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. 2
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said about the soul; let us consider the remaining questions, <dealing with> those which come
¬rst (De sensu 436 a 1“6).
From clause (3) we learn that in the PN Aristotle is working within the theoretical background
established in the DA. Aristotle presupposes the general account of the soul offered in the DA; he
intends to build on it, providing important clari¬cations concerning, among other things, his
account of perception and memory. Clause (2) makes it clear that the short treatises collected
under the label PN are immediately relevant to the study of animals. But Aristotle promptly adds
that these treatises are relevant to the study of all the beings that have life, including plants. Note,
however, that Aristotle is about to engage in a new enterprise. The object of the investigation is no
longer the soul but the living beings. The short treatises collected in the PN fully belong to the
science of nature and are immediately relevant to the study of life as encountered on earth. Today
it is not unusual to refer to the complex of problems and issues originating from the DA and the
PN as psychology. Psychology so understood is a complex business whose epistemological status is
dubious. Though the study of the soul offered in the DA is preliminary, and even necessary, to the
science of nature, the account of thought and thinking that Aristotle offers in the DA goes beyond
the boundaries of the science of nature. By contrast, the speci¬c studies that are collected in the
PN are meant to discuss some aspects of speci¬c types of life and are clearly subordinated to the
further study of animal life.
Aristotle™s science of nature 23
more on the boundaries of aristotle™s science
of nature
Each Aristotelian science is a structured body of knowledge. Aristotle™s
science of nature is no exception to the rule. From the opening lines of the
Meteorology we learn that the student of nature is engaged in a complex and
at the same time ambitious investigation of a speci¬c department of
reality: the natural world. In order to understand what gives structure to
this investigation and makes it a single inquiry rather than a collection of
loosely connected, if not disconnected, investigations, we have to bear in
mind that Aristotle™s science of nature is a causal investigation of the
natural world whose ultimate aim is to provide causal knowledge of this
speci¬c department of reality. But causal knowledge of speci¬c features of
the sublunary world can be gained only on the basis of some previous
knowledge of the celestial world. More directly, there are features of the
celestial region which play a causal role in the explanation of the natural
phenomena which take place in the sublunary region. I have argued that
this view is ultimately dependent upon a certain conception of the natural
world. Aristotle thinks of the natural world as a causal system consisting of
a celestial and a sublunary part causally interconnected in a speci¬c way.
However, the structure of the science of nature presented in the opening
lines of the Meteorology re¬‚ects not only a certain conception of the natural
world but also a certain view of the way natural investigation is to be
conducted. The discrete investigations listed at the beginning of the
Meteorology are preceded by an account of “the ¬rst causes of nature, and
natural change in general” “ clause (1). The language chosen for this brief
yet accurate description of the content of the Physics suggests that the
student of nature is expected to engage in a sensible investigation of nature.
This investigation is sensible in the sense that it is conducted on the basis of
a speci¬c conceptual apparatus. The opening lines of the Meteorology make
it clear that this conceptual apparatus grows out of a general account of
nature and change. It is precisely in this sense, and only in this sense, that
in the Physics Aristotle concerns himself with the foundation of the study
of nature. By looking at Physics 1 and the way the inquiry into nature is
introduced, I now would like to show that this foundation presupposes a
strong grasp of the boundaries of the science of nature.
Aristotle announces the topic of Physics 1 at the outset:
The science of nature, <like the other sciences>, must begin by trying to settle
the question of the principles (184 a 14“16).
Aristotle and the Science of Nature
24
Evidence that this logos is a somewhat independent and self-contained
study comes from the very end of the book. At this point, Aristotle is
manifestly con¬dent that the question raised at the beginning is settled:
That there are principles, and what and how many they are, let it be established
for us in this way. Let us now make a fresh start (192 b 2“4).
The principles Aristotle is interested in are the principles of nature,
which in the end turn out to be principles of change. Interestingly
enough, Aristotle does not pause to tell us what nature is. Nor does he
make an attempt to connect nature and change or to say what a principle
is. He takes a certain familiarity with these concepts for granted
and immediately engages in a study of the principles of nature.47 One
way to explain this strategy is to assume that Aristotle is provisionally
relying on the way nature, change, and principle were understood by his
contemporaries and predecessors, whom he refers to with the collective
title of physikoi. Suf¬ce it to say that in this tradition to have a certain
nature is not merely to be something or other, but rather to become
something or other (under certain circumstances). In this tradition the
study of the entire natural world was conducted on the assumptions that a
thing becomes what it is (again, under certain circumstances), and that
“nothing comes to be from what is not” (187 a 28“9).48 Also, in the light
of these assumptions, it is not dif¬cult to understand why the study of
nature was typically a study of the nature of things from the beginning, in
Greek ex arches: namely, a study of how natural things have become what
¯
they are, which in turn boils down to a study of the material principles
out of which these things are ultimately constituted.49

47 See also Bostock (1982: 179): “Aristotle opens Physics 1 by stating that an inquiry into nature like
other inquiries, should begin with an account of the relevant principles. He does not tell us what
he means by ˜nature™ “ for that we have to wait until book 2 “ and he does not tell us what he
means by a ˜principle™ in this context.”
48 See chapter 4, “The limits of Aristotle™s science of nature.”
49 The Hippocratic author of Ancient Medicine provides us with a vivid description of the study of
man in the tradition of natural investigation:
(1) certain sophistai and certain doctors assert that nobody can know medicine who is ignorant of
what a man is; he who would treat men properly must, they say, learn this [¼ what man is]. (2) But
this logos takes them into philosophy [philosophie]; it is the province of those who, like Empedocles,
¯
have written on nature; what man is from the beginning [ex arches], namely how man came into
¯
existence at ¬rst, and from what elements he was originally constructed (VT xx 1.1“7).
This frequently cited passage contains an attempt to separate medicine from an enterprise that has
obvious overlaps with medicine and that at the beginning of clause (2) is called philosophie. What
¯
follows in clause (2) is intended to provide some content to the name together with a description
of the way man is studied by “those who, like Empedocles, have written on nature.”
Aristotle™s science of nature 25
In Physics 1, Aristotle accepts the language of becoming and the con-
ceptual framework developed by his predecessors only to revise it in the
course of his investigation. For Aristotle, his predecessors and contem-
poraries were never entirely clear on the crucial distinction between
principles and ¬rst principles. As a result of this lack of clarity, they all
failed to offer an adequate starting point for their investigations. They all
agreed in making the contraries principles, but the way they selected their
contraries was not supported by a strong grasp of the distinction between
contraries and ¬rst contraries.50 More directly, they all failed to ¬nd out a
rational way to reduce the plurality and complexity of contrariety to two
primary contraries. In other words, in the natural world we are confronted
with fundamentally different contraries. These contraries are fundamen-
tally different in the sense that they cannot be explained away or elimin-
ated, though they can be understood in the light of a conceptual schema
whose generality enables the student of nature to grasp what they all have
in common. According to Aristotle, his predecessors and contemporaries
failed to work out the conceptual apparatus needed for an adequate
analysis of the fundamentally different contraries. Put differently, they
all adopted the language of contrariety, but failed to develop a theory of
contrariety.51 As for Aristotle, the ¬rst contrariety is secured through an
analysis of becoming conducted on the most general level. By his own
admission, in Physics 1, Aristotle concerns himself with all becoming; that
is, becoming in general (189 b 30):
for the natural procedure is ¬rst to say what is common to all cases, and only
then to consider what is peculiar to each <case> (189 b 31“2).
In this passage, Aristotle is not only announcing an analysis of becom-
ing in general; he is also making it clear that this general analysis of


50 Consider the following passage:
(1) It is then clear that everybody makes, in one way or another, the contraries principles. (2) And
this is plausible: the principles must come neither from one another nor from something else, and
everything else must come from them. (3) The primary contraries have these characteristics;
because they are primary they do not come from anything else; because they are contraries they do
not come from one another (Phys. 188 a 26“30).
Aristotle starts out with the claim that all his predecessors and contemporaries adopted the
language of contrariety “ clause (1). Clause (2) contains the reason for the universal recourse to
the language of contrariety. In clause (3), Aristotle makes it clear that the primary contraries (prota
¯
enantia) alone ful¬ll the general requirement that motivated his predecessors and contemporaries
in adopting the language of contrariety.
51 More on the language versus the theory of contrariety in chapter 4, “The limits of Aristotle™s
science of nature.”
Aristotle and the Science of Nature
26
becoming is only preliminary to a more substantive investigation of the
different cases of becoming. In other words, this general analysis does not
explain away the complexity and variety of the natural world; it only
provides an explanatory schema to deal successfully with it.52 It is precisely
for this reason that the principles Aristotle arrives at have little in common
with the principles discovered by his predecessors and contemporar-
ies. Whereas they ended up offering a set of things as the principles
of everything, Aristotle insists that his principles (matter, form, and
deprivation) are not things; they are types of things.53
In Physics 1, Aristotle™s investigation is conducted on the assumption
that there is change, and that change takes different forms and manifests
itself in different ways. However, in the intellectual background in which
Aristotle grew up, the existence of change could not be taken for granted.
As Aristotle himself points out, Parmenides and Melissus denied the
existence of change and argued that what is is one. This explains why
Aristotle does not begin with a review of the positions held by the
physikoi, but with a refutation of Parmenides and Melissus. Interestingly
enough, the reader is told not to take this refutation as a piece of science
of nature:
the question whether what is is one and is not subject to change does not belong
to <the science of> nature (184 b 25 “ 185 a 1).
In this passage Aristotle is not saying that a refutation of Parmenides
and Melissus is not possible. Nor is he saying that this refutation is not
relevant to the study of nature. Parmenides and Melissus happened to
raise aporiai that are relevant to the science of nature “ in Greek physikai
aporiai (185 a 18“19). Dealing “to some extent”54 with these aporiai is
perfectly appropriate, and perhaps even required, at the beginning of an
investigation of nature. But dealing with these aporiai is external to the
science of nature. Aristotle makes it abundantly clear that he considers the
Eleatic challenge a criticism moved by outsiders who happen to write
about nature. In Physics 1, Parmenides and Melissus are equated with
people who advance an eristic argument, a logos eristikos (185 a 8). They are
like people who have not mastered the standards of the discipline that
they happen to write about, and out of their incompetence argue from

