Heavenly Stuff: The constitution of the celestial objects and the theory of homocentric spheres in Aristotle's cosmology 3515097333, 9783515097338

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Theokritos Kouremenos Heavenly Stuff

PALINGENESIA Schriftenreihe für Klassische Altertumswissenschaft

Begründet von Rudolf Stark nach Otto Lendle und Peter Steinmetz herausgegeben von SEVERIN KOSTER –––– Band 96

Theokritos Kouremenos

Heavenly Stuff The constitution of the celestial objects and the theory of homocentric spheres in Aristotle’s cosmology

Franz Steiner Verlag Stuttgart 2010

Bibliografische Information der Deutschen Nationalbibliothek: Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar. ISBN 978-3-515-09733-8 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. © 2010 Franz Steiner Verlag, Stuttgart Druck: Offsetdruck Bokor, Bad Tölz Printed in Germany

To my brother Nikos and to my sister Chrissie

CONTENTS Preface………………………………………………………………………………9 1. ARISTOTLE’S COSMOLOGY 1.1. Plants and animals vs. celestial objects…….}………………………………11 1.2. The four traditional simple bodies ..…………..}}}}}}}}}}}…13 1.2.1. Fire, air, water and earth, and their qualities .….……}}}}}}}….13 1.2.2. The change of one simple body into another …….……}}}}}}}…14 1.2.3. The formation of compound bodies .….....…….……………………..….15 1.2.4. The mass-ratio of two traditional simple bodies on the cosmological scale ..…..……………..……………………}……16 1.2.5. The Sun and the change of the traditional simple bodies into one another ………….………………………………………..17 1.3. The ¿rst simple body…………………………………………………………}19 1.3.1. The upper body ……….….………………………………………………}19 1.3.2. The heavens.. ………...……………………………………………………20 1.3.3. Diurnal rotation and the concept of the celestial sphere ………………….21 1.3.4. Enter the ¿rst simple body ……..…..…………………………………….24 1.3.5. The non-diurnal motion of the Sun, the Moon and the planets …}}}26 1.3.6. The ¿rst simple body and the four traditional simple bodies ...…}……30 1.3.7. The eternity of the ¿rst simple body’s natural motion ..…….……………32 1.3.8. The ¿rst simple body and the stars, the planets, the Sun and the Moon ..……...…………………………………………………….32 1.4. Eudoxus’ theory of homocentric spheres and Aristotle’s Metaph. ȁ 8…}}33 1.4.1. A brief outline ..}…….…………………………………………………33 1.4.2. A closer view……}……………………………………………………… 35 1.4.3. “Failings” of the theory of homocentric spheres ..…….………………….38 1.4.4. Aristotle’s physicalization of the theory of homocentric spheres ..…….…}}}}}}}}}}}}}}}}40 1.4.5. The unmoved movers in the heavens ...……...…………………………….41 1.4.6. Ph. Ĭ 10 and the theory of homocentric spheres ...……..………………}43 1.5. What comes next ..…….….……………………………………………………46 2. THE STUFF OF THE HEAVENS 2.1. Introduction………………………………….}………………………………50 2.2. The first simple body in Cael. A 2 –3 ………..}}}}}}}}}}}…53 2.2.1. The first simple body in Cael. A ……………………}}}}}}}….53 2 2.2.2. The first simple body in Cael. A 3 .……………………}}}}}}}…57 2.2.3. The three senses of the noun ouranos in Cael. A 9 …………………..….58 2.2.4. aithƝr ..}}}}}}}}}}}}}}}}}}}}}}}}}}60

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Contents

2.3. The evidence from Cael. B 4……………………..……………………}……62 2.4. The ¿rst simple body in Cael. B 12 …………………………………………67 2.5. The evidence from the introduction to Cael. ………………………………..68 ī 2.6. The evidence from the introduction to Cael. B……………………………}69 2.7. Fire as the second upper body in the de Caelo………………………………}71 2.8. The argument in Mete. A 3 for the existence of the ¿rst simple body ..………74 2.8.1. An outline .……………………………………………………………….74 2.8.2. The preamble to the argument ..………………………………………….75 2.8.3. The argument ..……………………………………………………}}}77 2.8.4. The astronomical premises .}}}}}}}}}}}}}}}}……80 2.8.5. Conclusion .………………………………………………………………84 3. ARISTOTLE AND THE THEORY OF HOMOCENTRIC SPHERES 3.1. Introduction………………………………….}………………………………86 3.2. Is there a reference to the theory of homocentric spheres in Cael. B 6?………91 3.2.1. An argument in light of Ph. E 4 ……………………}}}}}}}….91 3.2.2. Aristotle and Callippus in Metaph. ȁ 8 ………………}}}}}}}…93 3.2.3. Concluding considerations .…………………….……………………..….96 3.3. Is there a reference to the theory of homocentric spheres in Cael. B 12?…………………………..……………………}…… 97 3.3.1. Introduction .}}}}}}}}}}}}}}}}}}}}}}}}97 3.3.2. The two problems Aristotle attempts to solve in Cael. B 12}}}………98 }………………………………………}99 3.3.3. The solution to the ¿rst problem 3.3.4. The ¿rst solution to the second problem………………………………}102 3.3.5. The second solution to the second problem }}}}}}………………103 3.3.6. Conclusion……………………………………………………………….110 3.4. The conception of the heavens and celestial motions in Cael. B 10 ...}}}111 3.4.1. Zodiacal motion as resisted by the diurnal rotation .……………}}}111 3.4.2. Cael. B 12 and the conception of celestial motions in Cael. B 10 ....……114 3.4.3. The rejection in Cael. B 9 of a Pythagorean celestial harmony ...………115 3.4.4. A hint for the forced motion of the wandering luminaries in Cael. B 1 .………………………………………………….116 3.5. Cael. A 4 and the theory of homocentric spheres}}}}}}}}}}}116 3.5.1. The last argument in Cael. A 4 ..…………………………………………116 3.5.2. The other arguments in Cael. A 4 ...…………………………………….120 3.5.3. The introduction to Cael. B 3 and the conclusion of Cael. B 2 ...………121 3.6. Metaph. ȁ 8 ..}}}}}}}}}}}}}}}}}}}}}}}}125 3.7. Conclusion….}}}}}}}}}}}}}}}}}}}}}}}}}}129 Appendixes .}}}}}}}}}}}}}}}}}}}}}}}}}}}132 Bibliography .}}}}..…….….…………………………………………………141 Index of passages }}}}}}}}}}}}}}}}}}}}}}}}}145

PREFACE As described by modern cosmology, the true composition of the universe bears no resemblance to our composition and to that of our surroundings, or to that of anything we can observe far beyond them. We, everything around us and all we can see consist of baryonic matter, but a not yet detected nor well understood “cold dark matter” dominates on the scales of galaxies and cluster of galaxies; over truly cosmological scales, dominant is a completely mysterious “dark energy”, the most abundant content of the universe. The idea that the cosmos, for the most part, contains something very different from what constitutes us, our local environment and its furniture can be traced back to Aristotle, though his conception of the cosmos is a very distant ancestor of ours: the stars of our galaxy, which are visible with the naked eye, arranged spherically around the Earth–that is, the celestial sphere, or the sphere of the ¿xed stars, physically conceived–with the ¿ve planets of our solar system known in antiquity–Saturn, Jupiter, Mars, Venus and Mercury–and the Sun and the Moon in between. Aristotle believed that all celestial objects consist of the same substance that pervades the heavens, which are almost the whole of the cosmos. This stuff is unlike those found near the center of the cosmos which compose us and everything immediately around us, the famous four elements introduced by Empedocles of Acragas in the ¿fth century BC. Within Aristotle’s physics, it is as puzzling as dark energy is today within our physics. It is commonly known as ether, and its distant descendant, “the luminiferous ether”, played a role in the development of Einstein’s special theory of relativity, and thus of his general theory, too, a pillar of modern physics and cosmology. I argue in this monograph that Aristotle did not introduce this heavenly stuff at one go, but originally as matter only of the remotest celestial objects from the Earth–the stars–and as ¿ller of the spherical shell they are ¿xed in–the crust, or nutshell, of the cosmos. I also argue that at no point in the development of his cosmological thought did Aristotle hold that the theory of homocentric spheres of Eudoxus of Cnidus, who seems to have aimed at modeling geometrically some aspects of the observed motions of the planets, the Sun and Moon, mirrors the structure of the heavens. I would like to thank Prof. Dr. Severin Koster for accepting this monograph in the Palingenesia series; Mr Harald Schmitt, Ms Katharina Stüdemann and Ms Susanne Szoradi of Franz Steiner Verlag for their help in the final run-up to publication; my friend and former student Alexandros Kampakoglou for aid with certain bibliographical items. That this work might not have been completed without the help, understanding and, above all, patience of my wife, Poulheria Kyriakou, is not an exaggeration. Theokritos Kouremenos Aristotle University of Thessaloniki

1. ARISTOTLE’S COSMOLOGY 1.1. PLANTS AND ANIMALS VS. CELESTIAL OBJECTS In Cael. B 5 Aristotle sets out to answer the surprising question why the direction of the diurnal rotation is from east to west, not the other way around.1 Since he believes that, in contrast to what is the case with plants and animals, substances coming into being and passing away, nothing occurs randomly in the eternal realm of celestial objects, there cannot but be some reason why the diurnal rotation is from east to west (287b24–28). His brief explanation is prefaced by some words of caution, betokening understandable distress at his raising and trying to settle, albeit tentatively, the issue at hand. To try to pronounce an opinion on intractable matters, such as the one Aristotle himself is looking into here, and the unwillingness to circumvent any subject might be considered a symptom of excessive eagerness to investigate or, worse, simple-mindedness. However, it is unfair, Aristotle continues, to chastise indiscriminately all those who dare tackle some very dif¿cult problems without ¿rst taking into account their reason for so doing, and without considering whether the con¿dence, with which they put forward their proposed solutions, is commensurate with human cognitive limitations or not. He concludes by saying that, in explaining why the diurnal rotation is from east to west, he will say just what seems to him to be the case, and that we ought to be grateful to future thinkers who might be successful in coming up with adequate explanations of necessarily compelling nature (287b28–288a2).2 Similar sentiments are expressed in Cael. B 12. Aristotle opens this chapter with the remark that he must attempt to state what seems to him to be the case as regards two bafÀing problems, whose dif¿culty anyone would acknowledge, concerning the celestial objects and their motions.3 His eagerness to attack such impenetrable questions is a sign of humility, not impetuousness, stemming from the willingness, due to a desire for knowledge, to be satis¿ed with making even very small steps towards an understanding of those things which we are most puzzled about (291b24–28). Before going on to put forward what by his lights is just a plausible solution to the problems at issue, Aristotle notes that it is good to try to expand our understanding of the celestial objects, though our starting points are necessarily scanty, for enormous distances separate us from the celestial phenomena (292a14–17).4 But his deep conviction that the study of these phenomena is an intrinsically worthy enterprise motivates him to forge stubbornly ahead. 1 2 3 4

For the diurnal rotation, and the associated concept of the celestial sphere, see 1.3.3. What Aristotle contrasts at the end of this passage are X¶JEMR³QIRSR and EdƒOVMF{WXIVEM ƒR„KOEM, however the latter might be understood. Here, too, “what seems to be the case” translates X¶JEMR³QIRSR (cf. previous note). Cf. Cael. B 3, 286a3–7.

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1. Aristotle’s cosmology

Aristotle stresses how dif¿cult it is to study the celestial objects also in the preface to PA (A 5), where he adds that the dif¿culty is more than adequately made up by how much excitement even a small progress in this area can generate. Contrasting the study of the eternal and divine celestial objects with the inquiry into transient plants and animals, he notes that the former is much worthier, for it deals with an eternal and divine, hence more valuable, subject-matter, but is unfortunately hampered by the fact that very few starting points are available to our senses, from which we can theorize about the celestial objects and those phenomena they exhibit that we desire most to understand. To obtain knowledge of perishable plants and animals is easier, because they live with us, here on Earth. As a consequence, we can learn much about each kind of plant and animal if we are willing to undertake suf¿cient efforts. If we manage to advance even a little our understanding of the heavens, however, this knowledge is so valuable that to possess it is more pleasurable than to have grasped all things that are close to us, just as to have been granted a mere glimpse of those we are in love with is more gratifying than the detailed inspection of many and much larger, or much more important, things (644b22–35).5 The beautiful PA passage might have inÀuenced a section in Cicero’s Lucullus, 127–128, where Cicero himself explains an Academic skeptic’s cognitive attitude towards the study of celestial objects. In Cicero’s view, the study of nature in general is a kind of natural food for thought. By inquiring into the highest reaches of the cosmos we are uplifted, and led to look down upon our totally insigni¿cant affairs. He admits that these are matters as extremely inscrutable as they are supreme in importance, and adds that if we chance upon some ideas about the heavens that appear to have a likeness to what is true, our mind is ¿lled with the kind of pleasure most appropriate to human beings. The Stoics, Cicero says, study the phenomena of the sky in order to affirm the truth of whatever conclusions they might be led to, but the Academic skeptics, wary of holding rash opinions, engage in the same branch of intellectual endeavor ready to be content with what seems to bear a likeness to the truth. Aristotle does not think that the celestial objects are different from plants and animals only insofar as our epistemic access to them is concerned. It is generally agreed that, within the framework of his physics, at least after an initial phase of its evolution, for which we have very little, if any, evidence, the celestial objects are assumed to be made out of a kind of matter totally different in nature from those kinds of matter that are thought to make up all plants and animals.6 The second 5 6

On the passages discussed so far see Falcon (2005) 85ff. An initial phase in the evolution of Aristotle’s physics, when he did not posit the existence of a special celestial matter, has been detected in the fragments of his early dialogue On Philosophy. See Solmsen (1960) 287, with n. 1, and Hahm (1982) 60, with n. 2. Hahm denies that in his lost work Aristotle introduced this novel kind of matter. Freudenthal (1995) 101–105 argues that is was introduced some time after the composition of the dialogue On Philosophy, as direct development of the physics Aristotle elaborated therein. Modern developmental accounts of Aristotle’s physics usually focus on the evolution of his views about the ultimate sources of all motion and change in the cosmos. Surveys in Graham (1996) 171–172 and Graham (1999) xiii–xiv.

1.2. The four traditional simple bodies

13

chapter of this study is an attempt at elucidating the stages at which Aristotle introduced this celestial matter.

1.2. THE FOUR TRADITIONAL SIMPLE BODIES 1.2.1. Fire, air, water and earth, and their qualities Everything within the scope of our immediate experience is, according to Aristotle, ultimately made up of four kinds of elementary body, matter continuous in all three dimensions, or of four simple bodies.7 These simple bodies are the “traditional” elements Empedocles of Acragas introduced into physics in the ¿fth century BC: ¿re, air, water and earth. Their simplicity lies in their unanalyzability into other bodies.8 Aristotle thinks of them as combinations of qualities, which form two pairs of contraries. Earth is dry and cold, water is cold and wet, air is wet and hot, ¿re is hot and dry (GC B 3, 331a3–6); 9 as he explains in Mete. A 3, what is habitually called “¿re” is the simple body of the same name when undergoing combustion (340b19–23). On what can be appropriately called “the cosmological scale” in this context, these four simple bodies are sorted out concentrically. The simple body earth is clumped around the center of the cosmos into a globe–the Earth; the simple body water is concentrated on the surface of this globe within a spherical shell of air, around which there is a spherical shell of ¿re.10 All things in our close surroundings are ultimately constituted by all of these four simple bodies, bound together in insigni¿cant amounts by comparison to how much of each exists in the cosmos (GC B 8, 334b30–335a9).11 This makes clear that, although the four traditional simple bodies are always neatly strati¿ed on the cosmological scale, on much smaller scales they are not separated at any given time. They cannot be completely sorted out, Aristotle explains in GC B 10, 337a7–15, because, on scales much smaller than the cosmological scale, they constantly transform into one another, and, as a result, the concentration of each on the cosmological scale contains bits of all others, an exception, as Aristotle seems to suggest in Mete. A 3, being the outermost part of the For the three-dimensional continuity of bodies see Cael. A 1, 268a1–10, an introductory characterization of what is studied in physics. 8 See the de¿nition of “element” in Cael. ī 3, 302a15–25. 9 The qualities constituting each and every portion of one of these four simple bodies can be paralleled to the so-called tropes, or abstract particulars, of modern metaphysics. Brief introductory account in Mellor & Oliver (1999) 17–20; fuller discussion in Williams (1999), Campbell (1999). Cf., though, Gill (1991a) 77–78. 10 Aristotle demonstrates in Cael. B 4 that the cosmos is strati¿ed into spherical shells, with the Earth as the central sphere. Some of his arguments are discussed below, in 2.3. 11 Aristotle’s explanation of why the constitution of any medium-sized object must include air and ¿re, too, is problematic. See Williams (1982) 178–179. Presupposed might conceivably be the assumption that all of the four traditional simple bodies are present near the surface of the Earth, where medium-sized objects exist, and the application of the principle that everything is made out of the body, or bodies, in which it is situated; see below, 1.3.1. 7

14

1. Aristotle’s cosmology

shell of ¿re (340b6–10; see Appendix 2), and perhaps the depths of the Earth (this seems to be implied by GC B 3, 330b33–331a1).12 As we will see next, such impurities must exist in the ¿rst place if the four Empedoclean simple bodies are to be transmuted into one another.

1.2.2. The change of one simple body into another We will leave aside for the time being what powers this change and how, to discuss how the analysis of the four traditional simple bodies into qualities allows them to turn into one another within the framework of Aristotelian physics. Aristotle describes three transmuting processes in GC B 4. By the ¿rst of them, ¿re transforms into air, air into water, water into earth, and earth into ¿re; this cyclical change can occur in the other direction. By the second process, ¿re turns into water, air into earth, water into ¿re, and earth into air. By the third process, ¿re and water change jointly into earth or air, air and earth into ¿re or water.13 The three processes that transmute one or two traditional simple bodies into another involve physical contact and interaction between two simple bodies.14 But the real agents are the contraries. Two traditional simple bodies act on each other in virtue of their contraries. The cold e.g. 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 come into contact, each quality acts on its contrary. The cold tries 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 (GC B 7, 334b20–29).15 But if the cold of e.g. earth assimilates itself to For ¿re inside the Earth see Mete. B 4, 360a5–6, B 8, 365b24–27. Probably the best explanation of its presence is the mixture of all four traditional simple bodies in the surface layers of the Earth. When Aristotle speaks in GC B 3, 330b33–331a1, of the two simple bodies earth and ¿re as the purest of the traditional simple bodies, for they are “extremes”, whereas the other two are “intermediates”, it is quite unlikely that he tacitly denies the existence of impurities in the surface layers of the Earth and in the lowest layers of the spherical layer of ¿re. On terrestrial ¿re see also Freudenthal (1995) 70–73. 13 For the three transmuting processes see the helpful account in Gill (1991a) 67–77. 14 For the requirement that there must be physical contact between an agent and what is being acted upon by the agent see Aristotle’s description in Ph. ī 2, 202a3–12, of how a change is brought about by an agent; cf. GC A 6, 322b22–25. 15 On Aristotle’s “law of action and opposite reaction” see GA ǻ 3, 768b15–25, and cf. Kouremenos (2002) 114–115. That something which is hot or cold in actuality is cold or hot in potentiality, and can thus, under the right conditions, become actually cold or hot is stated by Aristotle in GC B 7, 334b20–22; for the principle at work here see GC A 7, 323b18–324a9. The transformation of one, or two, of the four traditional bodies into another occurs, as explicitly said in GC B 7, 334b20–29, if two interacting contraries, each of which is in potentiality the other, are not equal, or, as Aristotle puts it in GC A 10, 328a23–31, when the quantity of one of the two interacting simple bodies does not match the amount of the other in power; what is called “power” here is the capacity of each mass to assimilate the other to itself, by acting on the antagonist in virtue of its having in actuality the quality the antagonist has only in potentiality. For how Aristotle supposes this power to be quanti¿able in theory–nothing hints that he 12

1.2. The four traditional simple bodies

15

the hot of ¿re, earth turns into ¿re, the dry being common to both. A simple body has turned into another by the ¿rst 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. Finally, in the third process, only one quality of each simple body turns into its contrary: e.g. the dry of ¿re assimilates to itself the wet of water, the cold of water assimilates to itself the hot of ¿re, and the result of the interaction is dry and cold earth. A mass of e.g. earth outside its “natural place”, where most of this simple body is collected at any given time, tends naturally to accrete to the clump. It moves there spontaneously, provided that no impediment stops it. This “natural motion” of the four traditional simple bodies is conceived of as following radii of the spherical cosmos. Two of these four simple bodies, earth and water, move towards the center of the cosmos, and are heavy insofar as they possess the potentiality to do so. The remaining two, air and ¿re, shoot up away from the center of the cosmos towards the periphery, and are thus light insofar as they have the potentiality to do so.16

1.2.3. The formation of compound bodies What happens if the contraries are equal in their powers? 17 If one can judge safely from GC B 7, neither agent turns into the other or suffers any change–the two simple bodies are left intact (334b20–23). However, if the contraries are equal in power only approximately, they 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 (334b23–29).18 The simple bodies cannot possibly be identi¿ed in a compound, but their potentiality is preserved in it, and so they will exist in actuality once again, when the compound will eventually decomever had to deal with the practical problem of really measuring it, or that he even simply felt the need for such measurements–see the discussion in Kouremenos (2002) 104–106 (its conclusions are applied next to the formation of composites from the four traditional simple bodies, on which see also the following section here, and to the transformation of one, or two, of the four traditional simple bodies into another, processes intimately related, as will be explained in a moment). 16 All quantities of a traditional simple body have an equal tendency to approach the center of the cosmos, or move away from it; cf. Cael. B 14, 297a8–30. For the rectilinear natural motion of the four traditional simple bodies see Cael. A 2, where, though, Aristotle does not consider it necessary to explicitly identify with radii of the spherical cosmos the paths followed by the naturally moving masses of the four traditional simple bodies; he simply characterizes the direction of motion along the paths at issue as “downward” and “upward”, or as being towards an unspeci¿ed middle-point, which is actually the center of the cosmos, and away from it. For weight and lightness see Cael. A 3, 269b20–29. 17 For Aristotle, comparable in power are not two contrary qualities themselves, but the quantities of two Empedoclean simple bodies, each of which interacts with the other in virtue of its being constituted by one of the two contrary qualities at issue. See above, n. 15, and the ¿nal paragraph of this section. 18 GC B 7, 334b20–29, is discussed in Kouremenos (2002) 108–109.

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1. Aristotle’s cosmology

pose (GC A 10, 327b20–31).19 Clearly, the transformation of the four traditional simple bodies into one another and the formation of compounds from all four of them are Àipsides of the same coin. Which dispositional properties emerge, and thus which compound body is generated, seems to be determined by how close to equality in power the contraries are (GC B 7, 334b23–29). 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 compound bodies depends on the relations in which these quantities happen to stand to one another (GC A 10, 328a23–31, de An. A 4, 408a14–15). It thus follows that whether the contraries are exactly equal in power, or unequal enough for the one to assimilate the other into itself, cannot but also depend on the relation between the amounts of the simple bodies that interact (this is also clear from 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).20

1.2.4. The mass-ratio of two traditional simple bodies on the cosmological scale As it turns out, the total amounts of the simple bodies ¿re and air existing in the cosmos at any given moment must have such a ratio to each other that their contraries, the dry and the wet respectively, are exactly equal in power; as with ¿re and air, so with air and water, water and earth, air and earth. The simple bodies in a pair are adjacent on the cosmological scale, so each acts on the other, and those in the ¿rst three pairs can turn into each other by the ¿rst of the three mechanisms for elemental change explained in GC B 4; the transmutation of the fourth pair into each other involves the second mechanism, whereby both qualities of a simple body change into their contraries. However, the possibility that one of the two simple bodies in a pair assimilates the other to itself on the cosmological scale must obviously be precluded, and so must be the possibility of a pair’s uniting into a compound body on that scale. That two of the Empedoclean simple bodies adjacent on the cosmological scale have always a certain mass-ratio on that scale is an assumption playing a crucial role in an argument Aristotle sets out in Mete. A 3 to drive home the unavoidable need for his belief that a ¿fth simple body exists besides ¿re, air, water and earth (340a1–13). This simple body is the aforementioned kind of matter which, as is generally agreed among scholars, the celestial objects are assumed to consist of within the framework of Aristotle’s physics, at least after a very poorly known early phase in

19 20

On the potential persistence of the four traditional simple bodies in a compound see most recently Scaltsas (2009) 242–258. For a discussion of this passage see Kouremenos (2002) 104–108.

1.2. The four traditional simple bodies

17

the evolution of his cosmology, which can very well be a ¿gment of scholarly imagination.21 On much smaller scales, of course, the four Empedoclean simple bodies always both transform into one another and unite into compound bodies. As a consequence, local mass-gains and mass-losses of each of these simple bodies must be assumed to balance out precisely, in order for the mass-ratio of a pair of adjacent simple bodies on the cosmological scale to be always the same. The ratio between a quantity of a traditional simple body and that of the cosmically adjacent such body into which it can turn is assumed in Mete. A 3 to be equal to the mass ratio of the simple bodies in question obtaining on the cosmological scale (340a11–13).

1.2.5. The Sun and the change of the traditional simple bodies into one another In GC B 10, Aristotle names “the double motion” of the Sun as the cause of the constant generation of the four traditional simple bodies from, and of their decay into, one another, as well as of the incessant formation of compound bodies from all of these four simple bodies, and of their decay: the apparent diurnal motion of the Sun, and its apparent annual motion in the ecliptic.22 He lays particular emphasis on the annual motion, though, perhaps because it relates to the life-cycles of plants and animals, compounds of the four traditional simple bodies in which Aristotle has keen interest (337a7–15; cf. 336a15–b24).23 This causal account is also hinted at in Cael. B 3, where Aristotle promises to be clearer later on, perhaps a reference to GC B 10. There, too, he is quite short on details, however. The apparent diurnal motion of the Sun mirrors the rotation of the Earth itself, and accounts for daily variations in the heating of the Earth by the Sun. The Sun’s apparent annual motion reÀects the Earth’s orbiting the Sun, and thus brings about seasonal variations in the solar heating of the Earth. It must be this heating that causes the four traditional simple bodies to change into, and interact with, one another on scales much smaller than the cosmological scale. In Cael. B 3 Aristotle hints at a possible role of the planets and the Moon as causes of the perpetual transformation of the four Empedoclean simple bodies into one another, as well as of the generation of various compound bodies, and thus of complex medium-sized objects, out of them (286b6–9). The Sun, Aristotle says in Cael. B 7, generates heat and light indirectly. Moving rapidly around the Earth, it acts on the mass of air which at any given moment the bulk of the Earth does not prevent from being so acted upon; this air-mass produces heat and light. The action of the Sun on the air is frictional, like the action of a rough surface on the inÀammable material of a match against which it is scratched. It is apparently in virtue of its being already hot that air can be further I have discussed the Mete. A 3 argument in Kouremenos (2002) 120–125. More detailed discussion of some of its aspects below, in 2.8. 22 The annual motion of the Sun in the ecliptic is discussed below, in 1.3.5. Its diurnal motion is due to its sharing in the diurnal rotation, for which see below, 1.3.3. 23 See Appendix 1. 21

18

1. Aristotle’s cosmology

heated by friction. Aristotle does not attempt to explain precisely how. But he adduces as empirical evidence for this mechanism the fact that projectiles moving through the air can heat it to such an extent that they are themselves set on ¿re, and even melt (289a19–35)! Now, if the Sun, like all celestial objects, is assumed to be made out of a kind of matter which is different from the four Empedoclean simple bodies, since Aristotle says in Cael. B 7, with speci¿c reference to the celestial objects, that everything consists of the simple body, or bodies, in which it is, or through which it moves (289a18–19), but places the simple body making up the celestial objects above both air (289a28–32) and ¿re (Mete. A 3, 340b6–10), how can there be friction between the air and the Sun if the Sun moves above the air? It is very dif¿cult to come up with a satisfactory answer. No direct clue as to a possible way around this problem is to be found in Aristotle’s surviving works.24 The motion of the Sun might be assumed to cause waves in the surrounding medium, which are transmitted ¿rst to the ¿re right below the Sun and, via ¿re, to the air around the Earth. These waves cause the ¿re and the air to light up, and heat them up, too, by producing “internal” friction in them; the source of sunlight is primarily the overlying ¿re, as well as the ¿re in the air, and secondarily the air itself, being by nature hot, as ¿re is.25 No matter how it is transmitted to the air via ¿re, the mysterious frictional action of the fast-moving Sun on ¿re does not seem to cause this simple body (let alone air) to combust, not even in its outermost reaches, where it is purest and could be assumed to ignite directly underneath the Sun, thereby accounting for the intense brightness of this celestial object. Aristotle differentiates the appearance of the simple body ¿re undergoing combustion from that of the Sun, in Mete. A 3: he believes that the Sun looks white-hot, not ¿ery (341a35–36).26 In Mete. A 4 Aristotle explains that, when heated by the Sun, the Earth generates ¿re and water-vapor (341b6–22). The source of water-vapor is obvious, the simple body water within and upon the Earth. For Aristotle, ice is water with an excess of the cold (GC B 3, 330b25–29), so he may well assume, by a simple analogy, that water with a de¿ciency of the cold is water-vapor, which is buoyant 24 See Appendix 2. 25 See Appendix 3. Cf. also ch. 2, n. 3 and 65. 26 It should be noted that, although in Cael. B 7 Aristotle sets out to explain how light and heat are generated by the celestial objects (289a19–21), at the end of the chapter he seems to suggest that his aim was to account solely for the heat generated by the Sun (289a32–33), thus leading Alexander of Aphrodisias, apud Simp., in Cael. 442.4–12 (Heiberg), to the–by no means implausible–assumption that Aristotle’s explanation of why all celestial objects are bright is in fact offered by the de¿nition of light in de An. B 7, 418b3–17: light is the actualization of the potential “transparent”, which is common to air, water, many solids and the celestial matter, by the presence in it of ¿re or the celestial matter (the latter is, of course, implicitly assumed to actualize “the transparent” only where it forms celestial objects, not around them). If so, Aristotle believes that the Sun and all the other celestial objects generate light directly. The fact that in Mete. A 3, 341a12–30, he mentions the simple body air to explain only the production of heat by the Sun seems to support Alexander’s view. Here, too, however, Aristotle speaks of the air as being “set on ¿re” by fast motion, like the Sun’s, which might suggest that the Sun produces heat and light indirectly, too, without having a ¿ery color.

1.3. The ¿rst simple body

19

in itself, and that this defect results from the action of air heated by the motion of the Sun. This air-mass is in contact with part of the Earth, and is thus able to heat cold water upon or within it, not to such an extent that water turns into air but suf¿ciently for it to evaporate, becoming lighter than it is as a liquid. Fire, moreover, is generated from earth, the simple body after which the Earth itself is named. Aristotle does not explain how solarly heated air causes the simple body earth to yield ¿re. Within his physics, only one possible explanation presents itself. At play here must be the last of the three processes that can turn one, or two, Empedoclean simple bodies into another: the hot in air assimilates to itself the cold in earth, and the dry in earth assimilates to itself the wet in air, the result of the interaction being dry and hot ¿re. Fire is naturally more buoyant than water-vapor and air, so it predominates at higher altitudes, and near the outer boundary of its cosmic stratum is at last free of all admixtures (see below, 2.7). As it shoots up towards its natural place, solarly produced ¿re will turn into water or air here, but assimilate these simple bodies to itself there; elsewhere, its interaction with water will produce earth (the cold in water will assimilate the hot in ¿re to itself and the dry in ¿re will assimilate the wet in air to itself, the result of the interaction being dry and cold earth). The motion of the Sun, through the heating of the adjacent strata of ¿re and air it somehow induces, powers the constant transmutation of the four Empedoclean simple bodies into one another, on scales much smaller than the cosmological scale, by perpetually seeding the stratum of air with the other three traditional simple bodies, which makes it possible for all four of them to interact with one another in all possible ways. The intensity of this process is not uniform. The Sun’s daily motion brings it below the horizon for part of the day, causing a diurnal cycle of increase and decrease in the amount of solar heating. Because of the annual motion, the amount of time the Sun spends above the horizon each day is not constant but varies throughout the year, superimposing on the diurnal cycle a longer undulation. Further undulations, of varying amplitudes, might be superimposed by the Moon, perhaps by the planets, too. 27

1.3. THE FIRST SIMPLE BODY 1.3.1. The upper body Those who are of the opinion that ¿re makes up the celestial objects, Aristotle observes in Cael. B 7, hold this view because they identify “the upper body”, the kind of matter ¿lling up the heavens, the celestial part of the cosmos, with the simple body ¿re, and think it logical that each being is constituted by the body or bod27

As already said, in Cael. B 3 Aristotle alludes to a possible role of the planets and the Moon as causes of the constant transmutation of the four traditional simple bodies into one another. The question which celestial objects, in Aristotle’s view, heat the Earth and the surrounding air is addressed in Appendix 4.

20

1. Aristotle’s cosmology

ies in which it is situated, a general principle whose validity Aristotle himself accepts (289a16–19). Plato was among those according to whom ¿re ¿lls up the heavens (for the most part), and is thus the (main) constituent of the celestial objects (Ti. 40a2–b8). For Aristotle, that the celestial objects consist of the body or bodies in which they are, and thus through which they move, entails that they consist of a simple body whose natural motion is circular, unlike the natural motion of ¿re, and the existence of which he has shown above (289a13–16). It is this ¿fth simple body, not one of the traditional simple bodies–not even ¿re, though it rises on top of the three other Empedoclean simple bodies–that in Aristotle’s view is the upper body, the sole constituent of the celestial objects (for a different meaning of the expression “upper body” see Appendix 2).

1.3.2. The heavens The heavens, the outermost realm of the cosmos which the upper body is assumed to pervade, are correspondingly called “the region of the cosmos where upper motions take place”–the motions of the celestial objects–“the upper regions” and “the upper place of the cosmos (see Mete. A 3, 339b17–18, 339b23 and 339b37; for another meaning of the expression “upper place” see Appendix 2).28 By way of contrast, Aristotle calls the rest of the cosmos, where the four traditional simple bodies are arranged in concentric spherical layers, “the region of the cosmos around the Earth” (Mete. A 2, 339a19–20). The celestial object nearest to the Earth is the Moon, so the lower boundary of the heavens is a sphere with the orbit the Moon follows each month as a great circle.29 If we assume that the Moon is constituted out of the body in which it is, and thus through which it moves, a body occupying the heavens which is not identified with one of the four Empedoclean simple bodies, it is improbable that the Moon partially sticks into the sublunary realm of the cosmos, i.e. into the cosmic stratum of the simple body ¿re be28

29

Cf. Oxford English Dictionary (2nd ed. on CD-ROM, version 1.02) under “heaven”: “The expanse in which the sun, moon and stars, are seen, which has the appearance of a vast vault or canopy overarching the earth, on the ‘face’ or surface of which the clouds seem to lie or Àoat; the sky, the ¿rmament. Since 17th. c. chieÀy poetical in the sing., the plural being the ordinary form in prose” (1a); “The plural is sometimes used for the realms or regions of space in which the heavenly bodies move” (3b); “In the language of earlier cosmography: Each of the ‘spheres’ or spherical shells, lying above or outside of each other, into which astronomers and cosmographers formerly divided the realms of space around the earth…” (4). In Cael. A 9 Aristotle assumes that the heavens comprise only two spherical shells. With the Greek noun ouranos (which from now on will be left untranslated into English) he refers to the matter, or body, ¿lling up each shell (it is not necessarily the same). A third sense of the Greek word as used by Aristotle picks out each of these two types of matter–or a single type differentiated according to the spherical shell it occupies–and all matter inside the sphere within the inner heavenly shell. See 2.2.3. See Mete. A 3, 340b6–10, where the Moon is mentioned as separating the heavens from the region of the cosmos around the Earth. Hence the names “sublunary” and “superlunary” for the two main realms in Aristotle’s cosmos. The orbit of the Moon around the Earth is assumed here to be very much like the apparent annual path of the Sun.

1.3. The ¿rst simple body

21

low, as it must do if its monthly circular orbit around the Earth marks off, in the above explained manner, the heavens from the sublunary part of the cosmos, and is traced by its center. The lower boundary of the heavens cannot be, strictly speaking, the sphere whose great circle is the orbit followed by the Moon each month. It is one inside it, with a smaller radius by at least a lunar radius. The upper boundary of the heavens, now, is the sphere to which we are led to believe that the stars seen with the naked eye are ¿xed, an illusion forming the basis of Greek astronomy and still useful for the scienti¿c treatment of many aspects of the sky. This illusion is due, ¿rst, to the Earth’s diurnal rotation and, second, to the apparent immobility of the celestial objects at issue relative to one another for very long spans of time. Generated naturally, the impression that the stars are luminous points of an enormous sphere, which is centered on the Earth and rotates once a day from east to west, the so-called celestial sphere, explains the customary description of these celestial objects as ¿xed.

1.3.3. Diurnal rotation and the concept of the celestial sphere The Earth rotates on its axis from west to east. It does so against the backdrop of the very distant stars, and completes a rotation in a day. As a result, some stars are seen to rise in the east, move along parallel circles and ¿nally set in the west. If the Earth had not been in the way, and the Sun had not swamped for part of the day the light of the stars, the latter would then be seen to describe complete circles in a day. An observer facing south in the Earth’s northern hemisphere sees only a small part of the circles traced by the southernmost stars. The farther away a star is from the south, the greater the unseen arc of its circle. Northerly stars do not rise and set. Every day, they stay above the horizon for twenty-four hours, and the diameters of their parallel circles decrease progressively, the nearer the stars are to a point that does not share in the diurnal rotation. The straight line joining the centers of the parallel circles traced by all stars passes through this point, as can be easily determined with a very simple sighting instrument.30 For considerably long periods, a star is seen to always rise and set in the same places on the horizon, and to not change its position in the sky relative to other stars. This does change, of course, but very slowly, due to the motion of the stars in space. But such changes were unknown to the ancients, hence the traditional description of the stars as “¿xed”, and were ¿rst measured in 1718 by Edmund Halley.31 30 See Evans (1998) 33–34. 31 What Halley measured was not the actual motion of the stars Sirius, Aldebaran and Arcturus in space, but their so-called proper motion (a star’s apparent angular motion across the sky relative to more distant stars, which is a projection onto the sky of the star’s real motions in space relative to the Sun). The places on the horizon where a star is seen to rise and set change very slowly mainly due to a totally different phenomenon (the precession of the Earth’s rotational axis about its orbital axis, on which see below n. 44).

22

1. Aristotle’s cosmology

Although the stars are not at equal distances from the Earth, they are so much removed from us that any sense of depth is lost. It seems to us that all stars, the most distant objects from us the naked eye can perceive, are equally distant from our planet. Geocentricity is thus a naturally born notion, though we often tend to scoff at it when looking at ancient cosmologies with the anachronistic spectacles of the principle named after Copernicus that can be justly said to be one of the foundations of modern cosmology, and according to which there exists no privileged point in the universe, such as the one our senses inevitably endow our planet with occupying.32 Anywhere in the universe, an observer will unavoidably get the impression of being located right in the middle of everything. Now, relativity of motion allows us to explain easily the risings and settings of the stars, as well as the observed circularity of their parallel diurnal paths and all other related phenomena, even if we consider the Earth to be stationary, which is by no means an unreasonable point of view, given that we are unable to perceive directly our planet’s diurnal rotation.33 We can very well assume that the stars are bright, point-like objects ¿xed to an enormous and transparent sphere, concentric with the comparatively insigni¿cant globe of the Earth. If extended to in¿nity, the horizon of any Earth-based observer bisects it (the horizon is an imaginary plane to which the plumb line is perpendicular; the projection of the upper end of the plumb line marks a point on the celestial sphere called “zenith”, whereas diametrically opposite to it is the point on the celestial sphere called “nadir”). This sphere is called “the celestial sphere”, for obvious reasons. A purely ¿ctional object, the celestial sphere rotates once a day, opposite to the Earth’s own rotation and about an axis which is nothing but a ¿ctional extension of the Earth’s own axis of rotation (that is, about the line on which the centers of the parallel circles described by the diurnal movement of the stars lie). The celestial sphere’s counterparts to the Earth’s equator and poles are thus appropriately conceived of as the celestial equator and poles respectively. A great circle on the celestial sphere which passes through the celestial poles and the zenith of an observer at the Earth’s midlatitudes cuts the horizon of the observer at the north and south points. The east and west points are found 90q measured clockwise from the north and south points respectively, at the intersections of the horizon and the celestial equator.34 The altitude of the celestial pole visible from a place–its angular distance above the horizon–is equal to the latitude of this location.

32 For “the Copernican principle” see e.g. Rowan-Robinson (2004 4 ) 63–64. 33 It was ¿rst demonstrated dynamically in 1851 by Léon Foucault, with the pendulum famously named after him. On Foucault’s pendulum see e.g. Kaler (2002) 48–50. 34 For the markedly different appearance of the celestial sphere from different latitudes of the Earth see e.g. Evans (1998) 32–33, or the relevant sections in any introduction to spherical astronomy, such as Kaler (2002), a useful book designed with the needs of scholars in the humanities especially in mind.

1.3. The ¿rst simple body

23

This is how Claudius Ptolemy describes the genesis of the concept of the celestial sphere, when he introduces the elementary assumptions on which all of astronomy is founded (Alm. 10.4–11.13 [Heiberg]):35 

8‡N QäR SÃR TVÉXEN zRRSfEN TIVi XS»X[R ƒT¶ XSME»XLN XMR¶N TEVEXLVœWI[N XSlN TEPEMSlNI½PSKSRTEVEKIKSR{REM· yÉV[RK‡VX³RXIPMSROEiXŸRWIPœRLROEiXS¾N †PPSYN ƒWX{VEN JIVSQ{RSYN ƒT¶ ƒREXSPÏR zTi HYWQ‡N EeIi OEX‡ TEVEPPœP[R O»OP[R ƒPPœPSMN OEi ƒVGSQ{RSYN QäR ƒREJ{VIWUEM O„X[UIR ƒT¶ XSÁ XETIMRSÁ OEi ÊWTIV z\ EºX¢N X¢N K¢N, QIXI[VM^SQ{RSYN Hä OEX‡ QMOV¶R IeN ¼]SN, }TIMXE T„PMR OEX‡X¶ƒR„PSKSRTIVMIVGSQ{RSYNXIOEizRXETIMRÉWIMKMKRSQ{RSYN, |[N‰RX{PISR ÊWTIVzQTIW³RXINIeNXŸRK¢RƒJERMWUÏWMR, IX’ EÃT„PMRGV³RSRXMR‡QIfRERXENzR XÚƒJERMWQÚÊWTIVƒT’ †PPLNƒVG¢NƒREX{PPSRX„NXIOEiH»RSRXEN, XS¾NHäGV³RSYN XS»XSYNOEi}XMXS¾NXÏRƒREXSPÏROEiH»WI[RX³TSYNXIXEKQ{R[NXIOEi±QSf[NÇN zTfTERƒRXETSHMHSQ{RSYN. Q„PMWXEHäEºXS¾N¤KIRIeNXŸRWJEMVMOŸR}RRSMERšXÏREeIiJERIVÏRƒWX{V[R TIVMWXVSJŸOYOPSXIVŸNUI[VSYQ{RLOEiTIViO{RXVSRIROEiX¶EºX¶TIVMTSPSYQ{RL· T³PSN K‡V ƒREKOEf[N zOIlRS X¶ WLQIlSR zKfRIXS X¢N SºVERfSY WJEfVEN XÏR QäR QŠPPSR EºXÚ TPLWME^³RX[R OEX‡ QMOVSX{V[RO»OP[R yPMWWSQ{R[R, XÏR H’ ƒT[X{V[ TV¶N XŸR X¢N HMEWX„WI[N ƒREPSKfER QIf^SREN O»OPSYN zR X® TIVMKVEJ® TSMS»RX[R, |[N‰RšƒT³WXEWMNOEiQ{GVMXÏRƒJERM^SQ{R[RJU„W:, OEiXS»X[RHäX‡QäRzKK¾N XÏR EeIi JERIVÏR †WXV[R yÉV[R zT’ ²PfKSR GV³RSR zR XÚ ƒJERMWQÚ Q{RSRXE, X‡ H’ †T[UIR ƒREP³K[N T„PMR zTi TPIfSRE· ÇN XŸR QäR ƒVGŸR HM‡ Q³RE X‡ XSMEÁXE XŸR TVSIMVLQ{RLR}RRSMEREºXS¾NPEFIlR, žHLHäOEX‡XŸRzJI\¢NUI[VfEROEiX‡PSMT‡ XS»XSMN ƒO³PSYUE OEXERS¢WEM T„RX[R ‚TPÏN XÏR JEMRSQ{R[R XElN yXIVSH³\SMN zRRSfEMNƒRXMQEVXYVS»RX[R. It is a reasonable assumption that the ancients got their ¿rst notions on the matters under consideration from the following kind of observations. They saw that the Sun, the Moon and the other celestial objects were carried from east to west always along parallel circles, and that they began to rise up from below, as if from the Earth itself, gradually getting up high and then in a similar fashion turning and getting lower, until they were gone from sight as if they had fallen to the Earth, and that after they had stayed invisible for some time, they rose and set once again, these times, as well as the places of risings and settings, being ¿xed and, for the most part, the same. What chieÀy led the ancients to the concept of the celestial sphere was the revolution of the ever visible stars, which was observed to be circular and to take place about a single center, the same [for all]. This point necessarily became [for the ancients] a pole of the celestial sphere. The stars that were closer to it revolved on smaller circles, while those farther away described ever larger circles in proportion to their distance, until the distance to the stars that became invisible was reached, of which those near the ever visible stars were observed by the ancients to stay invisible for a short time, while those farther away stayed invisible for longer, again proportionately [to their distance from the pole]. Originally, therefore, it was only this kind of observations that led the ancients to the aforementioned concept, but as their researches went on, they grasped that everything else was in accord with it, since all phenomena without exception contradict alternative notions.

The Sun, the Moon and the planets of our solar system, among which the Earth is obviously not counted here, participate in the diurnal rotation of the celestial 35

See also Gem., Isag. 12.1–4, and the introduction to Eucl., Phaen., which is perhaps unauthentic. The work’s attribution to Euclid has also been suspected. On its authenticity, as well as on that of its introduction, see Berggren & Thomas (2006 ) 8ff.

24

1. Aristotle’s cosmology

sphere, upon which their paths are projected. Unlike the stars, however, they do not move each along one single, perfect circle every day (see below, 1.3.5). Ultimately responsible for Aristotle’s belief in the sphericity of the cosmos is the relativity of motion manifested in the diurnal revolution of the stars, an apparent motion from which the concept of the celestial sphere ensues naturally.36 Compared with the size of the huge scales modern cosmology has accustomed us to ponder, Aristotle’s cosmos is thus a decidedly puny affair, extending only up to those bright stars visible to the naked eye, all of which are in the same region of the Milky Way galaxy as our Sun.37 A geometrically perfect sphere, whose center is coincident with the spherical Earth’s, it hangs not in void, or emptiness, but in nothingness.38 1.3.4. Enter the ¿rst simple body As is clear from Mete. A 6, 343b28–32, Aristotle knew that stars can be occulted by planets, just as the Sun can be eclipsed by the Moon, from whence it clearly follows that the Sun must be farther away from the Earth than the Moon. Moreover, since in Cael. B 12, 292a3–9, he mentions lunar occultations of planets, and knew that at least Mars, Jupiter and Saturn are for sure beyond the Sun (as follows from Cael. B 10), he had strong grounds for believing that the stars are the most distant contents of the cosmos from the Earth, whose center he took to be coincident with that of the cosmos, for, as said above, an observer located anywhere in the universe forms unavoidably the impression of being in the middle of it (for the relative distances of the celestial objects see 2.8.4). Since in Cael. B 8 Aristotle argues that the stars do not trace their diurnal circles moving independently of the enveloping mass of the upper body, a spherical shell (see Cael. B 4), but as ¿xed parts of this diurnally rotating object, he considers the celestial sphere a physical surface, the boundary-surface of the cosmos, not a merely useful, albeit naturally generated, illusion.39

36

Arguing in Cael. B 4 from a physical basis for the sphericity of the ouranos in the last of the three senses of the term we saw above, in n. 28, Aristotle strongly emphasizes that the rotation of the universe, whence its sphericity follows, is both an observed fact and a fundamental hypothesis, and that its sphericity can also be proven (287a11–14 ) . Questions such as the shape of the cosmos, as he explains in Ph. B 2, 193b22–32, can be tackled in two ways, either astronomically–this approach is adopted by Ptolemy, in the above translated passage from the Almagest–or physically, as Aristotle himself approaches the question of the shape of the universe in Cael. B 4. Some of the arguments Aristotle sets out in Cael. B 4 for the sphericity of the universe will be discussed below, in 2.3. 37 See e.g. Rowan-Robinson (20044) 1–3 and Kaler (2001) 3. Kaler’s book is a very informative and readable introduction to the stars for the general reader. 38 Aristotle states his conclusion that there is nothing outside our cosmos, not even void, at the end of Cael. A 9, as a corollary of his extended argument demonstrating the impossibility of a plurality of worlds (279a11–18). For the spherical cosmos as embodying true geometric perfection see the passage translated at the end of ch. 3, and cf. Kouremenos (2003b) 472–476. 39 On whether Cael. B 8 concerns the stars only see Appendix 7.

1.3. The ¿rst simple body

25

Like all celestial objects, the stars are spherical (for the sphericity of the celestial objects see Cael. B 8, 290a7–9, and B 11). Whether they are distributed at exactly, or approximately, equal distances from the center of the cosmos Aristotle does not explain. No part of them can stick outside the cosmos. The existence of the ¿fth simple body, which in Cael. B 7 is considered to be the ¿ller 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. Aristotle calls it “the ¿rst simple body” (Cael. A 3, 270b2–3), for its circular natural motion is prior to the rectilinear natural motion of any Empedoclean simple body. The circle is prior to the straight line because the former is complete, whereas the latter is incomplete, and what is complete is naturally prior to what is incomplete: a straight line can be in¿nite–lacking beginning or end or both–or ¿nite, in which case either of its “limiting points” can be produced, parts it hitherto lacked being thereby added to it (Cael. A 2, 269a18–23).40 Since in Cael. A 2 Aristotle contrasts the circular natural motion of the ¿rst simple body with the rectilinear natural motions of the four traditional simple bodies, he suggests to the careful reader that the point round which the ¿rst simple body performs its circular natural motion is tacitly, and neatly, assumed to be the same as that towards, or away from, which water and earth, or air and ¿re respectively, move naturally: the center of the cosmos, which is identical with the center of the Earth (268b17–269a9). 40

The straight lines Aristotle speaks of in Cael. A 2, 269a18–23, are undoubtedly geometric, not physical. He believes that the cosmos, being a rotating sphere, is ¿nite, so in it there cannot be infinitely large objects, whose straight edges would have lacked beginning and end. Nor, consequently, can any of the ¿nitely large, straight-edged objects existing in it at any given time keep on growing inde¿nitely, in which case an object’s edges would have been inde¿nitely extendable. That the universe could not have been a rotating sphere had it been in¿nite is demonstrated in Cael. A 5, 271b26–272a7; further arguments to the same effect are adduced below, in 272b17–273a6. In “Euclidean” geometry, the only one Aristotle knew, straight lines are arbitrarily extendable, however. As finally crystallized at some time around the end of the fourth century BC, moreover, this geometry does admit in¿nite straight lines (see Euc., Elementa 1.12 ) . Aristotle’s justly famous discussion of in¿nity in Ph. ī concerns physics, not mathematics, as he himself observes (see 5, 204a34–b4 ) , nevertheless his characterization of in¿nity (6, 206a9–29) can be safely assumed to allow the arbitrary extendibility of geometric magnitudes, banishing from geometry only in¿nitely large magnitudes. Nothing in Ph. ī is incompatible with the unquali¿ed claim in Cael. A 2, 269a18–23 that geometric lines can be inde¿nitely extended (cf. Cael. B 4, 286b20, and Ph. ī 4, 203b22–25). In Ph. ī Aristotle emphasizes that continued addition cannot exceed any assigned limit, unless physical objects are in¿nitely large (6, 206b20–27 ) . But he speaks having in mind only the partial sums of an in¿nite 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 in¿nite sequence, which can exceed any assigned limit–does by no means entail that geometric straight lines cannot be arbitrarily extended. Aristotle simply denies that an in¿nite number of parts, into which a material thing is potentially divisible by his lights, cannot but make the thing itself in¿nitely large, as his pupil Eudemus of Rhodes seems to suggest in a fragment of his Physics Simplicius has preserved (in Ph. 459.23–26 [Diels] = Eudem., fr. 62 Wehrli). For this assumption see Sorabji (1983) 334–335 (cf. Epicur. Ep. ad Hdt. 56–57, Lucr. 1.615–622).

26

1. Aristotle’s cosmology

Whether the circular motion at issue is the rotation of a disc, or of a number of concentric rings, of a spherical shell, or of many concentric spherical shells about axes passing through their center, which is the same as the Earth’s, Aristotle does not bother to make clear. Near the end of Cael. A 2, he unmistakably hints that the simple body introduced here makes up celestial objects–“things that move circularly”, in his own words, as well as continuously and everlastingly–whose motion he assumes to be the circular natural motion of their matter (269b2–13; translated in 2.2.1). Within the framework of the geocentric worldview, celestial objects are the only things that spring to one’s mind as those that always execute circular motion round the center of the cosmos. The Moon orbits the Earth, and appears to do so in a circle. The Sun appears to move circularly round the Earth, completing a trip in a year, whereas the Moon needs only about a month. In one day, the Sun is seen to describe another circle round the Earth, as is the Moon, a result of the Earth’s diurnal rotation. For the same reason, in a day the stars appear to trace out parallel circles, whose centers lie on the same line–the axis of the enormous celestial sphere, whose bright points are the stars, and which spins diurnally from east to west, i.e. opposite to the direction of the Earth’s actual rotation, whereas the Earth lays immobile at its center. As far as their apparent diurnal motion in a single day is concerned, the Sun and the Moon–actually their centers–can be treated as points on the celestial sphere. This holds equally true of the planets, whose apparent diurnal motion round the Earth in a day is thus circular. They, too, have another apparent motion round the Earth. In many respects, this motion is similar to the apparent, non-diurnal motion of the Sun, or to the real, non-diurnal motion of the Moon, round the Earth. It differs from either, in that it deviates from circularity (this, as it will turn out, is not an insigni¿cant complication). Compared, however, to the number of the planets, the number of the stars is immense, so circular motion round the Earth rules in the sky of the geocentric cosmos.

