Aristotle's de Caelo III: Introduction, Translation and Commentary [Translation ed.] 3515103368, 9783515103367

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Theokritos Kouremenos Aristotle’s de Caelo Γ

PALINGENESIA Schriftenreihe für Klassische Altertumswissenschaft

Begründet von Rudolf Stark herausgegeben von CHRISTOPH SCHUBERT –––– Band 100

Theokritos Kouremenos

Aristotle’s de Caelo Γ Introduction, Translation and Commentary

Franz Steiner Verlag

Coverabbildung: Phönix in einem Mosaik aus Antiochia am Orontes, jetzt im Louvre. Fondation Eugène Piot, Monuments et Mémoires, publ. par l’Académie des Inscriptions et Belles-Lettres 36, 1938, 100.

Bibliografische Information der Deutschen Nationalbibliothek: Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar. ISBN 978-3-515-10336-7 Jede Verwertung des Werkes außerhalb der Grenzen des Urheberrechtsgesetzes ist unzulässig und strafbar. Dies gilt insbesondere für Übersetzung, Nachdruck, Mikroverfilmung oder vergleichbare Verfahren sowie für die Speicherung in Datenverarbeitungsanlagen. Gedruckt auf säurefreiem, alterungsbeständigem Papier. © 2013 Franz Steiner Verlag, Stuttgart Druck: Offsetdruck Bokor, Bad Tölz Printed in Germany

μὴ εἰκῆ περὶ τῶν μεγίστων συμβαλλώμεθα Heraclitus, DK 22 B 47

CONTENTS Acknowledgments … … … … … … … … … … … … … … … … … … … ix Introduction 1. Aristotle’s cosmos … … … … … … … … … … … … … … … … … 11 2. The first simple body … … … … … … … … … … … … … … … … … 12 3. The Empedoclean simple bodies and their compounds … … … … … … 13 4. Celestial objects and the Empedoclean simple bodies … … … … … … 14 5. The contents of Cael. Γ … … … … … … … … … … … … … … … … 15 6. The present translation and commentary … … … … … … … … … … … 17 Translation … … … … … … … … … … … … … … … … … … … … … … 19 Commentary … … … … … … … … … … … … … … … … …… … … … … 33 Bibliography … … … … … … … … … … … … … … … … … … … … … 113 Index of passages … … … … … … … … … … … … … … … … … … … 116

ACKNOWLEDGMENTS I would like to thank Prof. Dr. Christoph Schubert for accepting this monograph in the Palingenesia series and his helpful comments, and the staff at Franz Steiner Verlag for their professional help. I would also like to express once again my gratitude to my friend and former student Alexandros Kampakoglou for making available to me a number of bibliographical items which otherwise I would not have obtained easily. Finally, I want to record here, too, my special indebtedness to my wife, Poulheria Kyriakou. I owe to her much more than having been spared mistakes and infelicities thanks to the selfless care with which she once again read my work. Theokritos Kouremenos Aristotle University of Thessaloniki

INTRODUCTION In Mete. A 2, 339a11–27, Aristotle asserts that there are five principles of material things, five kinds of matter, or body, continuous in all three dimensions and unanalyzable into material constituents. Of these five simple bodies, one makes up the celestial objects, whereas the other four, which exist because of four, here unspecified, principles, make up the realm of the cosmos near the Earth. They are the “traditional” elements Empedocles of Acragas introduced into physics in the fifth century BC: fire, air, water and earth. The opening of Cael. Γ announces that these simple bodies are the topic of the book. In it, however, we do not find the theory of the bodies at issue, though it is certainly presupposed. The following account is based, often almost verbatim, on Kouremenos (2010) ch. 1.

1. ARISTOTLE’S COSMOS The near-Earth realm of the cosmos as conceived by Aristotle is circumscribed in effect by the circular orbit of the Moon around the Earth: it is a sphere whose great circle is the lunar orbit (see Mete. A 3, 340b6–10). The interior of this sphere is stratified into an outermost spherical shell of fire, which is a highly flammable and extremely subtle gas (the fire of everyday experience is elemental fire undergoing combustion; see Mete. A 3, 340b19–23, and 4, 341b6–22). Next comes a spherical shell of air, and then a spherical shell of water blanketing almost all the surface of the Earth, a globular clump of the homonymous simple body which is homocentric with the spherical cosmos. Beyond the near-Earth, or sublunary, realm of the cosmos are the heavens: apart from the Moon, they contain the Sun, the five planets known in antiquity (Mercury, Venus, Mars, Jupiter and Saturn) and, finally, the fixed stars. Beyond them is the outermost boundary of the cosmos, a spherical surface analogous to the celestial sphere of astronomy (Aristotle demonstrates the stratification of the cosmos into concentric spherical layers in Cael. B 4). According to GC B 8, all objects in our close surroundings are ultimately made up of all four Empedoclean simple bodies, bound together in insignificant amounts by comparison to how much of each exists in the cosmos. As it is, though always neatly stratified on the cosmological scale, the four traditional simple bodies are not separated at any given time on much smaller scales. But the simple body which is the sole constituent of the celestial objects is completely separated from the other four simple bodies. It is called “the first element” in Mete. A 3, 339b16–19, where it is made clear that it not only makes up the celestial objects but also fills up the heavens. These lines are actually a note to an earlier discussion, in the de Caelo, of the nature of this simple body and its role as filler of the heavens.1 The introduction of a fifth element by Aristotle is one of his most notable contributions to physics. 1

For the priority of the de Caelo see Kouremenos (2010) 77 n. 53.

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2. THE FIRST SIMPLE BODY The existence of a fifth element, which in Cael. B 7, 289a11–19, is said to be the filler of the heavens and the sole constituent of the celestial objects, is demonstrated in Cael. A 2. Its properties are derived in Cael. A 3, where it is called “the first simple body” (270b2–3) because its circular natural motion is prior to the rectilinear natural motion of any Empedoclean simple body.2 A mass of e.g. earth outside its “natural place”, where most of this element is agglomerated at any given time, tends to accrete to the clump–it will move there spontaneously if nothing prevents it. This “natural motion” of the four traditional simple bodies follows radii of the spherical cosmos. Two of these simple bodies, earth and water, move towards the center of the cosmos; insofar as they have the potentiality to do so, they are heavy. But the other two, air and fire, shoot up away from the center and towards the periphery of the cosmos; insofar as they have the potentiality to do so, they are light. Hence there must be another element, the first, any quantity of which has a natural motion which is not radial, towards the center of the cosmos or away from it, but circular, about the center of the cosmos or a point on an axis through it: the whole existing mass of the first simple body cannot rotate like a flat disk about a single point since only one shape, the spherical shell, is appropriate for it. This important detail is not even hinted at in Cael. A 2–3, where Aristotle focuses only on circularity, alluding in passing even to the connection of the first simple body with heavenly objects. But it is obvious from Cael. B 4, 286b10–287a5, the beginning of an argument for the articulation of the cosmos into concentric spherical strata.3 The spherical shell is the only appropriate shape for the whole existing mass of the first simple body because, as this simple body is first in that it is prior to all other bodies, the shape at issue is prior to all three-dimensional shapes, for exactly the same reason that, according to Cael. A 2, 269a18–23, the circle is prior to the straight line, hence circular natural motion to rectilinear. Moreover, since it is circular, the natural motion of the first simple body cannot but be eternal. Assumed quite unambiguously in Cael. A 2, 269b6–9, and 3, 270b20–24, its eternity is explained in Cael. B 1, 284a3–6, on the ground that it is such, i.e. circular, that it lacks an end, unlike rectilinear motion. A quantity of the first simple body moves of its own accord in a circle, just as a stone falls spontaneously. The path of a falling stone is a straight line joining the center of the Earth, near which the stone will 2

3

The natural motion of the first simple body is shown in Cael. B 6 to be uniform, in contrast to the non-uniform zodiacal motions of the planets, the Sun and the Moon (see 288a13–18). For some reason this crucial fact about the first simple body is not even hinted at in Cael. A 2–3. It entails that this simple body makes up only the stars and a diurnally rotating shell whose fixed parts they are: not it but fire must make up the seven remaining celestial objects and fill up the lower part of the heavens in which these celestial objects undergo their zodiacal motions. I argue in Kouremenos (2010) ch. 2 that this must be Aristotle’s view on the cosmological role of the first element in the de Caelo, with the exception of B 7 which agrees with his revised view on this issue in Mete. A 2–3; see also commentary on 298a25–26 and Introduction, 6. On whether Aristotle thinks that the theory of homocentric spheres provides an even approximately true description of the structure of the heavens, be they wholly or partially made up of the first simple body (cf. previous n.), see Kouremenos (2010) ch. 3.

Introduction

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come to rest, and another point, at a finite distance, from which the stone started falling. Motion on such a path, though natural and thus effortless, cannot be eternal. But natural motion in a circle never reaches any boundary where it could come to a halt, for in a circle there is no endpoint, nor did it ever begin, for a circle does not begin at some point from which natural motion could have begun. This is explicitly stated in Cael. B 6, 288a22–27, an argument for the uniformity of the natural motion of the first simple body.

3. THE EMPEDOCLEAN SIMPLE BODIES AND THEIR COMPOUNDS In Cael. B 6, 288a27–b7, a second argument for the uniformity of this natural motion invokes the results established in Cael. A 3: the first simple body is ungenerated, indestructible and, in general, unchangeable. By contrast, on scales much smaller than the cosmological scale, the four Empedoclean elements constantly turn into one another, which is why the cosmic layer of each of them is contaminated with bits of all others, as well as why the first simple body is pure from all traces of foreign elements (see GC B 10, 337a7–15); an exception, Aristotle suggests in Mete. A 3, 340b6–10, is the outermost part of the fire-shell, perhaps the depths of the Earth, too, according to GC B 3, 330b21–331a1. He thinks of the traditional elements as made up each of two qualities, one from each of two pairs of contraries, the four principles associated in Mete. A 2, 339a11–27, with the traditional elements. Earth is dry and cold, water is cold and wet, air is wet and hot, fire is hot and dry (see GC B 3, 331a3–6). Aristotle considers this to be an empirical fact, and since the qualities at issue are shown in GC B 2 to be the simple qualities of perceptible bodies, those that give rise to all other qualities of such bodies, the bodies earth, water, air and fire must be simple, too, the elements of all other perceptible bodies (see GC B 3, 330a30–b7). As operative here, the pairs of contraries cold and hot, wet and dry cannot give rise to a fifth body, hence the first simple body cannot be qualified by their members. But the cold is potentially the hot and vice versa, and the dry is potentially the wet and vice versa: if the elements they characterize come into contact, each quality acts on its contrary, the cold e.g. trying to assimilate to itself the hot while its action is resisted by an opposite reaction, and the overpowered contrary will assimilate itself to the other, which will suffer a reciprocal change from the interaction (GC B 7, 334b20–30). The assimilation of the cold to the hot results in the transformation of e.g. earth into fire since the unaffected dry is shared by both. This is the first of the three mechanisms Aristotle sets out in GC B 4 by which one or two traditional elements can become another, and it is clear why the first simple body is ungenerated and indestructible since the other simple bodies can neither generate it nor be produced from it; hence he thinks he can argue that the first simple body must be exempt from all change whatsoever. 4 4

In assuming that the four traditional elements are subject to generation and decay Aristotle follows not Empedocles but Plato; see commentary on 298b33–299a1. His conception of each of these elements as the combination of two qualities was influenced by medicine; see Longrigg (1993) 220–226.

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Equality of the contraries in power results in the two elements being left intact, but if it is only approximate, the contraries cancel each other out, and are substituted by the properties of a compound, in whose formation the interaction of the two simple bodies results (see again GC B 7, 334b20–30). The nature of compound bodies depends on the relations in which the amounts of the elements making up the compounds stand to one another (see GC A 10, 328a23–31). Thus exact equality of the contraries or sufficiently large inequality for the one to assimilate the other into itself also depends on the relation between the interacting amounts of simple bodies. As it is, since two Empedoclean simple bodies adjacent on the cosmological scale are in contact and thus act on each other in virtue of their contraries, their total amounts in the cosmos must always be in such a ratio that the absorption of one by the other or the formation of a compound out of both cannot happen. This is a crucial assumption in Mete. A 3, 340a1–13, an argument for the existence of a fifth simple body. On much smaller scales, the four Empedoclean simple bodies always turn into one another. Local mass-gains and mass-losses of each of them must thus be assumed to balance out exactly if the mass-ratio of a pair of adjacent elements on the cosmological scale is to be always the same. This presupposes that the ratio between an amount of a traditional simple body and an amount of the cosmically adjacent simple body into which it can turn must be equal to the ratio between the quantities of the two simple bodies existing on the cosmological scale, an assumption stated in Mete. A 3, 340a11–13.

4. CELESTIAL OBJECTS AND THE EMPEDOCLEAN SIMPLE BODIES Precondition for the transformation of the four Empedoclean elements into one another on much smaller scales is evidently the seeding of the cosmic layer of each of them with amounts of all others. According to GC B 10, 337a7–15, this is caused by “the double motion” of the Sun, which thus powers the constant generation of the four traditional simple bodies from one another, or their decay into one another, as well as the incessant formation of compound bodies from all four of them and their decay (see 336a15–b26): the diurnal motion, responsible for a short cycle of variation in the amount of solar heating, and the annual motion in the ecliptic, which superimposes a longer undulation on the short cycle. Aristotle explains in Mete. A 4, 341b6–22, that the Earth generates water-vapor and fire as the Sun heats it. The source of the former is the simple body water upon and within the Earth, of the latter the simple body after which the Earth is named. By the last of the three processes that can turn one, or two, Empedoclean simple bodies into another, the hot in air, intensified by solar heating, assimilates to itself the cold in earth, and the dry in earth assimilates to itself the wet in air: the result is dry and hot fire. Naturally more buoyant than water-vapor and air, it shoots up towards its cosmic layer and, as it interacts with them, it might change into water or air somewhere but absorb these simple bodies to itself elsewhere; still elsewhere its interaction with water might yield earth (the cold in water will assimilate the hot in fire to itself and the dry in fire will assimilate the wet in air to itself: the result will be

Introduction

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cold and dry earth). Through the heating of the adjacent strata of fire and air it induces, the motion of the Sun perpetually seeds the cosmic layer of air with the other three traditional simple bodies, allowing all four of them to interact with one another in all possible ways. A possible role of the planets and the Moon as causes of the constant transmutation of the Empedoclean simple bodies into one another, as well as of the formation of various compound bodies and of complex medium-sized objects from the latter, is hinted at in Cael. B 3, 286b6–9, and in GA ∆ 10, 777b16–778a9, the synodic month is assumed to also regulate the heating of the Earth. Aristotle’s attempt at explaining how the celestial objects produce light and, at least the Sun, heat is problematic. He gives an account in Cael. B 7, 289a19–35, where he assumes that light and heat are produced by friction between the Sun and the air. But since in the earlier section of Cael. B 7, 289a11–19, he also posits that the first simple body, far above air, is the filler of the heavens and the sole constituent of the celestial objects, friction between air and the Sun is impossible.5

5. THE CONTENTS OF CAEL. Γ Setting out the topic of Cael. Γ in ch. 1, Aristotle says that the four traditional simple bodies, two of which are heavy and two light, as well as the things made up of them, i.e. all other stuffs and all medium-sized objects in the core of the cosmos, must be those things to which generation, if it really occurs, is restricted. Thus the introduction to Cael. Γ gives the impression that the treatise will deal with the four Empedoclean simple bodies and, if only at an introductory level, with the generation of their various compounds that the formation of complex medium-sized objects in the near-Earth part of the cosmos requires. As it is, readers are led to expect that Cael. Γ will cover most of the above, that it will be a brief but quite systematic treatment of the four traditional simple bodies following the introduction of the first simple body in Cael. A, which also includes extensive arguments for the finitude and eternity of the cosmos, and the discussion in Cael. B of the eternal heavens. In Cael. Γ, however, Aristotle answers only some very general questions about the traditional simple bodies, and his discussion is polemically framed as a critique of rival theories. Though presupposed in Cael. Γ, his crucial concept of the traditional simple bodies as combinations of qualities is treated in GC B, along with the germane topics of the production of these elements from one another and their mixing together into compounds; though the importance of the celestial objects in the constant transformation of the Empedoclean simple bodies into one another is clear from Cael. B 3, which seems to look forward to GC B 10, it is not even hinted at in Cael. Γ; weight and lightness are discussed in Cael. ∆. In Cael. Γ 1 Aristotle notes that some of his predecessors reject generation wholesale; others believe that all things did come into being once, though some are imperishable and some not; others hold that all things are subject to generation and 5

The production of heat and light by the Sun is explained frictionally without problems if the Sun is fiery and moves zodiacally in fire (cf. above, n. 2); see Kouremenos (2010) 84–85 n. 65.

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change, with the exception of one thing which transforms into all others but itself persists through change; others, finally, think that everything material is subject to generation, not out of bodies, though, but planes, which are also the ultimate products of material decay. A critique of this view, the basis of the physics in the Platonic Timaeus, takes up the rest of the chapter. The critique assumes that generated bodies consist of elements that are heavy and light, which means that they move naturally in a certain way. That all simple bodies must move naturally, and that some of them must be heavy and light, is established by Aristotle in ch. 2. At the end of this chapter Aristotle returns to the classification of views on generation in ch. 1, and argues that undoubtedly all bodies cannot be either subject to generation or ungenerated: only some bodies are subject to generation. Ch. 3 opens with the statement that it remains to be determined which bodies are subject to generation and why. The final answer to the first question is to be recalled from ch. 1: subject to generation are the four Empedoclean simple bodies, two of which are heavy and two light, and the things composed of them–all objects such as plants, animals and their various parts. Aristotle implies next that to answer both questions one must first see which of the bodies at issue are elements of the rest and why, how many they are and of what kind. This makes clear that the first of the two questions with which ch. 3 opens requires an implicit preliminary answer, from which the final answer given to it in ch. 1 will emerge, along with an answer to the second of these two questions: subject to generation are all things around us whose coming into being we observe–we cannot think of their coming into being as merely apparent, just an illusion. Why they come into being will be understood only after we have showed which of them are the elements of the rest and why these are the elements, the topic of ch. 3, how many these elements are, which is the topic of the next two chapters, and, especially, of what kind they are–that is, subject to generation, the topic of ch. 6. The answer to the second of the two questions with which ch. 3 opens is thus implicitly supplied by ch. 6: those objects around us whose coming into being we observe are truly subject to generation exactly because their elements are themselves subject to generation. Since ch. 3 determines the elements of the bodies that are subject to generation, not which type of these bodies contains their elements, it also fixes the number of these elements–they are four. Ch. 4 then explains why these elements cannot be infinite, and ch. 5 why they must be more than one. Both of these chapters criticize earlier views. Ch. 6 argues that bodies subject to generation have as elements bodies which themselves come into being and must do so from one another, a conclusion strengthened in ch. 7 with a critique of earlier views on the mode of the generation of these four elements. This chapter resumes the critique of Plato’s Timaeus, which continues in the eighth and final chapter of the book, where it is argued that the four Empedoclean simple bodies cannot be differentiated by the shape of their particles.

Introduction

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6. THE PRESENT TRANSLATION AND COMMENTARY It is clear from the above that the third book of the de Caelo can be studied independently of the other three books of the treatise as it has come down to us. Its study can serve as a general introduction to Aristotle’s theory of the four traditional elements and at the same time to the strongly dialectical character of his physics. The present work was motivated by the realization that, in its capacity to function as such an introduction, the third book of the de Caelo is not served well by the short section devoted to it in Jori (2009), the sole commentary on the entire de Caelo that has been published after Elders (1966), the sole modern commentary on the entire de Caelo and the only one available in English (Leggatt [1995] is restricted to the first two books). Though Elders discusses the third book at greater length, his comments are often unsatisfactory. The following translation and commentary are based on Allan’s OCT edition of the de Caelo, unless otherwise indicated. Though understandable, it is unfortunate that modern readers cannot enjoy a wide variety of easily available translations of Aristotle’s treatises, unlike the case with many other Greek texts, especially literary; Guthrie (1939) and Stocks (1922) are the only two translations of the entire de Caelo in English, both of which are deservedly considered classic works, and Leggatt (1995) is the most recent translation of the first two books of the treatise. There is no reason to repeat here what is well known about the difficulties that translating Aristotle presents. A few words, however, about a major departure in the commentary from accepted doctrine in Aristotelian scholarship are not out of place. This departure has already been mentioned above, in nn. 2–3. The commentary on 298a25–26 presupposes the theses I advanced in Kouremenos (2010): in the de Caelo, unlike in the first two chapters of Mete. A, which can be plausibly considered a later work, the first simple body is assumed to make up only the stars and a diurnally rotating shell whose fixed parts they are, whereas the simple body fire makes up the Moon, the Sun and the planets and fills up the lower part of the heavens, where these celestial objects move zodiacally; Aristotle never believed that the Eudoxean theory of homocentric spheres provided an even approximately true description of the structure of the heavens. In a happy coincidence my monograph came out shortly after Bowen & Wildberg (2009), a collection of essays on the de Caelo that ought to incite interest among scholars in this challenging work, all the more so since Falcon (2012) on Xenarchus now contributes significantly to our understanding of its reception in later thought. Inciting scholarly interest can only be served well by unorthodox perspectives. Whether or not the ‘heretical’ theses I argue for in Kouremenos (2010) “may cause more than a few readers to turn a deaf ear”, as a reviewer has ominously predicted (K. Bemmer: BMCR 2012.06.25), the reservations in his review or in the others that have appeared to date (see esp. that by A. Gregory, CR 62 [2012] 414–415) have not forced me to reconsider. These reservations concern mainly the first thesis, which is the most contentious. Regarding it, the situation is as follows. On the one hand, we have a canonical view that in the de Caelo, too, the first simple body is assumed to make up all luminaries and fill up the entire heavens; in the entire de Caelo this is

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bizarrely stated only in B 7. On the other hand, we have a number of passages in the de Caelo, including the first lines of the third book, which can be shown not to square with the canonical view. What are we supposed to do with them? One solution is the first thesis advanced in Kouremenos (2010), on which B 7 of the de Caelo is an addition to the main body of the work made in the light of Aristotle’s evolved view on the cosmological role of the first simple body in the beginning of the Meteorologica. What solution will be advocated by those who consider developmental hypotheses passé or are simply wary of assigning too much interpretive weight to a number of isolated passages? Will they push all recalcitrant passages under the carpet just to save the canonical view? If the problem lies with the number of isolated passages, which number would be large enough? It is preferable to adopt the only available solution, until it is argued convincingly that the passages at issue can be understood more satisfactorily by being brought into line with the canonical view.

TRANSLATION CHAPTER 1 [298a24] We have treated above of the first heaven and its parts, as well as of the celestial objects moving in it, their makeup and their natural properties, and of the fact that they are ungenerated and indestructible. Some of those things that are said to be natural are substances, the others actions and affections of substances. (I refer by the term “substances” to simple bodies, such as fire and [30] earth and the others on a par with them, and to those bodies that are made up of them, such as the whole cosmos and its parts, animals, plants and their parts; by “actions and affections” I refer to the motions of each of those substances, and to the motions of other substances which are caused by the former ones acting in virtue of their own powers, and to the alterations of substances [298b1] and to their transmutations into one another.) It is thus obvious that the study of nature deals mainly with bodies, for all natural substances are either bodies or have bodies and magnitudes. This is clear from both the definition [5] of natural things and the study of each of their categories. We have discussed the first element, its nature, its ungeneratedness and indestructibility. It remains to deal with the other two. Our discussion of them will turn out to also concern generation and decay. For generation [10] either is illusory or occurs only in these elements and their compounds. Whether it is real or not is perhaps the question that must be addressed first. On this issue, earlier lovers of truth disagree both among themselves and with the views we are now putting forth. Some of them [15] did away completely with generation and decay. They claim that nothing is subject to either generation or decay, which are mere appearances, e.g. the followers of Parmenides and Melissus, regarding whom we must think that, even if they are right about some things, they do not speak as is appropriate for physicists: for the existence of some ungenerated and completely unchangeable entities [20] rather concerns a science other than physics and prior to it. Since these thinkers held that there is nothing beyond sensible substances, however, and were the first to grasp that, if there will be knowledge and wisdom, some stable beings must exist, they transferred to sensible substances the stability of these beings. Others took the opposite view, as if [25] on purpose. For some maintain that nothing is ungenerated but all things are generated, though some things stay undecayed after they have come into being while others inversely decay, a view held mainly by those who follow Hesiod and, among the rest, by the earliest natural philosophers. Others say that all things [30] come into being and are in flux, none of them being stable, except a single one that persists and whose natural transformations are all other things; this seems to be what many others and Heraclitus of Ephesus mean. There are, finally, others who consider all bodies generated, constructed from planes and decaying into [299a1] planes.

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We will discuss the views of the others elsewhere. Those, now, who maintain the last view and regard all bodies as made up of planes happen to contradict mathematics in many other ways, which are easy [5] to see, though it is right either not to subvert mathematics or to do so only if arguments more compelling than its propositions are available, for the following1 are clearly established by the same reasoning, i.e. that solids consist of planes, planes of lines, and the latter of points; if so, the part of a line is not necessary a line. These issues [10] have already been discussed in our treatment of motion, when it was shown that there are no indivisible lengths. Let us examine briefly on this occasion, too, the impossible things concerning physical bodies that the proponents of indivisible lines happen to say. For, although the impossibilities resulting from the assumption of indivisible lines will also apply to physical bodies, [15] not all impossibilities this assumption engenders concerning physical bodies will apply to the indivisible lines themselves. This is so because mathematical objects are said to be products of abstraction, whereas physical objects are products of addition, and there are many properties that cannot belong to indivisibles but belong necessarily to physical bodies. Nothing divisible can belong to an indivisible, [20] but all physical properties are divisible in two senses, either in kind or accidentally: in kind as white or black are kinds of color, accidentally if they are properties of what is divisible, the sense in which all simple properties are divisible. For this reason it is the impossibilities related to [25] such properties that we must examine. If it is impossible for two parts, each of which lacks weight, to have weight in combination but all physical bodies or some of them have weight, e.g. earth and water, as our opponents themselves would admit, and a point lacks weight, then lines, too, clearly lack weight; if lines, however, so do [30] planes, and thus all bodies as well. That a point cannot have weight is evident. For everything which is heavy can be heavier, and everything which is light can be lighter, than [299b1] something else, though what is heavier or lighter need not perhaps be heavy or light, as something large can be larger, though what is larger is not always large, since there exist many things which are absolutely small, though they are larger than other things: so, if something [5] heavy that could be heavier were necessarily larger in weight, then everything heavy would be divisible, but a point has been assumed to be indivisible. Now, if what is heavy is dense, what is light is rare, and what is dense differs from what is rare in that it has greater mass in equal volume, assuming that a point is heavy or light, it is also [10] dense or rare: but what is dense is divisible, the point is indivisible. Also, if everything which is heavy is necessarily soft or hard, an impossibility easily follows from this, for soft is what retreats into itself, but what does so is divisible, and hard is what cannot do so. But, of course, from [15] parts which have no weight something heavy will not be made up. How will our opponents determine the number and the kind of the parts that are required for this if they are unwilling to resort to fictions? In addition to that, if one weight greater than another exceeds it by weight, each of the indivisibles, too, will turn out to have weight. If four points have weight, and what is composed of more points than four [20] is heavier than what is composed of four 1

Reading ™peˆ t£de for œpeita of modern editions. See commentary on 299a2–6.

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points and has weight, but what makes a body heavier than another, which is also heavy, is itself heavy, just like what makes one thing whiter than another, which is also white, is itself white, then the greater weight will be heavier by a point if we subtract from it a part which is equal to the lighter weight. Thus a point, too, will have weight. The demand, moreover, that the planes can be put together only along their sides is absurd: [25] for, just as a line is put together with a line both ways, and lengthwise and widthwise, a plane must also be put together with a plane in a similar manner. Now, a line can be joined together with a line by being put on top of it, not by being added to it. But, of course, if it is by being stacked on top of one another, too, that planes can be [30] put together, there will be a body which is neither an element nor made up of the elements, consisting of planes joined together in this manner. Further, if the weight of bodies depends on the number of their constituent planes, as is said in the [300a1] Timaeus, it is clear that lines and points, too, will have weight: for, as we have already said, they stand to one another in the same relation. If, on the other hand, differences in the weight of bodies are due not to this but to the fact that earth is heavy and fire light, [5] some planes will be heavy and some light, and this will also be the case with lines and points, since a plane making up earth will be heavier than one making up fire. In general, it turns out that magnitudes either do not exist or can be annihilated if, as points are to lines, so are lines to [10] planes and planes to bodies: for, if all of them decay into one another, they will decay into what is elementary, so that no bodies but only points could exist. Besides, if time is like magnitudes, it will or could disappear as well, since the indivisible now is like a point of a line. This difficulty also faces those who think that numbers make up the [15] cosmos, for there are some thinkers, such as certain Pythagoreans, according to whom nature consists of numbers, but physical bodies are observed to have weight and lightness, whereas units can neither make up bodies by being put together nor have weight.

CHAPTER 2 [20] That all simple bodies have necessarily a natural motion is evident from the following. Since they are observed to move, if they do not have a proper motion, it is necessary that they move forcedly. But forced motion and motion counter to nature are the same. If there is a motion which is counter to nature, though, a motion which is natural necessarily exists, [25] counter to which is the former; moreover, although there are many counter-natural motions, there is necessarily a single natural motion, since to move naturally means to move simply, whereas a body moves counter-naturally in many ways. This will be evident if we consider rest, too. That is, rest is necessarily either forced or natural, and a body rests forcedly where it moves forcedly, too, whereas it rests naturally where it moves naturally, too. [30] Therefore, since a body is observed to rest at the center of the cosmos, if it rests there naturally, then it clearly moves there naturally, too. If it

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rests forcedly, what prevents it from moving? If something at rest, we will recycle the same argument, since either it is due to its nature that the [300b1] first resting body is in this state or we necessarily go on ad infinitum, which is absurd; if something in motion prevents the body which rests at the center of the cosmos from moving, as Empedocles says that the vortex forces the Earth to rest, where could the Earth move, since it could not possibly move infinitely far away? Nothing impossible can happen, [5] and to move over an infinite distance is impossible. Necessarily, therefore, the Earth’s motion would stop somewhere, and there the Earth would rest not forcedly but naturally. If there is natural rest, however, there is also natural motion, i.e. motion directed towards the place of natural rest. Thus Leucippus and Democritus, who say that the first bodies are in constant motion in the [10] infinite void, must explain what kind of motion is this motion of the first bodies, as well as which motion is their natural motion, for, if an element is forced to move by another, there must also be some natural motion of each of them, counter to which is its forced motion; also, the first motion necessarily causes forced motion by being not forced itself but natural, for there will result an infinite regress [15] if no first mover which moves naturally exists but motion is always imposed by a prior mover whose motion is itself forced. The same difficulty must arise if, as is written in the Timaeus, the elements moved in a disorderly manner prior to the cosmogony, for this motion must have been either forced or natural. If [20] natural, careful consideration shows that the cosmos must have existed at the time, since motion must have been caused by a first, naturally moving mover and the elements, which moved not by force, must have been at rest in their proper places forming the same structure as they do at present, those with weight near its center and those with lightness away from [25] it, which is how the cosmos is spatially disposed now. In addition to that, one could ask the following question, whether some quantities of the elements, whose pre-cosmic motion was disorderly, could even have formed compounds such as those which make up the naturally constituted bodies, i.e. bones and tissues, as Empedocles claims [30] it happens when Love begins to assert itself. For he says many a head without neck sprouted. As for those who posit infinitely many elements, which move in the infinite void, if there is a single cause of motion for the elements, they must move with a single motion, and thus will not move in a disorderly manner, but if there are infinitely many [301a1] causes of motion for the elements, infinitely many must also be the motions with which the elements move; for, if there are finitely many, they will exhibit some order, and disorderliness cannot result from motion to different places, since in the actual universe, too, not all quantities of elemental matter move towards the same place but only quantities of the same element. What is disorderly, moreover, [5] is nothing but counter-natural, for the nature of sensible things is their proper order. As it is, that the infinitely many elements move without order is another absurd impossibility: the nature of things is that which most of them have most of the time, so our opponents happen to regard, contrary to the

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facts, [10] disorder as natural and orderly arrangement as counter-natural, although nothing natural results from chance. It seems that Anaxagoras got right at least this, since he begins his account of the cosmogony with the elements in a state of rest. Others, too, hypothesizing that the elements accrete, attempt to set them in motion by some mechanism and break their masses apart again, but this state of separation and [15] motion cannot be plausibly assumed to precede the cosmogony. This is why Empedocles omits a cosmogony at the time Love asserts itself. He could not posit a cosmogony since he assumes that the cosmos is generated from the separation of the elements and that Love mixes them together: the cosmos is made up of the elements in a state of separation, so it is necessarily produced [20] from a single composite entity. From the above it is clear that there is a natural motion of each simple body, a motion the simple body performs neither forcedly nor contrary to nature. The following makes clear that there must be some naturally moving bodies with the tendency to move naturally, in a straight line, towards the center of the cosmos or its periphery. We say that simple bodies must move naturally, but if there is no natural motile tendency in [25] that which moves, it cannot move either towards, or away from, the center of the cosmos. Let A be weightless and B heavy; let, moreover, the weightless body traverse the distance Γ∆ and B, in equal time, a greater distance ΓE, since it has weight. Now, assuming the division of the heavy body in the ratio of ΓE [30] to Γ∆ (since it is possible that this is the ratio between it and one of its parts), if the whole moves over the whole of ΓE, in the same time its part must move over Γ∆: the weightless and the heavy body will thus traverse equal distances, which is [301b1] impossible. The same argument applies to lightness. Further, if there is a simple body which moves but lacks either weight or lightness, its motion must be forced, hence infinitely fast. That which moves such a body is a force, but a smaller and [5] lighter body will be moved farther by the same force, so let A, which is weightless, be moved over ΓE and B, which has weight, be moved over Γ∆ in the same time: if the body which has weight is divided as ΓE is to Γ∆, it will turn out that the part subtracted from this body [10] is moved over ΓE in equal time, since the whole body was moved over Γ∆, the speed of the smaller body being to that of the greater in the ratio that the greater body has to the smaller, so the weightless body and that which has weight will be moved over equal distances in the same time, which is an impossibility. Consequently, since [15] the weightless body will be moved over a distance always greater than all assigned distances, it will be carried away to infinity. It is, therefore, evident that all bodies must have comparable weight or lightness. Since nature is what is in something and causes its motion, force what causes a thing to move but is in something else, or in the moving thing itself as something else, and all motion is either natural or forced, [20] natural motion, e.g. the downward motion of a stone, will be made faster by force, whereas counter-natural motion will be exclusively due to force. Air functions as a tool to either end in the physical world (because it is naturally both heavy and light). Thus, insofar as it is light, it will cause upward motion when it is pushed and takes over the [25] initiation of motion from the original motive force, but insofar as it is heavy, it will in-

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crease the speed of downward motion, since in either case the initial motive force transfers the moving object to the air, as if tying the former to the latter: the initial mover does not follow the forced motion of the object for this reason. Without a body such as air, there could be no forced motion. Like a tailwind, air also makes natural motion faster [30] by the same mechanism. That all simple bodies are either heavy or light, and how counter-natural motion is caused, is clear from the above. That subject to generation cannot be either all things or none at all follows from what has been said earlier on. It is not possible that all bodies are subject to generation, [302a1] unless it is also possible for void without body to exist, since the place that will be occupied by what is now coming into being when the process of its generation will have ceased must have previously been empty if no body existed in it. A body can come to be from another, e.g. fire from air, [5] but generation cannot occur from no pre-existing magnitude, for an actual body can certainly be generated from what is potentially this body, but if what is potentially this body is not previously another body in actuality, it can only be emptiness without body.

CHAPTER 3 [10] It remains to see which bodies are subject to generation and why. Since everywhere knowledge is obtained from first principles and first among the constituents of bodies are the elements, we must determine which of those bodies are elements and why, then how many they are and of which kind. This will become obvious [15] from the definition of element. Let an element of bodies be what other bodies are analyzed into, exists in them actually or potentially (we have yet to settle this issue) and is not itself analyzable into bodies different in kind; this is the meaning of the term “element” intended by everybody in all cases. If [20] now this is the definition of element, some bodies must be of this sort. For in flesh and wood and each body of this kind exists potentially fire and earth because it is evident that the latter separate out of the former, but flesh or wood does not exist in fire, either potentially or actually; otherwise it would separate out. [25] Accordingly, it does not exist in the single element, too, that some posit: for, if there will be flesh or bone or anything else, we cannot just say that it exists potentially in the single element without also explaining how it can be generated. Anaxagoras and Empedocles hold opposite views on the elements. Empedocles says that fire, earth and the bodies of the same kind as [30] these are the elements, all other bodies consisting of them, but Anaxagoras holds the opposite view, since he says that the homoeomers are the elements (i.e. flesh and bone and [302b1] each body of this kind) and regards air and fire as mixtures of these and all other seeds. According to him, each of them is a congeries of all invisible homoeomers, which is why all things are generated from them, for he considers fire and ether to be [5] the same body. All natural bodies have proper motions, but some motions are simple and the others composite, the latter being motions of composite bodies and the former of simple bodies, so it is clear that there are some simple bodies, for there are sim-

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ple motions, too. The existence of elements, as well as its explanation, is thus evident.

CHAPTER 4 [10] Next we will discuss whether they are finitely or infinitely many, and if the first, how many. First we must see that they are not infinitely many, as some believe, and we will begin with those thinkers who, like Anaxagoras, consider all homoeomers to be elements. None of those who hold this view [15] operates with the correct conception of the elements: since we see that many composite bodies are divisible into homoeomeric parts, e.g. flesh and bone and wood and stone, if composite bodies are not elements, then not all homoeomers will be elements but only those that are unanalyzable into bodies different in kind, as said [20] above. Even on this conception of the elements, moreover, it is not necessary to regard the elements as infinite in number, since the whole range of phenomena will be explained even if one posits finitely many elements: it will make no difference if the elements are only two or three, as Empedocles tries to show. For, since the advocates of infinitely many elements happen to view not all things as made up [25] of homoeomers (because they do not posit that a face is made up of faces, and similarly with any other of the naturally constituted things), it is clear that it is far better to hypothesize a finite multitude of principles, actually the smallest possible number, provided, of course, that all the same phenomena will be shown to follow, just as the mathematicians demand, who always [30] posit what is finite, either in kind or in number, as principles in mathematics. Moreover, if bodies are differentiated by their proper differences but there are finitely many bodily differences (bodies [303a1] are differentiated by their sensible qualities, which are finitely many, but this must be established), it is clear that the elements, too, must be finite in number. Others, i.e. Leucippus and Democritus of Abdera, hold another view with equally unacceptable [5] implications. They think that the primary bodies are infinite in number and indivisible in magnitude, and that neither a multiplicity can be generated from a unit nor a unit from a multiplicity, but all things are generated by the combination and entanglement of the elementary bodies. In a way these thinkers, too, consider all things to be numbers and made up of numbers; even though [10] they do not make it clear, this is what they mean. Moreover, they base their contention that the simple bodies are infinitely many on the grounds that these bodies differ in shape and that infinitely many shapes exist, but they did not specify what type of shape each element has and what its exact shape is, with the exception of fire, to which they assigned the sphere; air and [15] water and the rest they differentiated by greatness and smallness, regarding them like seed-medleys of all elements. First of all, Leucippus and Democritus, too, err in not positing finitely many principles, though they could then say all the same things. Also, if the bodily differences are not infinitely many, clearly [20] the elements, too, will not be infinitely many. Besides, by positing indivisible bodies Leucippus and De-

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mocritus must be in conflict with mathematics and reject many common beliefs and perceptual appearances, which have been discussed in our earlier treatment of time and motion. At the same time, they contradict themselves [25] out of necessity: if the elements are indivisible, air and earth and water cannot possibly be differentiated by greatness and smallness, for they cannot be generated from one another, since the largest elemental bodies will run out by being continually separated out, which is how Leucippus and Democritus explain the generation of water and air and earth from one another. Further, not even their own [30] theory appears to require an infinite multitude of elements if bodies are differentiated by shape and all shapes are made up of pyramids, rectilinear shapes of [303a1] rectilinear pyramids, the sphere of its eight parts: there must of necessity be some principles of shapes, so whether these are one or two or more, there will be an equal number of simple bodies. Finally, if each element has a proper motion [5] and the motion of a simple body is simple but there are not infinitely many simple motions, for they are no more than two, nor are there infinitely many places, the elements will be finite in number for this reason as well.

CHAPTER 5 Since the elements must of necessity be finite in number, it remains [10] to examine whether they are more than one, for some thinkers hypothesize only one: others identify it with water, others with air, others with fire and others with a substance which is finer than water but denser than air, and of which they say that it contains all the worlds because of its infinite extent. Those who hold that the single element is water or air or a body finer than water but [15] denser than air, all else being generated from it through condensation and rarefaction, unwittingly posit the existence of a substance more basic than their element. As they say, generation from the elements is a synthesis and the way back to the elements is an analysis, hence the substance whose particles are the smallest must of necessity be naturally prior: since, therefore, [20] they maintain that fire is the finest body, fire should be naturally primary–whether it is fire or not makes no difference, given that naturally primary must necessarily be not the intermediate body but one of the others. In addition to that, generation via condensation and rarefaction is nothing but generation involving fineness and thickness, for what is fine is rare, [25] according to the advocates of a single element, and what is dense is thick. Generation involving fineness and thickness is the same as generation involving largeness and smallness, however, since what is fine consists of small particles and what is thick of large particles, for what is fine disperses over a wide area, which is a property of a body consisting of small particles. As it is, those who posit a single element turn out to regard largeness and smallness [30] as the distinguishing feature of the other substances. But, in so doing, these thinkers turn out to relegate all the other substances to the category of relatives, for, on their theory, there will not be something which is fire, water or air unqualifyingly, but rather one and the same body will be fire relative to a sec-

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ond body [304a1] but air relative to a third, as on the theory of those who posit a multitude of elements and say that the elements are differentiated by largeness and smallness: since each body is defined by the size of its particles, sizes will have a ratio to one another, so that, given two bodies made up of particles whose sizes have [5] a certain ratio to one another, one must of necessity be air and the other fire, but the former must necessarily be earth, too, and another one water, for the sizes of particles can bear ratios to the sizes of smaller particles. Those who posit fire as single element escape this difficulty, but cannot avoid other absurdities. Some of these thinkers [10] assign a shape to fire, i.e. those according to whom this shape is the pyramid, and among them are those who put forth the naïve argument that the pyramid is the sharpest shape and fire the sharpest body, as well as those who advance the subtler argument that all bodies are made up of a body whose particles are the smallest and all solid [15] shapes of pyramids, whence follows that fire is pyramidal because this is the finest body and the pyramid the smallest and first shape, but the first shape belongs to the first body. Others say nothing about the shape of fire, but think that this body alone consists of the smallest particles, [20] and regard all other bodies as generated via its densification, as if from fine filings blown together. Both views face the same difficulties. If it is assumed that the first body is indivisible, our earlier arguments against this hypothesis will apply. No one, moreover, can make this assumption [25] if he wants to think like a physicist. For, if all bodies are comparable in terms of quantity, and the sizes of homoeomeric bodies are as the sizes of their elements (e.g. the sizes of all water and all air are as the sizes of their elements, and similarly for the other bodies), [30] but the quantity of air is greater than that of water and, in general, the quantity of the finer body is greater than that of the coarser, then it is clear that the element of water, too, will be smaller than that of air; thus, if the smaller magnitude is in the greater, the element of air must be divisible. [304b1] The same applies to the element of fire and of the finer bodies in general. If it is assumed that the first body is divisible, the thinkers who associate a shape with fire will turn out to deny that the part of fire is fire, since a pyramid is not made up of pyramids, and [5] that every body is either an element or consists of elements (since the part of fire is neither fire nor any other element); those who define the first body in terms of size will turn out to posit the existence of an element more basic than their element, and so on ad infinitum, if every body is divisible and element is what is smallest. They, too, moreover, will turn out [10] to hold that the same body is fire relative to one body but air relative to another, as well as water and earth. A mistake common to all who hypothesize a single element is that they allow for only one natural motion, the same for all bodies. We observe that every natural body contains a cause of motion. As it is, if all bodies [15] were one body, there would be one motion common to all of them, and the speed of this motion would be of necessity proportional to the quantity of the body, just as the greater the amount of fire, the faster its upward motion, but it is a fact that many bodies move faster downwards. For this reason, as well as because [20] it has already been agreed that there are several natural motions, it is evident that there cannot be only

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one element. Thus, since there is neither an infinity of elements nor a single element, the elements cannot but be more than one and finite in number.

CHAPTER 6 Now, first we must examine whether they are eternal or subject to generation and decay; after this issue has been settled, it will be clear both [25] how many they are and what their nature is. That they are eternal is impossible, since fire and water and each simple body are observed to decay. Their decay must necessarily either be infinite or come to a halt. If infinite, its duration will also be infinite, and also the duration of the inverse process of coming to be, since each [30] part decays and is generated in a different time. As a result, beyond an infinite time there will be another infinite time, when the duration of generation is infinite and succeeds the also infinite duration of decay. Thus beyond the infinite there is another infinite, [305a1] which is absurd. On the other hand, if decay comes to a halt, the body left at the end will be either indivisible or divisible, though it will never be in fact divided, a view Empedocles seems to espouse. It will not be indivisible, however, in light of our [5] earlier arguments; nor will it be divisible but never actually subject to decay, for a smaller body decays more easily than a larger, so if a large body decays in this manner and, as a result, is reduced to smaller bodies, it is plausible that a smaller body is subject to this process even more easily. We observe that there are two ways [10] in which fire decays: it does so due to its being acted upon by the opposite, when it is quenched, and spontaneously, when it dies out, but it is the smaller body that is acted upon by the larger, and the smaller the body being acted upon, the greater the speed of the action. Therefore, the elements of bodies must of necessity be subject to generation and decay. Since they are generated, their generation must be either from what is incorporeal or [15] from bodies, and if from bodies, either from one another or from some additional body. The view that they are generated from the incorporeal presupposes the existence of void without body. For everything that is generated is generated in something, and that in which generation occurs must either be incorporeal or contain a body: if it contains a body, there will be two bodies in the same place, that [20] which comes to be and that which pre-exists, but if it is incorporeal, it must necessarily be a void without body, and this has been shown to be impossible. Nor, moreover, can the elements be generated from some additional body, since it will turn out that prior to the elements is this other body. Now, if it has weight or lightness, [25] it will be one of the elements, whereas if it lacks a tendency to move naturally in either direction, it will be an immobile mathematical body, which will not be in some place, since a body which rests in a place can also move in that place, if forcedly, counter-naturally, and if not forcedly, naturally. As it is, if it occupies a place and is somewhere, it will be one of the elements, but if it is not in a place, nothing [30] will be generated from it, for what is generated and that from which it is generated must occupy the same place. The elements, therefore, cannot be generated either from what is incorporeal or from

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an additional body, so the only alternative that remains is that they are generated from one another.

