Simplicius: On Aristotle On the Heavens 1.2-3 9781472552228, 9780715639207

This is the first complete translation into a modern language of the first part of the pagan Neoplatonist Simplicius of

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Simplicius: On Aristotle On the Heavens 1.2-3
 9781472552228, 9780715639207

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Abbreviations In most cases works are referred to by author’s or editor’s name and date of publication, full information being provided in the Bibliography. However, the following abbreviations are used: CAG = Commentaria in Aristotelem Graeca, 23 vols, Berlin: G. Reimer, 1882-1909. DPA = Richard Goulet (ed.) (1989-), Dictionnaire des Philosophes Antiques, Paris: Editions du Centre National de la Recherche Scientifique. DSB = Charles Coulston Gillispie (ed.) (1970-80), Dictionary of Scientific Biography, 16 vols, New York: Charles Scribner’s Sons. LSJ = Henry George Liddell and Robert Scott (comps), Henry Stuart Jones (rev.), A Greek-English Lexicon, Oxford: Clarendon Press and New York: Oxford University Press, 1996. Photius = René Henri (ed. and trans.) (1959-91), Photius, Bibliotheca, 9 vols, Paris: Les Belles Lettres. RE = Paulys Realencyclopaedie der Classischen Altertumswissenschaft, 51 vols, Stuttgart: J.B. Metzler, 1893-1997. Suda = Ada Adler (ed.) (1928-38), Suidae Lexicon, 5 vols, Lepizig: Teubner. In addition the following names are used without dates: Bessarion for corrections by the Renaissance humanist recorded in Heiberg’s apparatus. Hankinson for Hankinson (2002). Heiberg for the editor of the text translated here, Heiberg (1894). Karsten for readings found in Karsten (1865). Moerbeke for Latin readings found in Bossier (2004). Moraux for the text of De Caelo found in Moraux (1965). Rescigno for Rescigno (2004).

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Introduction This volume translates the first half of Simplicius of Cilicia’s commentary on Aristotle’s De Caelo 1.2-4, in which Aristotle argues that the world is everlasting.1 The second half of this material will be translated in a second volume.2 Approximately 29% of this material is commentary in the ordinary sense, that is passage-by-passage explication of what Aristotle is saying. Another 11% (20,1-25,22 and 92,22-109,15) is more general philosophical discussion and treatment of some alternative views. The explications and general discussions, roughly 40% of 1.2-4, have already been translated into English in Hankinson (2002), a work to which I am much indebted. The other 60% is Simplicius’ discussion of the objections raised by his Christian contemporary John Philoponus3 (in a lost work which I shall call Against Aristotle) to Aristotle’s attempt to prove the everlastingness of the world. About 40% of that material containing Philoponus’ objections (roughly a fourth of 1.2-4) is translated in Wildberg (1987),4 another work to which I am much indebted. So what is new in this translation, somewhat more than one third of the whole, could be characterised as Simplicius’ responses to Philoponus. Since the debate between Simplicius and Philoponus is an extremely important item in the late stages of the transition from paganism to Christianity in the Byzantine Empire, it seemed desirable to include Simplicius’ responses in the Ancient Commentators on Aristotle series. But to print them in isolation did not seem reasonable since they obviously have to be read in connection with what they are responses to. Moreover, it is clear that a considerable portion of the material translated by Hankinson, e.g. the long excursus on coming to be at 92,22-109,15, is introduced by Simplicius in anticipation of his attack on Philoponus. The possibility of incorporating the two earlier translations into this one was considered, but it was decided that this was not feasible because of (hardly unexpected or surprising) differences in predilections between the two previous translators and between them and myself. Hence the decision to make a new translation which could rely on its predecessors for discussions of many issues5 and give readers direct access to a historically and philosophically important document in its entirety.

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Introduction 1. The intellectual background of Simplicius and John Philoponus 1a. Philosophy in Athens

It is convenient to begin with the succession of leaders of the Neoplatonic School in Athens (apparently an endowed institution) starting with: Plutarch of Athens (d. c. 432).6 Plutarch was succeeded for a brief period by: Syrianus of Alexandria (d. c. 437),7 who probably studied with Plutarch in Athens for some thirty years after preliminary schooling in Alexandria. A relative of Syrianus, Aedesia, married his pupil Hermeias of Alexandria, and they became the parents of two sons, Ammonius and Heliodorus, both probably born in Alexandria. I will discuss these three men in the next section. Syrianus was succeeded by: Proclus of Lycia (c. 411-485), about whom we are better informed because of the biography of him written by his pupil and probable successor: Marinus of Neapolis (modern Nablus, Palestine).8 Marinus’ date of death is unknown, and the succession after him is unclear. Among people who have been mentioned as possible heads of the Athenian school after Marinus are Isidore of Alexandria,9 a student of Proclus and Marinus who mainly taught in Alexandria; Zenodotus;10 and Hegias of Athens,11 a student of Proclus mentioned by Marinus in his life of Proclus. It is generally believed that the last head of the Athenian school was: Damascius of Syria,12 about whom Photius reports the following in his shorter summary of Damascius’ Life of Isidore: Damascius was given a thorough training in the art of rhetoric by Theon13 for three whole years and directed rhetorical studies for a further nine years. In Athens he had Marinus, the successor of Proclus, as his teacher of geometry, arithmetic, and the other branches of mathematics.14 The people who taught him in the study of philosophy were, in Athens, Zenodotus (also a successor of Proclus, the second after Marinus) and, in Alexandria, Ammonius Her-

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meiou.15 Damascius says that Ammonius was superior in no small measure to those of his time and especially in mathematics,16 and he records that Ammonius was the person who explained to him the works of Plato and the sequence of Ptolemy’s books on astronomy. However, he insists that what gave him his ability in the practice of dialectic were his associations with Isidore, who, he says, cast into shadow all people produced by time in that period in terms of his capacity in that sort of argumentation.17 In his commentaries on Aristotle Simplicius names two people as his teachers: Damascius and Ammonius. And at 462,20-3 of his commentary on De Caelo he refers to witnessing Ammonius make an astronomical observation in Alexandria. But he never mentions Athens. Perhaps the strongest evidence we have that Damascius taught Simplicius in Athens is Agathias’ report (Keydell (1967), 2.30.3) that (at a date not indicated) Damascius, Simplicius and five other ‘philosophers’ moved themselves to the court of Chosroes I (Persian emperor from 531 AD) in Ctesiphon, a departure standardly associated with the emperor Justinian’s decree of 529 prohibiting the teaching of philosophy and astronomy in Athens (Thurn (2000), 18.47), although Agathias mentions as motivation only the philosophers’ rejection of Christianity and their belief that they would be moving to an ideal society governed by a philosopher-king. In Agathias’ representation they found a corrupt society and a king who was no philosopher. Unable to bear the situation, they returned home as quickly as possible. Their return was made comfortable for them by the inclusion in the ‘Eternal Peace’ signed by Justinian and Chosroes in 532 of a clause stating that the men ‘should return to their own haunts (êthê) and live the rest of their lives eph’ heautois18 without fear’ without being compelled to change their beliefs. We know nothing about Damascius’ subsequent activity, but an inscription with the date 538 preserved in Homs, Syria (Jalabert and Mouterde (1959), 2336) is virtually identical with an epigram in the Greek Anthology which is ascribed to Damascius the Philosopher. Because of it scholars generally assume that Damascius was still alive in 538. 1b. Philosophy in Alexandria The preceding discussion shows the close links between the study of philosophy in Athens and in Alexandria in the fifth and earlier sixth century, beginning at least with Syrianus, so that what we have said makes exposition of developments at Alexandria somewhat easier. One of the pupils of Plutarch of Athens, and so an approximate contemporary of Syrianus, was Hierocles,19 a strong proponent of the view that there were no essential disagreements between Plato and Aristotle. Hierocles taught philosophy in Alexandria where he lectured on Plato’s Gorgias. He spent some time in Constantinople but he ran into trouble with the (Christian)

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rulers, was taken to court, and savagely beaten; he returned to Alexandria and taught philosophy there. Among his pupils in Alexandria were Theosebius,20 whom Damascius called ‘the Epictetus of our time’ and who invoked the god of the Jews to drive a demon from his wife, and (apparently) Aeneas of Gaza,21 a Christian sophist. We have seen that one of Syrianus’ pupils was Hermeias of Alexandria.22 After studying together with Proclus under Syrianus, Hermeias returned to Alexandria where he taught philosophy, apparently with a stipend from the city of Alexandria, which his children, Ammonius and Heliodorus,23 continued to receive after he died (around 455?), apparently at a rather early age since his children were still young and under the care of their mother Aedesia. It seems certain that Damascius would not have known Hermeias, but he stresses his excellent moral character and hard work (philoponia) while downplaying his philosophical originality. Aedesia took her two sons to Athens to study with Proclus. At some time thereafter (around 465-70) the brothers returned to Alexandria where Ammonius became the leading teacher of philosophy. It is generally assumed that Ammonius was still teaching in 517,24 but it seems unlikely that he lived much longer than that. There survive two texts of Zacharias Scholasticus, Bishop of Mytilene, which give us some picture of life in the schools of Alexandria. In one of them, The Life of Severus,25 Zacharias tells the story26 of Paralius, a pagan from Aphrodisias, who journeys to Alexandria in the 480s to study grammar, mainly with Horapollo,27 an associate of ‘Heraiscus,28 Asclepiodotus,29 Ammonius, and Isidore’, all people mentioned in Damascius’ Life of Isidore. Paralius is led deeper into paganism by Horapollo, but consultation with his Christian brother Athanasius and his brother’s companion Stephen provides Paralius with anti-pagan arguments with which he confronts his pagan teachers, whose responses leave him quite dissatisfied. Paralius becomes even more aggressive with his teachers after playing a role in the exposure of an alleged fraud in which Asclepiodotus’ barren wife is given a child by a priestess of Isis which the couple claim they themselves conceived in the temple of Isis. Horapollo’s pagan students become enraged with Paralius and, when neither Horapollo nor many Christian students are present, give him an extremely severe beating. Paralius manages to escape to some Christians, including Zacharias and some philoponoi, who are successful in intimidating the assailants in spite of being outnumbered. In the sequel, which I shall not go into, the philoponoi play the role of ominous troublemakers intent on destroying all traces of paganism in Alexandria. In other texts the philoponoi (also called spoudaioi (zealous) and brethren) appear as particularly pious Christians who, among other things, attend to the poor and the sick.30 The other relevant work of Zacharias is the dialogue Ammonius (Colonna (1973), also known as De Mundi Opificio). The work is self-consciously modeled on Platonic precedents – I would say particularly Plato’s Protagoras – but Zacharias shows himself uncertain about the difference