1.3.5. The non-diurnal motion of the Sun, the Moon and the planets The Greeks certainly knew very early on that the place on the horizon where the Sun rises gradually shifts from a southeastern point, where the Sun rises at winter solstice, to a northeastern one, were the Sun rises at summer solstice. Over the same period, the place of the Sun’s setting on the horizon is also displaced from a point in the southwest, where the Sun sets at winter solstice, to another in the northwest, where the Sun sets at summer solstice (the Sun rises and sets exactly in the east and west only at equinoxes, midway between the northernmost and southernmost limits to the motion of its rising and setting place). The direction of motion then reverses. The Greek word for solstice, tropƝ (see e.g. Hes., Op. 479 and 564), literally means “turning”, and denotes the reversals in the direction in which the Sun’s rising and setting places on the horizon are observed to move, one occurring at summer solstice, the other at winter solstice.

1.3. The ¿rst simple body

27

The English term “solstice”, from the Latin solstitium, refers to the apparent standing still of the Sun at the extreme northern and southern limits to the motion of its rising and setting points along the horizon, before it reverses direction. This motion is easily observed with the gnomon.41 It follows that the circular path of the Sun in the sky, unlike that of a star, is not the same every day. At equinoxes, it almost coincides with the celestial equator, which is bisected by the observer’s horizon–this is why at equinoxes the hours of daylight and darkness are equal. At solstices, it almost coincides with two small circles of the celestial sphere which are parallel to, and equidistant from, the celestial equator, one to the north, with its largest part above the horizon, and the other to the south, with its largest part below the horizon. These are the tropics–of Cancer, where the Sun is at summer solstice, when the time of daylight is the longest during the year, and of Capricorn, where the Sun is at winter solstice, when the time of daylight is at its annual minimum. Between a solstice and an equinox, the successive diurnal paths of the Sun coincide very closely with parallel, small circles of the celestial sphere sandwiched between a tropic and the celestial equator; over the course of a year, the Sun’s path is a spiral, which is traced out twice in this period. Spirals are described by the Moon and the planets, too, a coil corresponding to a diurnal revolution. What Plato calls in Lg. 7 “wanderings” of the Sun, the Moon and the ¿ve planets–their following, as he proceeds to explain, not always a single path but many–is chieÀy their tracing out spirals (822a4–8).42 In our extremely few sources for the early history of Greek astronomy, the spirals of the planets, the Sun and the Moon are ¿rst mentioned by Plato, in his Timaeus, alongside the correct explanation of the phenomenon (39a5–b2).43 The cause of these spirals is the fact that the angular distances of all celestial objects at issue here from the celestial equator (their “declinations”) are not constant. They change continuously. This is so because the Sun, the Moon and the planets do not just follow the celestial sphere in its diurnal rotation, as if they–or their centers–were ¿xed in it. Simultaneously, they each execute a slower, eastward motion across the ¿eld of stars in paths inclined to the celestial equator (a continuous, much slower change in the declinations of the stars was ¿rst detected by the astronomer Hipparchus of Nicaea, in the second century BC, and is due to the precession of the Earth’s rotational axis about its orbital axis).44 41

On the gnomon see Evans (1998) 27–30 and 53–54. It is a rudimentary, and probably the oldest, astronomical instrument–the simplest sundial. 42 Not the retrogradations of the planets, for which see below, since neither the Sun nor the Moon exhibits this phenomenon. 43 We should not, however, follow Dicks (1970) 129 and Vlastos (1975) 54–55 in attributing to Plato the discovery of either the phenomenon itself or its explanation. 44 On precession see e.g. Evans (1998) 245–246 and Kaler (2002) ch. 5. The Earth precesses pretty much like a spinning top, whose non-vertical rotational axis wobbles slowly about the vertical passing through the point of contact of the axis with the Àoor because the gravity of the Earth tugs on the top. The Earth’s rotational axis is at an angle to the plane of its orbit round the Sun. It wobbles slowly about the perpendicular to this plane because gravitational forces, due mainly to the Sun and Moon, are exerted upon its equatorial bulge.

28

1. Aristotle’s cosmology

In the case of the Sun, this motion marks out on the celestial sphere a great circle forming with the celestial equator an angle which is equal to the angular distance of each tropic from the celestial equator. This angle is actually the angle between the axis about which the Earth rotates and the perpendicular to “the ecliptic plane”, in which the Earth orbits the Sun in an eastward direction. Of course, to us it appears that it is the Sun that orbits the Earth from west to east along the ecliptic–which, regarded geocentrically, is just another great circle on the celestial sphere–completing a circuit in a year.45 By observing at regular intervals which stars appear in the west soon after sunset near the place on the horizon where the Sun has set, we are able to follow the path of the Sun over the course of a year among the stars of “the zodiacal constellations”; these constellations de¿ne on the celestial sphere a belt or band, which is called “the zodiac”. The ecliptic bisects the zodiac, and we can locate it quite accurately with the help of lunar eclipses. They occur when the Sun and the Moon are exactly on opposite sides of the ecliptic with the Earth in between, hence the name of this great circle on the celestial sphere. The other planets of our solar system also orbit the Sun in an eastward direction. With the exception of Pluto–which at any rate from August 2006 is not of¿cially categorized as a planet–they do so in planes inclined a few degrees to the ecliptic and passing through the broad belt of the zodiac, within whose boundaries the planets are always to be found. The Moon, too, orbits the Earth in a plane slightly inclined to the ecliptic, and in an eastward direction.46 Thus, to the Earth-based observer, the Moon and the ¿ve planets visible to the naked eye appear to move against the backdrop of the distant stars from west to east, traveling near the ecliptic. Each of these celestial objects needs a characteristically different time to complete a circuit with the exception of Venus and Mercury– like the Sun, they each need a year– and traces out a spiral wound about the celestial sphere, as its motion from west to east, in a path inclined to the celestial equator, combines with the much faster diurnal rotation, in which it participates.47 Clearly, the planets are naturally grouped together with the Sun and Moon by their traveling eastwards on, or very close to, the ecliptic–in general, within the zodiac. These seven celestial objects are thus characteristically distinguished from the stars in that they are seen to constantly shift positions, relative to both the stars and each other, because of their easterly motions. This is why the Greeks called them “wandering celestial objects”, in contrast to the ¿xed ones, the stars, or simply “wanderers”– planƝtes asteres, or just planƝtes, from whence is derived the modern term “planet”. 45

Since the Sun is much closer to the Earth than the celestial sphere, the geocentric ecliptic is actually a great circle on the celestial sphere which is coplanar with the circle of the Sun’s apparent, annual motion round the Earth. 46 The facts that the orbits of all planets are almost coplanar and that all planets orbit the Sun in the same direction are signatures of our solar system’s origin. 47 It follows that regular observations of the motion of the Moon and of the planets can also help de¿ne the position of the zodiac among the stars.

1.3. The ¿rst simple body

29

The planets, moreover, appear from the Earth to wander also in a manner totally peculiar to them. At regular intervals, their eastward motion is seen to be interrupted. A planet appears to be stationary in the sky, a phenomenon called “¿rst station”, then begins to move again, though in the opposite direction, but after a while stops for a second time (“second station”), and, ¿nally, when its motion resumes, the direction is once again to the east. As result of this reversal in the direction of its zodiacal motion called “retrogradation”, the planet is seen to trace out a looping or zigzag path;48 the shape of a retrograde path is not the same from one retrogradation to the next, a striking deviation from circularity in the path of the planet’s mainly eastward motion against the stellar backdrop. Retrogradations are as spectacular as they are puzzling within a geocentric world model. The phenomenon is explained easily from a heliocentric point of view, however, given the differently sized orbits of the planets around the Sun, and their unequal orbital speeds.49 So far we have dealt with departures from circularity, which characterizes the apparent motion of the stars, in the apparent motions of the planets. These celestial objects, however, along with the Sun and Moon, differ from the stars in another prominent respect, too. The stars trace out their apparent, diurnal paths in a regular manner, never slowing down or speeding up, for the rotation of the celestial sphere reÀects the rotation of the Earth on its axis, which is uniform, whereas the zodiacal motions of the planets, the Sun and the Moon against the backdrop of the celestial sphere have variable speeds. Since the Earth orbits the Sun not in a circle but in an ellipse, it moves along its orbit at a variable rate, and thus the Sun is seen by an Earth-based observer to move along the ecliptic at an inconstant rate. As a consequence, the lengths of the four seasons of the year are unequal.50 The variable speed at which the Moon orbits the Earth, and at which it is observed from the Earth to move through the zodiacal constellations in a circle inclined to the ecliptic, is more pronounced, for the eccentricity of the Moon’s elliptical orbit is larger than the Earth’s, which also re48 Illustrations in Gregory (2000) 133, ¿g. 23, Yavetz (1998) 265–267, ¿g. 36, 38, 40. 49 See Kaler (2002) 304–306. 50 The seasons are the Sun’s traversing the four quadrants into which the ecliptic is divided by four points. Two of them are the diametrically opposite points at which the circles of the ecliptic and the celestial equator intersect. They are called “equinoxes”, just like the moments of the year at which the Sun is found there. The other two points, called “solstices”, are the positions of the Sun at the similarly named moments of the year, and are also diametrically opposite: they are the midpoints of the two semicircles into which the ecliptic is divided by the equinoxes. The equinoxes and solstices, conceived of as points, are thus placed symmetrically round the ecliptic, at 90q intervals. The seasons are the Sun’s moving along the ecliptic from spring equinox to summer solstice (spring), from summer solstice to autumnal equinox (summer), from autumnal equinox to winter solstice (autumn) and from winter solstice back to spring equinox (winter). The lengths of the seasons are the times it takes the Sun to move over each quadrant of the ecliptic. For the inequality of the lengths of the seasons, or simply the inequality of the seasons, see Evans (1998) 210–211.

30

1. Aristotle’s cosmology

sults in a considerable enlargement of the lunar angular diameter at perigee (the point on the orbit of the Moon closest to the Earth).51 Variable are also the speeds at which the ¿ve planets appear from the Earth to move eastwards across the sky, again the consequence of orbital eccentricities, due to which are also variations in the brightness of the planets, especially prominent for Mars (in the case of Venus, as in Mercury’s, such variations result partly from the planet’s phases), as well as the non-uniform distribution of retrogradations around the zodiac.52 1.3.6. The ¿rst simple body and the four traditional simple bodies Nothing in Cael. A 2 suggests that the ¿rst simple body not only is the constituent matter of celestial objects but also ¿lls the heavens. Perhaps Aristotle expects his readers to infer this from the principle that all beings are made up of the same kind(s) of body in which they are, and through which they move. At the end of Cael. A 2 he says that the ¿rst simple body is separated from all simple bodies around us here near the center of the cosmos (269b13–15), thereby making it clear that no trace of the ¿rst simple body is found where the four traditional simple bodies are. He also adds that the nature of the ¿rst simple body is higher than the nature of any Empedoclean simple body, in proportion as the ¿rst simple body is farther away from the center of the cosmos than any of the traditional simple bodies (269b15–17). This remark might be meant to explain why the ¿rst simple body does not mix with the four other simple bodies–they are thus always con¿ned below it. Given the priority of the ¿rst simple body’s natural motion over the natural motions of the four Empedoclean simple bodies, whence it follows that the nature of the ¿rst simple body is higher than that of any traditional simple body, one is justi¿ed in thinking of the ¿rst simple body as being both spatially and axiologically separated from the other simple bodies existing in the cosmos (see also Appendix 2).53 Another reason why the ¿rst simple body is not present in the realm of the cosmos where the four traditional simple bodies are always con¿ned is that its presence there would have been otiose, for it does not decay into any of the four Empedoclean simple bodies, nor is it generated from any of them. One easily infers that this is so because the ¿rst simple body, unlike each traditional simple body, does not arise from a member of one of the two pairs of basic contrary quali51

For a striking photographic illustration of the large variation in the Moon’s apparent diameter at perigee and at apogee see Kaler (2002) 246. 52 For the variations in the brightness of the planets due to their orbital eccentricities and phases see Kaler (2002) 306–308. For the non-uniform distribution of planetary retrogradations around the zodiac see Evans (1998) 340, Zodiacal Inequality, with ¿g. 7.24; the epicyclic model of planetary motion (which is post-Aristotelian) is presupposed. 53 Against the view that the ¿rst simple body originally served as celestial matter and substance of man’s rational soul see Moraux (1963) 1213–1226, Hahm (1982) 66–67. The presence of the ¿rst simple body in compound bodies is assumed by Reeve (2002) 47–48.

1.3. The ¿rst simple body

31

ties, cold-hot and wet-dry, being combined with a member of the other pair.54 If the ¿rst simple body cannot turn into any other simple body and vice versa, however, it cannot also react with the other simple bodies to form compound bodies, so what could possibly be the purpose of its presence below the heavens? As Aristotle remarks in Cael. A 4, divine nature makes nothing purposeless (271a33). In Cael. A 3 he argues that no process in nature can yield the ¿rst simple body out of another simple body, or, conversely, another simple body out of the ¿rst simple body. The ¿rst simple body is, in other words, exempt from substantial change. If so, the ¿rst simple body, unlike the four traditional simple bodies, neither increases nor decreases locally at any given time; it does not suffer local mass-losses that would have been counterbalanced by local mass-gains occurring elsewhere in the part of the cosmos it ¿lls up, in order for the total amount of it existing in the cosmos to be always the same (see above, 1.2.4). Whence it follows that the ¿rst simple body cannot but also be free of all change in the degrees in which it possesses whatever other properties it might have beside mass, given that, all the time, the other four simple bodies turn locally into one another, and also suffer, again locally, variations in the degrees in which they each possess their properties other than mass, just as all of their living compounds do, which invariably undergo growth and diminution.55 The ¿rst step in this argument rests on the assumption that any two of the four traditional simple bodies can turn into each other, for they have contrary qualities as their constituents, each of which is in potentiality, and thus can become in actuality, the other.56 By Aristotle’s lights, this qualitative contrariety is reÀected in the rectilinear natural motions of the two simple bodies, for they have contrary directions.57 The natural motion of the ¿rst simple body is circular, however, and is not paired with a motion whose direction is contrary. Nature has, therefore, exempted the ¿rst simple body from qualitative contrariety with the four Empedoclean simple bodies, thus from substantial change as well. Reasoning as explained above, Aristotle then concludes that the ¿rst simple body does not suffer local gain and loss in mass, too, and is also free of all variation in the degrees in which it possesses whatever other properties might belong to it (Cael. A 3, 270a12–35). It is thus unclear how the ¿rst simple body can be perceptible; see Appendix 5. The text does not mention “change in degree” but only “change of properties”. In the case of the four traditional simple bodies, however, a change of properties results in substantial change, so it seems that, as regards the simple bodies, when Aristotle talks about their suffering “changes of properties” in this context, after he has shown that the ¿rst simple body does not participate in substantial change, unlike the four traditional simple bodies, he actually means “changes in the degrees in which properties are possessed”. That the hot and cold come in degrees is stated in GC B 7, 334b7 (the same must also apply to the other two tangible qualities, the wet and the dry); cf. B 3, 330b25–28. Which properties the ¿rst simple body can have beside corporeality, on which see Appendix 5, is totally unclear. It is remarkable that Aristotle does not argue against the alterability of the ¿rst simple body from the already established fact that that this simple body lacks tangible qualities; cf. Wildberg (1988) 87. 56 The contrary qualities are not explicitly mentioned; see Appendix 6. 57 Cf. GC B 3, 330b30–331a3, B 4, 331a14–20; see, moreover, Cael. ǻ 4, 311a16–29, for earth and water, air and ¿re (the objection in Wildberg [1988] 86 carries no force).

54 55

32

1. Aristotle’s cosmology

The crucial thesis that no motion is contrary to circular motion is established in Cael. A 4.58 That the ¿rst simple body is ungenerated, indestructible and absolutely unchangeable helps Aristotle establish that its circular natural motion does not speed up and slow down–it is totally uniform (see Cael. B 6, 288a27–b7). 1.3.7. The eternity of the ¿rst simple body’s natural motion As already said (1.3.4), in Cael. A 2 Aristotle implicitly assumes that the perpetual circular motions in the heavens are due to the natural motion of the ¿rst simple body, which is circular. Nowhere in this chapter, however, does he argue for the eternity of the ¿rst simple body’s natural motion. He assumes it to be easily derivable from the basic fact that the natural motion of the ¿rst simple body is circular. Any amount of the ¿rst simple body moves spontaneously in a circle, just as a rock falls spontaneously. The path of a falling rock is a straight line-segment joining the center of the Earth, near which the rock will be at rest, and another point, at a ¿nite distance, from which the rock started falling. Motion on such a path cannot be eternal. You can move in a circle forever without reaching any boundary, however, for in a circle there is no endpoint to serve as the terminus of your motion.59 The circular motion of the ¿rst simple body, being natural like the rectilinear motion of a falling rock, is completely effortless and tireless, unlike that of a living thing. It would stop only if a terminus intrinsic to the circle itself, which formed a physical barrier, were reached. However, given the absence of such a terminus on a circle, it is impossible for the natural motion of the ¿rst simple body to ever come to a stop, and since a circle also lacks a point, which is de¿ned intrinsically on it and from which the natural motion of the ¿rst simple body might have started, this motion is eternal.60 1.3.8. The ¿rst simple body and the stars, the planets, the Sun and the Moon Aristotle shows that the stars do not trace their parallel diurnal circles moving independently of the surrounding mass of the ¿rst simple body, which ¿lls up their realm, but as parts of this mass, which forms a spherical shell centered on the Earth: this shell rotates uniformly once a day from east to west, about an axis perpendicular to an equator on the same plane as the Earth’s which passes through the poles and center of the Earth (see above, 1.3.4). The diurnal rotation of this shell is the natural motion of the ¿rst simple body, and the stars are said to be ¿xed, or embedded, immovably in their “deferent” shell in the sense that their positions 58 See below, 3.5. 59 A circle can thus be conceived of as in¿nite: see Ph. ī 6, 206b33–207a10. 60 Cf. Ph. Ĭ 9, 265a27–b8, and Graham (1999) 160–161 ad loc. The reason why the natural motion of the first simple body is eternal is hinted at in Cael. B 1: this motion is such, i.e. circular, that it has no end (284a3–6). It is explicitly stated in Cael. B 6, 288a22–25, in another argument for the uniformity of the ¿rst simple body’s natural motion.

1.4. Eudoxus’ theory of homocentric spheres and Aristotle’s Metaph. ȁ 8

33

relative to the shell’s other parts are ¿xed–they move naturally as much as any other part of the ¿rst simple body. 61 The planets, however, cannot be assumed to be ¿xed in this shell, a physical analogue for the celestial sphere, nor can the Sun and the Moon, participation in the diurnal rotation being not their sole motion. From the Earth the Sun appears to orbit it once every year, just as the Moon orbits the Earth once a month (see 1.3.5). The annual motion of the Sun takes place in a plane slanted to the celestial equator, and its direction is from west to east. The Moon’s monthly orbit lies in a plane slightly inclined to the annual orbit of the Sun, and the direction of its motion in this orbit is also from west to east. All planets appear from the Earth to execute round it a motion which is similar to the Sun’s annual and the Moon’s monthly motion in that it has an easterly direction but only in general, for often each planet, if we disregard its participating in the diurnal motion and consider only its second motion under discussion now, is seen to stand still, resume moving but in reverse, stand still for a second time, and then start moving again in its principal eastward direction. The planets execute this interrupted motion keeping always quite close to the circular path of the Sun’s annual motion, crossing it to pass above or below, just as the Moon also does in its monthly course round the Earth. Their own paths, however, deviate markedly from circularity (see above, 1.3.5), due to the episodes of directional reversal. Each planet appears to complete a trip round the Earth not in the same time, with two exceptions, Venus and Mercury (each needs a year). The interval between two successive directional reversals is different for each planet. The non-diurnal motion of the planets, the Sun and the Moon does not have uniform speed. Because of the combination of the westward diurnal motion with a slower and–always or mainly–opposite motion in planes that are slanted to the equator of the celestial sphere, the planets, the Sun and the Moon are each seen to trace out in a day a circular loop of a spiral wound around this starry sphere, background against which the peculiar motions of the wanderers are projected.

1.4. EUDOXUS’ THEORY OF HOMOCENTRIC SPHERES AND ARISTOTLE’S METAPH. ȁ 8 1.4.1. A brief outline In light of Metaph. ȁ 8, scholars assume that, in order to handle the zodiacal motion, Aristotle considered the heavens not a single spherical shell of the ¿rst simple body but an onion-like structure made up of a number of concentric shells of this simple body, with no vacuum between two consecutive shells.62 61

It is not the case that the stars are carried round as if they were a dead weight. That they revolve diurnally as ¿xed parts of the rotating mass of the ¿rst simple body surrounding them is shown in Cael. B 8 (cf. Appendix 7). For this mass forming a spherical shell see the arguments Aristotle offers in Cael. B 4, some of which are discussed below, in 2.3. 62 See e.g. Bodnár & Pellegrin (2006) 271, Broadie (2009) 231; cf. Heglmeier (1996) 51.

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This view of the heavens was based on an insight of Aristotle’s older contemporary Eudoxus of Cnidus, a mathematician and astronomer.63 A point of the innermost of four homocentric spheres, all of which rotate about different axes simultaneously, can be made to revolve round the center of the system in a way broadly similar to that in which a planet is seen to move round the Earth: that is, with a fast motion, like the diurnal rotation, and with a slower, opposite motion charted against the backdrop of the system’s outermost sphere, an abstract stand-in for the star-spangled celestial sphere, and at times reversing direction. This results from the rotation of each sphere being superadded to that of the next lower sphere in the system. To achieve the trick, parameters such as rotational axes, directions and periods must be chosen appropriately. What matters here is that Aristotle is thought to have turned seven Eudoxean systems of homocentric spheres, ¿ve for the planets, one for the Sun and one for the Moon, each of which needed not four but three homocentric spheres, into as many systems of homocentric spherical shells of the ¿rst simple body, plugged into one another in the order he deemed correct. The celestial object itself is assumed to be immovably embedded within the mass of the innermost shell in its system, its motion being due to the rotation of this shell as modi¿ed by the rotations of the outer component parts of the system.64 Aristotle is credited with the addition of a number of extra spherical shells between two successive systems, also made up of the ¿rst simple body, in order to allow the outermost shell in the lower system to spin uninÀuenced by the innermost shell in the upper system, and to follow the diurnal rotation of the outermost shell in the Saturnian system, Saturn being the planet which is farthest out from the Earth (see Appendix 8). This shell shares its rotational period and direction with its counterparts in the six inner systems of shells, producing each the motions of Jupiter, Mars etc. None of its six inferior counterparts, however, need be assumed to carry “copies” of the stars. According to Simplicius, Theophrastus called anastrous, “lacking celestial objects”, all spheres except the centermost in a Eudoxean deferent system of a wanderer (in Cael. 493.11–20 [Heiberg] = Thphr., fr. 165B FHSG). 63 On the dates of Eudoxus see Zhmud (1998) 227–228. 64 Aristotle does not tell us how Eudoxus ordered the Moon, the Sun and the ¿ve planets. He remarks only that Callippus of Cyzicus, who “succeeded” Eudoxus and introduced a few modi¿cations to the original theory of homocentric spheres in an attempt to make it “yield the phenomena”, adopted the same ordering of the spheres as his predecessor–that is, he adopted the Eudoxean ordering of the seven wanderers (Metaph. ȁ 8, 1073b32–33). Aristotle’s comment might be understood as a hint that the Eudoxean ordering had not been universally accepted. We can assume that he followed the order adopted by Plato in R. 10, 616e4–617b5; it is also attested in the brief work de Mundo (2, 392a23–29) that has come down to us as part of the Corpus Aristotelicum. If so, the system of homocentric spheres for the Moon is inserted inside the system for the Sun. The system for the Sun is next inserted inside the system for Venus, which is plugged into the system for Mercury. The system for Mercury is plugged into the Martian system, that into the Jovian and the Jovian into the Saturnian. Later arrangements place the Sun after Venus and Mercury, and also exchange the places of these two planets.

1.4. Eudoxus’ theory of homocentric spheres and Aristotle’s Metaph. ȁ 8

35

1.4.2. A closer view The theory of homocentric spheres seems to have aimed at geometrically reproducing certain aspects of lunar, solar and planetary motion. (On the origins of the theory see below, 3.1.) Eudoxus assumed that the Moon, the Sun and the planets are each immovably af¿xed to its own sphere–in other words, that these seven celestial objects are just points of seven spheres, each of these seven spheres being the innermost one of a system of nested spheres. He posited four spheres for each of the ¿ve planets, three for the Sun and also three for the Moon. All spheres in a system are centered on the same point standing for the Earth, and are also assumed to simultaneously rotate uniformly on different axes, though not necessarily all in the same direction and with the same period. As already said, each sphere transmits its motion to the next one, so only the outermost sphere in a system rotates without being inÀuenced by the rotation of any of the rest; also, in all seven systems, the outermost sphere has the same direction and period of rotation. The stars are assumed to be af¿xed to it. Since there can be only one sphere of the ¿xed stars, one cannot avoid forming the impression that Eudoxus treated of seven highly idealized models of the cosmos, each being just the celestial sphere with the Earth at the center and with only one non-stellar celestial object inside (we have no evidence to assume that Eudoxus was interested in turning his theory of homocentric spheres into a physical system); from the Earth, this object appears to perform not a simple revolution but a complicated motion under the inÀuence of the combined rotations of all encasing spheres. A sphere is denoted by Si in the following outline of the theory. The index shows the order of the sphere in the system to which it belongs counting from the outside. In the lunar model, the equator of S2 stands for the ecliptic. The angle between the equators of S1 and S2 is set equal to the angle between the ecliptic and the celestial equator (the obliquity of the ecliptic). The angle, now, between the equators of S2 and S3 is set equal to the maximum observed latitudinal deviation of the Moon from the ecliptic.65 The Moon is af¿xed to the equator of S3. According to Simplicius, S3 spins slowly westwards, whereas S2 rotates faster in the opposite direction (in Cael. 494.23–495.16 [Heiberg ] ). Until recently, it was thought that, pace Simplicius, it must be S3 that rotates eastwards, completing a rotation in about a month, the time the Moon needs to traverse the background of the zodiacal constellations, and S2 that spins oppositely with a leisurely period of approximately 18.6 years, thus carrying westwards the points called “nodes”, where the Moon crosses over the ecliptic in its monthly journey around the Earth–otherwise, the Moon would not spend time both above and below the ecliptic in the same month, as is observed.66 The combined rotations of S3 and S2 resulted in the interval between every other return of the Moon to the 65 About 5q. For an introduction to the orbit of the Moon see Kaler (2002) 244–251. 66 See Heath (1981) 197 and Evans (1998) 307–308. For the possible origin of this mistaken view see Mendell (1998) 190 n. 14.

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plane of the ecliptic, the nodical or draconitic month, being shorter than the rotational period of S3 .67 It is now clear that there is no real problem with the original assignation of rotational directions to the Moon’s S3 and S2 by Simplicius.68 Neither it nor the alternative, though, seems to be fully compatible with all of the crucial details the commentator further provides.69 S1, ¿nally, accounts for the participation of the Moon in the diurnal rotation. The Sun, too, is a point on the equator of S3 . In the Sun’s model, moreover, as in the Moon’s, the ecliptic is not the equator of S3 but of S2. Here, too, the axes on which S3 and S2 spin form an angle. But it is tiny (the Sun’s deviation from the ecliptic is a ¿ction).70 According to Simplicius, S3 rotates eastwards at a very slow pace. It was included because at summer and winter solstice the Sun does not always rise at the same points on the horizon. S2 spins eastwards at a much faster pace (in Cael. 493.11–494.22 [Heiberg ] ). Conceivably, the lengths of the rotational periods of S2 and S3 were appropriately chosen by Eudoxus, so that the combined rotations of the two spheres resulted in the time, which the Sun took to traverse a circle almost coincident with the ecliptic, being longer than 365 days by a fraction of a day.71 As with the Moon, it is usually assumed in the relevant literature that, pace Simplicius, it must be S2 that rotates eastwards at a very slow rate, whereas S3 spins much faster in the same direction, for otherwise the Sun would stay for a very long time above and below the ecliptic, describing each year a small circle parallel to this great circle of the celestial sphere.72 Perhaps this problem would not be serious, the angle between the rotational axes of S2 and S3 having been assumed exceedingly small. 73 It does not really exist if S3 is assumed to spin westwards, as in the Moon’s case.74 S1 accounts for the participation of the Sun in the diurnal rotation, which is its function in the models of the Moon and the planets, too. S2’s equator stands for the ecliptic in the models of planets, too. Its period is equal to the tropical period of the planet, the time the planet needs to go all the way around the zodiac.75 S2 rotates from west to east. The celestial object itself is 67 68 69 70 71 72 73 74

75

For the various “months”, i.e. the different periods associated with the Moon’s complicated motion, see Kaler (2002) 233–234 and 250. See Mendell (1998) 193–194. See Yavetz (2003) 327–328. On its possible origin see Neugebauer (1975) 629–630. Cf. Mendell (2000) 98. See Mendell (2000) 95–100. See e.g. Heath (1981) 198–200 and Evans (1998) 308; cf. Linton (2004) 28 n. 7. For ancient values of this angle see e.g. Heath (1981) 198–200 and Evans (1998) 308. See Mendell (1998) 191–193, where it is mistakenly assumed that the Sun’s S3 is said by Simplicius to rotate westwards, and that scholarly accounts interchange not only the rotational speeds reported by the commentator for S2 and S3 in the deferent system of the Sun but also the directions in which these spheres spin. As is recognized in Mendell (2000) 97 n. 54, however, Simplicius leaves no doubt that the Sun’s S2 and S3 spin in the same direction, from west to east. Nevertheless, there seems to be nothing intrinsically wrong with the alternative hypothesis that the Sun’s S3, like the Moon’s, spins slowly westwards. For the periods of the planets, the tropical and the synodic (the latter’s role in the theory of homocentric spheres will be explained below), see Evans (1998) 295.

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¿xed on the innermost sphere S4. This sphere spins about an axis ¿xed on S3. In its turn, S3’s own axis of rotation is ¿xed on the equator of S2. Now, S3 and S4 spin oppositely, but with the same period. Due to the combined rotations of these two spheres, the celestial object traces a closed curve, which is moved eastwards by the rotation of S2. If this curve’s long axis of symmetry coincides with the ecliptic, or if only the center of this axis lies on the ecliptic, depending on the reconstruction of the theory as will be explained next, then the combined rotations of all three spheres cause the planet to trace above and below the ecliptic a more complicated curve, whereupon its motion is mainly to the east but reverses occasionally, and then resumes the principal direction. The common rotational period of S3 and S4 is the synodic period of the planet, the time between two successive retrogradations. According to what can be justly called the traditional reconstruction of the theory, which is due to Schiaparelli, the planet is set on the equator of the innermost sphere S4.76 The curve it traces due to the combined opposite rotations of S3 and S4 is 8-shaped, and is known as hippopede, “horse fetter”.77 The angle at which this retrogradation generator intersects itself is equal to the inclination between the rotational axes of S3 and S4. An alternative reconstruction, due to Yavetz, sets the planet on a circle of latitude near one of S4’s poles.78 On this reconstruction, the combined rotations of S3 and S4 make the planet trace an unremarkable elongated loop; unlike the hippopede, it does not intersect itself.79 On the traditional reconstruction, the shape of the retrogradation generator depends solely on the angle between the rotational axes of S3 and S4. On the alternative reconstruction, it is also determined by the latitude of the planet on S4.80 On Yavetz’s reconstruction, moreover, the retrogradation generator’s long axis of symmetry coincides with the ecliptic only if there is zero inclination between the plane of the ecliptic and that on which the axis of S4 is set before the whole system begins to move. If this inclination is not zero, then the retrogradation generator’s long axis of symmetry coincides with another great circle on S2, but its center remains on the ecliptic, and the planet’s path is still traced above and below this great circle on S2.81 On the traditional reconstruction, however, the center of the hippopede’s long axis of symmetry is displaced away from the ecliptic along with the rest of the axis if the angle at issue is not 90q. The hippopede’s long axis of symmetry, in other words, will lie on the equator of S2, with the planet threading its way below and 76 77 78 79 80 81

Schiaparelli (1875). The Italian astronomer is probably best known for his famous “discovery” of canali on Mars; see e.g. Lang (2003) 237–241. For the hippopede see e.g. Neugebauer (1953), Riddell (1979) and, especially, the detailed treatment in Mendell (1998). On iconography of horse fetters cf. Mendell (2000) 74 n. 21. Yavetz (1998) 225–237. In the alternative reconstruction, too, there is a role for the hippopede, not recognized in Yavetz (1998); but see Yavetz (2001) 70–75. Yavetz (1998) 226, with ¿g. 6 and 7 in 228. In each reconstruction, the path traced by the planet during retrogradation is markedly different. Yavetz (1998) 227–229, with fig. 8 and 9.

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above the ecliptic, only if it this angle measures 90q; otherwise, the entire trace of the planet will shift inappropriately to one side of the ecliptic only.82

1.4.3. “Failings” of the theory of homocentric spheres Irrespective of how it is reconstructed, the theory of homocentric spheres has no predictive power, and there is no evidence that coming up with even approximately accurate predictive models of celestial motions could have been a goal of Greek astronomers in the time of Aristotle and Eudoxus.83 With his theory, the Cnidian astronomer seems to have solely aimed at giving an idea of how some very broad aspects of the apparent motions of the Moon, the Sun and the planets can be reproduced geometrically if all celestial motion is assumed to be undeviatingly circular and totally uniform, like the diurnal revolution of the stars. He failed, or simply was not concerned, to account for some prominent phenomena known in his time, namely the inconstant speed of zodiacal motion, whether of the Sun, the Moon or a planet, and the changes in the Moon’s apparent diameter or in the brightness of the planets. His successors seem to have attempted to improve on his efforts.84 From Aristotle’s testimony in Metaph. ȁ 8, 1073b32–38, we know that a pair of spheres were added to the Eudoxean model of the Sun and another to the Moon’s by the astronomer Callippus of Cyzicus, with whom Aristotle was personally acquainted (Simp., in Cael. 492.31–493.11 [Heiberg]). Why Callippus added these extra spheres Aristotle does not clarify. Simplicius, who relies on the testimony of Eudemus, says that the motivation in the case of the Sun was to account for the inequality of the seasons–a phenomenon discovered in the ¿fth century by the astronomers Euctemon and Meton–in other words, to render the zodiacal motion of the Sun variable (in Cael. 497.15–24 [Heiberg]).85 82

Yavetz (1998) 229–230. That the hippopede, or Yavetz’ curve, had any role in the Eudoxean theory of the planets is denied by Bowen (2000b) 163–166; cf. n. 88 and 91 below. 83 “The predictive turn” of Greek astronomy seems to have occurred in the time of Hipparchus of Nicaea (second century BC), most probably under the inÀuence of Babylonian astronomy. See Evans (1998) 212–215 on the early history of solar theory. On Hipparchus and Babylonian astronomy see Toomer (1988). More general discussion in Jones (1996). 84 It is quite likely, moreover, that the theory of homocentric spheres began to be investigated in a purely geometric context. See Riddell (1979) for an intriguing study of the theory’s relevance to the problem of duplicating a cube, whose solution by Archytas of Tarentum, reportedly the teacher of Eudoxus (cf. D.L. 8.86), requires an ingenious kinematic construction of curves, exactly as does the theory of homocentric spheres. Riddell showed that Eudoxus could have provided a solution to the problem of doubling a cube via a quite simple modi¿cation to the deferent system for a planet in the theory of homocentric spheres, as Schiaparelli reconstructed it (see also Knorr [1993] 50–61). Eudoxus, though, could very well have started from geometry, and then gone on to astronomy. 85 As is clear from in Cael. 488.18–24 (Heiberg), Simplicius’ discussion of the theory of homocentric spheres in his comments on Cael. B 12 is based on the second book of Eudemus’ History of Astronomy, for the general content and organization of which see Bowen (2002a), and on a later, also lost, work On the Unwinding Spheres by Sosigenes (second century AD), a

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39

Similar motivation can be plausibly assumed in the case of the Moon.86 Later on, sometime in the third century BC, Autolycus of Pitane might have attempted to further modify the theory of homocentric spheres so as to make it yield a change in the Moon’s angular size and the brightness of the planets; his effort was unsuccessful.87 As reconstructed by Schiaparelli, moreover, the theory of homocentric spheres fails to give retrogradations of the planets with shapes that are even remotely similar to the ones that have already been observed in the sky, but, as reconstructed by Yavetz, it can postdict the shape of retrograde paths with surprising accuracy, provided that certain parameters are chosen appropriately and that one more sphere is added each to the Eudoxean models of Mars, Venus and Mercury, a further modi¿cation Callippus introduced into the original version of the theory, according to Aristotle’s testimony in Metaph. ȁ 8, 1073b32–38.88 The retrograde path obtained from a planet’s model, no matter whether the theory is reconstructed according to Schiaparelli or Yavetz, can be plotted pointwise on a plane with straightedge and compass, enhancing the probability that the theory of homocentric spheres arose from within geometry.89 teacher of Alexander of Aphrodisias (cf. n. 90 below). For Sosigenes and his lost treatise On the Unwinding Spheres see Moraux (1984) 335ff. It is often suggested that Simplicius knew Eudemus only via intermediaries such as Sosigenes (see e.g. Bowen [2002a] 317–318, Mendell [2000] 88–89). However, there seem to be cogent reasons to think that Simplicius had direct access to Eudemus’ works; see Zhmud (1998) 218 n. 23. 86 See Mendell (1998) 256. 87 Simp., in Cael. 504.22–505.11 (Heiberg); on what Simplicius says here about Venus see Bowen (2002b) 161. For the dates of Autolycus see Mendell (2000) 126 n. 98. What Autolycus actually did is unknown; Mendell (2000) 128 suggests that he might have attempted to remedy the situation not geometrically but via some physical assumptions. 88 Yavetz (1998) 243ff. (for Callippus see 257ff.; cf. Heglmeier [1996] 62–68). Operating within the reconstruction of the theory which is due to Schiaparelli, Mendell (1998) 216–217 thinks it very likely that Eudoxus thought of retrograde motion “qualitatively as a phenomenon requiring explanation”. This point can be used as an argument in favor of the traditional reconstruction of the theory; but see Yavetz (1998) 246ff. Goldstein (1997) 4 doubts the importance of retrogradations in fourth-century-BC Greek astronomy. His skepticism is supported strongly by Bowen (2001) 812–817/821–822 and (2002b) 157–158; see, however, the valid objections in Mendell (1998) 264 n. 5. Representing retrogradations need not have been the motivation for the introduction of the hippopede–at least not in the case of all planets. This is one possibility, alongside the representation of the distance from the Sun of Mercury and Venus, the two interior planets, and of the invisibility periods of all planets; see the conclusions in Mendell (1998) 228–229 (cf. 255–256 on Callippus). Mendell’s study of the mathematics of the hippopede shows that the theory of homocentric spheres, as traditionally reconstructed, can represent to some degree a number of planetary phenomena, none of which, though, can be selected as the theory’s empirical foundation in light of this mathematics alone. This can be an artefact of the dearth of historical evidence at our disposal concerning the theory; alternatively, it might show the fertility of Eudoxus’ brainchild, provided that Aristotle and Simplicius, on whose testimony our reconstructions of it rest, are mainly correct (cf. below, n. 91). 89 The pointwise construction is presented in Yavetz (2001) 77ff. For the possible importance of pointwise construction of curves in the time of Eudoxus cf. the interesting attempt at recovering Menaechmus’ solution to the problem of doubling a cube in Knorr (1993) 61–66. The emphasis on the possible emergence of the theory of homocentric spheres within a geometric

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Neither of the two reconstructions can mimic the variation in the shape of the retrograde path from one retrogradation to the next. Nor do they fare any better with the uneven bunching of retrogradations around the zodiac, for neither of them yields variable speed of zodiacal motion. The problem is hinted at by Simp., in Cael. 32.16–22 (Heiberg):  

3d K‡V TIVi )½HS\SR OEi /„PPMTTSR OEi Q{GVM XSÁ %VMWXSX{PSYN X‡N ƒRIPMXXS»WEN WJEfVEN¹TSU{QIRSM±QSO{RXVSYNXÚTERXiHM’ zOIfR[RzTIMVÏRXSWÉ^IMRX‡JEMR³QIRE TIVi QäR X¶ XSÁ TERX¶N O{RXVSR T„WEN P{KSRXIN OMRIlWUEM X‡N WJEfVEN, XÏR Hä ƒTSKIf[ROEiTIVMKIf[ROEiXÏRHSOS»RX[RTVSTSHMWQÏROEi¹TSTSHMWQÏROEiXÏRzR XElN OMRœWIWM JEMRSQ{R[R ƒR[QEPMÏR X‡N EeXfEN SºO eWG»SRXIN OEX’ zOIfREN X‡N ¹TSU{WIMNƒTSHMH³REM. The school of Eudoxus and Callippus and until Aristotle, assuming the unwinding spheres to be homocentric with the whole, attempted to save the phenomena through them, claiming that the spheres revolved about the center of the whole, but were unable to use these hypotheses to give an account of apogees and perigees, and of what seems to be direct and retrograde mo90 tion, and of the observed anomalies in the [celestial] motions.

1.4.4. Aristotle’s physicalization of the theory of homocentric spheres The Eudoxean theory of homocentric spheres is sketched out by Aristotle, in Metaph. ȁ 8. As is clear from the above, this is one of only two sources on which reconstructions of the theory are based, the other being Simplicius’ extensive commentary on Cael. B 12.91 Nothing in Metaph. ȁ 8 hints at the materiality of the spheres at issue, but this is implicit. In Cael. B 12, where the theory is undoubtedly presupposed, they are said to be spherical shells of an unnamed matter (293a4–11). That the ¿rst simple body is the only appropriate sort of matter is a reasonable assumption.92 context does not imply that Eudoxus had no concern with the ¿t of his theory with the phenomena of the sky (cf. Yavetz [1998] 252–253). On this view of the theory’s provenance, it might very well be the case that Schiaparelli and Yavetz have not in fact put forth competing reconstructions of the theory of homocentric spheres–they have instead recovered two different versions of it, both of which Eudoxus and his associates studied geometrically and with a view to possible applications in astronomy (cf. above, n. 84). 90 “The account of apogees and perigees” can be best understood as the explanation of the variations in the size of the Moon and the brightness of the planets via the assumption that each of these seven celestial objects revolves about the Earth at a variable distance, unlike in the theory of homocentric spheres, where all celestial objects orbit the Earth each at a constant distance (cf. Simp., in Cael. 504.22–26 [ H eiberg ] ) . The anomalies mentioned here are the variable speeds of zodiacal motions. The expression “unwinding spheres”, which also appears in the title of Sosigenes’ treatise mentioned above, in n. 85, is a metonymy for a system of homocentric spheres; see Mendell (2000) 92–93. 91 The reliability of Aristotle and Simplicius as sources for our knowledge of early Greek planetary theory, and so any reconstruction of a Eudoxean theory of the planets from the testimony of Aristotle and Simplicius, is summarily rejected by Bowen (2002b). 92 Cf. Gill (1991b) 260 n. 46.

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The theory of homocentric spheres calls for an onion-like structure of the heavens consisting in twenty-six spherical shells of the ¿rst simple body. If we add the extra–let us call them “Aristotelian”–shells of the ¿rst simple body that allow the outermost “Eudoxean” shell in an inferior celestial object’s deferent system to spin in the same sense and with the same period as the outermost shell in the Saturnian deferent system, the number of spherical shells of the ¿rst simple body making up the heavens increases to forty-three, and is raised to ¿fty-¿ve, when the improvements of Callippus of Cyzicus on the original theory of homocentric spheres are taken into consideration (1073b32–1074a12).93 As seen above, to better account for phenomena which Aristotle does not explain in Metaph. ȁ 8, Callippus added two spheres to Eudoxus’ solar system of homocentric spheres, two to the lunar, and a sphere each to the systems for Mercury, Venus and Mars (for the planets, Simp., in Cael. 497.22–24 [Heiberg], notes only that Eudemus, in his History of Astronomy, had explained the modi¿cations). This addition necessitates a further addition of ¿ve Aristotelian shells to the original seventeen such shells. Aristotle, however, has some qualms, which he does not explain, about adding an extra two spheres each for the Sun and the Moon. Accordingly, he proceeds to reduce the number of spherical shells of the ¿rst simple body making up the heavens from ¿fty-¿ve to forty-seven (1074a12–14). In all probability, this is a scribal error, or a calculational error on Aristotle’s own part, for the subtraction of four shells from a total of ¿fty-¿ve and a further subtraction of two more, the Aristotelian shells required by the two shells which have already been subtracted from the deferent system of the Sun, yields forty-nine, not forty-seven.94

1.4.5. The unmoved movers in the heavens The rotation of each of these spherical shells, the natural motion of the ¿rst simple body constituting each of them, has a so-called unmoved mover as its ¿nal, and perhaps ef¿cient, cause; bringing about motion without being itself in motion, a celestial unmoved mover is a perpetually active and disembodied intellect (Metaph. ȁ 7, 1072a19–b3 and b13–24).95 93

On the Aristotelian shells, which Aristotle himself calls “unwinding”, see Appendix 8. Participating in the rotation of a superior shell can be thought of as natural motion; see n. 112. 94 See Simp., in Cael. 503.10–20 (Heiberg) and Alex. Aphr., in Metaph. 705.39–706.8 (Hayduck). Sedley (2000) 331 n. 7 attributes the reduction in the number of the celestial unmoved movers from ¿fty-¿ve to forty-nine to Aristotle’s numerological concerns; see 3.2.2, however. 95 Aristotle thinks of unmoved movers as the originative links in the causal chains leading not only to substantial change in which individuals of various animal kinds are generated but also to our production of artifacts and effects of all kinds; see Ph. Ĭ 5, 256a4–21, and the discussion in Gill (1991a) 198–202. The belief that, ultimately, unmoved movers cause all heavenly motion makes good sense within Aristotle’s physics. It is celestial motions that cause the traditional four simple bodies to constantly turn into one another, thereby underpinning all substantial change and anthropogenic production. What is said in Metaph. ȁ 7 to be a ¿nal cause is the prime unmoved mover in the heavens, more on which below, but the same is clearly as-

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The shell of the ¿rst simple body, whose rotation such a mover causes, is said in Metaph. ȁ 7 to respond to its mover in a way that leaves no doubt that this shell is ensouled (1072b3–4).96 The moving disembodied intellect is perhaps to be understood as being simply the rotational period and direction of the shell which it moves, and the angle made by the equator of this shell with the referent plane of the equator of one of those other shells with which it forms a system. This set of parameters constitutes an intelligible form identical with the intellect whose eternally active thought thinks and knows this form. For Aristotle, the active intellect, the part of the soul that is capable of thought and knowledge, is identical with the object of its thought and knowledge, the form of something external to the soul somehow mapped on the intellect without informing a material substratum.97 It is by somehow sharing the same thoughts with its unmoved mover, where these thoughts are “stored”, that the soul of a spherical shell of the ¿rst simple body causes the in¿nitely many different values the parameters of the shell’s rotation might take to collapse into a de¿nite outcome.98 The nutshell of the cosmos, the spherical shell of the ¿rst simple body in the mass of which the stars are ¿xed, is made to move rotationally by the prime unmoved mover, under which the unmoved movers of all other shells of the ¿rst simple body are. How Aristotle understands the relation between the prime unmoved mover and its many subordinates is unclear. Given his explicit parallel in Metaph. ȁ 10 of the prime unmoved mover with the general of an army (1075a11–25), it seems that this celestial unmoved mover somehow “coordinates” all other such movers, perhaps in the sense that the intelligible form with which it is identical is a principle of them all. Indeed, the equator of the starry shell of the ¿rst simple body that the prime unmoved mover causes to rotate diurnally functions as the ultimate reference plane, to which the equators of all encased shells must be inclined each at the appropriate angle, and it is the rotational period of this shell that measures those of the encased shells.99 Aristotle might further believe that the prime unmoved mover coordinates all of its subordinates also in the sense that it always thinks, and thus is, the abstract mathematical structure realized materially in the heavens that is always being partially thought by the subordinate unmoved movers, each one of them thinking only the part appropriate to itself. If so, the spherical shell of the ¿rst simple body whose parts are the stars is the only one whose soul does not fully share the thoughts of its unmoved mover. In this respect, however, this shell is similar to all the other shells it contains, for its soul, too, shares the thoughts of the prime unmoved mover only in part. sumed to apply to all the other celestial unmoved movers. On their possibly being not simply ¿nal but also ef¿cient causes of motion see Graham (1999) 179–180. 96 The shell is said to be moved by its “desire” for the mover ; see Gill (1991b) 260 n. 44. On desire and celestial souls see also Falcon (2005) 87–97. 97 See de An. ī 4, 429a10–29, ī 7, 431b17, and ī 8. 98 Cf. Gill (1991b) 263. 99 For the conception of the prime celestial unmoved mover as coordinator of its many subordinates see Gill (1991b) 263–265.

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1.4.6. Ph. Ĭ 10 and the theory of homocentric spheres Metaph. ȁ, and chapter 8 in particular, carries forward Ph. Ĭ. In this elaborate book, Aristotle argues at length that to answer the question why motion and change in the cosmos are eternal, we must posit the existence of an immaterial unmoved mover as ¿rst cause of all motion, prerequisite of all change, and speci¿cally of “the ¿rst motion”–eternal rotation of one single object. The cause of this motion, however, must be itself unmoved. For, otherwise, we could not avoid wondering what might cause it to move, and so on ad in¿nitum. Moreover, had this cause been something material, it would not have been unmoved, let alone caused eternal locomotion.100 Aristotle, however, does not explain which object this unmoved mover causes to rotate, and how. But in Ph. Ĭ 10 he obscurely remarks that the unmoved mover is “situated” at the circumference of the object it causes to perform eternal rotational motion, and speci¿cally there where this motion is swiftest–i.e. where in the cosmos motion is swiftest (267b6–9). From this we can infer that in Ph. Ĭ he introduces the prime unmoved mover, which causes the physical analogue for the concept of the star-spangled celestial sphere to rotate once a day, from east to west. In Aristotle’s cosmos, the swiftest motion is of a point at the equator of this spherical shell of the ¿rst simple body.101 In Ph. Ĭ 5, moreover, Aristotle leaves open the possibility that the full explanation of eternal motion and change in the cosmos might require a multitude of unmoved movers, apparently because the diurnal rotation is not the only eternal motion in the celestial realm, though he does not try to hide his preference for a single unmoved mover (259a6–13). This is compatible with what is said in Metaph. ȁ 8, and thus it has been assumed that Ph. Ĭ must have been composed before Metaph. ȁ, where, it should be noted, the focus before ch. 8 is on the unmoved mover responsible for the rotation of the spherical shell of the ¿rst simple body carrying the stars round, as is clear from the opening of ch. 7 (1072a19–23).102 One can thus assume that Ph. Ĭ 5, and so Ph. Ĭ as a whole, must have been written by Aristotle with the theory of homocentric spheres in mind.103 This does not seem to be the case, however. The single object’s rotation brought about by the unmoved mover that is introduced in Ph. Ĭ is clearly assumed in Ph. Ĭ 10 as the only, or the most, uniform motion, sc. in the cosmos (267a21–b6). Aristotle states explicitly at the beginning of Cael. B 6, 288a13–17, his belief in the uniformity of the diurnal rotation of the spherical shell of the ¿rst simple body with the stars as its ¿xed parts, and there 100 An unmoved mover as ¿rst cause of motion seems to be tacitly introduced in Ph. H 1; for the unjustly unfavorable reception of this interesting book see Wardy (1990) 85–87. 101 Cf. Graham (1999) 177–178. A point at the equator of any spherical shell of the ¿rst simple body which is inside the shell carrying the stars round ¿xed in its mass, even if it rotates with the same period as the starry shell, moves with a slower linear speed, though at the same angular rate, since the radii of the two shells are unequal. See also 2.2.1 on “the ¿rst rotation”. 102 See Ross (1936)101–102 and cf. Graham (1999) 108. For Metaph. ȁ 8 as possibly a later addition to the book see Guthrie (1934), Frede (1971) 66–70. But cf. Frede (2000) 47–48. 103 Cf. Ross (1936)101–102, Gill (1991b) 257–258, Graham (1999) 119.

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can be no doubt that the rotations of all other shells of the ¿rst simple body assumed in Metaph. ȁ 8 to be nested within this starry shell are also unwaveringly uniform. Nowhere does Aristotle say this, but according to our sources, the point of the theory of homocentric spheres was to explain the observed motions of the Sun, the Moon and the planets as resultants of circular, uniform motions.104 Nothing suggests that Aristotle might have been unaware of this. If so, since the spherical shell of the ¿rst simply body in whose mass the stars are ¿xed moves, according to Ph. Ĭ 10, with the only, or the most, uniform motion in the cosmos, it can be concluded that Ph. Ĭ does not tacitly posit below this shell all the other shells of the ¿rst simple body assumed in Metaph. ȁ 8 to make up the heavens. In other words, Aristotle did not write Phys. Ĭ presupposing a cosmology based on a version of the theory of homocentric spheres.105 It can be objected that (a) when Aristotle says in Ph. Ĭ 10 of the diurnal revolution of the stars–the rotation of their deferent shell of the ¿rst simple body–that it is the only, or the most, uniform motion in the cosmos, he in fact compares it with the spiral motion of the Moon, the Sun or a planet having in mind the theory of homocentric spheres, not with the uniform rotation of any of these spheres, or of its Metaph. ȁ 8 physical analogue; (b) uniformity here is both of speed and of the path of motion, for in Aristotle’s physics uniformity can be understood in either way, as is clear from Ph. E 4, 228b15–28, and, as already pointed out, the theory of homocentric spheres was unable to reproduce the non-uniform speed of the zodiacal motion of the wanderers–we can assume that Aristotle did not care about this inability for the sake of the argument. The comparison, however, in (a) is quite unlikely if the spiral motion of the Moon, the Sun or a planet is assumed to result from a combination of a number of uniform rotations of spherical shells of the ¿rst simple body, “copies” of the deferent shell of the stars and thus naturally comparable to it, all the more so since their rotations are causally prior to the observed motions they produce. There is no point in comparing these observed motions with the diurnal rotation of the deferent shell of the stars and then declaring the latter, alone or especially, uniform in either sense of the term, if the former are each conceived of as resulting from the combined rotations of a number of deferent shells, each of which is as uniform a motion, once again in either sense of the term, as the diurnal rotation of the deferent shell of the stars (cf. ch. 3, n. 16). Aristotle’s remark in Ph. Ĭ 10 that the diurnal revolution of the stars, i.e. the rotation of their deferent shell of the ¿rst simple body, is the only, or the most, uniform motion makes good sense only if this revolution is compared with each wanderer’s zodiacal motion as is observed–that is, without its being understood within the framework of the physicalized theory of homocentric spheres. In Ph. Ĭ 10 Aristotle thinks that the ¿ve planets, the Sun and the Moon travel round the heavens without each being attached to the innermost of a number of simultaneously rotating deferent spherical shells, all of them made up of the ¿rst simple body. As re-

104 Simp., in Cael. 488.10–24 and 492.31–493.11 (Heiberg), translated below, in 3.1. 105 Cf. Easterling (1961) 138–148 on Cael. A–B, except B 12, on which see below, 3.3.