CHAPTER 7 But we must turn once again to the question how they are generated from one another, i.e. as Empedocles and Democritus think, [35] or as the advocates of reduction to planes do, or in some other [305b1] way. Those who agree with Empedocles and Democritus regard unwittingly the generation of the elements from one another as not real but apparent, for they hold that each element exists in the others and separates out, as if generation amounted to emptying out the contents of a vessel and were not [5] from some matter, nor did it involve change. Even if this is granted, though, the consequences are no less absurd, for any amount of a substance does not seem to become heavier if compressed, but those who say that water separates out of the air in which it exists are forced to admit the contrary by the fact that water, when it is produced from air, is heavier. [10] Also, when one of two bodies that are mixed together separates out, there is no reason why it should always occupy more space, but when air is generated from water, it occupies more space, since the finer body takes up more space. This is also clear during the transition from water to air: as water evaporates and is gasified, [15] its containers explode due to lack of space. Thus, if there is no vacuum at all and bodies cannot expand, as the advocates of the view criticized here hold, this clearly cannot happen, whereas if the vacuum does exist and expansion does occur, no explanation of the fact that the body which separates out must always take up more space is forthcoming. [20] Further, the generation of the elements from one another must of necessity come to a halt if in a finite body there is not an infinite multitude of finite quantities of another body. When water is generated from earth, a quantity has been subtracted from the earth if generation occurs through separation, and the same happens when water is generated from the remaining earth: thus, if this will go on for ever, [25] an infinitude will turn out to be in what is finite, but since this is impossible, the generation of the elements from one another could not go on for ever. It has, therefore, been determined that the transition from one element to another does not occur through separation. The remaining alternative is that one element turns into another, which can occur in one of two ways, i.e. either through change of shape, as when [30] a sphere and a cube are produced from the same wax, or via analysis into planes, as some hold. If through change of shape, it turns out that the existence of indivisible bodies is necessarily entailed: for, on the assumption that all bodies are divisible, the part of fire will not be fire, and a part of earth will not be earth, since neither [35] the part of a pyramid is necessarily pyramidal nor the part of a cube [306a1] cubical. If through analysis into planes, a first absurdity is that not all elements are generated from one another, as the advocates of reduction to planes are forced to, and do, admit. But that one single element is exempted from intertransmutation is neither plausible nor supported by

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observation [5], which shows that all elements, without exception, change into one another. The thinkers who put forth this view turn out to suggest a theory about the phenomena which, though, conflicts with the phenomena. The reason for this is that they do not start out from the right principles but wish to make everything conform to certain preconceived notions. The principles of sensible things must perhaps be [10] sensible, of eternal things eternal, and of perishable things perishable; in general, the principles must be of the same kind as the things they are principles of. However, the advocates of reduction to planes are so attached to their preconceived notions that they seem to behave like discussants defending a thesis, for they accept all consequences of their ideas on the belief that they start out from the right principles, as if some principles ought not [15] to be judged on the basis of their consequences, and principally of their ultimate goal: the ultimate goal of practical knowledge is the appropriate action, of a physical theory to fit those phenomena that present themselves to the senses consistently and indisputably. Also, the advocates of reduction to planes turn out to regard earth as the element in the strictest sense of the term and as the only imperishable body, if an undissolvable body is also imperishable and an [20] element, since only earth cannot be dissolved into another body. Lacking plausibility, too, are the free-floating triangles in their treatment of dissolving bodies: free-floating triangles appear in the transition from one body to another as a consequence of the fact that each body is not made up of the same number of triangles. Moreover, the advocates of reduction to planes must deny that generation is from bodies: [25] for, when a body is being generated from planes, it will not have been generated from bodies. In addition to that, they must deny the divisibility of all bodies and contradict the most exact sciences, which regard intelligible bodies, too, as divisible–I am speaking of the mathematical sciences–whereas they do not even grant the divisibility of all sensible bodies out of their desire to [30] save their hypothesis. For those who attribute a shape to each element and determine the nature of the elements geometrically cannot avoid regarding the elements as indivisible: a random division of a pyramid or a sphere will not yield as remainder a sphere or a pyramid, so that either the part of fire will not be fire, but there will be a body prior to [306b1] the element, for every body either is an element or consists of elements, or not every body will be divisible.

CHAPTER 8 In general, the attempt to associate certain shapes with the simple bodies is irrational, firstly because the whole space will not be [5] filled: three plane shapes are believed to be space-filling, the triangle, the square and the hexagon, and only two solid shapes, the pyramid and the cube, but those who try to assign shapes to the simple bodies necessarily need more than two shapes since they posit the existence of more than two elements. Secondly, we see that all simple [10] bodies, air and water in particular, take on the shape of the surrounding place: thus the shape of an element could not be conserved, unless an amount of an element would not

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be everywhere in contact with its container, but if the shape that is associated with this element will be distorted, the element will no longer be e.g. water, since it was its shape that differentiated it. It is thus clear that no [15] fixed shapes are associated with the elements. Indeed, it seems as if nature herself declares this to us, a fact which also conforms to reason: for, just as everywhere else the underlying matter must be formless and shapeless (since this is the condition that ensures the greatest degree of formability, as is written in the Timaeus, for the receptacle of all forms), similarly the elements must [20] be regarded as matter of compound bodies, which is why they can turn into one another when their differences with respect to affections are separated from them. In addition to the above, how could the generation of flesh and blood or any other continuous body be possible? It could not be from the elements themselves since no continuous body can be generated from their [25] juxtaposition, nor from the juxtaposition of the planes because the elements, not compounds of the elements, are generated from the juxtaposition of the planes. Therefore, those willing to scrutinize these theories instead of adopting them hastily will conclude that these theories deny the existence of generation. Nor do the affections, [30] powers and motions of the elements that the proponents of these theories had mainly in mind when they allotted shapes to the simple bodies fit the shapes at issue. Since e.g. fire is most able to move, heats and burns, some thinkers regarded it as spherical and others as pyramidal. For these are the most mobile of all shapes, on account of the fact that their contact-area is minimal and they have [307a1] the least base-area; they are also the most capable of heating and burning, on account of the fact that the entire surface of the sphere is an angle, whereas the pyramid has the acutest angles, angularity of shape being the cause of burning and heating, as they say. Firstly, as regards motion, both groups are wrong. For, even if we grant that [5] these are the most mobile shapes, nevertheless they are not most able to move with the natural motion of fire, since fire moves upwards in a straight line, whereas these shapes are most able to move circularly, with the so-called rolling motion. Secondly, if earth is cubical because it is stable and immobile, but rests not everywhere, only in its own place, [10] and moves away from another place unless prevented, which is also true of fire and the other elements, then it is clear that fire and each element will be spherical or pyramidal away from their own places but cubical in their own places. Also, if angularity of shape is the cause of burning and heating, all elements will turn out to be capable of heating, [15] perhaps in different degrees, since all of them have angles, e.g. the octahedron and the dodecahedron; even the sphere cuts, according to Democritus, who regards it as a mobile angle, so the difference will be one of degree, but this is patently false. It also turns out that even mathematical [20] bodies must burn and heat because they, too, have angles and among them must exist indivisible spheres and pyramids, all the more so if there exist indivisible mathematical magnitudes, as our opponents claim. However, if certain bodies burn and heat but others do not, these thinkers ought to have explained this difference, not simply stated it. Further, if what is burned [25] turns to fire, but fire is spherical or pyramidal, what is burned must of necessity become spherical or pyramidal. Ac-

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cept, therefore, as plausible the claim that fire cuts and divides to such a degree on account of its shape; that the pyramid makes pyramids or the sphere spheres is completely absurd, however, as is [30] the demand that the knife cuts things into knives or the saw into saws. It is, moreover, ridiculous to assign a shape to fire in order for this element only to divide. Fire is observed [33] to bring together and merge, rather than separate, things: it separates [307b1] unlike things and mixes together like things, and the capacity for mixing things together belongs intrinsically to it (the merging and uniting capacity is characteristic of fire), that for separating things accidentally (as fire brings together similar things, it expels unlike things). Thus the theorists who assign shapes to the simple bodies ought [5] to have chosen a shape for fire with an eye to both capacities or preferably to its mixing capacity. Also, since the hot and the cold have opposite capacities, it is impossible to assign a shape to the cold, for the assigned shape must be the opposite of the shape assigned to the hot, but nothing is the opposite of a shape; this is the reason why all theorists who associate shapes with the simple bodies have left out the cold, though they ought [10] either to have defined all simple bodies by shape or none. Some of them do attempt to explain the capacity of the cold, but end up contradicting themselves. They define as cold that whose particles are large because it compresses and cannot pass through pores. It is, therefore, evident that hot would be what can pass through pores, but such would be in all cases that whose particles are small, so [15] it turns out that the hot differs from the cold as regards the size, not the shape, of its particles. Finally, if the pyramids were of many sizes, the large ones would not be fire, and their shape would not cause burning but the opposite. It is thus clear from the above arguments that the elements do not differ in shape. Now, since [20] the most important differences between the elements are their differences with respect to affections, actions and capacities (we say that each natural thing can act and be affected and has capacities), we will first turn our attention to these. Our goal is to base on our conclusions about them our grasp of the differences between the elements.

COMMENTARY CHAPTER 1 298a24. Περὶ...τοῦ πρώτου οὐρανοῦ καὶ τῶν μερῶν: sc. aÙtoà. According to Simp., in Cael. 552.1–7 (Heiberg), Ð prîtoj oÙranÒj is tÕ a„qšrion p©n sîma, the first simple body or element which Aristotle added to the four Empedoclean ones (see Introduction, 1–2; cf. below, on 298a25–26 and 302b4–5). It is articulated into eight concentric spheres, actually spherical shells, which are its parts mentioned here: one is the sphere of the stars, the shell whose luminous parts are the stars, the outermost part and nutshell of the cosmos; seven more spherical shells are inside it, one for each of the seven wandering celestial bodies–the five planets known in antiquity, the Sun and the Moon. Simp. presupposes a further articulation of these seven shells into as many concentric sub-shells as are required by the theory of homocentric spheres of Eudoxus of Cnidus, which Aristotle outlines in Metaph. Λ 8, together with some modifications introduced by Callippus of Cyzicus, and one introduced by himself; Simp. gives more details in his comments on Cael. B 12, where the theory is presupposed (293a4–11). On the theory of homocentric spheres see Kouremenos (2010) 33–42, with further bibliography. However, in the de Caelo Ð prîtoj oÙranÒj is only the stuff making up the spherical shell whose bright parts are the stars and whose diurnal rotation is the only uniform motion in the heavens. See Cael. B 6, 288a13–18, where Ð prîtoj oÙranÒj and its uniform diurnal rotation, ¹ prèth for£, are contrasted with the wandering luminaries and their non-uniform motion through the zodiac: perˆ d tÁj kin»sewj aÙtoà, Óti Ðmal»j ™sti kaˆ oÙk ¢nèmaloj, ™fexÁj ¨n e‡h tîn e„rhmšnwn dielqe‹n. (lšgw d toàto perˆ toà prètou oÙranoà kaˆ perˆ tÁj prèthj for©j· ™n g¦r to‹j Øpok£tw ple…ouj ½dh aƒ foraˆ sunelhlÚqasin e„j ›n.) Cf. Cael. B 12, 292b22–25, where Ð prîtoj oÙranÒj is said to have a single motion–the diurnal rotation–in contrast to celestial bodies situated between it and the Earth; see also Metaph. Λ 7, 1072a19–24, and cf. 8, 1073a23–34. As it is, Ð prîtoj oÙranÒj is Ð oÙranÒj in the first of the three senses of the term Aristotle sets out in Cael. A 9: ›na mn oân trÒpon oÙranÕn lšgomen t¾n oÙs…an t¾n tÁj ™sc£thj toà pantÕj perifor©j, À sîma fusikÕn tÕ ™n tÍ ™sc£tV perifor´ toà pantÒj· e„èqamen g¦r tÕ œscaton kaˆ tÕ ¥nw m£lista kale‹n oÙranÒn, ™n ú kaˆ tÕ qe‹on p©n ƒdràsqa… famen (278b11–15; here ¹ ™sc£th perifor£ is used at first for the shell whose parts are the stars and then for its diurnal rotation). As Simp. takes it, Ð prîtoj oÙranÒj is Ð oÙranÒj in both the first and second of these three senses: ¥llon d’ aâ trÒpon tÕ sunecj sîma tÍ ™sc£tV perifor´ toà pantÒj, ™n ú sel»nh kaˆ ¼lioj kaˆ œnia tîn ¥strwn· kaˆ g¦r taàta ™n tù oÙranù ena… famen (278b16–18, where ¹ ™sc£th perifor£ is the shell of the stars; for the third sense of oÙranÒj see below, on 298a31). But this is not supported by the evidence. t¦ mšrh toà prètou oÙranoà are t¦ kat¦ t¦j

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diast£seij mÒria toà prètou oÙranoà discussed in Cael. B 2, where Aristotle identifies as upper/right part of the spherical shell in which the stars are fixed its hemisphere whose rotational pole is invisible from the Earth’s northern hemisphere–the southern celestial hemisphere; thus the other hemisphere, whose rotational pole is visible from the Earth’s northern hemisphere, i.e. the northern celestial hemisphere, is the lower/left part (for the expression t¦ kat¦ t¦j diast£seij mÒria see 285b33–286a2; cf. 284b15–24). Astronomically, his reasons for so doing are obscure; see Kouremenos (2010) 122–123. In Cael. A 3, 270b15–16, Aristotle refers to the stars and the constellations as t¦ o„ke‹a mÒria toà ™sc£tou oÙranoà = toà prètou oÙranoà (cf. Leggatt [1995] ad loc.), but here t¦ mšrh toà prètou oÙranoà cannot be used in this sense. The de Caelo cosmology does not seem to presuppose the Eudoxean theory of homocentric spheres; see Easterling (1961) and, for fuller discussion, Kouremenos (2010) ch. 3. 298a25. περὶ τῶν ἐν αὐτῷ φερομένων ἄστρων: Bekker and Guthrie print the variant fainomšnwn, which does not affect the meaning. As Simp. reads the expression Ð prîtoj oÙranÒj (see previous n.), t¦ ™n aÙtù ferÒmena ¥stra are all the celestial objects known in antiquity–the fixed stars and the seven wandering celestial objects (cf. the use of the noun in Cael. A 9, 278b16–18, quoted in previous n.). But it is fairly certain that here Aristotle can have in mind only the fixed stars (see previous n.; for ¥stra used in this sense cf. Cael. B 12, 292a11). ™n aÙtù feromšnwn does not suggest that these celestial objects move through the first simple body, which is shaped into a spherical shell, or that they are carried round by it, as if they were dead weight. They are fixed parts of the shell, and consist themselves of the first simple body, whose natural motion is the diurnal rotation. Aristotle explains in Cael. B 7 how they produce light; see Introduction, 4. 298a25–26. ἐκ τίνων τε συνεστᾶσι καὶ ποῖ’ ἄττα τὴν φύσιν ἐστί: the subject is unclear. Simp., in Cael. 552.7–19 (Heiberg), thinks it is Ð prîtoj oÙranÕj kaˆ t¦ mšrh, as well as t¦ ™n aÙtù ferÒmena ¥stra. Cf., however, the introduction to Cael. B 7: perˆ d tîn kaloumšnwn ¥strwn ˜pÒmenon ¨n e‡h lšgein, ™k t…nwn te sunest©si kaˆ ™n po…oij sc»masi kaˆ t…nej aƒ kin»seij aÙtîn (289a11–13). The plural in ™k t…nwn is misleading. As Aristotle goes on to say in Cael. B 7, 289a13–16, each celestial object is made up of the body in its environment, one which kÚklJ fšresqai pšfuken. Introduced in Cael. A 2, it is a simple body whose natural motion, unlike that of an Empedoclean simple body, is circular. In Cael. A 3 this body is shown to be exempt from generation, decay and change, and is named tÕ prîton tîn, sc. ¡plîn, swm£twn, “the first simple body” (270b2–3); see Introduction, 2–3. In Cael. A 2, 269b2–17, Aristotle suggests that it makes up those things which undergo eternal circular motion, apparently celestial objects, and that, on the cosmic distance ladder, it is farthest out from us on the Earth, whence follows that it is Ð prîtoj oÙranÒj–Ð oÙranÒj in the first, and not also in the second, of the three senses of the noun Aristotle explains in Cael. A 9 (see above, on 298a24, and below, on 298a31; the principle applied in Cael. B 7, 289a13–16, “each thing is made up of what is in its environ-

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ment”, must be tacitly invoked already in Cael. A 2). The natural motion of the first simple body is said in Cael. B 1, 284a35–b2 to be the diurnal rotation, ¹ prèth for£, not its combination with the zodiacal motion of the planets, the Sun and the Moon, too. In Cael. B 4, 286b10–287a5, only the starry envelope of the cosmos is shown to be a spherical shell from the assumption that it consists of the first simple body; as for the following cosmic layer which contains the planets, the Sun and the Moon, it is shown to be spherical from the fact that it is in conformal contact with the upper layer, unlike which thus it does not consist of the first simple body. From Cael. B 12, 291b28–292a3, where the cosmic distance ladder is outlined, it is clear that this body makes up only the nutshell of the cosmos and the luminaries fixed therein, the stars. The rest of the heavens must thus be fiery, and the planets, the Sun and the Moon, which it contains, cannot but be made up of fire. The beginning of Cael. Γ also leads to this conclusion: perˆ mn oân toà prètou oÙranoà…dielhlÚqamen prÒteron in 298a24–27 is repeated in 298b6–7 as perˆ mn oân toà prètou tîn stoice…wn…¢gšnhton. Now, in Cael. B 7 Aristotle undoubtedly thinks that all celestial objects, not only the fixed stars, consist of the first simple body, which also fills the whole heavenly realm of the cosmos. This is his doctrine in Mete. A 2–3; see also Metaph. Λ 8, 1073a23–36. On the orthodox view, the same doctrine is also found in the whole of the de Caelo, an earlier treatise; see e.g. Lee (1952) 12 n. b, Guthrie (1939) xiii–xiv. We can plausibly conclude that Mete. A 2–3 mark a later stage of the evolution of Aristotle’s theory of the first simple body, and that Cael. B 7 was written in light of the expanded cosmological role of this simple body in Mete. A 2–3. For another argument in support of the view presented here see Introduction, n. 2. 298a26–27. ἀγένητα καὶ ἄφθαρτα: the celestial objects referred to here, the fixed stars, are ungenerated and undecayable because they are made up of the first simple body. See previous n. 298a27–28. τῶν φύσει λεγομένων: sc. Ôntwn. Cf. Ph. B 1, 192b8–9: tîn Ôntwn t¦ mšn ™sti fÚsei, t¦ d di’ ¥llaj a„t…aj (the second category contains artifacts; see 192b27–32). According to Ph. B 1, 192b21–23, fÚsij is ¢rc¾ kaˆ a„t…a toà kine‹sqai kaˆ ºreme‹n ™n ú Øp£rcei prètwj kaq’ aØtÕ kaˆ m¾ kat¦ sumbebhkÒj. Cf. the shorter definition in ch. 2, 301b17–18. t¦ fÚsei legÒmena are defined in Ph. B 1, 192b13–15, in terms of fÚsij: toÚtwn mn g¦r ›kaston ™n ˜autù ¢rc¾n œcei kin»sewj kaˆ st£sewj, t¦ mn kat¦ tÒpon, t¦ d kat’ aÜxhsin kaˆ fq…sin, t¦ d kat’ ¢llo…wsin. Cf. Metaph. ∆ 4, 1015a13–19. 298a28. τὰ μέν ἐστιν οὐσίαι: in Ph. B 1, 192b32–33, a few lines after the definition of fÚsij quoted in previous n., Aristotle says that fÚsin d œcei Ósa toiaÚthn œcei ¢rc»n. kaˆ œstin p£nta taàta oÙs…a. 298a28. τὰ δ’ ἔργα καὶ πάθη τούτων: substances act on, and affect, other substances, causing them to move, alter or change into other substances. The term p£qoj is used in a different, though related, sense in 299a20. Cf. n. ad loc.

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298a29–32. λέγω δ’ οὐσίας…καὶ τὰ μόρια τούτων: Aristotle gives similar lists in Ph. B 1, 192b8–13, Metaph. ∆ 8, 1017b10–14, and Z 2, 1028b8–13. 298a29. ἁπλᾶ σώματα: i.e. stoice‹a tîn swm£twn. Cf. Aristotle’s definition of stoice‹on in ch. 3, 302a15–18, and Metaph. ∆ 3, 1014a26–35. 298a30. τὰ σύστοιχα τούτοις: sc. sèmata (see Mete. A 3, 340a5). Elsewhere, too, Aristotle lists only two of the simple bodies, and refers to the rest with this phrase (ch. 3, 302a29–30, GC A 1, 315a20–21; cf. Cael. B 4, 287b20–21). Obviously, he has in mind here not only the four Empedoclean simple bodies but also the first simple body. sÚstoica, therefore, cannot mean kat¦ sustoic…an legÒmena, ‘arranged by two in a two-column table whose rows contain opposite items and whose columns contain somehow similar ones’, as the term is used in the famous list of Pythagorean principles (Metaph. A 5, 986a22–26). This could apply only to the four Empedoclean simple bodies. For they can be arranged in a table whose rows contain the simple bodies both of whose defining qualities are contrary, not just one (each of the Empedoclean simple bodies is differentiated by two qualities, one from each of two pairs of contraries; see Introduction, 3). One column contains the two simple bodies which are light and the other the two simple bodies which are heavy (see GC B 3, 331a1–3, and 8, 335a5–6): fire air

water earth.

In light of Cael. A 2, 268b26–29, sÚstoica here stands for suggenÁ, “of the same kind”: ...tîn swm£twn t¦ mšn ™stin ¡pl© t¦ d sÚnqeta ™k toÚtwn (lšgw d’ ¡pl© mn Ósa kin»sewj ¢rc¾n œcei kat¦ fÚsin, oŒon pàr kaˆ gÁn...kaˆ t¦ suggenÁ toÚtoij); cf. Metaph. ∆ 8, 1017b10–11, and Ph. B 1, 192b8–12. 298a30. ὅσα ἐκ τούτων: i.e. sÚnqeta. Cf. Cael. A 2, 268b26–29, quoted in previous n. 298a31. σύνολον οὐρανόν: “the whole cosmos”. The noun is used here in the third of the three senses of the term Aristotle sets out in Cael. A 9: œti d’ ¥llwj lšgomen oÙranÕn tÕ periecÒmenon sîma ØpÕ tÁj ™sc£thj perifor©j· tÕ g¦r Ólon kaˆ tÕ p©n e„èqamen lšgein oÙranÒn (278b18–21). Here the phrase ¹ ™sc£th perifor£ picks out the spherical boundary surface enclosing the existing masses of all five simple bodies, collectively called sîma: it is the outer surface of a diurnally rotating shell of the first simple body whose fixed parts are the stars (Ð oÙranÒj in the first sense; for it and the second sense see above, on 298a24). 298a31. τὰ μόρια αὐτοῦ: these are the concentric spherical parts of the onion-like cosmos, each of which is made up of one of the five simple bodies in Aristotelian physics. Farthest out from the center is Ð prîtoj oÙranÒj, a diurnally rotating shell of the first simple body whose parts are the stars, and next is a shell of

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fire (see above, on 298a24 and 25–26, and Introduction, 1). The latter’s upper part must contain the planets, the Sun and the Moon (see above, on 298a25–26; for the articulation of the realm of these seven celestial objects according to the theory of homocentric spheres see above, on 298a24). After the fire-shell there is a stratum of air, then a layer of water, and, finally, the Earth, a globe of the simple body earth: most of its surface is covered by the layer of water, and its center is that of the whole cosmos. All celestial objects are parts of the cosmic strata in which they are situated (see above, on 298a25–26). They can thus be among the limbs of the cosmos mentioned here (cf. Metaph. Z 2, 1028b12–13). The first simple body is separated from the other simple bodies on all scales, but the Empedoclean simple bodies are sorted out only on the cosmological scale; see Introduction, 3. 298a31–32. τά τε ζῷα καὶ τὰ φυτὰ καὶ τὰ μόρια τούτων: the most fundamental parts of animals, Aristotle explains in PA B 1, 646a12–24, are the four Empedoclean simple bodies. There are two other categories: the homoeomeric parts, such as blood, flesh etc, which are made up of the four Empedoclean simple bodies and are called so because their divisions yield the same substance, and the unhomoeomeric parts, such as face, hands etc, which are made up of various homoeomeric parts and cannot be divided into things of the same kind; cf. the passage quoted below, on 302a12. To produce homoeomeric parts, the Empedoclean simple bodies are blended together, losing their individuality, into a new substance; see Introduction, 3 and cf. below, on 302a17–18. Like everything existing near the center of the cosmos, all homoeomeric parts are made up only of the Empedoclean elements, all four of them; see again Introduction, 3 and GC B 8. 298a32–34. τάς τε κινήσεις…τὴν ἑαυτῶν: in the second of these two categories of motions fall motions of substances caused by other substances, so the first must contain self-caused motions of substances. The latter are due to nature, an internal principle, i.e. cause, of motion, the former to force, an external principle of motion (for nature see above, on 298a27–28; dÚnamij, “force” or “capacity”, is defined in Metaph. ∆ 12, 1019a15–18, as a cause of change or motion “in the other”–it is not in what is moved or changed–or “qua other–it is in what is moved or changed, but is distinct from it, as, to use Aristotle’s example, in the case of a doctor who is healing himself, whereby agent and patient coincide, but incidentally only; cf. ch. 2, 301b17–19). Ph. Θ 4 complicates this division of motions by adding another one, into natural and forced or non-natural (254b12–14). In Ph. Θ 4 Aristotle regards animal-motion as natural and self-caused (254b14–15), and then argues that, since the traditional elements are not alive, their natural motions (see Introduction, 2) are not self-caused (254b34–255a10). The cause of the natural motion an amount of such an element undergoes is assumed to lie outside the amount of the element in Cael. ∆ 3, too. It is identified with the natural place of the simple body (see 310a31–b15, Ph. Θ 4, 255b13–17, and cf. Gill [2009] 153–158), which does not seem to allow us to assume that the natural motions of the four Empedoclean simple bodies are here considered to be motions of substances that are caused by other substances. Perhaps Aristotle is not interested here in whether the natural

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motions of the four Empedoclean simple bodies are really self-caused, as they appear to be, and simply lumps them together with the natural motions of plants and animals as self-caused. (In Ph. Θ 4, 254b24–33, he denies that even the natural motions of animals are self-caused. But what he establishes in Ph. Θ 4, that everything in motion is moved by something, which in effect collapses nature into passive capacity [see Metaph. ∆ 12, 1019a19–20], is unlikely to be at work in the de Caelo. In it the thesis Ph. Θ argues for, and Metaph. Λ further elaborates–all motion in the cosmos is ultimately due to at least one disembodied unmoved mover–is not presupposed; see Easterling [1961] 148–153 and, on Cael. B 12, cf. Kouremenos [2010] 100–101 nn. 35–36, 103 n. 39). Of all the different substances mentioned above, we should, strictly speaking, exclude the whole cosmos and some of its parts from those to whose motions Aristotle refers to here, for the cosmos does not move as a whole because not all its parts move. The Earth is the central part of the cosmos; not only does it not orbit the cosmic center, it also does not share in the diurnal rotation (see Cael. B 14). On the cosmological scale it is immobile. All water is on the Earth (see the Mete. A 3 passage quoted below). It, too, is immobile on this scale, and so is the lower part of the next cosmic stratum of air: it does not share in the diurnal rotation, which is imparted by the first simple body to the layer of fire and the upper air-layer (see Mete. A 3, 340b33–341a2, and cf. Phlp., in Mete. 37.8–14 [Hayduck]). Aristotle does say that the entire cosmos is rotating, however (see Cael. B 4, 287a11–12); he calls the diurnal motion “rotation of the whole cosmos” even when he explains that the lower stratum of air does not participate in it (see Mete. A 3, 341a2). He does so perhaps because he considers the Earth and the water on it to be an insignificant part of the cosmos, a mere nothing compared with the size of its surroundings: oÙdn g¦r æj e„pe‹n mÒrion Ð tÁj gÁj ™stin Ôgkoj, ™n ú sune…lhptai p©n kaˆ tÕ toà Ûdatoj plÁqoj, prÕj tÕ perišcon mšgeqoj (Mete. A 3, 340a6–8). The part of the stratum of air which does not share in the diurnal rotation is also an insignificant part of the cosmos. As it is, the substances referred to by the demonstrative pronoun toÚtwn could, in a sense, include the whole cosmos, as well as all of its parts, if each of those which do not participate in the diurnal rotation would be implicitly regarded as oÙdn mÒrion prÕj tÕ perišcon mšgeqoj. How the division of motions of substances at work here, into those that are self-caused and those that are caused by other substances, also applies to the motions of the celestial objects, if the latter are to be counted among the parts of the cosmos, is closely linked to the question of the makeup of the heavens; see above, on 298a31 and 298a25–26, and Kouremenos (2010) 46–49. Of the motions of the parts of plants and animals, as self-caused are probably to be regarded those reducible to natural motions of the fundamental parts, the four Empedoclean simple bodies, and as caused by other substances those that are effects of the motions of other parts of the organism, are initiated by the organism itself, or from substances outside it. 298a34–b1. τὰς ἀλλοιώσεις καὶ τὰς εἰς ἄλληλα μεταβάσεις: for a definition of ¢llo…wsij, “alteration”, see GC A 4, 319b6–14. Not all of the substances Aristotle lists in 298b29–32 can suffer this kind of change. That the whole cosmos is

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not subject to alteration follows from the fact that it is ungenerated and undecayable; see Cael. A 12, 283b17–22. The first simple body is also ungenerated, indestructible and unalterable; see Cael. A 3, 270a12–35, where it is contrasted with plants, animals, their parts and the four Empedoclean simple bodies, and Introduction, 3. The phrase e„j ¥llhla met£basij, “transition from one substance to another”, is used here as in ch. 7, 306a22–23, for the change of the traditional elements into one another (cf. the use of the noun in 306a4); see also GC B 4, 332a1–2. 298b1–4. φανερὸν…μεγεθῶν: according to Cael. A 1, 268a1–6, ¹ perˆ fÚsewj ™pist»mh scedÕn ¹ ple…sth fa…netai per… te sèmata kaˆ megšqh kaˆ t¦ toÚtwn oâsa p£qh kaˆ t¦j kin»seij, œti d perˆ t¦j ¢rc£j, Ósai tÁj toiaÚthj oÙs…aj e„s…n· tîn g¦r fÚsei sunestètwn t¦ mšn ™sti sèmata kaˆ megšqh, t¦ d’ œcei sîma kaˆ mšgeqoj, t¦ d’ ¢rcaˆ tîn ™cÒntwn e„s…n. Interpreting this passage, Simp., in Cael. 6.33–7.2 (Heiberg), identifies those of the naturally constituted things that are said to be sèmata kaˆ megšqh with simple bodies, stones, wood etc, those that are said to possess sîma kaˆ mšgeqoj with animals, plants etc, and thinks that ¢rca… of the latter are matter, form, motion etc. This is, in general, correct. The parallel passage in Cael. A 1 probably presupposes Ph. B 1, where Aristotle starts out with a list of natural substances similar to the one in the lines preceding the passage we are concerned with here, defines them as things with a nature, an internal cause of initiating and stopping locomotion and change in general (see above, on 298a27–28), and then goes on to identify nature with both matter and immaterial form: the latter is irreducible to matter but inseparable from it, unless in account, and is nature par excellence. Our passage divides natural substances into two categories whose members combine into the items in the third of the categories distinguished in Cael. A 1: natural substances are bodies, matter of hylomorphic compounds, or immaterial forms which come together with bodies to form hylomorphic compounds and cannot exist apart from bodies and magnitudes. According to Ph. B 9, 200a30–b8, physics studies both the matter and the form of naturally constituted things, whose form is not fully separable from matter even in account, hence Aristotle’s thesis here that physics deals mainly with bodies, not equally with bodies and non-bodily things. Since the largest parts of the cosmos are hylomorphic compounds, each being made up of a simple body and having a shape, there is a sense in which all simple bodies have form–as parts of the cosmos; as bodies, they cannot admit of hylomorphic analysis. This form, which is external to amounts of the four Empedoclean elements undergoing natural motion, must be related to the cause of this motion, on which see above, on 298a32–34. Being alive, the layer of the first element has also a form other than its shape–a soul–as does each planet, the Sun and the Moon; see Kouremenos (2010) 48 n. 111. On the difficulties raised by the corporeality of the first simple body see Kouremenos (2010) 136–137. For the whole cosmos as hylomorphic compound see Cael. A 9, 278a10–15, and Falcon (2005) 13 n. 31. 298b4–5. ἔκ τε τοῦ διωρίσθαι…θεωρίας: here Aristotle probably refers to his discussion in Ph. B 1. See previous n.

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298b6. τοῦ πρώτου τῶν στοιχείων: cf. Mete. A 3, 339b16–19. Aristotle calls it in Cael. A 3, 270b2–3, tÕ prîton tîn, sc. ¡plîn, swm£twn. On this simple body see above, on 298a25–26. For other expressions Aristotle uses for it see Moraux (1963) 1172. See also next n. 298b6–7. ποῖόν τι…ἀγένητον: cf. po‹’ ¥tta t¾n fÚsin ™st…, prÕj d toÚtoij Óti ¢gšnhta kaˆ ¥fqarta in 298a26–27. In 298b6–7 the first four lines of the book are rephrased. What this suggests is explained above, on 298a25–26. 298b8. τοῖν δυοῖν: the four Empedoclean simple bodies. They are two in species. Earth and water are heavy, with a downward natural motion, towards the center of the cosmos, whereas air and fire are light, having an opposite, upward, natural motion, towards the periphery of the cosmos. Cf. the mention of two kinds of natural motion for these four simple bodies in Mete. A 2, 339a11–19. 298b11. τοῖς ἐκ τούτων: these are the compound bodies made up of the traditional simple bodies and the structurally complex objects–plants, animals and their parts–mentioned in 298a31–32 into which these compounds are arranged. They are implicitly contrasted with the ungenerated and indestructible celestial objects mentioned at the beginning of the book, the fixed stars; see above, on 298a25. As argued above, on 298a25–26, almost everywhere in the de Caelo the planets, the Sun and the Moon seem to be assumed to consist of fire, not the ungenerated and undecayable first simple body. But this does not make them subject to generation and decay, for in the outermost part of the fire-shell, where they must be, there seem to be no traces of air, water or earth for these processes to occur; see Introduction, 3. 298b14–17. οἱ μὲν γὰρ αὐτῶν…Μέλισσόν τε καὶ Παρμενίδην: for Parmenides’ denial that tÕ ™Òn can come to be and pass away see DK 28 B 8.1–22. He does not state explicitly that coming to be and passing away are illusions, but this follows from DK 28 B 6–7. Melissus states it explicitly; see DK 30 B 8. 298b17–18. εἰ καὶ τἆλλα λέγουσι καλῶς: i.e. enai ¥tta tîn Ôntwn ¢gšnhta kaˆ Ólwj ¢k…nhta (298b19). 298b18. ἀλλ’ οὐ φυσικῶς γε δεῖ νομίσαι λέγειν: according to Aristotle, the contention that all beings are ungenerated and, in general, completely exempt from all change not only is wrong but also does not concern physics at all. Cf. his more strongly worded criticism of this contention in Ph. Θ 3, 253a32–b6, as “intellectual disease”: tÕ mn oân p£nt’ ºreme‹n, kaˆ toÚtou zhte‹n lÒgon ¢fšntaj t¾n a‡sqhsin, ¢rrwst…a t…j ™stin diano…aj, kaˆ perˆ Ólou tinÕj ¢ll’ oÙ perˆ mšrouj ¢mfisb»thsij· oÙd mÒnon prÕj tÕn fusikÒn, ¢ll¦ prÕj p£saj t¦j ™pist»maj æj e„pe‹n kaˆ p£saj t¦j dÒxaj di¦ tÕ kin»sei crÁsqai p£saj. œti d’ aƒ perˆ tîn ¢rcîn ™nst£seij, ésper ™n to‹j perˆ t¦ maq»mata lÒgoij oÙdšn e„sin prÕj tÕn maqhmatikÒn, Ðmo…wj d kaˆ ™pˆ tîn ¥llwn, oÛtwj oÙd perˆ toà nàn ·hqšntoj prÕj tÕn fusikÒn· ØpÒqesij g¦r Óti ¹ fÚsij ¢rc¾

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tÁj kin»sewj. According to Metaph. E 1, 1025b3–28, where physics is characterized as a theoretical science, all sciences mark off some beings, those which they study, but are not interested in what their objects are and whether such things actually exist: what the objects of their study are, thus whether such things exist, too, is considered to be self-evident, either to the senses or as postulate(s). The first alternative pertains to physics, the study of substances with an internal cause of initiating and stopping change, the second to mathematics. As it is, questioning, let alone denying, the existence of change is irrelevant to physics, whose starting point is the empirical given of change, just as the questions of the existence and nature of mathematical objects are irrelevant to mathematics. Cf. Ph. A 2, 184b25–185a17. 298b19–20. τὸ γὰρ εἶναι…ἢ τῆς φυσικῆς σκέψεως: that there are some beings which are ungenerated and exempt from all change concerns an inquiry prior to that into natural substances because what is uncompounded, e.g. beings without change, is prior to what is compounded, beings plus change, hence the study of the former is prior to that of the latter (for the principle “the uncompounded is prior to the compounded” see Metaph. M 2, 1076b18–19). Cf. Metaph. E 1, 1026a10–16: e„ dš t… ™stin ¢dion kaˆ ¢k…nhton kaˆ cwristÒn, fanerÕn Óti qewrhtikÁj tÕ gnînai, oÙ mšntoi fusikÁj ge (perˆ kinhtîn g£r tinwn ¹ fusik») oÙd maqhmatikÁj, ¢ll¦ protšraj ¢mfo‹n. ¹ mn g¦r fusik¾ perˆ cwrist¦ mn ¢ll’ oÙk ¢k…nhta, tÁj d maqhmatikÁj œnia perˆ ¢k…nhta mn oÙ cwrist¦ d ‡swj ¢ll’ æj ™n ÛlV· ¹ d prèth kaˆ perˆ cwrist¦ kaˆ ¢k…nhta. The independently existing substances of Metaph. E 1 which are exempt from change are considered divine, and the science which is prior to physics and studies them is identified with theology, whose priority is axiological, too, for it studies the ultimate causes in nature (1026a16–23). These divine substances must be the disembodied unmoved movers of Metaph. Λ, which do not seem to be presupposed in the de Caelo (see above, on 298a32–34): it is thus unlikely that the substances said in the lines under discussion to be ungenerated and exempt from all change are the same as the divine substances of Metaph. E 1, and thus that the science which is prior to physics and studies them is theology–at least as this science is conceived of in Metaph. E 1. Since in our lines the ungenerated beings exempt from all change are not said to exist independently, as those of Metaph. E 1 do, if this is not accidental, they are simply the forms of hylomorphic compounds studied in physics (see above, on 298b1–4, and cf. Metaph. Z 8, 1033b5–8, on the ungeneratedness of forms). The science studying them is that of being qua being. It studies the substantiality of natural substances, explaining it in terms of forms, and could include, or be reduced to, theology, insofar as in the de Caelo the shell of the eternal first element whose parts are the stars is alive, as are the other eternal celestial objects–each of them has its own inseparable form (see above, on 298b1–4). In Metaph. E 1, 1026a27–32, Aristotle also conceives of the science prior to physics as a general study of being qua being without making clear how the two conceptions of the science prior to physics, as theology and the study of being qua being, are supposed to be harmonized: e„ mn oân m¾ œsti tij ˜tšra oÙs…a par¦ t¦j fÚsei sunesthku…aj, ¹ fusik¾ ¨n e‡h prèth ™pist»mh· e„ d’ œsti tij oÙs…a ¢k…-

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nhtoj, aÛth protšra kaˆ filosof…a prèth, kaˆ kaqÒlou oÛtwj Óti prèth· kaˆ perˆ toà Ôntoj Î ×n taÚthj ¨n e‡h qewrÁsai, kaˆ t… ™sti kaˆ t¦ Øp£rconta Î Ôn. The relation between Aristotle’s various conceptions of the first philosophy, the science prior to physics, has been extensively discussed. For an overview see Wedin (2009); two classic developmental solutions to the problem are discussed in Code (1996). 298b21. ἐκεῖνοι: sc. oƒ perˆ MšlissÒn te kaˆ Parmen…dhn (298b17). 298b22. τοιαύτας: sc. ¢gen»touj kaˆ Ólwj ¢kin»touj (cf. 298b19). 298b23. εἴπερ ἔσται τις γνῶσις ἢ φρόνησις: cf. Aristotle’s famous discussion of the Platonic forms in Metaph. A 6, 987a29–b10, and M 4, 1078b12–17. 298b24. ἐπὶ ταῦτα τοὺς ἐκεῖθεν λόγους: sc. ™pˆ t¦ a„sqht¦ toÝj ¢pÕ t¦ ¢gšnhta kaˆ Ólwj ¢k…nhta tîn Ôntwn lÒgouj. 298b24–27. ἕτεροι δέ τινες…γίγνεσθαι: cf. Pl., Tht. 152d2–e9. 298b28–29. μάλιστα μὲν…οἱ πρῶτοι φυσιολογήσαντες: Aristotle adopts a very guarded attitude in Metaph. A 3, 983b27–984a3, to some who think that “the early theologians”, oƒ prîtoi qeolog»santej, among whom Hesiod and Homer must be numbered, had already advanced the views on water that Thales famously put forth (cf. Pl., Tht. 152d2–e9). Aristotle’s unnamed opponent is probably Hippias of Elis, as Snell (1944) suggested. Unlike here, in that passage he seems to be unwilling to treat seriously Hesiod and the rest of “the early theologians” as “early natural philosophers”; see Mansfeld (1985) 114–117 (not many lines below, however, in 984b20–32, he is willing to entertain the possibility that Hesiod had a hazy conception of the efficient cause, similar to that of Parmenides). Had he treated Hesiod as a forerunner of Thales here, he would have included the poet among those referred to next. On Aristotle and “the early theologians” see Palmer (2000) and the discussion in Bodéüs (2000) 78–81; cf. Zhmud (2006) 130–131. 298b29–33. οἱ δὲ…ὁ Ἐφέσιος: cf. ch. 5, 303b10–11, with n. ad loc. 298b33–299a1. εἰσὶ δέ τινες…ἐξ ἐπιπέδων: Plato, in Ti. 53c4–56c7, assumes that two kinds of elementary right triangles, isosceles and scalene, the latter having their hypotenuses double their shorter sides, make up the faces of the atoms of the four Empedoclean elements, which are regular polyhedra. The atoms of fire are tetrahedra–pyramids–those of air octahedra, those of water icosahedra, those of earth simple cubes. Since the planar constituents of atoms of fire, air and water are of the same kind, quantities of each of these stuffs can turn into another, and quantities of any two of them can turn into the third; none can turn into earth and vice versa, however. Empedocles had conceived of the four elements that are named after him as exempt from generation and decay (DK 31 B 17.30–35). Since all

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bodies other than the elements consist of the latter, Plato constructs all bodies from planes and breaks them up into planes. The author of the pseudo-Platonic Epinomis is also referred to here; cf. below, on 307a16. Xenocrates of Chalcedon may be included, too; see Isnardi Parente (1982) 362 and Dillon (2003) 117 n. 83. For Speusippus see Tarán (1981) 265. On the nature of the triangles see Miller (2003) 173–178. 299a1–2. περὶ μὲν οὖν…λόγος: in Cael. A 10, 279b17–31, Aristotle argues against the assumption that the cosmos is generated but indestructible in a manner easily generalized against those who think that all things are generated but some generated things are indestructible (Simp., in Cael. 293.12–15 [Heiberg], comments ad loc., following Alexander of Aphrodisias, that Aristotle argues against theologians such as Orpheus and Hesiod). Against those who think that all things are generated except one, that from which, as a persisting substratum, all other things come to be, Aristotle argues below, in ch. 5. 299a2–6. τοῖς δὲ…τῶν ὑποθέσεων: Aristotle, according to Simp., prîton œgklhma toÚtoij ™p£gei tÕ t¦j gewmetrik¦j ¢rc¦j ¢naire‹n prÒceiron enai lšgwn t¾n toÚtou katanÒhsin· diÕ kaˆ parÁken aÙt»n. lšgei d ¢naire‹n aÙtoÝj toÝj tîn gewmetrîn Órouj toà te shme…ou kaˆ tÁj grammÁj kaˆ tÁj ™pifane…aj· e„ g¦r shme‹on lšgousin, oá mšroj oÙqšn, gramm¾n d mÁkoj ¢platšj, ™pif£neian dš, Ö mÁkoj kaˆ pl£toj mÒnon œcei, oÙk ¥n pote ™k shme…wn gramm¾ gšnoito, éste oÙd ™k grammîn ™pif£neia oÙd ™x ™pifane…aj ¢baqoàj oÜshj sîma bebaqusmšnon· e„ d g…netai ™x ™pipšdou sîma, b£qoj ¨n œcoi tÕ ™p…pedon, kaˆ e„ ™k grammîn ™p…pedon, oÙk ¨n e‡h ¢plat¾j ¹ gramm», kaˆ e„ ™k shme…wn gramm», oÙk ¨n ¢merj e‡h tÕ shme‹on (in Cael. 562.21–30 [Heiberg]). In the pseudo-Aristotelian treatise On Indivisible Lines, however, there is a clear allusion to our passage which suggests that the author of this short treatise must have seen in the passage under discussion a reference to the mathematically inadmissible existence of indivisible lines as what, according to Aristotle, causes Plato’s construction of all bodies ultimately out of planes in the Timaeus to conflict with mathematics: Óti mn oân œk ge tîn e„rhmšnwn lÒgwn oÜt’ ¢nagka‹on ¢tÒmouj enai gramm¦j oÜte piqanÒn, fanerÒn. œti d kaˆ ™k tînde gšnoit’ ¨n fanerèteron. prîton mn ™k tîn ™n to‹j maq»masi deiknumšnwn kaˆ tiqemšnwn, § d…kaion À mšnein À pistotšroij lÒgoij kine‹n (969b26–31). The similarity between this and our passage has not escaped attention; see Moraux (1965) 105, Timpanaro Cardini (1970) 56 (apparatus criticus of each edition) and Joachim (1908) on LI 969b30–31. As the author of the pseudo-Aristotelian work read our lines, aƒ Øpoqšseij, whose clash with the construction of all bodies out of planes in the Timaeus precludes this scheme, as Aristotle has it, cannot be those Simp. thinks they are. Whatever they might be, however, there is clearly a problem with the implicit reading of our passage by the unknown author. For, immediately after it, in 299a6–11, Aristotle does introduce the mathematically inadmissible existence of indivisible lines as an implication of the Platonic construction of all bodies ultimately out of planes. The text, however, as it stands, leaves no doubt that Aristotle understands this to be a

