will say that a thing has changeability if and only if it is the subject of
any change through itself and it remains numerically identical through the change.
So far, Aristotle has shown that an object is a substance if and only if it has changeability.
Still, we may ask: what exactly in substances has changeability? It cannot be that the entire
substance has changeability since surely in a change in itself something must not remain one and
the same: otherwise no change would have occurred. Answering this question and tracing the
answer through Aristotle’s texts will occupy us the rest of this paper. A crucial piece to this
puzzle appears in On the Soul II.1. There, Aristotle states: “substance is a kind of what is, and
that in several senses: in the sense of matter or that which in itself is not a this, and in the sense
of form and essence, which is that precisely in virtue of which a thing is called a this, and thirdly
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in the sense of that which is compounded of both” (412a6). With this statement, he means that
for an object to be a substance it must have form—an immaterial essence which is often the
purpose or final cause of the object—and matter that is suited to fulfill the form. E.g., for an
object to be an eye, it must have the power of sight (which is the essence of the eye), and it must
have matter that enables it to see. Accordingly, he claims that “when seeing is removed the eye is
no longer an eye, except in name” (412b20). In the literature, Aristotle’s theory of the two-fold
nature of substances is called hylomorphism.
Now that we have established that substances have changeability and are hylomorphic, we
must ask: is it the form or the matter of a substance that has changeability? Or is it both? Already
in the previous quotation we see that a necessary condition of any change in which the substance
survives is that its essential form must survive as well, e.g., what makes the eye the thing it is
must necessarily remain fixed through the change. Hence the substance changes as a compound
of its matter and its accidental form. By accidental form I mean merely its account but not its
essence, i.e., the set of predicates that are said of the substance but that the substance could lose
without thereby ceasing to be the substance it is. For now I will state that this is a main feature
which is shared by all of Aristotle’s accounts of change, and, after discussing Plato as an
important target of this feature, I will prove that it is indeed present in several of the important
passages concerning change. For this paper, therefore, I will assume the following definition of
“Identity Through Change”: While the substance, as both its accidental form and its matter, is the
subject in every change in the substance, only its essential form remains one and the same
through the change.
III.
The Parmenidean Puzzle and Plato’s solution.
Historically, Aristotle’s immediate reason to uphold Identity Through Change was to solve a
puzzle that Parmenides had raised with his argument for the impossibility of change without
having to postulate the existence of Platonic Forms. In order to understand this statement, we
introduce Aristotle’s reconstruction of Parmenides’ argument: suppose that something comes to
be, i.e., changes. Then, it must do so either from what is or from what is not, both of which are
impossible. For what is cannot come to be (because it is already), and from what is not nothing
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could have come to be (because something must be underlying) (191a29).5 Plato thought he
could solve this puzzle, as is evident from the fact that he devotes an entire dialogue—the
Parmenides—giving replies to the possible responses of the Parmenideans against his theory of
Forms. I proceed to present Plato’s account of change by the Forms in order to highlight the
reasons that Aristotle champions against it.
In Phaedo, Plato’s Socrates narrates how, during his youth, he defended explanations of
growth that depended on the addition of similars to similars. As he narrates, “I thought before
that it was obvious to anybody that men grew through eating and drinking, for food adds flesh to
flesh and bones to bones, and in the same way appropriate parts were added to all other parts of
the body” (96c5). However, Socrates became disenchanted with this theory and instead came to
prefer an explanation of growth in terms of his Forms, i.e., non-material, abstract and universal
entities such as the Beautiful, itself by itself, the Good and the Great, etc. (100b4). If an object
‘x’ is said to be ‘F’, where ‘F’ is a Form, it is because the ‘F’ is in ‘x’ or, in Plato’s own words,
“if there is anything beautiful besides the Beautiful itself, it is beautiful for no other reason than
that it shares in that Beautiful” (100c2). Accordingly, every man grows because the Tallness in
him advances and the Shortness in him recedes, and our saying that he is taller than another man
has to be causally explained by comparing their participation in Tallness (102c1). As Plato
explains,
Not only Tallness itself is never willing to be tall and short at the same time, but also that
the tallness in us will never admit the short or be overcome, but one of two things
happens: either it flees and retreats whenever its opposite, the short, approaches, or it is
destroyed [in us] by its approach. (102d5)
Two features of the theory of Forms are particularly relevant to our discussion. First, the
Forms in us do not admit contraries, as is already evident in the last quotation. In fact, it is not
only that each Form in us does not admit contraries, but also in its own independent existence:
“the opposite itself could never become opposite to itself, neither that in us nor that in nature”
5
All translations of Plato are taken from Plato: The Complete Works, ed. John Cooper (Indianapolis: Hackett
Publishing Company, 1997).