1.4. Eudoxus’ theory of homocentric spheres and Aristotle’s Metaph. ȁ 8

45

gards uniformity of speed, he does not know whether each of these seven celestial objects always takes the same time to travel round the zodiac or not; if the second, whether the variation is random or not, and in either case, whether the different parts of a wanderer’s zodiacal path in which the celestial object speeds up or slows down might change in a manner obeying any short- or long-term regularities.106 In other words, there are certain senses in which the zodiacal motion of the wandering celestial objects could be only less uniform, with regard to speed, than the diurnal revolution of the stars, which is the rotation of their deferent shell of the ¿rst simple body, not completely non-uniform.107 It should be noted here that the planets, the Sun and the Moon are clearly said in Cael. B 6 to move against the background of the stars non-uniformly–with regard to speed, as appears from the context–whereas the diurnal rotation of the deferent spherical shell of the stars is uniform. This passage, 288a13–17, does not acknowledge the possibility that the zodiacal revolutions of the seven wanderers are only less uniform than the diurnal rotation of the deferent shell of the stars, not completely lacking uniformity.108 There is no reason why Aristotle would deny uniformity of path to the zodiacal motion of the Sun, or consider this motion to actually follow a path (imperceptibly) less uniform than the diurnal circles of the stars, unless he did so to bring the Sun into line with the planets and the Moon. He could think of the Moon as moving round the Earth not in a perfect circle in order for their separation to vary, which could explain the changes in the apparent diameter of the Moon, but also be ready to concede that this path is very much like a circle, and this is perhaps the reason why the Moon’s orbit might be said to be neither absolutely non-uniform nor as uniform as the perfectly circular orbits followed by the stars in their diurnal motion. Viewed very broadly, as eastward motions, the paths in which the planets travel through the zodiac could also be said to be similar to–and thus sharing only to some degree the uniformity of–the diurnal, perfectly circular paths of the ¿xed stars (cf. below, n. 113). Perhaps Aristotle prefers to think that the diurnal revolution of the stars–the rotation of their deferent shell of the ¿rst simple body–is the sole, and not simply the most, uniform motion in the whole of the heavens, as regards both speed and shape of path, but it is not unlikely that he considers the zodiacal motion of the Sun as following a path which is as circular–and thus uniform with regard to form–as the diurnal circle of any star. When he says in Ph. Ĭ 10 that the diurnal rotation of the deferent shell of the stars is the sole, or the most, uniform motion in the cosmos, he might opt for the ¿rst possibility with uniformity of speed paramount in his mind, regarding which the Sun’s zodiacal motion lacks uniformity as much as that of the planets and the Moon does, in contrast to the diurnal rotation of the deferent shell of the stars. His opting for the ¿rst possibility, moreover, might be suggested by the above mentioned passage from Cael. B 6, where he says with106 In R. 7, 530a4–b4, Plato seems to think that all astronomical periods are inconstant and vary randomly. See Gregory (2000) 64–67. 107 Ph. E 4, 228b18–19, seems to suggest Aristotle’s belief in a continuous gradation from perfect uniformity to complete non-uniformity. Cf. Ross (1936) 633 ad loc. 108 Cael. B 6, 288a13–17, is discussed below, in 3.1 and 3.2.1; cf. Cael. B 10, 291a34–b1.

46

1. Aristotle’s cosmology

out quali¿cation that the zodiacal motion of the wanderers is non-uniform–as regards speed–unlike the diurnal rotation of the deferent shell of the stars. If Aristotle thinks of this motion as the only, or the most, uniform in the heavens, which is suggested by Ph. Ĭ 10 and Cael. B 6, then it is hard to believe that he also considers the theory of homocentric spheres an even approximately correct physical description of this cosmic realm.109 What we must not lose sight of is the fact that in Metaph. ȁ 8 he outlines the theory of homocentric spheres, and sketches a structure of the heavens based on it, simply in order to give an example of how astronomy may contribute, with its study of celestial motions, to precisely determining the multitude of the unmoved movers that might be needed to explain the eternity of motion and change in the cosmos. From this, however, it does not follow that Aristotle accepts the theory of homocentric spheres, in its Callippean or Eudoxean version, as guide to the structure of the heavens, which seems to be suggested by Ph. Ĭ 10 and Cael. B 6, too, contrary to what is read in the relevant literature (cf. Simp., in Cael. 505.27–506.8 [Heiberg]).

1.5. WHAT COMES NEXT The third chapter of the present book is a fuller defense of this thesis. The second chapter argues that when Aristotle came up with the concept of the ¿rst simple body, he considered this new type of matter to be only the ¿ller of the uppermost place of the cosmos, where the stars are, and the constitutive matter of these celestial objects alone, not of the planets, the Sun and the Moon, too. Originally, that is, within Aristotle’s cosmology the ¿rst simple body served the limited purpose of turning the astronomical concept of the celestial sphere into a physical object–a diurnally rotating shell of matter, in the mass of which the stars were ¿xed as its parts, and thus the crust of the remaining cosmos. At the time, Aristotle thought that the cosmic stratum of the simple body ¿re reached up to the lower boundary-surface of the one single shell of the ¿rst simple body, ¿lling up the remaining part of the heavens, and also making up the planets, the Sun and the Moon. Later on, Aristotle thought he had strong reasons to extend dramatically the cosmological role of the ¿rst simple body into that of a sole upper body, a single ¿ller of the heavens and constituent of all celestial objects. He dilated its spherical shell so as to include the seven wanderers, and shrank compensatorily the underlying spherical layer of ¿re around that of the adjacent air. Cael. A 2–3 date from the ¿rst phase, Mete. A 2–3 from the second. Cael. B 7, and perhaps B 8, was written in view of the expanded role of the ¿rst simple body. 109 The view rejected here seems to be supported by Lloyd (1996)168, who says that the theory of homocentric spheres “was supposed to give a good ¿rst-stage approximation to a solution” to problems posed by the speed of the zodiacal motion of the non-¿xed celestial objects, and the stations and retrogradations of the planets, “which Aristotle himself felt con¿dent enough about to adapt for his own metaphysical purposes” (showing the existence of order in the heavens). Cf. Falcon (2005) 75 n. 19.

1.5. What comes next

47

Carried round diurnally, like the stars, with the surrounding mass, the ¿ve planets, the Sun and the Moon, unlike the stars, were not thought of as being ¿xedly embedded in it, but as being able to pursue, simultaneously with their participation in the diurnal rotation, each a characteristic motion in the opposite direction, which was not analyzed into uniform and circular components, as in the Metaph. ȁ 8 cosmology, which is based on the theory of homocentric spheres. Aristotle does conclude in Cael. B 8 that neither the stars nor the other celestial objects, the planets, the Sun and the Moon, move “by themselves”, for all of them are spherical, and thus lack protruding locomotive organs, nor do they appear to roll (290a7–b11; cf. Cael. B 11). This does not entail the Metaph. ȁ 8 cosmology, however. He shows ¿rst that the stars do not trace their parallel diurnal circles moving independently of the surrounding mass, but as ¿xed parts of this mass, and then proceeds to bolster his conclusion based on the obvious sphericity of the Sun and the Moon, which he extends to all celestial objects. From this, however, it does not follow that the ¿ve planets, the Sun and the Moon are each ¿xed in a spherical deferent shell, just as the stars are ¿xed in a single such shell. If it did–from the principle invoked in Cael. B 11, 291b17–18, “what holds of one celestial object holds of all”–it could also follow that the stars, too, have zodiacal motion. A celestial object does not move zodiacally just as naturally moving matter–or matter forced to move by some naturally moving matter–moves: for its zodiacal motion is also caused by a soul–see below–which must be unlike the soul of a terrestrial animal. Following Plato (Lg. 10, 899a2–4), Aristotle might consider a celestial soul capable of bringing about motion thanks to its having “extremely amazing powers”–that is, even if what it moves lacks locomotive organs, being spherical, and does not roll. Now, the Sun and the Moon have observedly spherical shape, lack locomotive organs, and do not roll. So, if all celestial objects can be plausibly assumed to be spherical and also not to roll, this supports, if applied to the stars alone, the already established conclusion that these celestial objects move by being ¿xedly embedded in the rotating mass of a deferent spherical shell. However, this conclusion need not apply to each of the ¿ve planets, the Sun and the Moon (on Cael. B 8 see also Appendix 7). If so, Aristotle’s cosmology is totally in line with what was observationally known in his day about the motion of each planet, the Sun and Moon, for it assumes that each of these celestial objects moves zodiacally, opposite to the direction of the ¿xed stars, just as it appears to do. A conception of the physical structure of the heavens based on the theory of homocentric spheres, in either of its versions available to Aristotle, yields zodiacal motions of the ¿ve planets, the Sun and the Moon which are incompatible with observation, strikingly so in the case of the planets. When the upper body in the realm of the planets, the Sun and the Moon was the simple body ¿re, the diurnal motion of each of these seven celestial objects was enforced, being due to participation in the diurnal rotation imposed on the cosmic layer of ¿re by the overlying spherical shell of the ¿rst simple body. Its zodiacal motion was due to its motive and guiding soul, which might or might not

48

1. Aristotle’s cosmology

have been considered immediately subordinate to an unmoved mover.110 The deferent shell of the stars was in all probability assumed from the beginning to be guided by its own soul, which determined the direction and the period of the rotation of this shell–the natural motion of the ¿rst simple body.111 Subsequently, with the promotion of the ¿rst simple body into the sole upper body, the diurnal motion of the Sun, the Moon and all ¿ve planets became natural.112 What about their zodiacal motion, however? If it followed perfectly circular paths and had uniform speed, it could be thought of as the natural motion of the ¿rst simple body, the souls of the planets, the Sun and Moon only guiding it, each of them being guided in its turn by an immaterial unmoved mover. But it is not circular–probably with the sole exception of the Sun–nor does it have uniform speed. How could it be the natural motion of the ¿rst simple body? 113 110 For views on the position of the celestial unmoved movers in the evolution of Aristotelian physics see the survey in Graham (1996) 171–172. 111 I agree with Ross (1936) 97–98 that Aristotle’s explanation of celestial motion in the de Caelo requires souls; for the opposite view see Guthrie (1939) xxix–xxxvi. Although Aristotle strongly denies in Cael. B 1, 284a27–31, that the spherical shell of the first simple body with the stars as its parts is constrained by a soul to undergo eternal rotation which is not the natural motion of the first simple body, in Cael. B 2, 284b6–34, this shell is said to be alive and ensouled. Aristotle, moreover, says in Cael. B 5 that the direction of its diurnal rotation, from east to west, is not accidental but what is best for it, for nature always does choose the best from among all available possibilities (288a2–12). Nature here can be plausibly identified with the shell’s soul. Its role is thus not to power the shell’s rotation but to ¿x its direction, probably its period, too, collapsing into a single actuality the existing possibilities for how fast the first simple body constituting the shell undergoes its natural motion, as well as in what direction (cf. above, 1.4.5). That souls are also involved in the motions of the planets, the Sun and the Moon is assumed in Cael. B 12, 292a18–21. A denial in Cael. B 9, 291a22–26, that all celestial motion is either due to soul or enforced, i.e. mechanically, must be read within its context. What Aristotle thinks not to be either due to soul or enforced is celestial motion not as he understands it but through a stationary medium; cf. ch. 2, n. 42, and 3.4.3. Celestial souls differ radically from terrestrial ones; see Falcon (2005) 87–97. 112 Since a planet, the Sun and the Moon must also move opposite to the diurnal rotation, but the natural motion of the ¿rst simple body cannot be simultaneously in opposite directions, if the ¿rst simple body can undergo natural motion only, we need to distinguish between its “passive” and “active” natural motion. Consider a spherical shell of this simple body in the Metaph. ȁ 8 cosmology. It undergoes “passive” natural motion in following the rotation of the shell inside which it is nested and which does not spin in the direction of its rotation–its “active” natural motion–but oppositely. The opposite rotation, however, could be the motion proper to this mass of the ¿rst simple body, which is why we can consider it a “passive” natural motion. If the Aristotelian heavens are structured as proposed here, the participation of the Sun, the Moon and the planets in the diurnal rotation was considered their passive natural motion when Aristotle came to think of them as consisting of the ¿rst simple body. In executing passive natural motion, the seven wandering celestial objects followed the diurnal rotation of the shell of the ¿rst simple body whose non-¿xed parts, unlike the stars, they were. But the zodiacal motion of these masses of the ¿rst simple body could not be easily thought of as active natural motion of the ¿rst simple body, guided in each case by a soul. See the following discussion. In Aristotle’s surviving works there is no mention of species of natural motion. 113 In Cael. B 10, 291a34–b10, Aristotle assumes that each of the wandering celestial objects moves zodiacally along its own circle. However, since this passage, which is quoted and translated below, in 2.2.1, is incompatible with a conception of the heavens based on the theory of

1.5. What comes next

49

The soul of a wanderer could “tell” it to vary the pace of its natural motion as necessary. A planet could slow down so much that from the Earth its motion would be seen to temporarily come to a stop, though in fact it does not. The changes in the direction of its motion could also be guided by its soul–if the direction of the natural motion of the ¿rst simple body is chosen by a soul. But the natural motion of the ¿rst simple body has uniform speed and is eternal because this simple body is ungenerated, indestructible and totally changeless, and its natural motion is circular. How the expanded role of the ¿rst simple body–whose nature is to always orbit circularly and uniformly a point on an axis passing through the center of the cosmos–as ¿ller of the whole of the heavens and single constituent of all celestial objects could be brought into line with the lack of circularity in the zodiacal motion of at least the planets, as well as with the lack of uniform speed in the zodiacal motion of all wanderers, was perhaps one of the toughest open problems in Aristotle’s cosmology. He need not have considered it solvable, assuming that he thought of the heavens as intrinsically intelligible, though not fully intelligible to us.114 homocentric spheres (see 3.1, 3.2.1, with n. 16, and 3.4.1), the unquali¿ed assumption–in a certain sense allowable within the framework of the theory of homocentric spheres–that at least each planet moves along a circle against the backdrop of the zodiacal constellations should not be understood literally (cf. above, 1.3.4 and 1.4.6). The same must hold for Aristotle’s characterization of all celestial objects as X‡zKO»OPMEWÉQEXE or X‡zKOYOPf[NJIV³QIREWÉ- QEXE (Cael. B 3, 286b6–7, and Mete. A 2, 339a12–13); cf. the expression X‡JIV³QIREXŸR JSV‡RXŸR zKO»OPMSR in Cael. B 14, 296a34–35, for the planets, the Sun and the Moon as sharing in the diurnal rotation and simultaneously undergoing zodiacal motion (see also Metaph. ȁ 8, 1073a28–32). Easteling (1961) 138–148 argues that in Cael. A–B Aristotle operates not with the Metaph. ȁ 8 cosmology, which is based on the theory of homocentric spheres, but with Plato’s Timaean cosmology, where the planets, the Sun and the Moon perform their zodiacal motions in coplanar circles, centered on the Earth. Even if Plato could account for the retrogradations of the planets in the manner Knorr (1990) 313–317 suggests, however, the Timaeus circular motion of the planets among the stars of the zodiacal constellations cannot easily be accommodated with Aristotle’s awareness that the planets and the Moon vary their distances from the Earth (see Simp., in Cael. 505.21–27 [Heiberg] = Arist., fr. 211 Rose; translation below, in 3.6). Assuming that some parts of the ¿rst simple body move naturally in circles not homocentric with the cosmos is no less problematic than assuming that there are some parts of this simple body which move naturally not in circles. For another problem arising from Aristotle’s broad conception of the ¿rst simple body as sole upper body see ch. 2, n. 65. 114 See Falcon (2005) ch. 4. Cf. also the comparison in Cael. B 4, 287b14–21 (translated at the end of 3.7 below), of the ¿rst simple body with water, air and ¿re in terms of subtlety of texture, and thus in terms of the closeness to “geometric” perfection of the shape the mass of each of these simple bodies can take on at the cosmological scale; but ¿neness and coarseness, according to GC B 2, 329b15–330a29, derive from the basic tangible qualities, out of which the traditional simple bodies, unlike the ¿rst simple body, are thought to be constituted, so it is not clear how the ¿rst simple body can be considered much ¿ner, or much more “Àuid”, than even ¿re (cf. Appendix 5). Whether Aristotle’s heavenly stuff is hard or Àuid was a much discussed issue in medieval cosmology (see Grant [1996] 324ff.). Aristotle, however, certainly thinks of the ¿rst simple body as a tenuous–actually, the most tenuous–Àuid, and need not have been disturbed by the notion that some parts of it–the wandering luminaries–plow through the rest of its mass, despite his implicit reference in Cael. B 8, 290a5–7, to the continuity of the ouranos (for the meaning of the term ouranos in the context of these lines see Appendix 7).

2. THE STUFF OF THE HEAVENS 2.1. INTRODUCTION In Cael. B 7, 289a11–33, Aristotle leaves no doubt that he thinks of the ¿rst simple body, the new type of matter he introduced in Cael. A 2–3, as both making up a diurnally rotating spherical shell, ¿xed parts of whose mass are the stars, and ¿lling the rest of the heavens. The ¿rst simple body thus constitutes all celestial objects–the stars as well as the planets, the Sun and the Moon, the septet of the wandering luminaries that are below the stars, and thus much closer to the Earth:1 

4IViHäXÏROEPSYQ{R[R†WXV[RyT³QIRSR‰RIhLP{KIMR, zOXfR[RXIWYRIWXŠWMOEi zRTSfSMNWGœQEWMOEiXfRINEdOMRœWIMNEºXÏR. IºPSKÉXEXSRHŸOEiXSlNIeVLQ{RSMN yT³QIRSRšQlRX¶|OEWXSRXÏR†WXV[RTSMIlRzOXS»XSYXSÁWÉQEXSNzRÛXYKG„RIM XŸR JSV‡R }GSR, zTIMHŸ }JEQ{R XM IREM · O»OP. J{VIWUEM T{JYOIR· ÊWTIV K‡V Sd T»VMRE J„WOSRXIN IREM HM‡ XSÁXS P{KSYWMR, ´XM X¶ †R[ WÏQE TÁV IREf JEWMR, ÇN I½PSKSR ¸R |OEWXSR WYRIWX„REM zO XS»X[R zR SmN |OEWX³R zWXMR, ±QSf[N OEi šQIlN P{KSQIR. šHäUIVQ³XLNƒT’ EºXÏROEiX¶JÏNKfRIXEMTEVIOXVMFSQ{RSYXSÁƒ{VSN¹T¶ X¢NzOIfR[RJSVŠN. T{JYOIK‡VšOfRLWMNzOTYVSÁROEi\»PEOEiPfUSYNOEiWfHLVSR· IºPSKÉXIVSR SÃR X¶ zKK»XIVSR XSÁ TYV³N, zKK»XIVSR Hä ± ƒœV· SmSR OEi zTi XÏR JIVSQ{R[RFIPÏR· XEÁXEK‡VEºX‡zOTYVSÁXEMS¼X[NÊWXIXœOIWUEMX‡NQSPYFHfHEN, OEi zTIfTIV EºX‡ zOTYVSÁXEM, ƒR„KOL OEi X¶R O»OP. EºXÏR ƒ{VE X¶ EºX¶ XSÁXS T„WGIMR. XEÁXE QäR SÃR EºX‡ zOUIVQEfRIXEM HM‡ X¶ zR ƒ{VM J{VIWUEM, ·N HM‡ XŸR TPLKŸR X® OMRœWIM KfKRIXEM TÁV· XÏR Hä †R[ |OEWXSR zR X® WJEfVZ J{VIXEM, ÊWX’ EºX‡ QäR QŸ zOTYVSÁWUEM, XSÁ H’ ƒ{VSN ¹T¶ XŸR XSÁ OYOPMOSÁ WÉQEXSN WJElVER µRXSN ƒR„KOL JIVSQ{RLN zOIfRLN zOUIVQEfRIWUEM, OEi XE»X: Q„PMWXE ¯ ± PMSN XIX»GLOIRzRHIHIQ{RSN· HM¶HŸTPLWM„^SRX³NXIEºXSÁOEiƒRfWGSRXSNOEi¹TäVšQÏR µRXSNKfKRIXEMšUIVQ³XLN. Next we should speak of the so-called celestial objects, their constituents, shapes and mo2 tions. It is most reasonable, and consistent with what we have already said, to think of each celestial object as consisting of the body in which it moves, since we said that there is a [simple] body that by nature moves circularly. Those who think that the celestial objects are fiery put forth their view on account of this, i.e. because they say that the upper body is fire, thinking it reasonable that each thing consists of the matter in its surroundings, a view we share. The celestial objects generate heat and light as they move against the frictional resistance of the air, for motion naturally causes even wood, stone and iron to ignite, so it is reasonable that this applies to what is more similar to fire, as air is. For example, flying missiles catch fire themselves so that leaden balls melt, and if the missiles themselves catch fire, the same must happen to the air around them. The missiles themselves are heated because they move through the air, which turns into fire as is impacted by the motion. However, each celestial object is carried round in the sphere, so is not set on fire itself, whereas the air below the sphere of the circularly moving body is necessarily heated because of the rotation of the sphere, and espe-

1

2

This twofold division of the heavens is made explicit in Cael. A 9, 278b11–21, a passage discussed below, in 2.2.3. On the boundaries of the heavens see above, 1.3.2. On the sphere mentioned in the concluding lines of this passage see below, 3.7; cf. Easterling (1961) 146–147. As is made clear by what follows, X‡†WXVE here are celestial objects, not only stars.

2.1. Introduction

51

cially where the Sun happens to be fixed right above. This is the reason why heat is produced as the Sun gets nearer, rises higher and reaches its highest altitude above us.

As Aristotle explains in Mete. A 3, the Sun produces heat because its motion is fast enough and takes place sufficiently close to the air. The motion of the Moon is not as fast, so despite the fact that the Moon is closer to the Earth than the Sun, we do not perceive any heat from its motion; although the stars orbit the Earth sufficiently fast, they do so at immense distances from the air to make it produce heat (341a12–30). What applies to the stars might or might not hold of the planets, too, which are not mentioned; at issue here seems to be the speed not of the zodiacal motion of the Sun and the Moon (as well of the planets) but of their diurnal motion minus the zodiacal.3 Leaving aside Aristotle’s curious belief that there can be friction between the celestial objects and air, despite the fact that the celestial objects do not move in this simple body, his view that the first simple body is the constituent matter of all celestial objects, and also pervades the whole of the heavenly realm, is unambiguously asserted in Mete. A 2 as well, where the readers are reminded of his earlier conclusions, evidently reached in the de Caelo, that there are five principles of all material things–five simple bodies. Four of them make up the region of the cosmos around the Earth (cf. 1.3.2), and thus all composite bodies which constitute everything within the scope of our immediate experience, whereas the fifth forms the material things that move circularly about (points which coincide with, or are on the same line passing through) the center of the cosmos–the celestial objects. Aristotle clearly speaks of the first simple body here. Two of the four other simple bodies, earth and water, move naturally towards the center of the cosmos in straight lines. Air and fire have a natural motion that is radial, too, but away from the center of the cosmos, towards its periphery. Of these four simple bodies, earth is the one sinking to the bottom, fire the one rising to the top. The other two are arranged in the middle, air closer to fire and water to earth (339a11–27): 

)TIMHŸK‡VHMÉVMWXEMTV³XIVSRšQlRQfEQäRƒVGŸXÏRW[Q„X[R, z\ÐRWYR{WXLOIRš XÏRzKOYOPf[NJIVSQ{R[RW[Q„X[RJ»WMN, †PPEHäX{XXEVEWÉQEXEHM‡X‡NX{XXEVEN ƒVG„N, ÐR HMTP¢R IREf JEQIR XŸR OfRLWMR, XŸR QäR ƒT¶ XSÁ Q{WSY XŸR H’ zTi X¶ Q{WSR· XIXX„V[RH’ µRX[RXS»X[R, TYV¶NOEiƒ{VSNOEi¼HEXSNOEiK¢N, X¶QäRXS»XSMN TŠWMR zTMTSP„^SR IREM TÁV, X¶ H’ ¹JMWX„QIRSR K¢R· H»S Hä ˆ TV¶N E¹X‡ XS»XSMN ƒR„PSKSR}GIM(ƒŸVQäRK‡VTYV¶NzKKYX„X[XÏR†PP[R, ¼H[VHäK¢N)· ±HŸTIViXŸR K¢R ´PSN O³WQSN zO XS»X[R WYR{WXLOIXÏRW[Q„X[R· TIVi S X‡ WYQFEfRSRXET„UL JEQäR IREM PLTX{SR. }WXMR H’ z\ ƒR„KOLN WYRIGŸN SÂXSN XElN †R[ JSVElN, ÊWXI TŠWEREºXSÁXŸRH»REQMROYFIVRŠWUEMzOIlUIR· ´UIRK‡VšX¢NOMRœWI[NƒVGŸTŠWMR, zOIfRLREeXfERRSQMWX{SRTVÉXLR. TV¶NHäXS»XSMNšQäRƒfHMSNOEiX{PSNSºO}GSYWE XÚX³T.X¢NOMRœWI[N, ƒPP’ ƒIizRX{PIM· XEÁXEHäX‡WÉQEXET„RXETITIVEWQ{RSYN HM{WXLOIX³TSYNƒPPœP[R.

3

Cf. 1.2.5, with n. 26, and Appendix 4. Aristotle recognizes the operation of another mechanism by which the air around the Earth is heated. Because of the rapid diurnal rotation of the spherical shell of the ¿rst simple body, which overlies the spherical shell of ¿re, quantities of the simple body ¿re are continually forced downwards, into the spherical shell of air, which is heated up; see Mete. A 3, 341a30–31, and cf. 340b32–341a9. But it is a reasonable assumption that the heating of the air is primarily due to the Sun.

52

2. The stuff of the heavens We have established earlier that one principle of material things makes up those that are in circular motion, and that there also exist four other [simple] bodies, because of the four principles, which have a twofold motion, away from and toward the center [of the cosmos]. Of these four bodies, which are fire, air, water and earth, the one always rising to the top is fire, the one always sinking to the bottom is earth; the other two bear to each other a relationship which is similar to that between earth and fire (air being the closest of the other four to fire, water to earth). The whole region of the cosmos around the Earth is made up of these four bodies, and it is to the phenomena that occur in this region that we say we must now turn our attention. This part of the cosmos is necessarily continuous with [the part in which] the upper motions [take place], so all of its powers are governed from there, for as first cause of motion for all things must be posited the origin of this motion;4 moreover, the first cause at issue is eternal, and there is no place where its motion stops, for it is always completed, but all of those four bodies stand apart from one another in places separated by finite distances.5

Aristotle’s belief that the first simple body makes up all celestial objects, and also pervades the whole of the heavens, is also unambiguously asserted in the next chapter, Mete. A 3. In this chapter, Aristotle states the question pertaining to the region of the cosmos immediately around us (cf. 1.3.2) that he will go on to deal with first (339b2–16): 

4VÏXSR QäR SÃR ƒTSVœWIMIR †R XMN TIVi X¶R OEPS»QIRSR ƒ{VE, XfRE XI GVŸ PEFIlR EºXSÁXŸRJ»WMRzRXÚTIVM{GSRXMO³WQ.XŸRK¢R, OEiTÏN}GIMX®X„\IMTV¶NXŒPPE X‡PIK³QIREWXSMGIlEXÏRW[Q„X[R. ±QäR K‡VHŸX¢NK¢N µKOSNTLPfOSN†RXMNIhL TV¶N X‡ TIVM{GSRXE QIK{UL, SºO †HLPSR· žHL K‡V ÑTXEM HM‡ XÏR ƒWXVSPSKMOÏR UI[VLQ„X[R šQlR ´XM TSP¾ OEi XÏR †WXV[R zRf[R zP„XX[R zWXfR. ¼HEXSN Hä J»WMR WYRIWXLOYlER OEi ƒJ[VMWQ{RLR S½U’ ±VÏQIR S½X’ zRH{GIXEM OIG[VMWQ{RLR IREM XSÁ TIViXŸRK¢RdHVYQ{RSYWÉQEXSN, SmSRXÏRXIJERIVÏR, UEP„XXLNOEiTSXEQÏR, O‰RIh XM OEX‡ F„USYN †HLPSR šQlR zWXMR. X¶ Hä HŸ QIXE\¾ X¢N K¢N XI OEi XÏR zWG„X[R †WXV[RT³XIVSR|RXMRSQMWX{SRIREMWÏQEXŸRJ»WMR¡TPIf[, O‰RIeTPIf[, T³WE, OEiQ{GVMTSÁHMÉVMWXEMXSlNX³TSMN; First of all, one must tackle a question concerning the so-called air, what we must suppose its nature to be in the part of the cosmos that contains the Earth, as well as how it is disposed in relation to the other so-called elements of material things. For the size of the Earth, by comparison to the structures around it, is not unclear, having now been shown by astronomical studies to be much smaller than even some celestial objects. Nor do we see water, and is impossible for it, to be aggregated separately from its mass existing around the Earth, i.e. both from as much of it as we see, seas and rivers, and from any that might be hidden from us deep underground. With regard, however, to what ¿lls up the space between the Earth and the most distant celestial objects, are we to think it is one body, or more, and if more, how many, and where does one stop and the other begin?

Next Aristotle reminds the reader that he has dealt with the first simple body, “the first element”, earlier on, an indisputable reference to the de Caelo, where he has also explained the nature of this simple body, and why it fills up the whole place of the cosmos where “the upper motions”, the motions of the celestial objects, take place. The first simple body is thus assumed to make up not only the stars, and a diurnally rotating shell in the mass of which they are fixed, but also the planets, the 4 5

See 1.2.5. See 1.3.7.

2.2. The ¿rst simple body in Cael. A 2–3

53

Sun and the Moon, and to pervade the place of the cosmos where these seven celestial bodies are situated (339b16–19): 

D,QlR QäR SÃR IhVLXEM TV³XIVSR TIVi XSÁ TVÉXSY WXSMGIfSY, TSl³R XM XŸR H»REQfR zWXMR, OEiHM³XMTŠN±TIViX‡N†R[JSV‡NO³WQSNzOIfRSYXSÁWÉQEXSNTPœVLNzWXf. We have already discussed the first element, what powers it has, and why it fills up the entire region of the cosmos where the upper motions take place.

It is thus natural to suppose that in the de Caelo Aristotle introduces the first simple body as filler of the whole heavens, and thus as the constituent matter of all celestial objects. In Lee’s edition and translation of the Meteorologica, a note on the passage just translated directs the reader to Cael. A 2–3.6 In the introduction to his edition and translation of the de Caelo, Guthrie sketches the cosmology developed in the de Caelo, referring parenthetically to Mete. A 3 for the role of the first simple body as both the filler of the whole heavenly part of the cosmos and the matter constituting all celestial objects.7 Cael. B 7, which Guthrie for some reason does not mention, seems to leave no doubt that this is indeed so.8 No matter what we read in Cael. B 7, the rest of the body of evidence in the de Caelo pertaining to this question forces us to reconsider, however. It seems that originally Aristotle conceived of the first simple body only as making up the stars and a spherical shell in the mass of which they are ¿xed–as the filler, that is, of only the outermost part of the most distant place of the cosmos from the Earth. As for what pervades the immediately lower place, and is the constitutive matter of the five planets, the Sun and the Moon, he could not but have agreed at the time with those who took it to be fire. It is only in a later phase of the development of his cosmological thought that he identified it with the first simple body. To this phase belong the Meteorologica, Cael. B 7, a later addition to the original bulk of the de Caelo, and perhaps B 8, too (on which see below, n. 41).

2.2. THE FIRST SIMPLE BODY IN CAEL. A 2–3 2.2.1. The first simple body in Cael. A 2 The first body is introduced in Cael. A 2 as a simple body, an elementary kind of matter that on account of its own nature, and not under the imposition of an external force, is perpetually in circular motion round a point that is the center of the cosmos, though Aristotle does not explain this. It is more appropriate to conceive of this motion as rotation of a spherical shell about an axis through the center of the cosmos, no mater whether one shares the 6 7 8

Lee (1952) 12 n. b. Guthrie (1939) xiii–xiv. See also Hankinson (1998) 181 (cf. [1995 a ] 120, [1995b] 150 ) , Broadie (2009) 232, Pellegrin (2009) 173 n. 11, Gill (2009) 139, and Easterling (1961) 146–147.

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view being developed here as to the role of the first simple body in the de Caelo or not. That the first simple body makes up celestial objects–either some or all of them–is not dwelt upon. But it is hinted at by Aristotle’s final argument for the existence of this simple body, where celestial objects are called “things that move circularly”.9 We see that the natural motion of fire is from the center of the cosmos upwards in a straight line. Circular motion is as counter-natural for fire as is rectilinear motion towards the center of the cosmos. If the simple body in circular motion round the center of the cosmos were fire, as some believe, then the things that revolve perpetually and continuously round this point–the only contents of the cosmos having continuous and eternal motions–would not but do so counter-naturally. (Aristotle’s tacit assumption here, for the sake of the argument, is that the revolving things in question, which can only be celestial objects, are made up not of the first simple body, as he himself maintains, but of fire.) But this is unacceptable. As is indisputable, anything counter-natural is not perpetual but, on the contrary, very transitory. The eternal circular motions round the center of the cosmos cannot plausibly be considered a unique exception to this. In Aristotle’s own words (269b2–13): 

4V¶NHäXS»XSMNIeQ{RzWXMRšO»OP.XMRiJSV‡OEX‡J»WMR, H¢PSRÇNIhL†RXMWÏQE XÏR‚TPÏROEiTVÉX[R, ·T{JYOIR, ÊWTIVX¶TÁV†R[OEišK¢O„X[, zOIlRSO»OP. J{VIWUEMOEX‡J»WMR. IeHäTEV‡J»WMRJ{VIXEMX‡JIV³QIREO»OP.XŸRT{VM\JSV„R, UEYQEWX¶R OEi TERXIPÏN †PSKSR X¶ Q³RLR IREM WYRIG¢ XE»XLR XŸR OfRLWMR OEi ƒâHMSR, SÃWER TEV‡ J»WMR· JEfRIXEM K‡V }R KI XSlN †PPSMN X„GMWXE JUIMV³QIRE X‡ TEV‡J»WMR. ÊWX’ IhTIVzWXiTÁVX¶JIV³QIRSR, OEU„TIVJEWfXMRIN, SºHäR£XXSREºXÚ TEV‡J»WMRšOfRLWfNzWXMRE¼XL¡šO„X[· TYV¶N K‡VOfRLWMR±VÏQIRXŸRƒT¶ XSÁ Q{WSYOEX’ IºUIlER. In addition to the above, if motion in a circle is for something its natural motion, there should evidently be among the simple and primary bodies one of such a nature as to naturally move in a circle, just as fire moves upwards and earth downwards. For, if the things that move circularly perform their revolutions counter-naturally, it is bizarre and totally absurd that this should be the only counter-natural motion which is eternal and continuous, for in all other things what is counter-natural comes to a stop most quickly. So, if the simple body that is being carried round is fire, as some believe, this motion is no less counter-natural for it than is motion downwards, for we observe the natural motion of fire to be away from the center in a straight line.10

Having set out his arguments for the existence of the first simple body, Aristotle ends Cael. A 2 with a cautious note, emphasizing that the first simple body is farther out from the center of the cosmos than any of the four traditional simple bodies. In Cael. B 12 he points out that the huge distance between us and the phenomena exhibited by the celestial objects is a reason for the tenuous evidential basis we have to build on in our efforts to understand these objects (292a14–17). As it is, in the closing lines of Cael. A 2 Aristotle signals once again that he introduces the 9 For an explanation of this description see above, 1.3.4. 10 Those who hold the view that the celestial objects are made out of fire include Plato and other members of the Academy. See above, 1.3.1; cf. Wildberg (1988) 70, with n. 64.

2.2. The ¿rst simple body in Cael. A 2–3

55

first simple body as an exotic matter making up some, or all, of the celestial objects, and, in view of Cael. B 7, as sole filler of the cosmic realm in which these objects are situated (269b13–17): 

(M³TIV z\ ‚T„RX[R †R XMN XS»X[R WYPPSKM^³QIRSN TMWXI»WIMIR ÇN }WXM XM TEV‡ X‡ WÉQEXEX‡HIÁVSOEiTIVišQŠN |XIVSROIG[VMWQ{RSR, XSWS»X.XMQM[X{VER }GSR XŸR J»WMR´W.TIVƒJ{WXLOIXÏRzRXEÁUETPIlSR. One would thus come to believe, in light of all the arguments laid out above, that there is some other [simple] body separated from those around us here, and of a higher nature in proportion as it is removed from all things existing here.11

If the first simple body is introduced as a simple body whose spatial separation from the center of the cosmos is the largest possible, which is what Aristotle clearly implies in the passage just translated, the conclusion naturally presents itself that in the de Caelo this simple body must be thought of as occupying only the outermost place of the cosmos, and as making up only the celestial objects embedded in the rest of its mass, which forms a spherical shell diurnally rotating on an axis passing through the center of the cosmos: the stars.12 11

12

X‡ zRXEÁUE cannot be “the sublunary world” (Guthrie [1939] 18). For, no matter how far inside the cosmos the first simple body reaches–whether it fills the heavens or not–it can be plausibly thought to possess a nature higher than the natures of the four traditional simple bodies in proportion to its distance not from their realm but from the center of the cosmos, identified here with the Earth (the latter is practically the center of the cosmos–a mere point; see below, 2.8.4). If the first simple body fills the heavens, it cannot be conceived of as being far removed from the sublunary world, unless, of course, with reference only to its outermost stratum, but here Aristotle clearly speaks of the whole mass of the first simple body. Cf. the translation of the term X‡zRXEÁUEin Moraux (1965) 6. The argument followed by the passage just discussed can be shown to contain a further indication that the first simple body is assumed in Cael. A 2 to make up only the stars and the deferent spherical shell in whose mass they are fixed (the outermost layer of the cosmos). Aristotle says in it that the celestial objects, which he implicitly assumes to consist of the first simple body, have continuous motions. According to Ph. E 4, 228a20–22, every motion is continuous, so a motion which is one simpliciter, in the sense that it is motion of a single thing and of a single kind and occurs uninterruptedly in a continuous stretch of time (see 228b1–11), must be continuous, and vice versa. In Ph. Ĭ 8 Aristotle denies that eternal motion of an object is one and continuous if it changes direction pausing at a turning point (262a12–15, b23–26 ) ; he grants oneness and continuity to motion along a circular path only (see Ĭ 9, 265a27–29). Aristotle’s criteria for oneness and continuity of eternal motion are not satisfied by the zodiacal motions of the planets, for these motions exhibit stations and retrogradations, and thus their paths deviate from circularity. The continuous motions of the celestial objects, which are assumed in Cael. A 2, 269b2–13, to be made up of the first simple body, cannot thus be the zodiacal motions of the planets, and these celestial objects cannot be assumed to consist of the first simple body. To this conclusion points already the characterization of the celestial objects with continuous motions as “things that move circularly”. Read strictly, it excludes the planets. If we read it loosely, the planets must still be excluded from among the things that move circularly, for the motions of these things are said to be continuous–unless, of course, we opt to understand continuity, too, loosely in this context. It is unlikely that Aristotle presupposes here an analysis of the zodiacal motion of a planet as resultant of many motions fully satisfying his criteria for oneness and continuity of eternal motion. An argument for the existence of

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Aristotle refers in Cael. B 10 to the rotation of this spherical shell as “the outermost rotation of the ouranos”–that is, of the cosmos or the material universe (for the meanings of the noun ouranos see below, 2.2.3). This is the rotation being undergone in the outermost place of the cosmos, the realm of the stars, by the substance saturating that place and composing the stars. It is also called “the first rotation”, and its short period is contrasted with the long periods of the zodiacal motions of the planets, the Sun and the Moon, all of them being executed below the stars (291a34–b10): 

)TIi K‡V ¹T³OIMXEM XŸR QäR zWG„XLR XSÁ SºVERSÁ TIVMJSV‡R ‚TP¢R X’ IREM OEi XEGfWXLR, X‡NHäXÏR†PP[RFVEHYX{VENXIOEiTPIfSYN(|OEWXSRK‡VƒRXMJ{VIXEMXÚ SºVERÚOEX‡X¶RE¹XSÁO»OPSR), I½PSKSRžHLX¶QäRzKKYX„X[X¢N‚TP¢NOEiTVÉXLN TIVMJSVŠNzRTPIfWX.GV³R.HMM{REMX¶RE¹XSÁO»OPSR, X¶HäTSVV[X„X[zRzPEGfWX., XÏRH’ †PP[RX¶zKK»XIVSRƒIizRTPIfSRM, X¶HäTSVVÉXIVSRzRzP„XXSRM. X¶QäRK‡V zKKYX„X[Q„PMWXEOVEXIlXEM, X¶HäTSVV[X„X[T„RX[ROMWXEHM‡XŸRƒT³WXEWMR· X‡ HäQIXE\¾OEX‡P³KSRžHLX¢NƒTSWX„WI[N, ÊWTIVOEiHIMOR»SYWMRSdQEULQEXMOSf. Since the outermost rotation of the ouranos is assumed to be simple, and the fastest of all celestial motions, whereas the revolutions of the other celestial objects are assumed to be slower and composite (for each of them moves along its own circle against the rotation of the ouranos), it makes good sense that the celestial object which is closest to the first and simple rotation completes a circuit of its own circle in the longest time, the one farthest out in the shortest, and similarly with the rest, the nearer needing a longer time, the one farther out a shorter. For the nearest one is most overwhelmed, but the remotest least, owing to the distance, and those in between proportionally to their distances, as is also demonstrated by the 13 astronomers.

the first simple body can be safely assumed to eschew such an elaborate theoretical presupposition as the theory of homocentric spheres, and to be based only on celestial motions that are empirically, and thus indisputably, known to be continuous, which are only the diurnal revolutions of the stars, the only celestial objects to which thus the argument applies. For, if the planets are not hypothesized in Cael. A 2, 269b2–13, to consist of the first simple body, neither are the Sun and Moon, both of which naturally fall in the same category of celestial objects as the planets, on account of the fact that they, too, exhibit zodiacal motion. It should be kept in mind, moreover, that in the case of the Sun and Moon, too, zodiacal motion, though circular, has non-uniform speed, and that for Aristotle motion of non-uniform speed lacks full oneness, and thus continuity, in direct proportion to the non-uniformity of its speed (on uniformity of speed and oneness see Ph. E 4, 228b15–229a3). In Cael. A 2, 269b2–13, would Aristotle let the first simple body, whose highness he stresses in 269b13–17, be sullied by tacitly assuming that this simple body constitutes objects with peculiar motions deficient–however slightly–in continuity and oneness? (Cf. the end of ch. 1.) How could the first simple body be so higher than the other simple bodies as it is removed from the center of the cosmos if it made up not only the celestial bodies which are most distant from this point–the stars–but also the luminaries situated near it–the planets, the Sun and the Moon? 13 For discussion of this passage, where Aristotle states the relationship between the time each of the five planets, the Sun and the Moon needs to complete a circuit of the zodiac and the celestial object’s distance from the Earth, and thus the center of the cosmos, see below, 3.4.1. The phrase “first rotation” (TVÉXLTIVMJSV„) or “first revolution” (of the stars, along their diurnal circles, or of their deferent spherical shell respectively) has an analogue in the phrase “second revolution” (HIYX{VETIVMJSV„), which occurs at the end of Cael. B 2 for the zodiacal motions of the planets, and tacitly of the Sun and Moon, too (285b28–33). Aristotle’s language here hints that in the de Caelo the first simple body (X¶ TVÏXSR XÏR W[Q„X[R) makes up

2.2. The ¿rst simple body in Cael. A 2–3

57

The suspicion that in Cael. A 2 Aristotle locates the first simple body only at the farthest reaches of the cosmos, beyond Saturn, the outermost planet, is amply confirmed by Cael. A 3.

2.2.2. The first simple body in Cael. A 3 In Cael. A 3, 270a12–35, Aristotle demonstrates the unchangeability of the first simple body (see 1.3.6), and then draws attention to the fact that his conclusion agrees with ta phainomena (270b1–5). As is clearly shown by what he says next (270b5–16), ta phainomena here comprise not only what is observed but also what is generally believed: 

 4„RXINK‡V†RUV[TSMTIViUIÏR}GSYWMR¹T³PL]MR, OEiT„RXINX¶RƒR[X„X[XÚUIf. X³TSRƒTSHMH³EWM, OEiF„VFEVSMOEit)PPLRIN, ´WSMTIVIREMRSQf^SYWMUIS»N, H¢PSR ´XMÇNXÚƒUER„X.X¶ƒU„REXSRWYRLVXLQ{RSR· ƒH»REXSRK‡V†PP[N. IhTIVSÃR}WXMXM UIlSR, ÊWTIV}WXM, OEiX‡RÁRIeVLQ{RETIViX¢NTVÉXLNSºWfENXÏRW[Q„X[RIhVLXEM OEPÏN. WYQFEfRIM Hä XSÁXS OEi HM‡ X¢N EeWUœWI[N dOERÏN, ÊN KI TV¶N ƒRUV[TfRLR IeTIlR TfWXMR· zR …TERXM K‡V XÚ TEVIPLPYU³XM GV³R. OEX‡ XŸR TEVEHIHSQ{RLR ƒPPœPSMNQRœQLRSºUäRJEfRIXEMQIXEFIFPLO¶NS½XI OEU’ ´PSRX¶R}WGEXSRSºVER¶R S½XIOEX‡Q³VMSREºXSÁXÏRSeOIf[RSºU{R. For all people have a conception of gods, and all assign the uppermost place of the cosmos to the divine, both barbarians and Greeks, as many of them as believe in gods, for the obvious reason that what is immortal is associated with what is immortal; it is truly impossible to be otherwise. Thus, if something that is divine exists, as is the case, what we have said concerning the first among the bodily substances has been well said. It is also adequately borne out by the evidence of observation, sufficiently at least for us humans to believe in it. For, according to what has been handed down from one generation to the next, in all past time nothing appears to have undergone changes either in the whole outermost ouranos or in any of its parts.

Here Aristotle considers the belief in immortal gods to be a reflection of the knowledge that in nature there exists a simple body which is first among the simple bodies, and which has been exempted by nature from participating in any kind of change–in this respect, the first simple body is parallel to the gods of popular beliefs. What matters for the issue at hand is that Aristotle associates the immortal gods with the uppermost place of the cosmos, obviously the place these gods call home, where–we are justified in assuming–he himself implicitly locates the first simple body.14 And this place can only be the place whose distance from the center only the stars, to which the first revolution essentially belongs, and their deferent shell, the nutshell of the cosmos and the first of all the layers of the cosmos which undergo the first rotation that does so naturally (cf. 3.4.1). For the sense in which zodiacal motion is composite–not a single motion but many–see 3.2.1. On the circularity of zodiacal motion see ch. 1, n. 113. 14 There seems to be no clear differentiation in the Homeric epics between Olympus and the upper sky (see Kouremenos, Parássoglou & Tsantsanoglou [2006] 189–190 ) , and Aristotle can very well be having in mind here that passage from the Odyssey which dwells on the inviolate stability and serenity perpetually enjoyed by Olympus, a place rid of all violent changes in its marvelously calm conditions, as befits the abode of immortal gods and goddesses, which is blissful in every respect (6.41–47 ). Probably due to this absence of a distinction between

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of the cosmos is the largest possible, where “the outermost rotation of the ouranos”, or “the first rotation”, takes place. If so, however, then the first simple body is introduced only as the matter making up the stars and the spherical shell in the mass of which they are fixed, not also as the filler of the place immediately below, and as constituent matter of the five planets, the Moon and the Sun situated therein. The evidence of the senses Aristotle brings in the lines from Cael. A 3 translated above to shore up his conclusion that the first simple body is completely unchangeable amounts to an almost explicit statement that in Cael. A 2–3 the first simple body has only this limited role: “according to what has been handed down from one generation to another”, he says, “in all past time nothing appears to have undergone changes either in the whole outermost ouranos”, i.e. where in the cosmos “the outermost rotation of the ouranos”, or “the first rotation”, takes place–the natural motion of the first simple body–“or in any of its parts” (the noun ouranos is employed here by Aristotle in two different senses, which will be seen in a moment).15 Before we see another association in Cael. A 3 of the first simple body with the uppermost place of the cosmos, the most distant from its center, where the stars are situated–celestial objects made out of the first simple body and embedded in the rest of its mass, which is shaped into a spherical shell enveloping all the other simple bodies–a fact concerning Aristotle’s expression “outermost ouranos” ought to be noted here.

2.2.3. The three senses of the noun ouranos in Cael. A 9 From Cael. A 9 it is obvious that in Cael. A 3 Aristotle uses the expression “outermost ouranos” for the first simple body, the substance that constitutes the outerOlympus and the sky in Homer, in early Greek cosmology “Olympus” became synonymous with the heavens. See Kouremenos, Parássoglou & Tsantsanoglou (2006)189–190 . 15 Aristotle apparently was not aware of the phenomena we call today “novae” and “supernovae”, or of any recorded changes in the brightness and color of a star, and thus he concluded reasonably, with a proper amount of caution, that perhaps no such changes ever take place, to support observationally his theoretically arrived at result that there exists in nature a simple body whose intrinsic properties do not admit of any change. On novae and supernovae, the most spectacular of the so-called variable stars, or eruptive variables, see the concise account in Kaler (2002) 133–134. In the Greek world, Hipparchus might have been the first to watch or record a “new star” ( see Plin., H.N. 2.95). On ancient non-Greek observations of such phenomena see Kelley & Milone (2005)144 –148. It was the observation of a new star by Tycho Brache in 1572 that eventually demolished the Aristotelian belief in the immutability of the heavens. Note that Aristotle undeniably subscribes to this belief provided that no observational evidence contradicts it; he does not seem to rule out the possibility that such evidence might appear eventually. Some of the stars seen with naked eye exhibit variations in brightness due to a wide variety of causes; see the discussion in Kelley & Milone (2005)138–144, and cf. Kaler (2002) 131–133. Aristotle’s testimony suggests that Greek astronomers at the time did not know of this phenomenon, unless it simply bears witness to gaps in his own knowledge of astronomy (cf. Lloyd [1996] 160–161).

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most layer of the ouranos, or the body that undergoes “the outermost rotation of the ouranos” (the term ouranos is now being employed in a different sense: “cosmos”, “material universe”). This chapter, moreover, implicitly locates the first simple body, just as is expected from the above, where popular belief situates the immortal gods: in the outermost and uppermost place of the cosmos. It leaves no doubt that the filler of the next cosmic place, where the planets, the Sun and the Moon are located, and thus the constituent matter of all of these seven celestial objects, too, is not the first simple body (278b11–21):  

t)RE QäR SÃR XV³TSR SºVER¶R P{KSQIR XŸR SºWfER XŸR X¢N zWG„XLN XSÁ TERX¶N TIVMJSVŠN, ¡ WÏQE JYWMO¶R X¶ zR X® zWG„X: TIVMJSV• XSÁ TERX³N· IeÉUEQIR K‡V X¶ }WGEXSROEiX¶†R[Q„PMWXEOEPIlRSºVER³R, zRÛOEiX¶UIlSRTŠRdHVÁWUEfJEQIR. †PPSR H’ Eà XV³TSRX¶ WYRIGäN WÏQE X® zWG„X: TIVMJSV• XSÁ TERX³N, zR Û WIPœRL OEi PMSN OEi }RME XÏR †WXV[R· OEi K‡V XEÁXE zR XÚ SºVERÚ IREf JEQIR. }XM H’ †PP[N P{KSQIR SºVER¶R X¶ TIVMIG³QIRSR WÏQE ¹T¶ X¢N zWG„XLN TIVMJSVŠN· X¶ K‡V ´PSROEiX¶TŠRIeÉUEQIRP{KIMRSºVER³R. We call ouranos, in one sense of the term, the substance of the outermost spherical shell of the cosmos,16 or the natural body that undergoes the outermost rotation of the cosmos,17 for we are in the habit of calling ouranos chiefly the outermost and uppermost place [of the cosmos], where we believe all divinity to have its seat. We call ouranos, in a different sense of the term, the body which is continuous with the outermost spherical shell of the cosmos; the Moon, the Sun and some celestial objects are in it, for we say that they, too, are in the ouranos.18 We also call ouranos the body contained within the outermost boundary-surface [of the cosmos], for we are used to call so the entire [existing body] and the whole [cosmos].19

16

Guthrie (1939) 89 and Longo (1961) 71 translate TIVMJSV„ with “circumference” and “periferia” respectively. It is clear, however, that what this term refers to is something threedimensional, not a boundary-surface. Moraux (1965) 35 translates it as “orbe”; an orb in this context is best understood as a spherical shell, not a sphere. Jori (2002) 191 translates TIVMJSV„ as “orbita”, but a kinematic translation is appropriate for the immediately following occurrence of the term in a prepositional phrase. 17 For this translation of the prepositional phrase zRX®zWG„X:TIVMJSV•cf. the use of zRJSV• at Mech. 8, 851b34 and zROMRœWIMat e.g. de An. A 2, 405a28, Ph. ǻ 4, 211a14. As is clear from what comes next, “the outermost rotation of the cosmos”, i.e. of the ouranos in the last of the three senses of the term Aristotle distinguishes here, is the rotation of the substance occupying the outermost and uppermost place of the cosmos, the diurnal rotation of a spherical shell made up of the first simple body and containing the stars, which also consist of the first simple body. “The outermost rotation in the cosmos” is a better translation of the expression š zWG„XL TIVMJSV‡ XSÁ TERX³N ! XSÁ SºVERSÁ, both here and in Cael. B 10 (translated above, in 2.2.1). 18 “Some celestial objects” refers to the five planets. 19 šzWG„XLTIVMJSV„ here is clearly a spherical boundary-surface, the outer one of the outermost spherical shell of the cosmos. There is no reason to assume that the theory of homocentric spheres in presupposed in this passage (see Leggatt [1995] 203 ad loc.). Any view about the structure of the ouranos in the second sense of the term (the body filling up the realm below the spherical shell of the first simple body at the farthest reaches of the cosmos down to the lower boundary of the heavens, a sphere just below the Moon) is irrelevant to what Aristotle is saying here.