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between the dramatic and narrative style of presentation. It begins with the author explaining the circumstances of the conversations he reports. A young man, referred to only as ‘B’, having developed inclinations to paganism, has abandoned his studies with Ammonius and come to Beirut to study law. Zacharias recounts for B a lecture on physics by Ammonius in which he raised doubts about the Christian denial of the everlastingness of the world. Zacharias very quickly comes to the rescue of the Christian position and takes over as the person asking the questions, even citing Plato in support of his views. Ammonius shows himself a completely co-operative interlocutor, although at crucial junctures he restricts himself to saying things like ‘It would seem so’. The conversation concludes with a long speech by Zacharias which he ends by quoting Christian scripture. Zacharias now explains to B that on the next day he continued his conversation, this time in the Museum, with Gesius,31 described as the leading pupil of Ammonius at that time but also a teacher of medicine. The conversation with Gesius is somewhat, but only somewhat, more heated than that with Ammonius, but we are told that Gesius came to feel dizzy and tied in knots and asked how Zacharias can turn against the views of the ancient philosophers. Professing concern for truth rather than antiquity, Zacharias, still citing much Plato, presses on, with Gesius showing considerable interest in his exposition of Christian views but continuing to offer contrasting pagan ones. Again Zacharias gets the last word. There then follows the description of a third conversation, again at a class of Ammonius on Aristotelian ethics at which Ammonius ‘suddenly’ introduces Plato’s theory of Ideas. When Zacharias asserts that Aristotle rejected this theory, Ammonius changes the topic to the everlastingness of the world. The conversation has the same tenor as the original one between the two men with Ammonius twice conceding, although not without some ambiguity, crucial claims.32 After the second of these concessions there is a third conversation with Ammonius in which, at Ammonius’ request, Zacharias offers a brief explanation of the doctrine of the Trinity, after which Ammonius says, ‘So these things are three in hypostasis and number but one in substance’ (1122-3), after which we are told by Zacharias as narrator: The audience made a loud cry and applauded with pleasure and joy, since the philosopher had brought together and drawn as conclusion what we were trying to prove with what we said. But he smiled gently and somewhat sardonically with a kind of blushing. He was silent, and then went on to another discussion. At this point Zacharias (as narrator) dismisses as irrelevant to present purposes many other conversations he had and asks his interlocutor if he is persuaded and ready to go home. The interlocutor asks Zacharias to say more to dispel his doubts.33 Zacharias obliges, and the conversation ends with a prayer to the Trinity.

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I have brought in these two texts of Zacharias because of their relevance to the question of the place of Christians and Christianity in the school which both Simplicius and Philoponus attended. No one, I think, doubts either that the school of Ammonius was a basically pagan institution or that many Christians attended it. However the Life of Severus makes clear that students wavered in their religious allegiances and might easily be tempted or persuaded to make a change or at least an experiment. It also makes clear that there was considerable tension between pagan and Christian students, at least if the Christians chose to express doubts about pagan practices. But I think it is significant that the pagan students are explicitly said to have assaulted Paralius when their pagan teacher, Horapollo, was absent. It is perhaps even more significant that Zacharias’ conversations with Ammonius and Gesius are quite congenial, involving no more antagonism than one would imagine in a discussion of whether Plato thought the world was everlasting; there is no suggestion that Zacharias is stepping out of line when he objects to Ammonius’ teaching, and Ammonius himself shows an interest in the doctrine of the Trinity. The question of the role of Christianity in the school of Ammonius requires mention of a well-known passage in Photius’ short summary of the Life of Isidore (Photius 242,292; cf. 242,179), in which Ammonius is described as a money-grubber (aiskhrokerdês ôn kai panta horôn eis khrêmatismon hontinaoun) who reached an agreement with the bishop of Alexandria.34 There have been many speculations about this agreement, but it is generally accepted that Ammonius made some concession allowing him to continue to teach pagan philosophy, possibly with pay from the city. I suggest that Ammonius may only have agreed not to discriminate in any way against Christians and (certainly) to eliminate the kind of physical attack made by Horapollo’s students on Paralius.35 2. The intellectual career of John Philoponus There survive all or parts of seven Aristotelian commentaries ascribed to Philoponus and printed in CAG; they are on Prior Analytics (CAG 13,2), Posterior Analytics (13,3), On Coming to be and Perishing (14,2), De Anima (15), Physics (16 and 17), Categories (13,1), and Meteorology 1 (14,1).36 The incipits of the first four of these (as listed here) indicate that the commentaries are based on the classes (sunousiai) of Ammonius; all but the first are described as also including some observations (epistaseis) of Philoponus himself. The unity, character, and dating of these works has been a matter of some discussion, but before saying something about that discussion, it will be helpful to bring in other works of Philoponus, the first of which I will call Against Proclus (Rabe (1899)). This work contains 18 books, each of which quotes an argument of Proclus (d. 485) for the everlastingness of the world, and proceeds to argue against it. It is important to see that Philoponus’ arguments are oriented negatively. His main intention is to show that Proclus’ arguments for the everlastingness

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of the world are inconclusive. In Against Proclus Philoponus announces that he intends to do the same thing for Aristotle’s arguments in a future work, presumably Against Aristotle: If say that the circular motion is without beginning or end by relying on Aristotle’s arguments we will see if any of those argument are necessary, if, god willing, we get to that point. There is no necessity of dealing with (gumnasein) them now, since the philosopher (Proclus) didn’t put forward any such things in his own discussions. And we will also ask whether there are any arguments through which we can prove that circular motion cannot be everlasting. At the moment we have proposed only this much: to respond to the arguments of Proclus; and, insofar as it was possible for us, we have only set down things directed at refuting his arguments.37 Of course, it is not always possible to distinguish neatly between a refutation of an argument for the everlastingness of the world and an argument establishing that it is not everlasting, but the generally negative tenor of Philoponus’ arguments against Proclus is clear. Not only does he say that a conclusion does not follow from the premisses provided, he also plays off the views of one earlier philosopher38 against another. In particular he is outspoken in rejecting a claim which Simplicius stresses: that there is no substantial disagreement between Plato and Aristotle.39 In fact, he thinks, of the two, only Aristotle believed in the everlastingness of the world. Although Against Proclus is unmistakably the work of a Christian – there are seven citations of scripture, on which Plato is said to be dependent, and opponents are accused of stitching together fallacious arguments which run counter to their own beliefs in order to overthrow ‘our truth’ – for the most part it could be read as part of an academic, secular, philosophical debate on the question whether the world is everlasting based on shared assumptions, e.g. that the world is in some sense the product of a good god, and a shared sense of relevant authorities, particularly Plato and Aristotle, but also others, e.g. Theophrastus, Alexander, Taurus, and Plotinus. To be sure, Philoponus’ discussion is not what we would expect in a scholarly or even philosophical debate. He can accuse his opponents of shamelessness (aneideia), mindlessness (agnômosunê), argumentative gamesmanship (philoneikia), etc. Yet the object of his passion is not the beliefs of his opponents, but, for very much the most part, their willful misreading of Plato and Aristotle, A reference to the present as ‘the 245th year of Diocletian’ at 579,14-15 provides a date of 529 for Against Proclus. Philoponus’ references in that work to his planned Against Aristotle make it seem likely that there was not a great gap between the two works. In addition to his responses to Against Aristotle in his commentary on De Caelo, Simplicius criticises other things said by Philoponus in that work at 1129,29-1152,19 and

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1156,28-1169,9 in his commentary on Aristotle’s Physics 8.1. Simplicius criticises another work in which Philoponus dissents from Aristotle on the everlastingness of the world at 1326,38-1336,24 in his commentary on Physics 8.10. The object of Simplicius’ polemic in this case cannot be Against Aristotle since he records three references by Philoponus to that work (1329,38-1330,1; 1333,31-2; 1334,40-1335,1). We do not know the name of this work, and its relation to other possible works by Philoponus is not clear. There survives an Arabic summary of a treatise by Philoponus, now usually called On the Contingency of the World (Contingency). It begins with a quotation from the treatise in which a clear distinction is made between refutations of arguments for the everlastingness of the world and arguments for its temporal creation. I have already composed books before in order to refute the sophistries and the equivocal statements by means of which Proclus, Aristotle and others among the ‘Eternalists’ put the case in favour of the eternity a parte ante of the world. Now, however, in this book I wish to demonstrate that the world is created in time, having come into existence after not having existed. I shall endeavour to make this clear and to validate the reasoning concerning this (matter). For with respect to a matter which can (only) be known by syllogistic reasoning, one can acquire perfect knowledge only through a combination of two things: one of them being the establishment by demonstration (of the true knowledge) concerning this (matter), and the other the refutation of the sophistries and equivocal statements which prevent the speculative thinker from accepting it. For if we (confine ourselves) to demonstrating the conception which to our mind is the true one and let be the sophistries which prevent this conception from being accepted, we give to what is false and to what is true an equal (status), inasmuch as there are sophistries (attendant) upon that which is false which have not as yet been refuted; (accordingly) the speculative thinker is not clear about their being sophistries. On the other hand, if we refute the sophistries which run counter to the (correct) demonstration, but do not demonstrate (the conception), the latter may be (regarded) by the speculative thinkers as uncertain, inasmuch as it has not yet been demonstrated. For this (reason) I consider it as necessary for the correctness of the debate to compose, after the books in which I have refuted the arguments of the eternalists, a book (devoted to) improving the proofs for the temporal creation of the world. I shall start upon this (task) at this place.40 Since Contingency also focuses on Aristotelian arguments, it is possible that it is identical with the work criticised by Simplicius in his commentary on Physics 8.10.41 There are four other forward references which are possibly to this work in Against Proclus.42