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(103b2). Thus, Plato’s solution to Parmenides’ argument is the existence of eternal immaterial
forms that do not come to be but whose advance or retreat from objects makes them come to be.
Second, Plato is also interested in identity through change. He reports that before Socrates
abandoned natural science, he held three views: that the man who grows is the subject of change;
that he is one and the same through the growth, and that the addition of similars to similars is the
agent of change. Thus he states: “the man grew from an earlier small bulk to a large bulk later,
and so a small man became big” (96d3). Later, he corrected this view. As we have seen, the
Forms in us are the agents of change: the man is said to have changed in virtue of his
participation in the Forms, but it is the advance or recession of them that causes the change.
However, the subject of change—the man—is still one and the same through the change
according to Plato: “[Tallness] is not willing to endure and admit shortness and be other than it
was, whereas I admit and endure shortness and still remain the same person and am this short
man” (102e3).
In general, for Plato the essence of matter is to be the subject of change—i.e. to receive
contraries—precisely because matter maintains its numerical identity through the change. In the
Timaeus, he considers the example of a portion of gold that is molded in different shapes. He
argues that when asked what is the portion of gold—i.e., what is the subject of the change in
shape—one’s safest bet is to say that it is gold, since that is what remains constant through every
reshaping (50b1). Accordingly, he states that the nature of matter is “to be available for anything
to make its impression upon” and that matter is “modified, shaped, and reshaped by the things
that enter it” (50c1). This is in direct contradiction with Identity Through Change. Where Plato
says that the agent is the subject of change and what is constant through it, Aristotle says that the
subject is matter and accidental form and that what is constant is essential form. Hence, although
Aristotle also desires to solve the puzzle that Parmenides has posed, he disagrees with Plato
because his views on predication, substantiality, and causation are mistaken.
IV.
Observances of Identity Through Change in Aristotle’s texts.
We now turn to several of Aristotle’s discussions concerning change in order that it may become
clear both that Identity Through Change holds up through Aristotle’s intellectual development
and so that we can understand some of the main arguments that result from it. In On Generation
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and Corruption I.4, Aristotle distinguishes between different types of change, including
alteration, growth and diminution, and coming-to-be and passing-away:
When the change from contrary to contrary is in quantity, it is growth and diminution; …
when it is in property, i.e., in quality, it is alteration; but when nothing persists of which
the resultant is a property … it is coming-to-be, and the converse is passing-away”
(319b32).
Here, we only discuss the case of growth6. In On Generation and Corruption I.5, Aristotle
argues that any account of growth must preserve three commonsense suppositions, namely that
“any and every part of the growing magnitude is made bigger … by the accession of something;
and thirdly in such a way that the growing thing is preserved and persists” (321a17)7. Thus,
Aristotle thinks that a satisfactory account of growth is one in which the subject of growth
remains one and the same through the change, at least in one sense. Note that this analysis of
growth is meant to count against Plato’s theory of growth via the Forms, since the Forms do not
conform to two of these three methodological requirements. For Plato, neither the parts of the
flesh nor of the Forms are made bigger; growth does not occur by the accession of anything.