52 In Phys. 1, Aristotle insists that “becoming is said in many ways” (190 a 31). More directly,
becoming something or other (e.g. becoming white or hot) is different from becoming simpliciter;
that is, coming into being, or coming into existence.
53 More on matter, form, and deprivation in chapter 4, “The limits of Aristotle™s science of nature.”
54 Aristotle adds the quali¬cation epi mikron (185 a 19).
Aristotle™s science of nature 27
false premises and violate the rules of the syllogism (185 a 9“10).55 In this
context, the student of nature is equated to the expert who has to protect
himself and his expertise from a criticism moved by someone who claims
to be an expert but in fact does away with the expertise and its principles
and by so doing reveals his incompetence. Antiphon the Sophist and his
supposed quadrature of the circle are mentioned (185 a 17). For Aristotle,
Antiphon made no positive contribution to geometry, and no one who
has mastered geometry should be impressed by it. A refutation of Anti-
phon is not even a business of the geometer, who instead is expected to
discuss the mistakes that are made by mathematicians (for instance the
supposed quadrature of the circle by means of segments or lunes).56
Building on the model of geometry, Aristotle seems to suggest that
refutation of Parmenides and Melissus is to be attempted either by

55 Aristotle™s language is not neutral with respect to the de¬nitions offered at the beginning of the
Topics and the SE. From the SE we learn that “eristic arguments, for example, are those which
deduce or appear to deduce a conclusion from premises that appear to be plausible but are not so”
(165 a 38 “ b 8).
56 The quadrature of the circle was already a major concern in the second half of the ¬fth century.
We ¬nd a reference to it beyond geometry in Aristophanes™ Birds (1001“5). Also in the light of this
fact, we should not be surprised to discover that the quadrature of the circle drew the attention of
outsiders such as Antiphon. In the secondary literature Antiphon is often presented as a dilettante
or an amateur who happened to be interested in this mathematical problem. But this is not
Aristotle™s view. Aristotle considers Antiphon an intruder with no genuine interest or competence
in mathematics. For an informative introduction to the problem of the quadrature of the circle
¨
and its discussion in the Aristotelian corpus, I refer the reader to Muller (1982: 146“64). The
supposed quadrature of the circle by means of segments of lunes is traditionally attributed to
Hippocrates of Chios, who is in all probability to be exonerated from this fallacy. See Lloyd (1988:
103“27). In Phys. 1, Aristotle restricts his discussion to the case of geometry. However, the
problem is a more general one, and ultimately goes back to the debate on the arts or technai that
took place in the second half of the ¬fth century. At the time, it was not uncommon for an expert
to have to protect himself and his arts against denigrators. The Hippocratic treatise The Art is a
defense of the art of medicine against “those who make an art [techne] out of vilifying the arts
¯
[technai ]” (De arte, I 1.1). What is remarkable about The Art is that the author is “fully aware of
the fact that not only the existence of medicine as an art was at stake in this debate, but equally
the existence of every other art and science. The general form given to the argument at the outset
of the author™s refutation is proof of this, for it undertakes to mount a defense on behalf of all the
arts, not just of medicine” ( Jouanna 1999: 246). It would be interesting to know who these
adversaries were, who at the time attacked the arts in general and medicine in particular. The
author of The Art is not helpful on this particular point. He refers to them by some plural
circumlocution such as “those who thus invade the art of medicine,” “those who attribute
recovery to change and deny the existence of the art.” Jacques Jouanna tentatively suggests the
name of Protagoras, who wrote a work entitled On Wrestling and the Other Arts: “Since the work
is known to have examined each art in particular it must have included objections against the art
of medicine. It is not impossible that The Art was in fact a reply to attacks that ultimately derived
from this work of Protagoras. Objections to the existence of the art of medicine may therefore
have come from the Sophistic circle” ( Jouanna 1999: 244). If we bear in mind this more general
debate over the arts that took place in the second half of the ¬fth century, it becomes easier for us
to understand why Aristotle equates Parmenides and Melissus to Sophists who advanced an eristic
argument (185 a 8).
Aristotle and the Science of Nature
28
another departmental science, if there is one, to which the science of
nature is subordinated, or by an <episteme > that is common to all
¯¯
<sciences> (alternatively: common to all <men>) (185 a 2“3). Aristotle
is remarkably reticent and does not discuss the alternative he is offering in
this passage. He is content with the result secured by the alternative,
namely that the refutation of the Eleatic position is not a piece of the
science of nature.57 In translating 185 a 2“3, I have made it explicit that the
relation between the science of nature and this other departmental science
envisioned by Aristotle must be a relation of subordination. Subordin-
ation is a well-known Aristotelian technique of coordination among
autonomous sciences. Aristotle thinks of the mathematical sciences as
forming a hierarchy, going from general mathematics to geometry and
arithmetic, and to optics, astronomy, and mechanics (subordinated to
geometry) and harmonics (subordinated to arithmetic).58 However, the
possibility that the science of nature is subordinated to some other science
is to be excluded by the fact that in the Metaphysics Aristotle presents the
science of nature together with ¬rst philosophy and then mathematics as
the three philosophies, in Greek philosophiai (1026 a 18“19). There is no
evidence that Aristotle has ever thought of the science of nature as a
subordinated science, either in the Metaphysics or elsewhere. We are
therefore left with the possibility that there is another episteme that deals
¯¯
with the Eleatic challenge precisely because this episteme is common to all
¯¯
sciences (alternatively: common to all men). Dialectic is in all probability
the episteme in question. This is not the place to enter into the much
¯¯
debated question of what exactly dialectic is and what function and role
Aristotle reserves to it. Suf¬ce it to say that an examination of the
arguments of Parmenides and Melissus, though relevant to the science
of nature, goes beyond the boundaries of the science of nature. Aristotle
does not deny that this examination can be conducted by the student of
nature. His view is that, in this examination, the student of nature
cannot invoke any of the principles appropriate to the science of nature,
which are likely to have no impact on Parmenides and Melissus. In
discussing their arguments, the student of nature should make use of
the general ability of examining a thesis only on the basis of the principles
that are common to him and to Parmenides and Melissus.59 These are in


57 Aristotle does not change his mind on this point. See Phys. 193 a 4“9. For a discussion of this
second passage, I refer the reader to Waterlow (1982: 30“1).
58 For an introduction to Aristotle™s conception of subordination see McKirahan (1978: 197“220).
59 Cf. Rhet. 1354 a 1“6.
Aristotle™s science of nature 29
fact the only things that are likely to be accepted by Parmenides and
Melissus.60

looking ahead
So far I have insisted on the unity of the natural world and argued that
Aristotle conceives of this world as a causally uni¬ed system. In the
following chapters I shall argue that Aristotle believes in the existence of
celestial and sublunary natures but does not believe in the uniformity of
nature. In the natural writings as well as elsewhere, there is evidence that
Aristotle is committed to the view that there is an important discontinuity
between the celestial and the sublunary worlds. Here is a passage that I
have discussed only in part and that I now quote in its entirety:
(1) Since these causes are four, it is the job of the student of nature to know about
them all, and he will give an answer to the “why?” [dia ti ] in the way appropriate
to the science of nature [physikos], bringing it back to them all: matter, form, that
¯
which originated the change, and that for the sake of which. (2) The last three
often come down to one: for what the thing is and that for the sake of which it is
are one, while that from which the change ¬rst originated is the same in form as
these: for it takes a man to generate a man “ and in general things that change by
being themselves changed. (3) Things that are not so fall beyond the province of
the science of nature: for they change without having change or a principle of
change, but by being not subject to change. (4) For this reason [dio] there are
three studies [pragmateiai ]: one that is concerned with the things that are not
subject to change, one with the things that are changed but imperishable, and
one with the things that are perishable (Phys. 198 a 22“31).
From this passage it is clear not only that the student of nature is
engaged in a causal investigation, but also that this causal investigation is a
search for all the relevant or appropriate causes. Aristotle makes the latter
point by saying that the student of nature is expected to answer the
question “why?” in the way that is appropriate to the science of nature
“ in Greek physikos, clause (1).61 Clause (2) starts out as a speci¬cation on
¯
the doctrines of the four causes: the form and the goal are numerically
one, and they are the same in form as the moving principle. This is one of
the many passages where Aristotle reports his favorite slogan that it takes a
man to generate a man. This time, however, Aristotle does not add “and

60 Even this brief and somewhat inadequate treatment of dialectic is suf¬cient to understand why
Aristotle insists on the genos-neutrality of dialectic. From the A post. we learn that dialectic is not
genos-oriented but is common to all the sciences (77 a 25“35).
61 For the interpretation of physikos I follow Simplicius, In Phys. 363. 6“7.
¯
Aristotle and the Science of Nature
30
the sun.”62 This small yet signi¬cant fact reveals that Aristotle is not
primarily interested in the unity of the natural world. This is con¬rmed
by what immediately follows in the passage. At the very end of clause
(2) Aristotle argues that the science of nature is about things that change by
being changed. From clause (3) we learn that not everything that changes is
itself changed; in fact, there are things that change without being changed.
These things are not changed because they do not have a principle of
change: more speci¬cally, they are not subject to change at all; they are
akineta. Also on the basis of this remark, Aristotle concludes that there are
¯
three studies or pragmateiai: (i) the study of that which is not subject to
change, (ii) the study of that which is subject to change but not perishing,
and ¬nally (iii) the study of perishable things “ clause (4). This conclusion
is mildly surprising. On the one hand, Aristotle claims that the domain of
the science of nature is the realm of change; on the other, he breaks this
science into two pragmateiai and, at least in this passage, shows no concern
for their coordination. This is not the only passage in the Aristotelian
corpus where the discontinuity of the natural world is stressed over its
unity. Lambda 1 is another remarkable case. I shall return to Lambda in
due course.63 For the time being, I am content to say that even when the
unity of nature becomes an overriding concern, Aristotle never fails to
remind the reader that there is an important discontinuity between the
celestial and the sublunary region. For instance, the investigation con-
ducted in the Meteorology crucially depends upon the assumption that the
totality of the sublunary bodies is continuous with the celestial body. In
this context, Aristotle is expected to insist on the continuity between the
celestial and sublunary region of the natural world. But even in the
Meteorology Aristotle does not fail to add a small yet signi¬cant quali¬ca-
tion. According to some of the MSS, the totality of the sublunary bodies
is somehow “ the Greek is pos “ continuous with the celestial body (339 a
¯
21“2). In the rest of the book I shall make an attempt to shed some light on
the force of the pos as well as on the consequences descending from it. I
¯
shall argue that according to Aristotle there is a lack of uniformity in
nature, which ultimately puts severe limits on what can be known about
the celestial natures. Aristotle seems to be reluctant to engage in an
investigation of the celestial natures when and where the lack of infor-
mation at our disposal cannot be overcome by an appeal to the similarities
that the celestial natures share with the sublunary natures.