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2. The stuff of the heavens

Of the three senses Aristotle gives in Cael. A 9 for ouranos, only two would be needed if, in explicating the senses of this noun, he assumed that the first simple body is the exotic matter of the stars, and of the diurnally rotating spherical shell in the mass of which they are fixed, as well as the constituent matter of the five planets, the Sun and the Moon, and the filler of the cosmic region in which these seven celestial objects are contained: one would be “first simple body”, the other “existing masses of all bodies”, of the first simple body as well as of each of the other four, whether free or in its manifold combinations with the remaining three. The suggestion that of the three different senses of the noun ouranos Aristotle distinguishes in Cael. A 9, the first two pick out a single kind of stuff, the first simple body, but regard it in terms of position within the large-scale structure of the cosmos might seem convincing at first glance. That Aristotle focuses here on something other than the nature of the material each of the first two meanings of the term ouranos picks out is unlikely, however.

2.2.4. aithƝr Back to Cael. A 3 now, having laid out the evidence of the senses in support of his conclusion that the first simple body is completely unchangeable, Aristotle mentions again only the uppermost place of the cosmos as being filled with this simple body. The first simple body is thus once again implicitly assumed to make up only the stars, not the five planets, the Sun and the Moon, and to constitute that spherical shell which encases the rest of the cosmos, and in the mass of which the stars are fixed, but not to also fill the next cosmic place, where the other seven celestial objects are located. With the passage at issue, Cael. A 3 effectively comes to a close (270b16–25):20 20

This passage contains a critique of the fifth-century-BC cosmologist Anaxagoras of Clazomenae for having wrongly used the noun EeUœV in the meaning “fire”. In Greek poetry this substantive seems to be mean indiscriminately “air”, “sky” or “heavens”, and in the fragments of his poetry Empedocles employs it for air (see Wright [1981] 23). Etymologically, EeUœV is connected to Greek nouns such as EeUVfE and EhUVL, which designate the clear and bright sky or weather, and to the associated adjective EhUVMSN, -SR, used to describe such sky or weather. Anaxagoras employed this noun to designate the element fire, apparently based on the paretymology of EeUœV from the verb EhUIMR, “to kindle”, in the transitive form, or “to blaze”, in the intransitive. However, a paretymology of EeUœV is central to Aristotle’s critique of Anaxagoras, too. He derives EeUœV from the phrase ƒIiUIlR, “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 EeUœV 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 reaffirms his bizarre view 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 EeUœV, or of its descendants in modern languages, meaning “first simple body”. However, Aristotle employs the noun in this sense only in connection with Anaxagoras. Philoponus pokes fun at Aristotle’s wish to attribute knowledge of the first simple body to the natural philosophers of a antediluvian past, noting that the doctrine of the first body was Aristotle’s own, and that with it Aristotle broke

2.2. The ¿rst simple body in Cael. A 2–3 

61

u)SMOI Hä OEi XS½RSQE TEV‡ XÏR ƒVGEf[R TEVEHIH³WUEM Q{GVM OEi XSÁ RÁR GV³RSY, XSÁXSR X¶R XV³TSR ¹TSPEQFER³RX[R ´RTIVOEi šQIlN P{KSQIR· Sº K‡V …TE\ SºHä HiN ƒPP’ ƒTIMV„OMNHIlRSQf^IMRX‡NEºX‡NƒJMORIlWUEMH³\ENIeNšQŠN. HM³TIVÇNyX{VSY XMR¶N µRXSN XSÁ TVÉXSY WÉQEXSN TEV‡ K¢R OEi TÁV OEi ƒ{VE OEi ¼H[V, EeU{VE TVSW[R³QEWER X¶R ƒR[X„X[ X³TSR, ƒT¶ XSÁ UIlR ƒIi X¶R ƒâHMSR GV³RSR U{QIRSM XŸR zT[RYQfEREºXÚ. %RE\EK³VENHäOEXEGV¢XEMXÚ ²R³QEXMXS»X. SºOEPÏN· ²RSQ„^IM K‡VEeU{VEƒRXiTYV³N. It seems, moreover, to be the case that a name used [for the first simple body] by the ancients, who had the same views [about this body] as we do, has come down to the present time. For we must hold that we form the same views neither once nor twice but infinitely often.21 As it is, in the belief that the first [simple] body is different from earth and fire and air and water, the ancients called [the substance pervading] the uppermost place [of the cosmos] aithƝr, a name which they decided to use because this body is ever [aei] in motion [thein]. But Anaxagoras misapplies this name, for he uses aithƝr instead of fire.22

Had Aristotle introduced the first simple body also as occupant of the second part of the heavens, which is closer to the Earth, and thus as matter constituting all of the five planets, the Sun and the Moon situated therein, no probable reason comes to mind why he would not have spoken in Cael. A 3 of the unavailability of any records of changes in “the uppermost place of the cosmos” as well as “in the cosmic region lying immediately below”–en tois hupokatǀ. This is Aristotle’s expression in Cael. B 6 for the domain of the planets, the Sun and the Moon. It appears side by side with the expression “first ouranos”, a variant of the phrase “outermost ouranos”, the first simple body whose natural motion is “the outermost rotation” of the cosmos, the diurnal rotation of a spherical shell made up of this simple body in the mass of which the stars, also consisting of the same simple body, are fixed. away from both past and contemporary orthodoxy regarding the constitution of matter at the most fundamental level (in Mete. 16.23–25 [Hayduck] ; cf. below n. 21). Aristotle’s attempt to project his doctrine of the ¿rst 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 ¿fth simple body is perhaps his single most important contribution to cosmology, but there is nothing in Cael. A 2–3 similar to the measured self-con¿dence 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). 21 All views, Aristotle declares confidently in Mete. A 3, too, but again without offering any argument for his audacious claim, appear among humans neither once nor twice or a few times only but infinitely often, in an ever repeating cycle (339b27–30). For, as he explains in Metaph. ȁ 8, it is reasonable to assume that each science and art had developed as much as possible many times in the long past, but each time got lost, though pitiful bits and pieces of old wisdom somehow managed to survive, and presumably served as seeds for the next blooming of civilization (1074a38–b14). In the Metaph. ȁ 8 passage, what we read in the Cael. A 3 passage translated here concerning the first simple body is said of not one but many first substances, all non-bodily: the unmoved movers in the heavens (see 1.4.5). From a fragment of his lost dialogue On philosophy (fr. 13 Rose) it appears that Aristotle blamed recurring natural catastrophes for the cyclical destruction of civilization. We have no evidence that he tried to present any empirical evidence for the repeating occurrence of such cataclysmic events. 22 The critique of Anaxagoras is repeated in Mete. A 3, 339b19–30 (the passage is translated below, in 2.8.2).

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2. The stuff of the heavens

As seen above, in 2.2.1, this rotation is also called “the first rotation”. Aristotle does say in Cael. B 6 of “the first rotation” that it is the motion of “the first ouranos” (288a13–17):23 

 4IViHäX¢NOMRœWI[NEºXSÁ, ´XM±QEPœN zWXMOEiSºOƒRÉQEPSN, zJI\¢N‰RIhLXÏR IeVLQ{R[R HMIPUIlR. (P{K[ Hä XSÁXS TIVi XSÁ TVÉXSY SºVERSÁ OEi TIVi X¢N TVÉXLN JSVŠN· zRK‡VXSlN¹TSO„X[TPIfSYNžHLEdJSVEiWYRIPLP»UEWMRIeN|R.) The next thing to go through after what has already been said concerns the motion of the ouranos, namely that it is uniform and not non-uniform. (I say this of the first ouranos and the first rotation, given that in the cosmic region lying immediately below many motions combine into a single motion.)

The absence of a reference to the cosmic region of the planets, the Sun and the Moon from Aristotle’s argument that the lack of recent or old records of changes in “the outermost ouranos” bolsters empirically the theoretically inferred unchangeability of the first simple body cannot but be significant. Nor can it be accidental that in Cael. A 3, each time Aristotle refers implicitly to the location of the first simple body, he mentions only the outermost and uppermost place of the cosmos, where the stars are, far beyond the Moon, the Sun and the planets.

2.3. THE EVIDENCE FROM CAEL. B 4 That the first simple body is assumed in Cael. A 2–3 to be only the matter of the stars, and of the spherical shell in whose mass they are ¿xedly embedded, the crust of the cosmos, is strongly confirmed by Cael. B 4. In this chapter, Aristotle demonstrates not only that the first simple body forms a spherical shell, thereby fixing the center of the cosmos it contains, but also that the whole cosmos is arranged in spherical, homocentric layers.24 Aristotle begins with the observation that, as the circle is first among plane figures because it is bounded by a single line, the sphere, which is enclosed by a 23 For discussion of this passage see 3.1–2. For “the ¿rst ouranos” cf. Metaph. ȁ 7, 1072a23. 24 There can be no doubt that the ouranos, in the first of the three senses Aristotle distinguishes in Cael. A 9, is assumed to be a spherical shell for the simple reason that it is a physical concretization of the basic astronomical concept of the celestial sphere (cf. ch. 1, n. 3 6 ) . Aristotle, however, wants to rule out the possibility that it is a polyhedral solid with many small faces, or perhaps a bumpy or spiked sphere (see Cael. B 4, 287a11–22). In either of these cases, each star would be observed to undergo diurnal motion in a circle; the ouranos would rotate diurnally, but it would not be a material object with the same shape as the celestial sphere of the astronomers. Cleomedes, Cael. 1.5.1–9 (Todd), after remarking that sight itself is thought to be sufficiently secure basis for our belief in the spherical shape of the cosmos, an obvious allusion to the phenomena from which the fundamental concept of the celestial sphere is formed, warns that not all things are as they appear to be, which in his view makes it imperative upon us to be able to argue for the spherical shape of the cosmos from what we perceive obviously and securely. However, what compels him to mistrust the evidence of the senses bearing on the issue at hand seems to be the huge separation of the celestial realm from us. Aristotle seems to think otherwise.

2.3. The evidence from Cael. B 4

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single surface, is first among solid figures. Being bounded by a single line and surface confers primacy to the circle and the sphere among plane and solid figures respectively, for in each class of things the one and the simple are by nature prior to the many and the composite. The notion of perfection is also brought in. A straight line, and thus a surface which is bounded by straight lines, is imperfect, for such a line can be produced ad libitum, but outside a circle no “parts” of it can be found by producing it. Furthermore, what is perfect is prior to what is imperfect, so the circle and the sphere turn out again to be the first of plane and solid figures respectively (286b10–26). Next, Aristotle argues that the circle will turn out to be first among plane figures, and analogically the sphere to be first among solids, also if the assignation of numbers is used to classify plane figures, whereby the circle must be given the number one, probably on account of the simple fact that the circle is bounded by a single line, or defined by a single point and a single distance from it, and the triangle the number two, which is the number of right angles a triangle’s interior angles add up to. The first solid shape, he concludes, is the shape of the first body, and since the first body is the first simple body, which executes “the outermost rotation”, the first simple body forms a spherical shell (286b32–287a5): 

t3XMQäRSÃRTVÏX³RzWXMRšWJElVEXÏRWXIVIÏRWGLQ„X[R, H¢PSR. }WXMHäOEiOEX‡ X¶R ƒVMUQ¶R XŸR X„\MR ƒTSHMHSÁWMR S¼X[ XMUIQ{RSMN IºPSKÉXEXSR, X¶R QäR O»OPSR OEX‡X¶|R, X¶HäXVfK[RSROEX‡XŸRHY„HE, zTIMHŸ²VUEiH»S. z‡RHäX¶IROEX‡X¶ XVfK[RSR, ± O»OPSN SºO{XM }WXEM WG¢QE. zTIi Hä X¶ QäR TVÏXSR WG¢QE XSÁ TVÉXSY WÉQEXSN, TVÏXSRHäWÏQEX¶zRX®zWG„X:TIVMJSV•, WJEMVSIMHäN‰RIhLX¶XŸRO»OP. TIVMJIV³QIRSRJSV„R. That the sphere is first among solid figures is, therefore, clear. We would accord it this place most reasonably also in case we made the ordering by number, associating the circle with the number one and the triangle with the number two, on account of the triangle’s having two right angles. For, if we pair the triangle with the number one, the circle will not be a figure any more. As it is, since the first shape belongs to the first body, and the [simple] body that undergoes the outermost rotation is first, the [simple] body that is in circular motion is shaped into a spherical shell.

If the first simple body forms a spherical shell, however, the cosmos, i.e. the ouranos in the last of the three senses of this term distinguished in Cael. A 9, is disposed in concentric spherical layers (287a5–11): 

/EiX¶WYRIGäN†VEzOIfR.· X¶K‡VXÚWJEMVSIMHIlWYRIGäNWJEMVSIMH{N. ÇWE»X[NHä OEi X‡ TV¶N X¶ Q{WSR XS»X[R· X‡ K‡V ¹T¶ XSÁ WJEMVSIMHSÁN TIVMIG³QIRE OEi ‚TX³QIRE ´PE WJEMVSIMH¢ ƒR„KOL IREM· X‡ Hä O„X[ X¢N XÏRTPERœX[R …TXIXEM X¢N zT„R[WJEfVEN.25 ÊWXIWJEMVSIMHŸN‰RIhLTŠWE· T„RXEK‡V…TXIXEMOEiWYRIG¢zWXM XElNWJEfVEMN.

25

In his Oxford Classical Texts edition of the de Caelo, Allan brackets the genitive X¢N XÏR TPERœX[R, sc. WJEfVEN, apparently regarding it as originally an interlinear or marginal comment; cf. Longo (1961). Moraux (1965) keeps it; cf. Pellegrin (2009) 173 n. 11, in whose view the cosmic realm of the planets is here assumed to be ¿lled with ¿rst simple body. X‡O„X[

64

2. The stuff of the heavens This is true of the [simple] body which is continuous with it, for what is continuous with a spherically shaped thing is itself spherical, as well as of the [simple] bodies nearer to the center of the cosmos, too, for bodies being in contact with, and contained by, a spherically shaped body must have spherical shape themselves, and [the content of ] the realm beneath the spherical shell of the planets touches the spherical shell above it. The entire nature is thus arranged in spherical shells, 26 all [simple] bodies in it being in contact, and continuous, with spherical layers.

The filler of the cosmic place in which the planets, as well as the Sun and the Moon, are situated is also the matter of these seven celestial objects. Aristotle argues that this filler, which is not identified, must be shaped into a spherical shell because it is continuous, more accurately in contact, with the first simple body above.27 This argument establishes only that the cosmic layer below the first simple body is spherical where it is in contact with the first simple body, for the latter forms a spherical shell. If it can somehow be argued that it is spherical even where it is not in contact with the superior layer, the reasoning automatically repeats for the successive cosmic strata. Aristotle can thus conclude successfully that the whole nature is arranged in spherical layers. The fire around the air is within the spherical shell of the body which makes up the Moon, the Sun and the five planets. It forms around the air a spherical shell, even where it is not in contact with the immediately superior stratum, because it has a natural tendency for radial motion away from the center of the cosmos: all parts of its mass arrange themselves equally far from this point, forming a layer with a spherical inner boundary.28 The same applies to the air below the spherical layer of fire. The sphere left vacant, which is concentric with the cosmos, is filled with the mass of earth, on whose surface the water is collected. Therefore, the surface of the Earth, and of the water resting on it, is spherical if considered on the large scale, which applies to the inner surface of the stratum of air, too (cf. Alex. Aphr., apud Simp., in Cael. 414.30–415.8 [Heiberg]).29 What is missing from this argument is easily supplied if the place of the cosmos that is immediately below the spherical shell of the first simple body in the X¢NXÏRTPERœX[R, sc. WÉQEXE, are the simple bodies below the lower boundary of the heavens, the stratum of fire immediately above the stratum of air, the stratum of air itself, the water pooled on the surface of the Earth, and the globe of Earth itself. Cf. Easterling (1961) 146, n. 2. 26 The noun implied as subject of ‰RIhLcan only be J»WMN. Cf. Cael. A 2, 268b11–13. 27 At the end of the argument, continuity is first casually replaced by contiguity, or “being in touch”, and then mentioned as equivalent to it, a sure sign that the term “continuous” is not employed stricto sensu. In another passage of Cael. B 4, which will be discussed below, Aristotle says that continuity here stands for contiguity (287a34–b1). For the distinction between the germane notions of contiguity and continuity see Ph. E 3. The boundary-surfaces of two successive cosmic strata are not fused or glued into one and the same surface, but are merely in the same place–with nothing between them. 28 Cf. Aristotle’s argument for the spherical shape of the Earth in Cael. B 14, 297a8–30. 29 Aristotle acknowledges in Mete. A 3 that the shape of the Earth deviates from perfect sphericity, while discussing the formation of clouds ( 340b32–36 ). Cael. B 14 proves only the overall sphericity of the Earth (see 297b23–298a9 for the most cogent arguments, which come from astronomy) . In Cael. B 4, moreover, Aristotle shows that the surface of water, which ¿lls the hollows of the Earth and covers most of its surface, must be spherical (287b4–14 ) .

2.3. The evidence from Cael. B 4

65

mass of which the stars are fixed is filled with fire–of a different variety from that collected nearer to the air and the Earth. Let us leave aside for the time being available evidence for the differentiation of fire in Aristotle’s physics with increasing distance from the center of the cosmos.30 It is clear that if he believed that the cosmic place of the planets, the Sun and the Moon were filled with the first simple body, he would not argue that the filler of this place is shaped into a spherical shell on account of the fact that it is in contact with the spherical shell of the first simple body above, which has the stars fixed in its mass: he would rather repeat the argument he gives for the shape of the outermost cosmic layer, in which the stars are embedded. In other words, if the place of the ¿ve planets, the Sun and the Moon below the stars were filled with the first simple body, this body could not but form a spherical shell for the reason that the sphere is first among solid shapes, and the first simple body must have the first solid shape. That a body in another body of a spherical shape, with which it is in contact, is itself shaped spherically applies to fire and air, for these simple bodies are by nature such as to admit of a spherical shape only in a spherical container, not to the first simple body, even if it were found below the place of the fixed stars, too. In Cael. B 4, as in A 9, Aristotle had a good opportunity to make perfectly clear, had he so wished, the role of the first simple body as ouranos in the first and second sense of the term distinguished in Cael. A 9. Once again he missed it, however. He seems to posit not a single upper body, the first simple body, occupying the heavens, but two. One is the body in which the planets, the Sun and the Moon are, and which makes up these seven celestial objects, the ouranos in the second sense of the term according to Cael. A 9. The first simple body, the ouranos in the first meaning of the term according to Cael. A 9, is around it. The stars are in, and consist of, the ¿rst simple body. An unambiguous reference to more than one body permeating the heavens occurs in another argument Aristotle gives in Cael. B 4 for the sphericity of the cosmos. Unlike in the proof from the same chapter discussed above, Aristotle here starts not with the first simple body but with the fact that the surface of the water in the hollows of the Earth is spherical. This is taken for granted, and is proven after the completion of the argument (287a30–b4): 

0„FSMH’ †RXMNOEizOXÏRTIViX¶Q{WSRdHVYQ{R[RW[Q„X[RXE»XLRXŸRTfWXMR. Ie K‡VX¶QäR¼H[VzWXiTIViXŸRK¢R, ±H’ ƒŸVTIViX¶¼H[V, X¶HäTÁVTIViX¶Rƒ{VE, OEi X‡ †R[ WÉQEXE OEX‡ X¶R EºX¶R P³KSR (WYRIG¢ QäR K‡V SºO }WXMR, …TXIXEM Hä XS»X[R), šHäXSÁ¼HEXSNzTMJ„RIMEWJEMVSIMHœNzWXMR, X¶HäXÚWJEMVSIMHIlWYRIGäN ¡ OIfQIRSR TIVi X¶ WJEMVSIMHäN OEi EºX¶ XSMSÁXSR ƒREKOElSR IREM· ÊWXI O‰R HM‡ XSÁXSJERIV¶RIhL´XMWJEMVSIMHœNzWXMR±SºVER³N. One could establish the same conclusion starting from the bodies nearer to the center of the cosmos. If water is collected around the earth, air around water and fire around air, the upper bodies, too, are disposed in the same manner (they might not be continuous with the

30

This evidence will be presented below, in 2.7. See also Appendix 2.

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2. The stuff of the heavens others, but are in contact with them).31 The surface of water is spherical, however, and what is continuous, or in contact, with what is spherical is itself necessarily spherical. Thus, this argument, too, could make clear that the cosmos is spherical.

Aristotle argues that water surrounds the mass of earth, which is gathered around the center of the cosmos, and is here implicitly assumed to be mostly covered with water; air surrounds water, and fire surrounds air; similarly, one of the upper bodies, that which the word ouranos picks out in the second of the three senses of this word Aristotle distinguishes in Cael. A 9, is arranged around all these four layers of body; in its turn, it is encased by the other upper body, the first simple body, or the ouranos in the first sense of the term according to Cael. A 9. Each lower layer of body is in conformal contact with the one above–it is not the case that each body is in contact with all of the lower bodies, as Aristotle’s carelessly loose wording suggests.32 So, if the surface of water on the Earth is spherical, as Aristotle will go on immediately to demonstrate, then the whole cosmos, the ouranos in the third sense of the term according to Cael. A 9, cannot but be both spherical and arranged in spherical layers.33 If Aristotle thought, when he wrote Cael. B 4, that the first simple body does not make up only the stars, and the spherical shell in whose mass these celestial objects are fixed, but instead fills the heavens throughout, thus composing the planets, the Sun and the Moon, too, obviously he would not refer in the passage just translated to “upper bodies”. He would speak of a single upper body instead.

31

“The upper bodies”, X‡†R[WÉQEXE, cannot possibly be identi¿ed with the shells of the first simple body which make up the heavens according to the cosmology Aristotle outlines in Metaph. ȁ 8 (discussed above, in 1.4.1–4). WÏQE here is an elemental type of matter, such as earth, water, fire, air or the first simple body, and not an object, such as a shell of any simple body. At any rate, if Aristotle operated here with the assumption that the heavens are a composite structure of concentric spherical shells made up of the first simple body, why would he need to prove the sphericity of these objects? It would be assumed ex hypothesi–along with their existence–in light of the theory of homocentric spheres. That this theory is not presupposed in Cael. B 4 has also been argued by Easterling (1961) 146–147, in whose view, however, the ¿rst simple body ¿lls the realm of–and thus forms–the ¿ve planets, the Sun and the Moon, too. More than one upper body is mentioned in Cael. B 1, 284a18–27, too. This passage is discussed below, in 3.4.4. 32 Cf. the conclusion in Cael. B 4, 287a5–11. 33 The outer surface of the stratum of air, which is not in contact with the overall spherical surface of the Earth and the water pooled in the hollows of it, is implicitly assumed to be spherical on account of the fact that air has a natural tendency for radial motion away from the center of the cosmos, so all parts of its mass would recede at equal speeds from this point, forming an expanding layer with a spherical outer boundary. The same reasoning applies to the outer surface of the layer of fire right above the layer of air, as well as to the outer surface of the inferior upper body Aristotle mentions–fire far above the stratum of air. The lower upper body is confined within the shell of the superior upper body, whose inner surface must thus be spherical like the outer surface of the lower upper body it touches conformally, and also restrains the fire below, which in turn confines the air. If so, the argument can show only the sphericity of the inner surface of the first simple body. As regards its outer surface, that it, too, must be spherical follows by analogy to what has been shown to be the case with all the other boundary-surfaces of the cosmic strata.

2.4. The ¿rst simple body in Cael. B 12

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2.4. THE FIRST SIMPLE BODY IN CAEL. B 12 A hint that the first simple body does not compose the Moon, the Sun and the five planets, nor does it thus fill up–in view of Cael. B 7–the lower part of the heavenly realm of the cosmos, where these celestial objects are, is also found in Cael. B 12. As already seen above, in 1.1, Aristotle opens Cael. B 12 with the cautious note that he must attempt to state what merely seems to him to be a plausible solution to two baffling problems (291b24–28). He then proceeds to state the first problem, which concerns the wandering celestial objects–the Moon, the Sun and the planets (291b28–292a3): 

u)WXMHäTSPPÏRµRX[RXSMS»X[RSºGOMWXEUEYQEWX³R, HM‡XfRETSX’ EeXfERSºOƒIi X‡ TPIlSR ƒT{GSRXE X¢N TVÉXLN JSVŠN OMRIlXEM TPIfSYN OMRœWIMN, ƒPP‡ X‡ QIXE\¾ TPIfWXEN. I½PSKSRK‡V‰RH³\IMIRIREMXSÁTVÉXSYWÉQEXSNQfEROMRSYQ{RSYJSV‡R X¶TPLWMEfXEXSRzPEGfWXENOMRIlWUEMOMRœWIMN, SmSRH»S, X¶H’ zG³QIRSRXVIlNžXMRE †PPLRXSME»XLRX„\MR. RÁRHäWYQFEfRIMXSºRERXfSR· zP„XXSYNK‡VPMSNOEiWIPœRL OMRSÁRXEM OMRœWIMN ¡ XÏR TPER[Q{R[R †WXV[R }RME· OEfXSM TSVVÉXIVSR XSÁ Q{WSY OEiTPLWMEfXIVSRXSÁTVÉXSYWÉQEX³NIeWMREºXÏR.34 There are many such problems, and not the least puzzling is why it is not the case that the remoter a celestial object is from the first rotation, the more its motions are, but those in the middle distance have the most motions. Since the first [simple] body has a single motion, it would seem reasonable that the celestial object nearer to it has the next smallest number of motions, e.g. two, the next three, or [that the number of motions increases in] some similar way. Actually, the opposite is true. For the Sun and the Moon have fewer motions than some of the wandering celestial objects, despite the fact that the later are farther away from the center [of the cosmos], and closer to the first [simple] body, than the Sun and the Moon.35

X‡TPERÉQIRE†WXVEare Mercury, Venus, Mars, Jupiter and Saturn–the planets–the Sun and the Moon (see above, 1.3.5). Below, in 292b19–25, Aristotle undoubtedly implies that the Sun and the Moon have each fewer motions than all planets, so we must assume (a) that he calls all planets XÏRTPER[Q{R[R†WXV[R}RME without realizing that this expression can be used for all the five planets, in contrast to the Sun and the Moon, but here, after the comparative zP„XXSYN, it suggests that he wants to refer only to some of the planets; (b) that the text is corrupt at this point; if the second, originally it must have read XÏR TPER[Q{R[R †WXV[R XŒPPE. Ross (1924) vol. 2, 394 suggests that the problem Aristotle states here (we would reasonably expect the number of a wandering celestial object’s motions to increase with the distance from the stars, which have a single motion only, but this is not the case) is raised even if the Sun and the Moon have fewer motions than some of the planets–Aristotle does not say more than the statement of the problem needs. Scholars have tried to explain the problematic phrase by trying to determine which version of the theory of homocentric spheres Aristotle operates with here (see Easterling [1961] 138–141, but cf. Manuwald [1989] 107–109). However, there are reasons to doubt that any of the two versions of the theory, the Eudoxean or the Callippean, is presupposed in Cael. B 12. See also next note. 35 The second solution to the second dif¿culty Aristotle tackles in Cael. B 12 hints unmistakably at the articulation of the whole celestial realm into as many concentric shells of matter as are required by the theory of homocentric spheres: the materiality of the Eudoxean spheres is clearly implied–they are said to be sǀmata, i.e. spherical shells of an unspeci¿ed kind of matter (293a4–11). It is thus reasonable to assume that the many motions of the Sun, the Moon or a planet Aristotle mentions here are the combined rotations of at least the spherical shells of the first simple body which make up the deferent system of the celestial object, perhaps the ro34

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The first simple body is evidently assumed here to compose only the stars and the spherical shell in the mass of which these celestial objects are fixed, the crust of the cosmos. For, if Aristotle took it to also occupy the cosmic place immediately below, and thus compose the handful of remaining celestial objects, the seven wandering ones, then it is very unlikely that he would refer to some of them as being nearer to the first simple body, as if this simple body were not also the constituent matter of all of these luminaries and the ¿ller of their realm! That it really is not is, therefore, a conclusion that can be safely inferred from Aristotle’s manner of speaking here. 2.5. THE EVIDENCE FROM THE INTRODUCTION TO CAEL. ī If the first simple body were introduced in Cael. A 2 as the single filler of the heavens and the constituent matter of all celestial objects, then Aristotle would not open Cael. ī 1, which treats of the four traditional simple bodies, with the statement that in the above discussion he has dealt with “the first ouranos”, and, after a rather long parenthesis about the subject-matter of physics, pick up again his point to say that the treatment of “the first element”, the first simple body, in the first two books of the de Caelo appropriately continues in the third book with the treatment of the other four elements. This passage, 298a24–b8, is evidence as clear and explicit as one would wish that it is only as the constituent matter of the stars, and of the spherical shell in the mass of which they are embedded, that the first simple body has been introduced at the very beginning of the treatise: 

36

4IVi QäR SÃR XSÁ TVÉXSY SºVERSÁ OEi XÏR QIVÏR, }XM Hä TIVi XÏR zR EºXÚ JIVSQ{R[R36 †WXV[R, zO XfR[R XI WYRIWXŠWM OEi TSl’ †XXE XŸR J»WMR zWXf, TV¶N Hä XS»XSMN ´XM ƒK{RLXE OEi †JUEVXE, HMIPLP»UEQIR TV³XIVSR. zTIi Hä XÏR J»WIM PIKSQ{R[RX‡Q{RzWXMRSºWfEM, X‡H’ }VKEOEiT„ULXS»X[R(P{K[H’ SºWfENQäRX„ XI‚TPŠWÉQEXE, SmSRTÁVOEiK¢ROEiX‡W»WXSMGEXS»XSMN, OEi´WEzOXS»X[R, SmSR X³RXIW»RSPSRSºVER¶ROEiX‡Q³VMEEºXSÁ, OEiT„PMRX„XI^ÚEOEiX‡JYX‡OEiX‡ Q³VMEXS»X[R, T„ULHäOEi}VKEX„NXIOMRœWIMNX‡NXS»X[RyO„WXSYOEiXÏR†PP[R, ´W[RzWXiREhXMEXEÁXEOEX‡XŸRH»REQMRXŸRyEYXÏR, }XMHäX‡NƒPPSMÉWIMNOEiX‡N IeN †PPLPE QIXEF„WIMN), JERIV¶R ´XM XŸR TPIfWXLR WYQFEfRIM X¢N TIVi J»WI[N dWXSVfEN TIVi W[Q„X[R IREM· TŠWEM K‡V Ed JYWMOEi SºWfEM ¡ WÉQEXE ¡ QIX‡ tations of this object’s similarly shaped and constituted unwinding shells, too (cf. previous note). However, the alternative solution to the second problem addressed in Cael. B 12 violates the principle based on which Aristotle sets out to solve the difficulties he comes to grips with in this chapter. This solution ought thus to be considered an addition to the main argument, probably not by Aristotle himself (see below, 3.3). The many motions of the Sun, the Moon or any planet can only be the following three: the diurnal rotation, the opposite motion through the zone of the zodiac, both of which are common to all ¿ve planets, the Sun and the Moon, and the retrograding, which is undergone only by the planets during the second of the other motions. If so, the Sun and the Moon have each fewer motions than any planet. Cf. Leggatt (1995) 246, on 291b28–292a9. The reading JEMRSQ{R[R is adopted by Guthrie (1939), following Bekker. It might seem preferable in light of the fact that in Cael. B 8 Aristotle argues that the stars do not move independently of the surrounding mass in which they are embedded (see Appendix 7) .

2.6. The evidence from the introduction to Cael. B



69

W[Q„X[R KfKRSRXEM OEi QIKIUÏR. XSÁXS Hä H¢PSR }O XI XSÁ HM[VfWUEM X‡ TSl„ zWXM J»WIM, OEizOX¢NOEU’ |OEWXEUI[VfEN.  4IViQäRSÃRXSÁTVÉXSYXÏRWXSMGIf[RIhVLXEM, OEiTSl³RXMXŸRJ»WMR, OEi´XM †JUEVXSROEiƒK{RLXSR· PSMT¶RHäTIViXSlRHYSlRIeTIlR. We have treated above of the first ouranos 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. Since of those things that are said to be natural some are substances, the others actions and affections of substances (I refer by the term “substances” to simple bodies, such as fire and earth and the others on a par with them, and to those bodies that are made up by them, such as the whole ouranos and its parts, animals, plants, as well as their parts, whereas by “actions and affections” I refer to the motions of each of those substances, and to the motions of other substances that are caused by the former ones acting in virtue of their own powers, and to the alterations of substances and their transmutations into one another), it is obviously bodies that the study of nature mainly deals with, for all natural substances are either bodies or have bodies and magnitudes. This is clear from both the definition of natural things and the study of each of their categories. We have already discussed the first element, its nature, its ungeneratedness and its indestructibility, so it remains to deal with the other two.37

Simplicius, in Cael. 551.25–552.7 (Heiberg), thinks that what is called here “first ouranos” is the entire existing mass of the first simple body, to aitherion sǀma, but understands this body to fill the whole heavens: “the first ouranos”, according to the commentator, are the eight spheres referred to as a single entity–that is, the deferent spherical shell of the stars and seven spherical shells inside it, all of them being concentrically arranged and each having one of the remaining seven celestial objects just above its lower boundary-surface (the further articulation of each of these seven shells into components of the same shape, according to Metaph. ȁ 8, is certainly presupposed by Simplicius, but is irrelevant here). However, if in Aristotle’s phrase “the whole ouranos” the noun is employed, as Simplicius himself implicitly assumes, in the last of its three senses distinguished in Cael. A 9, in the phrase “the first ouranos” it is used in the first of these senses. If so, this second expression picks out only the matter constituting the deferent spherical shell of the stars and the stars themselves. The introduction to Cael. B 6 offers, moreover, incontrovertible evidence that “the first ouranos” is the body which makes up only this shell, and the celestial objects embedded in its mass.38 This is also supported by the introduction to Cael. B as a whole.

2.6. THE EVIDENCE FROM THE INTRODUCTION TO CAEL. B Aristotle begins Cael. B 1 by reaffirming the conclusion he has reached in the last three chapters of the previous book that the whole ouranos is indestructible and 37

The four traditional simple bodies are said here to be two, simply because they fall into two pairs according to their natural rectilinear motion, earth and water being heavy, fire and air light, so that Aristotle can speak of two instead of four other elements existing alongside the first element, one heavy and one light. Cf. Guthrie (1939) 258–259 n. a. 38 See above, 2.2.4.

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ungenerated, which means that it is eternal (283b26–284a2). Clearly, ouranos is here employed in the last of its three senses distinguished in Cael. A 9. Going backwards, he then reminds the readers of his earlier result, in the second and third chapters of the previous book, concerning the existence and nature of a first simple body endowed with the only type of eternal motion, a fact already known to the ancients, as, by his lights, it turns out from the traditional belief in the immortality of the divine, which agrees well with his conclusion that the material universe is eternal (284a2–11). The ancients, Aristotle goes on, assigned to the gods the ouranos and the upper place of the cosmos on the belief that this substance alone, the ouranos, is eternal, which is in accordance with his own conclusions that it is ungenerated and indestructible, and that it does not move under the influence of some external force preventing it from exercising its own natural motion; for the work done by such a force, which, if it existed, the divine could not but be identical with, would be toilsome, in direct proportion to its eternal duration, and thus totally foreign to the blessed life divinity must enjoy (284a11–18). This natural motion of the ouranos is evidently the natural motion of the first simple body, for which ouranos stands. It is not clear whether this substantive, as a stand-in for a body, is used only in the first of its three senses Aristotle distinguishes in Cael. A 9, or in the second, too. “The upper place”, where the first simple body is implicitly but obviously located, can very well be assumed to be the whole heavens. If so, Aristotle here considers the first simple body the only upper body, which makes up all celestial objects. That the first simple body is assumed here to constitute only that spherical shell in the mass of which the stars are fixed, however, and thus to make up only these celestial objects, is shown beyond any doubt by the closing lines of the chapter, where the natural motion of the first simple body is casually equated with “the first rotation”, which is the diurnal rotation.39 Having elaborated against the view of the first simple body’s moving with a forced motion, which would have been contrary to the eons-old link between this body and the divine (284a18–35), Aristotle goes on to state what follows as regards our conception of this motion’s eternity if “the first rotation”, the motion of the first simple body, which is thus the ouranos only in the first of the three senses of this term distinguished in Cael. A 9, is as he believes–that is, not forced but natural (284a35–b5): 

)eHœ, OEU„TIVIhTSQIR, zRH{GIXEMX¶RIeVLQ{RSR}GIMRXV³TSRTIViX¢NTVÉXLNJSVŠN, Sº Q³RSR EºXSÁ TIVi X¢N ƒMHM³XLXSN S¼X[N ¹TSPEFIlR zQQIP{WXIVSR, ƒPP‡ OEi X® QERXIfZ X® TIVi X¶R UI¶R Q³R[N ‰R }GSMQIR S¼X[N ±QSPSKSYQ{R[N ƒTSJEfRIWUEM WYQJÉRSYNP³KSYN. ƒPP‡XÏRQäRXSMS»X[RP³K[R…PMN}WX[X¶RÁR. If, therefore, it is possible for the first rotation to be as we said, not only is it more elegant to think of its eternity in this manner, but in this way only we can give a coherent account of it

39

See above, 2.2.1.

2.7. Fire as second upper body in the de Caelo

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in agreement with the preconception we have concerning god.40 But enough of this subject for the time being.

“The upper place” of the cosmos, where Cael. B 1 implicitly locates the first simple body, is thus actually its “uppermost place”, which contains the outermost layer of the heavens and the cosmos, the spherical shell in whose mass the stars are fixed (cf. the passage from Cael. A 3 translated above, in 2.2.2).

2.7. FIRE AS SECOND UPPER BODY IN THE DE CAELO We have no evidence that Aristotle ever considered the possibility of a sixth simple body. If in the de Caelo, with the exception of the seventh chapter of the second book, perhaps of the following chapter, too, the matter of the planets, the Sun and the Moon, as well as the filler of their place in the cosmos, is not the first simple body, it must be one of the traditional four simple bodies.41 As already said above, in 2.3, the only reasonable choice is fire, at a very large distance from the air and the center of the cosmos. In other words, Aristotle’s implicit view in the main bulk of the de Caelo is that the planets, the Sun and the Moon are in the uppermost part of the cosmic place which is filled with fire, and consist of this simple body.42 40 For QERXIfEmeaning “common notion” see Simp., in Cael. 382.28–32 (Heiberg). 41 Aristotle might be alluding in Cael. B 8 to the first simple body as the sole kind of matter found in the heavens if ta astra in 290a7–12 are not only the stars but also the ¿ve planets, the Sun and the Moon: }XMH’ zTIiWJEMVSIMH¢X‡†WXVE, OEU„TIVSgX’ †PPSMJEWiOEišQlR ±QSPSKS»QIRSRIeTIlR, z\zOIfRSYKIXSÁWÉQEXSNKIRRÏWMR, XSÁHäWJEMVSIMHSÁNH»S OMRœWIMNIeWiOEU’ E¹X³, O»PMWMNOEiHfRLWMN, IhTIVSÃROMRIlXEMX‡†WXVEHM’ E¹XÏR, XŸRyX{VER‰ROMRSlXSXS»X[R· ƒPP’ SºHIX{VERJEfRIXEM(“Furthermore, since ta astra are spherical, as others affirm and as is consistent for us to say, for we make them out of a [simple] body with that shape, and since two motions are proper to what is spherical as such, rolling and rotation, if ta astra moved by themselves, they would undergo one of these two motions; but they are observed to move with neither ” ). It seems that in Cael. B 8 Aristotle is concerned only with the stars, whose diurnal revolution he assumes to result from the rotation of a spherical shell of the first simple body, whose fixed parts they are (see Appendix 7). The passage just translated introduces an argument to that effect, so we can quite plausibly identify ta astra referred to in it with the stars alone. But this argument shows that the stars neither roll nor rotate by analogy with what is true of the Sun and the Moon, the only celestial objects with spherical shape the naked eye can see, and since there can be no doubt that Aristotle took all celestial objects to be spherical, it can very well start off with a general fact about all luminaries leading to a conclusion applicable to the stars alone (see Appendix 7). If so, ta astra in our passage are the celestial objects, not just the stars, and in it the first simple body is assumed to make up all of them, and implicitly to pervade the whole heavens, too. 42 In Cael. B 9, where Aristotle argues against the belief of the Pythagoreans that the celestial motions produce a cosmic harmony, he seems to clearly deny the presence of fire in the heavenly realm of the cosmos: ÊWX’ zRXEÁUE PIOX{SR ÇN IhTIV zJ{VIXS X‡ WÉQEXE XS»X[R IhX’ zRƒ{VSNTPœUIMOIGYQ{R.OEX‡X¶TŠRIhXITYV³N, ÊWTIVT„RXINJEWfR, ƒREKOEl- SRTSMIlR¹TIVJYŠXÚQIK{UIMX¶R]³JSR, XS»XSYHäKMRSQ{RSYOEiHIÁV’ ƒJMORIlWUEM OEiHMEOREfIMR (291a18–22: “So let it be asserted here that if the masses of the celestial objects moved in an [immense] amount of either air or fire which pervaded the cosmos, as eve-

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According to Mete. A 4, the simple body inappropriately called “fire”, a combustible gas, comes in many nameless kinds (341b6–22): 

5IVQEMRSQ{RLNK‡VX¢NK¢N¹T¶XSÁšPfSYXŸRƒREUYQfEWMRƒREKOElSRKfKRIWUEMQŸ ‚TP¢R, ÊN XMRIN ShSRXEM, ƒPP‡ HMTP¢R, XŸR QäR ƒXQMH[HIWX{VER XŸR Hä TRIYQEX[HI- WX{VER, XŸRQäRXSÁzRX®K®OEizTiX®K®¹KVSÁƒXQfHE, XŸRH’ EºX¢NX¢NK¢NS½WLN \LVŠN OETRÉHL· OEi XS»X[R XŸR QäR TRIYQEXÉHL zTMTSP„^IMR HM‡ X¶ UIVQ³R, XŸR Hä ¹KVSX{VER¹JfWXEWUEMHM‡X¶F„VSN. OEiHM‡XEÁXEXSÁXSRX¶RXV³TSROIO³WQLXEMX¶ T{VM\· TVÏXSRQäRK‡V¹T¶XŸRzKO»OPMSRJSV„RzWXMRX¶UIVQ¶ROEi\LV³R, ·P{KSQIR TÁV (ƒRÉRYQSR K‡V X¶OSMR¶RzTiT„WLN X¢NOETRÉHSYN HMEOVfWI[N· ´Q[N HäHM‡X¶ Q„PMWXETIJYO{REMX¶XSMSÁXSRzOOEfIWUEMXÏRW[Q„X[RS¼X[NƒREKOElSRGV¢WUEM XSlN²R³QEWMR), ¹T¶HäXE»XLRXŸRJ»WMRƒœV. HIlHŸRS¢WEMSmSR¹T{OOEYQEXSÁXS· RÁRIhTSQIRTÁVTIVMXIX„WUEMX¢NTIViXŸRK¢RWJEfVEN}WGEXSR, ÊWXIQMOVŠNOMRœ- WI[N XYG¶R zOOEfIWUEM TSPP„OMN ÊWTIV X¶R OETR³R· }WXM K‡V š JP¶\ TRI»QEXSN \LVSÁ^{WMN. When the Earth is heated by the Sun, it necessarily gives off not one kind of exhalation, as some believe, but two, a more vaporous one and another more like the wind;43 the former arises from the water on the Earth and in it, the latter, which is smoky, from the dry Earth itself. Since it is hot, the windy exhalation rises to the top, and the more watery one sinks below, for it is heavy. The region of the cosmos around the Earth is, therefore, arranged in this manner. First beneath the [simple body with the] circular [natural ] motion comes the hot and dry [simple] body we call fire (there is no common name by which all kinds of the smoky exhalation are referred to, but it is the most combustible of all bodies, so we have to use this name for it), and the air is right below. We must think of this body we just called fire as a very inflammable material extending all around the outermost part of the spherical realm of the cosmos at the center of which the Earth is located, so that often a little motion suffices to make it ignite, like smoke. For flame is the boiling of a dry current.

As is explained in Mete. A 3, moreover, fire becomes more differentiated due to admixtures, apparently of water-vapor and air, the closer it is to the stratum of air surrounding the Earth and, consequently, the farther away from the first simple body above (340b6–29; on 340b6–10 see Appendix 2): 

8¶QäRK‡V†R[OEiQ{GVMWIPœRLN|XIVSRIREMWÏQ„JEQIRTYV³NXIOEiƒ{VSN, Sº QŸRƒPP’ zREºXÚKIX¶QäROEUEVÉXIVSRIREMX¶H’ £XXSRIePMOVMR{N, OEiHMEJSV‡N

rybody says, a powerful sound would necessarily arise, in which case it could not but reach here and wreak havoc”) . Note, however, that this follows from the premise that objects moving because they are fixed immovably in something else which moves, or moving in something else which also moves, do not generate sound; only objects moving in something unmoved produce sound (291a9–18). What Aristotle denies, therefore, is only that the celestial objects move in a stationary medium: he uses air or fire as example of such a medium, but it does not follow that he disagrees with the presence of fire in the heavens–what he rejects is simply the possibility that if fire suffuses a part of the heavens, which does seem to be his belief in most of the de Caelo as argued here, it can be stationary. Cf. 3.4.3. 43 The wind-like exhalation is earth, which is dry and cold, having turned into fire, which is hot and dry. The vaporous exhalation is water-vapor, i.e. water, which is cold and wet, on its way to being air, which is wet and hot. It is not as cold as liquid water, in all probability as a direct result from the action of Sun-heated air on it. See above, 1.2.5. The exhalation from the Earth is said to be like the wind probably because in Aristotle’s view this exhalation is the cause of winds; see Mete. B 4.

2.7. Fire as second upper body in the de Caelo

73

}GIMR, OEi Q„PMWXE ¯ OEXEPœKIM TV¶N X¶R ƒ{VE OEi TV¶N X¶R TIVi XŸR K¢R O³WQSR. JIVSQ{RSY Hä XSÁ TVÉXSY WXSMGIfSY O»OP. OEi XÏR zR EºXÚ W[Q„X[R, X¶ TVSWIGäN ƒIi XSÁ O„X[ O³WQSY OEi WÉQEXSN X® OMRœWIM HMEOVMR³QIRSR zOTYVSÁXEM OEi TSMIl XŸR UIVQ³XLXE. HIl Hä RSIlR S¼X[N OEi zRXIÁUIR ƒV\EQ{RSYN. X¶ K‡V ¹T¶ XŸR †R[ TIVMJSV‡RWÏQESmSR¼PLXMNSÃWEOEiHYR„QIMUIVQŸOEi]YGV‡OEi\LV‡OEi¹KV„, OEi´WE†PPEXS»XSMNƒOSPSYUIlT„UL, KfKRIXEMXSME»XLOEi}WXMR¹T¶OMRœWI[NOEi ƒOMRLWfEN, £NXŸREeXfEROEiXŸRƒVGŸRIeVœOEQIRTV³XIVSR. zTiQäR SÃR XSÁQ{WSY OEiTIViX¶Q{WSRX¶ FEV»XEX³RzWXMROEi]YGV³XEXSRƒTSOIOVMQ{RSR, K¢OEi¼H[V· TIVi Hä XEÁXE OEi zG³QIRE XS»X[R, ƒœV XI OEi · HM‡ WYRœUIMER OEPSÁQIR TÁV, SºO }WXM Hä TÁV· ¹TIVFSPŸ K‡V UIVQSÁ OEi SmSR ^{WMN zWXi X¶ TÁV. ƒPP‡ HIl RS¢WEM XSÁ PIKSQ{RSY ¹J’ šQÏR ƒ{VSN X¶ QäR TIVi XŸR K¢R SmSR ¹KV¶R OEi UIVQ¶R IREM HM‡ X¶ ƒXQf^IMRXIOEiƒREUYQfEWMR}GIMRK¢N, X¶Hä¹TäVXSÁXSUIVQ¶RžHLOEi\LV³R. }WXMR K‡V ƒXQfHSN QäR J»WMN ¹KV¶R OEi UIVQ³R,44 ƒREUYQM„WI[N Hä UIVQ¶R OEi \LV³R· OEi }WXMRƒXQiNQäRHYR„QIMSmSR¼H[V, ƒREUYQfEWMNHäHYR„QIMSmSRTÁV. It is our belief that the upper body extending as far as the Moon is different from both air and fire, but in it there are degrees of purity and cleanliness, and it is inhomogeneous, especially where it approaches the air and the region of the cosmos around the Earth.45 As the first element and the celestial objects in it move circularly, this motion causes the layer of the cosmos immediately below to combust due to separating off, and heat is thereby generated. A different way of saying the same thing is as follows. The body underneath the rotating heavens is a kind of matter, which is potentially hot and cold and dry and wet, and possesses potentially all other qualities consequent upon these; 46 it comes to acquire any of them in actuality due to motion and rest, the origin and cause of which we have explained earlier.47 The heaviest and coldest, earth and water, has separated off at the center [of the cosmos] and around it, being surrounded contiguously by air and [the latter by] what we habitually call fire, though it is not fire, which is an excess of heat and a kind of boiling.48 We must conceive of what we call air 44 45

46

47 48

For ]YGV³R, which is expected here instead of the UIVQ³R Fobes (1919) adopts, see the note in Lee (1952) 20. In what follows, Aristotle seems to be analyzing air into water-vapor and the earthy effluvium, which is inappropriately called fire. There is, however, no evidence that for some reason he privileges water, in its vaporous state, and fire over air, regarding them as simpler, and thus more fundamental, bodies than air. His reference, moreover, to purity and varying freedom from admixtures in the body surrounding the Earth suggests that he is having in mind simply the compresence of air, water-vapor and fire in the region of the cosmos immediately around the Earth. When he is saying that the body which occupies this region differs from air and fire, he is actually speaking of a commingling in the region at issue of these simple bodies with water-vapor. It attenuates with altitude, until fire is totally pure. Water-vapor, given off by the water on the Earth and in it, is more buoyant than liquid water, and thus rises up. Being heavier than air, however, it cannot reach very high altitudes, unlike fire, of course, which the Earth itself gives off. Fire rises up well beyond air, as far as is possible for it, until its progress is stopped by the spherical shell of the first simple body above. Air, fire and water-vapor constantly turn into one another on variously sized scales, much smaller, of course, than the scale of the cosmos. This constant flux is the reason why Aristotle says about the region of the cosmos immediately around the Earth that it is filled up with a configurable substratum, “matter”, not with stable simple bodies. See above, n. 3, and 1.2.5. What Aristotle refers to as separating off here is the perpetually ongoing process of one traditional simple body’s generation from the others in the cosmic region below the first simple body, which does not take part in this process, and the consequent commotion, as amounts of a traditional simple body sink, or rise up, where its bulk is found on the large scale of the cosmos. “Combustion” due to separating off in the region of the cosmos below the first simple

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2. The stuff of the heavens as wet and hot [at a low altitude] around the Earth, for it is vaporous and contains the exhalation from the earth, and as hot and dry farther out. The nature of the vapor is to be wet and cold, that of the exhalation to be hot and dry, and vapor is potentially water, the exhalation potentially fire.49

Although in Mete. A 2–3 the first simple body is assumed to fill the whole of the celestial realm of the cosmos, and thus to compose all celestial objects, the stars as well as the planets, the Sun and the Moon, if Aristotle’s views on the simple body fire at the time he wrote the de Caelo were already those put forth in the later Meteorologica, we can see how in the great bulk of the earlier treatise the first simple body can be thought of only as filler of the uppermost part of the heavens–as constitutive matter of the crust of the cosmos, and thus of the celestial objects fixed therein only, the stars–without the existence of a sixth simple body being presupposed in the remaining part of the heavens.50

2.8. THE ARGUMENT IN METE. A 3 FOR THE EXISTENCE OF THE FIRST SIMPLE BODY 2.8.1. An outline Why did Aristotle decide, at some time after the completion of the main bulk of the de Caelo as we know it, to extend the role of the first simple body, turning it into the constitutive matter of celestial objects tout court and the sole ¿ller of the whole heavens? As seen above, in 2.1, this development is reflected in Mete. A 2– 3 and Cael. B 7, a chapter which must be considered a later addition to the original form of the treatise, and possibly in the next chapter, too (see above, n. 41). It is likely that the change in Aristotle’s original view on the role of the first simple body is simply the generation of what we conventionally call fire. It cannot be a real conflagration sweeping through this region. Most of the simple body ¿re is in all probability produced from the simple body earth, which is clumped around the center of the cosmos. When Aristotle says “ t he heaviest and coldest, earth and water, has separated off at the center [of the cosmos] and around it” , the perfect tense generates a strong impression that he is speaking of a one-off event, the formation of the Earth, with its various water-masses, in the very distant past. In Aristotle’s cosmology, however, the cosmos as a whole never came into being and will never cease to be; see Cael. A 10–12. He might have written those lines with a hypothetical partial cosmogony in mind: primordially all matter, with the exception of the first simple body, was a mixture, in which the ingredients existed potentially, and which gradually separated off into the four traditional simple bodies (cf. Cael. B 14, 297a8–30, where this hypothesis is used to show that the shape of the Earth is spherical). Within Aristotle’s physics, the four traditional simple bodies pass constantly out of potentiality and into actuality on very small scales, compared to the scale of the whole cosmos, but on this scale, which is the largest in existence, such a process never took place. 49 The term is used here in the everyday sense. 50 The last of Aristotle’s arguments in Cael. A 2 for the existence of a first simple body in the cosmos–where, as seen in 2.2.1, he rejects fire as possible matter of the only existents with eternal and continuous motions and substitutes for it the first simple body–must thus concern the stars alone, not the five planets, the Sun and the Moon. See also above, n. 12.

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body had to do with a striking argument in Mete. A 3, not given in Cael. A 2, for the existence of this simple body. This argument shows that fire cannot fill the whole part of the cosmos above the stratum of air, and thus cannot make up all the celestial objects, nor can it only compose them while air surrounds them, filling almost all of the celestial realm; as it is, there must exist in nature one more simple body alongside the traditional four, a self-evident conclusion Aristotle does not draw explicitly. This is the first simple body, which pervades the heavens and makes up all celestial objects. Aristotle reasons as follows. The realm of the heavens is vast. So, if fire had filled it completely and thus made up the celestial objects, or, alternatively, if it had composed these objects but air had surrounded them, then either simple body would have existed in such a disproportionate amount relative to that of each of the other three traditional simple bodies that it would have absorbed all three long ago (see 1.2.4). That a fifth simple body, which not only makes up all celestial objects but also fills the heavens, must exist in nature follows naturally. Now, if by far the largest part of the celestial realm is assumed to lie below the stars, and to contain the seven remaining luminaries, the ¿ve planets, the Sun and the Moon, a variation of this argument could have easily led Aristotle to extend the role of the first simple body in the de Caelo. The basis of the argument is the vastness of the heavens, which contemporary astronomy has demonstrated satisfactorily, as Aristotle says, a hint that the extension in question had been motivated by the careful weighing of the cosmological implications of certain astronomical facts, which had been unknown, or had not been duly taken into account, when he introduced the concept of a first simple body into cosmology.