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mathematical difficulty with Plato’s theory distinct from those hinted at in our passage: œpeita dÁlon Óti toà aÙtoà lÒgou ™stˆ stere¦ mn ™x ™pipšdwn sugke‹sqai, ™p…peda d’ ™k grammîn, taÚtaj d’ ™k stigmîn· oÛtw d’ ™cÒntwn oÙk ¢n£gkh tÕ tÁj grammÁj mšroj gramm¾n enai· perˆ d toÚtwn ™pšskeptai prÒteron ™n to‹j perˆ kin»sewj lÒgoij, Óti oÙk œstin ¢dia…reta m»kh. Implicit here is the assumption that indivisible points qua constituents of lines are equivalent to indivisible lines; see below, on 299a9–11. On the other hand, it is difficult to accept the interpretation of our passage by Simp. Taking as a premise the first part of the passage just quoted, the commentator attributes to Aristotle the view that Plato’s construction of all bodies ultimately out of planar elements conflicts with mathematics in that it entails, among other things, that lines consist of divisible points. If this is what Aristotle said in our passage, how plausible is it that immediately next, based on the same premise, which is now explicitly stated, he would argue that, by making up all bodies ultimately of planes, Plato assumes in effect that lines consist of indivisible points, which are indistinguishable, as elements of lines, from indivisible lines? If, moreover, Aristotle wanted to argue, from the same premise, that Plato is committed to the assumption that lines consist of points, either divisible or indivisible, two alternatives which are equally unacceptable mathematically, why would he say of the first alternative only that it is easy to see but bother to flesh out the second, stating the premise whence both alternatives follow? Back now to the reading of the passage under discussion implicit in the treatise On Indivisible Lines, the problem with it noted above can be surmounted if the author had a de Caelo text with ™peˆ t£de instead of œpeita of modern editions in 299a6, the conjunction introducing a causal clause giving the reason for what is said in our passage. The variant œpeita dš, which is attested in a few manuscripts according to the apparatus criticus of modern editions, can be very plausibly assumed to have arisen through mistaken word-division: the original text read ™peˆ t£de. In other words, if the author of On Indivisible Lines saw in the passage under discussion a reference to the mathematically unacceptable existence of indivisible lines as what, in Aristotle’s view, causes Plato’s construction of all bodies out of planes to clash with mathematics, this is so because, in the author’s text of the de Caelo, this passage, 299a2–6, and the immediately subsequent one, 299a6–9, formed a unit, which read as follows: to‹j d toàton tÕn trÒpon lšgousi kaˆ p£nta t¦ sèmata sunist©sin ™x ™pipšdwn Ósa mn ¥lla sumba…nei lšgein Øpenant…a to‹j maq»masin, ™pipolÁj „de‹n (ka…toi d…kaion À m¾ kine‹n À pistotšroij aÙt¦ lÒgoij kine‹n tîn Øpoqšsewn), ™peˆ t£de dÁlon Óti toà aÙtoà lÒgou ™st…, stere¦ mn ™x ™pipšdwn sugke‹sqai, ™p…peda d’ ™k grammîn, taÚtaj d’ ™k stigmîn· oÛtw d’ ™cÒntwn oÙk ¢n£gkh tÕ tÁj grammÁj mšroj gramm¾n enai. If this is what Aristotle wrote, the Platonic theory subverts mathematics only insofar as it entails the existence of indivisible lines, not also because it and aƒ Øpoqšseij of mathematics clash: Aristotle’s point is that Plato’s theory entails that there are indivisible lines, so it and aƒ Øpoqšseij of mathematics clash, mathematics being thus subverted, which is unacceptable. Note that Ósa mn ¥lla in 299a3 does not point to two types of mathematical difficulties with Plato’s theory. Ósa dš occurs in 299a11, and intro-

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duces physical difficulties with Plato’s theory, so Ósa mšn in 299a3 is written with the distinction of mathematical from physical difficulties in mind, not of one class of mathematical difficulties from another. In 299a11–17 Aristotle does draw explicitly the distinction between the mathematical and the physical difficulties facing the theory, observing that all mathematical difficulties translate into physical ones, though not vice versa, and that next he will focus on physical difficulties not translatable into mathematical ones: in 299a3, as it is, the adjective ¥lla is added proleptically to Ósa mšn, in anticipation of the fact that the mathematical difficulties introduced by the relative clause are physical, too. Now, that these mathematical difficulties stem from the existence of indivisible lines, as proposed above on the evidence in the treatise On Indivisible Lines, is supported by the fact that the purely physical difficulties with Plato’s theory Aristotle says in 299a11–17 he will next focus on are explicitly said to stem from the existence of indivisible lines assumed by him to be implicit in Plato’s theory: the same must, consequently, apply to those physical difficulties introduced by the Ósa mšn clause in 299a3 that are also mathematical. aƒ Øpoqšseij of mathematics, which the Platonic theory is said to inadmissibly disturb, can be plausibly assumed to be the definitions of line and straight line (cf. LI 969b31–33), but also assumptions of existence (ØpÒqesij is used in this sense in APo. A 2, 72a14–24): Aristotle must have in mind the existence of incommensurable lines and irrational squares (cf. LI 969b33–970a5). He uses the term ØpÒqesij in EE B 11, 1227b23–32, also for a proposition assumed in a mathematical proof: the bisection of any given line (Euc., El. 1.10) might be implicit here (cf. Procl., in Euc. 277.25–279.4 [Friedlein]). Cf. LI 970a5–19. The clash of the hypothesis of indivisible magnitudes, which are smaller than any other magnitude, with mathematics is also emphasized in Cael. A 5, 271b8–13: ...kaˆ tÕ mikrÕn parabÁnai tÁj ¢lhqe…aj ¢fistamšnoij g…netai pÒrrw muriopl£sion. oŒon e‡ tij ™l£ciston ena… ti fa…h mšgeqoj· oátoj g¦r toÙl£ciston e„sagagën t¦ mšgista kine‹ tîn maqhmatikîn. toÚtou d’ a‡tion Óti ¹ ¢rc¾ dun£mei me…zwn À megšqei, diÒper tÕ ™n ¢rcÍ mikrÕn ™n tÍ teleutÍ g…netai pammšgeqej. Cf. ch. 4, 303a20–22, and 7, 306a26–30, with nn. ad loc. 299a6–8. ἔπειτα…ἐκ στιγμῶν: Simp., in Cael. 563.9–12 (Heiberg), sees in these lines an argument that can lead to the absurdity he thinks is implicit in the preceding lines, 299a2–6, but is used here to a different end. See, however, previous n. stigmîn = shme…wn. Cf. GC A 2, 317a11–12: oÙ g£r ™stin ™cÒmenon shme‹on shme…ou À stigm¾ stigmÁj. Simp., in Cael. 563.12–17 (Heiberg), explains correctly these lines as follows: tÕ d legÒmenÒn ™sti toioàton· Ön œcei lÒgon ™p…pedon prÕj sîma, toioàton œcei kaˆ gramm¾ prÕj ™p…pedon kaˆ stigm¾ prÕj gramm»n· pšrata g¦r p£nta· toà aÙtoà oân ™sti lÒgou tÒ te sîma ™x ™pipšdwn genn©n kaˆ tÕ ™p…pedon ™k grammîn kaˆ t¾n gramm¾n ™k stigmîn. ¢ll’ ™¦n ™k stigmîn ¹ gramm», œsontai mšroj aƒ stigmaˆ tÁj grammÁj. Planes must be lines lying one next to the other, lines strings of points. 299a8–9. οὕτω δ’ ἐχόντων…γραμμὴν εἶναι: éste oÙ p©n mšroj grammÁj gramm», e‡per kaˆ aƒ stigmaˆ mšrh tÁj grammÁj e„sin· éste kaˆ katal»xei

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¹ tÁj grammÁj tom», kaˆ oÙkšti ™p’ ¥peiron œstai diairet», e‡per ™k stigmîn ¹ gramm¾ sÚgkeitai (Simp., in Cael. 563.18–20 [Heiberg]). 299a9–11. περὶ δὲ τούτων…ἀδιαίρετα μήκη: if lines, which have length, are composed of indivisible points, the latter must themselves have length, hence they must be indivisible lines. Conversely, if indivisible lines exist, there is no distinction between lines and points. This is noted in LI 970b29–31: Ólwj te t… dio…sei stigm¾ grammÁj; oÙdn g¦r ‡dion ›xei ¹ ¥tomoj gramm¾ par¦ t¾n stigm¾n pl¾n toÜnoma. oƒ perˆ kin»sewj lÒgoi are Ph. Z: in ch. 1, 231a21–b18, Aristotle shows that continua are infinitely divisible, i.e. that they are not composed of indivisibles (cf. Simp., in Cael. 563.20–25 [Heiberg]). Simp. argues in Plato’s defense that Aristotle would have been correct in ascribing to Plato the untenable view that lines ultimately consist of points, i.e. indivisible lines, had Plato treated the planar components making up the faces of the polyhedral atoms of the four elements as mathematical surfaces without depth, which is not the case: the faces of the atoms are not composed of mathematical but of material surfaces of entities with depth (in Cael. 563.26–564.3 [Heiberg]). In the commentator’s view, there is no analysis of the Platonic atoms into planar components of their faces, so nothing compels us to view the surfaces making up the faces of the atoms as being analogically made up of lines, which are similarly, and equally untenably, composed of points, i.e. indivisible lines, as Aristotle has it. Even if Aristotle is right in treating Plato’s triangles as mathematical surfaces, however, it does not follow that, by constructing from mathematical surfaces the atoms of the four elements, which are mathematical polyhedra, just like the surface-elements of their faces are mathematical planes, Plato ends up positing in an unmathematical fashion points, or indivisible lines, as constituents of lines. There is nothing unmathematical in planes making up polyhedra as their faces, or planar elements thereof, nor does this lead to the conclusions that planes are composed of lines in some other sense than the mathematically unobjectionable one of their being bounded by lines, i.e. that they are rafts of lines lying one next to the other, and that lines are thus made up of consecutive points, which turn out to be indivisible lines–points need be nothing other than boundaries of lines. Cf. below, on 300a7–12. 299a13. καὶ νῦν: Aristotle means that physical absurdities implicit in the assumption of indivisible magnitudes have been set out ™n to‹j perˆ kin»sewj lÒgoij, i.e. in Ph. Z 1, 231b18–232a22, and 10, 240b8–241a26. 299a13–14. τὰ μὲν γὰρ ἐπ’ ἐκείνων ἀδύνατα συμβαίνοντα: i.e. t¦ mn g¦r ™pˆ tîn ¢tÒmwn grammîn ¢dÚnata sumba…nonta, such as those alluded to above, in 299a2–6, which are purely mathematical, independent, that is, of physical considerations. 299a14–15. καὶ τοῖς φυσικοῖς ἀκολουθήσει: sc. sèmasi. All mathematical absurdities implicit in the assumption of indivisible magnitudes are physical, too.

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299a15. τὰ δὲ τούτοις ἐπ’ ἐκείνων οὐχ ἅπαντα: i.e. t¦ d to‹j fusiko‹j sèmasi ¢kolouqoànta ¢dÚnata, Ósa sumba…nei lšgein to‹j poioàsi t¦j ¢tÒmouj gramm£j, ™pˆ tîn ¢tÒmwn grammîn oÙc ¤panta sumba…nei. Not all physical absurdities implicit in the assumption of indivisible magnitudes are mathematical, too. 299a15–17. διὰ…προσθέσεως: objects studied in mathematics, t¦ maqhmatik£, i.e. solids, surfaces, lines and points, are the products of abstraction, t¦ ™x ¢fairšsewj, from physical objects. Physical bodies studied in physics do have solids, surfaces etc. They rather than the denizens of a Platonic realm make up the subject matter of mathematics. See Ph. B 2, 193b23–25: kaˆ g¦r ™p…peda kaˆ stere¦ œcei t¦ fusik¦ sèmata kaˆ m»kh kaˆ stigm£j, perˆ ïn skope‹ Ð maqhmatikÒς. Mathematics, however, unlike physics, studies the shape of physical bodies independently of what these bodies are, i.e. things with natures, innate principles of starting and interrupting motion and various changes. This abstraction from motion and change is only intellectual–what is abstracted cannot exist without what it is abstracted from, the moving and/or changing physical bodies–and the study of its products does not lead to falsehoods. See Ph. B 2, 193b31–35: perˆ toÚtwn mn oân pragmateÚetai kaˆ Ð maqhmatikÒj, ¢ll’ oÙc Î fusikoà sèmatoj pšraj ›kaston· oÙd t¦ sumbebhkÒta qewre‹ Î toioÚtoij oâsi sumbšbhken· diÕ kaˆ cwr…zei· cwrist¦ g¦r tÍ no»sei kin»seèj ™sti, kaˆ oÙdn diafšrei, oÙd g…gnetai yeàdoj cwrizÒntwn. Abstraction from motion and change entails abstraction from weight and lightness, i.e. from the natural motions of the simple bodies making up all physical bodies near the center of the cosmos, and from all those properties with respect to which these physical bodies are capable of affecting one another. See Metaph. K 3, 1061a28–b4: kaq£per d’ Ð maqhmatikÕj perˆ t¦ ™x ¢fairšsewj t¾n qewr…an poie‹tai (perielën g¦r p£nta t¦ a„sqht¦ qewre‹, oŒon b£roj kaˆ koufÒthta kaˆ sklhrÒthta kaˆ toÙnant…on, œti d kaˆ qermÒthta kaˆ yucrÒthta kaˆ t¦j ¥llaj a„sqht¦j ™nantièseij, mÒnon d katale…pei tÕ posÕn kaˆ sunecšj, tîn mn ™f’ e$n tîn d’ ™pˆ dÚo tîn d’ ™pˆ tr…a, kaˆ t¦ p£qh t¦ toÚtwn Î pos£ ™sti kaˆ sunecÁ, kaˆ oÙ kaq’ ›terÒn ti qewre‹, kaˆ tîn mn t¦j prÕj ¥llhla qšseij skope‹ kaˆ t¦ taÚtaij Øp£rconta, tîn d t¦j summetr…aj kaˆ ¢summetr…aj, tîn d toÝj lÒgouj, ¢ll’ Ómwj m…an p£ntwn kaˆ t¾n aÙt¾n t…qemen ™pist»mhn t¾n gewmetrik»n), tÕn aÙtÕn d¾ trÒpon œcei kaˆ perˆ tÕ Ôn. Cf. Metaph. M 2–3, 1077b12–1078a31. By adding back all that has been subtracted, we transition from mathematical to the original physical objects, which is why the latter are said to be “products of addition” (t¦ ™k prosqšsewj). It is thus clear that all mathematical absurdities are physical absurdities, for they are impossibilities asserted of pared-down physical objects, but not the other way around: there are impossibilities asserted of what has been pared away from physical objects so as for the mathematical objects to be obtained. On abstraction see Mueller (1970) and Lear (1982). 299a17–18. πολλὰ δ’ ἐστὶν…ἀναγκαῖον: if indivisibles, whether points or lines, made up the rest of mathematical objects, then, although the latter are prod-

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ucts of abstraction from physical objects, it would be impossible to add back to these products of abstraction what they are abstracted from, and thus obtain the original physical objects as products of addition–what ought to be added back cannot belong to indivisibles, nor thus to what is made up of them. 299a19–20. ἐν ἀδιαιρέτῳ…ὑπάρχειν: the reason why if indivisibles constituted the rest of mathematical objects it would be impossible to add back to the latter what they are assumed to have been abstracted from is that mathematical objects are assumed to have been abstracted from divisibles, but nothing divisible can belong to indivisibles, nor to anything indivisibles might be assumed to make up. 299a20. τὰ δὲ πάθη: sc. t¦ a„sqht£, from which mathematical objects are abstracted. See Metaph. K 3, 1061a28–b4 (quoted above, on 299a15–17). A few lines below, in 299a23, they are called paq»mata. Cf. Sens. 6, 445b4–6: t¦ paq»mata t¦ a„sqht£, oŒon crîma kaˆ cumÕj kaˆ Ñsm¾ kaˆ yÒfoj, kaˆ barÝ kaˆ koàfon, kaˆ qermÕn kaˆ yucrÒn, kaˆ sklhrÕn kaˆ malakÒn. 299a20–21. διαιρετὰ…κατὰ συμβεβηκός: of the two senses in which, according to Aristotle, t¦ p£qh t¦ a„sqht£ are divisible, only the second is relevant to his argument. See next n. 299a21–22. κατ’ εἶδος…τὸ μέλαν: according to Sens. 6, 445b21–29, t¦ p£qh t¦ a„sqht£ are each divisible into species. There is a finite number of such species between two opposed extremes: ...pepšrantai t¦ e‡dh kaˆ crèmatoj kaˆ cumoà kaˆ fqÒggwn kaˆ tîn ¥llwn a„sqhtîn. ïn mn g£r ™stin œscata, ¢n£gkh peper£nqai t¦ ™ntÒj· t¦ d’ ™nant…a œscata, p©n d tÕ a„sqhtÕn œcei ™nant…wsin, oŒon ™n crèmati tÕ leukÕn kaˆ tÕ mšlan, ™n cumù glukÝ kaˆ pikrÒn· kaˆ ™n to‹j ¥lloij d¾ p©s…n ™stin œscata t¦ ™nant…a. tÕ mn oân sunecj e„j ¥peira tšmnetai ¥nisa, e„j d’ ‡sa peperasmšna· tÕ d m¾ kaq’ aØtÕ sunecj e„j peperasmšna e‡dh. A species is indivisible, so it is not divisibility by species that makes it impossible for t¦ p£qh t¦ a„sqht£ to belong to indivisibles. 299a22–23. κατὰ συμβεβηκὸς…διαιρετόν: insofar as they are diairet¦ kat¦ sumbebhkÒj, t¦ p£qh t¦ a„sqht£ are kat¦ sumbebhkÕj pos£. See the definition of posÒn in Metaph. ∆ 13, 1020a7–32: posÕn lšgetai tÕ diairetÕn e„j ™nup£rconta ïn ˜k£teron À ›kaston ›n ti kaˆ tÒde ti pšfuken enai. plÁqoj mn oân posÒn ti ™¦n ¢riqmhtÕn Ï, mšgeqoj d ¨n metrhtÕn Ï. lšgetai d plÁqoj mn tÕ diairetÕn dun£mei e„j m¾ sunecÁ, mšgeqoj d tÕ e„j sunecÁ· megšqouj d tÕ mn ™f’ e4n sunecj mÁkoj tÕ d’ ™pˆ dÚo pl£toj tÕ d’ ™pˆ tr…a b£qoj. toÚtwn d plÁqoj mn tÕ peperasmšnon ¢riqmÕj mÁkoj d gramm¾ pl£toj d ™pif£neia b£qoj d sîma. œti t¦ mn lšgetai kaq’ aØt¦ pos£, t¦ d kat¦ sumbebhkÒj, oŒon ¹ mn gramm¾ posÒn ti kaq’ ˜autÒ, tÕ d mousikÕn kat¦ sumbebhkÒj…tîn d kat¦ sumbebhkÕj legomšnwn posîn t¦ mn oÛtwj lšgetai ésper ™lšcqh Óti tÕ mousikÕn posÕn kaˆ tÕ leukÕn tù enai

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posÒn ti ú Øp£rcousi, t¦ d æj k…nhsij kaˆ crÒnoj· kaˆ g¦r taàta pÒs’ ¥tta lšgetai kaˆ sunecÁ tù ™ke‹na diairet¦ enai ïn ™stˆ taàta p£qh. lšgw d oÙ tÕ kinoÚmenon ¢ll’ Ö ™kin»qh· tù g¦r posÕn enai ™ke‹no kaˆ ¹ k…nhsij pos», Ð d crÒnoj tù taÚthn. See also Cat. 6, 5a38–b10. Aristotle asserts in Sens. 6, 445b29–30, that t¦ mn p£qh, sc. t¦ a„sqht£, æj e‡dh lektšon, Øp£rcei d sunšceia, sc. kat¦ sumbebhkÒj, ¢eˆ ™n toÚtoij–i.e. they are each indivisible as species but continuous, that is infinitely divisible, accidentally, insofar as they each belong to what is continuous. Since t¦ p£qh t¦ a„sqht£ are accidentally continuous, they cannot belong to indivisibles. If indivisibles made up the rest of mathematical objects, therefore, it would be impossible to add back to mathematical objects what they are assumed to have been abstracted from: they are assumed to have been abstracted from accidentally divisibles ad infinitum, t¦ p£qh t¦ a„sqht£, which cannot belong to indivisibles, nor to anything indivisibles might be assumed to make up. 299a23. ὅσα ἁπλᾶ τῶν παθημάτων: sc. Ósa e‡dei ¢dia…reta. 299a24. τοῦτον τὸν τρόπον: sc. kat¦ sumbebhkÒj. 299a24–25. διὸ τὸ ἀδύνατον ἐν τοῖς τοιούτοις ἐπισκεπτέον: sc. diÕ tÕ ¢dÚnaton perˆ tîn fusikîn swm£twn Ö sumba…nei lšgein to‹j poioàsi t¦j ¢tÒmouj gramm¦j ™n to‹j kat¦ sumbebhkÕj diaireto‹j ¡plo‹j paq»masin ™piskeptšon, where to‹j poioàsi t¦j ¢tÒmouj gramm£j = to‹j p£nta t¦ sèmata sunist©sin ™x ™pipšdwn. 299a25–26. εἰ δὴ…ἔχειν βάρος: cf. 299b14–23. 299a26–28. τὰ δ’ αἰσθητὰ…ὕδωρ: for the view that all four elements have weight, each in its cosmic stratum, where most of its mass existing in the cosmos is found, see Pl. Ti. 63b2–e7 (quoted below, on 307a9–11). For Aristotle’s distinction between absolute and relative weight and lightness see below, on 299b1–4. 299a28. ὡς κἂν αὐτοὶ φαῖεν: sc. oƒ poioàntej t¦j ¢tÒmouj gramm£j = oƒ p£nta t¦ sèmata sunist£ntej ™x ™pipšdwn. Cf. previous n. 299a28. εἰ ἡ στιγμὴ μηδὲν ἔχει βάρος: equivalently, e„ ¹ ¥tomoj gramm¾ mhdn œcei b£roj. Cf. above, on 299a9–11. Weight is accidentally divisible ad infinitum, so it cannot belong to indivisibles: thus indivisible points or, equivalently, indivisible lines cannot have weight. 299a29–30. δῆλον…οὐθέν: if indivisible points or, equivalently, indivisible lines do not have weight, physical bodies cannot have weight if they are made up of the four elements, whose fundamental corpuscles are, as Plato thinks, constructed from planes. For, according to Aristotle, Plato’s view entails that planes are made up of lines, which are constructed from indivisible points or lines: if the

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latter cannot have weight, however, physical bodies, which ultimately consist of these indivisibles, cannot have weight either. For Aristotle, weight and t¦ p£qh t¦ a„sqht£ in general are accidentally divisible ad infinitum, mirroring the divisibility of the physical bodies they belong to. If their accidental divisibility stopped at a certain scale, then, below it, physical bodies, being continua, would be made up of what would lack weight etc, that is of what would be non-physical–in other words, they would be reduced to mathematical objects, which is the absurd position Aristotle attributes to Plato here. See Sens. 6, 445b3–20: ¢por»seie d’ ¥n tij, e„ p©n sîma e„j ¥peiron diaire‹tai, «ra kaˆ t¦ paq»mata t¦ a„sqht£, oŒon crîma kaˆ cumÕj kaˆ Ñsm¾ kaˆ yÒfoj, kaˆ barÝ kaˆ koàfon, kaˆ qermÕn kaˆ yucrÒn, kaˆ sklhrÕn kaˆ malakÒn, À ¢dÚnaton. poihtikÕn g£r ™stin ›kaston aÙtîn tÁj a„sq»sewj (tù dÚnasqai g¦r kine‹n aÙt¾n lšgetai p£nta), ést’ ¢n£gkh, e„ ¹ dÚnamij, kaˆ t¾n a‡sqhsin e„j ¥peira diaire‹sqai kaˆ p©n enai mšgeqoj a„sqhtÒn (¢dÚnaton g¦r leukÕn mn Ðr©n, m¾ posÕn dš)· e„ g¦r m¾ oÛtwj, ™ndšcoit’ ¨n ena… ti sîma mhdn œcon crîma mhd b£roj mhd’ ¥llo ti toioàton p£qoj, ést’ oÙd’ a„sqhtÕn Ólwj· taàta g¦r t¦ a„sqht£. tÕ ¥r’ a„sqhtÕn œstai sugke…menon oÙk ™x a„sqhtîn. ¢ll’ ¢nagka‹on· oÙ g¦r d¾ œk ge tîn maqhmatikîn. œti t…ni krinoàmen taàta kaˆ gnwsÒmeqa; À tù nù; ¢ll’ oÙ noht£, oÙd noe‹ Ð noàj t¦ ™ktÕj m¾ met’ a„sq»sewj. ¤ma d’ e„ taàt’ œcei oÛtwj, œoike marture‹n to‹j t¦ ¥toma poioàsi megšqh· oÛtw g¦r ¨n lÚoito Ð lÒgoj. ¢ll’ ¢dÚnata· e‡rhtai d perˆ aÙtîn ™n to‹j lÒgoij to‹j perˆ kin»sewj. Admitting that t¦ p£qh t¦ a„sqht£ are not accidentally divisible below a certain scale, the smallest at which they are perceptible, would testify to the position of those who “posit indivisible magnitudes”, i.e. as constituents of physical bodies, if the physical bodies themselves stopped being divisible at the same scale, their indivisible quanta coinciding with those of each of t¦ p£qh t¦ a„sqht£, so that the reduction of physical objects to mathematical objects would be avoided. Aristotle does not hint at this after the lines under discussion when he argues that weight etc must be accidentally divisible ad infinitum. For his solution to the problem he raises in the passage just quoted see Sens. 6, 445b20–446a20. 299a30–31. ἀλλὰ μὴν…φανερόν: indivisible points or, equivalently, indivisible lines cannot have not only weight but also lightness and the rest of t¦ p£qh t¦ a„sqht£. Cf. below, on 299b5–6. 299a31–b1. τὸ μὲν γὰρ βαρὺ…εἶναι: if, for something heavy or light, there can always be found something less heavy or light, it does not follow that, according to Aristotle, there can always be found something heavier or lighter than a given heavy or light thing. For, in his cosmos, nothing is heavier than the sphere of the Earth, which the element earth forms on the cosmic scale; similarly, there is nothing lighter than the cosmic stratum of fire. To reach his conclusion that indivisible points or, equivalently, indivisible lines cannot have weight, Aristotle assumes that, if a body A is heavy, since a body B less heavy than A can always be found, A and B stand in the ratio of their weights: B is smaller than A, which can-

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not be indivisible, for it is divisible into B and the difference A−B, just as its weight is divisible into the weight of B and the difference of the two weights; a point, which is indivisible, or, equivalently, an indivisible line, cannot thus have weight, and similar reasoning shows that it cannot have lightness either. As it is, in the premise “for something heavy or light, something less heavy or light can always be found” it is implicitly assumed that what is less heavy or light than the assigned body is also smaller than it–otherwise the premise would be useless. In other words, Aristotle did not set out this premise with e.g. a wooden cube, less heavy than a smaller metal one, in mind. This premise does not necessarily apply to the composites of the Empedoclean simple bodies. Cf. Cael. ∆ 2, 309a2–5: tîn d sunqštwn…poll¦ barÚtera Ðrîmen ™l£ttw tÕn Ôgkon Ônta, kaq£per ™r…ou calkÒn. It applies, however, necessarily to these four simple bodies themselves. See ch. 5, 304b15–19, and Cael. ∆ 2, 309b12–14: fšretai dš ge q©tton tÕ ple‹on ¥nw pàr toà ™l£ttonoj, kaˆ k£tw d p£lin æsaÚtwj Ð ple…wn crusÕj kaˆ Ð mÒlibdoj· Ðmo…wj d kaˆ tîn ¥llwn ›kaston tîn ™cÒntwn b£roj. Of two quantities of a heavy or light simple body, the larger has a faster natural motion than the smaller, and is heavier or lighter. See Ph. ∆ 8, 216a13–16: Ðrîmen g¦r t¦ me…zw ·op¾n œconta À b£rouj À koufÒthtoj, ™¦n t«lla Ðmo…wj œcV [to‹j sc»masi], q©tton ferÒmena tÕ ‡son cwr…on, kaˆ kat¦ lÒgon Ön œcousi t¦ megšqh prÕj ¥llhla. Cf. below, on 301a29–32. See also next n. 299b1–4. τὸ δὲ βαρύτερον…μείζω ἑτέρων ἐστίν: air is heavier than fire, but is not heavy; water is lighter than earth, but is not light. The purpose of this note is to make clear that tÕ barÚ and tÕ koàfon in 299a31–b1 are tÕ ¡plîj barÚ and tÕ ¡plîj koàfon, though one could hardly assume that here Aristotle is concerned with tÕ prÕj ›teron barÚ and tÕ prÕj ›teron koàfon (for the terminology see Cael. ∆ 1, 308a7–8: lšgetai d¾ tÕ mn ¡plîj barÝ kaˆ koàfon, tÕ d prÕj ›teron). For, tÕ prÕj ›teron barÚ and tÕ prÕj ›teron koàfon are by definition barÚteron ˜tšrou and koufÒteron ˜tšrou; consequently, Aristotle could not have said in 299a31–b1 tÕ mn g¦r barÚ, sc. prÕj ›teron, ¤pan kaˆ barÚteron kaˆ tÕ koàfon, sc. prÕj ›teron, kaˆ koufÒteron ™ndšceta… tinoj enai. This note is very similar to Cael. ∆ 2, 309b5–8: tÕ g¦r ¡plîj koàfon ¢eˆ koufÒteron tîn ™cÒntwn b£roj kaˆ k£tw feromšnwn, tÕ d koufÒteron oÙk ¢eˆ koàfon di¦ tÕ lšgesqai kaˆ ™n to‹j œcousi b£roj ›teron ˜tšrou koufÒteron, oŒon gÁj Ûdwr. For Aristotle’s distinction between tÕ ¡plîj barÚ and tÕ ¡plîj koàfon, on the one hand, and tÕ prÕj ›teron barÚ and tÕ prÕj ›teron koàfon, on the other, see his explanation in Cael. ∆ 4, 311a16–29: prîton mn oân diwr…sqw, kaq£per fa…netai p©si, barÝ mn ¡plîj tÕ p©sin Øfist£menon, koàfon d tÕ p©sin ™pipol£zon. ¡plîj d lšgw e‡j te tÕ gšnoj blšpwn, kaˆ Ósoij m¾ ¢mfÒtera Øp£rcei· oŒon fa…netai purÕj mn tÕ tucÕn mšgeqoj ¥nw ferÒmenon, ™¦n m» ti tÚcV kwlàon ›teron, gÁj d k£tw· tÕn aÙtÕn d trÒpon kaˆ q©tton tÕ ple‹on. ¥llwj d barÝ kaˆ koàfon, oŒj ¢mfÒtera Øp£rcei· kaˆ g¦r ™pipol£zous… tisi kaˆ Øf…stantai, kaq£per ¢¾r kaˆ Ûdwr· ¡plîj mn g¦r oÙdšteron toÚtwn koàfon À barÚ· gÁj mn g¦r ¥mfw koufÒtera (™pipol£zei g¦r aÙtÍ tÕ tucÕn aÙtîn mÒrion), purÕj d barÚ-

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tera (Øf…statai g¦r aÙtîn ÐpÒson ¨n Ï mÒrion), prÕj ˜aut¦ d ¡plîj tÕ mn barÝ tÕ d koàfon· ¢¾r mn g¦r ÐpÒsoj ¨n Ï, ™pipol£zei Ûdati, Ûdwr d ÐpÒson ¨n Ï, ¢šri Øf…statai. The lines under discussion perhaps originated as a marginal note, not necessarily written by Aristotle himself, which eventually became incorporated into the text. 299b4–5. εἰ δὴ ὃ ἂν βαρὺ ὂν βαρύτερον ᾖ: sc. tinoj. Cf. 299b1. 299b5. ἀνάγκη βάρει μεῖζον εἶναι: sc. oá barÚteron. 299b5–6. τὸ βαρὺ ἅπαν διαιρετὸν ἂν εἴη: sc. ¢n£logon tù b£rei. For the proportionality see Cael. A 6, 273b3–5: e„ to…nun ¢n£logon t¦ megšqh to‹j b£resi, tÕ d’ œlatton b£roj toà ™l£ttonÒj ™sti megšqouj, kaˆ tÕ me‹zon ¨n e‡h toà me…zonoj. It is stated in the context of an argument that, if there is an infinite simple body AB, it cannot have finite weight, i.e. that a finite quantity of a heavy simple body cannot occupy an infinite volume: œstw g¦r peperasmšnon, kaˆ e„l»fqw tÕ mn ¥peiron sîma ™f’ ú tÕ AB, tÕ d b£roj aÙtoà ™f’ ú tÕ G. ¢fVr»sqw oân ¢pÕ toà ¢pe…rou peperasmšnon mšgeqoj ™f’ ú tÕ BD· kaˆ tÕ b£roj aÙtoà œstw ™f’ ú tÕ E. tÕ d¾ E toà G œlatton œstai· tÕ g¦r toà ™l£ttonoj b£roj œlatton. katametre…tw d¾ tÕ œlatton Ðposakisoàn, kaˆ æj tÕ b£roj toÜlatton prÕj tÕ me‹zon, tÕ BD prÕj tÕ BZ gegen»sqw· ™ndšcetai g¦r ¢fele‹n toà ¢pe…rou Ðposonoàn (273a27–b3). BZ and AB have thus absurdly the same weight (273b5–6: ‡son ¥ra œstai tÕ toà peperasmšnou kaˆ tÕ toà ¢pe…rou b£roj); on this argument cf. Kouremenos (2002b) 85–91. Let AB be a heavy point or indivisible line, and Γ its weight. If AB is heavier than Β∆ with weight E 〈 Γ, it is Β∆ 〈 AB, for Γ = nE and AB = nΒ∆; AB is not indivisible. Aristotle assumes that the size of a light simple body and its lightness are also proportional (see Cael. A 6, 273a25–27); if AB with lightness Γ is lighter than Β∆ with lightness E 〈 Γ (cf. 299a31–b1), it follows again that AB is not indivisible. An opponent might object that there is no reason why a point or, equivalently, an indivisible line, assuming that it is heavy or light, must be heavier or lighter than something else, which is also smaller than it. Aristotle could answer that, if there were a heavy or light indivisible quantum AB, then, no matter how slow the speed of its natural motion would be, there could be a slower natural motion of a heavy or light body which would bear to AB the ratio of its speed to the speed of AB; hence, a heavy or light indivisible quantum AB cannot exist. See above, on 299a31–b1, for the proportionality assumed here, and cf. Ph. Z 2, 232b20–24: ™peˆ d p©sa mn k…nhsij ™n crÒnJ kaˆ ™n ¤panti crÒnJ dunatÕn kinhqÁnai, p©n d tÕ kinoÚmenon ™ndšcetai kaˆ q©tton kine‹sqai kaˆ bradÚteron, ™n ¤panti crÒnJ œstai tÕ q©tton kine‹sqai kaˆ bradÚteron. toÚtwn d’ Ôntwn ¢n£gkh kaˆ tÕn crÒnon sunecÁ enai. It can be argued along these lines that weight and lightness are not the only two among t¦ p£qh t¦ a„sqht£ (see above, on 299a20) that indivisibles must lack. See Cael. A 7, 275a2–10: e„ d¾ ØpÕ toà B tÕ A ™qerm£nqh À êsqh À ¥llo ti œpaqen À kaˆ Ðtioàn ™kin»qh ™n tù crÒnJ ™f’ oá G, œstw tÕ D toà B œlatton, kaˆ tÕ œlatton ™n tù ‡sJ crÒnJ œlatton kine…tw· œstw

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d tÕ ™f’ ú E ØpÕ toà D ºlloiwmšnon. Ö d» ™sti tÕ D prÕj tÕ B, tÕ E œstai prÕj peperasmšnon ti. œstw d¾ tÕ mn ‡son ™n ‡sJ crÒnJ ‡son ¢lloioàn, tÕ d’ œlatton ™n tù ‡sJ œlatton, tÕ d me‹zon me‹zon, tosoàton d Óson ¢n£logon œstai Óper tÕ me‹zon prÕj tÕ œlatton. 299b7–9. ἔτι εἰ…πλεῖον ἐνυπάρχειν: here tÕ barÚ and tÕ koàfon are to be understood not ¡plîj but prÕj ›teron. See Cael. ∆ 1, 308a29–33: ¡plîj mn oân koàfon lšgomen tÕ ¥nw ferÒmenon kaˆ prÕj tÕ œscaton, barÝ d ¡plîj tÕ k£tw kaˆ prÕj tÕ mšson· prÕj ¥llo d koàfon kaˆ koufÒteron, oá duo‹n ™cÒntwn b£roj kaˆ tÕn Ôgkon ‡son, k£tw fšretai q£teron fÚsei q©tton. 299b9–10. εἰ οὖν…καὶ μανή: the assumption that a point or, equivalently, an indivisible line has volume is strange. 299b10. τὸ μὲν πυκνὸν διαιρετόν: sc. tÕ mn puknÒn, manoà diafšron tù ™n ‡sJ ÔgkJ ple‹on ™nup£rcein, diairetÒn. What is spread throughout a given volume and constitutes a dense body is divisible into what occupies an equal volume constituting a less dense, or a rarer, body and the difference between the two densities. 299b10–11. ἡ δὲ στιγμὴ ἀδιαίρετος: what constitutes a hypothetically dense point or, equivalently, an indivisible line, both of which are bizzarely assumed here to be three-dimensional, must be divisible into that which constitutes a less dense, though equal in volume, or rarer indivisible and the difference between the two densities, hence it cannot be indivisible. 299b11–12. εἰ δὲ…εἶναι: according to Mete. ∆ 4, 382a8–11, tîn d swmatikîn paqhm£twn taàta prîta ¢n£gkh Øp£rcein tù ærismšnJ, sklhrÒthta À malakÒthta. ¢n£gkh g¦r tÕ ™x Øgroà kaˆ xhroà À sklhrÕn enai À malakÒn. In another sense prîta are the wet and the dry; see GC B 2, 330a8–29. 299b12. ῥᾴδιον…συναγαγεῖν: the absurdity is that, even if points or, equivalently, indivisible lines could be heavy, some would be hard and some soft if they were things delimited by shape (see previous n.). If some were soft, they would be divisible (see next n.). Hence all of them should be hard. This is absurd for the reason explained in Cael. B 3, 286a23–24: tîn g¦r ™nant…wn e„ q£teron fÚsei, ¢n£gkh kaˆ q£teron enai fÚsei, ™£n per Ï ™nant…on, kaˆ ena… tina aÙtoà fÚsin. Cf. GC A 8, 326a13–14: ¢ll¦ m¾n e„ sklhrÒn, kaˆ malakÒn. tÕ d malakÕn tù p£scein ti lšgetai· tÕ g¦r ØpeiktikÕn malakÒn (I adopt the punctuation of Joachim [1922]). Indivisibles could not thus have shape. Nor could they be the fundamental constituents of anything with shape. 299b13–14. μαλακὸν…τὸ μὴ ὑπεῖκον: for the conclusion see previous n. On Øpe‹kon cf. the GC A 8 passage quoted there and Mete. ∆ 4, 382a11–14: œsti d sklhrÕn mn tÕ m¾ Øpe‹kon e„j aØtÕ kat¦ tÕ ™p…pedon, malakÕn d tÕ Øpe‹-

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kon tù m¾ ¢ntiperi…stasqai· tÕ g¦r Ûdwr oÙ malakÒn· oÙ g¦r Øpe…kei tÍ ql…yei tÕ ™p…pedon e„j b£qoj, ¢ll’ ¢ntiperi…statai. For the definition of the motion called ¢ntiper…stasij see below, on 301b23–25. 299b14. ἐκ μὴ ἐχόντων βάρος: sc. ™k stigmîn m¾ ™cÒntwn b£roj, or, more generally, ™x ¢diairštwn m¾ ™cÒntwn b£roj. Aristotle will argue next that, if indivisibles, each of which is not heavy, are the ultimate constituents of heavy bodies, we cannot explain the fact that the latter are heavy by simply invoking the collective behavior of their constituents. 299b15. ἐπὶ πόσων: how many indivisibles, each of which lacks weight, must come together for the weight of the compound to emerge? 299b16. ἐπὶ ποίων: how are the indivisibles, each of which lacks weight, and a number of which, no matter how large, need to come together for the weight of the compound to emerge, to be differentiated from those that come together to constitute a light compound? 299b16–17. πῶς…πλάττειν; sc. oƒ poioàntej t¦j ¢tÒmouj gramm£j = oƒ p£nta t¦ sèmata sunist£ntej ™x ™pipšdwn. Any answers to the questions in the two previous nn. could only be figments of the imagination. 299b17. καὶ εἰ…βάρει: cf. 299b4–5. 299b19. τὸ δ’ ἐκ πλειόνων ἢ τοδὶ: sc. tÕ d’ ™k pleiÒnwn stigmîn À aƒ tšttarej. 299b20. βαρέος ὄντος: sc. toud…, i.e. toà ™k tett£rwn stigmîn. 299b21–22. ὥστε τὸ μεῖζον μιᾷ στιγμῇ: if things are ultimately made up of indivisible points, one thing exceeds another by a number of its constituents, and their difference can be one single point. Cf. the argument in LI 971a11–14 against the composition of lines from points: kaˆ gramm¾ d grammÁj stigmÍ enai me…zwn· ™x ïn g¦r sÚgkeitai, toÚtoij kaˆ Øperšxei. toàto d’ Óti ¢dÚnaton, œk te tîn ™n to‹j maq»masi dÁlon… Moraux (1961) 26–27 has proposed that éste and œstai in 299b22 should change places; cf. below, on 299b23. We can just remove éste, however, and keep œstai where it is. 299b22–23. ἀφαιρεθέντος τοῦ ἴσου: sc. tù koufotšrJ, i.e. ¢faireqšntwn tett£rwn stigmîn. On œstai before the participle see previous n. 299b23. ὥστε καὶ ἡ μία στιγμὴ βάρος ἕξει: Moraux (1961) 26–27 brackets éste, and takes kaˆ ¹ m…a stigm¾ b£roj ›xei as a result clause generated by his proposal that éste and œstai in 299b21–22 should change places. Here éste can be kept, however.

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299b23–24. ἔτι…ἄτοπον: Aristotle turns his sights on the assumption that the triangles, from which the polyhedral corpuscles of the four elements are constructed in the Timaeus, can join only along their sides to produce the corpuscles. 299b25–26. ὥσπερ…κατὰ πλάτος: as is clear from 299b27–29, that lines can be joined together lengthwise, kat¦ mÁkoj, means that they can be added to produce a line longer than any of its parts, whereas that lines can be combined widthwise, kat¦ pl£toj, means that they can pile up on top of one another, as if they were very thin beams, to produce a raft whose width increases with the addition of each beam. But lines lack width, so they cannot be added widthwise. Aristotle treats lines ungeometrically as planes with tiny width not because he himself conceives of them as such, but because, in his view, Plato does (hence, perhaps, the emphatic repetition of this point in 299b27–29). By his lights, if the particles of the elements consist of planes, as Plato has it, then, as bodies consist of planes, planes are made up of lines, and lines consist of points (see 299a6–8). Lines are implicitly assumed to make up planes by joining together widthwise, i.e. piling up in the dimension of width they lack; points are implicitly assumed to make up lines by being strung in a row, i.e. piling up in the dimension of length they lack. 299b26–27. δεῖ…τὸν αὐτὸν τρόπον: sc. sunt…qesqai, kaˆ kat¦ mÁkoj kaˆ kat¦ pl£toj. The absurdity Aristotle deduces in 299b29–31 from this and the previous premise is that the triangles, of which the polyhedral corpuscles of the four elements are made up in the Timaeus, can not only join along their sides to produce the corpuscles of the elements but also pile up on top of one another, generating bodies which are neither particles of the elements nor made up of them. It leaves no doubt that joining together widthwise is not assumed to apply to lines and planes in the same sense. Widthwise combination of planes is not side-by-side arrangement in the manner of tiles, as is the case for lines, but stacking one on top of the other. Just as lines can be stacked one on top of the other in the dimension they lack, width, to produce planes, the latter, too, can be stacked one top of the other in the dimension they lack, depth, to produce solids. This is not what Aristotle himself believes, but what he thinks Plato ought to believe; see previous n. His argument would have gained in clarity had he said that, just as sunt…qesqai kaˆ kat¦ mÁkoj kaˆ kat¦ pl£toj applies to lines, sunt…qesqai kaˆ kat¦ pl£toj kaˆ kat¦ b£qoj applies to planes. 299b27–29. γραμμὴ…προστιθεμένη: cf. above, on 299b25–26. 299b29–30. ἐνδέχεται συντίθεσθαι: sc. ™p…pedon ™pipšdJ. 299b30–31. ἔσται…ἐπιπέδων: see above, on 299b26–27. By positing that the polyhedral corpuscles of the four elements, the basic constituents of all other bodies, are made up of elementary triangles joined together edge to edge, Plato leaves the door open to the possible existence of bodies which, absurdly, are neither corpuscles of the elements nor made up of them. Cf. ch. 5, 304b4–6, and 7, 306a26–b2.