62 But he does at 194 a 13.
63 Chapter 4, “The limits of Aristotle™s science of nature.”
chapter 2

Bodies




bodies and magnitudes
The science of nature is clearly concerned for the most part with
bodies and magnitudes, the affections and motions of these, and the
principles of this kind of substance (Aristotle, DC 268 a 1“6).
By this point I hope to have established that Aristotle sees his science of
nature as a systematic whole. It should also be clear that this science is
seen as a systematic whole because it presents an account of a world that is
similarly systematic. More directly, and more boldly, the science of nature
mirrors the system of nature. Aristotle™s conception of the natural world
follows from the research program conducted in the science of nature. In
other words, it is the study of the celestial and sublunary bodies that leads
him to believe that the natural world is a causal arrangement of a certain
type, and to the view that the study of the celestial world should precede,
rather than follow, the study of the sublunary world. In the ¬rst two
books of the DC are collected the results that Aristotle reached in the
study of the celestial world. In the following chapters, I shall focus on
speci¬c parts of the DC and show how unusual Aristotle™s conception of
the celestial word is, especially if it is considered in its historical context in
relation to his predecessors and successors. In this chapter, I would like to
focus on the very beginning of the DC, which I have quoted in the
epigraph, and discuss the idea that bodies and magnitudes are the object
of the science of nature.
For Aristotle, bodies are magnitudes; they are magnitudes of a certain
kind. In the lines that immediately follow the quoted passage, Aristotle
provides three distinct but related de¬nitions of body by recourse to the
notions of continuity and divisibility. Continuity is reduced to divisibility:
something is continuous if, and only if, it can be divided in ever-divisible
parts (268 a 6“7). If a magnitude can be divided in one dimension it is a
line; if it can be divided in two dimensions it is a surface; and ¬nally if it
31
Aristotle and the Science of Nature
32
can be divided in three dimensions it is a body. A body is therefore a
magnitude divisible in three dimensions “ Def. 1. Since for Aristotle there
cannot be more than three dimensions, to say that a body is divisible in
three dimensions is the same as saying that it is divisible in all dimensions.
Hence a body is a magnitude divisible in all dimensions “ Def. 2 (268 a
7“10). Admittedly, “dimension” does not occur in the text. Aristotle spells
out Defs. 1 and 2 by saying that body is to epi tria <diaireton>.1 But a few
lines below Aristotle says that a body has all dimensions, diastaseis (268 b
6“7). The Greek even has a word for each of the three dimensions: length,
breadth, and depth are mekos, platos, and bathos respectively.2 Finally, it is
¯
not dif¬cult to ¬nd a de¬nition of body that makes an appeal to the
dimension distinctive of body: depth. In the Timaeus Plato de¬nes body
by saying that it also has depth (53 c 5“6). Interestingly enough, there is
no mention of divisibility in the Timaeus. In due course I shall argue that
in the DC Aristotle intends to offer a de¬nition of body that is alternative
to the one presented in the Timaeus. On Aristotle™s interpretation, Plato is
committed to atomism. For the time being, however, I limit myself to
saying that ancient atomism is a family of different theoretical positions,
all sharing the view that the ultimate magnitudes from which the world is
constructed are indivisible magnitudes. By stating that a body is a con-
tinuous magnitude divisible in three or all dimensions, Aristotle is
reacting against the supposed atomism of the Timaeus (and its Academic
varieties).
The equivalence between Def. 1 and Def. 2 ultimately rests on the
conviction that there are three, and only three, dimensions. Aristotle
cannot take it for granted that there are only three dimensions but has
to provide some evidence in support of this claim. Since antiquity
commentators have routinely complained that the evidence Aristotle
offers is surprisingly weak. He is content to make an appeal to (i) the

1 Both diaireton and diastaton are grammatically possible. By understanding diaireton one does not
deny that bodies are three-dimensional but stresses that bodies are divisible in three dimensions.
More directly, bodies are divisible in three dimensions because they are three-dimensional. If one
understands diastaton, it becomes dif¬cult to see why Aristotle introduces the notion of continuity
“ divisibility “ in lines 268 a 6“7 rather than in line 268 a 24.
2 Aristotle can refer to the three dimensions as diastemata (rather than diastaseis). Cf. Phys. 209 a
¯
4“5: “<Place> has three dimensions [diastemata], length, breath, and depth, by which every
¯
body [soma] is delimited.” In Phys. 4 Aristotle takes it for granted that each body occupies a
¯
certain place by virtue of the fact that each body is surrounded by other bodies. There is no need
to enter into a discussion of the Aristotelian notion of place. Suf¬ce it to say that it is distinctive
of Phys. 4 to conceive of the body as a magnitude extended in three dimensions, themselves
conceived as intervals between two extremities. The Greek diastemata points to the fact that a
¯
dimension is always an interval between two extremities.
Bodies 33
authority of the Pythagoreans, who claimed that the number three is
distinctive of the all and the totality of the things that are; that is, the
things that exist (268 a 10“13); (ii) the use of the number three in ritual
practices (268 a 13“15); and ¬nally (iii) the linguistic usage, according to
which the Greek panta is used when there are at least three things (268 a
¯
15“19). This re¬‚ection on the language enables Aristotle to add that pan,
panta, teleion are formally synonymous and to claim that body alone
is teleion among magnitudes “ Def. 3. From Metaph. ” 16 we learn that
what is called teleion is (i) that outside of which it is not possible to ¬nd
even a single one of its parts, or (ii) that which in respect of excellence and
goodness cannot be surpassed in its genus, or ¬nally (iii) that which
has reached its end or its ful¬llment. Moreover, this tri-partition is
reduced to a bi-partition. What is called teleion is (i) that which lacks
nothing in respect of goodness and cannot be surpassed and has nothing
to be found outside it (1021 b 31“3) or (ii) that which in general is not
surpassed in its genus and has nothing outside it (1021 b 32 “ 1022 a 1).
The strategy Aristotle follows in the Metaphysics is intricate; but even
without tracing the intricacies of this chapter it is possible to highlight
what is relevant for the present discussion. The notions of completeness
and perfection con¬‚ate in the honori¬c epithet of teleion. When Aristotle
claims that something deserves this epithet, he may want to say that
something is (i) perfect, or (ii) complete, or ¬nally (iii) perfect and
complete. There is no doubt that when we read that body alone is teleion
among magnitudes, we are to understand that body alone is complete
among magnitudes. On the assumption that Aristotle has suf¬ciently
proved that there are only three dimensions, we can safely infer that body
alone is complete among magnitudes since body alone extends in all
dimensions. But however dif¬cult it may be for us to accept it, we cannot
a priori exclude that, when we read that body alone is teleion among
magnitudes, Aristotle means to say that body alone is complete and perfect
among magnitudes.3
Only a closer look at the strategy adopted by Aristotle may help us to
decide which notion of teleion is required. In particular, it would be a

3 The claim that bodies are perfect magnitudes may even look absurd to some of us. Cf. Wildberg
(1988: 22) and Leggatt (1995: 170). Aristotle shares with us the assumption that the aim of science
is to provide an objective description of the natural world. But the natural world as it is conceived
by Aristotle is not a value-free world. Quite the contrary. Aristotle is committed to the view that
there are values in the natural world, or that values are part of the furniture of the natural world.
Our job as students of nature is to attain understanding of the perfection and goodness of the
natural world, on the crucial assumption that we can objectively make value judgments about the
natural world.
Aristotle and the Science of Nature
34
mistake to think that the opening lines of the DC are merely devoted to
the introduction of a certain conception of the body. This chapter is
designed to lead to a speci¬c conception of the all or the totality of the
¯
things that exist “ in Greek to pan. Defs. 1“3 prepare this particular
conception of the all. From Def. 1 to Def. 3 Aristotle is inviting the reader
to think of a body as a three-dimensional magnitude. But this is not the
only way in which a body can be conceived. A body can also be conceived
as a part of a whole. Put differently, a body can be conceived as a part of
the all or the totality of the bodies that exist. By inviting the reader to
think of a body as a part of the all, Aristotle introduces a certain concep-
tion of the all. This is not a mere collection or sum of separate parts but
consists of parts that are appropriately related to one another. At the
beginning of the DC, Aristotle does not engage in a discussion of the
structure of the all. He does, however, suggest that each body is in contact
with the immediately surrounding bodies, and that by being in contact
with one another they all together form a uni¬ed whole (268 b 5“8). The
information supplied is not suf¬cient to form an adequate conception of
the all. But if this book is addressed to an intelligent, educated reader who
has already studied the Physics, there is no doubt that this reader is being
encouraged to conceive of the totality of the bodies as a plenum. In the
Physics, Aristotle argues against the existence of void, and for the claim
that each body, by being in contact with the immediately surrounding
bodies, occupies a certain place in the plenum. In the DC, Aristotle adds
that this plenum is ¬nite in extension, ungenerated and imperishable. But
the reference to contact immediately suggests that this plenum displays a
certain kind of unity. Minimally, it displays causal unity.4 From the
Physics the reader learns that change always presupposes an agent and a
patient. For Aristotle, contact is necessary for the agent to act on the
patient, and for the patient to be affected by the agent. The reference to
contact is therefore enough to alert the reader to the fact that the different
parts of the plenum are causally related to one another in a certain way. In
the course of the DC, Aristotle will argue that the heavens are made of a
simple body, which naturally performs circular motion, and which cannot
be reduced to earth, water, air, and ¬re. According to Aristotle, this
particular body, by simply being in contact with the sublunary bodies,
has an in¬‚uence on them. Note, however, that Aristotle is committed to
the view that this body cannot be acted upon by the sublunary bodies.