Now, since the subject of growth is available to receive contraries in that at least each and
every one of its parts has grown in magnitude, then surely it is not exactly the same as it was
before the change. If the Forms are not the subject of growth, what that which grows? I.e., “Is it
that to which something is added? If, e.g., a man grows in his shin, is it the shin which is
greater—but not that whereby he grows, viz. not the food? Then why have not both grown?”
(321a30). Note that this is a direct response to Plato’s discussion in Phaedo. In particular, it
criticizes Plato’s assertion that natural science is unable to determine which thing has grown
when two things are put together (96e5). Aristotle’s solution to this puzzle is developed in two
steps: one for the non-homoeomerous parts of the object, and one for its homoeomerous parts.
For Aristotle, an object is homoeomerous if and only if any part of it is of the same type as the
6
A complete treatment of the subject would include alteration, locomotion and even, possibly, coming-to-be, since
in Physics I.8 Aristotle argues that even things that come-to-be simpliciter come-to-be from some underlying thing
(190b2). For considerations regarding space, these further topics are left undiscussed.
7
Aristotle does not only postulate these three requirements: he has arguments for upholding them. While interesting
in our own right, for our purposes it suffices to state his results.
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whole. For instance, “any part of water is water” (328a11). Now, first, a non-homoeomerous
object grows because each of its homoeomerous parts (which necessarily exist) grows (321b18).
E.g., the hand, which is comprised of parts of flesh and parts of bone, grows precisely because
the parts of bone and flesh grow. In turn, these homoeomeries, which have “a twofold nature; for
the form as well as the matter is called flesh or bone” (321b20), grow in form. Matter cannot
account for their change since, according to Aristotle, growth in terms of matter is “like what
happens when a man measures water with the same measure; for what comes-to-be is always
different. And it is in this sense that the matter of the flesh grows, some flowing out and some
flowing in” (321b23). The idea in this passage is that when a material body grows, it not only
acquires matter but also disposes of it in what could (at least in principle) be a complete way.
Therefore, if one wants the object’s identity to be preserved thorough growth, it should not
depend on the integrity of its material constitution, e.g., the Ship of Theseus, whose parts are
exchanged at sea until its original constitution has been entirely replaced.
Now, using the three requirements of any account of growth that Aristotle has introduced,
he concludes that bodies grow because their homoeomerous parts grow in form. In particular, the
first and second requirements are crucial: “that every part should grow—and grow by the
accession of something—is possible in respect to form, but not in respect to matter” (321b22).
Possibly, that such parts grow in form means that one’s account of every homoeomerous part
acquires more predicates, and thus the body acquires more properties. As evidence for this
reading, note that Aristotle points out that a mixture of water and wine is said to be the growth of
wine (and not water) if the resulting mixture “acts as wine” (321a34)—i.e., certain predicates
said of the wine essentially are also said of the mixture, and hence the essential form of the wine
is preserved. Presumably, however, the mixture will acquire certain predicates that are said of
water: it will lose some of its redness, etc. Therefore the subject of growth is not only the matter
comprising the wine, but also its accidental form. Thus, this is a direct observance of our
principle of Identity Through Change.
Aristotle takes up the matter of growth again in On the Soul II.4, where he seeks a
definition of the nutritive soul, i.e., the soul responsible in natural beings for their reproduction
and growth. Here, Aristotle understands the soul of a body as the cause or source of the body in
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three senses: “it is the source of movement, it is the end, it is [its] essence” (415b9). For him,
reproduction and growth are due to a psychic power instead of a mere physical interaction
between elements. Thus he criticizes those who say that “fire [is] the cause of nutrition and
growth” (416a11) on the grounds that such growth would be boundless, since it is the nature of
fire to burn as long as it is fueled. Rather, living beings have a natural size that is best suited for
the fulfillment of their essence whose existence can only be understood in the presence of a
psychical power. As Aristotle explains, “limit or ratio are marks of soul but not of fire, and
belong to the side of account rather than that of matter” (416a17).