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299b31–300a7. ἔτι…πυρός: these lines are perhaps to be placed before ¢ll¦ m¾n Óti t¾n stigm¾n oÙc oŒÒn te b£roj œcein, fanerÒn in 299a30–31. 299b31–300a1. ἔτι…διώρισται: the weight of a corpuscle of an element depends on the number of triangles making up the faces of the corpuscle. This is asserted implicitly in Ti. 55e7–56b6 for fire, air and water, the elements whose particles are made up of the same kind of triangles. 300a1–3. δῆλον…εἰρήκαμεν: see 299a6–8. The original position of this and the next argument seems to have been before the argument in 299a30–b7 that points cannot have weight. Here evidence is offered that Plato in the Timaeus thinks of points as having weight. If the weight of a corpuscle of an element depends on the number of triangles making up the faces of the corpuscle, the triangles cannot but be heavy; as planes are to solids, however, so are lines to planes, and points to lines; hence, if the weight of solids is due to that of their planes, points, too, are heavy. 300a3. εἰ…τὸν τρόπον: sc. e„ d m¾ pl»qei barÚtera t¦ sèmata tîn ™pipšdwn. Aristotle here considers an alternative to the dependence of the weight of a Platonic corpuscle on the number of triangles making up the faces of the corpuscle. 300a4. ἀλλὰ…κοῦφον: earth is heavy and fire is light not because the particles of earth consist of a greater number of heavy triangles, the particles of fire of fewer, but rather because the specific arrangement of certain triangles, which is earth, has weight, whereas the different manner of arrangement of triangles of another kind, which is fire, has lightness. The dependence of the weight of a corpuscle of an element on the number of triangles making up the faces of the corpuscle is implicitly asserted in Ti. 55e7–56b6 for fire, air and water. However, that earth is heavier than all the other three elements cannot be accounted for on the same principle. It is not true that a corpuscle of earth, a heavier element than fire, is necessarily made up of a larger number of triangles than that making up a fire corpuscle; see the discussion of the Timaean structure of matter in Vlastos (1975) 69–79. A different principle is thus needed to explain, within the Timaeus cosmology, why earth is heavier than all the other three elements. 300a4–7. ἔσται…πυρός: if weight and lightness are the combinations into corpuscles of triangles that per se lack weight and lightness, the triangles nevertheless are heavy and light as constituents of heavy and light corpuscles. As planes are to solids, however, so are lines to planes and points to lines; hence, if the weight and lightness of solids is conferred to their planes, points, too, are heavy and light. 300a7–12. ὅλως…σῶμα δὲ μηθέν: if, as planes are to solids, so are lines to planes and points to lines, the construction of all bodies out of planes in the Ti-

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maeus entails either that no magnitudes exist or, if they exist, that they can be annihilated by dissolving into planes, which can then decay into lines, which in their turn can decay into points. Since the possibility that all bodies decompose into points amounts to the annihilation of all magnitude, points here are not treated any more as indivisible lines, which are magnitudes, but conventionally, i.e. as lacking size completely. Therefore, if, as planes are to solids, so are lines to planes and points to lines, the construction of all bodies out of planes in the Timaeus entails absurdly the construction of all magnitude, one-, two- and three-dimensional, out of points without magnitude–that is, the non-existence of magnitudes; for no matter how many sizeless points might be added together, no magnitude will ever appear. On the other hand, if, as planes are to solids, so are lines to planes and points to lines, the dissolution of all bodies into planes in the Timaeus leaves open the possibility of planes decaying catastrophically on the cosmic scale into lines and those into points, in which case magnitudes, and thus the cosmos itself, would absurdly disappear! This two-pronged argument harks back to the characterization of Plato etc as o‰ p©n sîma genhtÕn poioàsi, suntiqšntej kaˆ dialÚontej e„j ™p…peda kaˆ ™x ™pipšdwn in 298b33–299a1. Cf. GC A 2, 316a14–34: œcei g¦r ¢por…an, e‡ tij qe…h sîm£ ti enai kaˆ mšgeqoj p£ntV diairetÒn, kaˆ toàto dunatÒn. t… g¦r œstai Óper t¾n dia…resin diafeÚgei; e„ g¦r p£ntV diairetÒn, kaˆ toàto dunatÒn, k¨n ¤ma e‡h toàto p£ntV diVrhmšnon, kaˆ e„ m¾ ¤ma diÇrhtai· k¨n e„ toàto gšnoito, oÙdn ¨n e‡h ¢dÚnaton. oÙkoàn kaˆ kat¦ tÕ mšson æsaÚtwj, kaˆ Ólwj dš, e„ p£ntV pšfuke diairetÒn, ¨n diaireqÍ, oÙdn œstai ¢dÚnaton gegonÒj, ™peˆ oÙd’ ¨n mur…a muri£kij diVrhmšna Ï, oÙdn ¢dÚnaton· ka…toi ‡swj oÙdeˆj ¨n dišloi. ™peˆ to…nun p£ntV toioàtÒn ™sti tÕ sîma, diVr»sqw. t… oân œstai loipÒn; mšgeqoj oÙ g¦r oŒÒn te· œstai g£r ti oÙ diVrhmšnon, Ãn d p£ntV diairetÒn. ¢ll¦ m¾n e„ mhdn œstai sîma mhd mšgeqoj, dia…resij d’ œstai, À ™k stigmîn œstai, kaˆ ¢megšqh ™x ïn sÚgkeitai, À oÙdn pant£pasin, éste k¨n g…noito ™k mhdenÕj k¨n e‡h sugke…menon, kaˆ tÕ p©n d¾ oÙdn ¢ll¦ fainÒmenon. Ðmo…wj d k¨n Ï ™k stigmîn, oÙk œstai posÒn. ÐpÒte g¦r ¼ptonto kaˆ e$n Ãn mšgeqoj kaˆ ¤ma Ãsan, oÙdn ™po…oun me‹zon tÕ p©n. diaireqšntoj g¦r e„j dÚo kaˆ ple…w, oÙdn œlatton oÙd me‹zon tÕ p©n toà prÒteron, éste k¨n p©sai sunteqîsin, oÙdn poi»sousi mšgeqoj. See also next n. 300a10–11. πάντα…ἀναλυθήσεται: if (a) bodies decay into planes, lines and points, (b) planes into lines and points and (c) lines into points, then bodies, planes and lines will all decay into points. Points, not bodies, are here assumed implicitly to be the true elements Plato absurdly posits in the Timaeus. Cf. previous n. and an argument in LI 972a6–13 against the view that lines are made up of indivisible lines or, equivalently, points (see above, on 299a9–11): œti diairo‹t’ ¨n ¤panta kaˆ ¢nalÚoito e„j stigm£j, kaˆ ¹ stigm¾ mšroj sèmatoj, e‡per tÕ mn sîma ™x ™pipšdwn, tÕ d’ ™p…pedon ™k grammîn, aƒ d grammaˆ ™k stigmîn. e„ d’ ™x ïn prètwn ™nuparcÒntwn ›kast£ ™sti, stoice‹£ ™sti taàta, aƒ stigmaˆ ¨n e‡hsan stoice‹a swm£twn. éste sunènuma stoice‹a, oÙd' ›tera tù e‡dei. fanerÕn oân ™k tîn e„rhmšnwn Óti oÙk œsti gramm¾ ™k stigmîn. See also the

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argument in Metaph. M 2, 1077a31–b2: œti tÕ mn sîma oÙs…a tij (½dh g¦r œcei pwj tÕ tšleion), aƒ d grammaˆ pîj oÙs…ai; oÜte g¦r æj edoj kaˆ morf» tij, oŒon e„ ¥ra ¹ yuc¾ toioàton, oÜte æj ¹ Ûlh, oŒon tÕ sîma· oÙqn g¦r ™k grammîn oÙd’ ™pipšdwn oÙd stigmîn fa…netai sun…stasqai dun£menon, e„ d’ Ãn oÙs…a tij Ølik», toàt’ ¨n ™fa…neto dun£mena p£scein. tù mn oân lÒgJ œstw prÒtera, ¢ll’ oÙ p£nta Ósa tù lÒgJ prÒtera kaˆ tÍ oÙs…v prÒtera. Cf. ∆ 8, 1017b17–21, and see Kouremenos (2003) 342–345. 300a12–14. πρὸς δὲ τούτοις…οἷον στιγμὴ γραμμῆς ἐστιν: if the elements were indivisible points, not bodies, which is what, as Aristotle takes it, Plato’s Timaeus in effect posits (see previous n.), then, just as bodies could dissolve into points, time could also dissolve into “nows” without duration. See Aristotle’s argument in Ph. Z 10, 240b20–241a6 against the possibility that something without parts, such as a point, moves: metaballštw g¦r ™k toà AB e„j tÕ BG, e‡t’ ™k megšqouj e„j mšgeqoj e‡t’ ™x e‡douj e„j edoj e‡te kat’ ¢nt…fasin· Ð d crÒnoj œstw ™n ú prètJ metab£llei ™f’ oá D. oÙkoàn ¢n£gkh aÙtÕ kaq’ Ön metab£llei crÒnon À ™n tù AB enai À ™n tù BG, À tÕ mšn ti aÙtoà ™n toÚtJ tÕ d’ ™n qatšrJ· p©n g¦r tÕ metab£llon oÛtwj ecen. ™n ˜katšrJ mn oân oÙk œstai ti aÙtoà· meristÕn g¦r ¨n e‡h. ¢ll¦ m¾n oÙd’ ™n tù BG· metabeblhkÕj g¦r œstai, ØpÒkeitai d metab£llein. le…petai d¾ aÙtÕ ™n tù AB enai, kaq’ Ön metab£llei crÒnon. ºrem»sei ¥ra· tÕ g¦r ™n tù aÙtù enai crÒnon tin¦ ºreme‹n Ãn. ést’ oÙk ™ndšcetai tÕ ¢merj kine‹sqai oÙd’ Ólwj metab£llein· monacîj g¦r ¨n oÛtwj Ãn aÙtoà k…nhsij, e„ Ð crÒnoj Ãn ™k tîn nàn· a„eˆ g¦r ™n tù nàn kekinhmšnon ¨n Ãn kaˆ metabeblhkÒj, éste kine‹sqai mn mhdšpote, kekinÁsqai d’ ¢e…. toàto d’ Óti ¢dÚnaton, dšdeiktai kaˆ prÒteron· oÜte g¦r Ð crÒnoj ™k tîn nàn oÜq’ ¹ gramm¾ ™k stigmîn oÜq’ ¹ k…nhsij ™k kinhm£twn· oÙqn g¦r ¥llo poie‹ Ð toàto lšgwn À t¾n k…nhsin ™x ¢merîn, kaq£per ¨n e„ tÕn crÒnon ™k tîn nàn À tÕ mÁkoj ™k stigmîn. Cf. the argument in LI 971a13–21. 300a14–15. τὸ δ’ αὐτὸ συμβαίνει: sc. ¢naire‹sqai tÕn crÒnon À ™ndšcesqai ¢naireqÁnai. Although from 300a17–19 it appears that the absurdity which is at issue here is a variant of mhdšn pot’ enai mšgeqoj in 300a8, this is not a problem; see previous and next n. 300a15–17. καὶ…τῶν Πυθαγορείων τινές: …oƒ PuqagÒreioi…tÕn…Ólon oÙranÕn kataskeu£zousin ™x ¢riqmîn, pl¾n oÙ monadikîn, ¢ll¦ t¦j mon£daj Øpolamb£nousin œcein mšgeqoj (Metaph. M 6, 1080b16–20). Number is here assumed to be a multitude of indivisible units; see Metaph. I 1, 1053a30: Ð d’ ¢riqmÕj plÁqoj mon£dwn, and M 9, 1085b22: tÕ g¦r plÁqoj ¢diairštwn ™stˆn ¢riqmÒj. If they have a size, they are indistinguishable from points conceived of as indivisible lines, so in constructing the cosmos out of numbers the Pythagoreans, whom Aristotle refers to here, end up positing points as the true elements, just as Plato does, according to Aristotle, in the Timaeus. The view that all things are made up of numbers is also attributed in ch. 4, 303a8–10, to Leucippus

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and Democritus. There it is made clear that, though this thesis is not explicitly espoused by the atomists, it is what they mean when they posit atoms as the elements. On the construction of physical reality out of numbers Aristotle ascribes to the Pythagoreans see Huffman (1993) 57–64. 300a18–19. τὰς δὲ μονάδας…συντιθεμένας: see above, on 300a7–12. This objection to the “Pythagorean” construction of the cosmos out of numbers is fully set out in Metaph. M 8, 1083b11–19: tÕ d t¦ sèmata ™x ¢riqmîn enai sugke…mena, kaˆ tÕn ¢riqmÕn toàton enai maqhmatikÒn, ¢dÚnatÒn ™stin. oÜte g¦r ¥toma megšqh lšgein ¢lhqšj, e‡ q’ Óti m£lista toàton œcei tÕn trÒpon, oÙc a† ge mon£dej mšgeqoj œcousin· mšgeqoj d ™x ¢diairštwn sugke‹sqai pîj dunatÒn; ¢ll¦ m¾n Ó g’ ¢riqmhtikÕj ¢riqmÕj monadikÒj ™stin. ™ke‹noi d tÕn ¢riqmÕn t¦ Ônta lšgousin· t¦ goàn qewr»mata pros£ptousi to‹j sèmasin æj ™x ™ke…nwn Ôntwn tîn ¢riqmîn. 300a19. οὔτε βάρος ἔχειν: as shown above, in 299a25–b14. The criticism is repeated in Metaph. N 3, 1090a30–35: oƒ mn oân PuqagÒreioi kat¦ mn tÕ toioàton oÙqenˆ œnoco… e„sin, kat¦ mšntoi tÕ poie‹n ™x ¢riqmîn t¦ fusik¦ sèmata, ™k m¾ ™cÒntwn b£roj mhd koufÒthta œconta koufÒthta kaˆ b£roj, ™o…kasi perˆ ¥llou oÙranoà lšgein kaˆ swm£twn ¢ll’ oÙ tîn a„sqhtîn.

CHAPTER 2 300a20–21. Ὅτι…πᾶσιν: since t¦ ¡pl© sèmata are among t¦ fÚsei legÒmena Ônta (see ch. 1, 298a27–30), this follows directly from Aristotle’s definition of fÚsij, for which see above, on 298a27–28. Cf. ch. 5, 304b13–14. 300a22–23. κινεῖσθαί γε…κίνησιν: sc. kine‹sqa… ge ¢nagka‹on b…v ¥llo Øp' ¥llou tîn ¡plîn swm£twn (cf. 300b11–12) e„ m¾ fÚsei kine‹tai, equivalently e„ m¾ Øf' ˜autoà kine‹tai. See also above, on 298a32–34. 300a23. τὸ δὲ βίᾳ καὶ παρὰ φύσιν ταὐτόν: if we assume that each of the simple bodies lacks a natural motion and thus moves only forcedly, i.e. that it cannot move of itself, for it naturally rests, but only when another simple body acts on it, its forced motion is counter to its nature in the sense of being opposed to rest. 300a23–25. ἀλλὰ…αὕτη: if we assume that each of the simple bodies lacks a natural motion and thus moves only counter to its nature, we negate our assumption, for the motion of a simple body which is counter to its nature is defined with reference to its natural motion, whence follows that the simple body has a natural motion. See also Cael. B 13, 294b32–295a7. Cf. Cael. B 3, 286a18–20: Ûsteron d tÕ par¦ fÚsin toà kat¦ fÚsin, kaˆ œkstas…j t…j ™stin ™n tÍ genšsei tÕ par¦ fÚsin toà kat¦ fÚsin, and 286a23–26: tîn g¦r ™nant…wn e„ q£teron

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fÚsei, ¢n£gkh kaˆ q£teron enai fÚsei, ™£n per Ï ™nant…on, kaˆ ena… tina aÙtoà fÚsin· ¹ g¦r aÙt¾ Ûlh tîn ™nant…wn, kaˆ tÁj ster»sewj prÒteron ¹ kat£fasij (lšgw d’ oŒon tÕ qermÕn toà yucroà)… For the contrariety of natural and counter-natural motion see Cael. A 2, 269a9–12 (quoted in next n.). The premises of Aristotle’s argument clearly define the counter-natural motion of a simple body with reference to its rest, which is what is natural for it, but this does not create a problem for him; see 300a27–29 and cf. Cael. B 13, 295a4–7. 300a25–27. καὶ εἰ…ἕκαστον: a simple body moves naturally with a single motion, whereas there are many counter-natural motions of it. Elsewhere, however, a simple body is said to have one counter-natural motion, for such motion is the contrary of natural motion. See Cael. A 2, 269a9–12: œti e„ ¹ par¦ fÚsin ™nant…a tÍ kat¦ fÚsin kaˆ e$n ˜nˆ ™nant…on, ¢n£gkh, ™peˆ ¡plÁ ¹ kÚklJ, e„ m¾ œstai kat¦ fÚsin toà feromšnou sèmatoj, par¦ fÚsin aÙtoà enai. The first of the definitions of contraries in Metaph. ∆ 10, 1018a25–31, could be invoked here to establish that, if there exists at least one motion with which a simple body moves naturally, there exist as many counter-natural motions as the contraries of it, whereas the second of these definitions is implicit in Cael. A 2: ™nant…a lšgetai t£ te m¾ dunat¦ ¤ma tù aÙtù pare‹nai tîn diaferÒntwn kat¦ gšnoj, kaˆ t¦ ple‹ston diafšronta tîn ™n tù aÙtù gšnei, kaˆ t¦ ple‹ston diafšronta tîn ™n taÙtù dektikù, kaˆ t¦ ple‹ston diafšronta tîn ØpÕ t¾n aÙt¾n dÚnamin, kaˆ ïn ¹ diafor¦ meg…sth À ¡plîj À kat¦ gšnoj À kat’ edoj. See also Falcon (2005) 59–62 and Hankinson (2009) 94–97. How Aristotle establishes here that a simple body, if it moves naturally, does so with a single motion but has many counter-natural motions is obscure. The reason he gives for the uniqueness of a simple body’s natural motion, kat¦ fÚsin mn g¦r ¡plîj, suggests that he thinks that the natural motile behavior of a simple body cannot but be simple, too, in the sense ‘not multifarious’; that a simple body has a single natural motion is assumed elsewhere, too, but what follows seems to contradict it (see below, on 301b23). Simp., in Cael. 581.19–24 (Heiberg), explains the uniqueness of the natural motion of a simple body and the plurality of its counter-natural ones as follows: e„ ¥ra kine‹tai t¦ ¡pl© sèmata par¦ fÚsin, ¢n£gkh enai aÙtîn kaˆ kat¦ fÚsin k…nhsin. ¢ll¦ k¨n tÕ par¦ fÚsin kinoÚmenon p£ntwj kaˆ kat¦ fÚsin kine‹tai, oÙk ½dh, Ósai aƒ par¦ fÚsin e„sˆ kin»seij, tosaÚtaj ¢n£gkh t¦j kat¦ fÚsin enai· ™n p©si g¦r monacîj mn tÕ katorqoàn, tÕ d parekba…nein toà Ñrqoà kaˆ ¡mart£nein pollacîj· ¡mart…a dš tij kaˆ parškbasij toà kat¦ fÚsin ¹ par¦ fÚsin k…nhsij. 300a27. ἔτι…δῆλον: sc. Óti ¢nagka‹on Øp£rcein k…nhsin to‹j ¡plo‹j sèmasi fÚsei tin¦ p©sin (300a20–21). As is clear from what follows, here ¹ ºrem…a is tîn ¡plîn swm£twn. 300a30. ἐπεὶ…μέσου: observation shows that the simple body earth rests at the center of the spherical cosmos, with which the sphere it forms, the Earth, is concentric. Cf. the introduction of another observational datum, the diurnal rota-

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tion, in an argument in Cael. B 4, 287a11–12, for the sphericity of the cosmos: œti d ™peˆ fa…netai kaˆ ØpÒkeitai kÚklJ perifšresqai tÕ p©n… That the four Empedoclean simple bodies have rectilinear natural motions is also thought to be an observational datum. See Cael. A 2, 269b12–13: purÕj g¦r k…nhsin Ðrîmen t¾n ¢pÕ toà mšsou kat’ eÙqe‹an. Cf. ch. 5, 304b13–14. 300a30–31. εἰ μὲν κατὰ φύσιν: sc. mšnei ™pˆ toà mšsou. 300a32. εἰ δὲ βίᾳ: sc. mšnei ™pˆ toà mšsou. 300a32–33. εἰ μὲν…λόγον: if the Earth rests at the center of the cosmos by force and what holds it there rests, too, the initial question, whether the Earth is at rest naturally or forcedly, is raised for what is supposed to hold the Earth immobile. 300a33–300b1. ἀνάγκη…ἀδύνατον: if what holds the Earth immobile is itself at rest naturally, its motion to where it rests is its natural motion; if its rest is forced, it is imposed on it by something else, whose rest, if not natural, is forcedly imposed on it by something else, and so on ad infinitum, which is absurd. A simple body is implicitly assumed to support the Earth, as was by Thales (water), Anaximenes, Anaxagoras and Democritus (air); see Cael. B 13, 294a10–b30. 300b1–3. εἰ δὲ…ἠρεμεῖν: Aristotle considers the possibility that the Earth is forced to rest by something which is not itself at rest but in motion, such as the vortex Empedocles hypothesized. The vorticial explanation of the immobility of the Earth is criticized in Cael. B 13, 295a7–b9; see Leggatt (1995) 260. Empedocles seems to have believed that in each cosmic cycle the Earth does not rest necessarily at the center of the cosmos; see Trépanier (2003). 300b3–8. ποῦ…φορά: if the Earth is forced to rest by something which is not itself at rest but in motion, since it could not possibly move to infinity if not acted upon by what prevents it from moving, it would traverse a finite distance and stop moving; it would rest naturally, not forcedly, where it would stop, hence its motion to that place would be natural, just like its rest. 300b8–11. διὸ…κίνησις: t¦ prîta sèmata are atoms, t¦ megšqh t¦ ¥toma (Metaph. Z 13, 1039a10). See Metaph. Λ 6, 1071b33–37, a critique of Leucippus and Plato: ¢eˆ g¦r ena… fasi k…nhsin. ¢ll¦ di¦ t… kaˆ t…na oÙ lšgousin, oÙd', ædˆ æd…, t¾n a„t…an. oÙdn g¦r æj œtuce kine‹tai, ¢ll¦ de‹ ti ¢eˆ Øp£rcein, ésper nàn fÚsei mn æd…, b…v d À ØpÕ noà À ¥llou æd…. eta po…a prèth; diafšrei g¦r ¢m»canon Óson. Cf. Metaph. A 4, 985b3–20. 300b11–12. εἰ γὰρ…στοιχείων: according to the testimonies about Democritus, the motion of atoms is caused by the impact of other atoms (DK 68 A 47); the motion of impacting atoms is also caused by their collisions with other atoms, and

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so on ad infinitum. There is some evidence on the basis of which it seems that atoms were not thought to come into contact but rather to repel one another when the distances between them became very short; see Taylor (1999a) 184–185, 188–189. 300b12–13. ἀλλὰ…ἐστιν: see the argument in 300a20–25. 300b13–16. καὶ δεῖ…κινήσει: if the motion of atoms is caused by the impact of other atoms, whose motion is in its turn caused by their collisions with other atoms, and so on ad infinitum, there is an infinite regress, which is clearly considered inadmissible. The chain of motions, each of which causes the immediately next one, must, therefore, end with a first motion, which, unlike those after it, is natural, not forced–what undergoes this first motion moves by itself, not by something else. The existence of a self-moving first mover as the ultimate cause of motion in every chain of motions, each of which causes the immediately next one, is elaborately established in Ph. Θ 5, where one of Aristotle’s argument hinges on the rejection of an infinite regress of causally linked forced motions (256a13–21); on this premise see Graham (1999a) 90–91. The argument against an infinite regress of causally linked forced motions in Ph. H 1, 242a49–243a2, is not applicable to atoms, for in it the movers undergoing those motions each of which causes the immediately next one are contiguous–unless, of course, Aristotle loses sight of, or disregards, the difference between his dynamics and that of the atomists. 300b16. τὸ αὐτὸ δὲ τοῦτο: i.e. e„j ¥peiron „šnai, e„ m» ti œstai kat¦ fÚsin kinoàn prîton, ¢ll’ ¢eˆ tÕ prÒteron b…v kinoÚmenon kin»sei. 300b17. ἐν τῷ Τιμαίῳ: see Ti. 29d7–30a6 and 52d1–53b5. 300b18–19. ἀνάγκη…φύσιν: if the pre-cosmic motion of the elements, according to the Platonic Timaeus, were forced, as might be suggested by its being disorderly, an infinite regress would arise, for which see above, on 300b13–15. To avoid this inadmissible infinite regress, one must posit a first mover, whose motion is self-caused, i.e. not forced but natural, as the first cause of the motion of the elements before the formation of the Timaean cosmos. Within Aristotle’s cosmology, however, the assumption that the first, naturally moving mover of the four Empedoclean elements might bring about their disorderly, or forced, motion is absurd, the fact that in our context it is assumed to have done so in a pre-cosmic epoch notwithstanding. For, in the cosmos, it causes the orderly, natural motion of minute quantities of the Empedoclean elements to their natural places, where, at any time, virtually all of their amounts existing in the cosmos are accreted. Could it have ever caused the opposite effect? If not, the elements must have moved naturally in the Timaean pre-cosmic era, too. If they had, the cosmos could not but have formed before it existed, an absurdity Aristotle goes on to derive immediately next. On the natural motion of the Empedoclean elements as caused in Aristotelian cosmology by at least one naturally moving mover, the diurnally rotating shell of the first simple body, see Introduction, 4; cf. Kouremenos (2010) 46–49.

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300b20. ἀνάγκη κόσμον εἶναι: sc. prˆn genšsqai tÕn kÒsmon. 300b21. τό τε γὰρ πρῶτον κινοῦν: t¦ stoice‹a must be supplied as the object from 300b18. See above, on 300b18–19. 300b21–22. κινεῖν, αὐτὸ κινούμενον κατὰ φύσιν: Alexander of Aphrodisias, according to Simp., in Cael. 584.29–585.1 (Heiberg), preferred the variant reading aÙtÒ over aØtÒ. Simp. remarks that the latter is found in many mss. It is also found in the majority of surviving mss. Moraux (1965) prints accordingly kine‹n ˜autÕ kinoÚmenon kat¦ fÚsin. Adopting one or the other reading does not affect the meaning. aÙtÒ requires t¦ stoice‹a as implicit object of the infinitive (see 300b18). 300b22. καὶ τὰ κινούμενα μὴ βίᾳ: sc. stoice‹a (see 300b18). 300b22–23. ἐν τοῖς οἰκείοις ἠρεμοῦντα τόποις: if the elements moved naturally in the Timaean pre-cosmic era, they could do so only towards their natural places, where their natural motion would come to a halt. Thus the cosmos must have existed in the pre-cosmic era, too, which is absurd. See above, on 300b18–19. 300b23. ἥνπερ ἔχουσι νῦν τάξιν: the stratification of the four Empedoclean elements on the cosmic scale. See above, on 298a31. 300b23–25. τὰ μὲν…τοῦ μέσου: quantities of earth and water, the two heavy simple bodies, move naturally towards the center of the cosmos, whereas quantities of air and fire, the two light simple bodies, move naturally towards the periphery of the cosmos, away from the center. See GC B 3, 330b30–33: Ôntwn d tett£rwn tîn ¡plîn swm£twn, ˜k£tera to‹n duo‹n ˜katšrou tîn prètwn ™st…n, pàr mn kaˆ ¢¾r toà prÕj tÕn Óron feromšnou, gÁ d kaˆ Ûdwr toà prÕj tÕ mšson (cf. above, on 298b8), and Cael. A 3, 269b23–26: barÝ mn oân œstw tÕ fšresqai pefukÕj ™pˆ tÕ mšson, koàfon d tÕ ¢pÕ toà mšsou, barÚtaton d tÕ p©sin Øfist£menon to‹j k£tw feromšnoij, koufÒtaton d tÕ p©sin ™pipol£zon to‹j ¥nw feromšnoij. 300b25. τὴν διάστασιν: Longo (1961) lists in his apparatus criticus the readings di£taxin, printed by Moraux (1965) and Guthrie (1939), and t£xin. In favor of di£stasin, the lectio difficilior, cf. Mete. A 2, 339a26–27: taàta d t¦ sèmata p£nta peperasmšnouj dišsthke tÒpouj ¢ll»lwn. Cf. Elders (1966) ad loc. 300b27. ἔνια: sc. tîn stoice…wn, here clearly some amounts of the elements. 300b29–31. καθάπερ…ἐβλάστησαν: the introductory Î is omitted from the quotation of DK 31 B 57.1 (but see GA A 18, 722b20, where the line is quoted again). Cf. Ph. B 8, 198b16–32. Simp., in Cael. 586.16–23 (Heiberg), explains Aristotle’s point as follows: e„ mn g¦r oÙc oŒÒn te Ãn ¢t£ktwj kinoÚmena kaˆ

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oÛtw kine‹sqai, æj m…gnusqa… pote ¢ll»loij t¦j e„rhmšnaj m…xeij, oÙ p£ntV ¢t£ktwj ™kine‹to· tÕ g¦r ¥takton ¢ÒristÒn ™stin, éste kaˆ micqÁnai ¨n kaˆ m¾ micqÁnai· éste oÙk Ãn ¡plîj ¢tax…a. e„ d ™dÚnato kaˆ tÒte mignÚmena taàta poie‹n pàr kaˆ gÁn kaˆ Ûdwr kaˆ ¢šra kaˆ t¦ ™k toÚtwn zùa kaˆ fut£, diÒti oƒ g…nesqai tÕn kÒsmon lšgontej ™n tÍ genšsei aÙtoà t¦ zùa oÙk ™k zówn dhlonÒti ¢ll’ ™k tîn swm£twn sugkrinomšnwn poioàsi, kaˆ tÒte ¨n kÒsmoj Ãn. On the interpretation of the difficult prepositional phrase ™pˆ tÁj filÒthtoj see Wright (1981) 46 and 50–51. Cf. below, on 301a16. 300b31–32. τοῖς δ’…ποιοῦσιν: sc. stoice‹a (see 300b18). After the prepositional phrase, tù kenù is implied (cf. 300b8–11). Aristotle turns his sights on Leucippus and Democritus once again. 300b32. εἰ μὲν ἓν τὸ κινοῦν: here tÕ kinoàn is the internal cause of an atom’s natural motion. Cf. Simp., in Cael. 588.12–13 (Heiberg): e4n d lšgei tÕ kinoàn oÙ tù ¢riqmù ¢ll¦ kat¦ tÕ edoj, oŒon barÚthta À koufÒthta. Aristotle complains in 300b8–11 that the atomists did not specify whether the eternal motion of the atoms in the void is natural or forced, and which is their natural motion. In 300b11–16 he argues that, if the eternal motion of the atoms in the void is forced, which is what Leucippus and Democritus seem to think, then there must exist a natural motion of the atoms, too. He assumes now that the atoms move naturally, each having an internal cause of natural motion. The possibility he considers first is that all atoms have the same internal cause of natural motion. 300b32–33. ἀνάγκη…κινηθήσεται: from the hypothesis that all atoms possess the same internal cause of natural motion follows that there is a single natural motion for all of them, so they do not move without order. The disorderliness of atomic motion is taken for granted, probably as an axiom of atomist physics. If a natural atomic motion exists, therefore, it will be disorderly. The hypothesis, however, that all atoms have the same internal cause of natural motion conflicts with the postulated disorderliness of atomic motion, and is thus rejected. 300b33–301a1. εἰ δ’…εἶναι: Aristotle now considers the hypothesis of infinitely many different, apparently in species, internal causes of natural motion for the infinitely many different kinds of atoms, which means that there is an infinity of natural atomic motions. It is clear from what comes next in 301a1–2 (e„ g¦r peperasmšnai, t£xij tij œstai) that only an infinity of natural atomic motions is compatible with the postulated disorderliness of atomic motion. There can be no doubt that Aristotle considers an infinity of natural atomic motions absurd, most probably on the grounds that natural motions are simple but simple motions are finitely many in species. See Simp., in Cael. 588.17–19 (Heiberg): kaˆ toàto e„pën oÙkšti ¥topon ™p»negken ¥llo æj e„j toàto ¥topon ¢pagagën tÕn lÒgon tÕ t¦j for¦j ¢pe…rouj enai· tîn g¦r ¡plîn kin»sewn t¦ e‡dh peperasmšna ™st…n· À g¦r kÚklJ À ¥nw À k£tw. For finitely many simple, and thus natural, motions see ch. 4, 303b4–8. Cf. Cael. A 7, 274b2–4: ¡plÁ mn g¦r ¹ toà

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¡ploà sèmatoj k…nhsij, aƒ d’ ¡pla‹ peperasmšnai kin»seij e„s…n. The simplicity of natural motions is also invoked in ch. 3, 302b5–9, to establish the existence of elements. See nn. ad loc. 301a1–2. εἰ γὰρ…ἔσται: the species of the natural motions of the atoms cannot be finitely many, as they would be in case there were finitely many species of internal causes of natural motion for the infinitely many kinds of atoms, for otherwise natural atomic motion would exhibit order. See above, on 300b32–33. The variant reading peperasmšna, sc. t¦ kinoànta, does not affect the meaning of the text. 301a2–4. οὐ γὰρ μόνον: Aristotle here explains why the species of the natural motions of the atoms cannot be finitely many. If they were, one could account for the disorderliness of atomic motion (see above, on 300b32–33) only by invoking the different places in the universe to which atoms with different natural motions are carried. But this is not tantamount to disorderliness, for simple bodies with different natural motions move to different natural places in the actual universe, too, in which the natural motions of the simple bodies are finitely many in species but by no means disorderly. 301a4–5. ἔτι…παρὰ φύσιν: having argued that the disorderliness of atomic motion is incompatible with the existence of natural atomic motion, for it leads to an absurd infinitude of species of natural atomic motion, Aristotle now sets out a premise of his next argument to the effect that the sheer description of the eternal motion of the atoms in the void as disorderly is absurd. 301a5–6. ἡ γὰρ…ἐστίν: cf. Ph. Θ 1, 252a11–12, where Aristotle asserts ¢ll¦ m¾n oÙdšn ge ¥takton tîn fÚsei kaˆ kat¦ fÚsin· ¹ g¦r fÚsij a„t…a p©sin t£xewj. 301a7. τὸ ἄπειρον ἄτακτον ἔχειν κίνησιν: tÕ ¥peiron refers collectively to the atoms (cf. 300b8–10 and 31–32). The adverb ¢e… is implied (see 300b8–10). 301a7–9. ἔστι γὰρ…χρόνον: this is the second premise of the argument. Nature being what characterizes most things of a certain kind for most of the time, or always (cf. Ph. B 8, 198b35–36: …p£nta t¦ fÚsei À a„eˆ oÛtw g…gnetai À æj ™pˆ tÕ polÚ, tîn d’ ¢pÕ tÚchj kaˆ toà aÙtom£tou oÙdšn), if the atoms always move without order in the void, which, alongside the atoms, makes up the atomist universe, disorderliness is the nature of this infinite collection of simple bodies. 301a9. αὐτοῖς: i.e. to‹j ¥peira ™n tù ¢pe…rJ kenù t¦ stoice‹a ¢eˆ kinoÚmena poioàsin. 301a9–10. τοὐναντίον…κατὰ φύσιν: it turns out that Democritus and Leucippus, contrary to the basic fact that the nature of things is the order which is ap-

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propriate to them (the first premise of the argument), identify absurdly the nature of the infinite collection of simple bodies they posit with disorderliness. 301a10–11. τὴν δὲ…παρὰ φύσιν: Simp., in Cael. 589.20–21 (Heiberg), supplies correctly the implicit condition required to complete the argument–e‡per tÕn ¥peiron crÒnon ¢t£ktwj kinoÚmena ™p’ Ñl…gon katall»lwj sumplekÒmena t£ttetai kaˆ kosme‹tai, sc. t¦ stoice‹a. 301a11. καίτοι…κατὰ φύσιν: cf. the passage quoted above, on 301a7–9. 301a11–12. ἔοικε…λαβεῖν: the object of the infinitive, toàto aÙtÒ, is the thesis implicitly established above, in 301a4–11, by the argument against the atomists–the ordered cosmos cannot arise from a pre-cosmic state characterized by the disorderly motion of the elements, which also follows from the critique of Timaeus in 300b16–25. In support of this conclusion, Aristotle now cites two of his predecessors, first Anaxagoras and then Empedocles. 301a12–13. ἐξ ἀκινήτων γὰρ ἄρχεται κοσμοποιεῖν: sc. ™x ¢kin»twn g¦r ¥peiron crÒnon kaˆ oÙk ¢t£ktwj kinoumšnwn tîn stoice…wn… Aristotle here praises Anaxagoras for positing an infinitely long state of rest of the elements prior to the cosmogony rather than a pre-cosmic state characterized by disorderly motion of the elements. In the surviving fragments of Anaxagoras’ work, only the beginning of the cosmogonic rotation that Mind imposed on the pre-cosmic mixture of the elements is mentioned; see DK 59 B 12–13. In Ph. Θ 1, 252a3–25, Aristotle criticizes Anaxagoras for what he praises him here: e„ d¾ taàt’ ¢dÚnata, dÁlon æj œstin ¢dioj k…nhsij, ¢ll’ oÙc Ðt mn Ãn Ðt d’ oÜ· kaˆ g¦r œoike tÕ oÛtw lšgein pl£smati m©llon. Ðmo…wj d kaˆ tÕ lšgein Óti pšfuken oÛtwj kaˆ taÚthn de‹ nom…zein enai ¢rc»n, Óper œoiken 'EmpedoklÁj ¨n e„pe‹n, æj tÕ krate‹n kaˆ kine‹n ™n mšrei t¾n fil…an kaˆ tÕ ne‹koj Øp£rcei to‹j pr£gmasin ™x ¢n£gkhj, ºreme‹n d tÕn metaxÝ crÒnon. t£ca d kaˆ oƒ m…an ¢rc¾n poioàntej, ésper 'AnaxagÒraj, oÛtwj ¨n e‡poien. ¢ll¦ m¾n oÙdšn ge ¥takton tîn fÚsei kaˆ kat¦ fÚsin· ¹ g¦r fÚsij a„t…a p©sin t£xewj. tÕ d’ ¥peiron prÕj tÕ ¥peiron oÙdšna lÒgon œcei· t£xij d p©sa lÒgoj. tÕ d’ ¥peiron crÒnon ºreme‹n, eta kinhqÁna… pote, toÚtou d mhdem…an enai diafor£n, Óti nàn m©llon À prÒteron, mhd’ aâ tin¦ t£xin œcein, oÙkšti fÚsewj œrgon. À g¦r ¡plîj œcei tÕ fÚsei, kaˆ oÙc Ðt mn oÛtwj Ðt d’ ¥llwj, oŒon tÕ pàr ¥nw fÚsei fšretai kaˆ oÙc Ðt mn Ðt d’ oÜ· À lÒgon œcei tÕ m¾ ¡ploàn. diÒper bšltion æj 'EmpedoklÁj, k¨n e‡ tij ›teroj e‡rhken oÛtwj œcein, ™n mšrei tÕ p©n ºreme‹n kaˆ kine‹sqai p£lin· t£xin g¦r ½dh tin’ œcei tÕ toioàton. ¢ll¦ kaˆ toàto de‹ tÕn lšgonta m¾ f£nai mÒnon, ¢ll¦ kaˆ t¾n a„t…an aÙtoà lšgein, kaˆ m¾ t…qesqai mhdn mhd’ ¢xioàn ¢x…wm’ ¥logon, ¢ll’ À ™pagwg¾n À ¢pÒdeixin fšrein. 301a13. καὶ οἱ ἄλλοι: it is not necessary that anybody other than Empedocles, who is mentioned in 301a15–16, is meant. Cf. Ph. Θ 1, 252a19–21: diÒper

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bšltion æj 'EmpedoklÁj, k¨n e‡ tij ›teroj e‡rhken oÛtwj œcein, ™n mšrei tÕ p©n ºreme‹n kaˆ kine‹sqai p£lin. 301a13–14. συγκρίνοντές πως πάλιν κινεῖν καὶ διακρίνειν: the implicit object is t¦ stoice‹a. Empedocles (see previous n.) hypothesizes that the simple bodies accrete each to its own place making the cosmos (sugkr…nontej) and, by some mechanism (pwj), are then set in disorderly motion, the mass of each fragmenting into pieces (kine‹n kaˆ diakr…nein). This disorderly motion leads the simple bodies back (p£lin) to a pre-cosmic state, in which the elements are implicitly assumed to be at rest, as is clear from the next sentence, and from which a new cosmos will spring forth, in an infinitely repeated cycle of cosmic birth and death. Aristotle’s point is that Anaxagoras and Empedocles agree that the cosmogony cannot be preceded by disorderly motion of the elements, though Anaxagoras posits a single cosmogony whereas Empedocles believes in an infinite succession of cosmogonies. The state of rest posited by Empedocles prior to a cosmogony is compared in Ph. Θ 1, 252a3–25, quoted above, on 301a12–13, with the Anaxagorean pre-cosmic state. Cf. Ph. Θ 1, 250b23–29, where, as in 252a3–25, Aristotle reports that Empedocles posits one state of rest when Love controls the elements completely, and one when Strife is symmetrically in full control. In the lines under discussion, as is clear from 301a15–18, the state of rest at the time of Love’s complete dominance is at issue. O’Brien (1969) ch. 2 argues for a single state of rest at the time of Love’s complete control. The reconstruction of the Empedoclean cosmology is problematic; see Graham (1999b) 159–162 and cf. below, on 301a16. 301a14–15. ἐκ διεστώτων δὲ καὶ κινουμένων: i.e. ™k diestètwn d kaˆ ¢t£ktwj kinoumšnwn tîn stoice…wn. 301a15. τὴν γένεσιν: sc. toà kÒsmou. 301a16. τὴν ἐπὶ τῆς φιλότητος: sc. gšnesin toà kÒsmou. The Empedoclean cosmogony presupposes (a) the stratification of the elements into the large-scale structure of the cosmos, when advancing Strife, which unites particles of the same element, controls the universe at the large scale; (b) the beginnings of the formation of living beings under the action, at small scales, of retreating Love, which mixes the particles of different elements so as to generate compound entities. Empedocles omitted a cosmogony, according to Aristotle, when the relationship of Strife and Love is reversed, i.e. when Love is wresting control of the four elements away from Strife, mixing them together and razing the large-scale structure of the cosmos. By Aristotle’s lights, the elements are in disorderly motion at this phase in the cyclical history of the universe: since he thinks that it is impossible for the cosmos to be generated from a state in which the elements undergo disorderly motion, he implicitly praises Empedocles for positing that the elements must enter a state of rest between this period of disorder and the next cosmogonical event (according to Aristotle, in the Empedoclean cosmology there are two diametrically opposed states of rest of the elements, one when Love controls the elements com-

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pletely, and one when Strife does so; see above, on 301a13–14). Elsewhere, however, in GC B 6, 334a5–7, Aristotle reports that Empedocles says that the cosmos is the same symmetrically under the growing control of either Strife or Love: ¤ma d kaˆ tÕn kÒsmon Ðmo…wj œcein fhsˆn ™p… te toà ne…kouj nàn kaˆ prÒteron ™pˆ tÁj fil…aj. See Wright (1981) 40–56, esp. 46, and Inwood (2001) 44–49. 301a17. συστῆσαι τὸν οὐρανὸν: sc. ™pˆ tÁj filÒthtoj. tÕn oÙranÒn = tÕn kÒsmon. Cf. 301a19, and see above, on 298a31. 301a17. ἐκ κεχωρισμένων μὲν κατασκευάζων: i.e. ™k kecwrismšnwn mn tîn stoice…wn kataskeu£zwn tÕn oÙranÒn. Cf. 301a18–19. 301a18. σύγκρισιν: sc. tîn stoice…wn. Here sÚgkrisij is the jumbling together of particles of different elements, whereas in 301a13–14 sugkr…nontej refers to the accretion of particles of the same element. 301a20. ἐξ ἑνὸς καὶ συγκεκριμένου: the mixture of the four elements. The cosmos comes to be from this primordial mixture after the disorderly motions of its particulate constituents has ceased. 301a20–23. ὅτι µὲν…ἐκ τῶνδε δῆλον: de…xaj, Óti ¢n£gkh to‹j ¡plo‹j sèmasi kat¦ fÚsin Øp£rcein tin¦ k…nhsin, ™fexÁj de…knusin, Óti to‹j kat¦ fÚsin kinoumšnoij oÙ p©sin ¢ll’ ™n…oij aÙtîn, to‹j ™p’ eÙqe…aj p©sin, ¢n£gkh ·op¾n Øp£rcein b£rouj À koufÒthtoj· tÕ g¦r kÚklJ kinoÚmenon ™xÇrhtai toÚtwn· kaˆ Óti kat¦ t¦j ·op¦j taÚtaj ™stˆn aÙto‹j ¹ kat¦ fÚsin k…nhsij (Simp., in Cael. 591.21–25 [Heiberg]). b£roj À koufÒthj is here called ·op¾ b£rouj À koufÒthtoj, a tendency to move naturally, in a straight line, down or up, i.e. towards the center of the cosmos or its periphery, respectively. The greater this tendency, the faster the rectilinear motion, in direct proportion to the size of the naturally moving body; see Ph. ∆ 8, 216a13–16, quoted above, on 299a31–b1. Here size is assumed to be proportionate to the amount of body; see above, on 299b5–6. The spearhead of the following argument is the proportionality between the size of the body which has the tendency to move naturally in a straight line, i.e. which has weight or lightness, and the speed of its natural rectilinear motion. If a body moves naturally in a straight line but has no weight or lightness, it can only be sizeless, and its natural motion must be infinitely slow–in other words, it cannot move naturally. See below, on 301a32–b1. On this and the next argument see also Kouremenos (2002b) 50–57. 301a23. κινεῖσθαι: sc. fÚsei. The subject is ›kaston tîn ¡plîn swm£twn. 301a25. κινεῖσθαι: sc. ™p’ eÙqe…aj. Cf. above, on 301a20–23. 301a25–26. ἢ πρὸς τὸ μέσον ἢ ἀπὸ τοῦ μέσου: sc. toà pantÒj. Aristotle considers first the possibility that a simple body, though it has no weight, moves