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The works of Philoponus which are thought to be later than these works on the everlastingness of the world are all embedded in Christian controversies43 involving first and foremost the Monophysites of Alexandria and the ‘orthodox’ Chalcedonians, focused principally on the question whether Christ has two natures, human and divine, or just one nature which is a composite of those two natures. The Chalcedonian position included the claim that, although god and Christ were of two natures, they were one hypostasis, with the clear implication that the Trinity contains one hypostasis. Philoponus, who took the view that the Monophysite/Chalcedonian controversy was essentially verbal and could be settled by straightening out terminology, found the idea that one hypostasis (which he understood as an individual thing) could have two natures unacceptable, and adopted the position that god and Christ were two hypostases with a single composite nature, the Trinity therefore being three hypostases, all of the same nature. In explanations of his conception of Christ Philoponus made frequent reference to the way that soul and body combined to make one composite, the person, hardly the most transparent of analogies, and to the way that different properties or natures, e.g. rational and biped, combine to make a single property or nature, human. However, Philoponus was a convinced nominalist, and for him the nature of Christ and its components were universals and so not real entities, i.e. not hypostases. This meant that the Trinity contained three real entities, all of them divine, with the result that Philoponus became associated with a faction of the Monophysites, labeled Tritheists by their opponents. It appears that the heresy of Tritheism was started by a philosophically trained Monophysite with the improbable moniker ‘John Wineskinshoes’ (Askozangês), who in the mid 550s44 came to Alexandria and ingratiated himself with a grandson of the pro-Monophysite Empress, Theodora, a man named Athanasius. Athanasius was a student of Sergius of Tella, who, as an elderly man was consecrated Bishop of Antioch by Monophysites, a position he held for the last four years of his life while remaining in Alexandria. Sergius, who is addressed in two works of Philoponus, On the Creation of the World45 and On Wholes and Parts,46 died in 560. Athanasius sent John’s florilegium of texts supporting Tritheism to Philoponus, who wrote a Tritheistic book, presumably his On the Trinity, a work dated to 567,47 and sent it to Athanasius. The Alexandrians knew of this work and, undoubtedly influenced by the Monophysite leader, Theodosius,48 anathematised it along with Philoponus’ other books and Philoponus himself.49 Philoponus managed to be the source of a further division among the Tritheists with his works on the resurrection.50 In his work on heretics Timothy, elder of Hagia Sophia in the late sixth century, distinguishes between those Tritheists who ‘follow the grammarian called a hard labourer (philoponos), but is rather a labourer in vain (mataioponos) … and say that the body which we now have will not be raised as incorporeal, but rather we will receive another body in place of it’, on the one hand, and

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others who agree with them on all other matters but reject John Philoponus’ doctrine of the resurrection ‘by means of which he did away with the resurrection of bodies’ (Migne (1865), 44A-B). Later Timothy tells us that the leader of this latter group of Tritheists was named Conon, and he distinguishes between Cononites (Konônitai) and Philoponites (Philoponiakoi). He also describes their division in more detail: Previously the followers of Conon had accepted the writings of John the Grammarian of Alexandria, called Philoponus, his writing against the Hellenes51 along with his other writings, but finally they rejected the Grammarian and his works. For this John in his books against the Hellenes and his other writings claimed that all these perceptible objects which we see were brought into existence from not being with respect to both form and matter. For these perishable things come to be and perish both in their form and their matter, and in place of these, other imperishable and eternal bodies better than these visible ones are created by god; and he says that there is an end (sunteleia) or rather a passing (pareleusis) of the visible world and the creation of a new one. He defines resurrection of the dead as the indissoluble union of rational souls with an incorruptible body. As we said, Conon and his associates first accepted the writings in which he taught these things and blessed (makarizein) Philoponus himself in writing and orally both when he was alive and after his death, but when he was dead they rejected both him and his writings. They published treatises in which they say that the perceptible bodies which we see do not perish in their matter but remain the same and visible without perishing forever; they only perish in form. And again they say that the same matter is shaped anew and receives a better form which is imperishable and eternal. They say that the world comes to be with respect to both matter and form, but perishes or passes only with respect to form; for … they accept that matter endures forever. And they define resurrection of the dead as a second and indissoluble union of this body with the rational soul. (Migne (1865), 61B-64A) In something more than a century after Philoponus’ death all forms of Monophysitism and their leading exponents were anathematised at the Ecumenical Council of Constantinople of 681-2, subscribed to by both the Byzantine Emperor and the Bishop of Rome. By that time the Monophysite heresy had evolved into (or been renamed) Monothelitism, the doctrine that Christ and god have a single will. In this case the anathematisation takes the form of the incorporation with approval of a letter by Sophronius, Bishop of Jerusalem from 633/4-638, into the minutes of the Council. Sophronius wrote the letter at the time of his elevation, explaining his anti-Monothelite orthodoxy to his fellow patriarchs and urging it on them. The letter incorporates a long list of people and sects, starting

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with Simon Magus, who are to be anathema forever and severed from the Trinity, a list which includes ‘John the Grammarian, who is called a hard labourer (philoponos) but should be called a labourer in vain (mataioponos), Conon, and Eugenius, three thrice-cursed champions of Tritheism’ (Riedinger (1990), 480,14-16). I wish to say more about one other Christian work of Philoponus, On the Creation of the World (Reichardt (1897)), which is really a commentary on the account of creation in the book of Genesis (the Hexameron). While insisting that Moses’ purpose in giving the account was to bring humans to a knowledge of god and not to do natural philosophy, Philoponus sees him as prefiguring later scientific views (for example, Philoponus identifies the heaven created in Genesis 1.1 with the ninth starless sphere postulated to explain the precession of the equinoxes) and works to show that the cosmos envisaged in Genesis and elsewhere in the bible is consistent with the pagan world-picture and should be understood in terms of it. Philoponus explains his purpose in terms of pagan belittling of Christian ideas as unscientific, but he is also intent on dismissing the ideas of the Christian Theodore of Mopsuestia52 and his followers. Theodore’s extant writings are scattered and often fragmentary, and Philoponus cites him only on what for us are probably relatively minor cosmological issues (e.g. whether god created angels on or before the first day). However, Philoponus’ On the Creation has been associated with another contemporary work known to us as the Christian Topography of Cosmas Indicopleustes (Wolska-Conus (1968-73)), in which the author rejects the view of the world as a sphere with a spherical earth at its centre, and defends the view of the earth as a flat rectangle below which there is nothing and above which the stationary heaven arches like a tent, being joined to the earth at its extremities. There are no indisputable references in either On the Creation or the Topography to the other work,53 but the overlaps in subjects are clear, as is the temporal and spatial contiguity of Philoponus and Cosmas. Both were from Alexandria. Cosmas refers to a prediction (made in Alexandria in late summer 546) of two eclipses, a solar one to occur on 6 February 547, a lunar one to occur on 17 August 547, both of which did take place. A terminus ante quem for On the Creation is provided by Philoponus’ reference to Sergius of Tella, who, as already mentioned, is thought to have died in 560.54 It seems to me plausible to date On the Creation to the late 550s but Wolska ((1962), pp. 163-5) wished to make it somewhat earlier (before 553). We have seen that Philoponus wrote a series of explicitly Christian or at least anti-pagan works which can be dated between 529 and the earlier 570s. His commentaries on Aristotle are thought to be for the most part earlier than this, dating back to at least 517. The contrast between positions staunchly advocated by Philoponus in one or another of the Christian works and those tacitly condoned or explicitly espoused in one or another commentary on Aristotle has led to several theories about Philoponus’ intellectual development. It has been proposed that Philo-

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ponus converted to Christianity after having pursued the pagan subjects of grammar and philosophy. This proposal is now, I think, universally rejected, but the issue of explaining the relation between Philoponus’ explicitly Christian works and his commentaries remains unresolved. It is possible that the most satisfactory resolution lies in insisting that a commentary can be an explanation of a work to which the personal views of the commentator are irrelevant, but many scholars who have worked on Philoponus are not persuaded that this approach is adequate. In a detailed and penetrating study, Verrycken (1990) distinguished between two Philoponi, Philoponus 1, whose written works date before Against Proclus, and Philoponus 2, whose work begins with Against Proclus. Verrycken’s attempt to explain the change in Philoponus is not satisfactory,55 but it is not clear that a better alternative is available. I myself find it problematic that in order to make his distinction Verrycken has to suppose that our texts of Philoponus’ commentaries on the Physics, Meteorology, and Posterior Analytics include passages added by Philoponus after 529 and before he concentrated his entire attention on intramural Christian doctrine. One cannot, of course, exclude such a hypothesis, but I myself would rather rely on the notion of the commentary as doctrinally neutral than on the supposition of textual additions when the supposition is based entirely on alleged doctrinal divergences and there is no stylistic evidence of interpolation and no clear forward or backward references. The only Philoponus commentary on Aristotle to which a precise date can be attached is the one on the Physics, in which 517 (‘the 233rd year of Diocletian’) is given as an example of one way of specifying the present (703,17). Attempts to organise even the ‘first versions’ of the other Aristotelian commentaries chronologically around this date have not led to any clearly satisfactory picture. Sorabji ((1987), pp. 37-8), working independently of Verrycken’s theories and using criteria based on content, put the commentaries on De Anima, On Coming to be and Perishing, and Categories prior to 517. Of these Verrycken expresses confidence only about the positioning of the last before 517, but the two alleged references to it in the commentary on the Physics on which he relies have been disputed.56 Only one other work of Philoponus, the lost Summikta Theôrêmata, can be reasonably asserted to date from before 517, since Philoponus refers to it at 156,16-17 of the commentary on the Physics, a passage assigned by Verrycken to the first version of that commentary. As for the terminus ante quem for the Aristotle commentaries, we can perhaps only say that it seems unlikely that Philoponus continued to concern himself with such matters when he had turned to theological questions. This would only give us a date of 550, which could be moved back – with nothing like certainty – to as early as, say, 535 or 540. The only commentary (parts of) which can be dated after 529 with some certainty is that on Meteorology 1, where Philoponus would most plausibly be seen as referring to Against Aristotle (16,30-2; 24,38-25,2; 91,18-20).57

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3. The intellectual career of Simplicius We have seen that both Philoponus and Simplicius were students of Ammonius. It is generally assumed that Philoponus began his studies with Ammonius c. 510. Simplicius says (26,19; cf. ‘whoever he is’ at 49,24-5 and 90,12) that, as far as he knows, he has never seen the man he is arguing against. The veracity of this assertion has been doubted, and, given that Philoponus published a number of Ammonius’ lecture courses, it seems unlikely to be true if Simplicius was still studying with Ammonius after (or much after) Philoponus arrived there. The birth date assigned to Simplicius in those reference works which make it c. 490 would probably rule out the possibility that Simplicius was gone from Alexandria by the time Philoponus was studying with Ammonius, but, as far as I can see, no evidence precludes making that date 10 or even 20 years earlier. With such a date we could suppose that Simplicius left Alexandria for Athens around the time that Philoponus began studying with Ammonius. CAG contains commentaries ascribed to Simplicius on four Aristotelian works: De Caelo (CAG 7), Physics (9 and 10), Categories (8), and De Anima (11).58 The ascription of the last of these to Simplicius has been disputed. Internal references indicate that the first three were composed in the order listed, and that the last, if it is a work of Simplicius, was written after the commentary on the Physics. The controversy with Philoponus necessitates that our commentary was written after Against Aristotle; and if it was written not much after, this would give a date in the early or mid 530s. Simplicius refers to things Damascius said when he was still alive at 776,32-3 of his commentary on the Physics, and, as already mentioned, it is thought that Damascius was still alive in 538. We might then conclude that the extant commentaries on Aristotle by Simplicius were written between the early 530s and the mid 540s. We know nothing about when or where Simplicius died. It is now generally assumed that our commentary was written after Simplicius left the court of King Chosroes, that is after 532. But much ink has been spilled over the question where Simplicius went after leaving Persia, since Tardieu put forward the thesis59 that he (and his associates) did not return to either Athens or Alexandria,60 as was standardly assumed, but settled in Harran (Carrhae), now in southeast Turkey, near Syria. Initial enthusiasm for Tardieu’s view seems to have waned,61 and we are left in the position of having to confess that we do not know. However, it does seem to me likely that Simplicius thought of his attack on Philoponus as a continuation (now perhaps in a less friendly form) of the kind of discussion represented in Zacharias of Mytilene’s Ammonius.