2.8.2. The preamble to the argument The first part of the preamble to the argument in Mete. A 3 for the existence of the first simple body seems to hint at the extension in Mete. A 2–3 of the role originnally accorded to this simple body in the earlier de Caelo. In it, Aristotle repeats from Cael. A 3 his confident identification of what the ancients called aithƝr with his first simple body. aithƝr is said in Cael. A 3 to be an ancient name for the substance pervading “the uppermost place” of the cosmos, a clue that the first simple body is assumed to fill the heavens only in part, making up the stars and the spherical shell in whose mass they are fixed. In Mete. A 3, however, the noun is assumed to have been used by the ancients for the substance pervading “the upper regions” of the cosmos, i.e. the whole heavens (339b19–30): 

/Ei XE»XLR XŸR H³\ER Sº Q³RSR šQIlN XYKG„RSQIR }GSRXIN, JEfRIXEM Hä ƒVGEfE XMN ¹T³PL]MNE¼XLOEiXÏRTV³XIVSRƒRUVÉT[R· ±K‡VPIK³QIRSNEeUŸVTEPEM‡RIhPLJI XŸRTVSWLKSVfER,  R%RE\EK³VENQäRXÚTYViXEºX¶RšKœWEWUEfQSMHSOIlWLQEfRIMR· X„XIK‡V†R[TPœVLTYV¶NIREM, OƒOIlRSNXŸRzOIlH»REQMREeU{VEOEPIlRzR³QMWIR, XSÁXSQäR²VUÏNRSQfWEN· X¶K‡VƒIiWÏQEU{SR…QEOEiUIl³RXMXŸRJ»WMRzSfOEWMR ¹TSPEFIlR, OEiHMÉVMWER²RSQ„^IMREeU{VEX¶XSMSÁXSRÇN¸RSºHIRiXÏRTEV’ šQlRX¶

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2. The stuff of the heavens EºX³· Sº K‡V HŸJœWSQIR…TE\ SºHä HiN SºH’ ²PMK„OMNX‡NEºX‡N H³\ENƒREOYOPIlR KMKRSQ{RENzRXSlNƒRUVÉTSMN, ƒPP’ ƒTIMV„OMN. Now, this is not an opinion we alone happen to hold, but seems to be an ancient belief also held by people in the past. What is called aithƝr was given in antiquity this name, which Anaxagoras, as it seems to me, believed to mean the same as the word “fire”. He thought that the upper regions are full of fire, and that the ancients called aithƝr the substance up there, but was correct only in the latter. For they seem to have believed that this body is always [aei] in motion [theon] and is also somehow divine [theion] in nature, and resolved to name it aithƝr, on account of its being unlike all bodies found close to us. For, in our view, the same beliefs come back in a cycle among people not once or twice or a few times, but infinitely often.

Interesting is also the second part of the preamble, where Aristotle rejects in very poignant terms the view that fire composes all celestial objects (here called “objects in motion”), and also fills the heavens (339b30–37): 

t3WSMHäTÁVOEUEV¶RIREfJEWMX¶TIVM{GSROEiQŸQ³RSRX‡JIV³QIREWÉQEXE, X¶ Hä QIXE\¾ K¢N OEi XÏR †WXV[R ƒ{VE, UI[VœWERXIN ‰R X‡ RÁR HIMOR»QIRE HM‡ XÏR QEULQ„X[RdOERÏNhW[N‰RzTE»WERXSXE»XLNX¢NTEMHMO¢NH³\LN· 51 PfERK‡V‚TPSÁR X¶ RSQf^IMR QMOV¶R XSlN QIK{UIWMR IREM XÏR JIVSQ{R[R |OEWXSR, ´XM JEfRIXEM UI[- VSÁWMRzRXIÁUIRšQlRS¼X[N. IhVLXEMQäRSÃROEiTV³XIVSRzRXSlNTIViX¶R†R[X³TSR UI[VœQEWM· P{K[QIRHäX¶REºX¶RP³KSROEiRÁR. Those who say that pure fire not only constitutes the objects in motion but is what surrounds them, too, while air occupies the space between them and the Earth, would have ceased to hold this childish view if they had known what astronomy has now satisfactorily shown. For it is very naïve to think that each object in motion is small because it seems so to us when we observe it from here. We have already discussed this in our studies of the upper place, but let us give the same argument here, too.

When Aristotle says “it is very naïve to believe that each of the celestial objects is small” (cf. [Pl.] Epin. 982e6–983a6), he has in mind primarily the fact that the size of the Sun, which is larger than the Earth, is a multiple of the Moon’s. This ratio interests him not per se, but insofar as it is the ratio between the Earth-Sun distance and the Earth-Moon distance; the argument following the lines just translated relies, as said above, on the immense size of the celestial realm, for whose qualitative estimate this ratio provides the baseline. But the topic has not been discussed 51

Alexander of Aphrodisias thought that šTEMHMOŸH³\E is that fire both makes up the celestial objects and saturates the whole heavens, whereas air fills the space between the lower boundary-surface of the heavens and the Earth’s surface. Cf. Phlp., in Mete. 22.3–8 (Hayduck): ± QäR%P{\ERHVSN^LXIlRzRXEÁU„JLWMX¶RJMP³WSJSR, IeX‡SºV„RMET„RXETYV³NIeWM OEUEVSÁ OEi QŸ X‡ †WXVE Q³RSR (X‡ K‡V JIV³QIRE WÉQEXE P{KIMR X‡†WXVE), ƒPP‡ OEiX‡QIXE\¾XÏR†WXV[RHMEWXœQEXE· XSlNK‡VXSÁXSP{KSYWMR|TIWUEMX¶T„RXEX‡ QIX‡XŸRK¢ROEiX¶¼H[VQ{GVMX¢NWJEfVENX¢NWIPLRMEO¢Nƒ{VEP{KIMR( “Alexander says that here the philosopher seeks to decide whether the whole heavens are purely fiery, not only the celestial objects–what he labels “moving objects” are the celestial objects–but also the spaces between them, for those who hold this view claim as a consequence that the space above the earth and water up to the lunar sphere is filled with air ”). Philoponus thinks that, on the childish view, fire also occupies the place between the lower boundary-surface of the heavens and the surface of the Earth. This is clearly not so, however. See also below n. 55.

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in the de Caelo, the only surviving work of his to which Aristotle can possibly refer back as “studies of the upper place”, and where, as seen above, he sets out an argument which is partly to the same effect as the one following the passage just translated–the argument in Cael. A 2, discussed in 2.2.1–but otherwise markedly different, not the very same one, as he seems to claim here.52 If Aristotle does say in the passage under discussion that he is going to repeat an argument from the de Caelo, specifically from Cael. A 2, the only part of the earlier work where we would expect to find the argument following next, it can be plausibly assumed that he intended to append this argument to the original version of Cael. A 2, and to also revise all relevant parts of the earlier work, in light of his views on the first simple body we find in Mete. A 2–3.53 However, for some reason he never got around to doing it, though he either inserted Cael. B 7, or rewrote the original version of this chapter, and added perhaps a brief note to B 8 (see above, n. 41). Alternatively, he might have found the opportunity to make all, or most, of the required revisions, but somehow it is the early draft of the de Caelo that got transmitted down to us, with the sole exception of Cael. B 7, and perhaps B 8, too.

2.8.3. The argument In Aristotle’s own words, the argument he gives in Mete. A 3 for the existence of the first simple body, the first known in the history of cosmology for the existence of “missing matter”, unfolds as follows (340a1–13): 

52

)e K‡V X„ XI HMEWXœQEXE TPœVL TYV¶N OEi X‡ WÉQEXE WYR{WXLOIR zO TYV³N, T„PEM JVSÁHSR‰R¤R|OEWXSRXÏR†PP[RWXSMGIf[R. ƒPP‡QŸRSºH’ ƒ{VSNKIQ³RSYTPœVL· 54 TSP¾ K‡V ‰R ¹TIVF„PPSM XŸR eW³XLXE X¢N OSMR¢N ƒREPSKfEN TV¶N X‡ W»WXSMGE WÉQEXE, O‰R Ie H»S WXSMGIf[R TPœVLN ± QIXE\¾ K¢N XI OEi SºVERSÁ X³TSN zWXfR·55

Ideler (1834–36) vol. 1, 339 and Lee (1952) 15 n. c think that in the passage just translated Aristotle refers back to Cael. B 7. But all we have there is a statement that fire neither is the constituent matter of the celestial objects nor surrounds them. 53 That the Meteorologica comes after the de Caelo is evident from Mete. A 1, 338a20–25, as well as from A 2. In Mete. A 6 Aristotle refers to the occultation of a star in the Twins by Jupiter which he had observed himself; it has been dated to 5 December 337 BC by Cohen & Burke (1990). An occultation of Mars by the Moon referred to in Cael. B 12, again as having been observed by him in person, is dated to 4 May 357 BC; see Schoch (1927 ) col. XX (cf. Guthrie [1939] 204 n. a), Stephenson & Clark (1978) 5–6, Stephenson (2000), Savoie (2003), Kelley & Milone (2005)131; on pretelescopic observations of the phenomenon of lunar occultation see White (1987) 16. A mention of the occultation of the star in the Twins by Jupiter would be apposite in Cael. B 12. Its absence perhaps suggests that Cael. A and B, which form a unit, were written before the first eight chapters of Mete. A, which also form a unit. 54 Sc. X‡HMEWXœQEXE¤R. The Greek clearly suggests that all celestial objects are now assumed to be surrounded by air, but to consist of fire. 55 Cf. Phlp., in Mete. 23.36–24.3 (Hayduck): QIXE\¾HäK¢NOEiSºVERSÁX³TSRITI, JLWiR± %P{\ERHVSN P{K[R OEPÏN, X¶R QIXE\¾ X¢N K¢N OEi X¢N z\[X„X[ TIVMJSVŠN· SºVER¶R K‡V XŸR ƒTPER¢ WJElVER ÈR³QEWIR. SºOSÁR OEi ´XI z^œXIM, Ie TÁV OEUEV¶R IhL X¶ QIXE\¾X¢NK¢NOEiXÏR†WXV[R, SºX¶RQ{GVMX¢NWIPœRLN}PIKIR, ƒPP‡X¶RƒT¶K¢N

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2. The stuff of the heavens SºHäRK‡VÇNIeTIlRQ³VMSR±X¢NK¢NzWXMRµKOSN, zRÛWYRIfPLTXEMTŠROEiX¶XSÁ ¼HEXSN TP¢USN, TV¶N X¶ TIVM{GSR Q{KIUSN. ±VÏQIR H’ SºO zR XSWS»X. QIK{UIM KMKRSQ{RLRXŸR¹TIVSGŸRXÏRµKO[R, ´XERz\¼HEXSNƒŸVK{RLXEMHMEOVMU{RXSN¡TÁV z\ƒ{VSN· ƒR„KOLHäX¶REºX¶R}GIMRP³KSR·R}GIMX¶XSWSRHiOEiQMOV¶R¼H[VTV¶N X¶Rz\EºXSÁKMKR³QIRSRƒ{VE, OEiX¶RT„RXETV¶NX¶TŠR¼H[V. If ¿re ¿lled the spaces [between the celestial objects] and the celestial objects [themselves] consisted of fire, each of the other elements would long ago have vanished. Neither can the spaces be filled only with air, however, in which case the air would be much more abundant than is required for it to be in a relation of proportional equality to the other kindred [simple] bodies, even if two elements filled the place between the Earth and the [outermost surface of the] ouranos. For the volume of the Earth, on which all existing water is contained, is, as we might say, no part of the surrounding magnitude. When air is generated by separation from water or fire from air, however, we do not observe so great a disparity in volume, and any small amount of water necessarily bears to the air generated from it the ratio in which water and air stand to each other on the scale of the cosmos.

By pointing out that “the volume of the Earth, on which all existing water is contained, is, as we might say, no part of the surrounding magnitude”, i.e. of the volume of the cosmos, which is here assumed to be of vast size, Aristotle in effect says this: on the cosmic scale, the mass of the simple body earth, as well as that of water, bears to the mass of fire, if this simple body makes up the celestial objects and fills the whole of their realm, or to that of air, if fire composes all celestial objects but it is air that fills the rest of the heavens, the ratio of a sphere’s center, a mere dimensionless point, to the sphere itself. This is either no ratio at all or an infinitely large one. Here we have what amounts to the earliest surviving statement of a fundamental principle of Greek astronomy, i.e. “that the Earth”, as Ptolemy puts it, “has, to the senses, the ratio of a point to the distance of the sphere of the so-called fixed stars” from the Earth (Alm. 20.5–7 [Heiberg]). Compared, in other words, with the spherical Earth, the sphere which is the boundary-surface of the whole cosmos is to be considered infinite. It is not really infinite, of course. For, otherwise, as Aristotle argues in Cael. A 5, it could not rotate in a finite time (272b28–273a6). SimiQ{GVMX¢NƒTPERSÁN(“Aristotle, Alexander correctly observes, called “t he place between the Earth and the ouranos” the place between the Earth and the outermost surface [of the cosmos], for it is the sphere of the fixed stars that he called ouranos. Therefore, when he was trying to determine whether the place between the Earth and the celestial objects is filled with pure fire, he was speaking of the place not down to the Moon but from the Earth up to the sphere of the fixed stars”). Alexander is certainly right (with a minor “correction”, as will be seen next). But the correct reading of the phrase at issue does not allow one to reason as Philoponus does (see also n. 51). Philoponus next informs us that Alexander took fire, on the hypothesis Aristotle puts forth and rejects here, to constitute the stars and their sphere, too–i.e. the spherical shell in the mass of which these celestial objects are fixed–with air filling the rest of the heavens. Alexander, consequently, understood “t he place between the Earth and the ouranos” as that between the Earth and the inner surface of the spherical shell in which the stars are fixedly embedded; Philoponus makes clear that, in Alexander’s view, the second hypothesis Aristotle considers understands fire as the constituent matter of the planets, the Sun and the Moon, too. However, Aristotle’s text gives a strong impression that the stars, too, are surrounded by air on this hypothesis, not only the planets, the Sun and the Moon. Cf. n. 54.

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larly, the volume of the Earth is not actually dimensionless–this would be a contradiction in terms–but turns out to be so for all practical purposes if compared to the finite, though by far larger, sphere of the whole cosmos. This is why Aristotle says that “the volume of the Earth … is, as we might say, no part of the surrounding” volume of the cosmos, and Ptolemy adds that it is for the senses, not in reality, that the Earth is as nothing but a mere point “to the distance of the sphere of the so-called fixed stars” from it.56 Aristotle assumes tacitly that the mass of air, too, is no part of that of fire on the scale of the cosmos, if it is fire that makes up the celestial objects and also saturates the enormous spaces between them, or inversely that the mass of ¿re is no part of that of air on the scale of the cosmos, if the celestial objects consist of fire but it is air that surrounds them. Unless the masses of two adjacent simple bodies bear to each other a rather small ratio, however, the overwhelmingly abundant simple body cannot but assimilate the other into itself. Each has the power to turn the other into itself, and this ratio is the condition for the two opposite powers to balance each other out. But it does not obtain if the mass of air on the cosmic scale is no part of that of fire–that is, if the masses of these two adjacent simple bodies on the cosmic scale have to each other an inordinately large, and not a small, ratio. On the first part of the hypothesis to be refuted, all air would long ago have vanished from the cosmos, having augmented insignificantly its enormous fire content, and the same would then have happened to all original water and earth. Similarly, on the second part of the hypothesis to be refuted–that is, if the celestial objects are assumed to be composed of fire but be surrounded by air, the filler of virtually the whole heavens–the fire of the luminaries, logically almost the whole mass of this simple body originally existing in the cosmos, would not but long ago have turned into air, together with all of the original water and earth.57 The crucial assumption behind this argument is that the power of fire to turn air into fire and the antagonistic power of air to turn fire into air balance out on the scale of the cosmos if the amounts of the two simple bodies that exist in the cosmos bear to each other a small ratio. Aristotle attempts to support this assumption with empirical evidence. If water turns into air, he says, in all probability a reference to the evaporation of boiling water, or if air transforms into fire, we do not see an inordinately large quantity of air or fire being generated, i.e. one which is out of all proportion to the original amount of water or fire. The ratio that a mass of air, or water, has to the mass of fire, or air, into which it can transmute, is tacitly but undoubtedly understood to be equal to the ratio between the masses of air and fire, or water and air, existing on the cosmic scale. 56

Cf. Aristarch. Sam., de magn. et dist. Sol. et Lun., Hyp. 2 (Heath): the Earth bears to the sphere of the Moon the ratio of a point. In his lost work, where he set out the heliocentric hypothesis, Aristarchus proposed that between the circular orbit of the Earth round the Sun and the sphere of the stars obtains the ratio which obtains between a sphere’s center and its surface; see Archim., Aren. 135.8–136.1 (Heiberg). 57 For the change of the traditional simple bodies into one another see 1.2, esp. 1.2.4.

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Why this must be so is not difficult to see. If the amounts of fire and air must be at any time in a certain ratio on the scale of the cosmos, in view of the fact that transmutations of one simple body into the other occur always on much smaller scales, it must be assumed that local mass-losses and -gains for each of the two simple bodies balance out on the cosmic scale. This is so if the ratio an amount of air, or fire, has to the amount of fire, or air, into which it transforms is always equal to the ratio between the entire quantities of air and fire that exist in the cosmos at any given time, and if the turning into air of any quantity of fire is counterbalanced by the reverse transformation of an equal amount of air into fire somewhere else in the cosmos.58

2.8.4. The astronomical premises The astronomical premises of Aristotle’s argument in Mete. A 3 for the existence of a first simple body that constitutes all of the celestial objects, and also ¿lls the heavens, are, first, the vastness of the boundary-surface of the cosmos, which answers to what is called in astronomy the celestial sphere or the sphere of the fixed stars, and, second, the identification of the comparatively insignificant Earth with the center of the cosmos for practical purposes. That the Earth is small is demonstrated, argues Aristotle in Cael. B 14, by the fact that the appearance of the sky at night changes noticeably with latitude: traveling e.g. to the south, we note that in Cyprus and Egypt stars which are always seen above the horizon in Greece rise and set; we also see new stars, not observed in Greece (297b30–298a9). This demonstrates beyond doubt that the Earth is a sphere, and that its circumference is not large–otherwise, such a small shift in latitude would not cause the appearance of the starry sky to vary so rapidly. However, it does not prove that the Earth is so small by comparison to the sphere on which the stars appear to be fixed that it does not make any difference if we treat it as the center of this sphere. Here one needs the arguments Ptolemy uses to show that the Earth bears, to the senses, the ratio of a point to the sphere of the fixed stars. 58

That the amount of water, which turns into a given amount of air, is generated when an equal amount of air turns into water is stated in Ph. ǻ 9, 216b26–28. A few lines below, moreover, it is said that the quantity of water produced from a given quantity of air is always equal to the quantity of water which turns into this quantity of air, and that when a quantity of air is generated from a given quantity of water, in some other place of the cosmos an equal amount of water turns into an equal amount of air (217a13–18). For the interpretation of these two passages see Simp., in Ph. 686.22–687.3 (Diels), Phlp., in Ph. 671.10–672.17 (Vitelli). Their context is an argument for the existence of vacuum in the cosmos: if no vacuum exists, when water becomes air, which occupies more space, the cosmos must heave, unless always an equal quantity of air turns into an equal quantity of water elsewhere in the cosmos; fine-tuning of this sort is inadmissible, however, so if the cosmos does not constantly heave and ripple, vacuum must exist in it. Aristotle does not think that the cosmos quivers, or that vacuum exists in it. His argument in Mete. A 3 under discussion here, however, leaves no doubt that he finds nothing objectionable with the fine-tuning rejected by whoever devised the argument for the existence of vacuum he records in Ph. ǻ 9.

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They certainly lay well within the grasp of Greek astronomers contemporary with Aristotle: the angular distances and magnitudes of the stars are observed to be the same from any place on the Earth; the gnomons and the centers of armillary spheres set up anywhere on the Earth work as if they were placed at the center of the Earth; for any observer on the Earth, ¿nally, the horizon bisects the celestial sphere (Alm. 20.7–21.6 [Heiberg]).59 As for the other premise, Aristotle notes in Mete. A 8 that contemporary astronomy has shown that the Sun is larger than the Earth, and that the distance from the Earth to the stars exceeds by a large factor the distance from the Earth to the Sun, as the Earth-Sun distance is larger than the Earth-Moon distance (345b1–5). In Mete. A 8 he refutes the view of Anaxagoras, Democritus and their followers that the Milky Way is the light of stars within the shadow cast by the Earth as it obstructs the sunlight from our view at night (345a25–31). Democritus must have agreed with Anaxagoras that the Sun is smaller than the Earth (DK 59 A 42). If so, the shadow of the Earth extends indefinitely, and we see, as a result, many more stars within it, the Milky Way, than outside it, where diffuse sunlight swamps most stars.60 Aristotle counters that the Sun is larger than the Earth, so when the Earth hides from our view the Sun at night, its shadow is a cone. Since the distance from the Earth to the stars exceeds by far the Earth-Sun distance, just as the Earth-Sun distance is quite larger than the Earth-Moon distance, the tip of this conical shadow must be close to the Earth; if so, the shadow of the Earth cannot extend to the very distant stars (345b5–9). Presupposed in Mete. A 8 is probably the work of Eudoxus, whom our sources credit with the oldest estimate of the ratio the Sun’s diameter bears to the Moon’s. According to Archimedes’ testimony (Aren. 136.21–137.6 [Heiberg]), Eudoxus estimated this ratio at 9 to 1; Archimedes’ father Pheidias at 12 to 1; Aristarchus of Samos arrived at a ratio greater than 18 to 1 but less than 20 to 1. Only Aristarchus’ calculation has come down to us, in his small treatise On the Sizes and Distances of the Sun and the Moon. Once the ratio of the Earth-Sun distance to the Earth-Moon distance has been obtained, simple considerations show that this is also the ratio between the Sun’s diameter and the Moon’s. The Moon eclipses the Sun totally, so the two celestial objects have the same angular size. If the ratio of the Earth-Sun distance to the Earth-Moon distance is n times, it follows that the Moon must be n times smaller than the Sun. Aristarchus also proves that the diameter of the Sun bears to the Earth’s a ratio greater than that which 19 has to 3 but less than that which 43 has to 6 (to put it differently, the diameter of the Sun is between 6.33 and 7.17 Earth diameters), as 59 See Evans (1998) 77. 60 If Democritus and Anaxagoras assumed that all stars outside the shadow of the Earth shine with reflected sunlight (see n. 64), it is not easily understood why in Aristotle’s report this group of stars are said to be obscured by the Sun’s rays. Aristotle might misrepresent the position of Democritus and Anaxagoras, who believed that somehow most stars congregate in a narrow band of the sky, the Milky Way, and shine with their own light only, being immersed in the shadow of the Earth and thus deprived of sunlight, whereas the few ones outside this band glow with reflected sunlight only, their own light being swamped by the Sun’s.

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well as that the Moon’s diameter has to the Earth’s a ratio greater than that which 43 has to 108 but less than that which 19 bears to 60 (equivalently, the Moon’s diameter is between 0.398 and 0.317 of the Earth’s).61 It was perhaps Eudoxus who pioneered the geometric technique Pheidias and Aristarchus also used to calculate the ratios of the Earth-Sun distance to the EarthMoon distance, and of the Sun’s diameter to the Moon’s.62 All three astronomers were most probably aware that they had underestimated the distance of the Sun from the Earth relative to the Moon’s, as well as how much the Sun’s diameter exceeds the Moon’s.63 Aristarchus’ technique for comparing the diameters of the Sun, Moon and Earth depends, among other things, on the ratio the Sun-Earth distance has to the Moon-Earth distance. However, since no surviving source credits Eudoxus and Pheidias with estimates of the ratios the diameters of the Sun and Moon have to the Earth’s, there is no reason to assume that this technique, too, had been invented by Eudoxus and been also used by Pheidias and Aristarchus. In Mete. A 8 Aristotle gives the impression that he knows estimates of those ratios, with which Eudoxus could be plausibly credited. But it need not be so. Eudoxus, or another astronomer contemporary with Aristotle, could as well have argued non-quantitatively to the effect that the Moon is smaller and the Sun larger than the Earth. Such an argument is most probably all that Aristotle can presuppose in Mete. A 8. One has no difficulty concluding that the Moon is smaller than the Earth if it is known from the duration of lunar eclipses that the diameter of the shadow cast by the Earth can cover a body a few times larger in diameter than the Moon. Thus, even if the Earth and the Sun were of equal magnitude, contrary to the opinion of Anaxagoras and Democritus, the shadow cast by the former would extend arbitrarily far, and its diameter would be the same at any distance away from the Earth. In that case, however, not only the Moon but also the planets Mars, Jupiter and Saturn that are farther out from the Earth than the Moon would be seen to be eclipsed by entering into the Earth’s shadow, their brightness being noticeably dimmed as they would shine by their own light only, without the additional illumination they get from the Sun.64 This phenomenon is not observed. Consequently, the shadow of the Earth does not reach as far out as any of the three planets. But if so, the Earth and the Sun cannot be of equal magnitude, as initially assumed. Nor can the 61 The calculation is succinctly presented in Evans (1998) 68–71. 62 See, however, Heath (1981) 331–332. 63 Cf. the critique of Aristarchus in Evans (1998) 71–72. 64 Olympiodorus, in Mete. 67.32–37 (Stüve), attributes to Democritus and Anaxagoras the opinion that all celestial objects produce their own light and also reflect sunlight, as is clear from the coal-like glow of the Moon during lunar eclipses. (This is why, according to Olympiodorus, the ¿xed stars in the Earth’s shadow were hypothesized by Democritus and Anaxagoras to shine constituting the Milky Way, despite the fact that the Earth lies between these stars and the Sun; see above n. 60.) There is no evidence that Aristotle held such a view. If, however, he paid any attention to the glow of the Moon during lunar eclipses, he might very well have explained it in the manner of Democritus and Anaxagoras (his different opinion on the nature of the Milky Way notwithstanding).

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Sun be smaller than the Earth, as Democritus and Anaxagoras believed, for the same reason. The Sun must be larger, and the spherical Earth must cast a conical shadow, whose tip lies between Moon and Mars–quite close, that is, to the Earth. This is the reason why we do not see eclipses of the planets Mars, Jupiter or Saturn. It follows that the shadow of the Earth cannot reach the stars, pace Anaxagoras and Democritus. Aristotle most probably presupposes such an argument in Mete. A 8, and concludes that the distance from the Earth to the fixed stars cannot but exceed by a large factor the Earth-Sun distance, just as the Earth-Sun distance is larger than the Earth-Moon distance, based on a similarly qualitative argument. As said above, the ratio of the Earth-Sun distance to Earth-Moon distance is the baseline for estimating qualitatively that the distance between the Earth and the stars is immense, whence it follows that the size of the celestial sphere, the boundary-surface of the cosmos, is vast. In Mete. A 6, Aristotle reports that he had observed an occultation of a star in the Twins by Jupiter, a phenomenon analogous to the eclipsing of the Sun by the Moon, and also mentions Egyptian observations of occultations of planets by other planets, and of stars by planets (343b28–32). He refers to Egyptian, as well as Babylonian, records of occultations of the planets by the Moon in Cael. B 12, where he says that he himself had observed the Moon occulting Mars (292a3–9). Occultations of the planets by the Moon show that the Moon is closer to the Earth and the planets farther away; occultations of stars by planets, on the other hand, show that the planets are closer to the Earth and the stars farther away. Whether it was known in Aristotle’s time that all planets can occult stars cannot, of course, be determined. If so, since it is impossible for the planets to occult all stars, that the planets are closer to the Earth and all stars farther away could easily be concluded from the simple fact that from the Earth all stars appear to be equally far away. One could reach the same conclusion based only on the occultation Aristotle reports of a star in the Twins by Jupiter. As is shown by Cael. B 10, in Aristotle’s time it was understood that the longer the tropical period of a wandering celestial object–i.e. the time the luminary needs to complete its eastward trip against the backdrop of the stars–the farther away this object must be from the Earth (cf. Pl., R. 10, 617a4–b4, Ti. 38c7–d4). The shortest tropical period, about a month, belongs to the Moon. The tropical periods of Mercury and Venus are the same as the Sun’s, one year, so the principle breaks down for Mercury, Venus and the Sun. However, it takes Mars about two years to go all the way around the stars, whereas Jupiter and Saturn need about twelve and thirty years respectively. The Moon is thus closer to the Earth and the Sun farther away, as solar eclipses also show; the Moon, moreover, is closer to the Earth than the planets, all the more so since it is known to occult planets. Two planets, Mercury and Venus, lie together with the Sun between the Moon and Mars, which is followed by Jupiter. Farthest away from the Earth is Saturn. In view of the occultation of the star in the Twins by Jupiter, it would be strange to think that the stars lie between Jupiter and Saturn, and not beyond the latter. Placing the stars beyond Saturn neatly separates them in space from all five planets, the Sun and Moon, seven celestial objects naturally grouped together, and differenti-

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ated from the stars, on account of the fact that they always change positions relative to each other and the stars. The vastness of the heavens, now, follows easily if what holds for the Moon and Sun, in terms of their relative sizes and distances from the Earth, is extrapolated to the planets and the stars. The Sun is farther away from the Earth, and larger, than the Moon. If this applies to the planets, too, and the farther away from the Earth a planet is, as can be determined from the tropical period, with the two exceptions of Venus and Mercury, the larger than its immediate predecessor it is, we must reach the conclusion that, since all planets appear insignificant, in comparison with the Moon and Sun, they must be inordinately far from us. Consequently, the distance of the stars from the Earth must be enormously larger than that of Saturn, the remotest planet, from the Earth. Eudoxus, and any other astronomer contemporary with Aristotle, could not have said anything more about the distance of the stars from the Earth.

2.8.5. Conclusion If Aristotle did originally conceive of the first simple body as the constituent matter of the stars only and of the spherical shell in whose mass they are fixed, the outermost layer of the cosmos, when contemporary astronomers first understood the vastness of the heavens, or he himself realized the implications of this fact for his cosmology, it might have dawned on him that the belief in a cosmos made mostly of fire, the matter of the five planets, the Sun and the Moon and the filler of almost the whole of the heavens, had a grotesque consequence: the simple bodies air, water and earth ought to have long vanished from “the cosmos”, assuming, of course that nature–who in Aristotle’s view does nothing in vain, and whom he shows in Cael. B 3 to include necessarily all four traditional simple bodies, if she comprises a first simple body, as she must–would have ever allowed these three simple bodies to come into existence, in order for them to merely pass out of existence almost immediately. 65 65

When fire filled the part of the heavens below the deferent spherical shell of the stars, the problem with the friction-based account Aristotle sets out in Cael. B 7 of how all the heavenly objects produce light, and at least, or only, the Sun heat–see above, 2.1 and 1.2.5, and cf. Appendix 4–applied to the stars alone. The generation of light by the planets, the Sun and the Moon and the production of heat by perhaps only the Sun were most probably accounted for frictionally, too. At the time, however, all of these seven celestial objects were assumed to move through an extremely flammable medium–the same simple body they were made of–as the analogy between projectiles and celestial objects in Cael. B 7 suggests if understood literally. Friction would be generated as a wandering celestial object moved against the background of the zodiac, oppositely to the rotation of the medium which followed the rapid diurnal rotation. The brightness of a planet would increase and decrease (for Aristotle’s awareness of this phenomenon see Simp., in Cael. 505.21–27 [Heiberg] = Arist., fr. 211 [Rose]; translation below, in 3.6) as the planet would approach, and recede from, the center of the cosmos in its non-circular motion among the stars of the zodiacal constellations (for the non-circularity of zodiacal motion, at least for the planets, see 1.4.6). The Moon would not produce either much light on its own–only a faint glow, observable during lunar eclipses; cf. above, n. 64–or

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Aristotle’s simple solution, as argued above, was to extend the role he had originally accorded to the first simple body. So this simple body evolved into the constituent matter of all celestial objects, not only the stars, and into the filler of the whole heavens, thereby reducing radically, but naturally, the abundance of fire in the universe. The absurdity that led to this development supplied Aristotle with a novel, and by his lights powerful, argument for the existence of a first simple body, proudly set out in Mete. A 3 as cure for childish opinions about the cosmological role of fire.

heat because the linear speed of its zodiacal motion relative to the opposite motion of the medium was not suf¿ciently fast. See 3.4.1, and cf. Mete. A 3, 341a12–30, where the comparison of the speed of the stars, the Moon and the Sun seems to suggest that it is not the zodiacal motion of these two wandering celestial objects that matters but their diurnal motion minus their zodiacal (see above, 2.1, and Appendix 4). However, the first simple body is assumed in this passage to fill the whole of the heavens, and thus to constitute all celestial objects. This requires a quite different account of how the wandering celestial objects produce light, and (at least) only the Sun heat–the same one that applies to the stars, to which the wandering celestial objects are now assimilated in a crucial respect, their constitution. But such an account is by no means easily forthcoming (see above, 1.2.5, and Appendixes 2–3). Extending the role of the first simple body certainly had its price. Cf. the end of 1.5.

3. ARISTOTLE AND THE THEORY OF HOMOCENTRIC SPHERES 3.1. INTRODUCTION In Cael. B 6 Aristotle contrasts “the first rotation” which is uniform–that is, the diurnal rotation undergone by “the first ouranos” (equivalently, “the outermost ouranos”; see above, 2.2.4), with the non-uniform motions of the Sun, the Moon and the planets in the cosmic region below “the first ouranos”. In all probability, these motions are the zodiacal motions, not their combination with the diurnal rotation into spiral motions (on which see above, 1.3.5; cf. below, n. 16). Uniformity here is clearly of speed (288a13–17): 

4IViHäX¢NOMRœWI[NEºXSÁ, ´XM±QEPœN zWXMOEiSºOƒRÉQEPSN, zJI\¢N‰RIhLXÏR IeVLQ{R[R HMIPUIlR. (P{K[ Hä XSÁXS TIVi XSÁ TVÉXSY SºVERSÁ OEi TIVi X¢N TVÉXLN JSVŠN· zRK‡VXSlN¹TSO„X[TPIfSYNžHLEdJSVEiWYRIPLP»UEWMRIeN|R) The next thing to go through after what has already been said concerns the motion of the ouranos, namely that it is uniform and not non-uniform. (I say this of the first ouranos and the first rotation, given that in the cosmic region lying immediately below many motions combine into a single motion.)

When Aristotle says that in what lies below “the first ouranos” a multitude of motions combine into a single motion–the zodiacal motion of each planet, the Sun and the Moon–we are tempted to read an allusion to the theory of homocentric spheres, and thus to the cosmology set out in Metaph. ȁ 8, which is based on it.1 If so, the many motions Aristotle speaks of here are combined rotations of nested homocentric spheres, or rather of concentric spherical shells of the first simple body, at least three for each planet and two for the Sun and Moon each (without the spheres producing the diurnal rotation).2 The rotation of each shell must be assumed uniform. As it is, the zodiacal motion of the Sun, the Moon and each of the planets said by Aristotle in the passage just translated to be composite and non-uniform is non-uniform not really but only apparently. For the true motion of each wanderer is primarily the rotation of the spherical shell of the first simple body in which the object is ¿xed. But this rotation is ex hypothesi uniform, as are the rotations of all other spherical shells in the celestial object’s deferent system, each of which is inwardly transmitted to the object-carrying shell, set at the system’s core, so as for the observed zodiacal motion of the object to be produced. That the nested homocentric spheres, after which the Eudoxean theory is named, are assumed to rotate uniformly is strongly emphasized in the anecdotes 1 2

See Leggatt (1995) 235 on Cael. B 6, 288a15–17. For the theory of homocentric spheres see above, 1.4.1–3; presupposed here is 1.4.6.

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about the theory’s origins. According to a story in Simplicius, Plato firmly believed that all celestial motion is circular, orderly and uniform, and thus set before contemporary astronomers the following problem: by hypothesizing which circular, uniform and orderly motions of the wandering celestial objects–the Moon, the Sun and the planets–can we “save the phenomena” of these celestial objects? The phenomena at issue here are the inconstant speed with which all of the seven wandering celestial objects travel against the background of the zodiacal constellations, as well as the stations and retrogradations of the planets, due to which the zodiacal motion of these celestial objects is seen to depart from circularity, markedly unlike the Sun’s and Moon’s.3 As the story in Simplicius has it, Eudoxus put forth his theory of homocentric spheres exactly in response to Plato’s challenge (in Cael. 492.31–493.11 [Heiberg]): 

/Ei IhVLXEM OEi TV³XIVSR, ´XM ± 4P„X[R XElN SºVERfEMN OMRœWIWM X¶ zKO»OPMSR OEi ±QEPäN OEi XIXEKQ{RSR ƒRIRHSM„WX[N ƒTSHMHS¾N TV³FPLQE XSlN QEULQEXMOSlN TVS½XIMRI, XfR[R ¹TSXIU{RX[R HM’ ±QEPÏR OEi zKOYOPf[R OEi XIXEKQ{R[R OMRœWI[R HYRœWIXEMHMEW[U¢REMX‡TIViXS¾NTPER[Q{RSYNJEMR³QIRE, OEi´XMTVÏXSN)½HS\SN ± /RfHMSN zT{FEPI XElN HM‡ XÏR ƒRIPMXXSYWÏR OEPSYQ{R[R WJEMVÏR ¹TSU{WIWM. /„PPMTTSN Hä ± /Y^MOLR¶N 4SPIQ„VG. WYWGSP„WEN XÚ )ºH³\SY KR[VfQ. QIX’ zOIlRSR IeN %UœREN zPUÌR XÚ %VMWXSX{PIM WYKOEXIFf[, X‡ ¹T¶ XSÁ )ºH³\SY I¹VIU{RXE W¾R XÚ %VMWXSX{PIM HMSVUS»QIR³N XI OEi TVSWERETPLVÏR· XÚ K‡V %VMWXSX{PIM RSQf^SRXM HIlR X‡ SºV„RME T„RXE TIVi X¶ Q{WSR XSÁ TERX¶N OMRIlWUEM žVIWOIR š XÏR ƒRIPMXXSYWÏR ¹T³UIWMN ÇN ±QSO{RXVSYN XÚ TERXi X‡N ƒRIPMXXS»WEN ¹TSXMUIQ{RLOEiSºOzOO{RXVSYN, ÊWTIVSd¼WXIVSR. It has been said above, too, that Plato, having unhesitatingly assigned the properties of being circular, uniform and orderly to celestial motions, set before the mathematicians a problem, i.e. which things must be supposed if the phenomena the wandering celestial objects present are to be saved via circular, uniform and orderly motions, and that Eudoxus of Cnidus was the first to attack this problem via hypotheses involving the spheres known as unwinding.4 Callippus of Cyzicus, a student of Polemarchus, who was an associate of Eudoxus, went to Athens after him and spent time with Aristotle, correcting and fleshing out with him the discoveries of Eudoxus. Operating on the belief that all celestial objects must move about the center of

3

4

According to Vlastos (1975) 111–112, saving those phenomena the wandering celestial objects exhibit entails that they “have to be rehabilitated by a rational account which resolves the prima facie contradictions besetting their uncritical acceptance”, contradictions evidently arising when one considers the totally uniform–in terms of both speed and shape of path–diurnal motion of the stars. Goldstein (1997) 7 notes that the oldest known occurrence of the expression “to save the phenomena” is in Plu., de Facie 923A, but we also find it in a long passage from Geminus’ lost epitome of Posidonius’ Meteorologica, which Simplicius quotes through Alexander of Aphrodisias (in Phys. 291.21–292.31 [Diels] ) ; if this quotation is accurate, the ¿rst known occurrence of the phrase is pushed back to the first century BC (cf. Evans & Berggren [ 2 006] 50, and see 15–22 on Geminus’ chronology) . For saving phenomena which exhibit anomalies as amounting to setting up hypotheses free of anomalies, and working mathematically one’s way from thence back to the phenomena at issue, see Krafft (1965) 8–11, according to whom the phrase “to save the phenomena” was employed only by philosophers, not astronomers (14–15); cf. ȀȐȜijĮȢ (2005) 211 n. 44. Sc. homocentric. Cf. ch. 1, n. 90.

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3. Aristotle and the theory of homocentric spheres the universe, Aristotle liked the hypothesis of the unwinding spheres, for in it the spheres are assumed to be concentric with the universe and not eccentric, as posterity believed.5

Earlier on, Simplicius contrasts the hypothesis that the motions of the planets are actually circular, orderly and uniform with the opposing evidence from observation (in Cael. 488.10–24 [Heiberg]): 

D3 H{ KI ƒPLUŸN P³KSN S½XI WXLVMKQS¾N EºXÏR ¡ ¹TSTSHMWQS¾N EºXÏR S½XI TVSWU{WIMN ¡ ƒJEMV{WIMN XÏR zR XElN OMRœWIWMR ƒVMUQÏR TEVEHIG³QIRSN, O‰R S¼X[ JEfR[RXEMOMRS»QIRSM, SºHäX‡N¹TSU{WIMNÇNS¼X[NzGS»WENTVSWfIXEM, ƒPP‡‚TPŠN OEi zKOYOPfSYN OEi ±QEPIlN OEiXIXEKQ{REN X‡N SºVERfEN OMRœWIMN ƒT¶ X¢N SºWfEN EºXÏR XIOQEMV³QIRSN ƒTSHIfORYWM· QŸ HYR„QIRSM Hä HM’ ƒOVMFIfEN yPIlR, TÏN EºXÏR HMEOIMQ{R[R JERXEWfE Q³RSR zWXi OEi SºO ƒPœUIME X‡ WYQFEfRSRXE, ›K„TLWER I¹VIlR, XfR[R ¹TSXIU{RX[R HM’ ±QEPÏR OEi XIXEKQ{R[R OEi zKOYOPf[R OMRœWI[R HYRœWIXEM HMEW[U¢REM X‡ TIVi X‡N OMRœWIMN XÏR TPERŠWUEM PIKSQ{R[R JEMR³QIRE. OEi TVÏXSN XÏR D)PPœR[R )½HS\SN ± /RfHMSN, ÇN )½HLQ³N XI zR XÚ HIYX{V. X¢N %WXVSPSKMO¢N dWXSVfEN ƒTIQRLQ³RIYWI OEi 7[WMK{RLN TEV‡ )ºHœQSY XSÁXS PEFÉR, …]EWUEMP{KIXEMXÏRXSMS»X[R¹TSU{WI[R4P„X[RSN, ÊNJLWM7[WMK{RLN, TV³FPLQE XSÁXS TSMLWEQ{RSY XSlN TIVi XEÁXE zWTSYHEO³WM, XfR[R ¹TSXIUIMWÏR ±QEPÏR OEi XIXEKQ{R[ROMRœWI[RHMEW[U®X‡TIViX‡NOMRœWIMNXÏRTPER[Q{R[RJEMR³QIRE. The true account accepts neither their stations nor their retrogradations nor any additions or subtractions in the numbers of their motions, though they appear as moving in this manner, and does not allow hypotheses of such a kind, but proves from the real nature of celestial motions that they are simple, circular, uniform and orderly. Being unable to understand how, given the truth concerning these motions, the phenomena they exhibit are not real but mere appearances, the astronomers contented themselves with discovering what ought to be assumed if the phenomena presented by the motions of the celestial objects known as wandering were to be saved through uniform, orderly and circular motions. As Eudemus says in the second book of his History of Astronomy, followed by Sosigenes, who relies on the authority of Eudemus, the first among the Greeks to work on such hypotheses was Eudoxus of Cnidus, after Plato, as is reported by Sosigenes, had set the following problem for people who had stud-

5

The historicity of this account has been dismissed on the weak grounds that its source in Simplicius is not the fourth-century-BC Eudemus but the much later Sosigenes, who is far less trustworthy; see the passage translated next and Zhmud (1998) 218. Not much can be built on the fact that Simplicius names only Sosigenes as his source for Plato’s role in the development of the theory of homocentric spheres. Only a couple of lines earlier, the Neoplatonist commentator mentions both Sosigenes and Eudemus as his sources for Eudoxus and the theory of homocentric spheres, and emphasizes that Sosigenes followed Eudemus; moreover, we cannot but consider quite seriously the possibility that Simplicius knew Eudemus exclusively through the account of Sosigenes (see ch. 1, n. 85). Knorr (1990) has attempted to cast doubts on the historicity of Plato’s reported responsibility for the genesis of Eudoxus’ theory of homocentric spheres by arguing that in Plato’s astronomy, as appears from the so-called myth of Er at the end of the Republic, the zodiacal motion of the planets is not uniform. However, the weird myth of Er does not commit Plato to the belief in the non-uniformity of the zodiacal motion of the planets, which he undoubtedly considered uniform at least when he wrote the tenth book of the Laws (see 897e11–898d5, where the circularity, and unwavering uniformity in all other respects than path-shape, of the zodiacal motion of all wandering celestial objects is derived from the hypothesis that rational soul causes all celestial motions). This is by no means to suggest that the story in Simplicius about the origins of the theory of homocentric spheres is to be accepted as historical fact (cf. Gregory [2000] 97–100). See below, n. 8 and 9.

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ied these things: given what hypothesized orderly and uniform motions, the phenomena ex6 hibited by the motions of the wandering celestial objects could be saved.

The belief that the motion of the Moon, the Sun and the five planets is actually uniform and, in the case of the planets, circular, too, is attributed to the Pythagoreans by Geminus, the author of an introductory textbook in astronomy, who seems to have written in the first century BC.7 Geminus considers this belief to be the foundation of all astronomy. The Pythagoreans were, in his view, the first to study astronomy, and it was they who first stated the problem of how the phenomenon of non-uniformity exhibited by the zodiacal motion of the Moon, the Sun and the five planets, and that of departures from circularity in the case of the planets, can be accounted for by means of hypotheses of circular and uniform motions, probably as being the true ones all these celestial objects undergo (1.19.1–1.21.7 [Aujac]): 

D9T³OIMXEM K‡V TV¶N ´PLR XŸR ƒWXVSPSKfER PM³R XI OEi WIPœRLR OEi XS¾N I TPE- RœXEN eWSXEGÏN OEi zKOYOPf[N OEi ¹TIRERXf[N XÚ O³WQ. OMRIlWUEM. Sd K‡V 4YUEK³VIMSM TVÏXSM TVSWIPU³RXIN XElN XSME»XEMN ^LXœWIWMR ¹T{UIRXS zKOYOPfSYN OEi ±QEP‡N šPfSY OEi WIPœRLN OEi XÏR I TPERLXÏR ƒWX{V[R X‡N OMRœWIMN. XŸR K‡V XSME»XLR ƒXE\fER Sº TVSWIH{\ERXS TV¶N X‡ UIlE OEi EeÉRME, ÇN TSXä QäR X„GMSR OMRIlWUEM, TSXä Hä FV„HMSR, TSXä Hä yWXLO{REM· S¿N HŸ OEi OEPSÁWM WXLVMKQS¾N zTi XÏR I TPERLXÏR ƒWX{V[R. SºHä K‡V TIVi †RUV[TSR O³WQMSR OEi XIXEKQ{RSR zR XElN TSVIfEMNXŸRXSME»XLRƒR[QEPfERX¢NOMRœWI[NTVSWH{\EMXS†RXMN· EdK‡VXSÁFfSY GVIlEM XSlN ƒRUVÉTSMN TSPP„OMN EhXMEM KfRSRXEM FVEHYX¢XSN OEi XEGYX¢XSN. TIVi Hä XŸR †JUEVXSR J»WMR XÏR ƒWX{V[R SºHIQfER HYREX¶R EeXfER TVSWEGU¢REM XEGYX¢XSN OEiFVEHYX¢XSN. HM’ RXMREEeXfERTVS{XIMRERS¼X[, TÏN‰RHM’ zKOYOPf[ROEi±QEPÏR OMRœWI[RƒTSHSUIfLX‡JEMR³QIRE. It is a basic assumption of all astronomy that the Sun, the Moon and the five planets move without varying their speeds, circularly and oppositely to the rotation of the cosmos. For the Pythagoreans, who were the first to approach inquiries of this kind, hypothesized that the motions of the Sun, the Moon and the five planets are uniform and circular. The reason is that they did not accept in things eternal and divine such disorder as faster motion at one time, slower at another, and stopping at yet another, pauses called “stations” in connection with the

6

7

Simplicius clearly holds that what ought to be assumed if the phenomena exhibited by the motions of the celestial objects known as wandering are to be saved through uniform, orderly and circular motions cannot be true to physical reality, for he believes that astronomers are unable to understand the truth concerning the motions of the wandering celestial objects, and to then explain the phenomena at issue in light of this understanding as appearances, which is why they must have recourse to merely saving these phenomena through hypotheses. Simplicius here seems to adopt the so-called instrumentalist interpretation of saving the phenomena popularized by Duhem (1908) as ultimate goal of Greek astronomy, from Plato onwards down to Ptolemy (against which see Lloyd [1991], Musgrave [1991]): the phenomena are said to be saved if they are reproduced in a systematic way, and can also be predicted (assuming that prediction is a desideratum, which could not have been in the case of the theory of homocentric spheres) from models, i.e. hypotheses, void of explanatory content, i.e. which do not refer to, or describe, the real workings of nature, for the latter is inaccessible to experience. In Ptolemy’s Almagest the phrase “to save the phenomena” occurs once (Alm. 532.19–533.3 [Heiberg]), but is used in a thoroughly realist sense; cf. Goldstein (1997) 8. On Geminus’ date see above, n. 3.

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3. Aristotle and the theory of homocentric spheres five planets. One would not accept such anomaly of movement even in the walking of an orderly and decorous person. The business of life is often the cause of slowness and quickness in humans, whereas in the case of the incorruptible nature of the celestial objects it is impossible to invoke any cause of quickness and slowness. This is why the Pythagoreans put forth the following problem: how could it be possible to explain the phenomena through circular and uniform motions?

The story of Plato’s central role in the development of the theory of homocentric spheres is certainly fictional. It can be plausibly assumed to have arisen from his works, as is often the case in the Greek biographical tradition.8 As for the alternative story in Geminus, it is no less suspect than the one Simplicius tells, which in all probability underlies it. This story smacks of the Neopythagorean tendency to connect with Pythagoreanism, and with the great Pythagoras himself, the rise of astronomy and mathematics in Greece. Neopythagoreanism begins in the first century BC, so its influence on Geminus is possible chronologically, and since another tendency in Neopythagoreanism is the attribution to Pythagoreanism of all things Platonic, a trend whose origins can be traced back in the Academy right after the death of Plato, it is likely that Geminus tells the same story as Simplicius, Plato having been replaced by the Pythagoreans.9 8

9

In R. 7 Plato has Socrates dream of a future astronomy, which will be pursued through problems, in the fashion of geometry, and will study intelligible motions at never varying speed in similarly unvarying paths, motions which those we see in the sky fall far short of in beauty and exactness, enmattered as they are (529c6–d5). The problems can only be the investigation of abstract mathematical structures variously and imperfectly realized in the sensible celestial motions, whose explanatory causes they are. Now, if we subtract Plato’s metaphysics, then, in light of the weight he lays in the Phaedo and Meno on hypotheses as the indispensable starting points in the investigation of philosophical and mathematical questions, springboards to approaching the abstract entities under study, it turns out that these problems are of the same kind as the one Plato challenged contemporary astronomers to address, according to the testimony of Simplicius, by means of hypotheses. Knorr (1990) 325, assuming that in all probability Simplicius’ only source for the story of Plato’s role in the development of the theory of homocentric spheres is Sosigenes, has argued quite plausibly that Plato’s mention in R. 7 of a future astronomy modeled on the paradigm of geometry “casts Socrates in very much the role that Sosigenes seems to have in mind for Plato when he says he “posed the problem to those engaged in astronomy”. It thus emerges as a likely source of the tradition on which Sosigenes relies for this claim”. A further likely source is a passage in Lg. 7 where Plato has the Athenian stranger say that if he and his interlocutors can show that each of the wandering celestial objects does not wander but appears to do so, they have found the basic piece of knowledge around which the astronomical education that is being developed in the Laws for the citizens of a future Cretan colony ought to be centered (821e7–822d1; though there is no doubt that the wandering of the planets, the Sun and the Moon Plato mentions in this passage is the spiral motion of each of these celestial objects arising from the combination of its zodiacal motion with the diurnal rotation in which it participates, that Plato has in mind the retrogradations of the planets, too, is not unlikely, pace Bowen [2007] 329 n. 5). Material in Plato’s biography can often be traced back to Plato’s works; see the exhaustive study by Riginos (1976); cf. Lefkowitz (1981) for the lives of Greek poets. We learn from the pseudo-Aristotelian work Problems that Archytas of Tarentum held the view that motion which is natural traces circles (XVI.9, 915a25–32 = DK 47 A 23a). Archytas was a prominent Pythagorean of Plato’s time, but as far as we know, he invoked the concep-

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3.2. IS THERE A REFERENCE TO THE THEORY OF HOMOCENTRIC SPHERES IN CAEL. B 6? 3.2.1. An answer in light of Ph. E 4 Back to the Cael. B 6 passage, a closer look at its part where a reference to a cosmology built on the theory of homocentric spheres can be seen, “in the cosmic region lying immediately below”–i.e. the shell of the first simple body, in the mass of which the stars are fixed–“many motions combine into a single motion”, gives a strong impression that it says nothing more than this, although Aristotle’s is certainly an idiosyncratic way of expressing it: the zodiacal motion of the Sun, the Moon or the planets lacks uniformity of speed, in contrast to the diurnal rotation. There seems to be no implicit distinction between non-uniform, apparent motion and uniform, real motion. Indeed, as Aristotle explains in Ph. E 4, in a context irrelevant to this distinction, or to the theory of homocentric spheres, if a motion does not have uniform speed, it is not a single motion unqualifiedly. We can view it as many motions, or sub-motions (228b15–18): 

u)XM H †PP[N TEV‡ X‡N IeVLQ{REN P{KIXEM QfE OfRLWMN š ±QEPœN. š K‡V ƒRÉQEPSN }WXMRÇNSºHSOIlQfE,ƒPP‡QŠPPSRš±QEPœN, ÊWTIVšIºUIlE·šK‡VƒRÉQEPSNHMEMVIXœ. A uniform motion is also said to be one, but not in the same sense as the other kinds of motion. The reason is that a non-uniform motion somehow seems not to be single, unlike a uniform one, e.g. a motion along a straight line, for a non-uniform motion is divisible.10

A motion with non-uniform speed can be thought of as being not single but composed of a number of motions–it is divisible, that is, as Aristotle puts it in the passage of Ph. E 4 just translated–in the following sense. In motion with uniform speed, equal lengths are moved over in equal times. However, if an object moves with non-uniform speed, it moves over unequal lengths in equal times, or over equal lengths in unequal times. The path of non-uniform motion is divided into tion of natural motion as circular only in the context of explaining why parts of plants and animals, such as stems, shoots, thighs, arms and trunks, are of curved shape. There is absolutely nothing to suggest that he inferred the circularity of all celestial motions simply from their naturalness, whence we could conjecture that he was the first to pose the astronomical problem whose statement Geminus attributes to the Pythagoreans. Nor is there any piece of evidence that Archytas did any work in astronomy; cf. Huffman (2005) 295. The most probable reason for the Greek belief in the circularity and uniformity of all celestial motions is simple: the wish to bring a few anomalies, the irregular and (in the case of the ¿ve planets only) non-circular motions of the seven wandering celestial objects, into line with the rule–the regular and circular motions of the fixed stars, the vast majority of the celestial objects the naked eye can observe. We can confidently suppose that no matter exactly when this belief took shape in Greece, no single individual or group was needed to form it in a stroke of trailblazingly original theorizing. We ought to resist the tendency of the Greeks to seek prǀtous heuretas, understandable though it may be, and not put much stock on either the story in Simplicius or its take in Geminus, preferable though the second may seem to the ¿rst. 10 Aristotle explains the other kinds of motion that is one, or single, in Ph. E 4, 228a20–b15.