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naturally in a straight line towards the center of the cosmos. A reductio ad absurdum, the argument is then said to also rule out the possibility that a simple body moves naturally in a straight line away from the center of the cosmos, though it has no lightness (see 301b1). 301a26. ἔστω γὰρ τὸ μὲν ἐφ’ οὗ Α ἀβαρές: that the simple body introduced here hypothetically is weightless does not mean that it is light. Unlike light simple bodies, it moves naturally towards the center of the cosmos, but, unlike those simple bodies which are heavy, does so without having weight. The letter A stands for the size of a part of this hypothetical simple body. It will turn out that a part of this simple body is not only weightless but also sizeless. 301a26–27. τὸ δ’ ἐφ’ οὗ Β βάρος ἔχον: the letter B stands for the size of a part of a heavy simple body. Next, the speeds with which A and B move naturally will be compared. 301a27–28. ἐνηνέχθω…τὴν ΓΕ: here the speeds of A’s and B’s natural motion are compared. In the time it takes the weightless A to move naturally over a distance Γ∆, the heavy B moves naturally over a distance ΓΕ > Γ∆ (the following sentence presupposes this inequality). See Ph. Z 2, 232a25–31: ...¢n£gkh tÕ q©tton ™n tù ‡sJ crÒnJ me‹zon kaˆ ™n tù ™l£ttoni ‡son kaˆ ™n tù ™l£ttoni ple‹on kine‹sqai, kaq£per Ðr…zonta… tinej tÕ q©tton. œstw g¦r tÕ ™f’ ú A toà ™f’ ú B q©tton. ™peˆ to…nun q©ttÒn ™stin tÕ prÒteron metab£llon, ™n ú crÒnJ tÕ A metabšblhken ¢pÕ toà G e„j tÕ D, oŒon tù ZH, ™n toÚtJ tÕ B oÜpw œstai prÕj tù D, ¢ll’ ¢pole…yei, éste ™n tù ‡sJ crÒnJ ple‹on d…eisin tÕ q©tton. Aristotle probably had in mind a diagram representing ΓΕ and Γ∆ as unequal straight lines. 301a28–29. μείζω…ἔχον: the justification of the inequality ΓΕ > Γ∆ is also its statement. Cf. previous n. Here Aristotle must presuppose the direct proportionality between weight or lightness and speed of natural motion; this proportionality is stated in Ph. ∆ 8, 216a13–16, quoted above, on 299a31–b1, and how it is stated leaves no doubt that Aristotle thinks of it as grounded in observation. Invoking here the fact that, of two bodies naturally moving in a straight line, the one with the greater weight moves faster, traversing a greater distance in a given time, suggests that, initially, A’s weightlessness is tacitly considered a simple case of having less weight than B does. It is, in fact, the limiting case, just as infinite weight is the limit of having more weight than B does. See below, on 301a32–b1. 301a29–32. ἐὰν δὴ…φέρεσθαι: if B is divided in two parts so that one of them is to B as Γ∆ is to ΓΕ, in the time it takes B to move naturally over ΓΕ, this part moves over Γ∆. Cf. Ph. ∆ 8, 216a13–16, quoted above, on 299a31–b1. See also Cael. A 6, 273b30–274a2, where the comparison of the speeds of the natural motion of two unequal heavy bodies is the ratio of the times, in which the two bodies traverse a given distance (for the comparison of speeds in this way cf. the pas-

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sage quoted above, on 301a27–28): e„ g¦r tosÒnde b£roj t¾n tos»nde ™n tùde tù crÒnJ kine‹tai, tÕ tosoàton kaˆ œti ™n ™l£ttoni, kaˆ t¾n ¢nalog…an ¿n t¦ b£rh œcei, oƒ crÒnoi ¢n£palin ›xousin, oŒon e„ tÕ ¼misu b£roj ™n tùde, tÕ dipl£sion ™n ¹m…sei toÚtou. 301a32–b1. ὥστε…ἀδύνατον: if a heavy body less than B traverses Γ∆ in the time in which B moves over ΓΕ, it and the weightless body A move naturally with equal speeds, which is impossible, for the same reason for which A and B are initially assumed to move naturally with unequal speeds. This impossible equality of speeds, however, is certainly not the absurdity to which Aristotle reduces the hypothesis of a weightless simple body which, though, moves naturally towards the center of the cosmos. Cael. A 6, 273b30–274a2, quoted in previous n., opens an argument against the existence of an infinitely heavy body. This is how the argument unfolds (274a2–18): œti tÕ peperasmšnon b£roj ¤pasan peperasmšnhn d…eisin œn tini crÒnJ peperasmšnJ. ¢n£gkh ¥ra ™k toÚtou, e‡ ti œstin ¥peiron b£roj, kine‹sqai mn Î tosÒnde Óson tÕ peperasmšnon kaˆ œti, m¾ kine‹sqai dš, Î ¢n£logon mn de‹ kat¦ t¦j Øperoc¦j kine‹sqai, ™nant…wj d tÕ me‹zon ™n tù ™l£ttoni. lÒgoj d’ oÙqe…j ™sti toà ¢pe…rou prÕj tÕ peperasmšnon, toà d’ ™l£ttonoj crÒnou prÕj tÕn me…zw peperasmšnon· ¢ll’ ¢eˆ ™n ™l£ttoni. ™l£cistoj d’ oÙk œstin. oÙd’ e„ Ãn, ÔfelÒj ti ¨n Ãn· ¥llo g¦r ¥n ti peperasmšnon ™l»fqh ™n tù aÙtù lÒgJ, ™n ú tÕ ¥peiron prÕj ›teron me‹zon, ést’ ™n ‡sJ crÒnJ t¾n ‡shn ¨n ™kine‹to tÕ ¥peiron tù peperasmšnJ. ¢ll’ ¢dÚnaton. ¢ll¦ m¾n ¢n£gkh ge, e‡per ™n ÐphlikJoàn crÒnJ peperasmšnJ d kine‹tai tÕ ¥peiron, kaˆ ¥llo ™n tù aÙtù toÚtJ peperasmšnon b£roj kine‹sqa… tina peperasmšnhn. ¢dÚnaton ¥ra ¥peiron enai b£roj, Ðmo…wj d kaˆ koufÒthta. kaˆ sèmata ¥r’ ¥peiron b£roj œconta kaˆ koufÒthta ¢dÚnaton. Weightlessness being the opposite of infinite weight, this argument can be easily adapted to show that there cannot exist a simple body which moves naturally towards the center of the cosmos without having weight. Weight is proportional to size, so a part A of such a simple body can only be sizeless. The body A, moreover, should move naturally in a given time over a distance having to the greater distance which B, a part of a heavy body, moves over in the same time the ratio it, A, bears to B. This ratio cannot be formed, however, for what is sizeless bears no ratio to what has size. The weightless A could thus move naturally in a given time only over a distance “always less”, i.e. than any assigned distance, such as ΓΕ, no matter how small–that is, it could move in a given time only over a vanishingly small or infinitesimal distance bearing no ratio to an assigned distance, which means that it could move naturally only with infinite slowness, or not move naturally at all. (Equivalently, it could traverse any assigned distance, no matter how small, in an infinitely long time.) For, if the weightless A is assumed to move in a given time over a distance Γ∆ which is not infinitesimal, and thus bears a ratio to the larger distance ΓΕ, it turns out that another body, too, traverses Γ∆ in the same time–a body which has weight, and is to the heavy body B which traverses ΓΕ in the given time as Γ∆ is to ΓΕ. In the lines under discussion Aristotle presents only the second part of this argument, but his

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next argument, in 301b1–16, leaves no doubt that the first part is also needed. Implicit is a generalization of what holds for Γ∆. No matter how small a part of ΓΕ is assumed to be moved over by the weightless A in a given time, it turns out to be traversed by the same part of the heavy B. The weightless A can thus move naturally in a given time only over a distance which is always less than any assigned distance, no matter how small, and so is no part of it, just as the weightless A is no part of the heavy B–it can only be a point; cf. 299a30–b7. The same conclusion follows if A lacks lightness. For the impossibility of infinite slowness, moving over a finite distance in an infinitely long time, see Ph. Z 7, 237b23–238a19. 301b1. ὁ δ’ αὐτὸς λόγος καὶ ἐπὶ κουφότητος: cf. the end of the passage quoted in previous n. 301b1–4. ἔτι…τὴν κίνησιν: since a part A of a hypothetically weightless simple body has been shown not to move naturally, if it can move, its motion can only be forced. Aristotle argues next that the forced motion of A can only be infinitely fast, which is absurd. The same conclusion follows if A lacks lightness. Aristotle does not state this, but see 301b16–17. See also Kouremenos (2002b) 50–57. 301b4–7. ἐπεὶ…τὴν ΓΔ: ΓΕ > Γ∆. Initially, A’s weightlessness is considered tacitly a case of having less weight than does B, as in the previous argument. For the inverse proportionality assumed here see Ph. H 5, 249b30–250a4: …e„ d¾ tÕ mn A tÕ kinoàn, tÕ d B tÕ kinoÚmenon, Óson d kek…nhtai mÁkoj tÕ G, ™n ÓsJ dš, Ð crÒnoj, ™f’ oá tÕ D, ™n d¾ tù ‡sJ crÒnJ ¹ ‡sh dÚnamij ¹ ™f’ oá tÕ A tÕ ¼misu toà B diplas…an tÁj G kin»sei, t¾n d tÕ G ™n tù ¹m…sei toà D· oÛtw g¦r ¢n£logon œstai. It is stated below, in 301b11–13. If the comparison of speeds is expressed as the ratio of the times in which a given distance is moved over, the proportionality is direct. 301b8–11. διαιρεθέντος…τὴν ΓΔ: if B is divided in two parts so that one of them is to B as Γ∆ is to ΓΕ, in the time it takes B to move forcedly over Γ∆, this part moves over ΓΕ, forced by the same mover. Cf. previous n. 301b11–13. τὸ γὰρ τάχος…πρὸς τὸ ἔλαττον: cf. above, 301b4–7. 301b13–14. ἴσον…ἀδύνατον: if a heavy body less than B is forced to move over ΓΕ in the time in which B, forced by the same mover, moves over Γ∆, it and the weightless body A move forcedly with equal speeds. This is impossible, for the same reason for which A and B are initially assumed to move forcedly with unequal speeds. 301b14–16. ὥστ’…ἂν φέροιτο: no matter how large a multiple of Γ∆ we assume ΓΕ to be over which the weightless A is hypothesized to move forcedly in a given time, it turns out that the same mover forces the same sub-multiple of the heavy B to move over ΓΕ in the same time. The weightless A can, therefore, trav-

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erse forcedly in a given time only an infinite distance, one always exceeding any assigned distance, no matter how large; equivalently, it can be forced to move over any finite distance only in an infinitesimal time. For the impossibility of moving infinitely fast, in which case a body would traverse an infinite distance in a finite time, see Ph. Z 7, 238a20–31. Cf. above, on 301a32–b1. The argument in the lines under discussion is markedly similar to that in Ph. ∆ 8, 215b19–216a11, against the possibility of motion in a vacuum, on which see Kouremenos (2002a); the two arguments are compared in 102–103. See also below, on 301b23–25. 301b17. διωρισμένον: i.e. such that it bears a ratio to the weight or lightness of other bodies. In the two previous arguments, the body A, which is assumed to lack weight or lightness, is clearly assumed to have a vanishingly small, i.e. infinitesimal, weight or lightness, as well as size, which is always less than the weight or lightness, and thus size, of any other body B, and thus does not stand to it in a ratio. Such a ‘magnitude’ cannot be reached or exceeded by means of any finite number of divisions of a given magnitude, just as, by means of any finite number of multiplications of a given magnitude, an infinite one cannot be reached or exceeded (in Cael. A 7, 275a22–24, an infinitesimal time is called ¥peiroj). If this were possible, weight or lightness, and size, would be ærismšnon: prÕj peperasmšnon g¦r ¢eˆ prostiqeˆj Øperbalî pantÕj ærismšnou, kaˆ ¢fairîn ™lle…yw æsaÚtwj (Ph. Θ 10, 266b2–4). Cf. Elders (1966) and Jori (2009) ad loc. 301b17–18. φύσις…ἀρχή: cf. above, on 298a27–28. 301b18–19. δύναμις…ἄλλο: cf. above, on 298a32–34. 301b20–22. τὴν μὲν…αὐτή: the natural motion of a stone is due to nature, a principle or cause of motion internal to the stone, more exactly to the heavy constituents of this object, and is made faster by force, a capacity in something external to the stone, namely in the surrounding air, for causing motion. As Aristotle explains below, naturally moving air ‘assists’ natural motion in it. On the other hand, the forced motion of a stone thrown upward is exclusively due to the motive capacity of the air surrounding the stone. See below, on 301b23–25. 301b22. πρὸς ἀμφότερα: i.e. prÕj kaˆ t¾n kat¦ fÚsin kaˆ t¾n par¦ fÚsin k…nhsin. 301b22. χρῆται: the implicit subject is ¹ fÚsij, not in the above explained technical sense (301b17–18) but in a looser one, very close to our ‘nature’. This is the meaning of the term in e.g. Cael. A 4, 271a33: Ð d qeÕj kaˆ ¹ fÚsij oÙdn m£thn poioàsin. Cf. GA A 22, 730b19–22: Ðmo…wj d kaˆ ¹ fÚsij ¹ ™n tù ¥rreni tîn spšrma proi+emšnwn crÁtai tù spšrmati æj Ñrg£nJ kaˆ œconti k…nhsin ™nerge…v, ésper ™n to‹j kat¦ tšcnhn gignomšnoij t¦ Ôrgana kine‹tai, and E 8, 789b2–4: DhmÒkritoj d tÕ oá ›neken ¢feˆj lšgein p£nta ¢n£gei e„j ¢n£gkhn oŒj crÁtai ¹ fÚsij.

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301b23. πέφυκε…βαρύς: in the following lines, Aristotle seems to think of air as both light and heavy in the sense that it can move naturally both upwards or downwards, but in 300a25–27 he says that a simple body moves naturally with a single motion, whereas there are many counter-natural motions of it. That a simple body has a single natural motion appears as a premise in an argument for the existence of the first simple body in Cael. A 2, 269a2–9, and in the proof of the crucial fact that this simple body is neither heavy nor light in A 3, 269b29–35. An argument in Cael. B 14, 296b25–297a2, that the Earth rests motionless at the center of the cosmos also relies on the same premise. Nevertheless, the assertion that air and water move naturally both upwards and downwards, whereas each of the other two Empedoclean simple bodies moves naturally in only one of these directions, fire upwards and earth downwards, is found in Ph. ∆ 8, 216a27–33, which is quoted in next n. In Cael. ∆ 4, 311a16–29, which is quoted above, on 299b1–4, air is thought of as light and heavy perhaps in the ‘static’ sense that it floats on top of earth and water but pools underneath fire, or in the ‘kinematic’ one that it has two natural motions, rising on top of earth and water but sinking beneath fire. A further problem arises from the claim in Cael. ∆ 4, 311b4–10, that air is heavy in its natural place, whereas it is light when in earth or water: in the lines discussed next, it is assumed that air is light in its natural place, too. 301b23–25. τὴν μὲν…ᾗ βαρύς: insofar as air is light and moves naturally upwards, it forces a stone to move non-naturally upwards, when it is pushed and takes over the initiation of motion from something other than the stone that has the capacity for causing the stone to move non-naturally–that is, from the thrower of the stone; insofar as air is heavy and can move naturally downwards, too, it makes faster the natural motion of a stone. According to Ph. ∆ 8, 216a27–33, a stone moving naturally, i.e. falling, in air or water, displaces a volume of the incompressible medium equal to its own, in the direction of the medium’s natural motion: ésper g¦r ™¦n ™n Ûdati tiqÍ tij kÚbon, ™kst»setai tosoàton Ûdwr Ósoj Ð kÚboj, oÛtw kaˆ ™n ¢šri· ¢ll¦ tÍ a„sq»sei ¥dhlon. kaˆ a„eˆ d¾ ™n pantˆ sèmati œconti met£stasin, ™f’ Ö pšfuke meq…stasqai, ¢n£gkh, ¨n m¾ sumpilÁtai, meq…stasqai À k£tw a„e…, e„ k£tw ¹ for¦ ésper gÁj, À ¥nw, e„ pàr, À ™p’ ¥mfw (on the double natural motion of air and water see previous n.; for fleshing out the lines discussed here, it suffices to assume that each simple body has a single natural motion). Now, this displacement can only cause in air or water a motion called ¢ntiper…stasij (cf. above, on 299b13–14), as a result of which air or water follows in the wake of the naturally moving stone and occupies immediately the place vacated by it. See Simp., in Ph. 1350.31–36 (Diels): ¢ntiper…stasij dš ™stin, Ótan ™xwqoumšnou tinÕj sèmatoj ØpÕ sèmatoj ¢ntallag¾ gšnhtai tîn tÒpwn, kaˆ tÕ mn ™xwqÁsan ™n tù toà ™xwqhqšntoj stÍ tÒpJ, tÕ d ™xwqhqn tÕ prosecj ™xwqÍ kaˆ ™ke‹no tÕ ™cÒmenon, Ótan ple…ona Ï, ›wj ¨n tÕ œscaton ™n tù tÒpJ gšnhtai toà prètou ™xwq»santoj. The naturally moving stone disturbs the air or water, which prior to the disturbance rested in its natural place and, for the duration of the stone’s motion, is constantly reorganizing its mass, so that all of its parts come to a state of rest again, symmetrically close to

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or away from the center of the cosmos–that is, as parts of a continuous spherical shell with no holes, like that introduced by the naturally moving stone. Cf. the explanation of the Earth’s shape in Cael. B 14, 297a8–12, where sphericity is accounted for as if it were the consequence of ¢ntiper…stasij: scÁma d’ œcein sfairoeidj ¢nagka‹on aÙt»n· ›kaston g¦r tîn mor…wn b£roj œcei mšcri prÕj tÕ mšson, kaˆ tÕ œlatton ØpÕ toà me…zonoj çqoÚmenon oÙc oŒÒn te kuma…nein, ¢ll¦ sumpišzesqai m©llon kaˆ sugcwre‹n ›teron ˜tšrJ, ›wj ¨n œlqV ™pˆ tÕ mšson. (Simp., in Cael. 542.27–30 [Heiberg], suggests that oÙc oŒÒn te kuma…nein might rule out the possibility of ¢ntiper…stasij in the mass of the simple body earth; but sugcwre‹n ›teron ˜tšrJ can be understood only as referring to the arrangement of this mass as if it had undergone such motion, its parts having given way to one another and come to rest equally far from the center at any distance from it so that the smaller ones inside could not possibly bulge, oÙc oŒÒn te kuma…nein, preventing the larger ones above from forming a sphere.) The air or water following in the wake of the naturally moving stone is, therefore, itself undergoing natural motion, and pushes the stone, whose motion is made faster as a result. In the case of a stone moving non-naturally upwards, initially the stone is moved by the thrower, who is in contact with it. By moving the stone in the air, the thrower disturbs the air, just as a stone moving naturally in it does, and, immediately upon loss of contact between the stone and the thrower, the naturally moving air, which flows in the wake of the forcedly moving stone, takes over from the thrower and, like a wind, pushes the stone further up! The thrower, that is, by moving the stone in the air, sets the latter in natural motion, and makes it capable of moving the stone, as soon as the thrower lets go of the stone. By moving forcedly the stone immediately upon the detachment of the object from the thrower, however, air keeps itself in natural motion, and the process feeds back on itself, making it possible for the stone to be moved non-naturally upwards by a succession of naturally moving movers: the parts of the mass of air in the stone’s path. Each is successively displaced so that (a) fresh air flows naturally behind the stone, (b) the mass of air, which was contiguous with it before its displacement, is, in turn, displaced, thereby pushing the stone further up. Cf. Ph. Θ 10, 266b27–267a20: perˆ d tîn feromšnwn œcei kalîj diaporÁsa… tina ¢por…an prîton. e„ g¦r p©n tÕ kinoÚmenon kine‹tai ØpÕ tinÒj, Ósa m¾ aÙt¦ ˜aut¦ kine‹, pîj kine‹tai œnia sunecîj m¾ ¡ptomšnou toà kin»santoj, oŒon t¦ ·iptoÚmena; e„ d’ ¤ma kine‹ kaˆ ¥llo ti Ð kin»saj, oŒon tÕn ¢šra, Öj kinoÚmenoj kine‹, Ðmo…wj ¢dÚnaton toà prètou m¾ ¡ptomšnou mhd kinoàntoj kine‹sqai, ¢ll’ ¤ma p£nta kine‹sqai kaˆ pepaàsqai Ótan tÕ prîton kinoàn paÚshtai, kaˆ e„ poie‹, ésper ¹ l…qoj, oŒÒn te kine‹n Ö ™k…nhsen. ¢n£gkh d¾ toàto mn lšgein, Óti tÕ prîton kinÁsan poie‹ oŒÒn te kine‹n À tÕn ¢šra [toioàton] À tÕ Ûdwr ½ ti ¥llo toioàton Ö pšfuke kine‹n kaˆ kine‹sqai· ¢ll’ oÙc ¤ma paÚetai kinoàn kaˆ kinoÚmenon, ¢ll¦ kinoÚmenon mn ¤ma Ótan Ð kinîn paÚshtai kinîn, kinoàn d œti ™st…n. diÕ kaˆ kine‹ ti ¥llo ™cÒmenon· kaˆ ™pˆ toÚtou Ð aÙtÕj lÒgoj. paÚetai dš, Ótan ¢eˆ ™l£ttwn ¹ dÚnamij toà kine‹n ™gg…gnhtai tù ™comšnJ. tšloj d paÚetai, Ótan mhkšti poi»sV tÕ prÒteron kinoàn, ¢ll¦ kinoÚmenon mÒnon. taàta d’ ¢n£gkh ¤ma paÚesqai,

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tÕ mn kinoàn tÕ d kinoÚmenon, kaˆ t¾n Ólhn k…nhsin. aÛth mn oân ™n to‹j ™ndecomšnoij Ðt mn kine‹sqai Ðt d’ ºreme‹n ™gg…gnetai ¹ k…nhsij, kaˆ oÙ sunec»j, ¢ll¦ fa…netai· À g¦r ™fexÁj Ôntwn À ¡ptomšnwn ™st…n· oÙ g¦r e$n tÕ kinoàn, ¢ll’ ™cÒmena ¢ll»lwn. diÕ ™n ¢šri kaˆ Ûdati g…gnetai ¹ toiaÚth k…nhsij, ¿n lšgous… tinej ¢ntiper…stasin enai. ¢dÚnaton d ¥llwj t¦ ¢porhqšnta lÚein, e„ m¾ tÕn e„rhmšnon trÒpon. ¹ d’ ¢ntiper…stasij ¤ma p£nta kine‹sqai poie‹ kaˆ kine‹n, éste kaˆ paÚesqai· nàn d fa…neta… ti e$n kinoÚmenon sunecîj· ØpÕ t…noj oân; oÙ g¦r ØpÕ toà aÙtoà. Aristotle’s rejection of the view that ¢ntiper…stasij alone can explain the motion of thrown objects, without the further assumption that the air winding up behind e.g. a thrown stone not just fills the place vacated by the stone but also moves the stone, is perhaps a critique of Plato (Ti. 79a5–80a2). See Simp., in Ph. 1351.28–29 (Diels), and cf. Ph. ∆ 8, 215a14–17: œti nàn mn kine‹tai t¦ ·iptoÚmena toà êsantoj oÙc ¡ptomšnou, À di’ ¢ntiper…stasin, ésper œnio… fasin, À di¦ tÕ çqe‹n tÕn çsqšnta ¢šra q£ttw k…nhsin tÁj toà çsqšntoj for©j ¿n fšretai e„j tÕn o„ke‹on tÒpon (relevant is also Ph. H 2, 243a20–b2). When a thrown object follows a curve during its fall, Aristotle would perhaps explain the shape of its trajectory as a result of the object’s undergoing two competing motions in directions at an angle to each other, one natural and the other counter-natural, which, or probably whose speeds, bear to each other a constantly varying ratio; see his short explanation of the motion of shooting stars in Mete. A 4, 342a24–27, and cf. the argument in [Arist.] Mech. 848b23–35. If the natural motion of air or water forcing a stone to move is slowed down proportionately to the size of the moved object, and thus to the amount of body in it, then, as the moved object shrinks to a vanishingly small size, the speed of its forced motion must tend not to infinity, as Aristotle argues in 301b1–16, but to a finite speed–that with which the mover, unencumbered by a moved object, would move naturally. On the cosmological role of air as cause of forced motion see Mete. A 3, 341a28–31. 301b26. ὥσπερ γὰρ ἐναφάψασα: Simp., in Cael. 596.20–21 (Heiberg), paraphrases it as ésper sunart»sasa kaˆ ™napod»sasa, the subject being ¹ kinoàsa dÚnamij. The implicit direct object picks out what is moved. Cf. next n. 301b26. παραδίδωσιν ἑκατέρῳ: Simp., in Cael. 596.22–23 (Heiberg), understands ˜katšrJ tîn ¢šrwn tù te ¥nw ™pwqoumšnJ kaˆ tù k£tw À ˜katšrJ tù te ¢šri kaˆ tù l…qJ. For the implicit subject and direct object see previous n. 301b27–29. εἰ…κίνησις: the pronoun toioàton can only stand for koàfon kaˆ barÚ. Cf. Simp., in Cael. 596.28–30 (Heiberg): e„ m¾ g¦r Ãn ti toioàton sîma tÕ sunergoàn, oÙk ¨n ¹ b…v k…nhsij toiaÚth Ãn· e„ m¾ g¦r ecš ti koàfon Ð ¢»r, oÙk ¨n tÕ barÝ ¥nw œfere, kaˆ e„ m¾ barÚ ti ecen, oÙk ¨n tÕ pàr ™pˆ tÕ k£tw ™k…nei. 301b29. συνεπουρίζει: according to Simp., in Cael. 596.32–597.5 (Heiberg), tÕ d sunepour…zein ¢pÕ tîn Ôpisqen pneÒntwn kaˆ t¾n naàn çqoÚntwn ¢nšmwn

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mete…lhptai, oÞj di¦ toàto oÙr…ouj kaloàsin æj kat¦ tÕ oÙra‹on tÁj neëj pnšontaj. m»pote d kaˆ ¢pÕ metafor©j tîn leÒntwn lšgetai, oÛj fasi tÍ ˜autîn oÙr´ ¢ntˆ m£stigoj pl»ttontaj ˜autoÝj e„j drÒmon ™laÚnein. 301b31–33. ὅτι…προειρημένων: lšgei oân, Óti ™k tîn e„rhmšnwn dÁlÒn ™stin, Óti oÜte p£ntwn gšnesij, e‡per dšdeiktai, Óti tÕ kukloforhtikÕn sîma ¢gšnhtÒn te kaˆ ¥fqartÒn ™stin, oÜte oÙdenÒj, e‡per di»legxe toÝj tîn Parmen…dou kaˆ Mel…ssou lÒgwn oÛtwj ¢koÚontaj æj p©n tÕ ×n ¢gšnhton legÒntwn (Simp., in Cael. 598.3–7 [Heiberg]). What is called here tÕ kukloforhtikÕn sîma is the first simple body; see above, on 298a25–26. For the critique of Parmenides and Melissus see ch.1, 298b14–24. 302a1. κενὸν…κεχωρισμένον: dittÕn g¦r tÕ kenÕn oƒ lšgontej aÙtÕ Øpet…qento, tÕ mn to‹j sèmasin ¢namemigmšnon kat¦ toÝj ™n aÙto‹j pÒrouj, oÞj ¹me‹j ¢šroj lšgomen mestoÚj, tÕ d kecwrismšnon tîn swm£twn tÒpon tîn swm£twn ginÒmenon (Simp., in Cael. 598.14–17 [Heiberg]). Aristotle rules out the existence of vacuum in Ph. ∆ 6–9. This result is also used in ch. 6, 305a14–22. 302a6–7. ἐκ…σῶμα: that is, ™k purÕj toà dun£mei gšnoit’ ¨n tÕ ™nerge…v pàr, where pàr tÕ dun£mei = ¢¾r Ð ™nerge…v. Cf. Metaph. Θ 8, 1049b24–27: ¢eˆ g¦r ™k toà dun£mei Ôntoj g…gnetai tÕ ™nerge…v ×n ØpÕ ™nerge…v Ôntoj, oŒon ¥nqrwpoj ™x ¢nqrèpou, mousikÕj ØpÕ mousikoà, ¢eˆ kinoàntÒj tinoj prètou· tÕ d kinoàn ™nerge…v ½dh œstin. Aristotle explains the mechanisms of elemental transformation in GC B 4; see below, on 302a17–18, and Introduction, 3.

CHAPTER 3 302a10–11. τίνων…ἐστιν: no explicit answer to either question is given in this or the following chapters. In ch. 1, 298b6–11, it is said that, since the first simple body is not subject to generation, the latter either does not occur or it occurs only in the four Empedoclean simple bodies, two of which are heavy and two light, as well as in the bodies that are made up of them. These are ultimately the bodies referred to by t…nwn. Simp., in Cael. 600.10–13 (Heiberg), thinks that only the Empedoclean simple bodies are implicit here, and that the answer to the second indirect question is that each comes to be from another (see ch. 6): ™lšgxaj oân kaˆ toÝj ¢nairoàntaj telšwj t¾n gšnesin kaˆ toÝj p£ntwn enai lšgontaj ™pˆ tÒ, t…nwn œsti gšnesij kaˆ di¦ t… œstin, ™tr£ph, t…nwn mn lšgwn, Óti tîn poiÒthtaj paqhtik¦j ™cÒntwn kaˆ ™p’ eÙqe…aj kinoumšnwn, di¦ t… d ¢ntˆ toà t…nwn ginomšnwn. What follows in 302a12–13, skeptšon po‹a tîn toioÚtwn, sc. genhtîn, swm£twn ™stˆ stoice‹a, rules this out, however. Here Aristotle explains how he will go about answering the second indirect question in the lines under discussion, and this question concerns the same bodies as the first: these bodies evidently cannot be the four Empedoclean simple bodies, the sought-after elements of the former. It is thus preferable to assume that t…nwn here and tîn toioÚtwn

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swm£twn in 302a12–13 probably refer to all bodies such as those Aristotle mentions below, in 302a21–22, some of which are determined to be elements of the rest: flesh, wood, fire, earth etc. A plausible, general characterization of these bodies would be “all those around us whose coming into being we observe”. The implicit answer to the second indirect question is probably that the composites among these bodies have as their elements simple bodies that, as Aristotle will argue below, in ch. 6, are subject to generation, to which, as a consequence, the composites are themselves subject. See below, on 302a12–14. 302a11. ἐν ἅπασιν…πρώτων: everywhere knowledge requires understanding the first principles of what we want to know. Cf. Ph. A 1, 184a12–14: tÒte g¦r o„Òmeqa gignèskein ›kaston, Ótan t¦ a‡tia gnwr…swmen t¦ prîta kaˆ t¦j ¢rc¦j t¦j prètaj kaˆ mšcri tîn stoice…wn. 302a12. τῶν ἐνυπαρχόντων: i.e. ™n to‹j genhto‹j sèmasi. The bodies subject to generation Aristotle refers to here are undoubtedly both those called homoeomeric, ÐmoiomerÁ, whose divisions always yield the same substance, and unhomoeomeric, ¢nomoiomerÁ. See Mete. ∆ 10, 388a13–20: lšgw d’ ÐmoiomerÁ oŒon t£ te metalleuÒmena–calkÒn, crusÒn, ¥rguron, katt…teron, s…dhron, l…qon, kaˆ t«lla t¦ toiaàta, kaˆ Ósa ™k toÚtwn g…gnetai ™kkrinÒmena–kaˆ t¦ ™n to‹j zóoij kaˆ futo‹j, oŒon s£rkej, Ñst©, neàron, dšrma, spl£gcnon, tr…cej, nej, flšbej, ™x ïn ½dh sunšsthke t¦ ¢nomoiomerÁ, oŒon prÒswpon, ce…r, poÚj, kaˆ t«lla t¦ toiaàta, kaˆ ™n futo‹j xÚlon, floiÒj, fÚllon, ·…za, kaˆ Ósa toiaàta. On the generation of homoeomers see below, on 302a17–18. ™nup£rconta ™n to‹j genhto‹j sèmasi are further sèmata–the constituents at every level of the hierarchy of the material organization of a compound body, at the bottom of which is the level of the irreducible elements, the simple bodies. Simple observation shows that the latter are four. 302a12–14. σκεπτέον…ποῖ’ ἄττα: since everywhere knowledge requires understanding the first principles of what we want to know about, and among all the constituents of the bodies subject to generation it is the elements that are the first principles of the bodies at issue, Aristotle will examine next which bodies among those that are subject to generation are elements of the rest and why, how many elements there are–the topics of the two following chapters–and of which kind they are, i.e. subject to generation, for the last question can only refer to the topic discussed in ch. 6, where Aristotle shows that bodies subject to generation have elements which themselves come into being. Ch. 3 determines the elements of the bodies at issue, not which type of these bodies contains their elements, and thus the number of these elements–four. Ch. 4 shows why they are finite and ch. 5 why they must be more than one. Both of these chapters criticize earlier views. The next chapter argues not only that the elements of the bodies that come into being are themselves subject to generation but also that they must come to be from one another, a conclusion strengthened in ch. 7 with a critique of earlier views on the mode of the generation of these elements. Of importance here seems to be only what is estab-

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lished in ch. 6, with which this partial survey of the following chapters of the book ends. It suggests an answer to the second question with which ch. 3 opens. Around us there exist bodies whose coming into being we observe: why is this so? In view of ch. 6, the answer, which is in accord with the axiom that knowledge requires understanding the first principles of what we want to obtain knowledge about, in this case the elements of the bodies whose generation we observe, is this: the elements of the composites among the bodies at issue, i.e. the four Empedoclean simple bodies, are themselves subject to generation. Cf. above, on 302a10–11. 302a13. διὰ τί ἐστιν: the question is answered in 302b5–9, at the end of the chapter, with an argument that establishes the existence of elements, which suggests that here the verb is existential, with stoice‹a as subject. The context, however, leaves no doubt that the verb is copulative, with taàta, sc. tîn toioÚtwn swm£twn, as subject and stoice‹a as predicate. Aristotle is not concerned with the general question why elements exist but with a particular one directly relevant to the topic of this chapter: why those bodies that will be shown next, on empirical grounds, to be elements of generated bodies are elements. See below, on 302b7–8. 302a14. τοῦτο: i.e. po‹a tîn toioÚtwn, sc. genhtîn, swm£twn ™stˆ stoice‹a, kaˆ di¦ t… ™stin, œpeita met¦ taàta pÒsa kaˆ po‹’ ¥tta. 302a15–18. ἔστω…τῷ εἴδει: cf. Metaph. ∆ 3, 1014a26–35. For ¢dia…reton e„j ›tera tù e‡dei see below, on 302b19–20. 302a17–18. τοῦτο…ἀμφισβητήσιμον: to produce homoeomeric composite bodies, the four Empedoclean simple bodies mix together, and each of them exists potentially in the mixture, which exists actually. See GC Α 10, 327b22–31: ™peˆ d’ ™stˆ t¦ mn dun£mei t¦ d’ ™nerge…v tîn Ôntwn, ™ndšcetai t¦ micqšnta ena… pwj kaˆ m¾ enai, ™nerge…v mn ˜tšrou Ôntoj toà gegonÒtoj ™x aÙtîn, dun£mei d’ œti ˜katšrou ¤per Ãsan prˆn micqÁnai, kaˆ oÙk ¢polwlÒta· toàto g¦r Ð lÒgoj dihpÒrei prÒteron, fa…netai d t¦ mignÚmena prÒterÒn te ™k kecwrismšnwn suniÒnta kaˆ dun£mena cwr…zesqai p£lin· oÜte diamšnousin oân ™nerge…v ésper tÕ sîma kaˆ tÕ leukÒn, oÜte fqe…retai, oÜte ˜k£teron oÜt’ ¥mfw· sèzetai g¦r ¹ dÚnamij aÙtîn. Understanding the formation of homoemeric composite bodies requires understanding how the four Empedoclean simple bodies are generated from, or turn into, one another. Aristotle describes three transmutation processes in GC B 4. By the first of them, fire transforms into air, air into water, water into earth, and earth into fire; this cyclical change can occur in the other direction. By the second process, fire turns into water, air into earth, water into fire, and earth into air. By the third process, fire and water change jointly into earth or air, air and earth into fire or water. All three processes involve physical contact and interaction between two Empedoclean simple bodies. They act on each other in virtue of their qualities (see below, on 302b7–8). The cold is potentially the hot, and the hot is potentially the cold, just as the dry is potentially the wet, and the wet is potentially the dry. If the simple bodies they characterize

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come into contact, each quality acts on its contrary. The cold tends to assimilate to itself the hot, and its action is being met by an opposite reaction: if one of the contraries is overpowered, it assimilates itself to the other, which also suffers a reciprocal change, as result of the interaction (see GC B 7, 334b20–30). But if the cold of e.g. earth assimilates itself to the hot of fire, earth turns into fire, the dry being common to both. A simple body has turned into another by the first of the three processes explained in GC B 4. In the second process, not just one but both qualities of a simple body turn into their contraries. In the third process, only one quality of each simple body turns into its contrary: e.g. the dry of fire assimilates to itself the wet of water, the cold of water assimilates to itself the hot of fire, and the result of the interaction is dry and cold earth. If the contraries are equal in their powers, neither agent turns into the other or suffers any change–the two simple bodies are left intact (see GC B 7, 334b20–24). However, if the equality is only approximate, the contraries cancel each other out, and in their place somehow emerge the dispositional properties of a compound, in whose formation the interaction of the simple bodies resulted (see GC B 7, 334b24–30). The simple bodies cannot possibly be identified in a compound, but their potentiality is preserved in it, and so they will emerge into actuality once again, when the compound will have decomposed. Which dispositional properties emerge, and thus which compound body is generated, seems to be determined by how close to equality in power the qualities are (see GC B 7, 334b24–30). Aristotle assumes that this closeness is continuously variable for each pair of contraries, which can easily allow for many kinds of compound bodies in the cosmos. Whether the contraries are approximately equal in power is determined by the amounts of the Empedoclean simple bodies entering into combination; for the nature of homoeomeric compound bodies is said to depend on the relations in which these quantities happen to stand to one another (see GC A 10, 328a23–31, de An. A 4, 408a14–15). As it is, whether the contraries are exactly equal in power, or unequal enough for the one to assimilate the other to itself, must also depend on the relation between the amounts of the interacting simple bodies (see also the discussion in GC B 6, 333a16–34, of the senses in which the four traditional simple bodies can be thought of as being comparable). See also Kouremenos (2010) 13–16. 302a21–23. ἐν…ἐκκρινόμενα: Simp., in Cael. 602.5–13 (Heiberg), allows us to get an idea of the kind of observations perhaps alluded to here. According to the commentator, Óti d ™kkr…netai pàr ™k sarkÒj, QeÒfrastoj mn ¢pÕ Ñfqalmîn ¢nqrèpou flÒga ™kkriqÁnai ƒstore‹, Megšqioj d Ð 'AlexandreÝj „atrÕj ™moˆ dihg»sato teqe©sqai „sciadikoà ¢ndrÕj pàr ¢pÕ toà „sc…ou ™xelqÕn kaˆ kaàsan t¦ strèmata, ™f’ ú kaˆ ™paÚsato tÕ p£qoj, dhloàsi d kaˆ aƒ tîn ¢nqr£kwn ™sc£rai ¢pÕ purÕj ginÒmenai kaˆ oƒ diakae‹j pureto…· ¢pÕ d xÚlwn pàr ™kb£llousi tÕ ›teron xÚlon æj trÚpanon ™n tù ˜tšrJ peristršfontej. Óti d gÁ toÚtoij œnesti, dhlo‹ ¹ met¦ t¾n kaàsin Øpoleipomšnh tšfra, dhlo‹ d kaˆ ¹ ™kkrinomšnh ØgrÒthj kaˆ Ð ™xatmizÒmenoj ¢»r. The Empedoclean elements are called in GC B 3, 330b2, t¦ ¡pl© fainÒmena sèmata. For the presence of all four of them in every object around us on Earth see GC B 8.