14

Introduction 4. Simplicius v. Philoponus on the everlastingness of the world

The first chapter of De Caelo is introductory, describing the study of nature as the study of body and characterising the continuity and completeness of bodies. It and Simplicius’ commentary on it, including a prologue to the whole of the commentary, are translated by Hankinson. In Aristotle’s developed view, the cosmos consists of a sublunary sphere which is surrounded by heaven. As a whole heaven revolves around the cosmos in the east-west direction, but it contains planetary spheres which are both carried around with the whole heaven and have their own motion counter to it. The sublunary sphere is composed of four elements or simple bodies, earth, water, air, and fire, the ‘entireties’ of which are distributed in regions, earth around the centre, water above it, then air, then fire. These elements have an impulsion to be in these regions, which are ‘proper’ to them, and so broken off parts of the entireties move toward the entireties when they are not in them. Both Simplicius and Philoponus assign to Aristotle (and themselves accept) a distinction between a pure air existing above the mountain-tops and a stagnant air existing among them. They frequently refer to the entirety of fire (or the fire and the pure air) in its proper region as the hupekkauma, borrowing the term from Aristotle’s Meteorology. The hupekkauma is taken to rotate from east to west along with heaven, whereas the entireties of earth, water, and stagnant air remain at rest. 4.1. Chapter 2, 268b11-269a18 (10,26-38,5) Aristotle begins chapter 2 by asserting that all motions are either simple, that is rectilinear or circular, or composed of simple motions because the only simple magnitudes are straight and circular lines.62 He characterises circular motion as motion around the centre, rectilinear motion as motion up or down, up being away from the centre, down to the centre. (268b1426) He then introduces a distinction between simple bodies, those which have in them a starting point or source (arkhê) of natural motion (he mentions fire and earth and things akin to them63) and composites of them, and says that the simple bodies necessarily have simple motions and that it is necessary that there be a simple body which moves naturally in a circle by its own nature. (268b26-269a7) Simplicius takes 269a7-9 to show that none of the four sublunary elements move in a circle naturally, and 269a9-18 to show that they don’t do so unnaturally (para phusin). The argument that they do not do so naturally depends upon two assumptions: Of the four sublunary simple bodies fire and air move up naturally, earth and water move down naturally (not stated until 269a17-18); there is a single natural motion for each of the simple bodies (269a8-9).

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The argument that they do not do so unnaturally also makes use of the following assumptions: unnatural motion and natural motion are contraries; one thing has one contrary;64 motion up and motion down are contraries. Clearly then fire, for example, cannot move in a circle unnaturally, because, if it did, circular motion would be contrary to motion up, and motion up would have two contraries. This argument is formally valid, but it leaves out the possibility that the body which moves in a circle is a sublunary element moving in a way which is neither natural nor unnatural. This possibility would be ruled out if Aristotle were correct when he says in the course of the argument that if motion in a circle is not natural, i.e. other than natural, for something, it is unnatural, i.e., in this context, contrary to natural, for it. Aristotle purports to justify this false claim by invoking the fact that motion in a circle is simple, and at 19,14-25 Simplicius tries (without success, I think) to explain why Aristotle is right. At 20,10 Simplicius turns to problems and begins by stating a view which he himself accepts (cf., e.g., 54,19-33): One should know that both Ptolemy in his book on the elements and in his optics, and the great Plotinus, and Xenarchus in his work on difficulties for the fifth substance say that motion in a straight line attaches to the elements when they are still coming to be and are in an unnatural region, when they have not yet taken on their natural one. And Aristotle seems to agree with this both in the fourth book of this treatise when he says that ‘the motion of each thing into its own place is its motion into its own form’ and in On Coming to be; and so too Alexander in his commentary on this work … . For, in fact, if the elements move from an alien place and an unnatural condition because they desire their proper places and their proper entirety, it is clear that they do not move when they are in a completely natural condition, but, as the men I have previously mentioned, Ptolemy, Xenarchus, and Plotinus, say, when the elements are in a natural condition and in their proper places, they either rest or move in a circle. Earth, water, and the air which is stagnant clearly rest, but fire and the air which is luminous (the hupekkauma) move in a circle, revolving with heaven in accordance with their close relation to it. (20,10-25) Simplicius obviously has to work to make this view compatible with Aristotle’s argument that fire, for example, does not move in a circle either naturally or unnaturally. And he does so at 21,13-25 by invoking a third category of motion which applies to pure air and fire, and the planetary spheres, hypernatural (huper phusin) motion. Left to itself the hupek-

16

Introduction

kauma would just rest, and left to themselves the planetary spheres would move from west to east, but both are carried in another way, east-west in a circle, by a superior body, heaven as a whole. However, this east-west motion is not a matter of constraint since the bodies in question are naturally suited to take it on. Simplicius ascribes this doctrine of hypernatural motion to all of the people mentioned in the previous quotation except Xenarchus,65 but this ascription has been doubted; it is certainly unclear that any of them used the term ‘hypernatural’.66 Simplicius then accepts Xenarchus’ claim that the motions of simple bodies when not in their natural place are not natural, but he thinks the claim is acceptable to Aristotle and not an objection to him. Simplicius’ response to another objection of Xenarchus is of some interest. The objection is that the simple bodies do not have a single natural motion since air moves down from fire, and water moves up from earth. To it Simplicius responds: Motion downward for air or upward for water is constrained not natural, and more and less do not change the species of something.67 But if someone wanted to say that one thing is less light and another less heavy because of a mixture of a contrary, he would be saying that these things are not simple in the strict sense (as Aristotle also thinks), but they move for the most part in accordance with what predominates, and sometimes they move in both directions. For what separates a simple body from a non-simple one is having a principle of a single nature (and it is perhaps for this reason that Aristotle often speaks as if he were discussing two simple bodies). (24,14-20) After discussing Xenarchus’ objections Simplicius, at 25,23, introduces Philoponus, whom he accuses of plagiarising Xenarchus. After explaining why he is bothering with what he considers to be empty babble, Simplicius turns to Philoponus’ first argument (26,31-27,4), which relies upon the claim that both earth and water (fire and air) move down (up), and says that if water and earth have the same motion,68 they have the same ‘nature’, but, in fact, earth is dry and water is moist. Here Philoponus is obviously relying on what Aristotle says later in De Caelo and On Coming to be and Perishing, and so is Simplicius in his reply. He first accuses Philoponus of making the unwarranted assumption that the same nature attaches to the same motions, when all Aristotle is committed to is that different natures attach to different motions. He then makes two more significant responses. He first makes a distinction between the generic sameness and specific difference of the downward motion of water and earth, and then, returning to the passages he has been commenting on, he says that Aristotle is only thinking of nature as it relates to motion, not qualities such as wetness and dryness. Philoponus continues at 28,1 with a second argument according to which if things of different natures can have the same motion (a premiss

Introduction

17

which Simplicius has already queried), then things which have different motions, e.g. heaven and the sublunary elements, might have the same nature, and so heaven might be perishable. To understand the argument let ‘N(x,y)’ be ‘x and y have different natures’, ‘M(x,y)’ be ‘x and y have different motions’ and ‘POS(p)’ be ‘It is possible that p’. Philoponus argues that: If POS (N(x,y) & ¬M(x,y)) then POS (M(x,y) & ¬N(x,y)). This assertion is reasonable enough, but it is not formally valid, as one can see if, to use an example of Simplicius, one takes ‘N(x,y)’ to be ‘x and y are of different species’ and ‘M(x,y)’ to be ‘x and y are in different genera’. Philoponus makes the unfortunate move of saying that the proposition is a case of ‘conversion with antithesis’, which should mean a case of the logical truth: If P → Q then ¬Q → ¬P,69 which it is not. So Simplicius is correct to ridicule Philoponus. But his discussion is not very clear or precise, and I think we have no reason to suppose that Philoponus was any more clear or precise. I doubt that any attempt to make sense of the dispute in logical terms would be fruitful. Simplicius already made his main points in conjunction with the first argument, although he repeats them again. At 30,26 Philoponus accepts the Aristotelian claim (not made until 269b18) that heaven is neither heavy nor light, but says correctly that this does not imply that heaven is neither hot nor cold, even if it is agreed that what is heavy is cold and what is light is hot; to get the inference we also need, e.g. that what is cold is heavy and what it hot is light, and these assertions do not follow from what has been granted. Simplicius supplies a tenuous argument for the needed premisses. Ultimately for him the more important point is the claim that, even if heaven is in some sense hot, its heat is not the same as sublunary heat and does not cause warmth in the way sublunary heat does; see, e.g., 87,29-88,28. At 31,6 Philoponus introduces a serious difficulty for Aristotle, who in this section of De Caelo speaks as if heaven were a unified thing with a single circular motion, when, in fact, the Eudoxan theory, which Aristotle accepts, divides heaven into multiple spheres, each with its own circular motion. Philoponus now allows that, e.g., water and earth move downward at different speeds and concludes that there should be as many simple bodies as there are heavenly spheres and sublunary elements. Simplicius grants that the heavenly bodies are different in kind without conceding that there is more than one simple body which moves in a circle, and he tries to side-step the objection by invoking Aristotle’s purposes in a way which he does frequently in disputing with Philoponus: now Aristotle only wants to distinguish the everlastingness of circular motion (and so of