4 On causal unity see chapter 1, “The unity, structure, and boundaries of Aristotle™s science of
nature.”
Bodies 35
From the Meteorology and the GC the reader will learn how the celestial
body and the sublunary bodies are causally related to one another. More
speci¬cally, the reader will learn that the different parts of the plenum are
related to one another in such a way that some of them have an in¬‚uence
on the others, and the latter would not be what they actually are without
this in¬‚uence. I have suf¬ciently insisted on this point in chapter 1. The
only thing that I would like to add now is that this particular conception
of the all forces Aristotle to revise and qualify his third de¬nition of
body: a body is a perfect magnitude in so far as it is a three-dimensional
magnitude. There is no doubt that only the all “ the totality of the
existing bodies “ deserves the honori¬c epithet of teleion without
quali¬cation (268 b 8“10).
If I am right, in the opening chapter of the DC Aristotle goes through
three de¬nitions of body with the ulterior purpose of introducing a certain
de¬nition of the all or the totality of the existing bodies. The word teleion
plays a crucial role in this strategy. It is used in two distinct ways
throughout the chapter. First, it is used to focus on three-dimensionality,
which for Aristotle is equivalent to three-divisibility (pace the atomists). It
is then used to focus on the unique case of the all. This is understood as a
uni¬ed whole constituted by the totality of the parts “ the totality of the
bodies “ that exist. The very same notion of teleion must apply in both
cases. In both cases this notion involves a reference to completeness and
perfection. This is required to do justice to the particular conception of
the all that Aristotle introduces toward the end of the chapter. The idea
that a body does not exist in isolation but is part of a causal system of
interconnected bodies plays an important role in the opening lines of
the DC. This idea helps us to understand why a discussion about bodies
leads to a certain conception of the all or the totality of the existing
bodies. It does not explain, however, why the all or the totality of the
existing bodies should be conceived as a uni¬ed whole. The disappoint-
ment for what appears to be a rather dogmatic approach is somehow
mitigated if we bear in mind that the DC is addressed to an intelligent,
educated reader. I have already argued that this reader is supposed to
study the DC after the Physics. I now add that familiarity with the Timaeus
and with the conception of the sensible world that is offered in that
dialogue is expected on the part of the reader. In the Timaeus the sensible
world is presented as a uni¬ed whole. But Plato thinks of it as a living
creature endowed with soul and understanding (30 b 6“7). This living
creature is the creation of a divine craftsman. There is a sense in which the
job of the divine craftsman is not different from that of any other
Aristotle and the Science of Nature
36
craftsman. He has to act on a material. This material is to be receptive of
the model in order to be made like the model. In 30 c 2 “ d 4, Timaeus
asks himself what this model is. Timaeus has just established that the
sensible world is a living creature. He now adds that an intelligible living
creature is its model. But it is signi¬cant that this intelligible living
creature must satisfy at least one further constraint. According to Ti-
maeus, it cannot be any of the intelligible living creatures that are mere
parts of a whole (30 c 4). For what is merely a part of a whole fails to
account for the goodness and beauty of the sensible world. What is a part
of a whole is in fact ateles (30 c 5). At least two things are to be noted here.
First of all, the occurrence of kalon at 30 a 5 dissipates, I think, any
reasonable doubt about the normative reading of ateles. Secondly, and
more importantly, this passage of the Timaeus is very close in language to
the end of the prologue to the DC.5 In as compressed a text as the
beginning of the DC, this is very unlikely to be a mere coincidence. My
suggestion is that this is a conscious echo of the Timaeus.
In antiquity Plato and Aristotle were not the only thinkers to claim that
the world is to be conceived as a uni¬ed whole of a certain kind. The
Stoics, too, conceived of the world as a whole. But they distinguished
between the all and the whole.6 It is not dif¬cult to ¬nd an explanation
for this distinction. Though the Stoics were committed to the view that
there is no void within the world, they had reasons to think that there is
void outside it. Whereas the Stoic all consisted of the whole together with
the surrounding void,7 the Stoic whole was thought of as a uni¬ed body
and as having a soul as the internal principle of unity (M ix 78). Simply
put, the Stoics admitted a hierarchy of principles of unity and argued that
the whole is held together by the best of these principles of unity: a soul
(M ix 81“4).8 Interestingly enough, the Stoics were not content to claim

5 Compare ton men oun en merous eidei pephykoton (Tim. 30 c 4) with ton men oun en moriou eidei
¯ ¯ ¯
somaton (DC 268 b 5).
¯¯
6 Sextus Emp., M ix 332 (¼ SVF ii 254 ¼ LS 44 a).
7 Apollodorus departed from the general Stoic theory and argued that by “all” is meant either (i)
the cosmos, or (ii) the system of the cosmos and the void outside it (Diog. Laert., vii 143 ¼ SVF iii
Apollodorus 9).
8 Sextus documents that the Stoics distinguished the uni¬ed bodies from both (i) the bodies that
are composed of separate parts (e.g. an army), and (ii) the bodies that are composed of contiguous
parts (e.g. a ship or a house). They further subdivided the uni¬ed bodies by appeal to the fact
that the principles that hold these bodies together are different. Some of these bodies are held
together by a mere hexis (stones), and others by a physis (plants); ¬nally some of them are
controlled by a soul or psyche (animals). Reinhardt insistently argued that this tri-partition of
¯
principles of unity (hexis, physis, and psyche ) goes ultimately back to Posidonius. See Reinhardt
¯
(1921: 347; 1926: 45“54; and 1935: 650“2). Pohlenz always spoke against this thesis. See
Pohlenz (1965: 172“98, and 199“232). According to Pohlenz, this classi¬cation of principles of
Bodies 37
that the world is held together by a soul. They explicitly took the view that
the world is an intelligent living being. By so doing, they put themselves
in continuity with the Platonic tradition of the Timaeus. There is no
doubt that a living being, either intelligent or not, is a uni¬ed whole in a
much stronger sense than the one suggested at the beginning of the DC.
Here Aristotle is content to say that the all is a uni¬ed whole because its
parts are in contact with one another; that is, because the totality of the
bodies are causally related to one another in a speci¬c way. He never
suggests that there is an internal principle which is ultimately responsible
for the fact that these parts are one thing rather that a mere plurality of
bodies. He is obviously reticent about taking this view. This reticence is
better understood, I think, as an implicit claim that the natural world as a
whole is not a living thing. This book is intended to cast some light upon
the reasons that might have led Aristotle to deny life, and therefore
understanding, to the natural world as a whole. On the one hand,
Aristotle seems to think that the celestial and sublunary bodies form a
causal system of a speci¬c type; on the other, he seems to think that this
causal system does not possess enough unity to be a living thing. Why? I
shall argue that the celestial and the sublunary world form a causal system
that admits an important discontinuity within itself.9

natural bodies
Divisibility and three-dimensionality are the two ingredients that
Aristotle uses in the formation of the notion of body in the prologue to

unity is not an original contribution of Posidonius. On the contrary, Posidonius could rely on a
well-established tradition, which ultimately goes back to Chrysippus. The dispute between
Reinhardt and Pohlenz concentrated on the way Plutarch, De defectu oraculum 28 (¼ SVF ii 366)
is to be read and understood. But the reader should see also [Philo], De aeternitate mundi 79“80
¨
(¼ SVF iii Boethus Sidonius 7). Here the Stoic Boethus is credited with an argument for the
eternity of the world that crucially depends on the classi¬cation of bodies into (i) bodies that are
composed of separate parts (ii) bodies that are composed of contiguous parts, and (iii) uni¬ed
bodies. This strongly suggests that the classi¬cation of bodies that makes appeal to different
principles of unity was part of the conceptual apparatus available to a Stoic philosopher well
before Posidonius.
9 Matthen (2001: 171“99) has recently argued for the view that Aristotle does not ¬t the Greek
cosmological tradition that thinks of the universe as an animal. According to Matthen,
“[Aristotle™s] cosmos falls short of the strong conditions of unity that characterize an animal” (198).
I am convinced that the lack of the relevant type of unity is the primary reason for the denial of a
soul, and therefore of life, to the natural world. In other words, Aristotle credits the natural world
with unity but not with uniformity, and the ultimate reason for the denial of uniformity is
Aristotle™s belief in the existence of an important discontinuity within the natural world. I shall
return to this topic in chapter 4, “The limits of Aristotle™s science of nature.” There I shall also
explore the consequences that immediately depend on the discontinuity in question.
Aristotle and the Science of Nature
38
the DC. This notion is nevertheless open to criticism. One may wonder
how useful this notion is in distinguishing a body from the corresponding
geometrical solid, for instance the Great Pyramid built by the Pharaoh
Cheops some 4,600 years ago from the corresponding geometrical ¬gure.
That a body is to be kept distinct from the corresponding geometrical
¬gure is also suggested by the language. Whereas the name soma is ¯
ambiguous and may be used to refer to the Great Pyramid of Cheops as
well as the corresponding geometrical solid, the term stereon is exclusively
used with reference to the latter. But it is easy to see that three-
dimensionality alone, or in combination with divisibility, is of no help
if we should want to distinguish a soma from the corresponding stereon. A
¯
geometrical solid also extends in three dimensions: it too may be de¬ned
as that which has length, breadth, and depth.10 Moreover, in this context
divisibility brings nothing to the notion of body that may enable one to
distinguish bodies from geometrical solids. By stating that a body is
divisible into ever-divisible parts, Aristotle simply presents himself as a
partisan of the continuum theory, like Anaxagoras11 (and later on the
Stoics12).
In the light of the strategy followed in the opening chapter of the DC,
this criticism represents an uncharitable misinterpretation of Aristotle™s
intentions. In this context, Aristotle does not intend to provide the best
possible de¬nition of body: that is, a de¬nition that among other things
may enable him to distinguish a body from a geometrical solid. Rather, he
introduces a de¬nition of body with the ulterior purpose of arriving at a
particular conception of the all or the totality of the existing bodies. It is
signi¬cant, I think, that in the rest of the DC Aristotle no longer speaks of
bodies as three-dimensional (or three-divisible) magnitudes but focuses
on natural bodies “ in Greek physika somata. Natural bodies are consti-
¯
tuted by a nature. By saying that a body is constituted by a nature,
Aristotle suggests that the body exhibits a characteristic behavior, and
that the nature of the body manifests itself in that particular behavior.
In the DA, Aristotle distinguishes the natural bodies that have life from
the natural bodies that do not (412 a 13). Natural bodies that have life are
living bodies. Life, as it is understood in the DA, minimally involves self-
nutrition, growth, and diminution (412 a 14“15). Self-nutrition, growth,