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302a25. τοιοῦτον: i.e. stoice‹on. Cf. ch. 5. 302a25. οὐδ’ ἐν ἐκείνῳ: sc. s¦rx À xÚlon ™nup£rcousin, oÜte kat¦ dÚnamin oÜte kat’ ™nšrgeian. Aristotle argues next against the first alternative only. 302a28–29. Ἀναξαγόρας…στοιχείων: see below, on 302a31. 302a29–30. τὰ σύστοιχα τούτοις: see above, on 298a30. 302a31. Ἀναξαγόρας δὲ τοὐναντίον: in view of what comes next, Aristotle means that, whereas Empedocles thinks of all homoeomeric bodies as mixtures of his four elements, which are simple bodies for Aristotle, too, Anaxagoras errs in treating the elements as mixtures of homoeomers. Cf. GC A 1, 314a24–b1. It has been argued that the term ÐmoiomerÁ had been used by Anaxagoras, but its Aristotelian provenance is more likely. Cf. Graham (2006) 210 n. 57. 302a31–b3. τὰ γὰρ…ἠθροισμένον: Anaxagoras posits an infinite, or indefinitely large, number of elements, all observable stuffs (e.g. air, fire, earth but also flesh, bone etc) and qualitatively determinate kinds of stuff (such as the hot and cold, wet and dry, light and dark etc), which are mixed together everywhere in the cosmos. See Graham (2006) 197–199 and 209–215 (with discussion of the seeds). 302b3–4. διὸ καὶ γίγνεσθαι πάντ’ ἐκ τούτων: i.e. ™x ¢šroj kaˆ purÒj, not in the sense that these two are elements of all the other substances, but that from both of them, which are mixed together with all other elements, the latter separated out during the cosmogony, so as for the cosmos to be articulated, and continue to separate out till today. What Aristotle goes on to say next suggests that he probably wrote with the beginning of Anaxagoras’ book in mind (DK 59 B 1): Ðmoà p£nta cr»mata Ãn, ¥peira kaˆ plÁqoj kaˆ smikrÒthta· kaˆ g¦r tÕ smikrÕn ¥peiron Ãn. kaˆ p£ntwn Ðmoà ™Òntwn oÙdn œndhlon Ãn ØpÕ smikrÒthtoj· p£nta g¦r ¢»r te kaˆ a„q¾r kate‹cen, ¢mfÒtera ¥peira ™Ònta· taàta g¦r mšgista œnestin ™n to‹j sÚmpasi kaˆ pl»qei kaˆ megšqei. See also next n. 302b4–5. τὸ γὰρ…ταὐτό: Aristotle objects to the use of the noun a„q»r by Anaxagoras in the sense ‘fire’. Cf. his attempt in Cael. A 3, 270b16–25, to attribute his doctrine of the first simple body to the ancients: œoike d kaˆ toÜnoma par¦ tîn ¢rca…wn diadedÒsqai mšcri kaˆ toà nàn crÒnou, toàton tÕn trÒpon ØpolambanÒntwn Ónper kaˆ ¹me‹j lšgomen· oÙ g¦r ¤pax oÙd dˆj ¢ll’ ¢peir£kij de‹ nom…zein t¦j aÙt¦j ¢fikne‹sqai dÒxaj e„j ¹m©j. diÒper æj ˜tšrou tinÕj Ôntoj toà prètou sèmatoj par¦ gÁn kaˆ pàr kaˆ ¢šra kaˆ Ûdwr, a„qšra proswnÒmasan tÕn ¢nwt£tw tÒpon, ¢pÕ toà qe‹n ¢eˆ tÕn ¢dion crÒnon qšmenoi t¾n ™pwnum…an aÙtù. 'AnaxagÒraj d katacrÁtai tù ÑnÒmati toÚtJ oÙ kalîj· Ñnom£zei g¦r a„qšra ¢ntˆ purÒj. The criticism is repeated in Mete. A 3, 339b21–23. In Greek poetry the noun a„q»r seems to be used indiscriminately in the sense ‘air’, ‘sky’ or ‘heavens’, and in the fragments of his

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poetry Empedocles employs it for air (see Wright [1981] 23). a„q»r is etymologically connected to Greek nouns such as a„qr…a and a‡qrh, which designate the clear and bright sky or weather, and to the associated adjective a‡qrioj, -on, used to describe such sky or weather. Anaxagoras used this noun to designate fire, apparently based on the paretymology of a„q»r from the verb a‡qein, “to kindle”, in the transitive form, or “to blaze”, in the intransitive. However, a paretymology of a„q»r is central to Aristotle’s critique of Anaxagoras, too. He derives a„q»r from the phrase ¢eˆ qe‹n, “to be eternally in motion”. But in his cosmology there is only one substance in a state of perpetual motion, the first simple body. As it is, in Aristotle’s view a„q»r denotes the first simple body, not fire, as Anaxagoras had erroneously thought. Since this is certainly an old word, which occurs already in the Homeric epics, Aristotle confirms his bizarre belief that men of old had known of the existence of a simple body radically different from those found around us on the Earth. Hence the quite common use, even in scholarly publications, of the noun a„q»r, or of its descendants in modern languages, for the first simple body. However, Aristotle uses the noun in this sense only in his critique of Anaxagoras. John Philoponus pokes fun at Aristotle’s wish to attribute knowledge of the first simple body to the natural philosophers of an antediluvian past, noting that the doctrine of the first simple body was Aristotle’s own, and that with it Aristotle broke away from both past and contemporary orthodoxy regarding the constitution of matter at the most basic level (in Mete. 16.23–25 [Hayduck]). Aristotle’s attempt to project his doctrine of the first simple body back to the ancients makes one suspect that he is trying to downplay both the radicalness and the problems of this doctrine. The introduction of a fifth simple body is perhaps his single most important contribution to cosmology, but there is nothing in Cael. A 2–3, where he introduces the first simple body, similar to the measured self-confidence with which he asks everybody to show understanding for any incompleteness in his work on the dialectical syllogism and be duly grateful to him for his discoveries (SE 34, 184b3–8). 302b5. κίνησις οἰκεία: i.e. non-forced, natural. Cf. ch. 2, 300a20–23. 302b6. τῶν δὲ…μικταί: Aristotle uses this distinction to also establish the existence of the first simple body. See Cael. A 2, 268b14–26: p£nta g¦r t¦ fusik¦ sèmata kaˆ megšqh kaq’ aØt¦ kinht¦ lšgomen enai kat¦ tÒpon· t¾n g¦r fÚsin kin»sewj ¢rc¾n ena… famen aÙto‹j. p©sa d k…nhsij Ósh kat¦ tÒpon, ¿n kaloàmen for£n, À eÙqe‹a À kÚklJ À ™k toÚtwn mikt»· ¡pla‹ g¦r aátai dÚo mÒnai. a‡tion d’ Óti kaˆ t¦ megšqh taàta ¡pl© mÒnon, ¼ t’ eÙqe‹a kaˆ ¹ perifer»j. kÚklJ mn oân ™stin ¹ perˆ tÕ mšson, eÙqe‹a d’ ¹ ¥nw kaˆ k£tw. lšgw d’ ¥nw mn t¾n ¢pÕ toà mšsou, k£tw d t¾n ™pˆ tÕ mšson. ést’ ¢n£gkh p©san enai t¾n ¡plÁn for¦n t¾n mn ¢pÕ toà mšsou, t¾n d’ ™pˆ tÕ mšson, t¾n d perˆ tÕ mšson. kaˆ œoiken ºkolouqhkšnai kat¦ lÒgon toàto to‹j ™x ¢rcÁj· tÒ te g¦r sîma ¢petelšsqh ™n trisˆ kaˆ ¹ k…nhsij aÙtoà. The simplicity of the straight line and the circle, in terms of which rectilinear and circular motion is defined as simple, is best understood as their uniformity. The straight line is uniform in the sense that all of its parts can be perfectly superimposed upon

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one another, as is also the case with the circle. See Ph. E 4, 228b19–28: œstin d ™n ¡p£sV kin»sei tÕ Ðmalîj À m»· kaˆ g¦r ¨n ¢lloio‹to Ðmalîj, kaˆ fšroito ™f’ Ðmaloà oŒon kÚklou À eÙqe…aj, kaˆ perˆ aÜxhsin æsaÚtwj kaˆ fq…sin. ¢nwmal…a d’ ™stˆn diafor¦ Ðt mn ™f’ ú kine‹tai (¢dÚnaton g¦r Ðmal¾n enai t¾n k…nhsin m¾ ™pˆ Ðmalù megšqei, oŒon ¹ tÁj keklasmšnhj k…nhsij À ¹ tÁj ›likoj À ¥llou megšqouj, ïn m¾ ™farmÒttei tÕ tucÕn ™pˆ tÕ tucÕn mšroj)· ¹ d oÜte ™n tù Ö oÜt’ ™n tù pÒte oÜte ™n tù e„j Ó, ¢ll’ ™n tù éj. tacutÁti g¦r kaˆ bradutÁti ™n…ote dièristai· Âj mn g¦r tÕ aÙtÕ t£coj, Ðmal»j, Âj d m», ¢nèmaloj. See also Leggatt (1995) 176–177. For the difficulties raised by the classification of motion in Cael. A 2, 268b14–26, see the discussion in Wildberg (1988) 44–50. 302b6–7. καὶ…εἰσι: the association of simple and composite motions with simple and composite bodies respectively appears also in Aristotle’s argument for the existence of the first simple body, the beginning of which is quoted in the previous n. See Cael. A 2, 268b26–269a2: ™peˆ d tîn swm£twn t¦ mšn ™stin ¡pl© t¦ d sÚnqeta ™k toÚtwn (lšgw d’ ¡pl© mn Ósa kin»sewj ¢rc¾n œcei kat¦ fÚsin, oŒon pàr kaˆ gÁn kaˆ t¦ toÚtwn e‡dh kaˆ t¦ suggenÁ toÚtoij), ¢n£gkh kaˆ t¦j kin»seij enai t¦j mn ¡pl©j t¦j d mikt£j pwj, kaˆ tîn mn ¡plîn ¡pl©j, mikt¦j d tîn sunqštwn, kine‹sqai d kat¦ tÕ ™pikratoàn. For the problems raised by this correlation see Wildberg (1988) 50–56. 302b7–8. φανερὸν…ἁπλαῖ: the reason why earth, water, air and fire are simple bodies, as is observed, is that their natural motions are simple since they are rectilinear; for Aristotle the rectilinearity of these natural motions is another empirical fact (see above, on 300a30). This is his answer to the second of the four questions in 302a12–14. Aristotle’s reasoning in these lines is similar to the conclusion of the argument for the existence of the first simple body whose earlier steps are quoted in the two previous nn. See Cael. A 2, 269a2–9: e‡per oân ™stin ¡plÁ k…nhsij, ¡plÁ d’ ¹ kÚklJ k…nhsij, kaˆ toà te ¡ploà sèmatoj ¡plÁ ¹ k…nhsij kaˆ ¹ ¡plÁ k…nhsij ¡ploà sèmatoj (kaˆ g¦r ¨n sunqštou Ï, kat¦ tÕ ™pikratoàn œstai), ¢nagka‹on ena… ti sîma ¡ploàn Ö pšfuke fšresqai t¾n kÚklJ k…nhsin kat¦ t¾n ˜autoà fÚsin· b…v mn g¦r ™ndšcetai t¾n ¥llou kaˆ ˜tšrou, kat¦ fÚsin d ¢dÚnaton, e‡per m…a ˜k£stou k…nhsij ¹ kat¦ fÚsin tîn ¡plîn. Cf. Wildberg (1988) 56–60 and Falcon (2005) 57–59. It is unlikely, however, that in the lines under discussion Aristotle is concerned to argue for the existence of elements in general. Which ones of the bodies that come into being must be elements of the rest has been empirically established earlier in the chapter–the four Empedoclean bodies. What is needed to round off Aristotle’s discussion is a theoretical reason why these four bodies are simple. All we have to do to obtain such a reason is simply to apply the argument in the lines commented upon for the existence of elements to the four Empedoclean bodies: there are simple bodies, which are elements, for there are simple motions, which must be proper to simple bodies, so the four Empedoclean bodies are simple, as we observe, exactly on account of the simplicity of their motion. Another explanation is implic-

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itly given in GC B 3, 330a30–b7. Earth, water, air and fire are simple bodies, as is observed, because the first is dry and cold, the second cold and wet, the third wet and hot, the fourth hot and dry, apparently another empirical fact: their differentiating qualities, which form two pairs of contraries, are the elementary qualities of all perceptible bodies, as has been shown in GC B 2, from which all other qualities of such bodies arise, so the perceptible bodies earth, water, air and fire that are differentiated by the elementary qualities of perceptible bodies cannot but be elementary, like their differentiating qualities, and thus simple. What is more, the fundamental qualities of perceptible bodies make it possible for us to find out by simple reasoning how many and which of these bodies are elements of the rest. According to GC B 3, 330b7–21, it is in pairs that they must be distributed to the simple bodies, apparently for no other reason than what Aristotle considers an undisputed doxographical fact, the obvious agreement among natural philosophers that the elements are to be conceived of in terms of dualities, and their pair-wise distribution is assumed to fix the number of the simple bodies. GC B 5, 332a34–b5, explains how: two of the six possible pair-wise arrangements of the four elementary qualities of perceptible bodies–cold and hot, wet and dry–are to be rejected as corresponding to simple bodies, for no body can have contrary properties, so we are left with four allowable arrangements–dry and cold, cold and wet, wet and hot, hot and dry–each of which must determine a simple body; these combinations characterize indeed bodies around us whose coming into being we observe–earth and water, air and fire–and which are also observed to be simple. 302b9. ὅτι…ἐστιν: the distinction implicit here is between a fact, Óti, empirically established and its scientific explanation, di¦ t…, provided by theory. Aristotle draws it clearly in Metaph. A 1, 981a24–b2: ¢ll’ Ómwj tÒ ge e„dšnai kaˆ tÕ ™paein tÍ tšcnV tÁj ™mpeir…aj Øp£rcein o„Òmeqa m©llon, kaˆ sofwtšrouj toÝj tecn…taj tîn ™mpe…rwn Øpolamb£nomen, æj kat¦ tÕ e„dšnai m©llon ¢kolouqoàsan t¾n sof…an p©si· toàto d’ Óti oƒ mn t¾n a„t…an ‡sasin oƒ d’ oÜ. oƒ mn g¦r œmpeiroi tÕ Óti mn ‡sasi, diÒti d’ oÙk ‡sasin· oƒ d tÕ diÒti kaˆ t¾n a„t…an gnwr…zousin. diÕ kaˆ toÝj ¢rcitšktonaj perˆ ›kaston timiwtšrouj kaˆ m©llon e„dšnai nom…zomen tîn ceirotecnîn kaˆ sofwtšrouj, Óti t¦j a„t…aj tîn poioumšnwn ‡sasin. See also 981b10–12: œti d tîn a„sq»sewn oÙdem…an ¹goÚmeqa enai sof…an· ka…toi kuriètata… g’ e„sˆn aátai tîn kaq’ ›kasta gnèseij· ¢ll’ oÙ lšgousi tÕ di¦ t… perˆ oÙdenÒj, oŒon di¦ t… qermÕn tÕ pàr, ¢ll¦ mÒnon Óti qermÒn. Cf. previous n.

CHAPTER 4 302b10–11. Πότερον…σκοπεῖν: ch. 3 leaves no doubt that there exist four simple bodies which are elements of generated bodies. Chs. 4 and 5 contain mainly criticism of earlier views on the number of the elements. 302b13. τὰ ὁμοιομερῆ: see above, on 302a12.

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302b14. καθάπερ καὶ Ἀναξαγόρας: it is not clear whether Anaxagoras hypothesized an infinite or merely indefinitely large number of elements (cf. Graham [2006] 197–198, with n. 26). Archelaus of Athens is probably also meant. 302b14–15. οὐθεὶς…τὸ στοιχεῖον: cf. the definition in ch. 3, 302a15–18. 302b15–17. ὁρῶμεν…λίθον: see ch. 3, 302a21–23, with n. ad loc. 302b18. οὐχ ἅπαν ἔσται τὸ ὁμοιομερὲς στοιχεῖον: Aristotelian simple bodies are homoeomeric–their portions are divided only into portions of the same substance (see GC A 10, 328a5–12). Not all homoeomers are simple bodies, or elements, as Anaxagoras has it, however. 302b19–20. ἀλλὰ…πρότερον: it is thus clear that ¢dia…reton e„j ›tera tù e‡dei in the definition of stoice‹on in ch. 3, 302a15–18, does not mean just ‘indivisible into parts of a body of a different kind’, in which case the definition would be satisfied by all homoeomers, but ‘unanalyzable, through any process, into parts of a body of a different kind’. 302b20–24. ἔτι…Ἐμπεδοκλῆς: having argued against the Anaxagorean conception of elements as homoeomers, Aristotle now turns his sights on the purportedly infinite multitude of such elements posited by Anaxagoras. It makes no difference whether one assumes the existence of infinitely many elements or, following Empedocles, thinks that the elements are finitely many, for in either case one can account equally well for the same range of phenomena (for p£nta g¦r taÙt¦ ¢podoq»setai cf. Metaph. Λ 8, 1073b32–1074a4: K£llippoj d t¾n mn qšsin tîn sfairîn t¾n aÙt¾n ™t…qeto EÙdÒxJ [toàt’ œsti tîn ¢posthm£twn t¾n t£xin], tÕ d plÁqoj tù mn toà DiÕj kaˆ tù toà KrÒnou tÕ aÙtÕ ™ke…nJ ¢ped…dou, tù d’ ¹l…J kaˆ tÍ sel»nV dÚo õeto œti prosqetšaj enai sfa…raj, t¦ fainÒmena e„ mšllei tij ¢podèsein, to‹j d loipo‹j tîn plan»twn ˜k£stJ m…an. ¢nagka‹on dš, e„ mšllousi sunteqe‹sai p©sai t¦ fainÒmena ¢podèsein, kaq’ ›kaston tîn planwmšnwn ˜tšraj sfa…raj mi´ ™l£ttonaj enai t¦j ¢nelittoÚsaj kaˆ e„j tÕ aÙtÕ ¢pokaqist£saj tÍ qšsei t¾n prèthn sfa‹ran ¢eˆ toà Øpok£tw tetagmšnou ¥strou). The lines under discussion bear comparison with Ph. Γ 7, 207b27–34, where Aristotle notes that his rejection of actual infinity is in line with mathematical practice: oÙk ¢faire‹tai d’ Ð lÒgoj oÙd toÝj maqhmatikoÝj t¾n qewr…an, ¢nairîn oÛtwj enai ¥peiron éste ™nerge…v enai ™pˆ t¾n aÜxhsin ¢diex…thton· oÙd g¦r nàn dšontai toà ¢pe…rou (oÙ g¦r crîntai), ¢ll¦ mÒnon enai Óshn ¨n boÚlwntai peperasmšnhn· tù d meg…stJ megšqei tÕn aÙtÕn œsti tetmÁsqai lÒgon Ðphlikonoàn mšgeqoj ›teron. éste prÕj mn tÕ de‹xai ™ke…noij oÙdn dio…sei tÕ [d’] enai ™n to‹j oâsin megšqesin. On this passage see Kouremenos (1995) 9–34. 302b24–28. ἐπεὶ…δείκνυσθαι: not only does Anaxagoras not need the hypothesis of infinitely many elements, which are homoeomers, he does not even ap-

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ply consistently another related one, that things have an infinity of homoeomeric constituents. Thus it is by far best to think that the principles, aƒ ¢rca…, the material principles or the elements of bodies, are finitely many, preferably as few as possible. As evidence that Anaxagoras does not think of all things as made up of an infinity of homoeomeric constituents Aristotle points out that his predecessor does not view faces or all other naturally constituted things, i.e. all other unhomoeomeric parts of living beings and the latter themselves, as made up of, and thus decomposable into, an infinity of smaller copies of themselves. 302b29–30. καθάπερ…τῷ ποσῷ: in arithmetic, the principles are finite, either in quantity, tù posù, for there is no actually infinite number, though numbers are potentially infinite in the sense that, no matter how great a number, a greater number can always be obtained, or in kind, tù e‡dei, for numbers fall into a few types, such as odd and even. In geometry, the principles are finite, too, either in quantity, for there in no actually infinite line, surface or solid, though all of them can be potentially infinite in a sense parallel to the above, or in kind, for all of them fall into a few types. In Ph. Γ 6, 206b20–27, Aristotle emphasizes that continued addition cannot exceed any assigned limit, unless physical objects are infinitely large. He does not rule out the infinite extendibility of magnitudes, however, on the basis of the finitude of all physical objects, including the cosmos. He speaks having in mind only the partial sums of an infinite series of decreasing terms in constant ratio–imagined as parts of a material thing–and their convergence to a limit: that no such partial sum can be arbitrarily large but all are less than the limit–in a counterintuitive contrast to the continually diminishing terms of the corresponding infinite sequence, which can exceed any assigned limit–does not entail that e.g. geometric straight lines cannot be arbitrarily extended. Aristotle simply denies that an infinite number of parts, into which a material thing is potentially divisible by his lights, necessarily makes the thing itself infinitely large, as his pupil Eudemus of Rhodes seems to suggest in a fragment of his Physics (Simp., in Ph. 459.23–26 [Diels] = Eudem., fr. 62 Wehrli; for this view cf. Epicur., Ep. ad Hdt. 56–57, Lucr., 1.615–622, and see Sorabji [1983] 334–335). It is this kind of infinity that in Ph. Γ 7, 207b27–34, quoted above, on 302b20–24, is rejected as superfluous for contemporary mathematics. In Cael. A 5, 271b26–272a7, Aristotle undoubtedly asserts the potential infinity of numbers and straight lines, hence surfaces and solids, too; cf. A 2, 269a18–23, and B 4, 286b20. 302b31–32. τὰς οἰκείας διαφοράς: at issue are tîn ¡ptîn aƒ prîtai diaforaˆ kaˆ ™nantièseij (GC B 2, 329b16–18). These are the qualities defining the Empedoclean simple bodies, hot/cold and wet/dry; see above, on 302b7–8. 302b32. αἱ δὲ τῶν σωμάτων διαφοραὶ πεπερασμέναι: since the fundamental qualities of perceptible bodies are four, there can be only four elements of perceptible bodies differentiated by these qualities. See above, on 302b7–8. Infinitely many bodily differences are ruled out in GC B 5, 332b30–333a15, together with an infinite multitude of elements to which they would belong. This passage reduces to

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absurdity the hypothesis that, when earth changes into water, water into air, and air into fire, the latter does not (only) change back into earth (by the first process described above, on 302a17–18): it (also) turns into a fifth element X0, which transforms (also) into X1 and not (only) back into fire, and so on ad infinitum (the hypothesis to be refuted is stated in the text as if each element cannot turn back into its predecessor in the series; this is not built into the refutation, however). Aristotle argues that the introduction of X0 introduces a new pair of contrary elementary qualities c0/c1 of perceptible bodies next to those two whose members define the four Empedoclean simple bodies, hot/cold and wet/dry. Fire is hot and dry, so if it is to change into a hypothetical element X0 different from the other three Empedoclean elements, X0 must be hot and dry, too, as well as c0, whose contrary c1 must be added to the qualities of fire: when fire changes into X0, two of its qualities, the hot and the dry, survive the change, the third one, c1, which is its opposite, c0, in potentiality, becoming c0 in actuality. If so, air must be characterized by c1, too, not only by the wet and the hot, water by c1, too, not only by the cold and the wet, and earth by c1, too, not only by the dry and the cold, for air changes into fire, water into air, and earth into water. Similarly, the introduction of X1 introduces a new pair of contrary elementary qualities c2/c3 of perceptible bodies next to the above three: hot/cold, wet/dry and c0/c1. X0 is hot, dry and c0, so if it is to change into a further element X1, the latter must be hot, dry and c0, too, as well as c2, whose contrary c3 must thus be added to the qualities of X0 and the four Empedoclean elements. With each Xn, a new pair of contrary elementary qualities ci/ci+1, i = 2n, of perceptible bodies is introduced, and the number of qualities characterizing each element increases. This is illustrated in the following table, where each Empedoclean element and each of its two qualities is denoted by the initial letter of the Greek word for it. The double-margin cells contain the cis introduced by the Xns. Γ ξ ψ

Υ ψ υ

Α υ θ

Π θ ξ

X0 θ ξ

X1 θ ξ

X2 θ ξ

X3 θ ξ

X4 θ ξ

X5 θ ξ

X6 θ ξ

X7 θ ξ

… … …

Xn θ ξ

… … …

c1

c1

c1

c1

c0

c0

c0

c0

c0

c0

c0

c0

…

c0

…

c3

c3

c3

c3

c3

c2

c2

c2

c2

c2

c2

c2

…

c2

…

c5

c5

c5

c5

c5

c5

c4

c4

c4

c4

c4

c4

…

c4

…

c7

c7

c7

c7

c7

c7

c7

c6

c6

c6

c6

c6

…

c6

…

c9

c9

c9

c9

c9

c9

c9

c9

c8

c8

c8

c8

…

c8

…

c11

c11

c11

c11

c11

c11

c11

c11

c11

c10

c10

c10

…

c10

…

c13

c13

c13

c13

c13

c13

c13

c13

c13

c13

c12

c12

…

c12

…

c15

c15

c15

c15

c15

c15

c15

c15

c15

c15

c15

c14

…

c14

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n+1 …

c2n …

… …

It is, therefore, clear that, if there is an actually infinite multitude of Xns, there is an actually infinite number of qualities belonging to each element: these should be

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captured by the definition of the element to which they belong, something impossible. Aristotle derives two further, related, absurdities from the hypothesis to be refuted, the impossibility of elemental change and the identity of all elements. Let it be assumed that water, air, fire, X0, X1, … , Xn, … can each turn at least into the immediately next or previous item in the series: for this to happen, only one of its qualities has to flip into its contrary. But the farther apart any two elements in the series are, the greater the number of qualities that must flip into their contraries to effect the change of one element into the other: so, if two elements are infinitely apart, an actually infinite number of qualities must flip into their contraries if one element is to change into the other, which is impossible, probably because it is tacitly assumed that the flippings occur sequentially and that elemental transformation happens in a finite time. It turns out, however, that an element cannot change even into the immediately next or previous item in the series. For, on the hypothesis Aristotle refutes, all elements turn out to be absurdly identical. This probably follows from the fact that each element turns out to share an actual infinity of qualities with any other and to differ from any other by only finitely many qualities: since, however, the addition of a finite number n, no matter how large, to the actual infinity cannot affect the latter, i.e. since n + ∞ = ∞, the addition of finitely many qualities to the actual infinity of qualities an element shares with any other cannot differentiate it from the others. What the elements share blots out their differences. 303a1. τοῖς αἰσθητοῖς: sc. p£qesi. Cf. GC A 1, 314b17–20. 303a1–2. δεῖ δὲ τοῦτο δειχθῆναι: see above, on 302b32. 303a2–3. φανερὸν…εἶναι: see above, on 302b32. 303a3–16. οὐδ’ ὡς…στοιχείων: Leucipp., DK 67 A 15. 303a5. τὰ πρῶτα μεγέθη: cf. t¦ prîta sèmata in ch. 2, 300b9, and t¦ megšqh t¦ ¥toma in Metaph. Z 13, 1039a10. 303a5–6. πλήθει μὲν ἄπειρα: the infinity of the number of atoms seems to have been deduced from the infinity of atomic shapes, for each of which there are infinitely many atoms. See below, on 303a10–12. 303a6–7. καὶ…ἕν: since an atom is an indivisible unit, a multiplicity cannot be generated from it, nor can it combine with other atoms into a unitary entity. The generation of a multiplicity from an atom entails the atom’s divisibility; the combination of many atoms into a unitary entity entails loss of their individuality. This is elaborated upon in GC A 8, 325a23–b5 (Leucipp., DK 67 A 7): LeÚkippoj d’ œcein ò»qh lÒgouj o†tinej prÕj t¾n a‡sqhsin ÐmologoÚmena lšgontej oÙk ¢nair»sousin oÜte gšnesin oÜte fqor¦n oÜte k…nhsin kaˆ tÕ plÁqoj tîn Ôntwn. Ðmolog»saj d taàta mn to‹j fainomšnoij, to‹j d tÕ e$n kataskeu£zousin æj oÙk ¨n k…nhsin oâsan ¥neu kenoà tÒ te kenÕn m¾ Ôn kaˆ

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toà Ôntoj oÙqn m¾ Ôn, fhsˆn enai tÕ kur…wj e$n pamplÁrej Ôn, ¢ll’ enai tÕ toioàton oÙc ›n, ¢ll’ ¥peira tÕ plÁqoj kaˆ ¢Òrata di¦ smikrÒthta tîn Ôgkwn. taàta d’ ™n tù kenù fšresqai (kenÕn g¦r enai), kaˆ sunist£mena mn gšnesin poie‹n, dialuÒmena d fqor£n. poie‹n d kaˆ p£scein Î tugc£nousin ¡ptÒmena (taÚtV g¦r oÙc e$n enai) kaˆ suntiqšmena d kaˆ periplekÒmena genn©n· ™k d toà kat’ ¢l»qeian ˜nÕj oÙk ¨n genšsqai plÁqoj, oÙd’ ™k tîn ¢lhqîj pollîn ›n, ¢ll’ enai toàt’ ¢dÚnaton· ¢ll’ ésper 'EmpedoklÁj kaˆ tîn ¥llwn tinšj fasi p£scein di¦ pÒrwn, oÛtw p©san ¢llo…wsin kaˆ p©n tÕ p£scein toàton g…nesqai tÕn trÒpon, di¦ toà kenoà ginomšnhj tÁj dialÚsewj kaˆ tÁj fqor©j, Ðmo…wj d kaˆ tÁj aÙx»sewj, e„sduomšnwn ˜tšrwn. Cf. above, on 300b11–12. See also the passage quoted below, on 303a8–10. 303a7. συμπλοκῇ: cf. the passage quoted in previous n. 303a8. περιπαλάξει: the noun seems to be derived from the verb peripal£sseqai, attested only in Hsch. π 1799 Schmidt: peripalacqÁnai· periplakÁnai. The mss readings are periplšxei and ™pall£xei. perip£laxin is a variant for ™p£llaxin apud Simp., in Cael. 609.24–25 (Heiberg): t¾n d sumplok¾n 'Abdhr‹tai ™p£llaxin ™k£loun, ésper DhmÒkritoj. The noun par£llaxin apud Thphr., Sens. 66 ( = Democr., DK 68 A 135), has also been corrected to perip£laxin. Against restoring perip£laxij as a hypothetical atomist term see McDiarmid (1958). 303a8–10. τρόπον…λέγειν: cf. ch. 1, 300a14–17, with nn. ad loc. t¦ Ônta are the derivative contents of the atomist universe, groups of atoms. Their identification with numbers, an extrapolation from the conception of the atoms as indivisible units, is also presupposed in Metaph. Z 13, 1039a3–14: ¢dÚnaton g¦r oÙs…an ™x oÙsiîn enai ™nuparcousîn æj ™ntelece…v· t¦ g¦r dÚo oÛtwj ™ntelece…v oÙdšpote e$n ™ntelece…v, ¢ll’ ™¦n dun£mei dÚo Ï, œstai ›n (oŒon ¹ diplas…a ™k dÚo ¹m…sewn dun£mei ge· ¹ g¦r ™ntelšceia cwr…zei), ést’ e„ ¹ oÙs…a ›n, oÙk œstai ™x oÙsiîn ™nuparcousîn kaˆ kat¦ toàton tÕn trÒpon, Ön lšgei DhmÒkritoj Ñrqîj· ¢dÚnaton g¦r ena… fhsin ™k dÚo e$n À ™x ˜nÕj dÚo genšsqai· t¦ g¦r megšqh t¦ ¥toma t¦j oÙs…aj poie‹. Ðmo…wj to…nun dÁlon Óti kaˆ ™p’ ¢riqmoà ›xei, e‡per ™stˆn Ð ¢riqmÕj sÚnqesij mon£dwn, ésper lšgetai ØpÒ tinwn· À g¦r oÙc e$n ¹ du¦j À oÙk œsti mon¦j ™n aÙtÍ ™ntelece…v. For Aristotle’s objection to what he considers an unacceptable identification of things with numbers see ch. 1, 300a17–19, with nn. ad loc. 303a10–12. καὶ…εἶναι: the infinite number of atomic shapes followed from the principle of sufficient reason–there is no reason why the atoms must be of one shape rather than any other. See Simp., in Ph. 28.4–11 (Diels): LeÚkippoj d Ð 'Ele£thj À Mil»sioj…¥peira kaˆ ¢eˆ kinoÚmena Øpšqeto stoice‹a t¦j ¢tÒmouj kaˆ tîn ™n aÙto‹j schm£twn ¥peiron tÕ plÁqoj di¦ tÕ mhdn m©llon toioàton À toioàton enai [taÚthn g¦r] kaˆ gšnesin kaˆ metabol¾n ¢di£leipton ™n to‹j oâsi qewrîn (Leucipp., DK 67 A 8). For the connection of pos-

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tulating infinitely many atomic shapes with accounting for the constant generation and change see GC A 2, 315b6–15 (Leucipp., DK 67 A 9). Aristotle singles out shape in GC A 8, 325b17–19, as the only differentiating property of atoms. There is good evidence, however, for the importance of size, too; see Taylor (1999b) 172. 303a12–14. ποῖον…ἀπέδωκαν: the context in which the spherical shape was associated with the atoms making up the observable stuff fire seems to have been the theory of the soul. See de An. A 2, 403b27–404a16 (Leucipp., DK 67 A 28). 303a15. τἆλλα: earth and all other observable substances made up of unobservable atoms. 303a15. μεγέθει καὶ μικρότητι διεῖλον: in order to differentiate earth, air and water, as well all other observable substances consisting of unobservable atoms, from one another, the atomist appealed to the average size of the elementary particles making up these bodies. See also next n. On whether, according to the atomists, there are infinitely many gradations of atomic size, just as there are infinitely many atomic shapes, see Taylor (1999b) 173–175. 303a15–16. ὡς…στοιχείων: what is called earth, water, air etc is actually a farrago, pansperm…a, of all elements, an agglomeration of atoms of all shapes and sizes. This entails an infinite number of atoms, and must be an exaggeration. An incomprehensibly large multitude of atoms, with an enormously large spread of shapes and sizes, is sufficient. Aristotle says in Ph. Γ 4, 203a19–22, that Democritus constructs the elements ™k tÁj pansperm…aj tîn schm£twn. ¹ pansperm…a ¢pe…rwn schm£twn kaˆ ¢tÒmwn is said to be the atomist stoice‹a tÁj Ólhj fÚsewj in de An. A 2, 404a1–5 (Leucipp., DK 67 A 28). Each observable substance appears different because atoms of certain shapes and sizes preponderate in its constitution. Cf. Thphr., Sens. 67, on how different taste-sensations, culo…, are generated according to Democritus (DK 68 A 135): æsaÚtwj d kaˆ t¦j ¥llaj ˜k£stou dun£meij ¢pod…dwsin ¢n£gwn e„j t¦ sc»mata. ¡p£ntwn d tîn schm£twn oÙdn ¢kšraion enai kaˆ ¢migj to‹j ¥lloij, ¢ll’ ™n ˜k£stJ poll¦ enai kaˆ tÕn aÙtÕn œcein le…ou kaˆ tracšoj kaˆ periferoàj kaˆ Ñxšoj kaˆ tîn loipîn. oá d’ ¨n ™nÍ ple‹ston, toàto m£lista ™niscÚein prÒj te t¾n a‡sqhsin kaˆ t¾n dÚnamin. 303a17–18. πρῶτον…λέγειν: cf. 302b20–30. 303a19–20. ἔτι…ἄπειρα: cf. 302b30–303a3. 303a20–22. πρὸς δὲ τούτοις…λέγοντας: by positing indivisible bodies, the atomists are in conflict with mathematics, which proves that solids are infinitely divisible. See Euc., El. 12.3: any pyramid with a triangular base is divided into two smaller pyramids, which have triangular bases and are similar to one another and to the given pyramid, and two equal prisms, which are greater than half of the

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given pyramid. But each of the two pyramids, into which the initial pyramid is divided, is further divided into two triangular pyramids, similar to one another and to the pyramid whose parts they are, and two equal prisms, which are greater than half of the pyramid whose parts they are, and so on. In other words, any triangular pyramid is divisible ad infinitum. But pyramids with polygonal bases are decomposable into triangular pyramids, as are polygonal prisms, for they are decomposable into triangular prisms, and a triangular prism is decomposable into three equal triangular pyramids (see El. 12.7): solids bounded by planes are thus divisible ad infinitum. For cones or cylinders and spheres see Euc., El. 12.10 and 17. Aristotle does not tire of emphasizing the incompatibility between indivisibles, be they the indivisible lines, to the existence of which Plato’s physics in the Timaeus he thinks is committed, or Abderitan atoms, and mathematics, where magnitudes of one, two and three dimensions are infinitely divisible. He mentions the clash two more times in this book: see ch. 1, 299a2–6, with n. ad loc., and 7, 306a26–30. 303a22–23. πολλὰ…κατὰ τὴν αἴσθησιν: on œndoxa, “common beliefs”, and t¦ fainÒmena kat¦ t¾n a‡sqhsin, “perceptual appearances”, with which they are contrasted here, for they, too, appear to people, see Irwin (1988) 37–39. 303a23–24. περὶ ὧν…κινήσεως: cf. ch. 1, 299a9–11, with n. ad loc. 303a24–25. ἅμα…ἀνάγκη: two beliefs of the atomists–that air, earth and water are each a farrago of an enormous number of atoms of vastly diverse shapes and sizes, and that each of these stuffs turns into the others–are incompatible. See next n. 303a25–27. ἀδύνατον…γίγνεσθαι: if air, earth and water differed in the average size of the atoms constituting them, as the atomists presumably assumed in their explanation of why water is subtler than earth and air than water, it would be impossible for them to turn into one another. The atomists assumed that air or water does not actually turn into water or earth respectively: instead, atoms of greater size than the average among the immense number of those making up a quantity of air or water separate out of the rest for some reason, and thus produce what is called water or earth respectively. But after a finite number of separations, no matter how large, a quantity of air or water would not but become depleted of atoms with the right average size to become water or earth respectively. As a result, the given quantities of air and water could not yield more bodily observable stuffs any longer. Aristotle does not object that such samples of air and water are never observed, which must be implicit, but points out the incoherence of the atomist explanation of what he considers a fundamental physical process. 303a27–29. ὑπολείψει…ἐξ ἀλλήλων: the atomists clearly accounted for the generation of the subtler stuffs among those which Aristotle considers simple bodies out of the grosser along the same lines as they explained the production of the latter out of the former. The criticism is repeated in ch. 7, 305b20–26.

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303a29–30. ἔτι…τὰ στοιχεῖα: even if the elements differed from one another in shape, as is the case according to Leucippus and Democritus (¹ toÚtwn ØpÒlhyij), they should not be assumed to be infinitely many, as Leucippus and Democritus hypothesize. 303a30–31. εἴπερ…σχήμασι: cf. above, on 303a10–12. 303a31–b1. τὰ δὲ σχήματα…μορίων: a solid which is bounded by planes can be decomposed into triangular pyramids, and a sphere can be divided by its equator, a meridian and another great circle at right angles to the other two into eight spherical pyramids, whose bases are not planes but parts of the sphere’s surface. 303b1–2. ἀνάγκη…τῶν σχημάτων: the principles of shapes, whether solid or planar, are those shapes into which all other shapes are decomposable, as illustrated in the previous clause. They are simple shapes. 303b2–3. ὥστε…τὸ πλῆθος: no matter whether there is a single principle of all solid shapes, two, as in Aristotle’s example, or more, if the simple bodies are differentiated by shape, they cannot but be as many as the principles of solid shapes, the simple solid shapes into which the solid shapes of all other bodies are decomposable. But the number of principles, even if greater than two, must be finite. Cf. the argument in 302b24–30. 303b4. οἰκεία κίνησις: see above, on 302b5. 303b5. καὶ…ἁπλῆ: on simple motions see above, on 302b6. 303b5–8. μή εἰσι δ’…τὰ στοιχεῖα: the kinds of simple motions, which must be the kinds of natural motions of simple bodies, are finitely many, and finitely many are thus the natural places, too, towards which the natural motions of the simple bodies are directed, hence the number of kinds of simple bodies, which rest in the finitely many natural places, and move naturally towards them with the finitely many kinds of natural motion, must be finite. Leaving aside the circular motion, which is the natural motion of the first simple body in, not towards, its natural place, the two kinds of rectilinear motion, towards and away from the center of the cosmos, are the natural motions of two kinds of simple bodies, the heavy and the light respectively (cf. the mention in ch. 1, 298b6–8, of the first simple body and two kinds of other simple bodies). Cf. Cael. A 7, 274a30–b5, where Aristotle argues against the existence of infinitely large bodies: ¢n£gkh d¾ sîma p©n ½toi ¥peiron enai À peperasmšnon, kaˆ e„ ¥peiron, ½toi ¢nomoiomerj ¤pan À Ðmoiomeršj, k¨n e„ ¢nomoiomeršj, ½toi ™k peperasmšnwn e„dîn À ™x ¢pe…rwn.–Öti mn to…nun oÙc oŒÒn te ™x ¢pe…rwn, fanerÒn, e‡ tij ¹m‹n ™£sei mšnein t¦j prètaj Øpoqšseij· peperasmšnwn g¦r tîn prètwn kin»sewn oÙsîn, ¢n£gkh kaˆ t¦j „dšaj tîn ¡plîn swm£twn enai peperasmšnaj. ¡plÁ mn g¦r ¹ toà ¡ploà sèmatoj k…nhsij, aƒ d’ ¡pla‹ peperasmšnai kin»-

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seij e„s…n· ¢n£gkh d k…nhsin œcein sîma p©n fusikÒn. A similar argument establishes in Cael. A 2, 268b14–269a9, the existence of the first simple body; see above, on 302b6, 6–7 and 7–8. In ch. 5, 304b19–21, Aristotle invokes the existence of finitely many kinds of natural motion to argue that there cannot be only one element, just as there cannot be infinitely many elements.

CHAPTER 5 303b9–10. ἐπεὶ…ἕν: see above, on 302b10–11. 303b10–11. ἔνιοι…πῦρ: cf. ch. 1, 298b29–33. This very brief doxography is expanded in Metaph. A 3, 983b6–984a8: tîn d¾ prètwn filosofhs£ntwn oƒ ple‹stoi t¦j ™n Ûlhj e‡dei mÒnaj ò»qhsan ¢rc¦j enai p£ntwn· ™x oá g¦r œstin ¤panta t¦ Ônta kaˆ ™x oá g…gnetai prètou kaˆ e„j Ö fqe…retai teleuta‹on, tÁj mn oÙs…aj ØpomenoÚshj to‹j d p£qesi metaballoÚshj, toàto stoice‹on kaˆ taÚthn ¢rc»n fasin enai tîn Ôntwn…tÕ mšntoi plÁqoj kaˆ tÕ edoj tÁj toiaÚthj ¢rcÁj oÙ tÕ aÙtÕ p£ntej lšgousin, ¢ll¦ QalÁj mn Ð tÁj toiaÚthj ¢rchgÕj filosof…aj Ûdwr fhsˆn enai…e„ mn oân ¢rca…a tij aÛth kaˆ palai¦ tetÚchken oâsa perˆ tÁj fÚsewj ¹ dÒxa, t£c’ ¨n ¥dhlon e‡h, QalÁj mšntoi lšgetai oÛtwj ¢pof»nasqai perˆ tÁj prèthj a„t…aj (“Ippwna g¦r oÙk ¥n tij ¢xièseie qe‹nai met¦ toÚtwn di¦ t¾n eÙtšleian aÙtoà tÁj diano…aj)· 'Anaximšnhj d ¢šra kaˆ Diogšnhj prÒteron Ûdatoj kaˆ m£list’ ¢rc¾n tiqšasi tîn ¡plîn swm£twn, “Ippasoj d pàr Ð Metapont‹noj kaˆ `Hr£kleitoj Ð 'Efšsioj. 303b11–12. οἱ δ’ ὕδατος…πυκνότερον: Aristotle also mentions a theory according to which the four Empedoclean bodies are generated from a single substance subtler than water but coarser than air, or subtler than air but coarser than fire. See GC B 5, 332a18–26, a passage concluding an argument in 332a4–18 to the effect that no Empedoclean body can be simpler than the rest and make them up as a single element (quoted below, on 304b14–15): Ð d’ aÙtÕj lÒgoj perˆ ¡p£ntwn, Óti oÙk œstin e$n toÚtwn ™x oá t¦ p£nta. oÙ m¾n oÙd’ ¥llo t… ge par¦ taàta, oŒon mšson ti ¢šroj kaˆ Ûdatoj À ¢šroj kaˆ purÒj, ¢šroj mn pacÚteron À purÒj, tîn d leptÒteron· œstai g¦r ¢¾r kaˆ pàr ™ke‹no met’ ™nantiÒthtoj· ¢ll¦ stšrhsij tÕ ›teron tîn ™nant…wn· ést’ oÙk ™ndšcetai monoàsqai ™ke‹no oÙdšpote, ésper fas… tinej tÕ ¥peiron kaˆ tÕ perišcon. Ðmo…wj ¥ra Ðtioàn toÚtwn À oÙdšn. Aristotle’s point is that, if e.g. a body finer than water, which is cold and wet, but coarser than air, which is wet and hot, generates each of them, this hypothetical body must be water and air, which are produced from it, and differentiated from each of these bodies by c0, a member of a pair of contraries c0/c1 other than hot/cold and wet/dry, whose other member must thus belong to water and air: the hypothetical body must be e.g. cold, wet as well as c0, water must be cold, wet and c1, air must be wet, hot and c1, so that the hypothetical body can turn into water, when its c0 turns into c1, and into air, when its

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cold turns into hot and its c0 into c1 (cf. above, on 302a17–18). This shows that the hypothetical body cannot be isolated (monoàsqai) from the qualities characterizing the Empedoclean simple bodies, as those who assume its existence and identify it with the infinite believe. Implying that this putative isolation, which would allow the identification of the hypothetical body with the infinite, was the motivation for positing the existence of such a body distinct from the Empedoclean bodies, Aristotle concludes that the infinite must either be identified with one of them or not exist at all. See also Ph. Γ 5, 204b22–35: ¢ll¦ m¾n oÙd e$n kaˆ ¡ploàn enai sîma ¥peiron ™ndšcetai, oÜte æj lšgous… tinej tÕ par¦ t¦ stoice‹a, ™x oá taàta gennîsin, oÜq’ ¡plîj. e„sˆn g£r tinej o‰ toàto poioàsi tÕ ¥peiron, ¢ll’ oÙk ¢šra À Ûdwr, Ópwj m¾ t«lla fqe…rhtai ØpÕ toà ¢pe…rou aÙtîn· œcousi g¦r prÕj ¥llhla ™nant…wsin, oŒon Ð mn ¢¾r yucrÒj, tÕ d’ Ûdwr ØgrÒn, tÕ d pàr qermÒn· ïn e„ Ãn e$n ¥peiron, œfqarto ¨n ½dh t«lla· nàn d’ ›teron ena… fasin ™x oá taàta. ¢dÚnaton d’ enai toioàton, oÙc Óti ¥peiron (perˆ toÚtou mn g¦r koinÒn ti lektšon ™pˆ pantÕj Ðmo…wj, kaˆ ¢šroj kaˆ Ûdatoj kaˆ Ðtouoàn), ¢ll’ Óti oÙk œstin toioàton sîma a„sqhtÕn par¦ t¦ kaloÚmena stoice‹a· ¤panta g¦r ™x oá ™sti, kaˆ dialÚetai e„j toàto, éste Ãn ¨n ™ntaàqa par¦ ¢šra kaˆ pàr kaˆ gÁn kaˆ Ûdwr· fa…netai d’ oÙdšn. Cf. above, on 302a17–18. The intermediate substance, whose existence Aristotle rejects, is usually identified with Anaximander’s infinite; part of the passage just quoted is DK 12 A 16. Kahn (1960) 44–46 reviews the grounds for the identification; see, however, Palmer (2009) 338 n. 18. Elsewhere Aristotle takes a different view of Anaximander’s infinite; see below, on 303b15–16. 303b12–13. ὃ…ἄπειρον ὄν: cf. Anaximand., DK 12 A 11, and see previous n. 303b15–16. ὅσοι μὲν οὖν…γεννῶσιν: the condensation and rarefaction of a single basic substance into a multitude of derivative substances seems to have been introduced by Anaximenes. See Simp., in Ph. 24.26–25.1 (Diels): 'Anaximšnhj d EÙrustr£tou Mil»sioj…m…an mn kaˆ aÙtÕj t¾n Øpokeimšnhn fÚsin kaˆ ¥peirÒn fhsin…¢šra lšgwn aÙt»n· diafšrein d manÒthti kaˆ puknÒthti kat¦ t¦j oÙs…aj. kaˆ ¢raioÚmenon mn pàr g…nesqai, puknoÚmenon d ¥nemon, eta nšfoj, œti d m©llon Ûdwr, eta gÁn, eta l…qouj, t¦ d ¥lla ™k toÚtwn (DK 13 A 5). In Ph. A 4, 187a12–23, Aristotle connects the processes of condensation and rarefaction with the theory of the intermediate substance (see above, on 303b11–12): æj d’ oƒ fusikoˆ lšgousi, dÚo trÒpoi e„s…n. oƒ mn g¦r e$n poi»santej tÕ [×n] sîma tÕ Øpoke…menon, À tîn triîn ti À ¥llo Ó ™sti purÕj mn puknÒteron ¢šroj d leptÒteron, t«lla gennîsi puknÒthti kaˆ manÒthti poll¦ poioàntej (taàta d’ ™stˆn ™nant…a, kaqÒlou d’ Øperoc¾ kaˆ œlleiyij, ésper tÕ mšga fhsˆ Pl£twn kaˆ tÕ mikrÒn, pl¾n Óti Ð mn taàta poie‹ Ûlhn tÕ d e$n tÕ edoj, oƒ d tÕ mn e$n tÕ Øpoke…menon Ûlhn, t¦ d’ ™nant…a diafor¦j kaˆ e‡dh)· oƒ d’ ™k toà ˜nÕj ™noÚsaj t¦j ™nantiÒthtaj ™kkr…nesqai, ésper 'Anax…mandrÒj fhsi, kaˆ Ósoi d’ e$n kaˆ poll£ fasin enai, ésper 'EmpedoklÁj kaˆ 'AnaxagÒraj· ™k toà m…gmatoj g¦r kaˆ oátoi ™kkr…nousi t«lla (Anaximand., DK 12 A 16).