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unequal lengths, each of which is moved over in successive equal times, or into equal lengths, each of which is moved over in successive unequal times.11 Aristotle’s view of non-uniform motion as motion in which unequal lengths are traversed in successive equal times (that is, as a series of uniform motions, different from one another with regard to speed) is made clear by an argument he sets out in Ph. Z 7. It shows that there is no motion, or coming to rest, over an infinitely long distance in a finite time, no matter whether the motion is assumed to have uniform or non-uniform speed (238a20–29): 

D3EºX¶NHäP³KSNOEi´XMSºH’ zRTITIVEWQ{R.GV³R.†TIMVSRSm³RXIOMRIlWUEMSºH’ ›VIQf^IWUEM, S½U’ ±QEPÏN OMRS»QIRSR S½X’ ƒR[Q„P[N. PLJU{RXSN K„V XMRSN Q{VSYN · ƒREQIXVœWIMX¶R´PSRGV³RSR, zRXS»X.TSW³RXMHM{\IMWMRXSÁQIK{USYNOEiSºG´PSR (zRK‡VXÚTERXiX¶´PSR), OEiT„PMRzRXÚhW.†PPS, OEizRyO„WX.±QSf[N, IhXIhWSR IhXI†RMWSRXÚz\ƒVG¢N· HMEJ{VIMK‡VSºH{R, IeQ³RSRTITIVEWQ{RSR|OEWXSR· H¢PSR K‡V ÇN ƒREMVSYQ{RSY XSÁ GV³RSY X¶ †TIMVSR SºO ƒREMVIUœWIXEM, TITIVEWQ{RLN X¢N ƒJEMV{WI[NKMKRSQ{RLNOEiXÚTSWÚOEiXÚTSW„OMN. The same reasoning shows that there cannot be motion or coming to rest of infinite extent in a finite time, regardless of whether or not the moving object moves uniformly.12 For, if a part is taken which will measure the whole time, then the body moves in this part over a segment of the magnitude [which will be traversed in the whole time] but not over the whole of it (for the body moves over the whole magnitude in the whole time), and in another equal part over another segment, and in each equal part similarly, whether the part [of the whole magnitude traversed by the body in each of the equal divisions of the whole time] is [always] equal or unequal. It makes no difference, if only each segment is finite, for it is clear that the time will be exhausted but the infinite magnitude will not, the subtraction of its parts being finite, with regard to both how much [we subtract each time] and how many times [we subtract].13

If the path of motion with non-uniform speed is divided into unequal lengths traversed in successive equal times, it is also divided into equal lengths traversed in successive unequal times: in Ph. Z 2 Aristotle defines the faster of two motions as the one in which a longer distance is traversed in a given time, or a given distance is moved over in a shorter time (232a25–27). 11

There are various kinds of non-uniformity (ƒR[QEPfE), Aristotle goes on to explain after the passage just translated: one involves a difference in the path of motion, for it is impossible for a motion to be uniform if its path is a non-uniform magnitude, such as a broken line or, generally, any magnitude with parts which do not fit into one another ; a second kind involves a difference in the motion’s “manner”–that is, variation of speed (228b21–28). If a motion is nonuniform because its path is a non-uniform magnitude, it is clearly divisible into as many motions as are non-fitting parts of its path strung together into an only apparently single path (see Ross [1936] 633, on Ph. E 4, 228b17–18). But motion over each of these parts is uniform–any of them is necessarily uniform with itself. Similarly, a motion lacking uniformity, in the sense now that its speed is variable, is divisible into many uniform sub-motions, each of which has invariable speed. Direct evidence for this is offered by the passage translated next. 12 For the argument Aristotle mentions here see Ph. Z 7, 237b23–238a19: motion cannot take an infinite time if it is over a finite magnitude, once again irrespective of whether it is assumed to have uniform or non-uniform speed. For discussion see White (1992) 62–69. 13 On the possibility of motion to infinity in a finite time see Stewart (1993) 149–154, a discussion of the issue from a modern mathematical and physical perspective.

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Applying this to the case of the Sun, we conclude that, since in the passage from Cael. B 6 under discussion here Aristotle implies that many motions combine into the zodiacal motion of the Sun, he conceives of this motion in light of the determination of the inequality of the seasons by his contemporary Callippus of Cyzicus.14 According to Callippus, in its eastward journey round the center of the cosmos the Sun moves over the four equal arcs, into which its circular path, the ecliptic, is naturally divided by the equinoctial and solstitial points, in 94, 92, 89 and 90 days; these are the lengths of spring, summer, autumn and winter in this order (cf. ch. 1, n. 50).15 It can be, moreover, reasonably conjectured that Aristotle conceives of the non-uniformity in the zodiacal motion of the Moon and the planets along similar lines, although at the time no Greek astronomer could have expressed it quantitatively, as for the case of the Sun, with even the slightest accuracy.16 3.2.2. Aristotle and Callippus in Metaph. ȁ 8 Does not, however, Aristotle suggest in Metaph. ȁ 8 that of the modifications due to Callippus on the original Eudoxean version of the theory of homocentric spheres, the two extra spheres Callippus added each to the Eudoxean models of the Sun and Moon be better dropped (1073b38–1074a14), although he introduces the Callippean contributions by noting that in revising the theory Callippus was motivated exactly by the desire to bring it into agreement with the phenomena of the sky (1073b32–38)? There is not even an obscure hint as to which phenomena Callippus aimed to bring the original version of the theory of homocentric spheres into agreement with. However, from Simplicius’ commentary on Cael. B 12, which provides the basis for all modern reconstructions of the theory of homocentric spheres along with Metaph. ȁ 8, we know that Aristotle’s student Eudemus identified the phenomenon at issue in the case of the Sun with the inequality of the seasons; accord14 See the second passage translated in the introduction to this chapter. 15 For the lengths of the seasons as measured by Callippus see Neugebauer (1975) 627. We know them from a papyrus dated to around 190 BC; see Neugebauer (1975) 686–687. 16 With the claim in Cael. B 6 that “in the cosmic region lying immediately below” the shell of the first simple body, in the mass of which the stars are fixed, “many motions combine into a single motion” we can compare the contrast in Cael. B 10 between the outermost rotation of the ouranos, a simple motion as well as the fastest in the heavens, and the slower, composite motions of the ¿ve planets, the Sun and the Moon (291a34–b1). Simplicity here means uniformity, as is clear from Metaph. I 1, 1053a8–12, so that a motion is composite means that it lacks uniformity; in the context of Cael. B 10, uniformity is not (primarily) of path but of speed. Moreover, in Cael. B 10 Aristotle is undoubtedly concerned with the zodiacal motion of the planets, the Sun and the Moon. The same can thus be plausibly assumed to be the case in Cael. B 6, too. Alternatively, the motion of each of the wanderers, into which a number of motions combine, could be its spiral motion, whose speed is variable (for this spiral motion see 1.3.5): the coils of the spiral path are unequal, their projections being wound about the celestial sphere, but are all traversed in a day. There is no reason to prefer this alternative. For an unjustified dismissal of Cael. B 6, 288a14–17 as illogical see Easterling (1961) 145–146.

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ing to Eudemus, moreover, this basic fact had been known to the earlier astronomers Euctemon and Meton, in the second half of the fifth century BC, although for some reason Eudoxus had not taken it into consideration (in Cael. 497.15–24 [Heiberg ] ).17 That Callippus added to the Eudoxean model of the Moon two extra spheres in an attempt at accounting for the lunar analogue to the inequality of the seasons, which Eudoxus had also ignored–the variable speed of the Moon’s motion from west to east against the background of the zodiacal constellations–is a quite reasonable assumption.18 The evidence from Metaph. ȁ 8 has been assumed to suggest that Aristotle was unaware of the phenomenon of the inequality of the seasons, which is hard to believe, for we ought to also assume that he had never heard of Meton and Euctemon; or that he did not consider it to be a problem admitting of a solution within the framework of the theory of homocentric spheres, at least not as Callippus tried to solve it by adding a couple of extra spheres to the model of the Sun originally proposed by Eudoxus.19 In laying out these alternatives it has been noted that the first possibility cannot be ruled out entirely, for Aristotle does not refer directly to the fact of the inequality of the seasons, and that, as regards the second possibility, he could not have justified his disagreement with Callippus. However, the first possibility can indeed be ruled out entirely, with a high level of confidence, in view of the passage from Cael. B 6 where the Sun, the Moon and the planets are all implied to have non-uniform zodiacal motion, in contrast to the uniform diurnal rotation, for in the Sun’s case this cannot but entail awareness of the inequality of the seasons on Aristotle’s part.20 As for the second possibility, it is agreed that by adding two extra spheres each to the Eudoxean models of the Sun and the Moon, Callippus intended to have each of these two celestial objects move along a hippopede, as a result of the combined rotations of the two extra spheres in its model.21 These two extra spheres are plugged into the system of the three homocentric spheres Eudoxus posited each for the Sun and the Moon, the celestial object itself being on the equator of the innermost Callippean sphere. Since the Sun and the Moon do not retrograde, in their Callippean models the breadth of the hippopede must be posited very small, so as to be unobservable. Motion along the curve thus turns into palindrome motion on 17

Rehm (1949) 1343 thinks that Eudoxus chose to ignore observational evidence guided purely by Platonic preconceptions of harmony, which is unlikely. Moreover, there are reasons to doubt that Euctemon and Meton did discover the phenomenon of the inequality of the seasons and its cause, the solar anomaly, based on observations, which Eudoxus might have pushed cavalierly aside. The lengths of the seasons attributed to Euctemon in the papyrus mentioned above, in n. 15, hints at an attempt to come up with a scheme for distributing 365 days as evenly as possible over the seasons; see Neugebauer (1975) 628. We can assume reliance on observations only for Callippus. Cf. Mendell (1998) 274 n. 71. 18 Cf. ch. 1, n. 86. 19 See Lloyd (1996) 178. Neugebauer (1975) 627 suggests that Aristotle had not been convinced of the existence of a solar anomaly. 20 Cael. B 10 provides further evidence; see above, n. 16. 21 See Neugebauer (1975) 625 and Mendell (1998) 256.

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its length. What matters is that, as the hippopede is being carried around eastwards, due to the motions of the first two Eudoxean spheres counting from the inside, whose rotations model the journey of the Sun or the Moon against the backdrop of the zodiacal constellations, it speeds up, or slows down, this motion, depending on which half of the curve the celestial object is traversing.22 It is thus made possible to obtain a periodic variation of the motion of the Sun and the Moon against the stellar background. For the Sun, motion along the hippopede would generate a variation to the lengths of the four seasons; in the case of the Moon, motion along the hippopede would produce the similar effect of a lunar zodiacal anomaly. Now, since Callippus had estimated the unequal lengths of the seasons and we have his values, it is an interesting and historically legitimate exercise to try and see if these values relate to the hippopede of the Sun. Could he have been able to construct a solar hippopede such that he could have then succeeded in deriving from it the values of the seasons or, inversely, could he have started from these values and then gone on to construct the right hippopede for the Sun? A negative answer makes it conceivable that Callippus himself never put much stock on his extension of Eudoxus’ original model of the Sun. If the same can be argued for the Moon, then it is also conceivable that Aristotle might follow Callippus himself, when he prefers in Metaph. ȁ 8 to let the extra spheres that the astronomer had introduced for the Sun and the Moon fall by the wayside. Mendell has answered the above question negatively, in his article on the mathematics of the hippopede. He has argued convincingly for the extreme unlikelihood that “Callippus could have come up with the values for the seasons from any hippopede”, or that “he would have found the required construction to yield his values for the seasons”.23 His conclusion is that the Callippean introduction of a hippopede “was at best suggestive of a solution” to the problem of the inequality of the seasons, “not a solution providing calculable values” for their lengths.24 The lunar anomaly is much more striking than the solar.25 It is unlikely, however, that Callippus might have had at his disposal a numerical handling of it comparable to that of the solar anomaly.26 Consequently, he could not have even attempted to inquire into whether it is possible to construct a lunar hippopede based on numerical parameters known from observations or, inversely, to derive such parameters from a lunar hippopede. Given the situation with the solar hippopede, Callippus might have suspected that, even if one had managed to get an arithmetical grip on the phenomenon of lu22 Cf. Neugebauer (1975) 625. 23 Mendell (1998) 256. 24 Mendell (1998) 260. 25 See Kaler (2002) 246. 26 Lunar anomaly, unlike other periodic phenomena of the sky known to the ancients, is hard to observe; cf. Goldstein (2002) 3. The Babylonians, who had determined the periods of lunar motion by about 500 BC, probably found the periodicity of the lunar anomaly from observations which were unavailable to the Greeks (see Goldstein [2002] 3–5); the Greeks must have learned this periodicity, along with other periods of lunar motion, from Babylonia, in Hipparchus’ time; see e.g. Jones (1991) 442.

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nar anomaly, it could not have been possible to fit the relevant parameters to a hippopede of the Moon or obtain them from it. 27 If Callippus did not manage to improve on Eudoxus in the cases of the Sun and the Moon, and his wish to do so, which Aristotle duly acknowledges, most probably with approval, in Metaph. ȁ 8, failed to bear results, there is no reason to blame Aristotle for having based his calculation in Metaph. ȁ 8 of the number of the celestial unmoved movers on the Eudoxean rather than the Callippean models of the Sun and the Moon.28 Confronted with the two equally unsatisfactory alternatives, the Eudoxean models of the Sun and the Moon, on the one hand, which failed to even address the inequality of the seasons and its lunar analogue, and their Callippean versions, on the other, which tried to incorporate what Eudoxus omitted but failed, Aristotle understandably went for the Eudoxean models. They accounted for some phenomena successfully (we pass over the question why Eudoxus assumed the existence of a deviation of the Sun from the ecliptic, or of any observational basis he might have believed he had for this assumption), so they could be used to give an illustration of how astronomy can aid philosophy in determining the precise number of unmoved movers in the celestial part of the cosmos.

3.2.3. Concluding considerations Let us now return to the hypothetical allusion in the Cael. B 6 passage translated at the beginning of the present chapter to the theory of homocentric spheres, hence to a putative distinction between the apparent, non-uniform zodiacal motions of the Sun, the Moon and the ¿ve planets and the true, uniform motions of these seven luminaries. The upshot of the above is that Aristotle is very unlikely to have made such an allusion in the passage at issue. This is further suggested by the following considerations. The original, Eudoxean, formulation of the theory of homocentric spheres did not aim at showing how the non-uniform zodiacal motion of the Sun, the Moon 27

Neugebauer (1975) 625 claims that with the introduction of the hippopede a quite satisfactory explanation for the lunar anomaly could have been achieved. He does not provide any reasons for his view, however, noting that “none of the extant sources gives numerical details, nor can we say for sure that Callippus actually used the hippopede for representing the lunar anomaly”. This use of the hippopede by Callippus is undoubtedly hypothetical. As for the numerical details, however, it is very unlikely that they got lost to us, and much more likely that Callippus had simply none to begin with. 28 This calculation is the context in which Aristotle sketches in Metaph. ȁ 8 the theory of homocentric spheres; cf. below, 3.6. Note that of the modifications due to Callippus on the original version of the theory, Aristotle accepts those that can be shown to have been successful on one of the modern reconstructions of the theory (that is, the extra spheres added to the original Eudoxean models of Mars, Mercury and Venus; see 1.4.3), but rejects those that most probably were unsuccessful (that is, the extra spheres with which Callippus augmented the Eudoxean models of the Sun and the Moon). Since we have no reason to suspect that this is pure coincidence, though it might well be, we are allowed to seriously entertain the possibility of a causal relationship between rejection and unsuccessfulness.

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and the planets could be produced from a combination of uniform motions.29 Callippus attempted to remedy the situation with regard to the Sun and Moon only, but failed. So how can Aristotle say in Cael. B 6 that “in the cosmic region lying immediately below” the shell of the first simple body in the mass of which the stars are fixed “many motions combine into a single motion”, i.e. the zodiacal motion of the Sun, the Moon or a planet, which is not uniform, but intend that although the zodiacal motion of each of these seven celestial objects is observed to lack uniformity, it is in fact a resultant of a number of uniform motions, which are real in contrast to the object’s zodiacal motion, as is shown by the theory of homocentric spheres? We have to assume that the remark was written when Aristotle either was unaware of the failure of the theory, in its Eudoxean or Callippean version, to account for the non-uniformity of solar, lunar and planetary zodiacal motion, or believed erroneously that Callippus was making progress, and that one day the theory of homocentric spheres would succeed in handling the non-uniformity of zodiacal motion, a belief which for some inexplicable reason led Aristotle to take the theory’s wished-for success for granted. If one is unwilling to entertain seriously either possibility, the remark under discussion cannot be plausibly read as an allusion to either of the two versions of the theory of homocentric spheres.30

3.3. IS THERE A REFERENCE TO THE THEORY OF HOMOCENTRIC SPHERES IN CAEL. B 12? 3.3.1. Introduction It seems, however, that an unmistakable allusion to the theory of homocentric spheres is found in Cael. B 12, 291b28–292a3 and 293a4–11. In the first of these 29 See 1.4.3. Cf. Heath (1981) 200 and Yavetz (1998) 225, 265–266. 30 Commenting on Cael. B 6, 288a15–17, Leggatt (1995) 235, who, as said above, sees in this passage an allusion to the theory of homocentric spheres, notes that what Aristotle says of “the first ouranos” in Cael. B 6–i.e. that its rotation is uniform–applies equally to the rotation of each sphere in the deferent systems postulated by the theory of homocentric spheres for each planet, the Sun and the Moon. This is indeed so, but suggests that no allusion to the theory of homocentric spheres is made in the passage at issue. For, as Leggatt admits in his introductory note to Cael. B 6, Aristotle regards the zodiacal motions of the planets (the Sun and Moon are not mentioned by Leggatt) as irregular–this is clear from the above-translated opening lines of the chapter: so, if the irregular motions in question are understood to be the non-uniform observed resultants of the uniform hypothesized rotations of nested homocentric spheres–as it must be if Aristotle alludes in Cael. B 6 to the theory of homocentric spheres–we face the grave difficulty that this theory was not able, and could not have been originally intended, to produce motions with variable speed from posited regular ones–testimony to this bear, among other things, the modifications Callippus suggested for the Sun and the Moon. Explaining the irregular motions of the planets, the Sun and the Moon as resultants of regular motions is clearly suggested to have been the aim of the theory of homocentric spheres in Bodnár & Pellegrin (2006) 271; cf. Hankinson (1995b) 150.

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two passages, no such hint need be seen. However, the second cannot be read otherwise. Aristotle opens this elaborate chapter with the remark that he must attempt to state what seem to him to be plausible solutions (to phainomenon) to two baffling problems, whose difficulty anyone would acknowledge. He goes on to apologetically explain that his eagerness to tackle such impenetrable matters should be considered modesty rather than impetuousness, for it stems from willingness, due to thirst for knowledge, to rest content with having made even little headway towards grasping the important things we are most puzzled about (291b24–28). The two problems in question are as follows.

3.3.2. The two problems Aristotle attempts to solve in Cael. B 12 Why are the motions of the Sun and the Moon not more but fewer than those of the planets, contrary to what we would expect based on the fact that all planets are nearer to the stars–a class of celestial objects each of which has a single motion, the same as that of any other member of this class–but the Sun and the Moon farther away (291b28–292a3)? 31 Why do the stars, which are so many as to seem innumerable, have each a single motion, one and the same, but the motions of each planet belong to a single celestial object, exactly as those of the Moon and the Sun do (292a10–14)? In itself, Aristotle’s statement of the first problem need not be understood as presupposing the theory of homocentric spheres.32 This interpretation seems to be forced upon us, however, in view of the second solution he offers to the second problem (293a4–11): 

31

/Ei}XMHM‡X³HIIR}GSYWMWÏQEEd†PPEMJSVEf, ´XMTSPP‡WÉQEXEOMRSÁWMREdTV¶ X¢N XIPIYXEfEN OEi X¢N IR †WXVSR zGS»WLN· zR TSPPElN K‡V WJEfVEMN š XIPIYXEfE WJElVEzRHIHIQ{RLJ{VIXEM, yO„WXLHäWJElVEWÏQ„ XMXYKG„RIM µR. zOIfRLN‰R SÃR OSMR¶R IhL X¶ }VKSR· EºX® QäR K‡V yO„WX: š hHMSN J»WIM JSV„, E¼XL Hä SmSR TV³WOIMXEM, TERX¶NHäTITIVEWQ{RSYWÉQEXSNTV¶NTITIVEWQ{RSRšH»REQfNzWXMR.

The single motion of the stars is their diurnal revolution. Aristotle says not that the motions of the Sun and the Moon are fewer than those of the planets, but that they are fewer than the motions of some of the wandering celestial objects (291b35–292a1): zP„XXSYN K‡V PMSN OEi WIPœRLOMRSÁRXEMOMRœWIMN¡XÏRTPER[Q{R[R†WXV[R}RME(“for the Sun and the Moon have fewer motions than some of the wandering celestial bodies do”). However, his point seems to be simply that the Sun and the Moon have fewer motions than all–not some–of the remaining wanderers we call planets; see ch. 2, n. 34. On purely a priori grounds, we would assume that the farther away a wandering celestial object is from the fixed ones–the stars–with their single motion–the diurnal revolution–the larger the number of its motions would be: this number, moreover, would increase either directly with distance from the stars or inversely with distance from the center of the cosmos, in a simple and orderly manner, at best arithmetically (see 291b28–292a3, translated above, in 2.4). 32 All planets have more motions, compared to the Sun and Moon, because they not only participate in the diurnal rotation and undergo zodiacal motion but retrograde, too, unlike the Sun and the Moon. Cf. Leggatt (1995) 246 on Cael. B 12, 291b28–292a9. A multitude of motions is ascribed to each planet, the Sun and the Moon in Cael. B 14, 296a34–296b1, too.

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There is, moreover, an additional reason why the other celestial motions belong [each] to a single celestial object, namely that the motions before the last one, which moves a single celestial object, move many material objects, for the last sphere rotates being nested in many spheres, each of which happens to be a material object. What the last sphere does, therefore, is shared by all other spheres; for each has its own natural motion, whereas the last one is as if it were simply added, but all material objects of finite size have motive power relative to certain other material objects finite in size.33

The reasons given above for denying that Aristotle hints in Cael. B 6 at the theory of homocentric spheres put us immediately on guard, however. If unambiguous evidence that the de Caelo cosmology is built on the theory of homocentric spheres, as is the cosmology Aristotle sketches in Metaph. ȁ 8, does turn up in the passage just translated, how are we to square the fact that Aristotle refers in Cael. B 6 to the non-uniform zodiacal motions of the Sun, the Moon and the planets with the inability of the theory to reproduce the non-uniformity of zodiacal motion? A time-honored, albeit not necessarily always commendable, and nowadays rather out of fashion, way around difficulties of this sort is to suspect the genuineness of the troublesome passage, bracketing it as an interpolation. In our case suspicion seems justified, as will be argued next.

3.3.3. The solution to the first problem To solve the problems he comes to grips with in Cael. B 12, Aristotle starts from the assumption that the celestial objects do not lack soul and are not lifeless objects, as we think of them, conveniently treatable like mere geometric points: they partake of life and goal-directed activity, and aspire to the possession of what is good (292a17–22).34 He then shows how this assumption can help us solve the first problem. That which is in the best condition possesses the relevant good without any activity, whereas that which is nearest to the good gets it with a little and simple effort. However, those which are farther removed need to expend more effort, and those which for any reason can aspire only to something lesser need not strive as 33

34

For how the earlier statement in Cael. B 12 discussed above, in n. 31, can be understood literally in light of the theory of homocentric spheres see Leggatt (1995) 246 on the statement of the first problem. t3Q[N H’ zO XÏR XSMS»X[R UI[VSÁWMR SºHäR †PSKSR ‰R H³\IMIR IREM X¶ RÁR ƒTS- VS»QIRSR. ƒPP’ šQIlN ÇN TIVi W[Q„X[R EºXÏR Q³RSR, OEi QSR„H[R X„\MR QäR zG³R- X[R, ƒ]»G[R Hä T„QTER, HMERSS»QIUE· HIl H’ ÇN QIXIG³RX[R ¹TSPEQF„RIMR TV„\I[N OEi^[¢N· S¼X[K‡VSºUäRH³\IMTEV„PSKSRIREMX¶WYQFElRSR (“If we approach, however, what puzzles us based on the following considerations, it will not appear unaccountable at all. We usually think of the celestial objects as mere objects and units with position, completely lacking life, whereas we ought to think of them as participating in activity and life. If so, what is the case will seem perfectly intelligible”). “Units with position” are points. Cf. de An. A 4, 409a6 š K‡V WXMKQŸ QSR„N zWXM U{WMR }GSYWE (“a point is a unit having position”); see also Metaph. B 2, 998a6.

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hard, only so much as is required for the attainment of their inferior goal. For example, a body is in the best condition without exercise, another only by means of little walks, while a third needs running and vigorous exertion and a fourth cannot achieve this particular goal, despite strenuous efforts, and thus must settle for another, lesser, goal that does not require so much hard work, which would be pointless. Inability to reach a goal can be explained either because the goal at issue is impossible to achieve, like repeating the same throw of dice a very large number of times; or because attaining it requires success at a large number of intermediate stages, directly proportionate to the difficulty of the process (292a22–b1). It is not dif¿cult to see how this helps solve the problem at hand.35 We ought to think, continues Aristotle, that the activity of the celestial objects is analogous to that of animals and plants. Here on Earth, our activity is varied and complex. We aim at many goods, some of which are not ends in themselves, for we are not in the best possible state, in which case we would be in no need to do anything. The activity of the other animals is not as intricate and diverse. That of plants is even less so, perhaps being of a single kind, for either there is only one end for plants to attain, as is ultimately the case for us, too, or there are in fact many ends for plants, too, but somehow all of them contribute to what is best for plants, an ultimate goal which is implicitly assumed to be inferior to those pursued by us and the other animals, hence to be attainable with comparatively simple activity (292b1–10). Here Aristotle is clearly drawing a parallel between animals and the planets, on the one hand, and between plants and the remaining wanderers, the Moon and the Sun, on the other. 35

Easterling (1961) 150–153 has argued that the thing in the best condition, which possesses the relevant good without any activity, is a celestial unmoved mover, presumably the one among the multitude of such movers that is traditionally called prime (on the celestial unmoved movers see 1.4.5); see also Easterling (1976) 263. But we should not lose sight of the fact that Aristotle goes on to give as example of a thing which is in the best condition, and possesses the relevant good without any activity, a body which need not expend any effort in order to be in the condition which is the best for bodies–probably in order to be healthy, as seems to be the case from 292b10–13. It is most unlikely that a general characterization of the prime unmoved mover would be next illustrated with such an example. Bodies in the best condition without exercise do not stand to those in need of only little walks, or to those in need of running and vigorous exertions, let alone to those unable to be in the best condition, no matter how exhausting their physical activity, as does the prime unmoved mover in the heavens to anything moved by it. We cannot plausibly consider them final causes of the activity in which all the other bodies engage. Nor could the condition of each of the privileged bodies be more plausibly cast in this role. Moreover, singling out this condition itself–independently of any body it might belong to–as a potential analogue of the prime unmoved mover in the heavens does not seem to work either, for the following reason. The condition in question is health. Health can be an unmoved mover, as an intelligible form in e.g. a doctor’s soul, with which, as intelligible form, it is identical (for this identity see ch. 1, n. 97; see also Metaph. Z 7, 1032a27–b23, as well as Z 9, 1034a21–25, and GC A 7, 324a24–b4; cf. Gill [1991a] 198–200). Intelligible forms, however, in human souls are universals (cf. APo B 19, 100a16), and for Aristotle universals are not substances, unlike the celestial unmoved movers (see Metaph. ȁ 5–6; Z 13 is also relevant). So how probable is it that he would use a non-substance as stand-in for the substance par excellence? The reference in Cael. B 12 to a celestial unmoved mover is assumed unquestioningly by Manuwald (1989) 104–115.

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In general, he goes on, some things already have what is best for them and partake of it, other things do not but attain it at once, by little and simple activity, a third class need to engage in varied and complex activity, and a fourth do not even aspire at attainment, for it is beyond their reach, being content to just come close to the ultimate end by expending much less effort (292b10–13). For example, if health is the end, one body is always healthy. Another must simply lose weight to be healthy. Another, however, must also jog in order to lose weight, while still another must also do something else just in order to be able to jog and, finally, yet another cannot attain to health but only to jogging or losing weight, which in this case is the end. What is really best for all is to attain the ultimate goal. If this is impossible, however, then the next best thing is always to reach as close as possible to it (292b13–19). The reason why the Earth stays immobile at the center of the cosmos, Aristotle concludes, is that it cannot even begin to attain an unspecified ultimate end, so for it to move in any way would be completely purposeless. As for the Sun and the Moon, the celestial objects which are nearest to the Earth, they have each only a few motions because they are unable to attain the ultimate end, which is here said to be a most divine principle, but can come as near it as is possible for them; this task does not require much kinetic activity, however. The ultimate end is well within the reach of the planets, though they must strive to attain it. As a consequence, they have more motions than the Sun and the Moon. The stars, the remotest celestial objects from the center of the cosmos, are, however, capable of reaching the ultimate end immediately, by a single motion (292b19–25).36 36

The final cause Aristotle mentions here as the most divine principle is unlikely to be the prime unmoved mover of Metaph. ȁ 8 (cf. previous note), for this ultimate end (whatever it might be) is said to be attained by the stars and the planets only, not by the Sun and the Moon. In the cosmology Aristotle presents in Metaph. ȁ 8, the prime unmoved mover is directly responsible, as a final cause, for the diurnal rotation of only one spherical shell of the first simple body–the one which carries the stars fixed in its mass. The deferent system of similarly constituted nested shells for each of the planets, the Sun and the Moon is encased in a shell which is rotationally indistinguishable from the stellar deferent shell so as to account for the participation of each of these seven celestial objects in the diurnal rotation. Consequently, the unmoved mover, which is the final cause of the rotational motion undergone by the outermost shell of the first simple body in the deferent system for each of the planets, the Sun or the Moon, is a replica of the prime unmoved mover qua final cause of diurnal rotation (exactly as what it moves is a starless replica of what is directly moved by the prime unmoved mover). The stars and all the ¿ve planets, it follows, are as able to attain an end that the prime unmoved mover is identical with as are the Sun and the Moon! A plausible case can be made that, since the prime unmoved mover seems to be the final cause not of the diurnal rotation alone but of the functioning of the whole heavens (see 1.4.5), ultimately the stars themselves are as unable to attain this end as are all the ¿ve planets, the Sun and the Moon! It seems preferable, therefore, to follow Ross (1936) 100 in equating the most divine principle Aristotle mentions here not with the transcendent end of Metaph. ȁ 8, the prime unmoved mover, but with one that is immanent in the soul of the spherical shell of the first simple body in the mass of which the stars are ¿xed (see 3.3.4), as well as in the souls enlivening the planets, and beckons these objects on to its attainment (the expression is borrowed from Ross), as health qua intelligible form in a doctor’s soul would beckon the doctor to self-healing (cf. previous note). This end, however, cannot be understood in the light of Cael. B 3 (see 1.2.5, and Appendix 4).

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3.3.4. The first solution to the second problem Having dealt with the first question, Aristotle next tackles the second: why a single motion, the diurnal revolution, is common to a very large number of celestial objects, the stars which are embedded in the mass of the diurnally rotating crust of the cosmos, whereas more than one motion belongs to each of the planets, the Sun and the Moon? His answer is based, as we expect, on his fundamental assumption that celestial objects do not lack souls–they are not merely lifeless chunks of matter. The ¿ve planets, the Sun and the Moon are each thought of as having its own soul. A single soul is assigned to all stars, and there can be no doubt that it animates not each of these celestial objects separately but the spherical shell of the first simple body in whose mass they are fixed as its parts, and whose diurnal rotation is responsible for their tracing out diurnal circles (292b25–293a4): 

4IVi Hä X¢N ƒTSVfEN ´XM OEX‡ QäR XŸR TVÉXLR QfER SÃWER JSV‡R TSP¾ TP¢USN WYR{WXLOIR †WXV[R, XÏR H’ †PP[R G[ViN |OEWXSR IhPLJIR eHfEN OMRœWIMN, HM’ İR QäR †R XMN TVÏXSR IºP³K[N SeLUIfL XSÁU’ ¹T„VGIMR· RS¢WEM K‡V HIl X¢N ^[¢N OEi X¢N ƒVG¢N yO„WXLN TSPPŸR ¹TIVSGŸR IREM X¢N TVÉXLN TV¶N X‡N †PPEN, IhL H’ ‰R HI WYQFEfRSYWEOEX‡P³KSR· šQäRK‡VTVÉXLQfESÃWETSPP‡OMRIlXÏRW[Q„X[RXÏR UIf[R, EdHäTSPPEiSÃWEM İRQ³RSRyO„WXL· XÏRK‡VTPER[Q{R[RİR±XMSÁRTPIfSYN J{VIXEMJSV„N. IJE»X:XISÃRƒRMW„^IMšJ»WMNOEiTSMIlXMR‡X„\MR, X®QäRQM•JSV• TSPP‡ƒTSHSÁWEWÉQEXE, XÚH’ yRiWÉQEXMTSPP‡NJSV„N. Concerning now the difficulty that a great multitude of celestial objects undergo the first revolution, a single motion, whereas each of the remaining celestial objects has separate motions of its own, one thing comes to mind first as a reasonable explanation of this fact. We must conceive of the first among these life-principles [i.e. the souls of celestial objects] 37 as being by far superior to the rest, superiority that would follow from proportionality, as the primary of these life-principles, despite its oneness, moves a multitude of divine objects, whereas the others, despite their being many, move only one each.38 For any one of the wandering celestial objects has several motions. This is, thus, nature’s way of restoring balance and introducing a kind of order, by assigning many celestial objects to a single motion but many motions to a single celestial object.

37 Cf. de An. A 1, 402a1–7, and B 4, 415b8. 38 The inverse proportionality Aristotle mentions here is, of course, entirely metaphorical: one : many :: many : one A single soul moves many celestial objects, the stars, whereas many (seven) souls manage only to move a single celestial object each–one of the planets, the Sun or the Moon; equivalently, a single motion (the diurnal revolution) is undergone by many luminaries, the stars, many motions belong to each of the remaining celestial objects, the planets, the Sun and the Moon (the participation of the wandering celestial objects in the diurnal rotation is clearly thought of as being due not to the same soul that makes the deferent shell of the stars to rotate diurnally, but to the soul of each of them separately). Expressed in terms of number of motions, this proportion is given observationally, and when we bolt onto it the assumption of souls driving the celestial objects, the enormous superiority of the soul that animates the deferent shell of the stars over the soul of each of the seven remaining celestial objects results, by Aristotle’s lights, from the psychical reformulation of the proportion at issue as its most plausible explanation.

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Aristotle hypothesizes that the soul animating the crust of the cosmos enjoys so great a superiority over the souls of the planets, the Sun and the Moon that, despite its being single, it is capable of moving a great many divine celestial objects, the stars. The souls of the planets, the Sun and the Moon form a second tier of celestial souls, and, despite their being many, are capable of moving only one celestial object each, though we might reasonably expect that collectively they could move a larger number of celestial objects than the celestial soul associated with the diurnal rotation. The inferiority of these seven celestial souls is evidenced by the fact that a planet, the Sun or the Moon has many motions. As seen above, for Aristotle this might mean that the soul of each planet, in contrast to the soul which is responsible for the diurnal revolution of the stars, strives to attain an end common to stars and planets, whereas the souls of the Sun and the Moon cannot attain this end, and thus can only aim at an inferior goal, hence each of these two celestial objects has fewer motions than any planet. Here, this fact is assumed to indicate the inferiority, or weakness, of the soul of the Sun, the Moon or a planet, as compared to the one animating the spherical shell of the first simple body in whose mass the stars are fixed. Had the soul of a planet, the Sun or the Moon animated more than a single celestial object, it goes without saying that it would have been unable to move all of them, which means that it could not have enlivened them.39

3.3.5. The second solution to the second problem The solution to the second difficulty opens in a way suggesting that another solution will follow. An alternative solution does follow, and unmistakably alludes to 39

The fact that in the passage just translated Aristotle clearly considers the soul animating the spherical shell of the first simple body in whose mass the stars are embedded to be the first principle in the heavens suggests that at the time he wrote Cael. B 12 he did not recognize a higher principle in the cosmos than its ensouled envelope, such as the prime unmoved mover of Metaph. ȁ 8; see also above, n. 35 and 36. This is not incompatible with the mention in the same chapter of a most divine principle, which is undoubtedly a final cause, just like the prime unmoved mover of Metaph. ȁ 8. If this principle is not transcendent, like the prime unmoved mover of Metaph. ȁ 8, but dependent on souls (cf. above, n. 36), then it can be said to enjoy primacy, insofar as it is the unmoved mover of the souls at issue and of the objects they animate, though insofar as its existence depends on these souls, they and all the bodies animated by them are prior, in particular the soul which “drives” the rotation of the deferent shell of the stars (for it is able to move the vast majority of celestial objects), and thus of the first simple body that constitutes this shell. At any rate, is it unlikely that in Cael. B 12 Aristotle presupposes the cosmology he sketches out in Metaph. ȁ 8–hence the prime unmoved mover in the heavens which is its hallmark–for in Cael. B 12, unlike in Metaph. ȁ 8, the planets, the Sun and the Moon are thought to be moved each by a single soul. Even if we suppose that Aristotle operates in Cael. B 12 with an early version of the Metaph. ȁ 8 cosmology, which assigned a single soul to the deferent system of each of the celestial objects below the stars, and not as many as the spherical shells of the first simple body making up the system, including those needed to insulate it from the one above, we cannot easily see how the inferiority of the seven souls of the planets, the Sun and the Moon to the one animating the spherical shell of the first simple body with the stars could be accommodated.

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the theory of homocentric spheres, as we saw in 3.3.2. These spheres are explicitly said to be material objects, so they are actually spherical shells of some unspecified kind of matter. Each such shell in the deferent system for a planet, the Sun or the Moon rotates as is proper to it, carrying round all other shells nested inside it, with the result that the outer shells have a more difficult task than the inner ones. The innermost shell in a system, with a single celestial object fixed in its mass, has the least difficult task of all, which is shared by all other shells in the system. Its own motive power might be larger, but in case it had carried round more than a single celestial object, all of the shells inside which it is nested, or the outermost one only, would have been unable to share in its task of moving the celestial objects. For all these shells are finite material objects, and thus a proportionately finite limit must exist to the motive power each of them has.40 What is striking about this alternative solution to the second of the two problems Aristotle addresses in Cael. B 12 is the violation of the programmatic assumption on which he says in the introduction to the main body of the chapter his solutions to both problems will be based. This assumption is that celestial objects are not lifeless things, mere lumps of matter–they have souls. What is the role assigned to the soul of a planet, the Sun or the Moon in the alternative solution to the second problem? In the first solution, it is the soul that moves the celestial object. But the alternative solution clearly gives this role to a system of nested spherical shells of matter, each of which spins carrying round those nested inside it, the celestial object being set in the mass of the innermost shell. In the first solution, it is a soul that is unable to move more than a single celestial object. In the second, however, this incapability cannot be psychical. It is the failure of a heavenly mechanical contrivance, as if celestial objects were lifeless objects, lacking soul.41 40 Cf. Simp., in Cael. 491.15–492.11 (Heiberg). 41 Simp., in Cael. 492.12–13 (Heiberg), seems to think that the second solution to the second problem Aristotle discusses in Cael. B 12 is intended to be understood in light of the first: HSOIlH{QSM±P³KSNSÂXSNÇNzT’ zOIfR.TVSM{REMXÚP{KSRXMTSPPŸR¹TIVSGŸRIREM X¢NƒTPERSÁNTV¶NX‡NTPER[Q{REN(“this argument seems to me to go through based on that other, according to which the sphere of the fixed stars enjoys much superiority over those of the wandering celestial objects”). In other words, the outermost spherical shell in the deferent system for Saturn is so superior to its analogue in the deferent system for any inferior celestial object that it can carry round the host of the stars, plus the other shells making up the Saturnian deferent system and the planet Saturn itself which is carried round by the innermost of those shells; each of this shell’s six lower counterparts is able to carry round only the other shells that make up its system, and the single celestial object carried round by the innermost of all those shells. In the first solution to the second problem Aristotle discusses in Cael. B 12 it is a soul which is responsible for the motion of the stars that is assumed to be superior to the souls responsible each for the motions of a planet, the Sun and the Moon. However, this translates, within the framework of the Metaph. ȁ 8 cosmology, to the kinetic superiority of the outermost shell in the deferent system for Saturn over its lower counterparts in the deferent systems for the other wandering celestial objects, as Simplicius seems to believe, if each of these shells–and any of the others nested inside them–owes its motive power to its soul. Undoubtedly, this cannot be the case, as will be argued next. By focusing on the outermost shell in the deferent system for each of the wandering celestial objects, as if the Metaph. ȁ 8 cosmology assigned to this shell alone the role of moving the luminary, Simplicius desperately

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True, the cosmology Aristotle sketches in Metaph. ȁ 8 based on the theory of homocentric spheres considers the rotation of each shell in the deferent system of a planet, the Sun or the Moon to be caused by the shell’s soul. This soul assimilates itself to a disembodied intellect, the shell’s unmoved mover and the ultimate transcendent cause of its rotational motion. But the alternative solution to the second of the two problems Aristotle tackles in Cael. B 12 cannot be understood as tacitly laying the blame for the inability of moving more than a single celestial object not on the nested shells themselves that make up the deferent system for each of the planets, the Sun or the Moon, but ultimately on their souls, or on the disembodied intellects unmovedly moving these souls. It is not only that the principle from which the alternative solution to the second difficulty addressed Cael. B 12 derives its force–all material objects of finite size have a motive power only relative to certain other material objects, also of finite size–rules out any role for souls: in Metaph. ȁ 8 Aristotle does not posit motive souls, to which the spherical shells of mater constituting the deferent system for a planet, the Sun or the Moon would owe their own motive powers, so that for a shell’s hypothetical failure to share in the task of those nested inside it we could hold responsible its weak motive soul. A shell’s soul, via assimilating itself to the shell’s transcendent unmoved mover, causes the shell’s rotation in the sense that it “guides” this motion. The unmoved mover of a shell is explicitly identified in Metaph. ȁ 7 as a final cause of motion, and final causes of motion do not cause motion by powering it but by providing a goal the motion, however powered, reaches. This goal, in our case, is best understood as the period and direction of a shell’s rotational motion, as well as the angle between the shell’s equator and a referent plane–that of the equator of one of those other shells with which a shell forms a system. Aristotle does not explain in Metaph. ȁ 8 what powers the shells, most probably because he tacitly assumes that they consist of the first simple body, its automatic natural motion being their rotation. If so, a shell’s soul, let alone its transcendent unmoved mover, cannot be plausibly thought to play any role in powering this rotation, and thus a shell’s counterfactual failure to share in the task of those nested inside it cannot be blamed on its weak soul. This conclusion stands even if in Metaph. ȁ 8 the unmoved mover of a shell is tacitly understood to be not only a final but also an efficient cause of motion, and holds for the alternative solution to the second problem discussed in Cael. B 12 if here, too, a shell is tacitly assumed to be made up of the first simple body. It is based on the analysis of the characterization of a shell’s transcendent unmoved mover as final cause of motion given in Metaph. ȁ 7 (see above, 1.4.5). It can also be arrived at independently of Metaph. ȁ 7, from Cael. B 1–2 and 5, buttressing this analysis. tries to harmonize the two solutions to the second problem discussed in Cael. B 12. But his attempt at harmonization fails in this respect, too. It entails that a single soul moves the stars and Saturn, for it is the outermost shell in the Saturnian deferent system which carries the stars round. The first solution to the second dif¿culty Aristotle tries to solve in Cael. B 12, however, clearly hands over responsibility for the motion of the stars to a soul distinct from any of those associated with the other celestial objects.

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Had a shell’s rotation been powered by its soul, it would not have been the natural motion of the first simple body. For in Cael. B 1 Aristotle emphatically denies that the spherical shell of the first simple body carrying the stars round is constrained by a soul to undergo eternal rotation which is not the natural motion of its constituent matter (284a27–31; on Cael. B 1 see above, 2.6) .42 But this shell is clearly considered ensouled and alive in Cael. B 12, as seen already, life and soul is ascribed to it also in Cael. B 2, 284b6–34, whereas in Cael. B 5 Aristotle assumes that the direction of its diurnal rotation, from east to west, is not accidental but what is best for it, nature always choosing the best from among all the existing possibilities (288a2–12). Nature here can be plausibly identified with the soul of the shell, whose role, as it turns out, is not to power the shell’s rotation but to determine its direction, probably its period, too, collapsing into a definite outcome the available possibilities for how fast the first simple body making up the shell undergoes its natural motion, and in what direction:43 these parameters, qua intelligible form in the shell’s soul, constitute the final cause of the shell’s rotation, its unmoved mover which can be supposed to exist independently of the soul, as a disembodied intellect to which the soul somehow assimilates itself. What turns out to hold for the envelope of the cosmos, the shell of the first simple body carrying the stars round, can be reasonably assumed to apply to all other shells of the same body that the cosmology outlined in Metaph. ȁ 8 posits according to the theory of homocentric spheres, for they are all replicas of the crust of the cosmos. An attempt to bring into line the two solutions to the second problem addressed in Cael. B 12 by assuming a role tacitly played in the second solution by souls must start from the hypothesis that at work in the second solution is a perhaps early version of the Metaph. ȁ 8 cosmology. It allotted a single soul to the deferent system for a planet, the Sun or the Moon–not as many as the shells of the first simple body in the system–and, accordingly, a single unmoved mover, immanent in the soul; in the hypothetical early version, the deferent system for Saturn comprised only three shells, otherwise a single soul would be responsible for the motion of the stars and Saturn, which is contrary to what Aristotle clearly posits in the first solution.44 For the attempted harmonization, however, whether a deferent system has a single soul or as many as its shells, with or without equinumerous transcendent unmoved movers, is irrelevant, if what was a single soul’s job originally was later on distributed to as many as the system’s shells, and at the same time the original soul’s immanent unmoved mover evolved into an equal number 42 43

44

For the soul as “force”, which prevents the natural motion of the simple bodies making up the compound body it ensouls, see de An. B 4, 416a6–9. In Cael. B 6, 288b12–22, Aristotle undoubtedly implies that the shell of the first simple body carrying the stars round cannot possibly rotate non-uniformly because its motion is not due to a soul, which prevents a simple body from its natural motion (cf. previous note) and could suffer loss of power, but natural. Precluded here is not that the soul of this shell somehow determines the speed and the period with which the shell rotates, as its constituent matter, the first simple body, executes its natural motion, but merely that the rotation with this speed and period is powered by the shell’s soul and is, consequently, not the natural motion of the first simple body. Cf. above, n. 39 and 41.

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of unmoved movers, one for each soul, all of which were recharacterized as transcendent. A single soul would have provided to the shells of the first simple body making up the deferent system it animated no more motive power than if multiplied by the number of the shells–certainly not on account of the fact that its unmoved mover was not only single but also immanent in it, which could not have made the rotation of the shells any less the natural motion of the first simple body.45 It should be noted, moreover, that the failed attempt to harmonize the two solutions to the second problem addressed in Cael. B 12 necessarily involves tinkering with the framework within which the problematic second solution is to be understood–the Metaph. ȁ 8 cosmology. This is clearly a further troubling feature of the solution at issue. Nor does Aristotle’s solution to the first of the two difficulties he tackles in Cael. B 12 presuppose the Metaph. ȁ 8 cosmology, as seen above, in n. 36: within the framework of this cosmology, it is by no means the case that the Sun and the Moon are unable to reach the end the planets and the stars attain, and that in achieving this end the planets undergo more motions than the stars, as Aristotle hypothesizes in the solution to the first problem he discusses in Cael. B 12. If the solutions to both problems must cohere, however, it turns out to be impossible to harmonize the two solutions to the second problem by positing–in line with the conclusion of ch. 2–that, in the second, all nested spherical shells into which the heavens are structured according to the Metaph. ȁ 8 cosmology, except the one carrying the stars round–the outermost shell in Saturn’s deferent system–are assumed to be made up of the simple body fire, not of the first simple body, and thus that the soul animating the deferent system for a planet, the Sun or the Moon both guides and powers the rotation of the system’s shells, which is not the natural motion of their matter. A further dif¿culty with the alternative solution to the second problem Aristotle discusses in Cael. B 12 is that even if we try to consider this solution a materialist exercise, added as an afterthought to illustrate the point that the psychical approach, at least to the second problem tackled in this chapter, need not be the only possibility, it is nevertheless suspect. It is unclear why Aristotle would suppose that, had the innermost spherical shell of the first simple body in the deferent system of e.g. the Sun been studded with celestial objects, either all of the other spherical shells inside which it is nested, or just the outermost one, would have failed to share in its task of moving the multitude of celestial objects.46 Operative here seems to be a principle Aristotle enunciates in Ph. H 5 for powers moving weights, though the alternative solution to the second problem he attempts to solve in Cael. B 12 makes no mention of weight (250a9–19): 45 46

For Simplicius’ attempt to harmonize the two solutions to the second problem Aristotle addresses in Cael. B 12 see above, n. 41. Cf. Simp., in Cael. 492.13–17 (Heiberg): the shell carrying the stars round–the outermost shell in the Saturnian deferent system–is capable of moving all these celestial objects and a multitude of shells nested inside it; so why would the outermost shell in the deferent system of a planet below Saturn, as well as in that of the Sun or the Moon, have been incapable of moving the shells nested inside it in case the innermost of them had carried round more than a single celestial object? For Simplicius’ answer see above, n. 41.

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3. Aristotle and the theory of homocentric spheres /Ei Ie X¶ ) X¶> OMRIl zRXÚ ( XŸR+, SºO ƒR„KOL zR XÚ hW. GV³R. X¶ zJ’ SÂ) X¶ HMTP„WMSRXSÁ>OMRIlRXŸRšQfWIMERX¢N+· IeHŸX¶%XŸRX¶&OMRIlzRXÚ(´WLRš X¶+, X¶QMWYXSÁ%X¶zJ’ Û)XŸRX¶&SºOMRœWIMzRXÚGV³R.zJ’ ÛX¶(SºH’ }R XMRM XSÁ ( XM X¢N+ ƒR„PSKSR TV¶N XŸR ´PLR XŸR + ÇN X¶ % TV¶N X¶ )· ´P[N K‡V Ie }XYGIR Sº OMRœWIM SºH{R· Sº K‡V Ie š ´PL eWG¾N XSWœRHI OfRLWIR, š šQfWIME Sº OMRœWIM S½XI TSWŸR S½X’ zR ±TSW.SÁR· ImN K‡V ‰R OMRSfL X¶ TPSlSR, IhTIV  XI XÏR RI[POÏRX{QRIXEMeWG¾NIeNX¶RƒVMUQ¶ROEiX¶Q¢OSN·T„RXINzOfRLWER

 If E moves a weight F over distance C in time D, then E need not move double the weight F over half the distance C in the same time. Now, if A moves a weight B over distance C in time D, then E, the half of A, will not move the weight B in time D, or in any part of D, over a part of the distance D between which and D obtains the ratio which obtains between A and E. It might well not move this weight at all. For, if a power, considered as a whole, moves a given weight [over a given distance], half this power cannot be assumed to move [the weight] over any part of the distance and in any time. Otherwise, a man could be capable of moving a ship single-handedly, assuming that the power of the haulers and the distance all of them moved a ship is divided proportionately to their number. 47

What seems to be assumed in the alternative solution to the second problem Aristotle discusses in Cael. B 12 is this. In Ph. H 5, if E moves a weight F over distance C in time D, then E need not move double the weight F at all; similarly, had the innermost spherical shell of the first simple body in the deferent system of e.g. a planet, as envisaged in the cosmology of Metaph. ȁ 8, been laden with more than one celestial object, then either all of the other spherical shells inside which it is nested, or the outermost one, would have failed to carry round the shells nested inside them, and thus to be able to share in the innermost shell’s task of moving a multitude of celestial objects. The innermost shell in the system, with a single celestial object fixed into its mass, is assumed to be the least weighed down of all, no shell being nested inside it. It might have a considerably larger load-carrying capacity. But if more than one celestial object had been embedded in its mass, either all of the surrounding shells, or the outermost one, could not have rotated due to overload. These shells are finite material objects, and thus a proportionately finite limit must exist to the load each of them can carry round. If operative in the alternative solution to the second problem Aristotle discusses in Cael. B 12 is the principle enunciated in Ph. H 5 for powers moving weights, how is this compatible with the fundamental fact that the first simple body lacks weight? 48 It might, of course, be objected that, in this solution, a planet, the Sun or the Moon is indeed assumed to be a load carried round by the innermost shell of the first simple body in a deferent system of nested such shells posited for each of these seven celestial objects according to the theory of homocentric spheres, just as each shell is assumed to be a load carried round by the shell inside which it is 47 eWG»N, here translated with “power”, is equivalent to H»REQMN. Cf. Ph. H 5, 250a4–7. 48 Cf. Simp., in Cael. 492.21–22 (Heiberg). Simplicius proposes that assumed here is only a symmetry between a mover and what this mover can move, just as something heavy and its mover must be symmetrical. In all probability, he means that a mover is incapable of moving something heavy, unless its power exceeds the object’s weight by a certain quantity. But he does not flesh out his suggestion. What is the analogue of weight here?