10 Euclid, Elementa xi, Def. 1: “body [stereon] is that which has length, breadth, and depth.”
11 Cf. Simpl., In Phys. 155. 21“30 (¼ DK 59 b 1); 164. 17“20 (¼ DK 59 b 3); 164. 26 “ 165. 1 (¼ DK 59 b 6).
12 Cf. Stob., Ecl. i 142. 2“7 (¼ Aetius i 16. 4 ¼ SVF ii 482 ¼ LS 50 a), Diog. Laert., vii 150 (¼ SVF ii
¨
482 ¼ LS 50 b).
Bodies 39
and diminution are constitutive of perishable life. In other words, what-
ever is alive and perishable is minimally subject to growth and dimin-
ution; in addition, both growth and diminution require the use of
nourishment, which is not possible without engaging in self-nutrition.13
Each of these activities is itself normally constituted by activities. For a
peach tree, for example, to be engaged in reproduction implies having
leaves and pink ¬‚owers growing on its stems at a certain time of the year,
and to bear soft round fruits with pinkish yellow skin and juicy ¬‚esh
ripening at a different time. All the characteristic activities of the peach
tree are to be explained by appealing to the appropriate nature: a soul of a
certain kind. The soul is an internal principle of regulation and unity: it
governs the characteristic activities of the peach tree and shapes them into
a uni¬ed behavior “ the distinctive behavior of the peach tree. In the DA,
Aristotle famously argues that the soul is the ¬rst actuality of a body which
is not only natural but also organic (412 b 5“6). In all probability, Aristotle
is inviting us to think of the body as an organ or a tool of the soul.14 He
obviously does not intend to deny that the body in question has organs.
Quite the contrary: an organ may be composed of organs.15 However, the
organs in question need not be eyes, limbs, and the like. Most living
bodies display a much simpler organization. Several times Aristotle says
that the roots are to plants what the mouth is to animals.16 He often
adds that the entry of the nourishment is the upper part of the living
body. In other words, branches, leaves, ¬‚owers, and fruits appear to us to
be the upper part of the peach tree, but they are in fact the lower part of
the plant.17 His insistence on this apparently curious, if not bizarre,
doctrine is not gratuitous. By so doing, Aristotle points at a fundamental


13 It should be noted that the power of self-nutrition is also the power of self-replication or
generation of a like self. Aristotle is committed to the view that the use of nourishment and
reproduction are aspects of the same power. In the DA, Aristotle is pushing the overall view of the
nutritive soul as that which has the capacity to save (the Greek verb is sozein, 416 b 18) a certain
¯
form of organization. Put differently, the living body is the bene¬ciary of the operations of the
nutritive soul, but the goal of these operations is the soul itself. By saving that which has the soul,
namely the ensouled body, the nutritive soul saves itself.
14 There has been a great amount of discussion on the meaning of the Greek organikon in this
context. On the very idea that the body is a tool or instrument of the soul, see Menn (2003: 83“
139, in particular 108“12). I refer the reader to this paper for a convenient summary of the ongoing
discussion on the meaning of organikon in DA 412 b 5“6.
15 I owe this point to Alan Code.
16 DA 412 b 3; IA 705 b 7“8; PN 468 a 9“11.
17 Phys. 199 a 27“9; IA 705 a 27 “ b 2; PN 467 b 2; 467 a 33“4; 468 a 4“12. Aristotle does not know
of photosynthesis. For him, plants take in nourishment through the roots. Leaves are for the sake
of the fruit (they are regarded as a shelter for it).
Aristotle and the Science of Nature
40
truth: life implies organization; if something is a living body, it is
minimally structured with a lower and an upper part. However, Aristotle
is also committed to the view that there are different degrees of organiza-
tion which correspond to distinct forms of life, themselves ¬xed with the
help of a certain number of activities which are necessarily realized in a
living body of a certain type. If the living bodies of the sublunary world
are all engaged in self-nutrition, growth, and diminution, some of them
are capable of bodily displacement in the form of progressive motion “ in
Greek poreia. The capacity for poreia takes different forms: some animals
move around by walking, others by ¬‚ying, and others by swimming or
creeping. But if an animal is capable of poreia, it possesses the maximum
degree of organization available in the natural world. According to
Aristotle, its nature must be a soul minimally equipped with the capacity
for perception, and phantasia. This latter is the capacity to form repre-
sentations of a certain kind on the basis of perception. It is intuitively
clear why poreia, perception, and phantasia go together: to move around,
a living body must be sensitive to the environment, and perception and
phantasia are the minimal cognitive equipment required to navigate from
one place to another. A living body capable of poreia is therefore equipped
with an appropriate locomotory apparatus as well a sensory apparatus of
the right kind. From the IA we learn that the sensory apparatus is always
implanted in the front of the living body (705 b 8“13), and that the actual
mechanism of locomotion always involves the existence of another im-
portant symmetry: the existence of a right and a left side of the living
body (705 b 30 “ 706 a 26). In short, an upper and a lower part, a front
and a back, and ¬nally a right and a left side must be present to those
living bodies that are equipped with the capacity for poreia and are not in
some way mutilated. Since these living bodies possess the maximum
degree of complexity available in the natural world, in the DC Aristotle
calls them “perfect bodies” (284 b 21“4).
So far I have argued that Aristotle™s science of nature is concerned with
natural bodies. A clari¬cation, nevertheless, is needed. In the DC Aristotle
is concerned with natural bodies in so far as they are endowed with the
capacity to undergo motion from one place to another. This capacity is
not to be confused with the capacity for poreia. Aristotle credits only a
limited group of sublunary living bodies with poreia. By contrast, all
natural bodies are credited with the capacity to be moved from one place
to another. This capacity can be explained by recourse to the material
principles of natural bodies. Aristotle has a hierarchical conception of
body such that natural bodies are themselves composed of natural
Bodies 41
bodies.18 For example, a man is composed of ¬‚esh, bones, and sinews,
which in turn are composed of earth, water, air, and ¬re in a certain ratio.
Earth, water, air, and ¬re are at the bottom of the hierarchy and deserve
the honori¬c title of <sublunary> simple bodies. Aristotle conceives of
them as homogeneous bodies endowed with the capacity to perform a
simple motion “ either the downward or the upward motion. In other
words,
1. If x is a sublunary SB, than x has the
capacity to perform either UpM or DnM.
The simple motion of a sublunary simple body is routinely described as a
motion towards a certain place “ either towards the center or the extrem-
ity of the natural world.19 Simple motion is a case of change from one
place to the other, and a change is normally named after the new state of
affairs which emerges from it. Each simple body, under the appropriate
circumstances, invariably terminates its motion when it has reached its
own natural place. In the DC ¬re is explicitly said “to rise over all <the
bodies> that move upwards” (311 a 17“18), and earth “to settle below all
<the bodies> that move downwards” (269 b 24“5). Since the four
sublunary simple bodies come to rest in four different places, they
perform four different natural motions. I shall return to the notion of
natural motion in chapter 3. For the time being, I am content to note that
Aristotle consistently says that ¬re moves towards the extremity of the
natural world but never claims that ¬re comes to rest at the extremity of
the natural word. For Aristotle, the extremity of the natural world is
occupied by the simple body which is naturally moved in a circle “ the
<celestial> simple body. This body is emphatically not a boundary
preventing the sublunary simple bodies from getting dispersed. There is
no room in the natural world as it is understood by Aristotle for un-
bounded motions: that which is in motion is always capable of being at
rest, and that which is at rest is always capable of being in motion.

18 I borrow the phrase “hierarchical conception of body” from an unpublished paper that Alan Code
presented at the USC/Rutgers Annual Conference in Ancient Philosophy in December 2000. As
Code points out, this conception of body extends outside the realm of nature. Natural bodies are
in fact the material principles of arti¬cial bodies “ artifacts are made of natural bodies. The
consequence is that earth, water, air, and ¬re, by being the material principles of a natural body,
are the material principles of an arti¬cial body as well.
19 Aristotle speaks as if there were something that is the extremity and the center of the natural
world. In other words, he speaks as if the center and the extremity of the natural world had reality
prior to, and independent of, the simple body that moves towards them. But since the center and
the extremity are places, and a place is always the limit of a body, they cannot exist independently
of the body they contain. On this point, see Waterlow (1982: 115).
Aristotle and the Science of Nature
42
Aristotle is famously committed to the view that nature is always an
internal principle of motion and rest. In other words, motion and rest
are facets of the same nature “ the nature of something.20

the science of nature is concerned for the most part
with bodies and magnitudes
Let us return now to the opening sentence of the DC:
The science of nature is clearly concerned for the most part with bodies and
magnitudes, the affections and motions of these, and the principles of this kind
of substance (DC 268 a 1“6).
This characterization of the science of nature is to be understood in the
light of Aristotle™s conception of science. Each Aristotelian science is
about a certain department of reality, namely about a certain genos.21
From the Analytics we know that each Aristotelian science provides a
demonstration from proper principles of the per se attributes of the ousia.
Right at the beginning of the DC Aristotle is offering a characterization of
the science of nature that makes use of this conceptual apparatus: the
science of nature is concerned with a speci¬c department of reality “
bodies and magnitudes “ and the job of the student of nature is to provide
an explanation of the per se attributes of bodies and magnitudes “
affections and motions “ on the basis of appropriate principles. What
are the bodies and magnitudes Aristotle is thinking of at the beginning of
the DC? Compare this passage with the beginning of Zeta 2, where
Aristotle offers bodies as the most obvious example of ousia:
(1) ousia is thought to belong most obviously to bodies; (2) and so we say that
both animals and plants and their parts are substances, (3) and so are natural
bodies such as ¬re and water and earth and everything of that sort, (4) and
all things that are parts of these or composed of these (either of parts or of the
whole bodies), for example the heaven and its parts, stars and the moon and the
sun (Zeta 1028 b 8“13).
In this passage we are encouraged to think of the heaven in its entirety as
well as the stars, the sun, and the moon as bodies “ clause (4). For