Aristotle proceeds by criticizing the accounts of previous philosophers concerning
nutrition. He states: “one set of thinkers assert that like is fed, as well as increased in amount, by
like. Another set … maintains the reverse, viz. that what feeds and what is fed are contrary to
one another” (416a29). Aristotle dismisses these theories because they fail to make a distinction
between digested and undigested matter. I.e., the food that a living being ingests is a contrary to
it, since it is not comprised of the same elements. However, in digestion, the body turns the food
into an aggregate of elements like those of its organs so it can be assimilated. As Aristotle
explains, “taking food in the sense of undigested matter, it is the contrary that is fed by it; taking
it as digested it is like what is fed by it” (416b6). Note that this is an attempt to understand the
growth of living beings by feeding, and thus Aristotle approaches this problem with the same
methodological approach as in On Generation and Corruption I.5. Accordingly, he points out
that in nutrition there must be a subject of growth that is constant through the change—that
which is fed—and that food has the power to increase the bulk of this subject in magnitude by
the accession of like to like.
Nonetheless, there is a further complication in the case of living beings. Aristotle states:
“nothing except what is alive can be fed” (416b10). By this, he means that food not only has the
power to increase the bulk of an object in magnitude (as in the case of growth in general), but
also to preserve the life of the being that feeds on it just in case it is living (416b14). This point is
particularly relevant to our discussion, since it helps us identify the living being—as both form
and matter—with the subject of nutrition: “what is fed is the besouled body and just because it
has soul in it” (416b10). Accordingly, Aristotle analyses the process of nutrition into three
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factors: “what is fed, that wherewith it is fed, and what does the feeding” (416b20), or, in our
terminology, the subject of change, the agent of change, and what remains constant through the
change. Respectively, what feeds is the nutritive soul, what is fed is the besouled body, and that
wherewith it is fed is the food (416b23). Since the nutritive soul is part of the end and essence of
the living being, we have that what remains constant through nutrition is the essential form.
Similarly, the subject of change is the living being considered both in its form and its matter.
Hence, we have here another observance of Identity Through Change.
Relatedly, in Politics III.3, Aristotle discusses how pluralities remain constant through
change, by considering the specific example of the state, which is comprised of citizens. In his
words: “shall we say that while the race of inhabitants remains the same, the city is also the
same, although the citizens are always dying and being born, as we call rivers and fountains the
same, although the water is flowing away and more coming?” (1276a35). Note that in this
example not only the citizens have changed, but also the accidental form of the state, i.e., when
describing the state we could include the fact that its citizens have changed in number and race,
etc. Nonetheless, Aristotle argues that the essential form of the state—its political organization as
it is legislated in a constitution—and not its material composition—how many and what race of
citizens are counted as part of the state—is constant through the change. This way, the
undesirable result that the state changes if all of its original inhabitants have died, even if every
inhabitant in the current state observes the same constitution and ideals, is avoided. Thus, “since
the state is a partnership, and is a partnership of citizens in a constitution, when the form of the
government changes, and becomes different, then it may be supposed that the state is no longer
the same” (1276a35) and, more generally “we speak of every union or composition of elements
as different when the form of their composition alters” (1276b6). This is similar to our findings
in On Generation and Corruption I.5, because the state, in its accidental form and material
composition, is the subject of the change, and its essential form is one and the same through the
change. Hence this is another case of Identity Through Change.
Some commentators such as Graham argue that Aristotle’s ideas of substantiality change
too drastically from his earlier texts to his latter ones to present any unifying theory of change.
Graham contends that in earlier texts Aristotle spouses a theory, S1, of atomic substantialism
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according to which “the basic entities are indivisible substances which fall under natural kinds”
and later on a theory, S2, of hylomorphic substantialism according to which “substances are
complexes of form and matter” (Graham 1987). Furthermore, in Aristotle’s Two Systems he
argues S1 and S2 are incommensurable, i.e., both systems commit Aristotle to different
metaphysical ideas that cannot be simultaneously obtained. However, we have shown that the
principle Identity Through Change remains constant throughout Aristotle’s texts: from the
Categories to the Politics, which are widely recognized as early and later texts, respectively.