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303b16–17. οὗτοι…ποιοῦντες: if there is only one element, a single substance which is condensed or rarefied into a multitude of other substances, it turns out that a different substance is prior to it, and it is this substance which must be considered the sole element. Cf. 304b6–9. 303b17. ἐκ τῶν στοιχείων: since the theory Aristotle criticizes here posits a single element, the plural can only refer to those substances into which the single element turns by undergoing condensation or rarefaction, and which are then put together to form various complex entities–the latter are analyzable into their constituents, which are elements in the sense that some things can be analyzed into them, not in the sense that they are truly basic. Cf. the transformations of air according to Anaximenes in the testimony quoted above, on 303b15–16. 303b18. ἡ δ’ εἰς τὰ στοιχεῖα διάλυσις: ÐdÒj can be plausibly supplied after the prepositional phrase as a counterpart of gšnesij in the previous line–if the generation of complex entities from their elements amounts to the combination of the latter, the way back to the elements is an analysis. Cf. GC A 3, 318b2–14. 303b18–19. ὥστ’…τὸ λεπτομερέστερον: if the generation of complex entities from their elements amounts to the combination of the latter and the way back to these elements is an analysis, assuming that the elements at issue are not really elementary but products of the condensation and rarefaction of one element, as the theory criticized here posits, the way to this one element, too, cannot but be an analysis. If so, analysis singles out as element the stuff which is the product of the greatest possible rarefaction of the hypothetical single element; on this stuff as tÕ leptomeršsteron see below, on 303b26–27. All other stuffs into which the purported single element turns by undergoing condensation and rarefaction are analyzable into the one defined by the highest degree of rarefaction the hypothetical single element can possibly undergo, so it is this most rarefied stuff that ought to be considered the single element. As defined in ch. 3, 302a15–18, an element is something into which something else can be divided or analyzed, and which itself is not further divisible or analyzable into anything else different in kind. But density is divisible; see ch. 1, 299b10, with n. ad loc. Given any number of stuffs with varying density as their sole differentiating feature, therefore, if one among them is to be singled out as the sole element of the rest, it can only be the one with the lowest density–the most rarefied, into which all the rest are analyzable. 303b20. φασί: e.g. Anaximenes. See above, on 303b15–16. 303b21–22. διαφέρει…τὸ μέσον: oÙdn dš, fhs…, diafšrei, k¨n m¾ tÕ pàr Ï prîton mhd leptÒteron kat’ aÙtoÚj· kaˆ oÛtw g¦r ¢kolouqe‹ ¥llo ti lšgein aÙtoÝj tÕ leptÒteron kaˆ stoiceiwdšsteron, e„j Ö ¹ ¢n£lusij g…netai toà Øpotiqemšnou Øp’ aÙtîn stoice…ou mšsou Ôntoj kaˆ tÍ manèsei kat’ aÙtoÝj ¢naluomšnou e„j leptÒteron. Ósa oân manèsei g…netai, taàta m©llÒn ™sti stoice‹a (Simp., in Cael. 616.15–20 [Heiberg]).

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303b22–23. ἔτι…γεννᾶν: cf. the transformations of air according to Anaximenes in the testimony quoted above, on 303b15–16. 303b25–26. τὸ λεπτότητι καὶ παχύτητι: sc. t«lla genn©n. 303b26. τὸ μεγέθει καὶ μικρότητι: cf. previous n. 303b26–27. λεπτὸν…τὸ μεγαλομερές: what is leptÒn or manÒn consists of small particles, in contrast to what is pacÚ or puknÒn, which consists of large particles. Cf. GC B 2, 329b34–330a4: ™peˆ g¦r tÕ ¢naplhstikÒn ™sti toà Øgroà di¦ tÕ m¾ ær…sqai mn eÙÒriston d’ enai kaˆ ¢kolouqe‹n tù ¡ptomšnJ, tÕ d leptÕn ¢naplhstikÒn (leptomerj g£r, kaˆ tÕ mikromerj ¢naplhstikÒn· Ólon g¦r Ólou ¤ptetai· tÕ d leptÕn m£lista toioàton), fanerÕn Óti tÕ mn leptÕn œstai toà Øgroà, tÕ d pacÝ toà xhroà. In Cat. 8, 10a16–23, the distinction is fleshed out in terms of the distance between the particles: tÕ d manÕn kaˆ tÕ puknÕn kaˆ tÕ tracÝ kaˆ tÕ le‹on dÒxeie mn ¨n poiÕn shma…nein, œoike d ¢llÒtria t¦ toiaàta enai tÁj perˆ tÕ poiÕn diairšsewj· qšsin g£r tina m©llon fa…netai tîn mor…wn ˜k£teron dhloàn· puknÕn mn g¦r tù t¦ mÒria sÚnegguj enai ¢ll»loij, manÕn d tù diest£nai ¢p’ ¢ll»lwn· kaˆ le‹on mn tù ™p’ eÙqe…aj pwj t¦ mÒria ke‹sqai, tracÝ d tù tÕ mn Øperšcein tÕ d ™lle…pein. It is unclear if views of some earlier thinker(s) are presupposed here. 303b27–28. τὸ γὰρ ἐπεκτεινόμενον ἐπὶ πολὺ λεπτόν: here tÕ leptÒn is conceived of as fluid. Cf. GC B 2, 329b34–330a4, quoted in previous n. 303b29–30. μεγέθει…οὐσίαν: if there is only one element and all other substances, such as fire, water and air, result from its condensation and rarefaction, the determination of what these other stuffs each are, what distinguishes one from another, is based on the size of the particles of the single element–if small, they make up the fine or rare stuffs resulting from rarefaction, whereas, if large, they constitute those thick or coarse stuffs resulting from condensation. Aristotle seems to assume here that, when the single element condenses, its particles expand; when it suffers rarefaction, they shrink. 303b30–304a1. οὕτω…ἀήρ: if each derivative substance is differentiated from the others by the size of the particles of the single element making it up, it turns out that there is no unqualified fire, water and air–the same stuff will be fire to another stuff made up of particles sufficiently larger than those making up the initial stuff, but air to yet another, whose particles are smaller. Cf. 304b9–11. 304a1–3. τοῖς…φάσκουσιν: the atomists. See above, on 303a15 and 15–16. 304a3–7. ἐπεὶ…λόγους: if all derivative substances are differentiated from one another by the size of the particles of the single element constituting them, it will always be possible to form the ratio of the size of the particles in one stuff to

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the size of those in another. If one stuff will be to another as air to fire, it will be to a third as earth to water, depending on the ratio the size of its particles has to the size of the particles of the other stuff. ¢n£gkh tÕ mn ¢šra enai tÕ d pàr tÕ d gÁn tÕ d’ Ûdwr must be interpreted consistently with (œstai) tÕ aÙtÕ prÕj mn tÒde pàr, prÕj dš ti ¥llo ¢»r in 303b32–304a1. tÕ ™nup£rcein ™n to‹j me…zosi toÝj tîn ™lattÒnwn lÒgouj asserts the comparability of particle-sizes. 304a7–8. ὅσοι…τὸ στοιχεῖον: cf. above, on 303b10–11. Aristotle proceeds to distinguish between two versions of the view he criticizes here, that fire is the single element, and two variations of the first version, but their advocates cannot be determined. 304a9–10. οἱ μὲν…ποιοῦντες: cf. ch. 4, 303a4–14, on the atomists. 304a11–12. τῶν μὲν…τὸ πῦρ: this is how the particles of fire are described in the Platonic Timaeus. See 55d7–56b6, the assignment of cubical, icosahedral, octahedral and pyramidal shape to the particles of earth, water, air and fire: t¦ d gegonÒta nàn tù lÒgJ gšnh diane…mwmen e„j pàr kaˆ gÁn kaˆ Ûdwr kaˆ ¢šra. gÍ mn d¾ tÕ kubikÕn edoj dîmen· ¢kinhtot£th g¦r tîn tett£rwn genîn gÁ kaˆ tîn swm£twn plastikwt£th, m£lista d ¢n£gkh gegonšnai toioàton tÕ t¦j b£seij ¢sfalest£taj œcon· b£sij d ¼ te tîn kat’ ¢rc¦j trigènwn Øpoteqšntwn ¢sfalestšra kat¦ fÚsin ¹ tîn ‡swn pleurîn tÁj tîn ¢n…swn, tÒ te ™x ˜katšrou sunteqn ™p…pedon „sÒpleuron „sopleÚrou tetr£gwnon trigènou kat£ te mšrh kaˆ kaq’ Ólon stasimwtšrwj ™x ¢n£gkhj bšbhken. diÕ gÍ mn toàto ¢ponšmontej tÕn e„kÒta lÒgon diasózomen, Ûdati d’ aâ tîn loipîn tÕ duskinhtÒtaton edoj, tÕ d’ eÙkinhtÒtaton pur…, tÕ d mšson ¢šri· kaˆ tÕ mn smikrÒtaton sîma pur…, tÕ d’ aâ mšgiston Ûdati, tÕ d mšson ¢šri· kaˆ tÕ mn ÑxÚtaton aâ pur…, tÕ d deÚteron ¢šri, tÕ d tr…ton Ûdati. taàt’ oân d¾ p£nta, tÕ mn œcon Ñlig…staj b£seij eÙkinhtÒtaton ¢n£gkh pefukšnai, tmhtikètatÒn te kaˆ ÑxÚtaton ×n p£ntV p£ntwn, œti te ™lafrÒtaton, ™x Ñlig…stwn sunestÕj tîn aÙtîn merîn· tÕ d deÚteron deutšrwj t¦ aÙt¦ taàt’ œcein, tr…twj d tÕ tr…ton. œstw d¾ kat¦ tÕn ÑrqÕn lÒgon kaˆ kat¦ tÕn e„kÒta tÕ mn tÁj puram…doj stereÕn gegonÕj edoj purÕj stoice‹on kaˆ spšrma· tÕ d deÚteron kat¦ gšnesin e‡pwmen ¢šroj, tÕ d tr…ton Ûdatoj. For the triangles see above, on 298b33–299a1. For the volumes of the pyramid, the octahedron and the icosahedron see Vlastos (1975) 89 and Brisson & Mayerstein (1995) 51. 304a14–15. τὰ δὲ…ἐκ πυραμίδων: cf. ch. 4, 303a31–b1. 304a15–16. τῶν μὲν…λεπτότατον: cf. above, on 304a11–12. See also the implicit characterization of fire particles in Ti. 58a4–b2: ¹ toà pantÕj per…odoj, ™peid¾ sumperišlaben t¦ gšnh, kukloter¾j oâsa kaˆ prÕj aØt¾n pefuku‹a boÚlesqai sunišnai, sf…ggei p£nta kaˆ ken¾n cèran oÙdem…an ™´ le…pesqai. diÕ d¾ pàr mn e„j ¤panta diel»luqe m£lista, ¢¾r d deÚteron, æj

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leptÒthti deÚteron œfu, kaˆ t«lla taÚtV. Cf. Pl., Cra. 412c6–413c3: “dikaiosÚnh” dš, Óti mn ™pˆ tÍ toà dika…ou sunšsei toàto ke‹tai tÕ Ônoma, ·®dion sumbale‹n· aÙtÕ d tÕ “d…kaion” calepÒn. kaˆ g¦r d¾ kaˆ œoike mšcri mšn tou Ðmologe‹sqai par¦ pollîn, œpeita d ¢mfisbhte‹sqai. Ósoi g¦r ¹goàntai tÕ p©n enai ™n pore…v, tÕ mn polÝ aÙtoà Øpolamb£nousin toioàtÒn ti enai oŒon oÙdn ¥llo À cwre‹n, di¦ d toÚtou pantÕj ena… ti diexiÒn, di’ oá p£nta t¦ gignÒmena g…gnesqai· enai d t£ciston toàto kaˆ leptÒtaton...Ð mn g¦r t…j fhsin toàto enai d…kaion, tÕn ¼lion· toàton g¦r mÒnon diai+Ònta kaˆ k£onta ™pitropeÚein t¦ Ônta. ™peid¦n oân tJ lšgw aÙtÕ ¤smenoj æj kalÒn ti ¢khkoèj, katagel´ mou oátoj ¢koÚsaj kaˆ ™rwt´ e„ oÙdn d…kaion omai enai ™n to‹j ¢nqrèpoij ™peid¦n Ð ¼lioj dÚV. liparoàntoj oân ™moà Óti aâ ™ke‹noj lšgei aÙtÒ, tÕ pàr fhsin· toàto d oÙ ·®diÒn ™stin e„dšnai. Ð d oÙk aÙtÕ tÕ pàr fhsin, ¢ll’ aÙtÕ tÕ qermÕn tÕ ™n tù purˆ ™nÒn. 304a21. συμφυσωμένου ψήγματος: doke‹ dš moi di¦ toÚtou, fhsˆn Ð 'Alšxandroj, toà parade…gmatoj tÕ ¥topon tÁj dÒxhj paradeiknÚnai· æj g¦r ™pˆ toà sumfuswmšnou y»gmatoj pacÚteron mšn ti ™x aÙtoà g…netai sîma, crusÕj mšntoi kaˆ aÙtÒ, oÛtw kaˆ ™k toà purÕj e„ toÚtJ g…noito tù trÒpJ pacÚtera sèmata, pàr ¨n e‡h kaˆ aÙt¦ pacÚthti kaˆ megšqei mÒnon diafšronta (Simp., in Cael. 621.20–25 [Heiberg]). If so, it is not clear how the first version of the view criticized here escapes this objection. 304a22–23. τὸ πρῶτον σῶμα: sc. tÕ pàr. 304a23–24. πάλιν…τὴν ὑπόθεσιν: cf. ch. 4, 303a20–24, with nn. ad loc. 304a25. φυσικῶς βουλομένοις θεωρεῖν: cf. ch. 1, 299a11–13. The physical argument Aristotle sets out next rests on two premises: the total quantity of air existing in the cosmos is greater than that of water, thus occupying a proportionately greater volume, and the quantity of fire on the cosmic scale is greater than that of air; the elemental corpuscles of air and water, as well as fire and air, if such corpuscles existed, would have volumes in the ratio of the volumes these substances occupy on the scale of the cosmos. From theses premises follows that a hypothetical element of air would be greater than its analogue for water, that of fire than its analogue for air: if an element of fire existed, its volume would be divisible into the volume of the element of water and their difference, as well as into the volume of the element of air and their difference. 304a27. τῶν ὁμοιομερῶν: cf. above, on 302b18. 304a28–29. οἷον…τῶν ἄλλων: if elemental corpuscles of air and water existed, they would have volumes in the ratio of the volumes that these substances occupy on the scale of the cosmos, and the same would apply to other pairs of the bodies Aristotle considers simple. Cf. Mete. A 3, 340a8–13: Ðrîmen d’ oÙk ™n

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tosoÚtJ megšqei gignomšnhn t¾n Øperoc¾n tîn Ôgkwn, Ótan ™x Ûdatoj ¢¾r gšnhtai diakriqšntoj À pàr ™x ¢šroj· ¢n£gkh d tÕn aÙtÕn œcein lÒgon Ön œcei tÕ tosondˆ kaˆ mikrÕn Ûdwr prÕj tÕn ™x aÙtoà gignÒmenon ¢šra, kaˆ tÕn p£nta prÕj tÕ p©n Ûdwr. See also ch. 7, 305b11–16. 304a30. ὁ δ’ ἀὴρ πλείων τοῦ ὕδατος: see the passage quoted in previous n. 304a30–31. τὸ λεπτομερέστερον τοῦ παχυμερεστέρου: the conclusion Aristotle draws next leaves no doubt that tÕ leptomeršsteron is not regarded here as made up of smaller elementary particles than those making up tÕ pacumeršsteron. 304b1–2. τῶν λεπτομερεστέρων: only the first simple body can be finer than fire. Cf. the passage quoted below, on 306b9–15. 304b2. εἰ δὲ διαιρετόν: for the rest of the protasis see 304a7–8 and 22–23. 304b2–3. τοῖς μὲν σχηματίζουσι τὸ πῦρ: i.e. to‹j mn scÁma peri£ptousi tù pur… (cf. oƒ mn g¦r aÙtîn scÁma peri£ptousi tù pur… in 304a9–10). 304b3–4. συμβήσεται…πυραμίδων: if there are divisible elemental corpuscles of fire with pyramidal shape, since pyramids cannot be divided into smaller pyramids, not all parts of fire are themselves fire. But any part of fire is necessarily itself fire. A triangular pyramid is divisible into triangular pyramids; if it is a regular tetrahedron, though, it cannot be divided only into regular tetrahedra. This is perhaps what Aristotle means; see Heath (1949) 175. Alternatively, he originally wrote m¾ p£ntwj sugke‹sqai t¾n puram…da ™k puram…dwn, not m¾ sugke‹sqai t¾n puram…da ™k puram…dwn. Cf. ch. 7, 305b34–306a1: m¾ enai m»te tÕ tÁj puram…doj mšroj p£ntwj puram…da m»te tÕ toà kÚbou kÚbon. For his argument Aristotle needs just the fact that pyramids are not necessarily divisible into pyramids. See also ch. 7, 305b31–306a1, with n. ad loc. 304b4–6. ἔτι δὲ…οὐδέν: since the parts of pyramids need not themselves be pyramids, if the divisible elemental corpuscles of fire have pyramidal shape, not all bodies either consist of elements or are elements, for the parts of the fire corpuscles cannot themselves be fire or corpuscles of another element, fire being ex hypothesi the sole element. Cf. ch. 1, 299b23–31, and 7, 306a26–b2. 304b6–7. τοῖς δὲ τῷ μεγέθει διορίζουσι: sc.tÕ prîton sîma. They are apparently those mentioned in 304a18–21. 304b7–9. πρότερόν τι…στοιχεῖον: if Aristotle criticizes here the view of those mentioned in 304a18–21, the divisibility of fire0, the hypothetical single element whose fine filings are blown together, as it were, to form other bodies, can only entail that these filings are themselves congeries of even finer filings, of a yet subtler fire1, that are blown together, and so on ad infinitum. Cf. 303b13–22.

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304b9–11. ἔτι δὲ…γῆ: fire1 could be to fire0 as fire0 is to air in terms of subtleness (for the symbolism see previous n.). Moreover, the even finer fire2 could be to fire0 as fire0 is to water, whereas the still finer fire3 could be to fire0 as fire0 is to earth. Starting all over again with fire3, we go on ad infinitum. Cf. 303b30–304a7. 304b11–13. κοινὸν δὲ…τὴν αὐτήν: cf. above, on 303b5–8. 304b14–15. εἰ οὖν…τί ἐστι: if there is a single element, all bodies turn out to be this simple body. Cf. GC B 5, 332a4–18: e„ g£r ™sti tîn fusikîn swm£twn Ûlh, ésper kaˆ doke‹ ™n…oij, Ûdwr kaˆ ¢¾r kaˆ t¦ toiaàta, ¢n£gkh ½toi e$n À dÚo enai taàta À ple…w. e$n mn d¾ p£nta oÙc oŒÒn te, oŒon ¢šra p£nta À Ûdwr À pàr À gÁn, e‡per ¹ metabol¾ e„j t¢nant…a. e„ g¦r e‡h ¢»r, e„ mn Øpomšnei, ¢llo…wsij œstai· ¢ll’ Ãn gšnesij· ¤ma d’ oÙd’ oÛtw doke‹ éste Ûdwr enai ¤ma kaˆ ¢šra À ¥ll’ Ðtioàn. œstai d» tij ™nant…wsij kaˆ diafor¦ Âj ›xei ti q£teron mÒrion, tÕ pàr oŒon qermÒthta. ¢ll¦ m¾n oÙk œstai tÒ ge pàr ¢¾r qermÒj· ¢llo…ws…j te g¦r tÕ toioàton, kaˆ oÙ fa…netai· ¤ma d p£lin e„ œstai ™k purÕj ¢»r, toà qermoà e„j toÙnant…on metab£llontoj œstai. Øp£rxei ¥ra tù ¢šri toàto, kaˆ œstai Ð ¢¾r yucrÒn ti. éste ¢dÚnaton tÕ pàr qermÕn ¢šra enai· ¤ma g¦r tÕ aÙtÕ qermÕn kaˆ yucrÕn œstai. ¥llo ti ¥r’ ¢mfÒtera tÕ aÙtÕ œstai, kaˆ ¥llh tij Ûlh koin». The second part of the argument, which refutes the hypothesis of a single element, is problematic; see Williams (1982) 164. 304b15–19. καὶ ταύτην…θᾶττον: cf. above, on 299a31–b1.

CHAPTER 6 304b23–25. Ἐπισκεπτέον δὲ…ἐστιν: on the history of the transmutability of the elements at issue–fire, water, air and earth–cf. above, on 298b33–299a1. The arguments in ch. 6 do not fix their number. po‹a refers to the fact established in the second half of this chapter: these elements are generated from one another. 304b26. ὁρῶμεν: cf. the passage quoted below, on 305a31–32. 304b27–28. ἀνάγκη δὲ…τὴν διάλυσιν: to show that the four traditional simple bodies cannot be eternal, it is not enough to appeal to the empirical evidence of their decay. For this process might either continue for an infinitely long time or stop below the threshold of perception, which would mean that the four Empedoclean simple bodies are, contrary to the empirical evidence, eternal. Aristotle has thus to show that the decay of the four Empedoclean simple bodies cannot go on for an infinitely long time or eventually stop, leaving a stable residue. 304b28–305a1. εἰ μὲν…ὅπερ ἀδύνατον: if the decay of an amount of an Empedoclean simple body took an infinitely long time, the inverse process, the

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subsequent regeneration of the same quantity of this simple body, would not but need an infinitely long time, too, which would absurdly come after the first. (However, if an amount of an Empedoclean simple body took an infinitely long time to decay, does not this mean that it could never reach an end of this process so as for its regeneration to begin?) Cf. Lucr., 1.551–564: denique si nullam finem natura parasset / frangendis rebus, iam corpora materiai / usque redacta forent aevo frangente priore, / ut nil ex illis a certo tempore posset / conceptum 〈ad〉 summum aetatis pervadere finem. / nam quidvis citius dissolvi posse videmus / quam rursus refici; quapropter longa diei / infinita aetas anteacti temporis omnis / quod fregisset adhuc disturbans dissoluensque, / numquam reliquo reparari tempore posset./ at nunc nimirum frangendi reddita finis / certa manet, quoniam refici rem quamque videmus / et finita simul generatim tempora rebus / stare, quibus possint aevi contingere florem. 305a1–4. εἰ δὲ…λέγειν: DK 31 A 43a. According to Aristotle, Empedocles is forced to agree with the atomists that there are indivisible solid bodies: scedÕn d kaˆ 'Empedokle‹ ¢nagka‹on lšgein ésper kaˆ LeÚkippÒj fhsin· enai g¦r ¥tta stere£ kaˆ ¢dia…reta dš, e„ m¾ p£ntV pÒroi sunece‹j e„sin. toàto d’ ¢dÚnaton· oÙqn g¦r œstai stereÕn par¦ toÝj pÒrouj, ¢ll¦ p©n kenÒn. ¢n£gkh ¥ra t¦ mn ¡ptÒmena enai ¢dia…reta, t¦ d metaxÝ aÙtîn ken£, oÞj ™ke‹noj lšgei pÒrouj (GC A 8, 325b5–10). On the pores see also GC A 8, 326b6–28. They are not ken£, for Empedocles denies the existence of vacuum; see below, on 305b17. 305a4–5. ἄτομον μὲν…λόγους: cf. ch. 4, 303a20–24, with nn. ad loc. The same point is repeated in ch. 7, 306a26–30. 305a6–7. τὸ γὰρ…ἐστιν: this is why a mixture forms easier and faster, if its ingredients are finely divided. See GC A 10, 328a31–35: fanerÕn oân Óti taàt’ ™stˆ mikt¦ Ósa ™nant…wsin œcei tîn poioÚntwn· taàta g¦r d¾ Øp’ ¢ll»lwn ™stˆ paqhtik£. kaˆ mikr¦ d mikro‹j paratiqšmena m…gnutai m©llon, ·´on g¦r kaˆ q©tton ¥llhla meqist©sin, tÕ d polÝ kaˆ ØpÕ polloà cron…wj toàto dr´. 305a17. ἀφωρισμένον: Allan’s suggestion. Cf. 305a20–21: ¢n£gkh kenÕn enai ¢fwrismšnon. Longo (1961) prints the mss reading gennèmenon. 305a17. ἔν τινι γίνεται, καὶ: Simp., in Cael. 630.1–5 (Heiberg), notes approvingly that Alex. Aphr. suggested the addition of these words. 305a18–22. ἤτοι…πρότερον: prîton oân de…knusin, Óti ™x ¢swm£tou ¢dÚnaton genšsqai, diÒti Ð ™x ¢swm£tou gennîn lÒgoj kenÕn poie‹ kecwrismšnon, Óper ¢dÚnaton dšdeiktai. Óti d toàto oÛtwj œcei, de…knusin ™k toà p©n tÕ ginÒmenon sîma œn tini g…nesqai tÒpJ· p©n g¦r sîma m£lista genhtÕn kaˆ Øposšlhnon ™n tÒpJ enai ¢n£gkh· kaˆ t¦ ™k toà ¢swm£tou ¥ra ginÒmena stoice‹a sèmat£ ge Ônta ™n tÒpJ œstai tin…. ™n d¾ tù tÒpJ ™ke…nJ,

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™n ú g…netai kaˆ Ön katšcei ginÒmena, ½toi proãpÁrcš ti sîma katšcon aÙtÒn, À oÙdn Ãn ™n aÙtù sîma. ¢ll’ e„ mn Ãn ti sîma tÕ prokatšcon tÕn tÒpon, dÚo sèmata ™n tù aÙtù tÒpJ œstai tÒ te proãp£rcon kaˆ tÕ gegonÕj ™n tÍ aÙtÍ toà tÒpou perigrafÍ ¥mfw kecwrhmšna, kaˆ oÛtwj œstai sîma ™n sèmati kaˆ sîma di¦ sèmatoj cwroàn, Óper ¢dÚnaton kaˆ ™n tÍ FusikÍ ¢kro£sei œdeixen (Simp., in Cael. 629.18–29 [Heiberg]). Cf. ch. 2, 301b33–302a9. 305a25–26. μηδεμίαν δ’…μαθηματικόν: e„ d mhdem…an œcoi ·op»n, ¢k…nhton kaˆ maqhmatikÕn œstai. pîj g¦r ¨n kinhqe…h b£roj À koufÒthta m¾ œcon; m¾ kinoÚmenon d m»te kaqÒlou m»te kat¦ t¦ mšrh maqhmatikÕn ¨n e‡h· taÚtV g¦r m£lista tÕ fusikÕn sîma toà maqhmatikoà dien»noce tù kin»sewj ¢rc¾n ™n ˜autù œcein (Simp., in Cael. 631.1–5 [Heiberg]). 305a31–32. ἐπεὶ δ’…γίγνεσθαι: the conclusion of this chapter seems to be referred to in GC B 4, 331a7–23. This is the introduction to Aristotle’s explanation of the mechanisms through which the Empedoclean simple bodies can be transformed into one another: ™peˆ d dièristai prÒteron Óti to‹j ¡plo‹j sèmasin ™x ¢ll»lwn ¹ gšnesij, ¤ma d kaˆ kat¦ t¾n a‡sqhsin fa…netai ginÒmena (oÙ g¦r ¨n Ãn ¢llo…wsij· kat¦ g¦r t¦ tîn ¡ptîn p£qh ¢llo…ws…j ™stin), lektšon t…j Ð trÒpoj tÁj e„j ¥llhla metabolÁj, kaˆ pÒteron ¤pan ™x ¤pantoj g…gnesqai dunatÕn À t¦ mn dunatÕn t¦ d’ ¢dÚnaton. Óti mn oân ¤panta pšfuken e„j ¥llhla metab£llein, fanerÒn· ¹ g¦r gšnesij e„j ™nant…a kaˆ ™x ™nant…wn, t¦ d stoice‹a p£nta œcei ™nant…wsin prÕj ¥llhla di¦ tÕ t¦j diafor¦j ™nant…aj enai· to‹j mn g¦r ¢mfÒterai ™nant…ai, oŒon purˆ kaˆ Ûdati (tÕ mn g¦r qermÕn kaˆ xhrÒn, tÕ d’ ØgrÕn kaˆ yucrÒn), to‹j d’ ¹ ˜tšra mÒnon, oŒon ¢šri kaˆ Ûdati (tÕ mn g¦r ØgrÕn kaˆ qermÒn, tÕ d ØgrÕn kaˆ yucrÒn). éste kaqÒlou mn fanerÕn Óti p©n ™k pantÕj g…nesqai pšfuken, ½dh d kaq’ ›kaston oÙ calepÕn „de‹n pîj· ¤panta mn g¦r ™x ¡p£ntwn œstai, dio…sei d tù q©tton kaˆ bradÚteron kaˆ tù ·´on kaˆ calepèteron. See above, on 302a17–18.

CHAPTER 7 305b1–5. οἱ μὲν…μεταβάλλοντος: in ch. 3, 303a24–29, this theory is ascribed only to the atomists. The same criticism of it as in ch. 3 is repeated at the end of the first section of ch. 7, in 305b20–26, hence p£lin in 305a33. 305b2–3. λανθάνουσιν…γένεσιν: denying that the generation of the Empedoclean simple bodies really occurs is tacitly assumed to clash with observational evidence. See the passage quoted above, on 305a31–32. For the criticism implicit in lanq£nousin cf. GC A 1, 314a6–13: tîn mn oân ¢rca…wn oƒ mn t¾n kaloumšnhn ¡plÁn gšnesin ¢llo…wsin ena… fasin, oƒ d’ ›teron ¢llo…wsin kaˆ gšnesin. Ósoi mn g¦r ›n ti tÕ p©n lšgousin enai kaˆ p£nta ™x ˜nÕj gennîsi, toÚtoij mn ¢n£gkh t¾n gšnesin ¢llo…wsin f£nai kaˆ tÕ kur…wj

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gignÒmenon ¢lloioàsqai. Ósoi d ple…w t¾n Ûlhn ˜nÕj tiqšasin, oŒon 'EmpedoklÁj kaˆ 'AnaxagÒraj kaˆ LeÚkippoj, toÚtoij d ›teron. 305b3–5. ἐνυπάρχον γὰρ…μεταβάλλοντος: elsewhere Aristotle rejects the view that the generation of a simple Empedoclean body is its coming out of another such body, as if the latter were a vessel containing not the emerging body itself, as the view criticized here assumes, but its matter regarded as separate from the vessel. See GC A 5, 320a32–b12: …potšrwj ¹ aÜxhsij g…netai, pÒteron ™k kecwrismšnhj aÙtÁj kaq’ aØt¾n tÁj Ûlhj, À ™nuparcoÚshj ™n ¥llJ sèmati; À ¢dÚnaton ¢mfotšrwj; cwrist¾ mn g¦r oâsa À oÙdšna kaqšxei tÒpon À oŒon stigm», À kenÕn œstai kaˆ sîma oÙk a„sqhtÒn. toÚtwn d tÕ mn oÙk ™ndšcetai, tÕ d ¢nagka‹on œn tini enai· ¢eˆ g£r pou œstai tÕ gignÒmenon ™x aÙtoà, éste k¢ke‹no, À kaq’ aØtÕ À kat¦ sumbebhkÒj. ¢ll¦ m¾n e‡ g’ œn tini Øp£rxei, e„ mn kecwrismšnon oÛtwj éste m¾ ™ke…nou kaq’ aØtÕ À kat¦ sumbebhkÒj ti enai, sumb»setai poll¦ kaˆ ¢dÚnata, lšgw d’ oŒon e„ g…gnetai ¢¾r ™x Ûdatoj, oÙ toà Ûdatoj œstai metab£llontoj, ¢ll¦ di¦ tÕ ésper ™n ¢gge…J tù Ûdati ™ne‹nai t¾n Ûlhn aÙtoà. ¢pe…rouj g¦r oÙdn kwlÚei Ûlaj enai, éste kaˆ g…gnesqai ™ntelece…v. œti d’ oÙd’ oÛtw fa…netai gignÒmenoj ¢¾r ™x Ûdatoj, oŒon ™xiën Øpomšnontoj. 305b4–5. ἀλλ’ οὐκ…μεταβάλλοντος: according to Aristotle, generation is always the change of some matter into what is generated, not the emergence of the latter from a container. When an Empedoclean simple body is generated from another, the latter contains neither the former, whose generation is thus its being freed from its vessel, nor a matter separate from itself, from which the former is generated: it is itself this matter. See above, on 302a17–18. 305b5–10. ἔπειτα…ἐστιν: the view criticized here implies not only that the generation of the four traditional bodies is an illusion but also, and no less absurdly, that, when a heavy simple body comes out of a light one, it is heavy on account of its suffering compression upon coming out, whereas, within its light and uncompressed container, it is itself light and uncompressed. Compression, however, clearly does not make something heavy. 305b10–11. ἔτι δὲ…ἐπέχειν: a further problem with the view criticized here is that, if a quantity of e.g. air, when it is seen to be generated from e.g. water, is hypothesized to be separated out of the water with which it is mixed, it is mysterious why the quantity of air will always be observed to have greater volume, and thus occupy more space, than does the amount of water, out of which the air supposedly comes. For it is not necessarily the case that, when two ingredients of a mixture separate, one of them occupies more space. 305b11–16. ὅταν δ’…στενοχωρίαν: cf. above, on 304a28–29. 305b14. τῇ μεταβάσει: cf. above, on 298a34–b1.

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305b17. οἱ ταῦτα λέγοντες: Empedocles, who denied the existence of vacuum (see DK 31 B 13). Without vacuum, we are unable to explain not only the regularity with which air is observed to expand, when it supposedly comes out of water, but the fact of expansion, too. Cf. Ph. ∆ 9, 216b22–30: e„sˆn dš tinej o‰ di¦ toà manoà kaˆ puknoà o‡ontai fanerÕn enai Óti œsti kenÒn. e„ mn g¦r m¾ œsti manÕn kaˆ puknÒn, oÙd sunišnai kaˆ pile‹sqai oŒÒn te. e„ d toàto m¾ e‡h, À Ólwj k…nhsij oÙk œstai, À kumane‹ tÕ Ólon, ésper œfh Xoàqoj, À e„j ‡son ¢eˆ metab£llein ¢šra kaˆ Ûdwr (lšgw d oŒon e„ ™x Ûdatoj ku£qou gšgonen ¢»r, ¤ma ™x ‡sou ¢šroj Ûdwr tosoàton gegenÁsqai), À kenÕn enai ™x ¢n£gkhj· sumpile‹sqai g¦r kaˆ ™pekte…nesqai oÙk ™ndšcetai ¥llwj. On Xuthus see Ross (1936) 593. By Aristotle’s lights, the hypothesis of the vacuum does not really explain the phenomenon at issue. He rules out the existence of vacuum in Ph. ∆ 6–9. 305b18. εἰ δ’ ἔστι κενὸν καὶ ἐπέκτασις: this is the view of the atomists. If the vacuum exists, then the expansion of air, when it supposedly comes out of water, can be explained prima facie; but why this expansion always occurs still does not admit of a rational explanation. Aristotle explains in Ph. ∆ 9, 217a26–b12, the expansion and contraction accompanying the generation of the Empedoclean simple bodies from one another without bringing in the vacuum, whose existence he rejects: œsti d kaˆ sèmatoj Ûlh kaˆ meg£lou kaˆ mikroà ¹ aÙt». dÁlon dš· Ótan g¦r ™x Ûdatoj ¢¾r gšnhtai, ¹ aÙt¾ Ûlh oÙ proslaboàs£ ti ¥llo ™gšneto, ¢ll’ Ö Ãn dun£mei, ™nerge…v ™gšneto, kaˆ p£lin Ûdwr ™x ¢šroj æsaÚtwj, Ðt mn e„j mšgeqoj ™k mikrÒthtoj, Ðt d’ e„j mikrÒthta ™k megšqouj. Ðmo…wj to…nun k¨n Ð ¢¾r polÝj ín ™n ™l£ttoni g…gnhtai ÔgkJ kaˆ ™x ™l£ttonoj me…zwn, ¹ dun£mei oâsa Ûlh g…gnetai ¥mfw. ésper g¦r kaˆ ™k yucroà qermÕn kaˆ ™k qermoà yucrÕn ¹ aÙt», Óti Ãn dun£mei, oÛtw kaˆ ™k qermoà m©llon qermÒn, oÙdenÕj genomšnou ™n tÍ ÛlV qermoà Ö oÙk Ãn qermÕn Óte Âtton Ãn qermÒn, ésper ge oÙd’ ¹ toà me…zonoj kÚklou perifšreia kaˆ kurtÒthj ™¦n g…gnhtai ™l£ttonoj kÚklou, ¹ aÙt¾ oâsa À ¥llh, ™n oÙqenˆ ™ggšgone tÕ kurtÕn Ö Ãn oÙ kurtÕn ¢ll’ eÙqÚ (oÙ g¦r tù diale…pein tÕ Âtton À tÕ m©llon œstin)· oÙd’ œsti tÁj flogÕj labe‹n ti mšgeqoj ™n ú oÙ kaˆ qermÒthj kaˆ leukÒthj œnestin. oÛtw to…nun kaˆ ¹ prÒteron qermÒthj t¾n Ûsteron. éste kaˆ tÕ mšgeqoj kaˆ ¹ mikrÒthj toà a„sqhtoà Ôgkou oÙ proslaboÚshj ti tÁj Ûlhj ™pekte…netai, ¢ll’ Óti dun£mei ™stˆn Ûlh ¢mfo‹n· ést’ ™stˆ tÕ aÙtÕ puknÕn kaˆ manÒn, kaˆ m…a Ûlh aÙtîn. œsti d tÕ mn puknÕn barÚ, tÕ d manÕn koàfon. When Aristotle denies that something must be added to the same matter so as for air to be generated from water, he rejects the explanation of this process by positing the expansion of the generating body, i.e. the addition of more void space between the particles of water. 305b20–26. ἀνάγκη δὲ…ἀλλήλων: cf. ch. 3, 303a24–29, with nn. ad loc. On the impossibility of an infinity of finitely small and equal portions of a body in a finite amount of another body cf. Ph. A 4, 187b7–34, a critique of Anaxagoras (on his view of the elements, which is attacked here, see above, on 302a31–b3): e„ d¾

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tÕ mn ¥peiron Î ¥peiron ¥gnwston, tÕ mn kat¦ plÁqoj À kat¦ mšgeqoj ¥peiron ¥gnwston pÒson ti, tÕ d kat’ edoj ¥peiron ¥gnwston po‹Òn ti. tîn d’ ¢rcîn ¢pe…rwn oÙsîn kaˆ kat¦ plÁqoj kaˆ kat’ edoj, ¢dÚnaton e„dšnai t¦ ™k toÚtwn. oÛtw g¦r e„dšnai tÕ sÚnqeton Øpolamb£nomen, Ótan e„dîmen ™k t…nwn kaˆ pÒswn ™st…n. œti d’ e„ ¢n£gkh, oá tÕ mÒrion ™ndšcetai Ðphlikonoàn enai kat¦ mšgeqoj kaˆ mikrÒthta, kaˆ aÙtÕ ™ndšcesqai (lšgw d tîn toioÚtwn ti mor…wn, e„j Ö ™nup£rcon diaire‹tai tÕ Ólon), e„ d¾ ¢dÚnaton zùon À futÕn Ðphlikonoàn enai kat¦ mšgeqoj kaˆ mikrÒthta, fanerÕn Óti oÙd tîn mor…wn Ðtioàn· œstai g¦r kaˆ tÕ Ólon Ðmo…wj. s¦rx d kaˆ Ñstoàn kaˆ t¦ toiaàta mÒria zóou, kaˆ oƒ karpoˆ tîn futîn. dÁlon to…nun Óti ¢dÚnaton s£rka À Ñstoàn À ¥llo ti Ðphlikonoàn enai tÕ mšgeqoj À ™pˆ tÕ me‹zon À ™pˆ tÕ œlatton. œti e„ p£nta mn ™nup£rcei t¦ toiaàta ™n ¢ll»loij, kaˆ m¾ g…gnetai ¢ll’ ™kkr…netai ™nÒnta, lšgetai d ¢pÕ toà ple…onoj, g…gnetai d ™x Ðtouoàn Ðtioàn (oŒon ™k sarkÕj Ûdwr ™kkrinÒmenon kaˆ s¦rx ™x Ûdatoj), ¤pan d sîma peperasmšnon ¢naire‹tai ØpÕ sèmatoj peperasmšnou, fanerÕn Óti oÙk ™ndšcetai ™n ˜k£stJ ›kaston Øp£rcein. ¢faireqe…shj g¦r ™k toà Ûdatoj sarkÒj, kaˆ p£lin ¥llhj genomšnhj ™k toà loipoà ¢pokr…sei, e„ kaˆ ¢eˆ ™l£ttwn œstai ¹ ™kkrinomšnh, ¢ll’ Ómwj oÙc Øperbale‹ mšgeqÒj ti tÍ mikrÒthti. ést’ e„ mn st»setai ¹ œkkrisij, oÙc ¤pan ™n pantˆ ™nšstai (™n g¦r tù loipù Ûdati oÙk ™nup£rxei s£rx), e„ d m¾ st»setai ¢ll’ ¢eˆ ›xei ¢fa…resin, ™n peperasmšnJ megšqei ‡sa peperasmšna ™nšstai ¥peira tÕ plÁqoj· toàto d’ ¢dÚnaton. On the impossibility of an actual infinity of finitely small but unequal, continually diminishing portions of a body in a finite amount of another body cf. above, on 302b29–30. 305b29–30. ἢ γὰρ…κύβος: Simp., in Cael. 636.20–27 (Heiberg), sees here an allusion to Pl., Ti. 50a4–b4. In this passage, the transformation of one element into another is illustrated with the image of a malleable piece of gold taking on a variety of shapes: œti d safšsteron aÙtoà pšri proqumhtšon aâqij e„pe‹n. e„ g¦r p£nta tij sc»mata pl£saj ™k crusoà mhdn metapl£ttwn paÚoito ›kasta e„j ¤panta, deiknÚntoj d» tinoj aÙtîn e$n kaˆ ™romšnou t… pot’ ™st…, makrù prÕj ¢l»qeian ¢sfalšstaton e„pe‹n Óti crusÒj, tÕ d tr…gwnon Ósa te ¥lla sc»mata ™neg…gneto, mhdšpote lšgein taàta æj Ônta, ¤ ge metaxÝ tiqemšnou metap…ptei. Plato’s own view of elemental transformation is referred to next. 305b31. ὥσπερ ἔνιοί φασιν: cf. ch. 1, 298b33–299a1, with n. ad loc. 305b31–306a1. εἰ μὲν…κύβον: if the transformation of an Empedoclean simple body into another happens because its particles change shape and turn into particles of the other simple body, the particles at issue cannot be divisible. Divisibility is presumably implicit in the hypothesis that, on a microscopic level, the four Empedoclean simple bodies are distinguished from one another in respect of the shape of their particles. Since a shape is divisible not only into smaller copies of itself, it is not necessary that any part of fire or earth, if their particles are assumed to have e.g. pyramidal and cubic shape respectively, is itself fire or earth, for

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pyramids and cubes cannot be divided only into pyramids and cubes. According to Aristotle, however, any part of fire or earth is necessarily itself fire or earth. The view criticized here cannot, therefore, avoid attributing indivisibility to the corpuscles of the Empedoclean simple bodies, which is, though, no more palatable than endowing them with divisibility. The reasons are explained in the expanded version of this argument at the end of the chapter (306a26–b2). On the analyzability of pyramids into pyramids see also ch. 5, 304b2–4, with nn. ad loc. 306a1–5. εἰ δὲ…εἰς ἄλληλα: see above, on 298b33–299a1. The exception of earth from the cycle of elemental transformation is stated in Ti. 54b6–d2: t¦ g¦r tšttara gšnh di’ ¢ll»lwn e„j ¥llhla ™fa…neto p£nta gšnesin œcein, oÙk Ñrqîj fantazÒmena· g…gnetai mn g¦r ™k tîn trigènwn ïn proVr»meqa gšnh tšttara, tr…a mn ™x ˜nÕj toà t¦j pleur¦j ¢n…souj œcontoj, tÕ d tštarton e$n mÒnon ™k toà „soskeloàj trigènou sunarmosqšn. oÜkoun dunat¦ p£nta e„j ¥llhla dialuÒmena ™k pollîn smikrîn Ñl…ga meg£la kaˆ toÙnant…on g…gnesqai, t¦ d tr…a oŒÒn te· ™k g¦r ˜nÕj ¤panta pefukÒta luqšntwn te tîn meizÒnwn poll¦ smikr¦ ™k tîn aÙtîn sust»setai, decÒmena t¦ pros»konta ˜auto‹j sc»mata, kaˆ smikr¦ Ótan aâ poll¦ kat¦ t¦ tr…gwna diasparÍ, genÒmenoj eŒj ¢riqmÕj ˜nÕj Ôgkou mšga ¢potelšseien ¨n ¥llo edoj ›n. Cf. GC B 4, 331a7–23, quoted above on 305a31–32, and B 5, 332a27–30. 306a5–17. συμβαίνει…αἴσθησιν: Aristotle thinks that the atomism of Leucippus and Democritus is more firmly grounded in empirical reality than the theory of the elements in the Platonic Timaeus. See GC A 2, 315b24–316a14: ¢rc¾ d toÚtwn p£ntwn, pÒteron oÛtw g…netai kaˆ ¢lloioàtai kaˆ aÙx£netai t¦ Ônta kaˆ t¢nant…a toÚtoij p£scei, tîn prètwn ØparcÒntwn megeqîn ¢diairštwn, À oÙqšn ™sti mšgeqoj ¢dia…reton· diafšrei g¦r toàto ple‹ston. kaˆ p£lin e„ megšqh, pÒteron, æj DhmÒkritoj kaˆ LeÚkippoj, sèmata taàt’ ™st…n, À ésper ™n tù Tima…J ™p…peda; toàto mn oân aÙtÒ, kaq£per kaˆ ™n ¥lloij e„r»kamen, ¥logon mšcri ™pipšdwn dialàsai. diÕ m©llon eÜlogon sèmata enai ¢dia…reta. ¢ll¦ kaˆ taàta poll¾n œcei ¢log…an. Ómwj d toÚtoij ¢llo…wsin kaˆ gšnesin ™ndšcetai poie‹n [kaq£per e‡rhtai], tropÍ kaˆ diaqigÍ metakinoànta tÕ aÙtÕ kaˆ ta‹j tîn schm£twn diafora‹j, Óper poie‹ DhmÒkritoj· diÕ kaˆ croi¦n oÜ fhsin enai, tropÍ g¦r crwmat…zesqai. to‹j d’ e„j ™p…peda diairoàsin oÙkšti· oÙdn g¦r g…netai pl¾n stere¦ suntiqemšnwn· p£qoj g¦r oÙd’ ™gceiroàsi genn©n oÙdn ™x aÙtîn. a‡tion d toà ™p’ œlatton dÚnasqai t¦ ÐmologoÚmena sunor©n ¹ ¢peir…a. diÕ Ósoi ™nJk»kasi m©llon ™n to‹j fusiko‹j m©llon dÚnantai Øpot…qesqai toiaÚtaj ¢rc¦j a‰ ™pˆ polÝ dÚnantai sune…rein· oƒ d’ ™k tîn lÒgwn pollîn ¢qeèrhtoi tîn ØparcÒntwn Ôntej, prÕj Ñl…ga blšyantej, ¢pofa…nontai ·´on. ‡doi d’ ¥n tij kaˆ ™k toÚtwn Óson diafšrousin oƒ fusikîj kaˆ logikîj skopoàntej· perˆ g¦r toà ¥toma enai megšqh oƒ mšn fasi diÒti aÙtÕ tÕ tr…gwnon poll¦ œstai, DhmÒkritoj d’ ¨n fane…h o„ke…oij kaˆ fusiko‹j lÒgoij pepe‹sqai. See LI 968a9–14 for an argument involving forms and establishing the existence of indivisibles. For the Neoplatonist response to 306a1–307b18 see Mueller (2012) and Opsomer (2012).