´ ´
20 Cf. Bodnar (1997b: 81“117). In this excellent article, Bodnar rightly insists on the fact that the
simple bodies possess a fully ¬‚edged nature, namely a nature that is a principle of both motion
and rest. I agree with his arguments against recent interpretations suggesting that the nature of a
simple body is somehow incomplete. See Gill (1989: 236“40) and Cohen (1994: 150“9).
21 On this point see chapter 1, “The unity, structure, and boundaries of Aristotle™s science of nature.”
Bodies 43
Aristotle, they are made of a special simple body. This body is distinct
from, and not reducible to, earth, water, air, and ¬re. The sun, the moon,
and the rest of the stars form a distinct class of bodies: the class of the
celestial bodies. Plants and animals open the list of the sublunary bodies.
They are a second class of bodies “ clause (2). Aristotle thinks of them as a
certain arrangement of bodily parts that are themselves composed of other
bodies. Aristotle calls earth, water, air, and ¬re natural bodies “ clause (3),
but he does not want to suggest that they are the only natural bodies.
Quite the contrary. The natural world as it is conceived by Aristotle is
composed of natural bodies. These natural bodies can be divided into
celestial and sublunary bodies. In the sublunary world, Aristotle admits a
further distinction into simple and composite natural bodies. Finally,
within the natural bodies he distinguishes the natural bodies that have
life, animals and plants, from the natural bodies that do not. By calling
earth, water, air, and ¬re natural bodies, Aristotle in all probability wants
to suggest that they are the natural bodies. Moreover, they are the natural
bodies because they are the ultimate material principles of all the natural
bodies populating the sublunary world.
By saying that the science of nature is concerned with bodies and
magnitudes, Aristotle offers a compressed but precise description of the
object of this science. Compare the list of natural bodies I have just
offered with the program of inquiry into the natural world presented at
the beginning of the Meteorology. Note that at the beginning of the DC
Aristotle adds a signi¬cant quali¬cation: the science of nature is con-
cerned for the most part with bodies and magnitudes. In all probability, the
addition is designed to remind the reader that the student of nature has to
deal with things such as place and time.22 If place is for Aristotle the limit
of a body, time is the measurement of the motion of a body. To put it in
another way, we learn nothing about place and time independently of the
fact that there is a body and this body is liable to motion and is
immediately surrounded by other bodies. The following sentence may
also be intended to cast some light on Aristotle™s reasons for the addition
of “for the most part”:
For of the things constituted by nature some are bodies and magnitudes, others
have body and magnitude, others are principles of those that have <body and
magnitude> (DC 268 a 4“6).



22 Cf. Simpl., In DC 7. 20“8.
Aristotle and the Science of Nature
44
The text is dif¬cult, but plants and animals presumably are the things that
have body and magnitude.23 If this is correct, Aristotle is not only
committed to the view that animals and plants are living bodies but also
to the view that they have (a) body. This further view is to be understood
in the light of Aristotle™s distinctive conception of the soul. In the DA,
Aristotle explicitly takes the view that animals and plants are natural
bodies that have life (412 a 13“15). There he is also committed to the view
that the provider of life, the soul, is not a body (412 a 17). It is notoriously
dif¬cult to provide an adequate description of the position of Aristotle
and do justice to his distinctive attempt to avoid both dualism and
reductionism. On the one hand, Aristotle seems to be persuaded that
animals and plants are living bodies, and the provider of life, the soul, is
nothing over and above those living bodies; on the other, he consistently
argues against the corporeality of the soul. For him, animals and plants
are not just bodies but ensouled bodies. As this line of argument would
take me beyond our current scope, it has to be suf¬cient here to say that, if
the incipit of the DC is to be taken as a compressed but adequate
description of the subject-matter of the science of nature, it cannot be a
surprise to discover that Aristotle makes an effort to do justice to this
crucial aspect of his doctrine of the soul.24
An Aristotelian science characteristically assumes the reality of its
subject-matter. The prologue to the DC con¬rms that the science of
nature is no exception to the rule. The student of nature is concerned
with bodies on the crucial assumption that bodies exist. Signi¬cantly
enough, the DC does not begin with an attempt to argue for the existence
of bodies but with a certain characterization of body “ Defs. 1“3. Since we
are at the beginning of the study of nature, this characterization is very
unlikely to provide us with an adequate conception of what a body is. We
have to go through the DC and the rest of the natural writings, including


23 Cf. Simpl., In DC 6. 34“7. 3.
24 Sharples (1998: 42) suggests an alternative translation of the passage, which has the advantage of
restoring the parallel with the previous sentence. According to the previous sentence, the science
of nature is concerned with (i) bodies and magnitudes, (ii) their affections, (iii) their principles.
Now Aristotle would continue as follows: of the things constituted by a nature (i) some are bodies
and magnitudes, (ii) others are things that bodies and magnitudes have, and (iii) others are
principles of these. Perhaps the Greek ta d™echei soma kai megethos can be interpreted either as
¯
“others have body and magnitude” or “others are ones that body and magnitude have.” But the
parallel passage we ¬nd at the beginning of the third book of the DC con¬rms that the traditional
interpretation is the right one:
the study of nature is concerned for the most part with bodies: for all natural substances are either
bodies or with bodies and magnitudes (298 b 2“4).
Bodies 45
the biological writings, to form this conception and to realize that a body
is minimally a three-dimensional magnitude. At the same time the initial
de¬nition cannot be solely a nominal de¬nition. It must grasp some
salient feature shared by all bodies. In the DC, Aristotle emphatically
claims that even a small deviation from the truth at the beginning of the
inquiry may make a great, if not an immense, difference at the end of the
inquiry (271b 1“17). Evidently, he is persuaded that a small mistake made
at the beginning of the inquiry may ruin the entire enterprise. It is
signi¬cant, I think, that Aristotle makes this comment with reference to
the belief in the existence of indivisible magnitudes. This comment sheds
some light on the reasons that may have motivated Aristotle to begin the
DC with a characterization of bodies in terms of continuity and divisibil-
ity. The fact that Aristotle always thinks of each body as part of a larger
system of bodies explains why he concludes the prologue to the DC with
the visionary sketch of the natural world as a uni¬ed whole of bodies that
are interacting in a certain way.25
A ¬nal clari¬cation is needed. Aristotle states that the science of nature
is concerned for the most part with bodies and magnitudes. But why
magnitudes? Doesn™t the student of nature study bodies only? Note, ¬rst
of all, that the expression “body and magnitude” is often used in contexts
in which the ambiguity of body between soma and stereon is crucial for the
¯
26
argument. Secondly, and more importantly, in antiquity this ambiguity
was usually exploited to provide a geometrical account of bodies. We have
already seen that in the Timaeus Plato provides a de¬nition of the body in
terms of three-dimensionality: a body also has depth (53 c 5“6). This
de¬nition allows Plato to switch from soma to stereon and vice versa.27
¯
This de¬nition is functional to a certain geometrical reconstruction of
reality, and in the Timaeus a geometrical structure is in fact assigned to
earth, water, air, and ¬re. This structure consists of regular polyhedra,
which are constructed out of two elementary triangles (the half-equilateral
and the half-square isosceles). The general result is that each body is
correlated with a regular polyhedron. More precisely, any part of earth
consists of cubes, which are constructed out of half-square isosceles
triangles. Any part of ¬re consists of pyramids, which are constructed

25 I refer the reader to chapter 1, “The unity, structure, and boundaries of Aristotle™s science of
nature,” for the signi¬cance of the quali¬cation “in a certain way.”
26 See, for example, the discussion of the Democritean arguments against the possibility that body
and magnitude are divisible at any point (GC 316 a 14“16 ¼ DK 68 a 48 b).
27 In the Timaeus the word soma is used to refer to both earth, water, air, and ¬re (e.g. 53 c 4“5, 57 c
¯
7“8) and the regular solids (e.g. 54 b 4“5, 55 a 7, 56 d 7, 56 e 2).
Aristotle and the Science of Nature
46
out of half-equilateral triangles. Finally, any part of air and water consists
of octahedra and icosahedra respectively, which are both constructed out
of half-equilateral triangles. Plato makes it also clear that the geometrical
structure is meant to account for the natural phenomenon of intertrans-
formation of these bodies. Fire, air, and water can be transformed into
one another because pyramid, octahedron, and icosahedron, that is to say
the solids they are associated with, are all constructed out of the same
triangle, the half-equilateral triangle. On the contrary, earth cannot be
transformed into water, air, or ¬re (and vice versa), because the cube, the
solid that is associated with earth, is constructed out of a different kind of
triangle, the half-square isosceles triangle. Plato is the champion of the
weak version of the theory of intertransformation. According to this
version, earth can be dissolved and dispersed in water, air, and eventually
¬re, but it can never be transformed into any one of them.28 On the
contrary, Aristotle is the champion of the strong version of this theory.
For Aristotle (and later on, for the Stoics),29 earth is included in the circle
of intertransformation and all simple bodies can be transformed into one
another. For Aristotle, the material principles of natural bodies are
themselves natural bodies, and more generally the material principles of
bodies are themselves bodies. The Timaeus is representative of a diamet-
rically opposed view. According to Plato, the material principles of bodies
are not bodies. Aristotle makes this assumption explicit in his critique of
the Platonic doctrine of intertransformation. He reads the Timaeus as
claiming that the material principles of bodies are triangular surfaces (306
a 23“6). For him, the phenomenon of intertransformation as it is de-
scribed in the Timaeus would involve a process of resolution into tri-
angles. This interpretation entails notable dif¬culties for Plato. First of all,
if the peculiar feature of a body is three-dimensionality, how is it possible
that a body (more so if it is a natural body) can be generated from surfaces
that do not possess this feature? Secondly, if bodies can be reduced to
mathematical entities, why must one stop precisely at these particular
surfaces, the triangular surfaces? Why cannot these surfaces be reduced to
lines, and ¬nally lines to points?
The use Plato makes of geometry in the Timaeus is open to different
interpretations, and Aristotle™s is only one among the several that are
possible. It is signi¬cant, I think, that a different reading of the Timaeus