18

Introduction

heaven) from the corruptibility of things which move in a straight line; later he will distinguish the heavenly spheres. And besides Aristotle often speaks as if there are only two sublunary elements, even though he is committed to four. At 32,1 Philoponus turns to Alexander’s claim (cf. 14,31-15,4) that Aristotle is restricting circular motion to motion around the centre of the universe. Philoponus objects that, if Alexander is right, Aristotle’s saying that the heavenly body moves in a circle is incompatible with the epicycles and eccentrics of astronomical theory and with the assumption that the stars revolve around their own axes. Although previously Simplicius seemed to endorse Alexander’s claim, he now backs off. Aristotle is here treating circular motion in general, and when elsewhere he speaks about the planetary spheres moving in a circle around the centre of the universe, he is talking about the astronomical theories which he knew, those of Eudoxus and Callippus. As for later theories, Simplicius treats them as hypothetical instruments to account for phenomena, not descriptions of reality. The discussion of the rotation of the stars is of some interest. Plato explicitly asserted that there was such a thing (Timaeus 40A8-B2), and Simplicius, not surprisingly, accepts it and assigns the view to Aristotle as well. However, he chooses to pick on Philoponus’ assertion that the astronomers believe in this rotation by pointing out that rotation is not relevant to astronomy because it cannot be observed; hence, Philoponus must have mistakenly read it into astronomical tables!70 As we have seen, in the generally accepted Neoplatonist cosmology, also assigned to Aristotle, the entireties of earth, water, and stagnant air are generally at rest and the entireties of luminous air and fire move in a circle. At 33,17 Philoponus objects that Aristotle bases his account of heavenly motion on the motion of heaven as a whole, but bases his description of sublunary motion on the behavior of pieces of the elements outside their natural entireties.71 Simplicius reaffirms his claim that Aristotle’s interest is in establishing the difference between the sublunary and superlunary realms, and for this purpose the behavior of bits not in their natural place is sufficient. He says (34,2-5), ‘If the entireties of the elements, which do not move in a straight line, are everlasting and their parts, which come to be and perish, do move in a straight line, it is reasonable that the difference with regard to parts shows most of all the transcendence of heaven’. At 34,5 Philoponus invokes the strict dichotomy ‘natural or unnatural’, this time to argue that Aristotle is committed to holding that the circular motion of the hupekkauma is unnatural. Simplicius ignores the fact that Aristotle supplies a justification for the dichotomy at 269a11-12, and simply rejects it by invoking his third alternative, ‘hypernatural’. Since Philoponus is able to take for granted that the circular motion is not unnatural, he can also use 269a11-12 to argue (at 34,33) that Aristotle is committed to the view urged by Xenarchus72 that circular motion is

Introduction

19

natural for fire, a view which Philoponus himself accepts and which he, like Xenarchus, takes to imply that heaven itself could be fire moving naturally in a circle. This consequence, which would mean that heaven could be perishable is, as Simplicius says many times, what Philoponus is mainly interested in (cf., e.g., 59,15-23). At 35,20 Simplicius commends Alexander’s account73 of the hupekkauma’s motion according to which it is possible to say that it is neither natural nor unnatural because it is not a simple motion but a mixed one in which, while the hupekkauma is moving in a circle, parts of it become denser and rarer and move up and down. Philoponus rejects Alexander’s account, insisting that the hupekkauma has a natural circular motion of its own. In addition to again invoking hypernaturalness, Simplicius claims that, even if heaven were fire and had a natural circular motion, it would still be everlasting. The remainder of the exchange (36,9-38,2) between Simplicius and Philoponus on Alexander’s conception of the motion of the hupekkauma is, with one exception, not especially interesting. At 36,21 Philoponus, citing epicyclic motion, says that this complexity of heavenly motion does not mean that the heaven does not have a single simple motion. After rebuking Philoponus for not understanding the instrumentalist character of mathematical astronomy, Simplicius responds: The motion of each of the things in heaven is simple and uniform. And even if more partial things are carried around by bigger wholes, the motion of the bigger wholes does not become composite – it remains simple and transmits to the things more partial than itself; and the motion of the more partial things is not composite, but it remains simple and they take on another more divine and simpler motion from the bigger wholes. (36,33–37,3) Simplicius, then, insists that the planetary motions which we call composite are really simple because of their hypernatural character. He does not here apply this point to the hupekkauma, perhaps because he is only concerned to defend Alexander against Philoponus, but later (54,12-33) he will say against Alexander that fire which rises into the hupekkauma casts off its rectilinear motion. 4.2. Chapter 2, 269a18-30 (38,6-49,25) Simplicius believes that at this point Aristotle has established that there is a body distinct from the four elements which moves in a circle naturally and that he gives two further arguments for the same conclusion at 269a32-b10. Simplicius takes it that in 269a18-30 Aristotle establishes that this body is prior to the four elements with the following argument:

20

Introduction [i] A circle is more complete than (and so prior to) a straight line; [ii] therefore, motion in a circle is more complete than (and so prior to) motion in a straight line; [iii] therefore what moves in a circle is more complete than (and so prior to) what moves in a straight line.

Aristotle’s treatment of priority does not appear to have raised questions in antiquity,74 but his claims about completeness did. Simplicius’ discussions of completeness do not always distinguish clearly among lines, motions, and moving bodies, and I will not always do so either, since it seems to me that the failure to make the distinction is usually harmless. Aristotle argues for premiss [i] by arguing against the view that a straight line is complete. A finite straight line is incomplete because it can be added to (according to Simplicius, what Aristotle means is that a finite straight line can be added to while preserving its form), and an infinite straight line is incomplete because it has no end (telos).75 Aristotle shows that a circle is complete because it is limited (peperasmenon) and has an end and because there is nothing outside it by which it can be increased. Simplicius takes the latter to mean that if a circle is added to, its form is changed. Most of the discussion of 269a18-30 centres around Alexander’s characterisation of completeness as having a beginning, middle, and end: a circle being complete because its beginning is its centre, its end is its circumference, and what is in between them is its middle. Simplicius objects to what Alexander says on the grounds that Aristotle is not talking about plane figures, but about lines, but he is happy with the idea that a linear circle is ‘completely complete’ because every point on it is beginning, middle, and end. This position enables him in effect to both reject and accept Alexander’s account of completeness in the case of circles. The order in which Simplicius presents and discusses Philoponus’ objections to Aristotle and Alexander is not as logical as one might like, but the main points are clear enough. I shall discuss only some of what is said, consigning certain passages which seem to repeat what is said elsewhere to notes.76 At 42,27 Philoponus, apparently accepting for the sake of argument that a circle is complete and a straight line incomplete (atelês), asks about Aristotle’s move from figures to motions, i.e. the move from [i] to [ii], making the claim that motion on a finite straight line has a beginning, middle, and end as much as motion in a circle does. Simplicius might have said that Alexander’s account is irrelevant, but instead he attacks Philoponus for saying that a straight line both lacks an end (is atelês), and has one. At 43,8, Philoponus argues more strongly that for Aristotle and his followers circular motion should be incomplete because they think it is everlasting and so has no beginning or end, but a finite rectilinear motion

Introduction

21

will be complete in this sense. Simplicius accepts this claim, but insists that circular motion is completely complete in the sense he previously invoked for the circle.77 Alexander’s definition of completeness clearly implies that an infinite straight line is incomplete, but would also seem to imply that a finite straight line is complete, as Philoponus has argued. To show that a finite straight line is incomplete Alexander relied on Aristotle’s remark that such a line can always be added to. An objection to this position is that the diameter of the cosmos, the longest straight line in the universe, cannot be added to. To this objection Alexander apparently responded that any finite straight line can be added to in theory (logos). Simplicius prefers to treat this issue by distinguishing between the form of a straight line, which is complete, although not as complete as the form of a circle, and the indefinite extension on which the form of a straight line is imposed: The form of straight line insofar as it is straight is everywhere complete both in a small straight line and in a large one, whereas the magnitude is complete in the straight line which takes on the whole measure of the cosmic straight line. The completeness of this cosmic straight line is also deficient with respect to form relative to the circular form and its completeness, because it does not converge into itself but flows out as far as it is able toward unmeasuredness and infinity, but its quantity is bounded by demiurgic measures. So this is what is meant by there being something outside of every finite straight line: that, insofar as it is up to it and its indefinite flow, it always has something deficient and can be added to. (39,28-40,1) Simplicius repeats this point at 44,3-15 and again at 46,33-47,1, in responding to Philoponus’ discussion of Alexander’s claim about extension in theory, a discussion the content of which Simplicius does not make clear, presumably because he has already rejected Alexander’s position. At 45,2 Philoponus turns to the thing that moves in a circle and accuses Aristotle of circular argument in inferring [ii] from [i] and [iii] from [ii]. Philoponus apparently takes for granted that the circle in [i] and [ii] and what moves in a circle in [iii] are the same thing, namely heaven. In response Simplicius insists that: the circle in [i] is not a particular circle at all; Aristotle is here making no use of the sphericity of heaven, which he proves in 2.4;78 in [ii] he is talking about the circular motion around us of the stars, whether or not they form a sphere; and in [iii] he infers that heaven is complete without saying anything about its sphericity. At 46,4 Philoponus, again relying on Alexander’s account of completeness, addresses the question whether Aristotle’s circle is a plane figure or a line. He says that if it is a figure, then because a plane circle is continuous its centre is not an actually existing thing, whereas the beginning and end of a finite straight line are actual, and in this sense an actually existing straight line would be more complete than a circle. Simplicius mocks the

22

Introduction

idea that the centre of the cosmos (and the poles) might not be actual and insists that an actually existing centre does not destroy the continuity of a circle, given the generally accepted Aristotelian definition of continuity. On the other hand, Philoponus says, if the circle is a line, it will be mathematical rather than natural (because without thickness) and its centre and what is between it will not be actual. Simplicius does not address the issue of whether the circle is mathematical or natural. He dismisses the issue of what is between centre and circumference as irrelevant to the case of the linear circle and repeats his claim about its ‘complete completeness’.79 At 47,10 Philoponus, apparently taking it for granted that the circle in question is a plane figure, argues that a circle or sphere can also be expanded to form a larger circle or sphere, citing as examples the growth of bodily parts. Simplicius’ sees his task as distinguishing this kind of expansion from the extension of a straight line. I cannot affirm that he is entirely successful or even clear. I quote only what he says about a (presumably theoretical) expansion of the cosmos: Even if the diameter of the universe were to increase, the spherical surface would not increase in the same way as the diameter. Rather the earlier part of the straight line which receives the addition remains (and that is why the part is thought to be incomplete), but nothing of the previous spherical surface or the circle remains; for the circuit of the circumference becomes different. Consequently one should not conceive of increase in the same way in the case of the circle and of the straight line, but in the one case where there is addition the addition is related to a deficiency, whereas in the other case something complete and determinate comes to be again out of something complete. (47,20-27) Simplicius concludes his discussion by considering a series of objections by Philoponus to Alexander’s characterisation of the complete as what has beginning, middle, and end. Philoponus claims that lots of complete things, e.g. arms, don’t have beginning, middle, and end. Simplicius, while continuing to say that Alexander’s characterisation is incorrect, claims that Philoponus is wrong and briefly indicates why in terms of Philoponus’ own examples. In addition Philoponus claims that one cannot say which of the dimensions of a body are beginning, middle, and end; Simplicius responds that even if the choice is arbitrary, the dimension chosen as length is first, that chosen as width is middle, and that chosen as depth is end.80 Philoponus also says that an infinite straight line, which has neither beginning nor end, has more of a claim to be complete than a finite one because it cannot be increased at all; Simplicius responds that infinite straight lines do not exist and are indefinite and incomprehensible.