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nested. This does not imply that the first simple body constituting the celestial object and the spherical shells in its deferent system has weight, however. One quantity of the first simple body can perhaps be a load for another, which moves it, in the sense that it resists motion, as if it were something heavy, an analogy intended to give an illustration of the relevant phenomenon–resistance to motion–from the familiar realm of the four other simple bodies. As it is, the principle which is enunciated in Ph. H 5 can be assumed to be operative in the alternative solution to the second difficulty Aristotle attacks in Cael. B 12 without implying that the first simple body has weight. It is applied to the first simple body, as offering resistance to motion, by a simple analogy with the things that have weight and, like the first simple body, resist motion. But how could Aristotle assume that a planet, the Sun or the Moon offers resistance to the motion of the innermost spherical shell of the first simple body in its deferent system? Certainly, one tends to think and speak of each of the wandering luminaries as being carried round by the shell in whose mass it is fixed. This, however, should not obscure the crucial fact that the celestial object is not to be considered a piece of foreign matter, somehow incorporated into the first simple body of this shell. It is a portion of the first simple body making up the shell: hence, it cannot be assumed to resist the shell’s rotation, for this rotation is also its own natural motion. The innermost spherical shell of the first simple body in the deferent system posited for a planet, the Sun or the Moon in the cosmology sketched out in Metaph. ȁ 8, which is built on the theory of homocentric spheres, is like the spherical shell of the same material whose parts are the stars, the crust of the cosmos, except that the latter has a huge number of luminous parts, any of the former only one. Had Aristotle thought that these luminous parts of the cosmic envelope for some reason tend to resist the natural motion of their surroundings, which, as a consequence, need to overcome this resistance, would he then have waxed lyrical in Cael. B 1 about how effortlessly the first simple body at the outermost reaches of the cosmos undergoes its natural motion (284a11–b5)? And how could overcoming this resistance not require the expenditure of wearying effort, given the huge multitude of the stars? 49 Finally, if Aristotle can be plausibly assumed to apply what holds for the spherical shell of the first simple body whose luminous sections are the stars–as regards the effortlessness of its resistless natural motion–to all of its “copies” in the cosmology of Metaph. ȁ 8, which is built on the theory of homocentric spheres, none of these “derivative” shells of the first simple body can be assumed to meet resistance, as it spins executing its natural motion, by those nested inside it.50 In the cosmology outlined in Metaph. ȁ 8, moreover, the innermost spherical shell of the first simple body in the deferent system for a planet, the Sun or the Moon cannot be assumed, as in the alternative solution to the second problem discussed in Cael. B 12, to carry with it a single object, in contrast to the other shells in the system, each of which carries with it many objects, i.e. the shells nested in49 Cf. Leggatt (1995) 251 on Cael. B 12, 293a4–11. 50 For the hypothetical case in which none of these derivative shells is assumed to consist of the ¿rst simple body see next paragraph, with n. 51.

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side it. This assumption holds only if each deferent system is considered in isolation, so that inside its innermost spherical shell there is nothing at all. In fact, however, the seven deferent systems for the five planets, the Sun and the Moon are plugged into one another in an appropriate order, each being sheathed in a system of unwinding spherical shells of the first simple body to prevent the rotation of the innermost shell in a superior deferent system from interfering with that of outermost shell in the deferent system immediately next in order; although no system of unwinding spherical shells is posited inside the innermost shell in the Moon’s deferent system, there are good reasons to believe that one is needed there, too, whatever explanation might be offered for Aristotle’s failure to mention it (see Appendix 8, with n. 20). Clearly, each of the spherical shells of the first simple body in the baroque onion-like structure into which Metaph. ȁ 8 analyzes the heavens carries with it, as it rotates, all those nested inside it, irrespective of whether it is last in the deferent system for a wandering celestial object or not. It is by no means the case that a shell, if it is the innermost of those composing a deferent system, carries with it a single object, unlike the rest around it, each of which carries with it many objects–unless by “object” we mean a luminary, in connection to the last shell of the first simple body in a deferent system, or a shell of the first simple body, in connection to the system’s other components. To assume that in the alternative solution to the second problem he tackles in Cael. B 12 Aristotle thinks otherwise is to assume that in this context he ignores fundamental aspects of his own physicalization of the theory of homocentric spheres in Metaph. ȁ 8. Is this plausible, however, if the solution in question is considered, as suggested above, his example of a materialist approach, within the framework of the physicalized theory of homocentric spheres set out in Metaph. ȁ 8, to the second of the two problems Cael. B 12 is devoted to? 51

3.3.6. Conclusion In all likelihood, therefore, the alternative solution to this problem is a thoughtlessly appended addition to the original version of the chapter by someone other than Aristotle himself, under the influence of Metaph. ȁ 8 and due to a hasty reading of Cael. B 12, 292b31–293a2, which ignored the force of a crucial term–the pronoun “each”: “the primary of these life-principles, despite its oneness, moves a multitude of divine objects, whereas the others, despite their being many, move only one each. For any one of the wandering celestial objects has several motions”. The presence of the pronoun “each”, indicating that the planets, the Sun and the Moon 51

This objection to the solution in question holds regardless of whether all nested spherical shells into which the heavens are structured according to the Metaph. ȁ 8 cosmology, except the one carrying the stars with it–the outermost shell in Saturn’s deferent system–are assumed to be made out of the simple body ¿re, not of the ¿rst simple body; in this case, the soul animating the deferent system for a planet, the Sun or the Moon would not only guide but also power the rotation of the system’s shells, which would not be the natural motion of their matter. For a defense of the solution criticized here see Manuwald (1989) 109–111.

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are each assigned a single soul, not many as in the cosmology sketched out in Metaph. ȁ 8, which physicalizes the theory of homocentric spheres, suggests that here Aristotle does not operate within the framework of this cosmology. If insufficient attention is paid to it, what Aristotle says seems to be understandable within this framework, and thus can be interpreted as presupposing it. The adverb “first” in Aristotle’s introduction to the solution he offers for the second difficulty he tackles in Cael. B 12–“one thing comes to mind first as a reasonable explanation of this fact”–compelled a hasty reader of Cael. B 12, 292b31–293a2, who was fascinated with the grand cosmological scheme laid out in Metaph. ȁ 8, to wonder what other solution Aristotle could have had in mind, and also to suspect that a second solution might have been originally included in the text but fell out: the reader’s temptation to supply another solution, within the framework of Metaph. ȁ 8, resulted in an alternative to the genuinely Aristotelian solution, which got incorporated into the text, having started its life as a scholium. The adverb “first” in the introduction to Aristotle’s solution suggests that the following explanation of the baffling fact at issue comes automatically to mind if we assume that the celestial objects are ensouled, though it need not be the only, or the correct, one. In view of the above discussion, however, it is hard to believe that the alternative solution in our text can be one of the explanations, if any, Aristotle had in mind.52

3.4. THE CONCEPTION OF THE HEAVENS AND CELESTIAL MOTIONS IN CAEL. B 10 3.4.1. Zodiacal motion as resisted by the diurnal rotation A conception in the de Caelo of the structure of the heavens that is based on a version of the theory of homocentric spheres, as in Metaph. ȁ 8, seems to be precluded by Cael. B 12 (see above, n. 35–36 and 39). Cael. B 10 shows that this is indeed so, and with the help of Cael. B 12 allows us to reconstruct an Aristotelian picture of the heavens considerably different from that in Metaph. ȁ 8. As already seen above, in 2.8.4, Aristotle states in Cael. B 10 the relation between the Moon’s, the Sun’s and a planet’s tropical period–the time each wandering celestial object needs to ¿nish a trip, moving (mainly, in the case of the planets) eastwards against the backdrop of the zodiacal constellations–and the relative distances of these seven celestial objects from the Earth, at the center of the cosmos: the longer the tropical period of a wandering celestial object, the farther away from the Earth the object. This relation breaks down for Mercury, the Sun and Venus. They have a tropical period of one year, so their order cannot be gleaned from the link of tropical periods with distances from the Earth: they can only be placed as a group below Mars, with a tropical period of about two years, and above the 52

Easterling (1961) 138–148 has argued that the whole of Cael. B 12 is a later addition by Aristotle himself to the original Cael. B, where the theory of homocentric spheres is not presupposed (for the opposite view see Manuwald [1989] 104–115). However, apart from the second solution to the second dif¿culty, the rest of the chapter does not seem suspect.

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Moon, whose tropical period of about a month is the shortest. Aristotle does not mention this complication.53 Within the Metaph. ȁ 8 cosmology, the tropical period of a planet, the Sun or the Moon is the rotational period of the second shell in the object’s deferent system, counting from the outside; the ¿rst shell, to which is assigned the diurnal rotation, does not influence the rotational period of the next one, or of any of the other two nested inside it. However, the tropical period is said in Cael. B 10 to be a function of the resistance the luminary meets revolving around the Earth opposite to “the outermost rotation of the ouranos”, the diurnal rotation of the shell carrying the stars with it (291a34–b10; translated above, in 2.2.1): the farther away from the Earth, and thus the closer to the stars, a planet, the Moon or the Sun is, the most impeded, and slowed down, is its eastward zodiacal motion by the opposite, much faster diurnal rotation of the shell of the ¿rst simple body whose bright parts are the stars.54 What Aristotle has in mind can be understood in the context of his “mechanics”, partly set out in Ph. ǻ 8: the speed of a moving object is inversely proportional to the resistance offered to the object by the medium through which the object moves; the motion of the object is slowed down in an inverse proportion to the density of the medium, and if the medium itself moves oppositely, then it is slowed down even further, most probably again in inverse proportion to the speed of the medium (215a25–b12).55 Assume that the eastward motion of the planets, the Sun and Moon against the ¿eld of stars occurs in a medium, which follows the diurnal rotation of the shell of the ¿rst simple body with the stars. Moreover, the outlying layers of the rotating medium can be assumed, in view of Mech. 1, 849b19–21, to move with greater linear speed than those lying closer to the rotational center, and in direct proportion to the distance from that center, just as if they belonged to a rotating, rigid spherical shell. If so, the planets, the Sun and Moon, if they are not all at the same distance from the Earth, must move eastwards each with a linear speed which is inversely proportional to the resistance of the medium–ultimately, of the ¿rst simple body carrying the medium round with it–that is, with a linear speed inversely proportional to the distance from the center of the cosmos. As it is, the farther away from the center of the cosmos each of the seven celestial objects at issue, the longer its tropical period. 53

Aristotle’s omission is judged unnecessarily harshly by Lloyd (1996) 170–172. It does not show that Aristotle’s declaration in Cael. B 10 that the order of the planets, the Sun and the Moon and their relative distances from the ¿xed stars or the Earth is adequately dealt with in astronomy is “partly just a matter of hand-waving”. At any rate, how would we be supposed to explain the hand-waving on Aristotle’s part here? 54 That Cael. B 10 cannot presuppose the theory of homocentric spheres, and thus the cosmology outlined in Metaph. ȁ 8, has been pointed out by Easterling (1961) 141–142 (see also Pellegrin [2009] 164–166, who acknowledges that Cael. B 10 raises doubts about Aristotle’s adherence to the theory in the de Caelo). Manuwald (1989) 113–115 argues otherwise. 55 Easterling (1961) 142 seems to think that the way in which, according to Cael. B 10, the planets, the Sun and the Moon are affected by the diurnal rotation of the shell of the ¿rst simple body whose parts are the stars is “clearly not mechanical”. What else could it be, though?

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Venus, the Sun and Mercury are exceptions. All three have the same tropical period, but cannot be reasonably assumed to lie equally far from the Earth, between Mars and the Moon. The two objects above the one closer to us are able to overcome the increased resistance their eastward motion meets, or it is the resistance itself that happens to decrease at their distances from the Earth. Alternatively, Aristotle could well assume that the Sun, Venus and Mercury are not suf¿ciently far away from one another in order for the different resistance each object meets with from the diurnally rotating medium to show up in a tropical period unequal to the tropical period of either of the other two. The astronomers who, as Aristotle says in Cael. B 10, showed the relation between distances from the Earth and tropical periods of the ¿ve planets, the Sun and Moon, most probably argued simply on the basis that objects moving along homocentric circles at the same linear speed will appear from the center to move each at a different angular rate, depending on how far from the common center of circular motion each is. For Aristotle this would be not a physical but an astronomical treatment of the issue at hand, abstracting from the resistance of the medium through which the planets, the Sun and the Moon orbit eastwards the center of the cosmos (cf. Ph. B 2, 193b22–32 and 194a7–12). A physical approach must take this resisting medium of motion into consideration. If the seven wandering celestial objects orbited the center of the cosmos from west to east at the same linear speed, through a medium offering the same resistance to all of them, their tropical periods would be unequal, as observed, if their distances from the center of the cosmos were unequal, and could thus be safely assumed to correlate with these distances–the farther away the celestial object from the center, the longer its tropical period, for it simply needs to circuit a longer track. Keeping on adding physical beef to the bare bones of the astronomical reasoning, however, we must next take into account the important fact that the medium, through which the Sun, the Moon and the planets orbit eastwards the center of the cosmos, undergoes itself a rapid, westward rotational motion. It thus resists the opposite motion of each of the wandering celestial objects in a direct proportion to its distance from the center of the cosmos, thereby reducing their linear speeds, hitherto assumed to be equal, in the same indirect proportion. As it turns out, the farther out one of these seven celestial objects from the Earth, the longer its tropical period not simply because it has to circuit a longer track, as it moves against the background of the zodiacal constellations at the same linear speed as the others, but also–which is what matters kinetically–because the linear speed of its eastward motion depends inversely on its remoteness from the Earth, due to the resistance of the westwards rotating medium through which it moves, resistance ultimately due to the rapid diurnal rotation of the ¿rst simple body that is followed by this medium. Explaining in Mete. A 3 why clouds do not form at high altitudes, Aristotle points out that the air above the sphere whose radius extends from the center of the Earth to the tops of the highest mountains follows the motion of the ¿rst simple body, which prevents the condensation of water vapor, and renders impossible the formation of clouds at suf¿ciently high altitudes: the air around the Earth, says Ar-

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istotle, is contiguously encased by a shell of ¿re, and this is contiguous with the ¿rst simple body, whose rotational motion is imparted to ¿re, and from it to the air below (340b32–341a9). This motion is not explicitly identi¿ed with the diurnal rotation. However, the identi¿cation is required in view of Aristotle’s theory of comets in Mete. A 7 (cf. Appendix 8, with n. 20). In the main bulk of the de Caelo, as argued in ch. 2, ¿re is assumed to ¿ll the region of the heavens where the planets, the Sun and the Moon are situated–as well as to constitute these seven celestial objects–and, therefore, to be that resisting medium in which, according to Cael. B 10, they move eastwards, round the center of the cosmos, against the backdrop of the zodiac. (Aristotle most probably did not think of the ¿rst simple body as a resisting medium; see the end of 3.7.) In Mete. A 3, unlike in the main bulk of the de Caelo, the ¿rst simple body is assumed to occupy the whole celestial realm, and the shell of ¿re enveloping the air is thus assumed to be much thinner than its de Caelo analogue, but this does not matter here. Whether Aristotle thinks of the ¿re-shell as following the diurnal rotation cannot depend on its thickness.

3.4.2. Cael. B 12 and the conception of celestial motions in Cael. B 10 Now, since the zodiacal motion is not natural for the constitutive matter of a wandering celestial object, it is both guided and powered by the soul which, according to Cael. B 12, enlivens the object–unlike the diurnal rotation of the shell of the ¿rst simple body whose parts are the stars. This is the natural motion of the ¿rst simple body, which the shell’s soul only guides, via determining its direction and period. Sharing in the diurnal rotation is forced upon each of the wandering celestial objects. However, we can easily see why, in the solution he suggests to the second problem he discusses in Cael. B 12, Aristotle regards the soul of each of the five planets, the Sun or the Moon responsible for all motions of the object: each day a wandering celestial object, unlike a star, does not follow the same circular path but a different coil of a spiral owing to its zodiacal motion, for which its soul is responsible (for this spiral motion see 1.3.5). None of the wanderers, that is, is a passive participant in the diurnal rotation of the ¿rst simple body–forced though it is to share in this motion–thanks to its active soul. A planet’s soul, moreover, in steering the luminary’s zodiacal motion, also determines when it will retrograde, as well as the shape of each retrograde path, and slows the planet down suf¿ciently for it to appear from the center of the cosmos stationary against the background of the stars before and after retrogradations. The souls of the Sun and the Moon are responsible for the variations in the speed of the zodiacal motion of these celestial objects, too, as well as for any deviations from circularity in the path of the Moon’s zodiacal motion, perhaps of the Sun’s, too (cf. above, 1.4.6). In tentatively solving the second of the two dif¿culties he addresses in Cael. B 12, Aristotle might posit a weakness in the souls of the wandering celestial objects, relative to the soul of the starry shell of the ¿rst simple body, exactly because each of these seven souls is not only a steerer but also a motor: having to

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force a mass of ¿re to move not only counter-naturally but also opposite to the rapidly rotating surroundings, while pursuing its unspeci¿ed ultimate goal, taxes it to such an extent that moving more than a single ¿reball would have been utterly impossible for it. However, it is not easy to see how this weakness can also be evinced in the case of the planets by their retrograding, which must punctuate their mainly eastward zodiacal motion in order for each of them to reach the ultimate goal attained at once by the stars via their diurnal revolution, and in the case of the Sun and the Moon by the lack of retrograding, a fact suggesting that these two wanderers cannot reach the end at issue. Would it not be much easier for the Sun and the Moon to attain this end if their motive souls had to overcome much less resistance of the oppositely moving medium? Why, moreover, could not a wandering celestial object reach this end by just participating inertly in the diurnal rotation, as if it were a star, without undergoing any other motion? If so, it would still be ensouled, as Aristotle posits in Cael. B 12, its soul being a principle not of motion but of persistence. Be that as it may, a more satisfactory teleological solution to the ¿rst problem Cael. B 12 addresses might be to posit that nature has ordained that the host of the stars, and each wanderer, undergo as many motions as required for the attainment of their common goal adumbrated in Cael. B 3 and GC B 10–powering the ceaseless transmutation of the Empedoclean simple bodies into one another, and thus all substantial change in the cosmos (see 1.2.5, and Appendix 4).

3.4.3. The rejection in Cael. B 9 of a Pythagorean celestial harmony That the seven wandering celestial objects move forcedly through a resisting medium due to their being ensouled is, at ¿rst glance, contradicted by the conclusion of Cael. B 9, where Aristotle argues against the Pythagorean theory of a celestial harmony produced by the motions of the celestial objects: had the celestial objects moved through ¿re, or air, diffused throughout the heavens, inevitably they would have produced a tremendous noise that would have shattered everything here on Earth; since this obviously does no happen, their motions cannot be due either to souls or force, as if nature kindly foresaw the detrimental effects which would have resulted if the motions of the celestial objects had been otherwise than they are now (291a18–26). But what Aristotle is interested in ruling out here is that the celestial objects move through an immobile medium, whether ¿re or air–it is in this case that, by his lights, they would have obliterated our surroundings. So he cannot implicitly deny that ¿re ¿lls partially the heavens, provided that it is not stationary, and that the wandering celestial objects are forced to move in this medium by their souls. He has argued that nothing produces sound if it is ¿xed into something moving, e.g. the mast and other parts of a ship, or if it moves in a moving medium, e.g. a ship in a river (291a9–18). The ¿rst part of this example evidently concerns the stars, parts of a rotating shell made out of the ¿rst simple body; the second applies to the ¿ve planets, the Sun and the Moon, which, as argued above, on the basis of Cael. B 10, move through a moving medium.

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3.4.4. A hint for the forced motion of the wandering luminaries in Cael. B 1 In Cael. B 1 Aristotle argues that the spherical shell of matter whose parts are the stars cannot be forced to rotate eternally by a soul, in which case its rotation would be a counter-natural motion for its matter, for he identi¿es this shell with the divine, as in Cael. A 2–3, and also considers a life of perpetual expenditure of effort foreign to the divine (284a11–18, 284a27–b5; see also above, 2.6). It follows that if the ¿ve planets, the Sun and the Moon are ¿reballs, forced by their souls to undergo zodiacal motion counter-naturally, they are not of divine nature, unlike the stars–at least as regards expenditure of effort. As already seen, Aristotle says in Cael. B 12 that the planets attain the same goal as the stars, “the most divine principle” (see above, n. 36), though they, unlike the stars, have to expend effort, whereas the Sun and the Moon can only come close to this goal. In a certain sense, therefore, all of the wandering celestial objects are divine, too, the planets more so than the Sun and the Moon. In Cael. B 1 Aristotle does suggest that the seven wandering celestial objects move counter-naturally, and thus forcedly. He denies that the rotating spherical shell of matter whose parts are the stars undergoes perpetually counter-natural motion due to its motive soul, notion he thinks the ancients turned into the myth of the heavens-supporting Atlas, as if “all upper bodies” were heavy and earthy, and so a soul were required to impose on each a counter-natural motion (284a18–27). As we saw above, in 2.3, more than one upper body are mentioned in Cael. B 4: one is the ¿rst simple body that makes up the stars and, as a spherical shell, also envelops them; another occupies the rest of the heavens, where the wandering celestial objects are, all of them consisting, just like the stars, of the upper body that surrounds them, and which we identi¿ed with ¿re in ch. 2. Aristotle’s emphatic denial, however, in Cael. B 1 that the spherical shell of the ¿rst simple body undergoes its diurnal rotation counter-naturally, due to a constraining motive soul, as if “all upper bodies” were such that a motive soul would be required to impose on each of them a counter-natural motion, clearly suggests this: the upper body making up and surrounding the planets, the Sun and the Moon undergoes all its motions–whether as constitutive matter of the wandering celestial objects, or as the ¿ller of the cosmic place in which they move–because it is of that sort. It is not, of course, heavy and earthy: Aristotle says this to illustrate vividly the catastrophic collapse of the heavens that would have resulted if the ¿rst simple body had been such that it could not have undergone diurnal rotation naturally, and a hypothetical Atlas-like soul imposing this counter-natural motion on it had suddenly ceased doing its job.

3.5. CAEL. A 4 AND THE THEORY OF HOMOCENTRIC SPHERES 3.5.1. The last argument in Cael. A 4 Further evidence that the de Caelo cosmology, unlike the one outlined in Metaph. ȁ 8, is not based on the theory of homocentric spheres is offered by the last

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argument in Cael. A 4, where Aristotle shows that the natural motion of the ¿rst simple body has no contrary motion, which would be the natural motion of another simple body (Cael. A 4 continues A 3, on which see 1.3.6).56 He assumes that each of two simple bodies with contrary natural motions can transform into the other. But since he also thinks that the ¿rst simple body is not subject to coming to be and passing away, he must show that the natural motion of this simple body has no contrary, be it the radial motion of the other simple bodies away, or towards, the center of the cosmos, or circular motion about (an axis through) this point but in the opposite sense to that in which the ¿rst simple body itself moves circularly about the same point by nature. For, if the natural motion of the ¿rst simple body and circular motion in the opposite direction were contraries, then the circular motion which is contrary to the natural motion of the ¿rst simple body would not but exist as natural motion of a simple body, into which the ¿rst simple body could decay, and from which it could also be generated. Aristotle does not consider radial motion away, or towards, the center of the cosmos and circular motion about this point to be contraries. Nor, moreover, does he think of two circular motions about the center of the cosmos but in opposite directions as contraries, unlike motions in opposite directions along two radii of the cosmos (270b32–271a22). (This does not mean that there is no sixth simple body. Although radial motion towards, or away, from the center of the cosmos is not the contrary of circular motion about this point, the ¿rst simple body does exist alongside the four traditional simple bodies.) Aristotle next gives a stronger argument, to the effect that there cannot be two simple bodies, both of which move, in virtue of their natures, circularly about the center of the cosmos in opposite, hypothetically contrary, directions (271a22–33): 

)eHäOEi¤RšO»OP.X®O»OP.zRERXfE, Q„XLR‰R¤RšyX{VE· *zTiX¶EºX¶K„V, ´XM ƒR„KOL X¶ O»OP. JIV³QIRSR ±TSUIRSÁR ƒV\„QIRSR IeN T„RXEN ±QSf[N ƒJMORIlWUEM XS¾NzRERXfSYNX³TSYN(IeWiHäX³TSYzRERXM³XLXINX¶†R[OEiO„X[OEiX¶TV³WUMSR OEi²TfWUMSROEiX¶HI\M¶ROEiƒVMWXIV³R), EdHäX¢NJSVŠNzRERXMÉWIMNOEX‡X‡NXÏR X³T[R IeWiR zRERXMÉWIMN·* Ie QäR K‡V hWEM ¤WER, SºO ‰R ¤R OfRLWMN EºXÏR, Ie H’ š yX{VEOfRLWMNzOV„XIM, šyX{VESºO‰R¤R· ÊWX’ IeƒQJ³XIVE¤R, Q„XLR‰RU„XIVSR¤R WÏQE QŸ OMRS»QIRSR XŸR E¹XSÁ OfRLWMR· Q„XLR K‡V ¹T³HLQE XSÁXS P{KSQIR, S Qœ zWXMR¹T³HIWMN. ±HäUI¶NOEišJ»WMNSºHäRQ„XLRTSMSÁWMR. If a circular motion were the contrary of another, then one of these motions would be purposeless. *For it is motion to the same place, because a circularly moving body, from whatever point it begins to move, must pass through all contrary places alike (the contrarieties of place are up and down, front and back, right and left), and the contrarieties of motion correspond to those of place.* For, if the two motions were equal, then the bodies would fail to move, and if one prevailed, then the other would be cancelled. So if there were two contrary circular motions, a purposeless body would exist that could not move as is natural for it. For a shoe which is never worn is purposeless. God and nature make nothing purposeless, however.

56

For the assumption that Cael. A 3 and 4, which form a unit, presuppose the theory of homocentric spheres see Cleary (1996) 198–199. This section is based on Kouremenos (2003a).

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In his Belles Lettres edition of the de Caelo, Moraux suggests that the part between the asterisks ought to be transposed to 271a19, after the end of the period before the beginning of this reductio ad absurdum argument, so as to explain the reason for Aristotle’s claim that motions along the semicircles of a circle in opposite directions are not contrary, even if each motion continues into the other semicircle (271a17–19).57 This part clearly intrudes between the statement of the absurdity Aristotle will go on to derive from the hypothesis of contrary circular motions and the reductio itself. As interpreted by the latest commentator of the de Caelo, the argument concerns two bodies moving in opposite directions along the same circle and colliding: if the two motions are equal in force, they cancel each other out; if one overpowers the other, the overpowered one stops, and the body with the dominant motion carries the other body along.58 The context of the argument, however, leaves no doubt that the two bodies at issue are simple, the ¿rst simple body and a sixth putative simple body, the two contrary circular motions being their natural motions. How else would Aristotle think of these natural but contrary circular motions if not as opposite rotations of two nested spherical shells, one of the ¿rst simple body and the other of the sixth simple body, about axes passing through the center of the cosmos, the common center of the shells? 59 Is it not unlikely that he would think of the two simple bodies his argument is about as being broken down into variously sized chunks, oppositely revolving round the Earth, in the same circular orbits, and unavoidably suffering collisions? Contrary to the interpretation of Aristotle’s reductio rejected here, he undoubtedly wants to argue that, no matter whether the opposite natural rotations of the two simple bodies are equal or one overwhelms the other, only one of the two simple bodies would fail to move naturally as it ought to, and thus would serve no purpose in nature. This must be what follows as a consequence of either case. It is the consequence of the ¿rst, too, in case the conditional “if the two motions were equal, then the bodies would fail to move” is a corruption of “if the two motions were equal, then one of the two bodies would fail to move” (IeQäRK‡VhWEM¤WER, SºO ‰R ¤R OfRLWMN ¢yR¶N² EºXÏR, sc. XÏR O»OP. JIVSQ{R[R). The only plausible way, moreover, to get the required result for either case is if the spherical shell of the inner simple body not only undergoes its natural rotation but is also forced to follow the rotation of the spherical shell of the outer simple body, and if the equality and inequality of the opposite rotational motions are the equality and inequality of their periods, the rotation that prevails being the one that has the shorter period.60 Let us assume ¿rst that the two spherical shells rotate oppositely about the same axis. If they do so with the same period, then points on the inner shell would 57 See Longo (1961) 304, on 271a23–28, whom Moraux follows here. 58 See Leggatt (1995) 187 ad loc.; cf. Hankinson (2009) 115. 59 Cf. Guthrie (1939) 31 n. b on 271a31: “the conception of two contrary circular motions amounts in fact to a conception of two heavenly vaults tending in different directions”. 60 That “equal motions” are motions of equal speed is clear from Ph. H 4, 248a13–18.

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appear to be stationary with respect to points on the outer shell. The inner simple body would, therefore, follow the natural motion of the outer one instead of undergoing its own, as it is supposed to. Now, if the rotation of the outer shell were dominant, i.e. if the outer shell had a shorter period, then points on the inner shell would appear to rotate in the direction of the outer shell with a longer period. In this case, too, the natural motion of the inner simple body would not take place. If the shells of the outer and inner simple body rotated on inclined axes, then the natural motion of the inner simple body would once again be masked. In the case of equal rotational periods, this is shown by the effect of the combined rotations of the innermost two of the spheres responsible for generating a planet’s motion in the Eudoxean theory of homocentric spheres (on the most recent of its available reconstructions, which is less constrained; see 1.4.2). A point of the shell of the inner simple body would not trace a circle, as the two shells would rotate jointly, and thus would not have a period of rotation. Instead, it would wobble above and below the equator of the enveloping shell, simultaneously undergoing longitudinal motion, though not all the way around its backdrop. Its projected trace on the shell of the outer simple body would be a closed curve. If the shells of the outer and inner simple body rotated on inclined axes but with unequal rotational periods, we revert to the case of the same axis and unequal rotational periods, with the addition of latitudinal motion undergone by the point on the shell of the inner simple body against the backdrop of the shell of the outer simple body.61 However, to have a natural rotation in a certain direction is what it is for something to be the inner simple body, just as to be worn on, and to protect, a foot is what it is for something to be a shoe. Making purposeless shoes never meant to be put on feet might not be inconceivable. Be that as it may, we cannot expect nature, teleologically operating, to “make” a purposeless simple body, one which is never allowed to move naturally. This argument also rules out pairs of concentric, oppositely rotating spherical shells of the ¿rst simple body, one of which would not but turn out to be as purposeless as it would be if it were made of a hypothetical sixth simple body. It thus rules out the cosmology Aristotle sketches out in Metaph. ȁ 8 based on the theory of homocentric spheres. For none of two nested and oppositely rotating spheres in this theory is purposeless, and the same clearly applies to their physical counterparts–nested spherical shells of the ¿rst simple body–in the Metaph. ȁ 8 cosmology, which is inspired by the theory of homocentric spheres. Had, therefore, Aristotle operated in the de Caelo with this cosmology, he would not have argued in Cael. A 4 against the existence of nested, oppositely rotating spherical shells of matter as he does, on the assumption that one of two such shells would have absurdly lacked purpose in nature.62 61 On oppositely rotating homocentric spheres see Mendell (1998) 181. 62 Wildberg (1988) 97 notes in passing the incompatibility of the argument from Cael. A 4 discussed above with the physicalized theory of homocentric spheres Aristotle presents in Metaph. ȁ 8. In light of this incompatibility, Wildberg argues that the physicalized theory of ho-

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If this argument has not been misinterpreted, it seems that Aristotle came up with it at a time when he was not yet familiar with, or had not yet paid any close attention to, the theory of homocentric spheres. This is a plausible explanation of his unawareness that, if two nested spheres rotate with unequal periods, in opposite senses and on axes that are inclined, the motion of the one combines with that of the other to bring about a result that can be easily considered their common purpose. Thus either sphere is purposeful. The sphere, which in the theory of homocentric spheres accounts for the eastward motion of e.g. a planet against the stellar backdrop, is the second in the deferent system of the planet, counting from the outside. It rotates on an axis at an angle to that of the ¿rst sphere, by which it is carried round and whose rotational period is much shorter, a day. But its proper rotational motion is not purposeless. The above discussed argument probably concerns only the case of nested spherical shells of matter rotating oppositely on the same axis and with the same period, or on inclined axes with unequal periods, but not the more complex case of inclined axes and equal periods, which Aristotle could in all likelihood have known only from the work of Eudoxus and his associates.

3.5.2. The other arguments in Cael. A 4 It can be objected that nowhere in Cael. A 4 does Aristotle mention concentric and oppositely rotating spherical shells of matter, as assumed above. He argues ¿rst that motion in a straight line is not the contrary of motion in a circle (270b32–271a5), and then proceeds to establish the following: contrary are not (i) the motion from any point A to any point B on a circle and the motion from point B to point A (271a5–10); (ii) opposite motions, be they in the same semicircle (271a10–13) or (iii) in two semicircles of a circle (271a13–17), even (iv) if each continues into the other semicircle (271a17–19); (v) opposite motions starting from any point on a circle (271a19–22). The argument that if two contrary circular motions had existed, then one of them would have been purposeless, and nature would thus have comprised a simple body forbidden by her to undergo the motion she herself had endowed it with, comes next. (i) – (v) seem to support the interpretation of this argument we rejected above. But given the most plausible construal of the reductio, (i) – (v) must be read in its light, not the other way around. The motions considered in (i) – (v) are best understood as undergone by points of two nested spherical shells. The shells rotate about the same axis passing through their common center, which is that of the cosmos, each due to the natural motion of its constituent matter, but oppositely. One spherical shell is made up of the ¿rst simple body, the other consists of a hypothetical sixth simple body. The two points do not “move” in the same circle, or in its semicircles. They “move” on coplanar circles of the two homocentric shells, or in their semicircles. For the purmocentric spheres cannot be reconciled with the theory of the ¿rst simple body which is developed in Cael. A. There is no reason to think that this is so, however, as is argued below, at the end of 3.5.3.

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poses of the argument, the two points can be simply assumed to “move” in one and the same circle, or in its semicircles. (i) – (v) show that each rotation cannot be the contrary of the other. This means that since one of them does exist, i.e. that of the ¿rst simple body, it is not necessary for the other to also exist as the natural motion of another, i.e. sixth, simple body, into which the ¿rst simple body would decay, and from which it would also be produced. With the concluding reductio Aristotle shows that, even if the two rotations had been contrary, one of them would not but have been the natural motion of a simple body absurdly incapable of moving naturally. Nature could not have allowed this to happen, though, so the assumption that the two rotations are contrary must be abandoned. Some comments are in place on two de Caelo passages related to the argument we discussed in 3.5.1.

3.5.3. The introduction to Cael. B 3 and the conclusion of Cael. B 2 The reductio ad absurdum argument in Cael. A 4 is alluded to in the introduction to Cael. B 3, where Aristotle tries to explain why the diurnal rotation is not the sole motion in the celestial realm of the cosmos (286a3–7): 

)TIiH’ SºO}WXMRzRERXfEOfRLWMNšO»OP.X®O»OP., WOITX{SRHM‡XfTPIfSYNIeWi JSVEf, OEfTIV T³VV[UIR TIMV[Q{RSMN TSMIlWUEM XŸR ^œXLWMR, T³VV[ H’ SºG S¼X[ XÚ X³T., TSP¾ Hä QŠPPSR XÚ XÏR WYQFIFLO³X[R EºXSlN TIVi T„QTER ²PfK[R }GIMR EhWULWMR. Since there are no contrary circular motions, it must be asked why there are more motions than one [in the heavens], though we are far removed from the objects we attempt to inquire into, not so much in space but rather because very few of the properties of these objects can be grasped by our senses.

According to Simplicius, in this passage Aristotle argues that, were the zodiacal motion of the seven wanderers the contrary of the diurnal rotation, there would be no need to explain why there is not only the diurnal rotation in the heavens but also the zodiacal motion–an explanation would be readily provided by an application of the principle that if one of two contraries exists, the other also exists necessarily (zodiacal motion is here tacitly considered, as in Plato’s Timaeus, to be circular, as well as always opposite to the diurnal rotation, even in the case of the planets; cf. ch. 1, n. 113). According to Cael. A 4, however, there are no contrary circular motions (in Cael. 395.19–396.5 [Heiberg]). The explanation Aristotle offers in Cael. B 3 is teleological. If there is going to be constant coming to be in the cosmos, in the celestial realm there must be one or more circular motions other than the diurnal rotation, which leaves the elements of all composite bodies, the simple bodies ¿re, air, water and earth, unchanged in position with respect to one another on the cosmological scale (286b1–9). He promises to give more details later on, perhaps a reference to GC B 10, where he singles out “the double motion of the Sun” as cause of generation and decay in the part of

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the cosmos where the four Empedoclean simple bodies are stratified: its participating in the diurnal rotation, and its opposite annual motion, due to which the four traditional simple bodies change places incessantly, on scales much smaller than the cosmological scale, interact with, and turn into, one another, their constant coming into being and decay underlying all similar processes higher up in the scale of material organization (337a7–15). In Cael. B 3 Aristotle leaves open the possibility that the ¿ve planets and the Moon, too, do play a role in this process, alongside the Sun (cf. 1.2.5, and Appendix 4). Although at the beginning of Cael. B 3 Aristotle denies that the zodiacal motion of the Sun, the Moon and each planet is the contrary of the diurnal rotation, he concludes Cael. B 2 by asserting off-handedly that “the second revolution”, a collective term for the zodiacal motion of the Sun, the Moon and the planets, and the diurnal rotation are contrary. In Cael. B 2 Aristotle addresses the question whether there is right and left to the cosmos, as the Pythagoreans believe. In his opinion, not only right and left but also front and back and top and bottom, which he conceives as intrinsic properties of things, de¿ned functionally and not merely by position, are to be sought for only in those beings which have an innate principle of their motion and changes–a soul–in other words, only in living beings: an organism’s upper body part receives nourishment and thus sets off growth, its front body part carries sense organs and thus initiates perception of the environment, and its right body part initiates locomotion (284b27–285a10). That the spherical shell of the ¿rst simple body enveloping the rest of the cosmos has within itself a principle of its motion and is alive, says Aristotle, has already been determined–probably a reference to Cael. B 1, 284a11–35, where it is simply taken for granted that the ¿rst simple body is alive–so it cannot but have right and left, as well as upper and lower, parts (285a27–31). Front and back parts are not mentioned, for the ¿rst simple body cannot be plausibly assumed to gather information about its surroundings through sense organs; in what follows, moreover, the right is tacitly conflated with the upper part, the left with the lower, for up and down are prior to right and left, and the assumption that the living spherical shell of the ¿rst simple body has an alimentary canal, or roots, would be grotesque. Aristotle identi¿es the upper and right part of this spherical shell, a physicalization of the fundamental astronomical concept of the celestial sphere, with its hemisphere under which an Earth-based observer sees the east, where the diurnal rotation “begins”, to be on his or her right side, and the stars to rise from her or his right hand. This hemisphere is further identi¿ed with the southern celestial hemisphere. For an observer in the Earth’s northern hemisphere facing north, the celestial sphere spins counterclockwise. The stars appear to move from right, where the east is, to left, and back to right. Now, if the observer faces south, the stars appear to move from left, where their diurnal motion now “starts”, to right, and back to left. In the southern hemisphere, things are, of course, reversed. For an observer facing south, the celestial sphere spins clockwise; the stars appear to move from left to right. If the observer faces north, the stars appear to move the other way around. Why does Aristotle privilege the perspective of an observer facing north in

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the Earth’s southern hemisphere over that of an observer in the Earth’s northern hemisphere facing in the same direction, given that in either case the spherical shell of the ¿rst simple body encompassing the rest of the cosmos “starts” its diurnal rotation from the right, and this rotation is thus to the right?63 At any rate, Aristotle concludes that the inhabitants of the Earth’s northern hemisphere live in the lower and left part of the cosmos, whereas the Pythagoreans, under the false belief that the inhabitants of the Earth’s northern hemisphere live where the diurnal rotation “starts” from the right, and is thus to the right, placed these people in the upper and right part of the cosmos, and located in the lower and left part of the cosmos the people living in the Earth’s southern hemisphere. But things are reversed as regards “the second revolution”. It and “the ¿rst rotation”, i.e. the diurnal rotation (cf. 2.2.1 and 2.2.4), form a pair of contrary motions (285b14–33): 

8ÏRHäT³P[R±QäR¹TäVšQŠNJEMR³QIRSNX¶O„X[Q{VSNzWXfR, ±H’ šQlR†HLPSNX¶ †R[. HI\M¶R K‡V yO„WXSY P{KSQIR, ´UIR š ƒVGŸ X¢N OEX‡ X³TSR OMRœWI[N· XSÁ H’ SºVERSÁƒVGŸX¢NTIVMJSVŠN, ´UIREdƒREXSPEiXÏR†WXV[R, ÊWXIXSÁX’ ‰RIhLHI\M³R, S H’ Ed H»WIMN, ƒVMWXIV³R. Ie SÃR †VGIXEM ƒT¶ XÏR HI\MÏR OEi zTi X‡ HI\M‡ TIVMJ{VIXEM, ƒR„KOL X¶ †R[ IREM X¶R ƒJER¢ T³PSR· Ie K‡V }WXEM ± JERIV³N, zT’ ƒVMWXIV‡ }WXEMš OfRLWMN, ´TIV S½ JEQIR. H¢PSR XSfRYR ´XM ± ƒJERŸN T³PSN zWXi X¶ †R[. OEi Sd QäR zOIl SeOSÁRXIN zR XÚ †R[ IeWiR šQMWJEMVf. OEi TV¶N XSlN HI\MSlN, šQIlNH’ zRXÚO„X[OEiTV¶NXSlNƒVMWXIVSlN, zRERXf[N¡ÇNSd4YUEK³VIMSMP{KSYWMR· zOIlRSM K‡V šQŠN †R[ TSMSÁWM OEi zR XÚ HI\MÚ Q{VIM, XS¾N H’ zOIl O„X[ OEi zR XÚ ƒVMWXIVÚ. WYQFEfRIM Hä XSºRERXfSR. ƒPP‡ X¢N QäR HIYX{VEN TIVMJSVŠN, SmSR X¢N XÏR TPERœX[R, šQIlNQäR zR XSlN †R[ OEi zR XSlN HI\MSlN zWQIR, zOIlRSM Hä zRXSlN O„X[ OEi zR XSlN ƒVMWXIVSlN· ƒR„TEPMR K‡V XS»XSMN š ƒVGŸ X¢N OMRœWIÉN zWXM HM‡ X¶ zRERXfENIREMX‡NJSV„N, ÊWXIWYQFEfRIMRšQŠNQäRIREMTV¶NX®ƒVG®, zOIfRSYNHä TV¶NXÚX{PIM. Of the [celestial] poles, the one seen above us is the lower part [of the ouranos], and the one invisible to us is the upper part. We call “right” the side of a thing from which its motion begins. The ouranos begins its rotation where the stars rise, so this must be its right side, and its left side must be where the stars set. Thus, if the rotation of the ouranos begins from the right, and is to the right, the pole we do not see must be the upper; for, if the visible pole were the upper, the rotation of the ouranos would be to the left, and we deny this. It is thus clear that the upper pole is the one invisible to us. The people who see this pole are in the upper hemisphere [of the ouranos] and [where the diurnal rotation is] to the right, and we are in the lower hemisphere and [where the diurnal rotation is] to the left, contrary to what the Pythagoreans claim. For they believe that we are in the upper hemisphere and in the right part, the others in the lower hemisphere and in the left part. The reverse is true. However, with regard to the second revolution, e.g. of the planets, we are in the upper hemisphere and in the right part,

63

Heath (1981) 231–232, following Simp., in Cael. 391.23–392.5 (Heiberg), thinks that the observer is supposed by Aristotle to lie on the axis of the celestial sphere, and that the diurnal rotation is supposed not only to start from the observer’s right hand which points to the east but also to proceed to the west over the front of his or her body: if so, the observer lies with her or his feet towards the north celestial pole, and with her or his head towards the south celestial pole. Braunlich (1936) 248–249 thinks that motion to the right is counterclockwise, and places the observer above the poles of the celestial sphere, which spins counterclockwise if viewed from above its southern pole. It is very unlikely that Aristotle would argue from the perspective of a hypothetical observer outside the cosmos, however.

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3. Aristotle and the theory of homocentric spheres whereas the others are in the lower hemisphere and in the left part. For the revolution of these celestial objects begins from the opposite side [to that where the diurnal rotation starts], the two motions being contrary, so that we are at the beginning of the second revolution, the others at its end.

In saying that the ¿rst and second revolutions are contrary, Aristotle probably speaks carelessly, perhaps because in this context nothing hinges on whether the ¿rst and second circular motions are contrary or not. If in the de Caelo Aristotle thinks, as argued above, of the seven celestial objects that undergo the second revolution, the planets, and Sun and the Moon, as consisting of ¿re, then since the ¿re making up these objects moves enforcedly in executing the second circular motion, not naturally, the description of the second revolution as the contrary of the ¿rst, which is the natural motion of the ¿rst simple body, does not entail that the ¿rst simple body could turn into ¿re, and vice versa. This would obtain only if the second revolution were the natural motion of a simple body. By contrast, in Cael. B 3 Aristotle must carefully specify, though he does not say it in so many words, that the ¿rst and second revolutions are not contrary, just as no circular motions are contrary, to preclude a possible explanation of why the ¿rst revolution is not the only motion in the heavens. Note that, as interpreted here, the argument in Cael. A 4 against the existence of two nested, naturally but oppositely rotating spherical shells of matter rules it out not because the motions under consideration are contrary, for no circular motions can be contrary in Aristotle’s view, but rather because one of them turns out to be purposeless. That the natural motions of the shells are contrary is simply Aristotle’s initial assumption to launch a reductio ad absurdum argument: if one of two hypothetically opposite natural motions existed, the other could not be undergone, a contradiction bolstering his earlier conclusion that there are no contrary circular motions. If so, there is no need to ask with Simplicius how Aristotle could not think of the ¿rst two spheres, counting from the outside, in the deferent system posited for one of the planets, the Sun or the Moon by the theory of homocentric spheres as having contrary rotations (in Cael. 154.22–29 [Heiberg]): 

>LXIlR †\MSR, TÏN SºO zRERXfE OfRLWfN zWXMR š XÏR TPER[Q{R[R X® X¢N ƒTPERSÁN WJEfVEN· Sº K‡V ƒRXMOMRSÁRXEM Q³RSR, ƒPP‡ OEi ƒT¶ XÏR ƒRXMOIMQ{R[R X³T[R zTi XS¾NƒRXMOIMQ{RSYNHSOSÁWMOMRIlWUEM, IhTIVšQäRƒTPERŸNƒT’ ƒREXSPÏRzTiH»WMR, Ed Hä TPERÉQIREMƒT¶ H»WI[N zT’ ƒREXSPœR· SºHä K‡V X¶ QŸzTi XSÁ EºXSÁ O»OPSY KfRIWUEMXŸROfRLWMRHSOIlO[P»IMRXŸRzRERXf[WMR· SºHäK‡VX‡ƒT¶XSÁQ{WSYOEi zTi X¶ Q{WSR zTi X¢N EºX¢N IºUIfEN ƒR„KOL OMRIlWUEM T„RXE SºHä ¹TERXŠR T„RX[N ƒPPœPSMN. It is worth asking how the motion of the wandering celestial objects is not contrary to the motion of the sphere of the ¿xed stars. For these celestial objects not only move in the opposite direction [to that in which the sphere of the ¿xed stars rotates], but also seem to move from contrary places to contrary places, if the sphere of the ¿xed stars spins westwards and the spheres of the planets spin eastwards. Contrariety, moreover, does not seem to be precluded by the fact that these motions are not all in the same circle, for not all rectilinear motions

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away from the center [of the cosmos] and toward it follow necessarily the same line, nor do necessarily all of them meet one another.

Simplicius takes the above discussed argument from Cael. A 4 to concern not two nested spherical shells of matter rotating in opposite senses but two objects moving oppositely in a circle, and eventually colliding. His question could also be raised by Aristotle’s argument as understood here, however. To answer it, all one has to point out is simply that the theory of homocentric spheres would force Aristotle not to change his view as to the absence of contrariety in circular motion but to realize that one of two opposite natural rotations of nested shells of matter need not be purposeless, which means that one cannot build on purposelessness a reductio ad absurdum type of argument to rule out the existence of contrary circular motions. 3.6. METAPH. ȁ 8 Is Aristotle’s cognitive attitude towards the outline of the structure of the heavens he gives in Metaph. ȁ 8, guided by the Eudoxean/Callippean theory of homocentric spheres, as cautious as that he adopts e.g. in Cael. B 12 towards the solutions to the problems he deals with there? 64 Does it only seem to him to be the case that the heavens comprise forty-three snugly nested spherical shells of the ¿rst simple body, in light of the theory of homocentric spheres as originally put forth by Eudoxus, or forty-seven (which is perhaps a copying error for forty-nine) if we adopt only in part this theory as modi¿ed by Callippus (see 1.4.4), all of which are centered on the Earth, and rotate simultaneously, though not necessarily about the same axis, with the same period and in the same sense? To answer this question, it suf¿ces to take a look at why Aristotle invokes the theory of homocentric spheres in Metaph. ȁ 8. He has shown that an unmoved mover causes the eternal rotation of the spherical shell in the mass of which the stars are ¿xed. This rotation is not the only eternal motion in the heavens, however, for eternal are also the motions of the ¿ve planets, the Sun and the Moon. Unmoved movers, therefore, must cause these motions, too. How many such movers there might exist in the heavens, however, can hinge on the analysis of the complex motion of each wanderer, and astronomy, the branch of mathematics which is most akin to philosophy, is the discipline we must turn to here (1073a23–b8). Aristotle will thus explain how some astronomers analyze the complex motion each of the seven wandering celestial objects undergoes. But he cautions that this account is intended solely to give us an idea of how the number of unmoved movers in the heavens can be calculated with the aid of astronomy, and to make it possible for the mind to ¿x its attention on a de¿nite multitude. In the future, Aristotle concludes before passing on to the theory of homocentric spheres, people must study the subject for themselves, but also learn from others, most probably as64

See 1.1, and 3.3.1. Cf. the view of Lloyd (1996) 168 cited in ch. 1, n. 109.

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tronomers, and if future generations will come to adopt a different view of celestial motions than the one he will sketch out next, then one will have to respect as much his astronomical authorities as their successors, but side with the more accurate party (1073b8–17).65 If the theory of homocentric spheres Aristotle proceeds to outline is supposed merely to give his audience an idea of how the number of unmoved movers in the heavens can be calculated with help from astronomy, it seems unlikely that his cognitive attitude towards the ability of this theory to shed light on the physical structure of the heavens is the one he adopts towards his answers to the tough questions he attempts to tackle in Cael. B 12. Not only does he not claim with certainty that the heavens consist of as many nested spherical shells of the ¿rst simple body as the Eudoxean or Callippean version of the theory demands after the addition of the unwinding shells, perhaps his own simple device to render the geometric theory physically plausible. It does not even seem to him that this can be the case. Otherwise, it is hard to explain why he cautions his audience that the sketch of the theory of homocentric spheres he is about to give is meant to be just an example of how the number of unmoved movers in the celestial realm of the cosmos can be calculated from what contemporary astronomy says about the motions of the planets, the Sun and the Moon (cf. Simp., in Cael. 505.27–506.8 [Heiberg]). In her or his discussion of the nature of spacetime, a metaphysician will touch upon the issue of whether spacetime has four or more dimensions, and it is conceivable that certain theories of physics will be mentioned within this context, according to which spacetime does possess more than four dimensions. Versions of string theory with a spacetime of ten or eleven dimensions can be given as illustrative examples in order, as Aristotle would say, to help one ¿x their attention on a de¿nite number of spacetime dimensions.66 However, the metaphysician need not simply suspend judgment about whether the picture of the fundamental level of physical reality painted by string theory is true or false. To him or her, this picture might very well seem far from being the case, given that string theory, despite its having been studied intensely for a considerable period of time, has failed to make any testable predictions, and is totally cut off from experiment.67 Aristotle’s unwillingness to believe that a physical model of the heavens based on the theory of homocentric spheres might be even approximately true can be plausibly assumed to result from his awareness that this theory cannot reproduce so many basic celestial phenomena that if we employ it in physics to understand 65

Aristotle’s remark about accuracy is censured by Lloyd (1996) 182 as a disclaimer which does not cut much ice, on the ground that Aristotle prefers to drop the extra spheres for the Sun and the Moon introduced by Callippus into the original version of the theory of homocentric spheres due to Eudoxus, a preference which in Lloyd’s opinion suggests that Aristotle “may be seriously out of his depth, in a way that shakes one’s con¿dence in his ability, indeed, to judge whose model was more accurate”; see the discussion in 3.2.2 on Aristotle and the extra spheres of Callippus, however. For a different interpretation of Aristotle’s reservations from the one proposed below see Bowen (2002b) 163–166. 66 On string theory see e.g. Woit (2007) 146–166 and Smolin (2007) 101–148; for a more demanding account see Penrose (2004) 869–933. 67 Cf. Woit (2007) 208–216; see also Smolin (2007) 149–176 and Penrose (2004) 887–890.