28 For a helpful presentation of this geometrical reconstruction see Vlastos (1975: 66“115).
29 For the Stoic theory of elemental change and its cosmogonic signi¬cance see Stob., Ecl. 1.10
(¼ Arius Didymus fr. 21 Dox. gr. ¼ SVF ii 413 ¼ LS 47 a).
Bodies 47
was advanced by Proclus in a work that he wrote in defense of Plato.
Though this work is now lost, a few citations are preserved by Simplicius
in his commentary on the DC.30 Proclus defended Plato by replying to
each of the objections moved by Aristotle. In particular, he defended
Plato against Aristotle™s criticism that the account of intertransformation
ends up with the claim that bodies are generated out of triangular
surfaces. Proclus conceived of the elementary triangles as solids, and read
the Timaeus as claiming that these triangles possess also depth; that is,
they possess a minimal thickness.31 If one follows the reading suggested
by Proclus, one must take three-dimensionality as a primitive feature.
Interestingly enough, there is little yet signi¬cant evidence that this
interpretation was not a late invention. We ¬nd it already in Epicurus,
who criticized the Platonic doctrine of body in his On Nature. Few
fragments survive of the original thirty-seven volumes that composed this
monumental work. Herculaneum Papyrus 1148 preserves fragments from
book xiv, which contained, among other things, a critique of the doctrine
of body advanced in the Timaeus. An edition of this book has recently
been published by Leone (1984). Column xxxviii of her edition suggests
that Epicurus took the Platonic triangles as indivisible three-dimensional
magnitudes.32 This interpretation has an obvious advantage: if the elem-
entary triangles possess a minimal thickness, they satisfy the de¬nition of
body offered at 53 c 5“6. In other words, these triangles also have depth.33

30 Simpl., In DC 648. 19“28. Simplicius quotes extensively from this book, though he never cites the
title of it. But in his commentary on the Timaeus Proclus himself tells us that he wrote a work
entitled Inquiry into Aristotle™s Objections against the Timaeus (In Tim. iii 279. 2“3). There is no
reason to think that the excerpts preserved by Simplicius come from a different work. On Proclus
and his defense of the doctrine of the Timaeus, see Siorvanes (1996).
31 The hypothesis of a minimal thickness of the elementary triangles was in¬‚uential in antiquity. We
¬nd a reference to this hypothesis both in Simplicius and in Philoponus. Cf. Simpl., In DC 563.
26 “ 564. 3, 573. 3“11, 577. 17“19; Philoponus, In GC 210. 12“16.
32 This is not the place to enter into a discussion of Epicurus™ criticism of the Timaeus. But the fact
that the elementary triangles of the Timaeus are thought of as possessing a minimal thickness is
enough evidence to discourage any attempt to establish a connection between Epicurus™
objections and Aristotle™s critique of Plato in the DC.
33 Even these few observations are enough to emphasize that it is not suf¬cient to attribute the label
of atomism to the Timaeus. Ancient atomism is not a monolithic doctrine but a constellation of
different positions. If it is true that the atomists share the hypothesis that there are entities that
cannot be further analyzed, it is also true that these entities can be conceived in different ways. I
only add that in the DC Aristotle is witness to a further version of atomism in which the atomic
entities are thought of as solids (305 b 28 “ 306 a 1). We know nothing about this particular
version of ancient atomism. Even if it is possible to conjecture that it is an Academic variation of
the doctrine put forward in the Timaeus and aimed at rendering this doctrine more acceptable, we
cannot exclude that it is only a theoretical possibility taken into account by Aristotle for reasons of
completeness. In any event, it is signi¬cant how in this case the atomic entities are not triangles
but regular polyhedra.
Aristotle and the Science of Nature
48
Aristotle may, or may not, be right in reading the Timaeus literally,
but he is surely right when he says that the doctrine of body of the
Timaeus commits Plato to atomism. Aristotle explicitly mentions
Democritus (307 a 16“17), and makes it clear that the Platonic account
is somehow a re¬nement and elaboration of the theory of Democritus
(306 a 26 “ b 2).
Let us return to the opening line of the DC. The fact that the Timaeus
is a polemical target of the DC explains why Aristotle begins this treatise
with a minimal notion of body: a notion that, among other things, does
not distinguish bodies from geometrical solids. Provisionally, Aristotle
accepts the ambiguity of body between soma and stereon. What matters
¯
to him, at least for the moment, is clarity about the fact that bodies
are magnitudes, and magnitudes are always divisible into ever-divisible
parts.

bodies and elements
Earth, water, air, and ¬re are the ultimate material principles of the
sublunary natural bodies, and precisely for this reason Aristotle refers to
them as the natural bodies par excellence. But at times Aristotle refers
to earth, water, air, and ¬re using the term element “ in Greek stoicheion.
In other words, earth, water, air, and ¬re are not only the natural bodies
par excellence; they are also the elements of the sublunary world. In order
to understand what the term stoicheion is intended to evoke it is necessary
to go back to the use of this term in the Platonic dialogues. According to
Simplicius (who, as he himself confesses, depends on Eudemus of Rhodes
for this information34) Plato was the ¬rst to introduce this term into the
technical vocabulary of Greek cosmology.35 Interestingly enough, in the
Platonic dialogues this term is normally used in reference to the letters of
the alphabet. Philebus 17 a “ 18 d is certainly among the more signi¬cant
passages regarding this subject. Here Socrates attributes to the god “ or
demigod “ Theut ¬rst the discovery of the vowels and then the discovery
of the other sounds that are not vowels but that can still be pronounced
(probably sounds such as /s/ and /m/). After the discovery of the vowels
and these other sounds, Theut would have demarcated a third group of



34 Simpl., In Phys. 7. 10“15 (Wehrli, Eudemos fr. 31).
35 Empedocles called his four principles roots, rhizomata.
¯
Bodies 49
mute sounds different from both (probably the consonants). Finally,
Theut would have given a name to each sound and would have called
the sounds thus distinguished letters “ in Greek stoicheia. Evidence that
the use of stoicheion in a cosmological context is derived from a re¬‚ection
on language is implicitly offered in a much celebrated passage from the
Timaeus. Here Plato exploits the letters of the alphabet in order to
illustrate one of the most characteristic theses of the entire dialogue.
According to Plato, the case of earth, water, air, and ¬re is not analogous
to that of the letters of the alphabet. Strictly speaking, their case is not
even remotely similar to that of the simplest composites that can be
formed into combinations taken from the letters of the alphabet: the
syllables (48 b 7 “ c 1). I have already shown how, in the Platonic
geometrical reconstruction, these four bodies are associated with four
regular polyhedra “ earth to a cube, water to an icosahedron, air to an
octahedron, and ¬nally ¬re to a pyramid “ and how, in their turn, these
four polyhedra are constructed out of two elementary triangles. According
to Plato, anyone who says that earth, water, air, and ¬re are the principles
of everything is committing an error. The true principles are the two
elementary triangles, which are really the letters of which the words, the
propositions, and, ultimately, the entire book of nature are composed. In
this passage from the Timaeus, we ¬nd, probably for the ¬rst time, the
indispensable conceptual elements for the elaboration of the well-known
and far-reaching metaphor of nature as a book. After Plato, the associ-
ation between the study of language and the study of nature is put
forward again on several more occasions. From this point of view, I ¬nd
the following testimony to be exemplary with regard to the Pythagorean
school of the Hellenistic age. The genuine philosopher, Sextus says,
resembles the scholar of language: just as the latter is concerned primarily
with the letters of the alphabet from which all verbal expressions can be
constructed, going from the most complex down to syllables, so too the
true student of nature, who concerns himself with everything, must above
all examine the elements (stoicheia) from which nature is constructed.36
This testimony is placed at the beginning of a passage that concludes with
the thesis that the principles or ¬rst elements of reality are the monad and

36 Sextus Emp., M x 249“50: “They [¼ the Pythagoreans] say that those who are engaged in
philosophy are like those who are concerned with language. The latter ¬rst examine the words
(the language is formed from words), and since the words are formed from syllables, they ¬rst
investigate the syllables; and as the syllables are resolved into the elements of the written speech,
they investigate these ¬rst. So likewise the true student of nature, as the Pythagoreans say, when
investigating the all, ought in the ¬rst place to establish the elements the all can be resolved into.”
Aristotle and the Science of Nature
50
the dyad.37 In an ef¬cacious way it shows how, from a certain point
onward, the association between language and reality has become a
commonplace in antiquity. It also documents how this association is
crucial for the derived use of stoicheion in the context of natural science.
It is a derived use that, after Plato and thanks mainly to Aristotle and to
the Stoic tradition, has entered, fully ¬‚edged, into the history of ideas.38
Therefore when Aristotle uses the term element in referring to earth,
water, air, and ¬re, he must be aware of the association between language
and nature suggested in the Timaeus and evoked, although in a less
explicit manner, in the Philebus. Aristotle must also accept the implicit
intuition involved in the association. Even for Aristotle, the physical
reality must be reducible to a ¬nite number of original components,
which represent the base of departure for the construction “ following
combinatory processes that imply also the alteration of the properties of
the initial components “ of more complex entities. More speci¬cally,
earth, water, air, and ¬re are the original components of each sublunary
natural body, and as such they are present in some ratio in each of these
bodies. Interestingly enough, Aristotle does not con¬ne his use of the
term stoicheion to the sublunary world. He is able to refer to the celestial
simple body as the ¬rst of the elements, to proton ton stoicheion, or the ¬rst
¯ ¯ ¯
39
element, to proton stoicheion. It is important to realize that this particular
¯
use of the term stoicheion is derived from the use of stoicheion with
reference to earth, water, air, and ¬re. The use of stoicheion in the context
of the physics of the sublunary world has not yet lost his intended force:
the elements are the ingredients that can be combined to form a more