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4.3. Chapter 2, 269a30-b17 (49,26-59,23) In this section of the commentary the remainder of chapter 2 is divided into five lemmas. Of these the first, third, and last lemmas (269a30-2 (49,26-50,4); 269b2-10 (52,19-53,18); and 269b13-17 (55,1-24)) are unproblematic for Simplicius, but the other two raise questions. For Simplicius the second (269a32-b2 (50,5-52,18)) is a new argument for the difference between heaven and the sublunary elements, and it raises a difficulty, which can be understood in terms of its last sentence. This may be paraphrased: Since circular motion is unnatural for the four elements, it is natural for something else. Here the antecedent is obviously problematic since earlier at 269a9-18 Aristotle committed himself to the view that circular motion is not unnatural for the four elements. Simplicius opts for what is apparently the only, albeit unsatisfactory, way out of this difficulty:81 here by ‘unnatural’ Aristotle does not mean ‘contrary to natural’, as he did at 269a9-18; he only means ‘other than natural’. He does not suggest that there is anything problematic about this dual use of the term ‘unnatural’,82 but unfortunately he is not usually specific about the sense in which he is using ‘unnatural’, making it difficult to be sure one is understanding what he is saying. In the second problematic lemma (269b10-13) Aristotle argues that fire cannot be what moves in a circle because, since motion up is natural for it, motion in a circle is unnatural for it. Simplicius does not explicitly say that in this case Aristotle means that circular motion is other than natural for fire, but it seems that he would have to, since he mentions as a premiss of the argument ‘motion in a circle is unnatural for fire’. However, on his interpretation, as opposed to Alexander’s, the point of the passage is not to prove that premiss, but to prove that heaven is not made of fire. At 55,25 Simplicius takes up an argument of Xenarchus designed to show that heaven might be made of fire. This time the argument is formulated as a denial of the principle that one thing has one contrary, and is based on two claims: Fire can be moved in many ways by constraint (i.e. unnaturally, in a way contrary to natural); Aristotle himself asserts in his ethical writings that both excess and deficiency are contrary to the mean. Against the first claim Simplicius responds that only simple motions are in question, and simple motions which are unnatural for something are natural for something else. Against the second he makes a point, which

24

Introduction

apparently Xenarchus himself recognised: excess and deficiency are contrary to each other, but what is contrary to the equality of the mean is inequality, which includes both excess and deficiency. Xenarchus attempts to apply this point to cosmic motion by saying that motion up is opposed to motion down as excess is opposed to deficiency, and rectilinear motion, which includes upward and downward motion, is opposed to circular as inequality is to inequality; given the existence of these two oppositions, one cannot rule out that heaven is made of fire. Simplicius denies the relevance of this point on the ground that Aristotle is not considering the opposition between rectilinear and circular motion, but is ruling out the possibility that both motion down and motion in a circle are contrary to motion up. After dealing with Xenarchus, Simplicius turns at 56,26 to Philoponus, who, not surprisingly, tries to exploit the (for Simplicius merely verbal) inconsistency between 269a9-18 and 269a32-b2 by arguing that Aristotle was either wrong to deny in the first passage that heaven might be fire moving unnaturally or wrong to say in the second that circular motion is unnatural for fire, this last statement also implying that one thing (upward motion) has two contraries. Simplicius, of course, invokes the two senses of ‘unnatural’, as he does in rejecting other arguments of the same kind offered by Philoponus. 4.4. Chapter 3, 269b18-270a12 (59,24-91,20) In this part of De Caelo Aristotle’s principal purpose is to prove that heaven is neither heavy or light. He defines light and heavy in terms of being naturally constituted to move up or down, and, takes it that, having shown that heaven is not so constituted, he has the result that it is not heavy or light. Obviously this argument does not work for those who, like Philoponus, don’t think Aristotle has established that heaven cannot move up or down.83 The last lemma in this section (270a3-12) is taken by Leggatt (1995), who calls the argument ‘rather desultory’, and others to be a second argument that heaven has no weight or lightness. Simplicius takes it to be an argument that the parts of heaven move in the same way as the whole, a conclusion which he uses as ammunition against Philoponus’ view that there is no important distinction between the heavenly and the sublunary. For Simplicius thinks that, whereas ‘parts’ of the heaven are never separated from it and so always move with it, when parts of the sublunary elements are separated from their whole they move either up or down, while the entireties are always either at rest (earth, water, and stagnant air) or moving in a circle (pure air and fire). However, in this lemma Aristotle says that parts of earth move naturally ‘to the same thing’ as the entirety of earth. Simplicius, quite rightly, takes this to be Aristotle’s view for all the sublunary elements, and so he has to find a sense in which parts and the entirety of a sublunary simple body move toward the same thing.

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He tries to do this in an important passage starting at 64,31.84 After suggesting that Aristotle might be talking about all the portions of earth rather than the entirety of it, Simplicius proposes as a second alternative that, for example, the whole earth ‘has a total convergence and impulsion (sunneusis kai rhopê) toward the centre even if it does not change place’, that ‘the desire (ephesis) of the whole and its parts is for the centre’. After extending this doctrine to the other sublunary elements, he denies that anything like it holds of heaven, which ‘has no desire for anything else and does not go in the direction of anything else but converges into itself and desires itself and its own soul and mind’. One way of expressing Simplicius’ position is to say that, although heaven has no weight or lightness at all, the entireties of the sublunary elements do have one or the other in an extended sense but not in the strict sense. Simplicius turns to Philoponus’ objections at 66,8. I present in sequence the most interesting parts of this discussion,85 beginning at 66,33 where we get our first trace of Philoponus’ attempt to drive a wedge between Plato and Aristotle, something which is, of course, completely alien to Simplicius’ harmonising interpretation of the two men. According to Philoponus, Plato held that heaven is made of the purest form of the four elements and mainly of fire.86 Simplicius agrees with this interpretation, but whereas Philoponus wants to stress the continuity between the ordinary and the purest forms of the elements, Simplicius insists on their discontinuity. Earlier Simplicius has given a fuller account of the views of Plato and Aristotle: So, according to Plato, the dodecahedron was also the shape of a simple body, that of heaven, which he calls aithêr. But if he says that heaven is made of fire, he means that it is made of light, since he also says that light is a form of fire. But the stars are made of the four , not the ones involved in coming to be, but of fire insofar as they shine, of earth insofar as they have resistance to sensation, and of the intermediates insofar as they have intermediate . So if Aristotle also agrees that they are visible and tangible, he too does not decline to construct heavenly things from these highest forms , in which the perfection of the elements also is; for he thinks that heaven completely transcends the four sublunary elements, which move in a straight line and are imperfect. Similarly, if he also says it is simple, it is reasonable for him to deny that it is a composite of these . We will learn that he says it is a living thing with a soul, and he thinks that living things have composite bodies. (12,26-13,3)87 We can perhaps summarise Simplicius’ interpretation as follows. For Plato heaven is composed of one kind of fire, called light, and the heavenly bodies are composed of all four elements, so that one can also say that heaven is composed mostly of fire. However, the elements making up

26

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heaven are not the ordinary ones in the sublunary world; they are the highest forms of the elements, so that heaven transcends the sublunary world in the way Philoponus tries to deny. Plato does not stress this transcendence in the way Aristotle does. On the other hand, Aristotle does not stress the fact that heaven is a composite, but rather stresses its simplicity, However, Aristotle also calls the elements in our world simple, although in fact they never occur in a pure form without intermixture.88 Hence we can say that for both men heaven is a transcendent composite of the purest forms of the four elements, with the purest form of fire, which can be called aithêr, dominating. At 67,24 Simplicius turns to Plato’s account of weight, according to which the elements are attracted to things of their own kind, and this attraction is weight, and up and down are defined relative to each element, so that, e.g., for someone located on earth, earth appears heavier than fire, but for someone located in fire, fire would appear heavier than earth. It appears from 68,6-10 that Philoponus invoked Themistius for the claim that Plato rejected the view that elements in their proper region are light or heavy. According to Simplicius Plato held only that heavy and light are natural properties, and to refute Themistius’ claim he explains Plato’s conception of up and down, heavy and light.89 For Simplicius the crucial point here is that Themistius agrees that the alleged absence of impulsions from the elements in their proper places does not imply a significant similarity between heaven and the sublunary world (70,11-16; 72,29– 73,4). However, Simplicius chooses to spend a lot of time on Philoponus’ arguments that there is no good ground for thinking that the entireties of the elements have weight or lightness or that heaven does have them, and to insist that, even if either claim were true, the imperishability of heaven would not be undermined. The discussion is rendered difficult because, as we have seen, Simplicius holds that although the entireties of the sublunary elements do not have weight or lightness in the primary sense because, like heaven, they do not move in a straight line, there is another sense in which they do, namely they have an impulsion or desire to be in the place where they are. In the first of these arguments (71,25-72,10) Philoponus accepts, at least for the sake of argument, Aristotle’s claim at 4.3, 310b3-5 that if the earth were moved away from the centre of the cosmos it would return there (by moving in a straight line), but denies that this entails that the earth has weight. Philoponus makes an analogy, saying that even if one supposed that if the cosmos were moved it would return to the same place, he could make no claim about its having weight or lightness because the terms ‘up’ and ‘down’ only apply to motions inside the cosmos. Simplicius assumes (or chooses to assume) that Philoponus is making the hypothesis that the cosmos might be moved up or down, and says that this hypothesis, unlike the hypothesis about the earth, makes no sense; he does not question the meaningfulness of hypothesising that the cosmos might change place (even though it has no place). Philoponus concedes that