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306a7–8. τὸ…ἀρχάς: the theory of the elements in Plato’s Timaeus hypothesizes wrongly mathematical, i.e. intelligible and unchangeable, principles of physical, i.e. sensible and changeable, things–the Empedoclean elements. As Aristotle points out in 306a9–11, the principles must be of the same kind as the things they are principles of. For him, the principles of the elements at issue are sensible–each is defined by two tangible qualities, one from each of two pairs of contraries: qermÒn/yucrÒn, xhrÒn/ØgrÒn. See GC B 2, 329b7–18, and Mete. A 2, 339a11–19. 306a8–9. δόξας ὡρισμένας: Plato’s emphasis on the beauty of the four regular solids he associates with the four Empedoclean elements, and of the triangles constituting their faces, is probably meant here. See Ti. 53c4–54b2: prîton mn d¾ pàr kaˆ gÁ kaˆ Ûdwr kaˆ ¢¾r Óti sèmat£ ™sti, dÁlÒn pou kaˆ pant…· tÕ d toà sèmatoj edoj p©n kaˆ b£qoj œcei. tÕ d b£qoj aâ p©sa ¢n£gkh t¾n ™p…pedon perieilhfšnai fÚsin· ¹ d Ñrq¾ tÁj ™pipšdou b£sewj ™k trigènwn sunšsthken. t¦ d tr…gwna p£nta ™k duo‹n ¥rcetai trigènoin, m…an mn Ñrq¾n œcontoj ˜katšrou gwn…an, t¦j d Ñxe…aj· ïn tÕ mn ›teron ˜katšrwqen œcei mšroj gwn…aj ÑrqÁj pleura‹j ‡saij diVrhmšnhj, tÕ d’ ›teron ¢n…soij ¥nisa mšrh nenemhmšnhj. taÚthn d¾ purÕj ¢rc¾n kaˆ tîn ¥llwn swm£twn Øpotiqšmeqa kat¦ tÕn met’ ¢n£gkhj e„kÒta lÒgon poreuÒmenoi· t¦j d’ œti toÚtwn ¢rc¦j ¥nwqen qeÕj oden kaˆ ¢ndrîn Öj ¨n ™ke…nJ f…loj Ï. de‹ d¾ lšgein po‹a k£llista sèmata gšnoit’ ¨n tšttara, ¢nÒmoia mn ˜auto‹j, dunat¦ d ™x ¢ll»lwn aÙtîn ¥tta dialuÒmena g…gnesqai· toÚtou g¦r tucÒntej œcomen t¾n ¢l»qeian genšsewj pšri gÁj te kaˆ purÕj tîn te ¢n¦ lÒgon ™n mšsJ. tÒde g¦r oÙdenˆ sugcwrhsÒmeqa, kall…w toÚtwn Ðrèmena sèmata ena… pou kaq’ e$n gšnoj ›kaston Ôn. toàt’ oân proqumhtšon, t¦ diafšronta k£llei swm£twn tšttara gšnh sunarmÒsasqai kaˆ f£nai t¾n toÚtwn ¹m©j fÚsin ƒkanîj e„lhfšnai. to‹n d¾ duo‹n trigènoin tÕ mn „soskelj m…an e‡lhcen fÚsin, tÕ d prÒmhkej ¢per£ntouj· proairetšon oân aâ tîn ¢pe…rwn tÕ k£lliston, e„ mšllomen ¥rxesqai kat¦ trÒpon. ¨n oân tij œcV k£llion ™klex£menoj e„pe‹n e„j t¾n toÚtwn sÚstasin, ™ke‹noj oÙk ™cqrÕj ín ¢ll¦ f…loj krate‹· tiqšmeqa d’ oân tîn pollîn trigènwn k£lliston ›n, Øperb£ntej t«lla, ™x oá tÕ „sÒpleuron tr…gwnon ™k tr…tou sunšsthken. diÒti dš, lÒgoj ple…wn· ¢ll¦ tù toàto ™lšgxanti kaˆ ¢neurÒnti d¾ oÛtwj œcon ke‹tai f…lia t¦ «qla. On the beauty of the regular solids and the triangles constituting their faces see Artmann & Schäfer (1993). 306a9. ἴσως: Aristotle allows that some principles of sensibles are not themselves sensible. These are clearly not the ones at issue here, however. 306a12. τούτων: sc. tîn ærismšnwn doxîn. 306a17. τὸ φαινόμενον ἀεὶ κυρίως κατὰ τὴν αἴσθησιν: only a selected set of perceptual appearances can be securely relied upon to either confirm a theory, if it fits them, or reject it, if it conflicts with them, for not all perceptual appearances are true, and to fit those that are reliable enough is the goal of physical theories.

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306a20–23. ἀλλὰ…τριγώνων: recall that, according to Plato’s Timaeus, the atoms of fire are regular pyramids, those of air regular octahedra and those of water regular icosahedra. Their faces, equilateral triangles, can consist of an equal number of elementary triangles. Simp., in Cael. 647.3–14 (Heiberg), explains Aristotle’s objection as follows: prÕj t¦ perˆ tÁj gÁj ·hqšnta to‹j ™x ™pipšdwn lšgousi t¦ sèmata Øpant»saj nàn prÕj t¦ perˆ tîn ¥llwn triîn stoice…wn ™n…statai ™pˆ mn tÁj gÁj tÕ m¾ metab£llein e„j t¦ ¥lla kaˆ ™k tîn ¥llwn a„tias£menoj, ™pˆ d tîn triîn metab£llein e„j ¥llhla legomšnwn ¥topon ™p£gei tÕ ™x ¢n…swn tù ¢riqmù trigènwn sugkeimšnwn aÙtîn tîn te „sopleÚrwn kaˆ ™x ïn t¦ „sÒpleura sÚgkeitai sumba…nein ™n tù g…nesqai ™x Ûdatoj ¢šra À ™x ¢šroj Ûdwr paraiwre‹sqa… tina tr…gwna. e„ g¦r tÕ mn Ûdwr ™x e‡kosi trigènwn „sopleÚrwn ™st…n, Ð d ¢¾r ™x Ñktè, ™¦n ™x Ûdatoj dialuqšntoj ¢¾r g…nhtai, ˜nÕj Ødat…ou sèmatoj e„j e‡kosi tr…gwna dialuqšntoj dÚo g…netai ¢šroj, kaˆ t¦ tšssara tr…gwna paraiwre‹tai, æj ¨n e‡poi tij, m£thn· k¨n ™x ¢šroj Ûdwr g…nhtai, triîn ¢šroj dialuqšntwn swm£twn e„j ˜nÕj Ûdatoj sÚstasin tšssara p£lin pleon£zei. Cf. below, on 307a2–3. 306a26–30. πρὸς δὲ…τὴν ὑπόθεσιν: cf. ch. 4, 303a20–22, with n. ad loc. 306a30–b2. ἀνάγκη γὰρ…διαιρετόν: see above, on 305b31–306a1. Cf. [Arist.] LI 968a14–18 = Xenocrates fr. 127 Isnardi Parente. Cf. ch. 5, 304b4–6.

CHAPTER 8 306b3–9. ὅλως δὲ…ποιεῖν: since there is no vacuum, it is impossible for the corpuscles of the four Empedoclean elements to have shapes, for one who thinks otherwise must single out four solid shapes, one for the corpuscles of each element, such that they leave no gaps between them and fill space, but there are only two solid shapes that can fill space, the cube and the pyramid, as there are three shapes that can fill a plane–the triangle, the square and the hexagon. In all probability, here Aristotle speaks of regular polygons and polyhedra, singling out implicitly as main target of his criticism the theory of the elements in Plato’s Timaeus, where the existence of empty space is denied (see 58a4–c4). That regular tetrahedra can fill space is wrong. Which tetrahedra can fill space is a problem still not completely solved; for its history see Senechal (1981). 306b9–15. ἔπειτα…αὐτῶν: since air and water take on the shape of their container, if on a microscopic scale each of these elements consisted of particles with a certain shape, the particles in contact with the container would conform to the shape of their container, where they touched it, and thus lose the shape assumed to be characteristic for the simple body they were particles of. For Aristotle, the accuracy with which all four Empedoclean simple bodies take on various shapes is not the same. According to Cael. B 4, 287b14–21, the farther away from the center of the cosmos a simple body, the greater the degree of its subtlety, and the more accu-

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rate and uniform the shape it can take on: Óti mn oân sfairoeid»j ™stin Ð kÒsmoj, dÁlon ™k toÚtwn, kaˆ Óti kat’ ¢kr…beian œntornoj oÛtwj éste mhqn m»te ceirÒkmhton œcein paraplhs…wj m»t’ ¥llo mhqn tîn [par'] ¹m‹n ™n Ñfqalmo‹j fainomšnwn. ™x ïn g¦r t¾n sÚstasin e‡lhfen, oÙdn oÛtw dunatÕn ÐmalÒthta dšxasqai kaˆ ¢kr…beian æj ¹ toà pšrix sèmatoj fÚsij· dÁlon g¦r æj ¢n£logon œcei, kaq£per Ûdwr prÕj gÁn, kaˆ t¦ ple‹on ¢eˆ ¢pšconta tîn susto…cwn. 306b15–16. ἀλλ’…ἐστίν: it is presumably by having the Empedoclean elements, particularly air and water, conform to the shape of their containers that nature herself seems to show us that the simple bodies at issue are not determined by the shape of their corpuscles. 306b17. ἀειδὲς καὶ ἄμορφον: i.e. ¢schm£tiston (see Ph. A 7, 191a2). For the formlessness of the substrate, i.e. matter, see Ph. A 7, 191a7–12: ¹ d Øpokeimšnh fÚsij ™pistht¾ kat’ ¢nalog…an. æj g¦r prÕj ¢ndri£nta calkÕj À prÕj kl…nhn xÚlon À prÕj tîn ¥llwn ti tîn ™cÒntwn morf¾n [¹ Ûlh kaˆ] tÕ ¥morfon œcei prˆn labe‹n t¾n morf»n, oÛtwj aÛth prÕj oÙs…an œcei kaˆ tÕ tÒde ti kaˆ tÕ Ôn. 306b18–19. καθάπερ ἐν τῷ Τιμαίῳ γέγραπται: diÕ kaˆ p£ntwn ™ktÕj e„dîn enai creën tÕ t¦ p£nta ™kdexÒmenon ™n aØtù gšnh, kaq£per perˆ t¦ ¢le…mmata ÐpÒsa eÙèdh tšcnV mhcanîntai prîton toàt’ aÙtÕ Øp£rcon, poioàsin Óti m£lista ¢èdh t¦ dexÒmena Øgr¦ t¦j Ñsm£j· Ósoi te œn tisin tîn malakîn sc»mata ¢pom£ttein ™piceiroàsi, tÕ par£pan scÁma oÙdn œndhlon Øp£rcein ™îsi, proomalÚnantej d Óti leiÒtaton ¢perg£zontai. taÙtÕn oân kaˆ tù t¦ tîn p£ntwn ¢e… te Ôntwn kat¦ p©n ˜autoà poll£kij ¢fomoièmata kalîj mšllonti dšcesqai p£ntwn ™ktÕj aÙtù pros»kei pefukšnai tîn e„dîn (Ti. 50e4–51a3). Various interpretations of Plato’s receptacle are surveyed in Miller (2003) ch. 1; see also Johansen (2004) ch. 6. 306b20. ὥσπερ ὕλην εἶναι τοῖς συνθέτοις: i.e. ¢eidÁ kaˆ ¥morfa enai. 306b21–22. τῶν κατὰ τὰ πάθη διαφορῶν: Aristotle calls them t¦j o„ke…aj diafor£j in ch. 4, 302b31–32. The Empedoclean elements are differentiated by their tangible qualities, with respect to which these simple bodies act upon one another (hence kat¦ t¦ p£qh): qermÒn/yucrÒn, xhrÒn/ØgrÒn. Two of them, one from each of the two pairs of contraries they form, define each element: when they are separated from the elements, i.e. when either one or both of them transform into, and are replaced by, their contraries, the elements turn into one another, as Aristotle explains in GC B 4. For more details see above, on 302a17–18. For the phrase aƒ kat¦ t¦ p£qh diafora… cf. 307b20 and GC A 1, 314b17–18. 306b22–26. πρὸς δὲ…στοιχείων: if the Empedoclean simple bodies are assumed to be differentiated by the shape of their particles, the generation of com-

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posites, such as flesh and bone, will be explained be means of juxtaposition, sÚnqesij, of particles of these simple bodies, but juxtaposition of discrete building blocks cannot account for the continuity of composites–they are homoemeric, according to Aristotle, no matter how finely they are divided. On sÚnqesij, contrasted with kr©sij or m…xij, “blending” or “mixing”, the process which, according to Aristotle, produces homoemeric composite bodies, and whereby the four Empedoclean elements stop existing actually at any microscopic level of material structure, see GC A 10, 327b33–328a31. For the status of the ingredients in a mixture see also the passage quoted above, on 302a17–18. The triangular planes making up the corpuscles of the elements in Plato’s Timaeus cannot account for the continuity of composites: these planes are assumed to generate the corpuscles of the elements, not what is generated from the elements, too. 306b26–29. ὥστ’…ὄντων: cf. ch. 7, 306a1–17. 306b29. τὰ πάθη: i.e. t¦j kat¦ t¦ p£qh diafor£j. See above, on 306b21–22. 306b30. τὰς δυνάμεις: see above, on 298a32–34. aƒ kat¦ t¦ p£qh diafora… endow the Empedoclean elements with their dun£meij. 306b33. οἱ μὲν…πυραμίδα: for the spherical shape of fire particles in atomism see ch. 4, 303a3–14. For the pyramidal shape of fire particles according to Plato see Ti. 55d7–56b6 (quoted above, on 304a11–12). 306b33–307a1. ταῦτα…βεβηκέναι: this is how the particles of fire are described in the Platonic Timaeus. See 55d7–56b6 (quoted above, on 304a11–12). It is not clear whether the atomists argued along the same lines or Aristotle simply assumes that they did. For a pyramidal particle of fire, tÕ ™lac…stwn ¤ptesqai kaˆ ¼kista bebhkšnai means that it has the fewest faces which can touch its surroundings, compared with the particles of the other three Empedoclean simple bodies, whose shapes are three of the remaining four regular polyhedra. For a spherical atom of fire, the phrase means that a sphere touches a plane or spherical surface in a point. Democritus seems to have devoted a work to this topic: in the list of his works preserved by Diogenes Laertius, 9.45–49, there appears the title Perˆ diaforÁj gnèmhj (Heath [1981] vol. 1, 178–179, has plausibly proposed gwn…hj instead of gnèmhj) or Perˆ yaÚsioj kÚklou kaˆ sfa…rhj. 307a2. τὸ μὲν ὅλον ἐστὶ γωνία: the entire surface of a sphere is a solid angle. For, just as a circle can be thought of as an infinitely-sided polygon and each point of its circumference as vertex of an angle, which means that the entire circumference is everywhere angular, a sphere can be similarly thought of as a polyhedron with infinitely many faces, each point of its surface being the vertex of a solid angle, which means that the entire surface of the sphere is everywhere angular. In IA 9, 708b22–23, Aristotle considers both an angle and curvature as bending of a straight line, whence it follows that the entire circumference of a circle and the

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entire surface of a sphere are angles: œsti g¦r k£myij mn ¹ ™x eÙqšoj À e„j periferj À e„j gwn…an metabol». Cf. Simp., in Cael. 662.10–12 (Heiberg): e„ g¦r tÕ sugkekammšnon ™stˆ gwn…a, ¹ d sfa‹ra kaq’ Ólhn ˜aut¾n sugkškamptai, e„kÒtwj Ólh gwn…a lšgetai. 307a2. ὀξυγωνιώτατον: cf. ÑxÚtaton, used for the pyramidal shape of particles of fire in Pl., Ti. 55d7–56b6 (quoted above, on 304a11–12). See also the passage quoted in next n. 307a2–3. καίει…φασίν: in Pl., Ti. 56d1–57b7, the action of fire on the other elements, i.e. burning, is explained by the sharp angles of the fire particles. They break down, or divide, the particles of the other elements into the planes constituting their faces: gÁ mn suntugc£nousa purˆ dialuqe‹s£ te ØpÕ tÁj ÑxÚthtoj aÙtoà fšroit’ ¥n, e‡t’ ™n aÙtù purˆ luqe‹sa e‡t’ ™n ¢šroj e‡t’ ™n Ûdatoj ÔgkJ tÚcoi, mšcriper ¨n aÙtÁj pV suntucÒnta t¦ mšrh, p£lin sunarmosqšnta aÙt¦ aØto‹j, gÁ gšnoito–oÙ g¦r e„j ¥llo ge edoj œlqoi pot’ ¥n–Ûdwr d ØpÕ purÕj merisqšn, e‡te kaˆ Øp’ ¢šroj, ™gcwre‹ g…gnesqai sust£nta e$n mn purÕj sîma, dÚo d ¢šroj· t¦ d ¢šroj tm»mata ™x ˜nÕj mšrouj dialuqšntoj dÚ’ ¨n geno…sqhn sèmata purÒj. kaˆ p£lin, Ótan ¢šri pàr Ûdas…n te ½ tini gÍ perilambanÒmenon ™n pollo‹j Ñl…gon, kinoÚmenon ™n feromšnoij, macÒmenon kaˆ nikhqn kataqrausqÍ, dÚo purÕj sèmata e„j e$n sun…stasqon edoj ¢šroj· kaˆ krathqšntoj ¢šroj kermatisqšntoj te ™k duo‹n Óloin kaˆ ¹m…seoj Ûdatoj edoj e$n Ólon œstai sumpagšj. ïde g¦r d¾ logisèmeqa aÙt¦ p£lin, æj Ótan ™n purˆ lambanÒmenon tîn ¥llwn Øp’ aÙtoà ti gšnoj tÍ tîn gwniîn kaˆ kat¦ t¦j pleur¦j ÑxÚthti tšmnhtai, sust¦n mn e„j t¾n ™ke…nou fÚsin pšpautai temnÒmenon–tÕ g¦r Ómoion kaˆ taÙtÕn aØtù gšnoj ›kaston oÜte tin¦ metabol¾n ™mpoiÁsai dunatÕn oÜte ti paqe‹n ØpÕ toà kat¦ taÙt¦ Ðmo…wj te œcontoj–›wj d’ ¨n e„j ¥llo ti gignÒmenon Âtton ×n kre…ttoni m£chtai, luÒmenon oÙ paÚetai. t£ te aâ smikrÒtera Ótan ™n to‹j me…zosin pollo‹j perilambanÒmena Ñl…ga diaqrauÒmena katasbennÚhtai, sun…stasqai mn ™qšlonta e„j t¾n toà kratoàntoj „dšan pšpautai katasbennÚmena g…gneta… te ™k purÕj ¢»r, ™x ¢šroj Ûdwr· ™¦n d’ e„j taàta ‡V kaˆ tîn ¥llwn ti suniÕn genîn m£chtai, luÒmena oÙ paÚetai, prˆn À pant£pasin çqoÚmena kaˆ dialuqšnta ™kfÚgV prÕj tÕ suggenšj, À nikhqšnta, e$n ™k pollîn Ómoion tù krat»santi genÒmenon, aÙtoà sÚnoikon me…nV. Cornford (1937) 224–228, whom I follow in reading e„j taàta instead of Burnet’s e„j taÙt£ at the beginning of the last clause, discusses the passage lucidly; he correctly saw in dialuqšnta a clear hint at the floating triangles that Aristotle criticizes in ch. 7, 306a20–23. See also Ti. 61d5–62a6, the explanation of the sensation of hot. 307a7–8. ταῦτα δ’…κύλισιν: it is difficult to imagine a tetrahedron rolling! 307a8–9. ἔπειτ’…μένειν: see Plato’s description of earth particles in the Timaeus passage quoted above, on 304a11–12.

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307a9–11. μένει δ’…ὡσαύτως: according to Plato, each element, not only earth, has weight in what Aristotle calls its natural place. See Ti. 63b2–e7: e‡ tij ™n tù toà pantÕj tÒpJ kaq’ Ön ¹ toà purÕj e‡lhce m£lista fÚsij, oá kaˆ ple‹ston ¨n ºqroismšnon e‡h prÕj Ö fšretai, ™pemb¦j ™p’ ™ke‹no kaˆ dÚnamin e„j toàto œcwn, mšrh toà purÕj ¢fairîn ƒsta…h tiqeˆj e„j pl£stiggaj, a‡rwn tÕn zugÕn kaˆ tÕ pàr ›lkwn e„j ¢nÒmoion ¢šra biazÒmenoj dÁlon æj toÜlattÒn pou toà me…zonoj ·´on bi©tai· ·èmV g¦r mi´ duo‹n ¤ma metewrizomšnoin tÕ mn œlatton m©llon, tÕ d plšon Âtton ¢n£gkh pou katateinÒmenon sunšpesqai tÍ b…v, kaˆ tÕ mn polÝ barÝ kaˆ k£tw ferÒmenon klhqÁnai, tÕ d smikrÕn ™lafrÕn kaˆ ¥nw. taÙtÕn d¾ toàto de‹ fwr©sai drîntaj ¹m©j perˆ tÒnde tÕn tÒpon. ™pˆ g¦r gÁj bebîtej geèdh gšnh diist£menoi, kaˆ gÁn ™n…ote aÙt»n, ›lkomen e„j ¢nÒmoion ¢šra b…v kaˆ par¦ fÚsin, ¢mfÒtera toà suggenoàj ¢ntecÒmena, tÕ d smikrÒteron ·´on toà me…zonoj biazomšnoij e„j tÕ ¢nÒmoion prÒteron sunšpetai· koàfon oân aÙtÕ proseir»kamen, kaˆ tÕn tÒpon e„j Ön biazÒmeqa, ¥nw, tÕ d’ ™nant…on toÚtoij p£qoj barÝ kaˆ k£tw. taàt’ oân d¾ diafÒrwj œcein aÙt¦ prÕj aØt¦ ¢n£gkh di¦ tÕ t¦ pl»qh tîn genîn tÒpon ™nant…on ¥lla ¥lloij katšcein–tÕ g¦r ™n ˜tšrJ koàfon ×n tÒpJ tù kat¦ tÕn ™nant…on tÒpon ™lafrù kaˆ tù bare‹ tÕ barÝ tù te k£tw tÕ k£tw kaˆ tÕ ¥nw tù ¥nw p£nt’ ™nant…a kaˆ pl£gia kaˆ p£ntwj di£fora prÕj ¥llhla ¢neureq»setai gignÒmena kaˆ Ônta–tÒde ge m¾n ›n ti dianohtšon perˆ p£ntwn aÙtîn, æj ¹ mn prÕj tÕ suggenj ÐdÕj ˜k£stoij oâsa barÝ mn tÕ ferÒmenon poie‹, tÕn d tÒpon e„j Ön tÕ toioàton fšretai, k£tw, t¦ d toÚtoij œconta æj ˜tšrwj q£tera. 307a16. οἷον…δωδεκάεδρον: the regular octahedron is the shape of the corpuscle of air in Pl., Ti. 55d7–56b6. On the dodecahedron, the one of the five regular solids which is not the shape of the particle of an element in the Platonic theory of the elements, unlike in [Pl.], Epin. 981b3–c8, see Ti. 55c4–6. On the theory of the elements in the pseudo-platonic work see Falcon (2005) 77–83. 307a17. ἡ σφαῖρα ὡς γωνία τις οὖσα: cf. above, on 307a2. 307a17. τέμνει: cf. above, on 307a2–3. 307a19–20. ἅμα δὲ…γωνίας: Aristotle considers the attribution of physical properties to mathematical objects absurd. See above, on 299a15–17. 307a22. φασίν: Plato is probably meant. See GC A 2, 315b24–316a14, quoted above on 306a5–17. 307a24–26. ἔτι…πυραμίδας: the triangles making up the faces of the particles of what is being acted upon by fire and is burning reshuffle into pyramids. See the passage quoted above, on 307a2–3. 307a31–32. πρὸς…τῷ πυρί: cf. above, on 307a2–3.

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307a32–b4. δοκεῖ…τὸ ἀλλότριον: according to Aristotle, whereas the hot brings together and unites things of the same kind, the cold mixes together both like and unlike things. See GC B 2, 329b24–32: qermÕn d kaˆ yucrÕn kaˆ ØgrÕn kaˆ xhrÕn t¦ mn tù poihtik¦ enai t¦ d tù paqhtik¦ lšgetai· qermÕn g£r ™sti tÕ sugkr‹non t¦ ÐmogenÁ (tÕ g¦r diakr…nein, Óper fasˆ poie‹n tÕ pàr, sugkr…nein ™stˆ t¦ ÐmÒfula· sumba…nei g¦r ™xaire‹n t¦ ¢llÒtria), yucrÕn d tÕ sun£gon kaˆ sugkr‹non Ðmo…wj t£ te suggenÁ kaˆ t¦ m¾ ÐmÒfula, ØgrÕn d tÕ ¢Òriston o„ke…J ÓrJ eÙÒriston Ôn, xhrÕn d tÕ eÙÒriston mn o„ke…J ÓrJ, dusÒriston dš. Cf. Mete. ∆ 1, 378b10–25. 307b6. τὸ θερμὸν…τῇ δυνάμει: see previous n. 307b8. οὐθὲν δ’ ἐναντίον ἐστὶ σχήματι: in view of mšgeqoj g£r ti tÕ scÁma in de An. Γ 1, 425a18, i.e. metrhtÒn ti posÒn according to the definition of posÒn in Metaph. ∆ 13, 1020a7–11, this follows from the denial that there are contraries of pos£ in Cat. 6, 5b11–15, though it concerns only ¢riqmht¦ pos£, the first of the two categories of posÒn distinguished in Metaph. ∆ 13, or ¢fwrismšna/diwrismšna pos£ in the terminology of Cat. 6, 4b20–25. scÁma is gšnoj poiÒthtoj, according to Cat. 8, 10a11–15: according to 10b12–17, however, not all poiÒthtej have contraries, and though scÁma is not named in this context, that a scÁma qua poiÒthj does not have a contrary is suggested by the denial a few lines below, in 10b26–11a14, that it admits of a more and a less. 307b11–13. φασὶ…πόρων: Aristotle probably has in mind Plato’s explanation of the sensation of cold. See Ti. 62a6–b6: t¦ g¦r d¾ tîn perˆ tÕ sîma Øgrîn megalomeršstera e„siÒnta, t¦ smikrÒtera ™xwqoànta, e„j t¦j ™ke…nwn oÙ dun£mena ›draj ™ndànai, sunwqoànta ¹mîn tÕ noterÒn, ™x ¢nwm£lou kekinhmšnou te ¢k…nhton di’ ÐmalÒthta kaˆ t¾n sÚnwsin ¢pergazÒmena p»gnusin· tÕ d par¦ fÚsin sunagÒmenon m£cetai kat¦ fÚsin aÙtÕ ˜autÕ e„j toÙnant…on ¢pwqoàn. tÍ d¾ m£cV kaˆ tù seismù toÚtJ trÒmoj kaˆ ·‹goj ™tšqh, yucrÒn te tÕ p£qoj ¤pan toàto kaˆ tÕ drîn aÙtÕ œscen Ônoma. 307b16–17. εἰ ἄνισοι αἱ πυραμίδες: according to Plato, the particles of the Empedoclean elements come in various sizes, for there is not a single number of elementary triangles making up the square faces of the cubical earth particles, and the equilateral triangles which are the faces of the tetrahedral, octahedral and icosahedral particles of fire, air and water respectively. See Pl., Ti. 57c7–d6. 307b19–21. ἐπεὶ δὲ…δυνάμεις: cf. ch. 1, 298a29–b1. For the phrase aƒ kat¦ t¦ p£qh diafora… cf. 306b21–22, with n. ad loc. On the relationship between p£qh and dun£meij see above, on 306b30. Justified here is the topic of book ∆. 307b23. τούτων: sc. tîn dun£mewn, i.e. baršoj kaˆ koÚfou. Cf. the introductory lines of book ∆. tîn paqîn, though, will also do; see above, on 299a20.

BIBLIOGRAPHY EDITIONS Works of Aristotle, Lucretius, Plato and Theophrastus are quoted from the following editions: Aristotle Categoriae (Cat.): L. Minio-Paluello. 1949. Aristotelis Categoriae et Liber De Interpretatione. Oxford (many reprints). Physica (Ph.): W.D. Ross. 1950. Aristotelis Physica. Oxford (many reprints). de Caelo (Cael.): D.J. Allan. 1936. Aristotelis De Caelo Libri Quattuor. Oxford (many reprints). de Generatione et Corruptione (GC): M. Rashed. 2005. Aristote: De la génération et la corruption. Paris. Meteorologica (Mete.): F.H. Fobes, 1919. Aristotelis Meteorologicorum Libri Quattuor. Cambridge MA (repr. Hildesheim 1967). de Sensu et Sensibilibus (Sens.): W.D. Ross. 1955. Aristotle: Parva Naturalia. Oxford (repr. 2001). de Anima (de An.): W.D. Ross. 1956. Aristotelis De Anima. Oxford (many reprints). de Incessu Animalium (IA): W. Jaeger. 1913. Aristotelis De Animalium motione et De animalium incessu; ps.-Aristotelis De spiritu libellus. Leipzig. de Generatione Animalium (GA): H.J. Drossaart Lulofs. 1965. Aristotelis De Generatione Animalium. Oxford (repr. 1972). Metaphysica (Metaph.): W.D. Ross, 1924. Aristotle’s Metaphysics. 2 vols. Oxford (repr. 1953). de Lineis Insecabilibus (LI): M. Timpanaro Cardini. 1970. Pseudo-Aristotele: De lineis insecabilibus. Milan. Lucretius C. Bailey. 19222. Lucreti De Rerum Natura Libri Sex. Oxford (many reprints). Plato J. Burnet. 1900–1907. Platonis Opera. 5 vols. Oxford (many reprints). Theophrastus de Sensibus (Sens.): H. Diels. 1879. Doxographi Graeci. Berlin (repr. 1965).

OTHER LITERATURE* Artmann, B. & L. Schäffer. 1993. “On Plato’s “Fairest Triangles” (Timaeus 54a)”, Historia Mathmatica 20, 255–264. Bodéüs, R. 2000. Aristotle and the Theology of the Living Immortals. Albany NY (English translation by J. Garrett of Aristote et la théologie des vivants immortels, Montreal & Paris 1992). Bowen, A.C. & C. Wildberg (eds.). 2009. New Perspectives on Aristotle’s De caelo, Philosophia Antiqua 117, Leiden & Boston. *

For a comprehensive bibliography on the de Caelo see Bowen & Wildberg (2009).

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INDEX OF PASSAGES Anaxagoras DK 59 B 1: 80 B 12–13: 66 Anaximander

192b8–9: 35 192b8–13: 36 192b13–15: 35 192b21–23: 35 192b27–32: 35 192b32–33: 35

DK 12 A 11: 93 A 16: 93

B 2 193b23–25: 47 193b31–35: 47

Anaximenes

B 8 198b16–32: 63 198b35–36: 65

DK 13 A 5: 93 B 9 200a30–b8: 39 Aristotle Γ 4 203a19–22: 89 Cat. Γ 5 204b22–35: 93 6 4b20–25: 112 5a38–b10: 49 5b11–15: 112

Γ 6 206b20–27: 85 Γ 7 207b27–34: 84, 85

8 10a11–15: 112 10a16–23: 95 10b12–17: 112 10b26–11a14: 112

∆ 8 215a14–17: 75 215b19–216a11: 72 216a13–16: 51, 68, 69 216a27–33: 73

APo A 2 72a14–24: 45

∆ 9 216b22–30: 103 217a26–b12: 103

SE

E 4 228b19–28: 82

34 184b3–8: 81

Z 1 231a21–b18: 46 231b18–232a22: 46

Ph. A 1 184a12–14: 77 A 2 184b25–185a17: 41 A 4 187a12–23: 93 187b7–34: 103–104 A 7 191a2: 108 191a7–12: 108

Z 2 232a25–31: 69 232b20–24: 52 Z 7 237b23–238a19: 71 238a20–31: 72 Z 10 240b8–241a26: 46 H 1 242a49–243a2: 62 H 2 243a20–b2: 75

B 1 192b8–12: 36

117

Index of passages H 5 249b30–250a4: 71

274a2–18: 70

Θ 1 250b23–29: 67 252a3–25: 66, 67 252a11–12: 65 252a19–21: 66–67

A 7 274a30–b5: 91–92 274b2–4: 64–65 275a2–10: 52 275a22–24: 72

Θ 3 253a32–b6: 40

A 9 278a10–15: 39 278b11–15: 33 278b16–18: 33, 34 278b18–21: 36

Θ 4 254b12–14: 37 254b14–15: 37 254b24–33: 38 254b34–255a10: 37 255b13–17: 37

A 10 279b17–31: 43 A 12 283b17–22: 39

Θ 5 256a13–21: 62 Θ 10 266b2–4: 72 266b27–267a20: 74–75 Cael. A 1 268a1–6: 39 A 2 268b14–269a9: 92 268b14–26: 81 268b26–29: 36 268b26–269a2: 82 269a2–9: 73, 82 269a9–12: 60 269a18–23: 12, 85 269b2–17: 34 269b6–9: 12 269b12–13: 61 A 3 269b23–26: 63 269b29–35: 73 270a12–35: 39 270b2–3: 12, 34, 40 270b15–16: 34 270b16–25: 80 270b20–24: 12 A 4 271a33: 72 A 5 271b8–13: 45 271b26–272a7: 85 A 6 273a25–27: 52 273a27–b3: 52 273b3–5: 52 273b5–6: 52 273b30–274a2: 70

B 1 284a3–6: 12 284a35–b2: 35 B 2 284b15–24: 34 285b33–286a2: 34 B 3 286a18–20: 59 286a23–24: 53 286a23–26: 59–60 286b6–9: 15 B 4 286b10–287a5: 12, 35 286b20: 85 287a11–12: 38, 61 287b14–21: 107–108 287b20–21: 36 B 6 288a13–18: 12, 33 288a22–27: 13 288a27–b7: 13 B 7 289a11–13: 34 289a11–19: 12, 15 289a13–16: 34 289a19–35: 15 B 12 291b28–292a3: 35 292a11: 34 292b22–25: 33 293a4–11: 33 B 13 294a10–b30: 61 294b32–295a7: 59 295a4–7: 60 295a7–b9: 61 B 14 296b25–297a2: 73

118

Aristotle’s de Caelo Γ 297a8–12: 74

∆ 1 308a7–8: 51 308a29–33: 53 ∆ 2 309a2–5: 51 309b5–8: 51 309b12–14: 51 ∆ 3 310a31–b15: 37 ∆ 4 311a16–29: 51–52, 73 311b4–10: 73

330b7–21: 83 330b21–331a1: 13 330b30–33: 63 331a1–3: 36 331a3–6: 13 B 4 331a7–23: 101, 105 332a1–2: 39 B 5 332a4–18: 92, 99 332a18–26: 92 332a27–30: 105 332a34–b5: 83 332b30–333a15: 85

GC A 1 314a6–13: 101–102 314a24–b1: 80 314b17–18: 108 314b17–20: 87 315a20–21: 36

B 6 333a16–34: 79 334a5–7: 68 B 7 334b20–24: 79 334b20–30: 13, 14, 79 334b24–30: 79

A 2 315b6–15: 89 315b24–316a14: 105, 111 316a14–34: 57 317a11–12: 45

B 8 335a5–6: 36

A 3 318b2–14: 94

Mete.

A 4 319b6–14: 38

A 2 339a11–19: 40, 106 339a11–27: 11, 13 339a26–27: 63

A 5 320a32–b12: 102 A 8 325a23–b5: 87–88 325b5–10: 100 325b17–19: 89 326a13–14: 53 326b6–28: 100 A 10 327b22–31: 78 327b33–328a31: 109 328a5–12: 84 328a23–31: 14, 79 328a31–35: 100 B 2 329b7–18: 106 329b16–18: 85 329b24–32: 112 329b34–330a4: 95 330a8–29: 53 B 3 330a30–b7: 13, 83 330b2: 79

B 10 336a15–b26: 14 337a7–15: 13, 14

A 3 339b16–19: 11, 40 339b21–23: 80 340a1–13: 14 340a6–8: 38 340a8–13: 97–98 340a11–13: 14 340b6–10: 11, 13 340b19–23: 11 340b33–341a2: 38 341a2: 38 341a28–31: 75 A 4 341b6–22: 11, 14 342a24–27: 75 ∆ 1 378b10–25: 112 ∆ 4 382a8–11: 53 382a11–14: 53–54

119

Index of passages ∆ 10 388a13–20: 77

∆ 4 1015a13–19: 35

de An.

∆ 8 1017b10–11: 36 1017b10–14: 36 1017b17–21: 58

A 2 403b27–404a16: 89 404a1–5: 89

∆ 10 1018a25–31: 60 A 4 408a14–15: 79 Γ 1 425a18: 112 Sens.

∆ 12 1019a15–18: 37 1019a19–20: 38 ∆ 13 1020a7–11: 112 1020a7–32: 48

6 445b3–20: 50 445b4–6: 48 445b21–29: 48 445b20–446a20: 50 445b29–30: 49

E 1 1025b3–28: 41 1026a10–16: 41 1026a16–23: 41 1026a27–32: 41

PA

Z 2 1028b8–13: 36 1028b12–13: 37

B 1 646a12–24: 37

Z 8 1033b5–8: 41

IA

Z 13 1039a3–14: 88 1039a10: 61, 87

9 708b22–23: 109–110 Θ 8 1049b24–27: 76 GA I 1 1053a30: 58 A 18 722b20: 63 K 3 1061a28–b4: 47, 48 A 22 730b19–22: 72 Λ 6 1071b33–37: 61 ∆ 10 777b16–778a9: 15 Λ 7 1072a19–24: 33 E 8 789b2–4: 72 Metaph. A 1 981a24–b2: 83 981b10–12: 83 A 3 983b6–984a8: 92 983b27–984a3: 42

Λ 8 1073a23–34: 33 1073a23–36: 35 1073b32–1074a4: 84 M 2 1076b18–19: 41 1077a31–b2: 58 1077b12–17: 47 M 3 1077b17–1078a31: 47

A 4 985b3–20: 61 M 4 1078b12–17: 42 A 5 986a22–26: 36 M 6 1080b16–20: 58 A 6 987a29–b10: 42 M 8 1083b11–19: 59 ∆ 3 1014a26–35: 36, 78

120 M 9 1085b22: 58 N 3 1090a30–35: 59

Aristotle’s de Caelo Γ 12.3: 89 7: 90 10: 90 17: 90

EE Eudemus B 11 1227b23–32: 45 fr. 62 Wehrli: 85 [Aristotle] Hesychius Mech. π 1799 Schmidt: 88 848b23–35: 75 Leucippus LI 968a9–14: 105 968a14–18: 107 969b26–31: 43 969b31–33: 45 969b33–970a5: 45 970a5–19: 45 970b29–31: 46 971a11–14: 54 971a13–21: 58 972a6–13: 57 Democritus

DK 67 A 7: 87–88 A 8: 88 A 9: 89 A 15: 87 A 28: 89 Lucretius 1 551–564: 100 615–622: 85 Melissus DK 30 B 8: 40

DK 68 A 47: 61 A 135: 88, 89

Parmenides

Diogenes Laertius

DK 28 B 6–7: 40 B 8.1–22: 40

9.45–49: 109 Empedocles DK 31 A 43a: 100 B 13: 103 B 17.30–35: 42 B 57.1: 63

Philoponus in Mete. (Hayduck) 16.23–25: 81 37.8–14: 38 Plato

Epicurus

Ti.

Ep. ad Hdt.

29d7–30a6: 62 50a4–b4: 104 50e4–51a3: 108 52d1–53b5: 62 53c4–54b2: 106 53c4–56c7: 42 54b6–d2: 105 55c4–6: 111

56–57: 85 Euclid El. 1.10: 45

121

Index of passages 55d7–56b6: 96, 109, 110, 111 55e7–56b6: 56 56d1–57b7: 110 57c7–d6: 112 58a4–b2: 96–97 58a4–c4: 107 61d5–62a6: 110 62a6–b6: 112 63b2–e7: 49, 111 79a5–80a2: 75

Cra.

596.22–23: 75 596.28–30: 75 596.32–597.5: 75–76 598.3–7: 76 598.14–17: 76 600.10–13: 76 602.5–13: 79 609.24–25: 88 616.15–20: 94 621.20–25: 97 629.18–29: 100–101 630.1–5: 100 631.1–5: 101 636.20–27: 104 647.3–14: 107 662.10–12: 110

412c6–413c3: 97

in Ph. (Diels)

[Plato]

981b3–c8: 111

24.26–25.1: 93 28.4–11: 88 459.23–26: 85 1350.31–36: 73 1351.28–29: 75

Proclus

Theophrastus

in Euc. (Friedlein)

Sens.

277.25–279.4: 45

66: 88 67: 89

Tht. 152d2–e9: 42

Epin.

Simplicius Xenocrates in Cael. (Heiberg) 6.33–7.2: 39 293.12–15: 43 542.27–30: 74 552.1–7: 33 552.7–19: 34 562.21–30: 43 563.9–12: 45 563.18–20: 45–46 563.20–25: 46 563.26–564.3: 46 581.19–24: 60 584.29–585.1: 63 586.16–23: 63–64 588.12–13: 64 588.17–19: 64 589.20–21: 66 591.21–25: 68 596.20–21: 75

fr. 127 Isnardi Parente: 107

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91.

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und Textgeschichte 2007. 154 S., geb. ISBN 978-3-515-09102-2 92. Efstratios Sarischoulis Schicksal, Götter und Handlungsfreiheit in den Epen Homers 2008. 312 S., geb. ISBN 978-3-515-09168-8 93. Ugo Martorelli Redeat verum Studi sulla tecnica poetica dell’Alethia di Mario Claudio Vittorio 2008. 240 S., geb. ISBN 978-3-515-09197-8 94. Adam Drozdek In the beginning was the apeiron Infinity in Greek philosophy 2008. 176 S. mit 11 Abb., geb. ISBN 978-3-515-09258-6 95. Eckart Schütrumpf Praxis und Lexis Ausgewählte Schriften zur Philosophie von Handeln und Reden in der klassischen Antike 2009. 368 S., geb. ISBN 978-3-515-09147-3 96. Theokritos Kouremenos Heavenly Stuff The constitution of the celestial objects and the theory of homocentric spheres in Aristotle’s cosmology 2010. 150 S., geb. ISBN 978-3-515-09733-8 97. Bruno Vancamp Untersuchungen zur handschriftlichen Überlieferung von Platons „Menon“ 2010. 115 S., geb. ISBN 978-3-515-09811-3 98. Marietta Horster / Christiane Reitz (Hg.) Condensing texts – condensed texts 2010. 776 S., geb. ISBN 978-3-515-09395-8 99. Severin Koster Ciceros Rosciana Amerina Im Prosarhythmus rekonstruiert 2011. 178 S., geb. ISBN 978-3-515-09868-7 100. Theokritos Kouremenos Aristotle’s de Caelo Γ Introduction, Translation and Commentary 2013. 121 S., geb. ISBN 978-3-515-10336-7

This is the first full-scale commentary on Aristotle’s de Caelo Ɗ to appear in recent decades. de Caelo Ɗ can serve as a good introduction to Aristotle’s physics and its character. In it he answers some very general questions about the elements of all material things except celestial objects: how many these elements are, why they cannot be infinitely many but must be more than one, whether they are eternal or can be generated and decay, and, if the second, how. His discussion is often

framed as a critique of rival theories, and he argues systematically against the geometrical theory of the elements in Plato’s Timaeus, which adds greatly to the interest of the work. The commentary adduces many parallel passages from Aristotle’s other works to round off the reader’s understanding, and the introduction offers a brief but comprehensive overview of the Aristotelian theory of the elements, which de Caelo Ɗ often takes for granted.

www.steiner-verlag.de Franz Steiner Verlag

ISBN 978-3-515-10336-7