37 This passage has often been considered an indirect testimony on Plato™s unwritten doctrines. See
¨
Testimonia Platonica 32 in Gaiser (1962) and Testimonia Platonica iii 12 in Kramer (1989).
38 A history of the notion of stoicheion was attempted by Diels (1899). This work initiated a debate
that continued for half a century. See Voll-Graff (1949: 89“115), Koller (1955: 161“74), and above
all Burkert (1959: 167“97). This last article represents the most mature fruit from this debate. It is
not necessary here to go into the details of Burkert™s proposal, which in many ways recti¬es or
corrects the thesis advanced by Diels. It is enough to remember that the word stoicheion was
coined in the second half of the ¬fth century bce, and it is indisputably tied to the linguistic
observation. Its use in a cosmological context is therefore derived. Moreover, there is no reason to
doubt Eudemus™ testimony that attributes the paternity of this use to Plato. Burkert nevertheless
makes note of how Eudemus™ testimony attributes to Plato the usage of stoicheion in a physical
context, but not necessarily in reference to earth, water, air, and ¬re (cf. Simpl., In Phys. 7. 12“15).
In light of Tim. 48 b 7 “ c 1, Eudemus™ caution is more than understandable. For the use of
stoicheion in reference to earth, water, air, and ¬re we must search elsewhere. First Aristotle and
then the Stoics codi¬ed and made traditional this particular usage. For the Stoic tradition, the
most signi¬cant testimony is collected by Arius Didymus and preserved in Stobaeus. Cf. Stob.,
Ecl. i 129. 1 “ 130. 20 (¼ Arius Didymus, fr. 21 Dox. gr. ¼ SVF ii 413 ¼ LS 47 a).
39 See DC 298 b 6; Meteor. 338 b 2, 339 b 16“17, 340 b 11.
Bodies 51
complex yet intelligible reality. Since the celestial world is part of the
natural world, the celestial simple body can surely be regarded as an
element or a stoicheion of this department of reality, even though, strictly
speaking, it does not enter into any of the combinations that are formed
from earth, water, air, and ¬re.40

the hellenistic conception of body
In these pages I have made an effort to reconstruct a few notions of body
that play an important role in the science of nature as it is conceived by
Aristotle. Among other things, I have tried to distinguish the notion of
natural body from that of mere body. I now wish to take a wider
perspective and bring to light the different strategies that in antiquity
were adopted to distinguish natural bodies from mathematical entities.
The testimonies that Sextus Empiricus collects in M i and in PH iii are an
ideal point of departure for an investigation of this type. Among the
de¬nitions of body reported in M i 21 there is one that Sextus attributes
explicitly to Epicurus. To the usual three-dimensionality, this de¬nition
adds an ingredient that we have not encountered in Aristotle: antitupia.41

40 This does not explain, however, why the celestial simple body is called the ¬rst element (or the
¬rst of the elements). I shall return to Aristotle™s language and its signi¬cance in the Epilogue.
41 Sextus Emp., M i 21: “(1) body is either a conjunction by aggregation of magnitude, shape and
antitupia, as Epicurus says; (2) or that which is extended in three dimensions, namely length,
breadth, and depth, as the mathematicians say, (3) or that which is extended in three dimensions
and has antitupia, again as Epicurus says, so that in this way he can distinguish <body> from
void, (4) or antitupos mass, as others say.” In this passage Sextus reports four de¬nitions of body,
two of which are explicitly attributed to Epicurus. The ¬rst Epicurean de¬nition involves: (i)
magnitude, (ii) shape and (iii) antitupia “ clause (1). In the second, only two items are recorded:
(i) three-dimensionality and (ii) antitupia “ clause (3). Here I con¬ne myself to this second
de¬nition of body. Its usage is amply attested to by Sextus. See Sextus Emp., PH iii 38; 126; 152
and M ix 226. Elsewhere we are given a third Epicurean de¬nition that makes reference to the
following three ingredients: (i) size, (ii) shape, and (iii) weight. See [Plutarch], Placita 887 e 3“4
¨
(¼ Aetius i 3. 18 partim). This de¬nition and the previous one seem to be fused in M x 240. In this
last case, body is that which is endowed with (i) magnitude, (ii) antitupia, and (iii) weight. In our
passage, Sextus gathers two other de¬nitions of body, the ¬rst of which makes reference only to
three-dimensionality “ clause (2). It is signi¬cant, I think, that Sextus attributes this de¬nition to
the mathematicians. The fourth and last de¬nition makes reference to (i) mass and (ii) antitupia “
clause (4). This con¬rms, at least indirectly, the importance of the reference to antitupia in the
Hellenistic de¬nitions of body. In his recent translation of M i, David Blank suggests that this last
de¬nition be considered an interpolation. Cf. Blank (1998: 96n39). In his view, this de¬nition is
out of place, and its presence can be explained only by hypothesizing the intervention of someone
with a good knowledge of the doxographical tradition. The same de¬nition is found, again, in
[Plutarch], Placita 882 f 4, and Stob., Ecl. i 140. 15. In reality, if mass and antitupia are considered
as two distinct ingredients (as I have implicitly proposed), then it is not very dif¬cult to assimilate
this de¬nition into the previous ones. It too is construed as a conjunction of a certain number of
ingredients (in this case two).
Aristotle and the Science of Nature
52
The property to which Epicurus refers is the one that bodies exhibit when
they are touched and that may be described as resistance to contact. The
way in which Sextus reports this same de¬nition in PH iii 39 nevertheless
suggests that its function is decidedly more general than the one that he
recognizes in M i 21. In PH iii 39 the de¬nition of body appears at the end
of a conventional series of de¬nitions of mathematical entities: point,
line, and surface. According to some, Sextus says, in order to move from
the notion of surface to that of body, it is not suf¬cient to add depth,
bathos; one must refer also to antitupia.42 The impression one obtains is
that the latter ingredient is indispensable because the bodies being referred
to are not bodies in general but are instead natural bodies. They can be
distinguished from the mathematical entities that we generally call solids
only if we attach to depth an ingredient that is not shared by these latter
ones. Although Sextus tells us nothing about the identity of those advo-
cating this position, in light of M i 21, it would seem natural to assume
that they are Epicureans. The de¬nition of body that calls upon three-
dimensionality and antitupia is contrasted by Sextus to the Stoic de¬n-
ition that we know to have been formulated by Zeno of Citium.
According to this de¬nition, body is that which is capable of acting or
being acted upon.43 However, the situation is decidedly more compli-
cated. If it is true that these two de¬nitions are juxtaposed also in the
testimony collected in the Philosophical History traditionally attributed to
Galen,44 it is almost certain that this comparison re¬‚ects the more general
comparison between Epicureanism and Stoicism. Even if the de¬nition of
body in terms of three-dimensionality and antitupia is never attributed to
Zeno of Citium and his successor Cleanthes, it is not dif¬cult to ¬nd
testimonies that assign this same de¬nition to the Stoics in general. As a
matter of fact, it is impossible to con¬ne the use of this de¬nition solely to
the Epicureans. Presumably, this de¬nition was an intellectual heritage in
the Hellenistic age, and in the speci¬c case of the Stoics, at least from a
certain point onward, it was placed alongside the traditional de¬nition of
body in terms of acting and being acted upon.45
Once it is ascertained that the de¬nition of body in terms of three-
dimensionality and antitupia enjoyed great popularity in the Hellenistic
42 Sextus Emp., PH iii 39: “(1) Others say that body is that which is extended in three dimensions
and has antitupia. (2) For they say that point is that which has no parts, line length without
breadth, plane length with breadth; (3) when this latter gains both depth and antitupia there is a
body “ which is our present subject “ composed of length, breadth, depth, and antitupia.”
43 This de¬nition of body is explicitly ascribed to Zeno in Cicero, Acad. i 39 (¼ SVF i 90 ¼ LS 45 a).
44 [Galen], Hist. philos. 23 (¼ Dox. gr. 612.19 “ 613.2).
45 For this claim see Mansfeld (1978: 134“78).
Bodies 53
time, there remains the task of clarifying exactly what its speci¬c function
was. The context of Sextus™ two testimonies is illuminating in this regard.
In M i 21, the de¬nition of body in terms of three-dimensionality
and antitupia appears immediately after a de¬nition that makes use of
the notion of three-dimensionality only (and which Sextus attributes
signi¬cantly to the mathematicians). In PH iii 37, the same de¬nition is
preceded by the purely mathematical ones of point, line, and surface.
Something similar occurs also in the testimony gathered in the Philo-
sophical History. Even here the de¬nition of body in terms of three-
dimensionality and antitupia is found next to that of point, line, and,
above all, body as three-dimensional entity. The context in which the
notion of antitupia is usually mentioned seems to suggest that its primary
function is to introduce an element capable of unraveling the ambiguity
of the Greek term soma, differentiating natural bodies from the corres-
¯
ponding three-dimensional mathematical entities. What other reason
would [Galen] have for mentioning the de¬nition of body as an entity
extended in length, breadth, and depth, after having already made refer-
ence to two de¬nitions of body, one in terms of acting and being acted
upon and the other in terms of three-dimensionality and antitupia? The
only (convincing) reason, at least to my mind, is that he wishes to
differentiate the latter two de¬nitions of body, which belong to the
province of the science of nature, from the ¬rst de¬nition of body, which
is purely mathematical.46 If I am right, the Epicureans as well as the Stoics
have recourse to both a general and a speci¬c notion of body. The general
notion can be formulated in the following way: body is that which extends
in three dimensions “ length, breadth, and depth. It is easy to see how this
characterization is equivalent to the Defs. 1 and 2 introduced in the
prologue to the DC. By this point I hope to have shown that a de¬nition
of this type does not permit a distinction between solids and natural
bodies. It is precisely for this reason that the Stoics as well as the
Epicureans (and Aristotle too) adhere to a more speci¬c de¬nition of
body. This second de¬nition enables them to differentiate the case of the
Pyramid of Cheops from that of the corresponding geometric ¬gure. In


46 The idea that, for the Stoics, three-dimensionality was not by itself suf¬cient to characterize a
physical body seems also to be indirectly con¬rmed by a testimony of Diogenes Laertius about
the Stoic Apollodorus of Seleucia. In this case, the entity that extends itself in three dimensions is
not called soma but stereon soma (where stereon quali¬es soma and speci¬es the type of body that is

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