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someone might not accept his hypothesis about the cosmos, but considers the possibility of a star falling from heaven, and says such a star would return in a straight line to heaven. Simplicius does not dispute this claim, but seems to think it sufficient to claim a difference between the desire of, say, fire, to be near heaven, which is better than fire, and the desire of a star to return to heaven, which is of the same nature. He does not clarify this claim, but simply repeats his point that Philoponus’ argument does not undermine the view that heaven is imperishable. At 73,4 Simplicius turns to Philoponus’ attempt to dispute the relevance of the fact that the parts of heaven have never been observed to perish.90 Philoponus accepts that heaven is the ‘more authoritative’ (kuriôteron) part of the cosmos, but claims that, although the more authoritative parts of an animal – he refers to the heart – are less easily affected than other parts, they are not imperishable.91 Simplicius disputes Philoponus’ claim about affectability, and insists that everything which comes to be in time undergoes change and eventually perishes. At 74,16 Philoponus takes up the difficult topic of the lightness or heaviness of the intermediate elements, water and air, citing the fact that, according to 4.4, 311b6-13, water is light in earth but heavy elsewhere and air is light in earth and water but heavy elsewhere to argue that the elements are not intrinsically heavy or light. Simplicius insists that nothing has been said to undermine the absolute heaviness or lightness of earth and fire, and that the relative heaviness and lightness of water and air does nothing to undermine the claim that heaven is neither heavy nor light. At 75,16 Philoponus tries to develop an argument that even if the four elements do have weight or lightness in all locations, Aristotle’s inference that heaven is neither heavy nor light because it does not move in a straight line is unsound since heaven could be heavy or light and still not be able to move in a straight line. To make his case Philoponus assumes that heaven is a rigid spherical body and therefore cannot move by mutual interchange of parts with other things (antiperistasis).92 For this reason, heaven requires a void into which to move, but there is no void inside or outside the cosmos into which it could move in a straight line even if it were heavy or light. Simplicius’ first response to Philoponus is eristic. How, he asks, can Philoponus accept that heavy and light are defined in terms of motion down or up and say that heaven might be heavy or light even though it can’t move down or up? But Philoponus is obviously offering a specific reason why heaven might not be able to move up or down even if it had an impulsion to do so. Simplicius other response is of more substance. Whereas Philoponus makes the claim that heaven does not move in a straight line basic to Aristotle’s argument, Simplicius insists that what is basic is that heaven moves in a circle naturally, this natural motion being obvious to perception and showing that heaven does not have weight. At 78,17 the issue of disagreement between Plato and Aristotle arises again. Simplicius and Philoponus accept that Plato held that both nature

28

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and soul play a role in the circular motion of heaven. Philoponus points out that, although Aristotle sometimes seems to think that heaven has a soul, at 2.1, 284a27-35 he criticises Plato for assigning a role to soul. Philoponus then develops an argument against Aristotle for thinking that heavenly motion could be due to nature alone: if heaven, which is finite, is moved only by nature, then this nature will be finite and unable to impart an infinite circular motion. Simplicius is concerned to show against both Philoponus and Alexander that Aristotle did not criticise Plato on this score and that he does not waver in his belief that the motion of heaven is due to both nature and soul. 81,3 marks the beginning of a series of arguments by Philoponus for the idea that heavenly matter is the same as the fire of the hupekkauma, so that heaven and the hupekkauma really constitute a single entity. Philoponus first brings in Aristotle’s statement in the Meteorology that heaven cannot be made of fire because, if it were, everything else would have been destroyed long ago. Philoponus says that the same thing should be true in the case of the hupekkauma, which is made of fire. The way out of this difficulty for Philoponus is to accept Aristotle’s view that the fire of the hupekkauma does not burn in the way the fire around us does. However, this means that heaven could be made of the same kind of fire as the hupekkauma and therefore be perishable. Simplicius insists that the issue here is not burning but elemental interchange, and he agrees that if heaven (or heaven plus the hupekkauma) were able to interchange with the lower elements, Philoponus’ claim would be correct, but, of course, he believes that heaven cannot undergo interchange with the rest of the world.93 At 81,22 Philoponus adds that the much greater size of a fiery heaven would not necessitate that heaven would overwhelm the other elements. Simplicius replies, quite correctly, that although a larger mass of, e.g., water might be as cold as a smaller one, the larger mass nevertheless cools more and is warmed up less than the smaller one.94 Philoponus also argues, starting at 82,14, that if heaven were hot in the way the hupekkauma is, this would not change the way things are in our world, since more distant spheres would have no effect on less distant ones, since both have the same nature, and the effect of the hupekkauma on what is beneath it would be the same as it is now. Simplicius derides Philoponus for suggesting that what he has called the authoritative part of the universe might have no effect on the other parts if it had the same qualities they do. Unfortunately Philoponus also shows that he believes that the distance of the sun affects how much it heats the earth, giving Simplicius the opportunity to lecture him with his own account of why, e.g., the sun heats more in summer than winter. Starting at 88,28 Philoponus provides Simplicius with a field day by listing many properties which heaven shares with things in the sublunary world, e.g. three-dimensionality; Simplicius is particularly ‘shocked’ that Philoponus compares the brightness of heaven with that of fireflies and

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the heads and scales of fish. Not even Philoponus’ hero David would say such a thing!95 Simplicius admits that there is a level of abstraction at which this commonality holds, but, citing the way in which all things are descended from the One, he insists that underlying the applicability of common terms to heaven and our world is a radical difference, even though there is also an important interconnectedness. 5. The text This translation is based on Heiberg’s edition of Simplicius’ commentary, printed as volume 7 of CAG, which I wish to discuss briefly here. My remarks are based on Heiberg’s preface to his edition (cited here by Roman numeral page) and his earlier, more detailed but slightly discrepant report to the Berlin Academy (Heiberg (1892)). These remarks relate only to book 1. For Heiberg the most important manuscript is: A Mutinensis III E 8, thirteenth-fourteenth century, in the Este Library in Modena (Wartelle (1963), no. 1052). Heiberg ((1892), p. 71) singles out A for its correctness and purity. But he admits that it is badly deficient and hastily written, with frequent incorrect divisions of words, misunderstandings of abbreviations, arbitrary use of accents and breathing marks, extremely many omissions, and frequent insertions in a wrong place of words occurring in the vicinity. A glance at the apparatus on almost any page of Heiberg’s edition makes clear how often he feels forced to depart from A. On the whole these departures seem justified, but there are some cases where he follows A and produces a text which seems to me impossible or at least very difficult. Heiberg thought that A and another text derived independently from a lost archetype. That other text is: B Ottobonianus gr. 83, sixteenth century, in the Vatican Library (Wartelle (1963), no. 1896). B stops in book 1 (at 292,25 in Heiberg’s text), the remaining pages being torn out. Heiberg stresses its defective quality. Among the other manuscripts which Heiberg cites are:96 C Coislinianus 169, fifteenth century, in the National Library in Paris (Wartelle (1963), no. 1560). D Coislinianus 166, fourteenth century, in the National Library in Paris (Wartelle (1963), no. 1558).

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Introduction E Marcianus 491, thirteenth century, in the library of San Marco in Venice. (Mioni (1985), pp. 299-300; not in Wartelle (1963)).

Heiberg took D and E to be significantly different from A and B, and C to be intermediate between D and E, on the one hand, and A and B, on the other. C and D are, in fact, not complete texts of Simplicius’ commentary, but texts of De Caelo with extensive marginalia, the majority of which are derived from Simplicius’ commentary (not necessarily word-for-word quotations). According to Heiberg E, which is a complete (although lacunose) text, and D were copied from the same prototype, E being copied by an uneducated scribe. E was corrected by Bessarion (E2), using the Latin translation of William Moerbeke, a work to which I shall return shortly. Heiberg also cites three printed versions of the commentary in his apparatus: (a) The editio princeps of the Greek text. Simplicii Commentarii in Quatuor Libros de Coelo, cum Textu Ejusdem, Venice: Aldus Romanus and Andrea Asulani, 1526. (b) The editio princeps of the Latin translation of William Moerbeke. Simplicii philosophi acutissimi, Commentaria in Quatuor Libros De coelo Aristotelis. Venice: Hieronymus Scotus, 1540. (c) Karsten (1865). Citations of (a) are rare because Heiberg ((1892), 75) realised that it was a translation back into Greek of Moerbeke’s Latin translation.97 However, he did not realise that (b) was ‘corrected’ in the light of (a). In my reports on what is in Heiberg’s apparatus criticus I omit what he says about (b), but, when it seems to me useful, I do cite as ‘Moerbeke’ the readings in the recent edition of Moerbeke’s translation of Simplicius’ commentary on book 1 (Bossier (2004)). Karsten’s edition was published one year after his death. It includes no critical apparatus, and has no preface by Karsten. Throughout it is based on single manuscripts. For 1-94,16 Karsten relied on a ms. Heiberg took to be descended from B: Taurinensis C.I.13, sixteenth century, in the National Library in Turin (Wartelle (1963), no. 2086). And for the rest of book 1 he relied on a ms. Heiberg took to be derived from E: Parisinus, gr. 1910, fifteenth century, in the National Library in Paris (Wartelle (1963), no. 1396).

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In the absence of a critical apparatus or inspection of these manuscripts, it is impossible to tell what alterations of his source Karsten made, but there is little doubt that he made ‘improvements’.98 I have sometimes thought it desirable to adopt them rather than what Heiberg prints. For Karsten’s readings I have relied on Heiberg’s apparatus, which includes an extensive, although not complete, record of Karsten’s text. My departures from Heiberg’s text are recorded in the footnotes and in the ‘Textual Questions’. For the text of De Caelo itself I have relied on Moraux. 6. Brackets and parentheses Square brackets are placed around lower case Roman numerals which I have inserted for clarification. Angle brackets are used to set off major and possibly debatable insertions made for clarification. (Many minor insertions such as the substitution of a noun for a pronoun are made without remark when they are judged to be relatively certain; in particular I have frequently inserted a proper name where Simplicius has only a ‘he’ or a third person singular verb.) If an insertion represents an addition to the Greek text a note explaining this is attached. Parentheses are used as punctuation marks and to enclose Greek words inserted as information. Occasionally they are used to mark an insertion by Simplicius in a quotation. Notes 1. That is, has no temporal beginning or end. 2. Mueller (forthcoming 2011). 3. i.e. John the lover of work; also known as John the grammarian (grammatikos, professional teacher of language and literature) and John of Alexandria. Simplicius never refers to his opponent by name, but does indicate that he called himself a grammarian. It cannot be established or ruled out that the epithet ‘Philoponus’ is based on a connection between John and the Christian zealots known as philoponoi. On the three ways of referring to John see Sorabji (1987), pp. 5-6. 4. Of the 135 ‘fragments’ printed by Wildberg (1987), 103 are taken from the commentary on 1.2-4 of De Caelo and 26 from Simplicius’ commentary on chapter 1 of book 8 of the Physics. The remaining six are from al-Farabi (3), Symeon Seth, al-Sijistani, and an anonymous British Museum manuscript. At 1117,19-1118,5 of his commentary on the Physics Simplicius informs us that Philoponus devoted five books of Against Aristotle to De Caelo and one book to Physics 8. 5. In particular I refer the reader to Hankinson’s translation for discussion of the philosophical meaning and merits of what is said by both Aristotle and Simplicius. The notes in Wildberg’s translation are largely textual, but Wildberg (1988) is essentially a philosophical commentary on the fragments of Against Aristotle; to facilitate the reader’s use of this material I have provided an index to the fragments taken from the text translated in this volume as Appendix 1. I would also like to record here my indebtedness to Rescigno (2004), which provides a text, Italian translation, and analysis of the fragments of Alexander’s commentary on book 1 of De Caelo. In Appendix 2 I give an index to those fragments which are taken from the text translated in this volume.