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the structure of the heavens, the result is a celestial realm bearing at best a most tenuous resemblance to ours. When he remarks that we must have recourse to astronomy, the branch of mathematics closest to philosophy, in order to ¿nd out how many unmoved movers there might be in the heavens from the analysis of the complex motion of each planet, the Sun and Moon, in effect he reminds his audience of the af¿nity between astronomy and philosophy, physics in particular, as a warning. Whether the answer we will get to the questions with which our concern is here merits even provisional acceptance cannot but hang on whether the astronomical theory to which we can have recourse, i.e. the theory of homocentric spheres, is a geometric model of the heavens suf¿ciently faithful to the phenomena observed in this cosmic realm for physics to meaningfully built on. Observing in Ph. B 2 that astronomy is among “the physical branches” of mathematics, Aristotle adds that this is so because astronomy is a sort of inverse geometry. Geometry can only be understood to deal with abstractions from physical reality, whereas astronomy takes the abstractions of geometry to be models of physical reality, injecting them back, as it were, to where they ultimately came from (194a7–12). In a given astronomical modeling of physical reality, the kinship of astronomy with physics is manifested as a close enough ¿t between model and the actual world. It is on the existence of such a ¿t that the worth of this modeling to physics depends. Aristotle, as seen above, was aware that the planets, the Sun and the Moon move eastwards against the backdrop of the zodiacal constellations at variable speeds, and since he mentions in Metaph. ȁ 8 the modi¿cations by Callippus to the original version of the theory of homocentric spheres, he certainly also knew about the theory’s inability to account for this phenomenon, though Callippus had tried to attack the problem in the case of the Sun and the Moon. Thanks, moreover, to the decision of Simplicius to quote from Sosigenes extensively, we know that in his lost treatise Physical Problems Aristotle brought a dif¿culty against the theory of homocentric spheres from the fact that the planets do not always appear to move at the same distance from the Earth and the center of the cosmos. For within the framework of either version of the theory, this phenomenon, too, is not obtainable. Concerning the variation in the distance of the planets from the Earth, Sosigenes says the following (in Cael. 505.21–27 [Heiberg] = Arist., fr. 211 [Rose]): 

4SP{QEVGSN K‡V ± /Y^MOLR¶N KR[Vf^[R QäR EºXŸR JEfRIXEM, ²PMK[VÏR Hä ÇN SºO EeWULX¢N S½WLN HM‡ X¶ ƒKETŠR QŠPPSR XŸR TIVi EºX¶ X¶ Q{WSR zR XÚ TERXi XÏR WJEMVÏR EºXÏR U{WMR· HLPSl Hä OEi %VMWXSX{PLN zR XSlN *YWMOSlN TVSFPœQEWM TVSWETSVÏR XElN XÏR ƒWXVSP³K[R ¹TSU{WIWMR zO XSÁ QLHä hWE X‡ QIK{UL XÏR TPERœX[R JEfRIWUEM. S¼X[N Sº TERX„TEWMR ›V{WOIXS XElN ƒRIPMXXS»WEMN, O‰R X¶ ±QSO{RXVSYNS½WENXÚTERXiTIViX¶Q{WSREºXSÁOMRIlWUEMzTLK„KIXSEºX³R. Polemarchus of Cyzicus seems to have been aware of it, but did not consider it important on account of its being not observable (?), for he liked the idea that the spheres themselves are so placed within the cosmos as for their centers to coincide with its middle. Aristotle, too, knew of it, for in his work Physical Problems he raises another dif¿culty with the hypotheses

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of the astronomers from the fact that the magnitudes of the wandering celestial objects do not appear to be [always] equal.68 Therefore, he was not perfectly satis¿ed with the homocentric spheres, though their being centered on the middle of the cosmos and rotating about it won him over.69

If Aristotle were aware of the limitations of the theory of homocentric spheres but hoped for insights from this theory into the structure of the heavens, he would not differ at all from the Platonists who adopted blindly the Timaeus theory of the elements, and whom he blames in Cael. ī 7 for discoursing about phenomena without speaking in accordance with the phenomena at issue (306a5–7). What these people lose sight of is, in his view, the basic truth that as the goal of various branches of productive knowledge is the making of artifacts, so the goal for physics is to give a full causal explanation of phenomena presenting themselves regularly and undoubtedly to the senses (306a16–17). This is just what Aristotle himself would lose sight of if he thought that physics, based on the theory of homocentric spheres, could come to understand the organization of the heavens and the mechanisms that are responsible for the production of the various celestial motions other than the diurnal rotation. In Metaph. B 2 Aristotle might hint at the inability of the theory of homocentric spheres to reproduce the shapes of the paths of successive planetary retrogradations (997b34–998a6):70 

%PP‡QŸR SºHäXÏREeWULXÏR ‰R IhLQIKIUÏR SºHäTIVi X¶R SºVER¶R š ƒWXVSPSKfE X³RHI. S½XI K‡V Ed EeWULXEi KVEQQEi XSMEÁXEf IeWMR SgEN P{KIM ± KI[Q{XVLN (SºUäR K‡V IºU¾ XÏR EeWULXÏR S¼X[N SºHä WXVSKK»PSR· …TXIXEM K‡V XSÁ OER³RSN Sº OEX‡ WXMKQŸR±O»OPSNƒPP’ ÊWTIV4V[XEK³VEN}PIKIRzP{KG[RXS¾NKI[Q{XVEN), S½U’ Ed OMRœWIMNOEi|PMOINXSÁSºVERSÁ´QSMEMTIViÐRšƒWXVSPSKfETSMIlXEMXS¾NP³KSYN, S½XIX‡WLQIlEXSlN†WXVSMNXŸREºXŸR}GIMJ»WMR. On the other hand, astronomy would be neither about sensible lines nor about this ouranos. For neither are sensible lines such as those a geometer’s proofs are concerned with (since nothing sensible is as straight or circular, given that a ruler touches a circle not at a point but as Protagoras used to say taking exception to the geometers), nor are the motions and helixes of the ouranos such as those about which astronomy gives proofs.

The helixes mentioned at the end of the passage are obviously curves traced by celestial motions, and they are sensible lines, such as those mentioned at the beginning of the quote. To show that astronomy can be thought not to deal with the X‡QIK{ULXÏRTPERœX[Ris best understood as a reference not only to the magnitudes of the brightness of the planets but also to the magnitude of the apparent diameter of the Moon. Pace Mendell (2000) 127, nothing suggests that only one of these phenomena is meant here. On changes in brightness as changes in size see Bowen (2002b) 161. 69 Lloyd (1996) 179–180 does not take into account this interesting testimony, blaming Aristotle for making no reference in Metaph. ȁ 8 to “how to deal with the Achilles’ heel of concentric theory, the apparent variation in the distances of the non-¿xed stars, as judged by their varying brightness and apparent diameter”; nor does Bowen (2002b) 161–162. 70 The context is a discussion about whether mathematical objects are a distinct class of existents between non-sensibles, such as the Platonic forms, and sensibles. 68

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heavens we see, Aristotle argues ¿rst that since this science brings geometry to bear on the study of celestial motions, it does not actually deal with the curves we see celestial motions trace out, for these curves are sensible, but as Protagoras had pointed out, the lines geometry studies differ from sensible lines. Moreover, Aristotle goes on, the curves we see celestial motions trace are not similar to the curves astronomy studies. If he is not saying the same thing twice, dissimilarity here is a difference between the geometric models of celestial motions which astronomers study and the features of the actual celestial motions themselves that is independent of very broad considerations such as those of Protagoras. Speci¿c to astronomy, it is observationally con¿rmed in each particular case, and is assumed to offer a further reason, besides the Protagorean argument, for the view that this science does not really deal with the heavens we see. Aristotle calls the irregular twists and turns of the intestines “helixes” (see PA ī 14, 675b22–27). In our context, this term might well be employed for the lines traced by the planets as they circuit the zodiac, moving mainly eastwards but periodically exhibiting retrograde motion, whose episodes are unevenly spaced around the zodiac, along looped or zigzag paths.

3.7. CONCLUSION The upshot of the above is that even if Aristotle believed that all celestial motions would eventually be shown to be really uniform and circular, since the theory of homocentric spheres could not show how the observed lack of uniformity of speed in the zodiacal motion of the planets, the Sun and the Moon, and of circularity in the zodiacal motion of at least the planets, could epiphenomenally arise from a combination of a number of perfectly circular and uniform motions, he thought best to simply view as real the observed zodiacal motions of the seven wandering celestial objects. Originally, when Aristotle thought of these seven celestial objects as being made out of, and also moving through, ¿re, he believed that each of them was carried round westwards by the diurnal rotation of the spherical shell of the ¿rst simple body encompassing the rest of the cosmos, and simultaneously pursued at a slower speed its own course against the background of the stars in the opposite direction, its soul both propelling and guiding its zodiacal motion. Later on, however, when he reached the conclusion that the ¿rst simple body was the only simple body in the heavens, there was no need any more to assume that an action on the Moon, the Sun and the planets, due to which each participated in the diurnal rotation, reached down from the outermost layer of the cosmos, via the medium of the simple body which surrounded these objects, and through which they all moved eastwards. For the wandering celestial objects were now parts of the outermost layer of the cosmos, probably very far below the other and much more populous group of bright parts of this layer–the stars–and their diurnal rotation was thus the natural motion of the ¿rst simple body, but “passively” so–just as the diurnal rotation of e.g. the second (counting from the outside) spherical shell of the

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¿rst simple body in the deferent system hypothesized for a wandering celestial object in Metaph. ȁ 8 is a “passive” natural motion of the ¿rst simple body (for the distinction between “active” and “passive” natural motion see ch. 1, n. 112). However, the blatant lack of circularity in the zodiacal motion of at least the ¿ve planets did not square with the conception of this motion as “active” natural motion of the ¿rst simple body, whose speed and direction was regulated by the guiding soul of the planet (see also the end of 1.5). Aristotle’s conclusion that the ¿rst simple body was the sole ¿ller of the heavens, and so the constituent matter of all celestial objects, entailed a radical change in the properties of this simple body at a certain distance from the center of the cosmos. He had to assume that for some reason many parts of the spherical shell of the ¿rst simple body near its outer surface stood out as spherical objects, the stars, all of them immovable relative to the surrounding mass whose natural motion was the diurnal rotation. Closer to the center of the cosmos, seven parts of the ¿rst simple body somehow also stood out from their surroundings as seven additional globular objects–the ¿ve planets, the Sun and the Moon–each following the diurnal rotation of its surroundings, as if it were a star, but also moving through it at a slower speed and oppositely (in the case of the planets, only principally so). When the ¿rst simple body had been introduced as the constituent matter of the cosmic envelope, and of those celestial objects that were inside it, Aristotle had assumed local changes in its properties–in its parts that were the stars. When he eventually came to believe that the ¿rst simple body was the only simple body in the heavens, “the upper body”, positing that its properties also changed locally in a radically different way with distance from the center of the cosmos had some troubling consequences (see also ch. 2, n. 65). In Cael. B 7, translated above at the beginning of 2.1, where Aristotle clearly assumes, unlike, as I have argued, in the main bulk of the de Caelo but in line with his view in the later Meteorologica, that the ¿rst simple body is the only simple body making up the heavens, he says that “each celestial object is carried round in the sphere” (289a28–29). If Aristotle is understood literally, what he is implying here is that the heavens are a single, diurnally rotating spherical shell of the ¿rst simple body.71 The existence of a single spherical shell of the ¿rst simple body in the cosmos is clearly hinted at again immediately next, when Aristotle remarks that “the air below the sphere of the circularly moving body is necessarily heated because of the rotation of the sphere, and especially where the Sun happens to be ¿xed right above” (289a29–32). That the Sun is here said to be ¿xed is not surprising. Aristotle is here interested in the Sun’s motion in a single day. As far as this motion is concerned, the Sun can be considered to be rigidly ¿xed in the spherical shell of the ¿rst simple body, as if it were one of the stars. Nothing in Aristotle’s physics dictates the Metaph. ȁ 8 articulation of the existing mass of the ¿rst simple body into a multitude 71

Cf. Easterling (1961) 146–147, who, though, thinks that in the de Caelo the ¿rst simple body makes up the planets, the Sun and the Moon and also ¿lls up their realm.

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of concentric spherical shells rather than the more straightforward one that seems to be implicit in Cael. B 7. The notion that of all the parts, into which the mass of the ¿rst simple body is structured, the seven small ones that are the Sun, the Moon and the planets plow through the main one as they move round the center of the cosmos, opposite to the main part’s rotation, is not problematic. For Aristotle did not consider the ¿rst simple body to be solid. According to Cael. B 4, the farther away from the center of the cosmos a simple body, the greater the degree of its subtlety, whence it follows that the ¿rst simple body, which is found beyond ¿re, is very much subtler than water, air and even ¿re itself (287b14–21): 

t3XM QäR SÃR WJEMVSIMHœN zWXMR ± O³WQSN, H¢PSR zO XS»X[R, OEi ´XM OEX’ ƒOVfFIMER }RXSVRSN S¼X[N ÊWXI QLUäR QœXI GIMV³OQLXSR }GIMR TEVETPLWf[N QœX’ †PPS QLUäR XÏR ?TEVA šQlR zR ²JUEPQSlN JEMRSQ{R[R. z\ ÐR K‡V XŸR W»WXEWMR IhPLJIR, SºHäR S¼X[ HYREX¶R ±QEP³XLXE H{\EWUEM OEi ƒOVfFIMER ÇN š XSÁ T{VM\ WÉQEXSN J»WMN· H¢PSR K‡V ÇN ƒR„PSKSR }GIM, OEU„TIV ¼H[V TV¶N K¢R, OEi X‡ TPIlSR ƒIi ƒT{GSRXE XÏRWYWXSfG[R. The above arguments have made it clear that the cosmos is spherical, and so accurately rounded that nothing made by our hands, or visible to us, can be compared to it. For none of the constituents making up any such thing can take on as uniform and accurate a shape as does the nature of the simple body that envelops the other simple bodies, given the evident fact that, as the distance of the simple bodies from the center of the cosmos increases, the subtler their texture becomes, by analogy to what holds true of earth and water.

APPENDIXES 1. “The double motion” of the Sun in GC B 10 A double motion is mentioned in GC B 10, 337a7–15, as causing the constant transformation of the four traditional simple bodies into one another. What Aristotle says not many lines above, in 336a31–b2, gives the impression that this double motion is not the Sun’s diurnal motion plus its annual motion in the ecliptic but its periodic approach to a place on the surface of the Earth and its subsequent retreat, which are conceived of as phenomena of the annual motion in the ecliptic. This impression is reinforced by the fact that 336a31–b2 opens with the emphatic statement that the Sun’s annual motion in the ecliptic, not the diurnal rotation of the cosmos, in which the Sun participates, is responsible for the substantial change perpetually occurring in the cosmos, and thus for the constant change of the four traditional simple bodies into one another that underpins it. However, what Aristotle means in this passage seems to be that the diurnal rotation of the cosmos is not to be posited as the sole cause of the explanandum. He stresses the continuity of the Sun’s being carried towards, and then away from, a part on the surface of the Earth, but in 336b3–4 he speaks of the diurnal rotation of the cosmos as being responsible for it. He thus leaves no doubt that he does take into account here the diurnal rotation. Otherwise, he could not say of the Sun’s approach to, and its ensuing motion away from, a place on the Earth that it is continuous due to the diurnal rotation. The Sun is carried in the course of a year ¿rst towards a part of the surface of the Earth, and then away from it, not only by its annual motion in the ecliptic but exactly on account of the fact that this motion is combined with the much faster diurnal rotation. Thus, for a place in the northern terrestrial midlatitudes, the Sun reaches its highest point in the sky near the zenith at summer solstice, when the circle it describes due to its diurnal motion coincides with the tropic of Cancer, but as far away from the zenith as is possible for it at winter solstice, when the circle of its diurnal motion will coincide with the tropic of Capricorn. Any doubts one might have that the double motion in 337a7–15 is the combination of the Sun’s annual motion with its much faster diurnal motion are dispelled by Cael. B 3, esp. 286b1–4.1

2. How can the Sun act frictionally on air? A solution to the dif¿culty is to assume that the matter out of which the celestial objects are constituted, and in which they move, is intermingled with ¿re and air.

1

See also the brief comment in Gill (1991a) 68, but contrast Williams (1982) 187–191.

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Cf. the prefatory note to Cael. B 7 in Guthrie (1939) 176–179, who tentatively refers the reader to Mete. A 3, 340b6–10, for a possible hint at the presence of air and ¿re in this matter, and Thorp (1982) 115–118, who cites the same passage. In it Aristotle says: 

8¶QäRK‡V†R[OEiQ{GVMWIPœRLN|XIVSRIREMWÏQ„JEQIRTYV³NXIOEiƒ{VSN, Sº QŸRƒPP’ zREºXÚ KIX¶ QäROEUEVÉXIVSRIREMX¶H’ £XXSRIePMOVMR{N, OEiHMEJSV‡N }GIMR, OEiQ„PMWXE¯OEXEPœKIMTV¶NX¶Rƒ{VEOEiTV¶NX¶RTIViXŸRK¢RO³WQSR

 It is our belief that the upper body extending as far as the Moon is different from both air and ¿re, but in it there are degrees of purity and cleanliness, and it is inhomogeneous, and especially where it approaches the air and the region of the cosmos around the Earth.

Philoponus, in Mete. 30.8–31.16 (Hayduck), understands X¶ †R[ OEi Q{GVM WIPœRLNWÏQEas the special kind of heavenly matter out of which the celestial objects are made, according to Aristotle, and through which they move, and from his comments we learn that Alexander of Aphrodisias shared this view. Cf. the commentary by Olympiodorus, in Mete. 28.12–26 (Stüve), who also refers to Alexander. However, as both Philoponus and Olympiodorus make clear, Alexander denied that Aristotle assumes in the passage under discussion here the commingling of the celestial matter with the traditional simple bodies. There can be no doubt, moreover, that X¶†R[OEiQ{GVMWIPœRLNWÏQErefers to “the atmosphere”, whose uppermost boundary is (approximately) a sphere with the orbit of the Moon around the Earth as a great circle (see 1.3.2). Air predominates near the Earth’s surface, where it forms the lower atmosphere, ¿re for the most part rushing naturally up as soon as it is generated from the mass of the Earth, towards the periphery of the cosmos, and accumulating in the upper atmosphere, where it predominates. The highest layer of the upper atmosphere is pure ¿re (the lower atmosphere is bounded by a sphere whose radius extends from the Earth’s center to the tops of its highest mountains, above which the formation of clouds is impossible: cf. Mete. A 3, 340b32–36). Below this outermost layer of the upper atmosphere, ¿re becomes more “contaminated” with air the closer it is to the lower atmosphere and the surface of the Earth.2 What Aristotle says in Mete. A 3, 340b6–10, must be understood in the context of his conclusion not many lines below, in 340b29–32:  

8SÁQäR SÃRzRXÚ†R[X³T.QŸWYRfWXEWUEMR{JLXE»XLR¹TSPLTX{SREeXfERIREM, ´XMSºO}RIWXMRƒŸVQ³RSRƒPP‡QŠPPSRSmSRTÁV. This, therefore, must be assumed to be the reason why clouds do not form in the upper place, i.e. that in it there is not just air but rather something more akin to ¿re.

Undoubtedly, Aristotle employs here the expression “upper place” for the upper atmosphere, not for the heavens. See also Ideler (1834–36) vol. 1, 346. 2

For the constant generation of ¿re from the Earth see 1.2.5. For Aristotle’s claim that “the atmosphere” is “different from both air and ¿re” see ch. 2, n. 45 and 46.

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3. Alternative solutions A hint that Aristotle had the concept of a wave propagating through matter is perhaps to be detected in Div. Somn. 2, 464a6–11: 

t;WTIVK‡V´XEROMRœW:XMX¶¼H[V¡X¶Rƒ{VE, XSÁU’ |XIVSRzOfRLWI, OEiTEYWEQ{RSY zOIfRSY WYQFEfRIM XŸR XSME»XLR OfRLWMR TVSM{REM Q{GVM XMR³N, XSÁ OMRœWERXSN Sº TEV³RXSN, S¼X[NSºHäRO[P»IMOfRLWfRXMREOEiEhWULWMRƒJMORIlWUEMTV¶NX‡N]YG‡N X‡NzRYTRME^S»WEN For, as when something sets in motion water or air, this moves something else and, although the original mover has stopped its activity, it happens that this kind of motion extends up to a certain point without the initial mover being present any more, likewise nothing prevents a certain motion and perception reaching dreaming souls.

Waves could be transmitted through the celestial matter surrounding the Sun, a Àuid which is much subtler than ¿re and air, let alone water, as Aristotle declares in Cael. B 4, 287b14–21. The motion of the Sun can thus be thought to produce in the air internal friction by generating waves in the Àuid medium surrounding the Sun, which are transmitted first to the ¿re under the Sun, and then to the air. According to Simplicius, in Cael. 440.23–35 (Heiberg), Alexander of Aphrodisias attempted to explain how the Sun can act on the air by pointing out that the Sun can set dry material on ¿re without affecting in the same manner the intervening air, just as the torpedo ¿sh was said to be able to deliver a shock through ¿shing nets, which do not have this power themselves: so it is not surprising if the Sun can affect the air in some mysterious manner without being actually in contact with it–the Sun transmits to the air “qualities” through the medium of heavenly matter separating the two, which functions like “a carrying vessel”. Simplicius denies that the celestial matter can transmit anything. The commentator is in favor of an alternative solution: the Sun emits material rays, which can pass unhindered through the extremely subtle celestial matter separating it from the air, being subtle themselves almost to the point of immateriality, but also through the air itself via some narrow passages in this simple body; reÀected “at equal angles” by solids–whether droplets of water only, and particles of earth which are suspended in the air, or also objects on the Earth the commentator does not clarify–these rays trap air, especially if they are reÀected “back upon themselves”, compress and set it in motion, with the result that heat issues from friction (in Cael. 440.35–441.21 [Heiberg]). But the doctrine of “corporeal” light is foreign to Aristotle.

4. Which celestial object(s) can heat the Earth? In Cael. B 7 Aristotle seems to think that, of all celestial objects, only the Sun can heat the Earth. It is quite close to the Earth, and its motion is suf¿ciently fast. The Moon is closer to the Earth than the Sun, but its motion is slow; the stars move fast enough, but are extremely far away from the Earth.

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This is not explained in Cael. B 7, but in Mete. A 3, 341a12–30. Aristotle here speaks of the Moon as being slower than the Sun perhaps because each of these two celestial objects participates in the diurnal rotation, but its diurnal motion is counteracted by a slower motion in the opposite direction, with a rate peculiar to each.3 If we consider only this motion, independently of the diurnal rotation, the Moon is faster than the Sun, but if we take into account the diurnal rotation, too, it is the Moon that appears to move around the Earth more slowly.4 All planets known in antiquity–Mercury, Venus, Mars, Jupiter, Saturn–appear to also move opposite to the diurnal rotation in which they participate, each at a different pace and with a different period allowing us to put them in order of relative distance from the Earth, as Aristotle himself is well aware (Cael. B 10), with the exceptions of Venus and Mercury, which require as much time as the Sun does, a year, to complete a trip round the Earth, traveling opposite to the diurnal rotation. However, since all planets turn out to be farther out from the Earth than the Moon, it is conceivable that Aristotle places all of them, Venus and Mercury included, suf¿ciently beyond the Sun for any of them to heat the Earth. This might be the reason why in Mete. A 3 Aristotle sees no need to compare the speed of any planet with the Sun’s and the Moon’s, although he knows that all planets are, like the Sun and the Moon, nearer to the Earth than the stars.5 If Aristotle hints in Cael. B 3, 286b6–9, that the Earth is heated not only by the Sun but also by the Moon and all of the planets, or by the Moon and only two planets, Venus and Mercury (assuming that in Cael. B 3 he tacitly adopts the other of their two possible orderings relative to the Sun, locating them between it and the Moon), then his views about which celestial objects can heat the Earth might have changed after he wrote Cael. B 3–unless, of course, in Mete. A 3 his point is simply that only the Sun can heat the Earth to such an extent that the effect is perceptible by us. In his biological works, there are isolated hints that the Earth is heated by the Moon.6 The notion of the Earth being heated by the Moon and the five planets, to a different extent by each depending on the distance of the luminary, would be particularly attractive to Aristotle. Cael. B 3 makes it clear that the heating of the Earth by the Sun, insofar as it powers the perpetual transformation of the four traditional simple bodies into one another, and thus all substantial change in the cosmos, is the ¿nal cause of the Sun’s existence: if the Earth were heated by the Moon and the planets, too, the heating of the Earth would account teleologically for the existence of all those luminaries, but not of the stars, too, of course. Be that as it may, Aristotle seems to regard the Sun as the sole driver of all substantial change also in Metaph. ȁ 5, 1071a13–17.7 However, an interesting 3 4 5 6 7

See 1.3.3 and 1.3.5. See Pl. Ti. 38e3–39b2, and Lg. 7, 822a4–c5; see also the analysis of the ¿rst of these two passages in Heath (1981) 169–170. Cf. ch. 2, n. 65. On the relative distances of the celestial objects from the Earth see 2.8.4. See GA B 4, 738a18–22, and ǻ 2, 767a3–8. Cf. Ph. B 2, 194b13.

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passage in GA ǻ 10, 777b16–778a9, names unambiguously the Moon alongside the Sun as a cause of the Earth’s heating, and thus of the constant substantial change in the cosmos:8 it is exactly the fact that the Moon shines with light borrowed from the Sun which is singled out by Aristotle here as an explanation of the crucial cosmological function performed by the Moon. In the cosmos, he says characteristically, the Moon plays the role of a smaller Sun. 5. Is the ¿rst simple body perceptible and “corporeal”? If the ¿rst simple body is not constituted by two fundamental qualities, one from each of two pairs, as Aristotle assumes in Cael. A 3, then since these qualities are the fundamental tangible qualities, according to GC B 2, 329b15–330a29, it follows from GC B 2, 329b6–10, that the ¿rst simple body is not perceptible, for in this passage Aristotle characterizes perceptible bodies as tangible, and thus the contrarieties that are the principles of perceptible bodies as tangible, too.9 Perhaps Aristotle’s view is that the ¿rst simple body is perceptible not qua tangible, which is the case with the four Empedoclean simple bodies that interest him in GC B 2, but only qua visible, or colored–put differently, insofar as the fractions of it which make up celestial objects are, in whatever manner, capable of actualizing “the transparent”, in which they are, i.e. turning it into light, and “moving” it, so as to produce their colors seen in this light.10 After noting in GC B 2, 329b10–13, that contrarieties perceived by sight or taste do not constitute any element (i.e. simple body), unlike those perceived by touch, despite the primacy of sight over touch, and thus of the former’s object over the latter’s, i.e. of color over tangible qualities, Aristotle says that being visible is an affection of a tangible object not qua tangible, which is what interests him in the context of GC B 2, but in virtue of something else: this is tacitly assumed to be irrelevant to the discussion in GC B 2, although it is acknowledged to be naturally prior (392b14–15). In this paraphrase, “tangible object” need not be assumed to be an oversight on Aristotle’s part for “perceptible object” in order for the obvious view that “being visible”, not just “being tangible”, means “being perceptible” to be attributed to him. The primacy, moreover, of sight and its object over touch and its object suggests that the conception of the ¿rst simple body as perceptible only insofar as it is visible, in contrast to the four traditional simple bodies, over which it enjoys primacy, and whose perceptibility is primarily due to their tangibility, would be attractive to him. But even if the problem of the perceptibility of the ¿rst simple body admits of a probable solution, there remains that of its corporeality.

8

Aristotle mentions the synodic month (the period of lunar phases) as regulating the heating of the Earth. 9 Cf. Wildberg (1988) 98–99. 10 For Aristotle’s interrelated de¿nitions of light and color see de An. B 7.

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Aristotle does not explain what it is that endows the four traditional simple bodies with corporeality. Perhaps it is their being combinations of two fundamental tangible qualities, corporeality emerging when a pair of such qualities combine.11 If so, what could account for the corporeality of the ¿rst simple body is not clear. See also ch. 1, n. 114. 6. The constituent qualities of the traditional simple bodies in Cael. A 3 In Cael. A 3 Aristotle does not explicitly mention the qualities of the four traditional simple bodies. In his own words (270a12–18): 

D3QSf[NH’ I½PSKSR¹TSPEFIlRTIViEºXSÁOEi´XMƒK{RLXSROEi†JUEVXSROEiƒREY\äN OEi ƒREPPSf[XSR, HM‡ X¶ KfKRIWUEM QäR …TER X¶ KMKR³QIRSR z\ zRERXfSY XI OEi ¹TSOIMQ{RSY XMR³N, OEi JUIfVIWUEM ÇWE»X[N ¹TSOIMQ{RSY X{ XMRSN OEi ¹T’ zRERXfSY OEi IeN zRERXfSR, OEU„TIV zR XSlN TVÉXSMN IhVLXEM P³KSMN· XÏR H’ zRERXf[R OEi Ed JSVEizRERXfEM It is equally reasonable to also assume that it [i.e. the ¿rst simple body] is ungenerated and indestructible and subject neither to increase nor change, for everything that comes to be does so from a contrary and a substrate, and similarly perishes both into a contrary and because of a contrary, while something persists as a substrate, as has been said in our ¿rst inquiries. However, the motions of contraries are contrary, too.

It is usually assumed that in this passage Aristotle calls “our ¿rst inquiries” his discussion in Ph. A 7, where the contraries are not each of the two pairs of qualities making up the Empedoclean simple bodies, but form and privation.12 But there is no reason why Aristotle’s “¿rst inquiries” mentioned here cannot be his discussion in GC B 4, where he brings the principle “generation is into contraries and out of contraries” (331a14) to bear on the explanation of how the traditional simple bodies can be generated from one another after he has analyzed them into contrary component qualities–the connection between this reduction and the principle, which is arrived at in Ph. A 7, is stated in 331a14–20. As Gill (1991a) 75–82 has shown, the principles required for all changes according to Ph. A 7–substrate or matter, form and privation–apply to the transmutation of the Empedoclean simple bodies into one another, whereby the Ph. A 7 pair of contraries collapses onto each of the two pairs of fundamental contrary qualities, out of which these four simple bodies are assumed to arise. 7. Which celestial objects is Cael. B 8 about? It is usually assumed that in Cael. B 8 Aristotle is concerned not only with the stars but also with the ¿ve planets, the Moon and the Sun.13 Simplicius, on the con11

I agree with Gill (1991a) 75–78 and 243–252 that in Aristotle’s physics there is no “prime matter”; she denies, though, that the traditional simple bodies consist of properties. 12 See Wildberg (1988) 80–85 and Leggatt (1995) 182. 13 See Guthrie (1939) 182–183 n. a, Leggatt (1995) 238–239 and Jori (2002) 461 n. 138.

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trary, thinks that in Cael. B 8 Aristotle deals exclusively with the stars. The commentator, moreover, leaves no doubt that this view was shared by Alexander of Aphrodisias.14 In Cael. B 8, 289b32–33, Aristotle reaches the following conclusion: 

0IfTIXEM XS¾N QäR O»OPSYN OMRIlWUEM, X‡ Hä †WXVE ›VIQIlR OEi zRHIHIQ{RE XSlN O»OPSMNJ{VIWUEM

 It remains that the circles are in motion and that the stars do not move themselves but do so being ¿xed in the circles.

Although the nouns astron and astƝr can mean either “star” or, generally, “celestial object”, be it a star, a planet, the Sun or the Moon, Aristotle’s reference not many lines below, in 290a18–20, to a prominent difference between the stars and the planets makes it clear that ta astra are the stars in the passage just translated: 

t3TIVEhXMSRhW[NOEiXSÁWXfPFIMRJEfRIWUEMXS¾NƒWX{VENXS¾NzRHIHIQ{RSYN, XS¾N HäTP„RLXENQŸWXfPFIMR Perhaps this also provides the explanation of why the ¿xed stars appear to twinkle, but the planets do not.

ta astra are, thus, the ¿xed stars in the opening lines of Cael. B 8, where Aristotle lays out the only three possible alternatives, among which he has to choose in this chapter (289b1–4): 

)TIi Hä JEfRIXEM OEi X‡ †WXVE QIUMWX„QIRE OEi ´PSN ± SºVER³N, ƒREKOElSR žXSM ›VIQS»RX[RƒQJSX{V[RKfKRIWUEMXŸRQIXEFSPœR, ¡OMRSYQ{R[R, ¡XSÁQäR›VIQSÁRXSN XSÁHäOMRSYQ{RSY Since it is observed that both the stars and the whole of the ouranos move, this motion necessarily happens because either both are stationary, or both move, or one is stationary and the 15 other moves.

The ¿rst of the senses of ouranos that are distinguished in Cael. A 9 (“the body in the mass of which the stars are ¿xed”, “the outermost stratum of the cosmos”) is clearly the one in which this noun is used here, even if in Cael. B 8 the ¿rst simple body is assumed to also ¿ll the rest of the heavens.16 In the second part of Cael. B 8, it is argued that ta astra do not move “on their own”, but as parts of a deferent spherical shell of the ¿rst simple body, from the facts that they are spherical, lacking means for locomotion, i.e. without appendages, unlike what is the case with the animals, and do not roll, as Aristotle infers 14

Simp., in Cael. 444.18–20 and 27–29, 448.27–449.2, 451.7–13 ( Heiberg). See also the comments in Moraux (1965) 160–161, n. 1 and 2 on page 73. 15 The stars are considered here a single thing–a multitude. 16 See ch. 2, n. 41; for the senses of ouranos see 2.2.3. The circles in Cael. B 8, 289b30–33, are the diurnal circles traced by the stars, here thought of as rigid rings of wire, like those in an armillary sphere, each of which carries round a star attached to it, as they all rotate synchronously. Of course, the stars are not literally carried round as a load; see 1.3.8.

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from the Sun and Moon, the only celestial objects with an observedly spherical shape (290a7–b11). In this context, ta astra is employed in the sense “celestial objects”. We need not conclude, however, that in Cael. B 8 Aristotle is concerned with the stars as well as with the planets, the Sun and the Moon. What the Sun and the Moon teach us about celestial objects tout court can very well lead us to a truth about the stars that does not apply necessarily to the planets, the Sun and the Moon–the principle “what holds of one celestial object holds of all” that Aristotle invokes in Cael. B 11, 291b17–18, is to be applied with due caution. The fact that all celestial objects are not animal-like, independent locomotors does not entail that the planets, the Sun and the Moon are all carried round the zodiac just as the stars revolve diurnally, each being part of a rotating shell of the ¿rst simple body, as in the Metaph. ȁ 8 cosmology, which is based on the theory of homocentric spheres.17 8. Aristotle’s “unwinding” spherical shells of the ¿rst simple body Aristotle proposes in Metaph. ȁ 8 that sandwiched between the last spherical shell of the ¿rst simple body in the deferent system for Saturn and the ¿rst one in Jupiter’s deferent system are a number of other spherical shells. It is these extra shells that allow the ¿rst shell for Jupiter to rotate in the same sense and direction, as well as with the same period, as the ¿rst one for Saturn (1073b38–1074a5). The ¿rst of these extra shells rotates about the same axis and with the same period as the fourth shell for Saturn but in the opposite sense, so their rotations cancel out, and a point of the ¿rst extra shell appears to rotate as if it belonged to the third shell for Saturn. Similarly, a point of a second extra shell rotating about the same axis and with the same period as the third shell for Saturn, but again in the opposite sense, appears to spin as if it belonged to the second shell for Saturn. With the addition of a third extra shell, the rotation of Saturn’s second shell is also cancelled out. The rotation of the third extra shell is indistinguishable from that of Saturn’s ¿rst shell, in the mass of which the stars are ¿xed. It is this third extra shell that contains the ¿rst shell of Jupiter, the Jovian counterpart to Saturn’s outermost shell explaining Jupiter’s participation in the diurnal rotation from east to west according to the theory of homocentric spheres.18 Similarly, the systems of deferent spherical shells of the ¿rst simple body for Mars, Mercury, Venus, the Sun and the Moon are sheathed each in a system of “unwinding” spherical shells.19 The function of the unwinding shells is to stop the transmission of motion from the innermost shell in the deferent system of Saturn, Jupiter, Mars etc to the 17

See also the discussion of Cael. B 8 in 1.5. That in Cael. B 8 Aristotle does not presuppose the theory of homocentric spheres had been pointed out in antiquity, by Alexander of Aphrodisias; see Simp., in Cael. 451.7–13 (Heiberg). 18 The outermost shell for Jupiter seems to be redundant, for it rotates indistinguishably from the shell immediately above. A solution to this problem is offered by Beere (2003). 19 Aristotle’s own term, which after him is not used only in this sense; see ch. 1, n. 90.

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outermost shell in the deferent system of Jupiter, Mars, Mercury etc; no unwinding shells are assumed inside the Moon’s deferent system.20 A system of n deferent spherical shells–with the sole exception of the Saturnian system–must be embedded in a system of n-1 unwinding spherical shells, so to the twenty-six spherical shells of the ¿rst simple body required by the theory of homocentric spheres as originally put forth by Eudoxus must be added seventeen more.21

20

But what Aristotle says in Mete. A 3, 340b32–341a9, and A 7, where he presents his theory of comets, seems to require them; cf. Heath (1981) 219. 21 On two homocentric spheres, which rotate about the same axis but oppositely to one another, see the excerpt from Sosigenes’ work On the Unwinding Spheres which is quoted by Simp., in Cael. 499.17–500.14 (Heiberg ) ; cf. Mendell (1998) 181 and (2000) 66–67.

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INDEX OF PASSAGES Alexander of Aphrodisias in Metaph. (Hayduck) 705.39–706.8: 41 n. 94 Anaxagoras DK 59 A 42: 81 Archimedes Aren. (Heiberg) 135.8–136.1: 79 n. 56 136.21–137.6: 81 Archytas of Tarentum DK 47 A 23a: 90 n. 9 Aristarchus of Samos

270a12–35: 31, 57 270b1–5: 57 270b2–3: 25 270b5–16: 57 270b16–25: 60 A 4 270b32–271a5: 120 270b32–271a22: 117 271a5–10: 120 271a10–13: 120 271a13–17: 120 271a17–19: 118, 120 271a19: 118 271a19–22: 120 271a22–33: 117 271a33: 31 A 5 271b26–272a7: 25 n. 40 272b17–273a6: 25 n. 40 272b28–273a6: 78 A 9 278b11–21: 50 n. 1, 59 279a11–18: 24 n. 38

de magn. et dist. Sol. et Lun. Hyp. 2: 79 n. 56 Aristotle APo B 19 100a16: 100 n. 35 Cael.

B 1 283b26–284a2: 70 284a2–11: 70 284a3–6: 32 n. 60 284a11–18: 70, 116 284a11–35: 122 284a11–b5: 109 284a18–27: 66 n. 31, 116 284a18–35: 70 284a27–31: 48 n. 111, 106 284a27–b5: 116 284a35–b5: 70

A 1 268a1–10: 13 n.7 A 2 268b11–13: 64 n. 26 268b17–269a9: 25 269a18–23: 25, 25 n. 40 269b2–13: 26, 54, 55 n. 12 269b13–15: 30 269b13–17: 55, 55 n. 12 269b15–17: 30 A 3 269b20–29: 15 n. 16 270a12–18: 137

B 2 284b6–34: 48 n. 111, 106 284b27–285a10: 122 285a27–31: 122 285b14–33: 123 285b28–33: 56 n. 13 B 3 286a3–7: 11 n. 4, 121 286b1–4: 132 286b1–9: 121 286b6–7: 48 n. 113 286b6–9: 17, 135

146

Index of passages

B 4 286b10–26: 63 286b20: 25 n. 40 286b32–287a5: 63 287a5–11: 63, 66 n. 32 287a11–14: 24 n. 36 287a11–22: 62 n. 24 287a30–b4: 65 287a34–b1: 64 n. 27 287b4–14: 64 n. 29 287b14–21: 49 n. 114, 131, 134 B 5 287b24–28: 11 287b28–288a2: 11 288a2–12: 48 n. 111, 106 B 6 288a13–17: 43, 45, 45 n. 108, 62, 86 288a22–25: 32 n. 60 288a27–b7: 32 288b12–22: 106 n. 43

292a10–14: 98 292a14–17: 11, 54 292a17–22: 99 292a18–21: 48 n. 111 292a22–b1: 100 292b1–10: 100 292b10–13: 100 n. 35, 101 292b13–19: 101 292b19–25: 101 292b25–293a4: 102 292b31–293a2: 110, 111 293a4–11: 40, 67 n. 35, 97, 98 B 14 296a34–35: 48 n. 113 296a34–296b1: 98 n. 32 297a8–30: 15 n. 16, 64 n. 28, 73 n. 48 297b23–298a9: 64 n. 29 297b30–298a9: 80 ī 1 298a24–b8: 68

B 7 289a11–33: 50 289a13–16: 20 289a16–19: 20 289a18–19: 18 289a19–21: 18 n. 26 289a19–35: 18 289a28–29: 130 289a29–32: 18, 130 289a32–33: 18 n. 26 B 8 289b1–4: 138 289b30–33: 138 n. 16 289b32–33: 138 290a5–7: 49 n. 114 290a7–9: 25 290a7–12: 71 n. 41 290a7–b11: 47, 139 290a18–20: 138 B 9 291a9–18: 71 n. 42, 115 291a18–22: 71 n. 42 291a18–26: 115 291a22–26: 48 n. 111 B 10 291a34–b1: 45 n. 108, 93 n. 16 291a34–b10: 48 n. 113, 56, 112

ī 3 302a15–25: 13 n. 8 ī 7 306a5–7: 128 306a16–17: 128 ǻ 4 311a16–29: 31 n. 57 de An. A 1 402a1–7: 102 n. 37 A 2 405a28: 59 n. 17 A 4 408a14–15: 16 409a6: 99 n. 34 B 4 415b8: 102 n. 37 416a6–9: 106 n. 42 B 7 418b3–17: 18 n. 26 ī 4 429a10–29: 42 n. 97 ī 7: 431b17: 42 n. 97 Div. Somn.

B 11 291b17–18: 47, 139 2 464a6–11: 134 B 12 291b24–28: 11, 67, 98 291b28–292a3: 67, 97, 98, 98 n. 31 291b35–292a1: 98 n. 31 292a3–9: 24, 83

GA B 4 738a18–22: 135 n. 6

Index of passages ǻ 2 767a3–8: 135 n. 6

I 1 1053a8–12: 93 n. 16

ǻ 3 768b15–25: 14 n. 15

ȁ 5 1071a13–17: 135

ǻ 10 777b16–778a9: 136

ȁ 7 1072a19–23: 43 1072a19–b3: 41 1072a23: 62 n. 23 1072b3–4: 42 1072b13–24: 41

GC A 6 322b22–25: 14 n. 14 A 7 323b18–324a9: 14 n. 15 324a24–b4: 100 n. 35 A 10 327b20–31: 16 328a23–31: 14 n. 15, 16 B 2 329b6–10: 136 329b10–13: 136 329b14–15: 136 329b15–330a29: 49 n. 114, 136 B 3 330b25–28: 31 n. 55 330b25–29: 18 330b30–331a3: 31 n. 57 330b33–331a1: 14, 14 n. 12 331a3–6: 13 B 4 331a14: 137 331a14–20: 31 n. 57, 137 B 6 333a16–34: 16

147

ȁ 8 1073a23–b8: 125 1073a28–32: 48 n. 113 1073b8–17: 126 1073b32–33: 34 n. 64 1073b32–38: 38, 39, 93 1073b32–1074a12: 41 1073b38–1074a5: 139 1073b38–1074a14: 93 1074a12–14: 41 1074a38–b14: 61 n. 21 ȁ 10 1075a11–25: 42 Mete. A 1 338a20–25: 77 n. 53 A 2 339a11–27: 51 339a12–13: 48 n. 113 339a19–20: 20

Z 7 1032a27–b23: 100 n. 35

A 3 339b2–16: 52 339b16–19: 53 339b17–18: 20 339b19–30: 61 n. 22, 75 339b23: 20 339b27–30: 61 n. 21 339b30–37: 76 339b37: 20 340a1–13: 16, 77 340a11–13: 17 340b6–10: 14, 18, 20 n. 29, 72, 133 340b6–29: 72 340b19–23: 13 340b29–32: 133 340b32–36: 64 n. 29, 133 340b32–341a9: 51 n. 3, 114, 140 n. 20 341a12–30: 18 n. 26, 51, 84 n. 65, 135 341a30–31: 51 n. 3 341a35–36: 18

Z 9 1034a21–25: 100 n. 35

A 4 341b6–22: 18, 72

B 7 334b7: 31 n. 55 334b20–22: 14 n. 15 334b20–23: 15 334b23–29: 15, 16 334b20–29: 14, 14 n. 15, 15 n. 18 B 8 334b30–335a9: 13 B 10 336a15–b24: 17 336a31–b2: 132 336b3–4: 132 337a7–15:13, 17, 122, 132 Metaph. B 2 997b34–998a6: 128 998a6: 99 n. 34

148 A 6 343b28–32: 24, 83 A 8 345a25–31: 81 345b1–5: 81 345b5–9: 81 B 4 360a5–6: 14 n. 12

Index of passages H 5 250a4–7: 108 n. 47 250a9–19: 107 Ĭ 5 256a4–21: 41 n. 95 259a6–13: 43 Ĭ 8 262a12–15: 55 n. 12 262b23–26: 55 n. 12

B 8 365b24–27: 14 n. 12 PA A 5 644b22–35: 12

Ĭ 9 265a27–29: 55 n. 12 265a27–b8: 32 n. 60 Ĭ 10 267a21–b6: 43 267b6–9: 43

ī 14 675b22–27: 129 SE Ph. 34, 184b3–8: 60 n. 20 B 2 193b22–32: 24 n. 36, 113 194a7–12: 113, 127 194b13: 135 n. 7

Fragments

ī 2 202a3–12: 14 n. 14

13 Rose: 61 n. 21 211 Rose: 48 n. 113, 84 n. 65, 127

ī 4 203b22–25: 25 n. 40

[Aristotle]

ī 5 204a34–b4: 25 n. 40

Mech.

ī 6 206a9–29: 25 n. 40 206b20–27: 25 n. 40 206b33–207a10: 32 n. 59

1 849b19–21: 112 8 851b34: 59 n. 17 Mu.

ǻ 4 211a14: 59 n. 17 2 392a23–29: 34 n. 64 ǻ 8 215a25–b12: 112 Pr. ǻ 9 216b26–28: 80 n. 58 217a13–18: 80 n. 58

XVI.9, 915a25–32: 90 n. 9

E 4 228a20–22: 55 n. 12 228a20–b15: 91 n. 10 228b1–11: 55 n. 12 228b15–28: 44, 91 228b15–229a3: 55 n. 12 228b18–19: 45 n. 107 228b21–28: 92 n. 11

Cicero

Z 2 232a25–27: 92

Alm. (Heiberg)

Z 7 237b23–238a19: 92 n. 12 238a20–29: 92

10.4–11.13: 23 20.5–7: 78 20.7–21.6: 81 532.19–533.3: 89 n. 6

H 4 248a13–18: 118 n. 60

Lucullus 127–128: 12 Claudius Ptolemy

Index of passages Cleomedes Cael. (Todd)

22.3–8: 76 n. 51 23.36–24.3: 77 n. 55 30.8–31.16: 133

1.5.1–9: 62 n. 24

in Ph. (Vitelli)

Diogenes Laertius

671.10–672.17: 80 n. 58

8.86: 38 n. 84.

Lucretius

Epicurus

1. 615–622: 25 n. 40

Ep. ad Hdt.

Olympiodorus

56–57: 25 n. 40

in Mete. (Stüve)

Euclid

28.12–26: 133 67.32–37: 82 n. 64

Elementa

Plato

1.12: 25 n. 40

Lg.

Phaen. (Menge)

7 821e7–822d1: 90 n. 8 822a4–8: 27 822a4–c5: 135 n. 4

2.1–6.14: 23 n. 35 Eudemus of Rhodes

10 897e11–898d5: 88 n. 5 899a2–4: 47

Fr. 62 Wehrli: 25 n. 40 R. Geminus Isag.

7 529c6–d5: 90 n. 8 530a4–b4: 45 n. 106

1.19.1–1.21.7: 89 12.1–4: 23 n. 35

10 616e4–617b5: 34 n. 64 617a4–b4: 83

Hesiod

Ti.

Op. 479: 26 564: 26

38c7–d4: 83 38e3–39b2: 135 n. 4 39a5–b2: 27 40a2–b8: 20

Homer

[Plato]

Od.

Epin.

6.41–47: 57 n. 14

982e6–983a6: 76

John Philoponus

Pliny

in Mete. (Hayduck)

N.H.

16.23–25: 60 n. 20

2.95: 58 n. 15

149

150 Plutarch de Facie 923A: 87 n. 3 Simplicius in Cael. (Heiberg) 32.16–22: 40 154.22–29: 124 382.28–32: 71 n. 40 391.23–392.5: 123 n. 63 395.19–396.5: 121 414.30–415.8: 64 440.23–35: 134 440.35–441.21: 134 442.4–12: 18 n. 26 444.18–20: 138 n. 14 444.27–29: 138 n. 14 448.27–449.2: 138 n. 14 451.7–13: 138 n. 14, 139 n. 17 488.10–24: 44 n. 104, 88 488.18–24: 38 n. 85 491.15–492.11: 104 n. 40 492.12–13: 104 n. 41 492.13–17: 107 n. 46 492.21–22: 108 n. 48 492.31–493.11: 38, 44, 87 493.11–20: 34 493.11–494.22: 36 494.23–495.16: 35 497.15–24: 38, 94 497.22–24: 41 499.17–500.14: 140 n. 21 503.10–20: 41 n. 94 504.22–26: 40 505.21–27: 48 n. 113, 84 n. 65, 127 505.27–506.8: 46, 126 551.25–552.7: 69 in Ph. (Diels) 291.21–292.31: 87 n. 3 459.23–26: 25 n. 40 686.22–687.3: 80 n. 58 Theophrastus of Eresus Fr. 165B FHSG: 34

Index of passages

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Franz Steiner Verlag

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64. Anika Strobach Plutarch und die Sprachen Ein Beitrag zur Fremdsprachenproblematik in der Antike 1997. VIII, 258 S., kt. ISBN 978-3-515-07007-2 65. Farouk Grewing (Hg.) Toto notus in orbe Perspektiven der Martial-Interpretation 1998. 366 S., kt. ISBN 978-3-515-07381-3 66. Friedhelm L. Müller Die beiden Satiren des Kaisers Julianus Apostata (Symposion oder Caesares und Misopogon oder Antiochikos) Griechisch und deutsch. Mit Einleitung, Anmerkungen und Index 1998. 248 S., kt. ISBN 978-3-515-07394-3 67. Reinhard Markner / Giuseppe Veltri (Hg.) Friedrich August Wolf Studien, Dokumente, Bibliographie 1999. 144 S., kt. ISBN 978-3-515-07637-1 68. Peter Steinmetz Kleine Schriften Aus Anlaß seines 75. Geburtstages herausgegeben von Severin Koster 2000. X, 506 S., geb. ISBN 978-3-515-07629-6 69. Karin Sion-Jenkis Von der Republik zum Prinzipat Ursachen für den Verfassungswechsel in Rom im historischen Denken der Antike 2000. 250 S., kt. ISBN 978-3-515-07666-1 70. Georgios Tsomis Zusammenschau der frühgriechischen monodischen Melik (Alkaios, Sappho, Anakreon) 2001. 306 S., geb. ISBN 978-3-515-07668-5 71. Alessandro Cristofori / Carla Salvaterra / Ulrich Schmitzer (Hg.) La rete di Arachne – Arachnes Netz

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Beiträge zu Antike, EDV und Internet im Rahmen des Projekts „Telemachos“ 2000. 281 S., geb. ISBN 978-3-515-07821-4 Hans Bernsdorff Hirten in der nicht-bukolischen Dichtung des Hellenismus 2001. 222 S., geb. ISBN 978-3-515-07822-1 Sibylle Ihm Ps.-Maximus Confessor Erste kritische Edition einer Redaktion des sacro-profanen Florilegiums Loci communes, nebst einer vollständigen Kollation einer zweiten Redaktion und weiterem Material 2001. 12*, CVIII, 1153 S., geb. ISBN 978-3-515-07758-3 Roderich Kirchner Sentenzen im Werk des Tacitus 2001. 206 S. mit 4 Tab., geb. ISBN 978-3-515-07802-3 Medard Haffner Das Florilegium des Orion Mit einer Einleitung herausgegeben, übersetzt und kommentiert 2001. VII, 267 S., geb. ISBN 978-3-515-07949-5 Theokritos Kouremenos The proportions in Aristotle’s Phys. 7.5 2002. 132 S., geb. ISBN 978-3-515-08178-8 Christian Schöffel Martial, Buch 8 Einleitung, Text, Übersetzung, Kommentar 2002. 723 S., geb. ISBN 978-3-515-08213-6 Argyri G. Karanasiou Die Rezeption der lyrischen Partien der attischen Tragödie in der griechischen Literatur Von der ausgehenden klassischen Periode bis zur Spätantike 2002. 354 S., geb. ISBN 978-3-515-08227-3

79. Wolfgang Christian Schneider Die elegischen Verse von Maximian Eine letzte Widerrede gegen die neue christliche Zeit. Mit den Gedichten der Appendix Maximiana und der0 Imitatio Maximiani. Interpretation, Text und Übersetzung 2003. 255 S., geb. ISBN 978-3-515-07926-6 80. Marietta Horster / Christiane Reitz (Hg.) Antike Fachschriftsteller Literarischer Diskurs und sozialer Kontext 2003. 208 S., geb. ISBN 978-3-515-08243-3 81. Konstantin Boshnakov Die Thraker südlich vom Balkan in den Geographika Strabos Quellenkritische Untersuchungen 2003. XIV, 399 S., geb. ISBN 978-3-515-07914-3 82. Konstantin Boshnakov Pseudo-Skymnos (Semos von Delos?) 7DDMULVWHUDWRXC3RYQWRX Zeugnisse griechischer Schriftsteller über den westlichen Pontosraum 2004. X, 268 S., geb. ISBN 978-3-515-08393-5 83. Mirena Slavova Phonology of the Greek inscriptions in Bulgaria 2004. 149 S., geb. ISBN 978-3-515-08598-4 84. Annette Kledt Die Entführung Kores Studien zur athenisch-eleusinischen Demeterreligion 2004. 204 S., geb. ISBN 978-3-515-08615-8 85. Marietta Horster / Christiane Reitz (Hg.) Wissensvermittlung in dichterischer Gestalt 2005. 348 S., geb. ISBN 978-3-515-08698-1 86. Robert Gorman The Socratic Method in the Dialogues of Cicero 2005. 205 S., geb. ISBN 978-3-515-08749-0 87. Burkhard Scherer Mythos, Katalog und Prophezeiung Studien zu den Argonautika des Apollonios Rhodios 2006. VI, 232 S., geb. ISBN 978-3-515-08808-4

88. Mechthild Baar dolor und ingenium Untersuchungen zur römischen Liebeselegie 2006. 267 S., geb. ISBN 978-3-515-08813-8 89. Evanthia Tsitsibakou-Vasalos Ancient Poetic Etymology The Pelopids: Fathers and Sons 2007. 257 S., geb. ISBN 978-3-515-08939-5 90. Bernhard Koch Philosophie als Medizin für die Seele Untersuchungen zu Ciceros Tusculanae Disputationes 2007. 218 S., geb. ISBN 978-3-515-08951-7 91. Antonina Kalinina Der Horazkommentar des Pomponius Porphyrio Untersuchungen zu seiner Terminologie 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