Aristotle’s unfaltering dedication to this principle—which depends on a hylomorphic theory of
substance—provides us with reasons to believe that Aristotle favored hylomorphism over
atomism. Moreover, as Michael J. Loux contends, Aristotle always held that a substance is a type
of “what is” that can bear properties and which has a telos or purpose.8 It seems unlikely that
Aristotle thought that atoms could be the bearers of complex properties such as being musical or
that atoms had the telos of seeing, but these are paradigmatic examples of what we want from an
Aristotelian substance. Thus, I argue that Graham is mistaken in believing that Aristotle held S1,
and thereby can claim that Aristotle’s discussions of change are consistent and based on a
hylomorphic theory of substances.
V.
Conclusion: How Identity Through Change solves the Parmenidean Puzzle.
I have presented the principle of Identity Through Change as a constant of Aristotle’s account of
growth. Similar analyses can be made concerning alternation and locomotion. However, we have
a more pressing issue at hand. I have claimed that Aristotle can solve Parmenides’ puzzle
without having to resort to using Platonic Forms. How then does Aristotle use Identity Through
Change to avoid the Parmenidean threat? The answer to this question can be found in Physics I,
where Aristotle introduces a more general account for change. In chapter 7, he argues that the
principles of change, i.e., the conditions necessary for change to happen, are not two contraries—
as in Plato’s account, which explained change in terms of a Form and its contrary—but rather,
two contraries plus an underlying subject of change (190b35). E.g., when the not-musical man
becomes musical, the musical and the unmusical are the two contraries, and the man is the
8
Michael Loux, “Substances, Coincidentals and Aristotle’s Constituent Ontology,” in Oxford Handbook of
Aristotle, ed. Christopher Shields (New York: Oxford University Press, 2012), 372-399.
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subject of change (190b31). Aristotle requires the third principle because “it is impossible for the
contraries to be acted on by each other” (190b32), e.g., the not-musical cannot act on the
musical, since by Plato’s own terms each Form recedes when its contrary approaches.
This way, by assuming that there is change, Aristotle proves that there must always be an
underlying subject (190b3)—the third principle. Schematically, this substance ‘x’, which is
numerically identical, is able to receive two contraries ‘F’ and ‘G’ at different times. Hence, its
account changes by the modification of its matter, in accordance with Identity Through Change.
As Aristotle explains,
The subject is one numerically, though it is two in form. (For there is the man, the gold—
in general, the countable matter; for it is more of the nature of a ‘this’, and what comes to
be does not come from it accidentally; the privation, one the other hand, and the
contrariety are accidental) (190b24).
By arguing for the existence of these bearers of predicates, Aristotle can explain how
they come to be “from what is not”. Namely, they come to be from what is not accidentally, i.e.,
from the negation of a predicate ‘F’, ‘F’ can come to be in a substance ‘x’, as in the non-musical
man that becomes musical. This is what he means when he states that “nothing can be said
without qualification to come from what is not. But nevertheless we maintain that a thing may
come to be from what is not in a qualified sense, i.e., accidentally” (191b14).
Thus, Aristotle has succeeded in proving Parmenides wrong, without having to recur to
Plato’s solution. For Aristotle, the Forms, which cannot affect one another, cannot be the agents
of change. The subject of change cannot be only matter, since our account of the changing
substance has also been modified; nor need matter be constant through the change, as we have
seen in On Generation and Corruption. Most importantly, Plato fails to notice that what is
constant through the change is the essential account of substances: their end or purpose.
Aristotle’s ideas concerning predication and substantiality have survived to this day in many
ways. E.g., his arguments for the existence of fundamental substances on which predication and
truth inhere have motivated our logical notions of predicates and individual-constants. However,
I take it that what is most important for Aristotle concerning Identity Through Change is the
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emphasis it places on the final essence of substances. For him, that things are capable of coming
to be is ultimately explained only by understanding nature teleologically.
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