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6. See, e.g., Saffrey and Westerink (1968), pp. xxvi-xxxv. 7. See, e.g., Dillon and O’Meara (2006), pp. 1-3. 8. See Saffrey and Segonds (2000), pp. IX-XXVIII. 9. See DPA 3, pp. 870-8 for the confusing information we have about Isidore, almost all of which is derived from Damascius’ Life of Isidore, a work which we know only through Photius 181 and 242, and various entries in the Suda. The most recent attempt to reconstruct the Life is Athanassiadi (1999). 10. Our only information about Zenodotus is that he was a favourite (paidika) of Proclus, who had highest hopes for him (Photius 242,154), and that he taught Damascius philosophical theory and was a successor of Proclus directly after Marinus (Photius 181,127a2-4). The last assertion has met with a great deal of scepticism; see, for example, RE, 2. Reihe, 10A, 51-2. 11. See DPA 3, pp. 530-1, where the idea that Hegias was head of the Athenian school is rejected, and for the contrary view DPA 3, p. 875. 12. See DPA 2, 541-93. For the very sparse direct evidence that Damascius was head of the school see p. 547, and for his relation to Simplicius’ commentary on book 1 pp. 577-8. A number of mss. attribute the commentary on 1 (but not 2-4) to Damascius, but the difficulties raised by assuming that in its present form it is due to Damascius seem insuperable. If one assumes that some truth lies behind the ascriptions to Damascius, the most plausible alternative seems to be to suppose that Simplicius reworked and considerably developed lectures of Damascius. 13. Little is known of Theon; see Martindale (1980), p. 1107, s.v. ‘Theon 4’. It is standardly assumed that Damascius studied rhetoric in Alexandria. Scholars have disagreed about whether he taught rhetoric there or in Athens. 14. Marinus is said to have taught the works of Aristotle to Isidore (Photius 242,42). 15. The Suda, s.v. Epsilon 3035 informs us that Ammonius’ brother Heliodorus also taught Damascius. 16. In his extended account of Damascius’ Life of Isidore Photius (242,79) says: ‘Ammonius worked very hard (philoponôtatos), and of all the exegetes who have lived up to now he is the most useful (reading pleiston with Athanassiadi (1993), p. 160). He mostly taught the works of Aristotle. Moreover, his discussions of geometry and astronomy were superior not just to his contemporaries but also to the older associates of Proclus – and I almost want to say ‘to everyone who has lived up to now’. 17. Photius 181, 126b40-127a14. 18. For some of the meanings associated with this phrase (‘without engaging in teaching’, ‘without interference in their religious beliefs’) see Hadot (1990), p. 279. 19. See Schibli (2002). 20. See RE, 2. Reihe, 5B, 2245-7. 21. See DPA 1, pp. 92-7. 22. See Bernard (1997), pp. 1-74. 23. See DPA 3, pp. 534-5. 24. The grounds for this assumption, if I understand them, are not strong. Philoponus’ commentary on Aristotle’s Physics (or a good part of it) is dated to 517, and, like all of Philoponus’ commentaries, it is assumed to be based on the lectures of Ammonius. See the next section of this Introduction. 25. I have used the English translation from the Syriac in Ambjörn (2008) and checked it against the French translation in Kugener (1907). Page references are to Kugener’s text and translation. 26. pp. 14-46. The story is retold by Trombley (1994), 2, pp. 1-29 with special emphasis on the role of the philoponoi.

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27. See DPA 3, pp. 806-8. Horapollo himself eventually converted to Christianity. 28. See DPA 3, pp. 628-30. Heraiscus was Horapollo’s father-in-law. 29. Of Alexandria; see DPA 1, pp. 626-31, where the textual complexities involving this Asclepiodotus and his father-in-law of the same name (Asclepiodotus of Aphrodisias) are explained. At 795,13-14 of his commentary on the Physics Simplicius calls him the best of Proclus’ pupils. Proclus, who dedicated his commentary on Plato’s Parmenides to Asclepiodotus, apparently wanted him to be his successor in Athens, but Asclepiodotus declined. 30. On the philoponoi see Wipszycka (1970). 31. The Suda ( s.v. Gamma 207) tells us that as a doctor (iatrosophist) Gesius gained great imperial honours and income; his teacher in medicine was a Jew. According to Sophronius in his Narration of the Miracles of Saints Cyrus and John (Marcos (1975), 30) Gesius underwent Christian baptism because of imperial pressure but remained a practising pagan; however, he experienced a change of heart when his visions of the two saints produced the cure of an ailment which he had been unable to deal with by his own ‘scientific’ methods. 32. ‘You seem to be speaking the truth’ (1056; kinduneueis alêthê legein); ‘you speak well’ (kalôs legeis; 1093). 33. Namely: (i) If, as Zacharias believes, god is going to transform this perishable cosmos into an immortal one, why didn’t he create an immortal one in the first place? (ii) Similarly with humans, who are going to become immortal? (iii) Why did god make humans free, if their freedom was going to produce their sinfulness? (iv) How can there be a resurrection of the body when bodies are often torn to bits by animals? 34. Either Peter Mongus, who died in 490, or his successor, Athanasius II, who died in 496; Peter was bishop at the time of the Paralius affair. 35. That Ammonius did this is perhaps confirmed by the fact that the Christian Philoponus published versions of Ammonius’ lectures as commentaries on Aristotle. 36. For the works of Philoponus see Sorabji (1987), pp. 231-5 or Scholten (1997), pp. 35-43. 37. Against Proclus 10.6.399,20-400,3. Other probable references to a future Against Aristotle: 6.6.134,16-17; 6.11.155,19-24; 7.6.258,22-259,1; 10.5.396,23-25; 11.14.461,1-2; 13.1.483,18-21. Simplicius mentions a backward reference to a previous Against Proclus in Against Aristotle at 135,26-136,1 of the commentary on De Caelo where he denies that he has ever seen Against Proclus. 38. Philoponus does not name contemporaries, although when he talks about incorrect ideas he frequently has contemporaries in mind. 39. See, e.g., Against Proclus 2.2.29,2-7. 40. Pines (1972), pp. 321-2. 41. For an alternative proposal see Wildberg (Furley and Wildberg (1991)), p. 100. 42. The most probable are 1.2,9,20-26 and 7.6,259,1-6. Less clear are 1.3.11,1417 and 5.4.117,20-1. Also unclear is the reference at 430,9-10 of Philoponus’ commentary on the Physics. 43. For a much more thorough discussion of Philoponus’ sectarian works see Grillmeier and Hainthaler (1996), pp. 107-46. 44. Elias of Nisibis (11th century) gives a date of 556/7 (Brooks (1910), p. 59). Most of the rest of this paragraph is based on the chronicle of Michael the Syrian (twelfth century) (Chabot (1901), pp. 251a-255a). 45. Reichardt (1897), 2,4-12, where Athanasius is also addressed. 46. Sanda (1930), p. 126.

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47. See Martin (1962). 48. De facto leader of the Monophysites, briefly (535-6) Bishop of Alexandria, but held by Justinian in Constantinople until his death in 567. 49. See Chabot (1933), pp. 111-12, where it is reported that the clergy of Alexandria unanimously accepted the following anathema pronounced by one Bishop John: a. Since our father and archbishop Theodosius, who is with the blessed, has taught and made known correctly and in accordance with the holy fathers what we should think and believe about the holy and consubstantial Trinity, we find that the writings of John the Grammarian, who is called ‘Philoponus’ but would more truly be called ‘The Heretic’, are full of atheisms and contradictions of the tractatus on the Holy Trinity written by our blessed father Theodosius, whom we have mentioned, and also of the doctrines of those fathers who teach the word of truth correctly. And we also anathematize all of the writings produced by that grammarian John who is called by the epithet ‘Philoponus’ but ought more truly be called ‘The Atheist’, and we anathematize those who accept those writings. And we also anathematize John the Grammarian himself and any priest who gives him communion until he does penance in this matter … . And we declare this John to be cut off from the holy and consubstantial Trinity and from our communion. 50. For what is known about these works see van Roey (1984). The year 574 is often associated with these works (see, e.g., Ebied, van Roey, and Wickham (1981), p. 22. The date is undoubtedly approximately correct, but I have been unable to determine what justifies the precise specification. The quotation which follows in the text suggests that the writings on the resurrection were Philoponus’ last. 51. Presumably at least Against Proclus and Against Aristotle. 52. Theodore (d. 428) was anathematized at the fifth Ecumenical Council (553) in the course of what is known as the three chapters controversy. 53. Cosmas shows at least an indirect awareness of one of Philoponus’ works on the everlastingness of the world, I would guess Against Aristotle, when he mentions the reference by an acquaintance named Anastasius to ‘one of those people who boast that they are Christians and who wants to speak against the Hellenes, but does not realize that he himself agrees with them in thinking as they do that heaven is forever turning around, even though he proclaims in his book that heaven is coming to an end’ (7,1). 54. Some have thought to date On the Creation to the period of Sergius’ bishopric (557-560) at Antioch because Philoponus addresses him as ‘honoured head’ (kephalê) and ‘greatest ornament among the high priests (arkhiereusi) of god’, but the argument has not been found decisive by others. 55. For extended criticism see Scholten (1996), pp. 129-43. 56. Scholten (1996), p. 125, n. 445. 57. See Wildberg (1987a), pp. 204-6. However, although I agree with Wildberg, that the last two are backward references, the first does look to me like a forward one. 58. For a full discussion of Simplicius’ oeuvre see Hadot (1990), pp. 289-303, and for a discussion of his style and methodology Baltussen (2008). 59. First in Tardieu (1986). 60. A return to Alexandria is quite compatible with Simplicius’ statement that he never saw Philoponus, since although Philoponus almost certainly would have been in Alexandria at that time, one would hardly expect either of the men to seek the other out, and Alexandria’s population in the sixth century may have been, say, 500,000; see Abbadi (1988), who gives a figure of 525,000.

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61. See, e.g., Fox (2005). Hadot (2007), a reaffirmation of Tardieu’s position, provides a thorough overview of the literature on the subject. 62. For Xenarchus’ objection to this assertion and the responses of Alexander and Simplicius see 13,22-14,29. 63. That is, water and air, but it is always easier for Aristotle to discuss the extreme elements, earth and fire, than the intermediate ones, water and air, because of the difficulty of associating four elements with two rectilinear motions; see Wildberg (1988), pp. 51-6. 64. For Xenarchus’ objections to this principle see 55,25-56,25. 65. Proclus is added to the list at 37,34. 66. For discussion of the possible origin of the notion of hypernatural motion see Wildberg (1988), pp. 128-30. 67. And so, e.g., even if air is less light than fire, it is still light. 68. Simplicius discusses and rejects Philoponus’ claim that water and earth have the same natural motion at 34,21-32. 69. See, e.g., 68,25-8 of the commentary on the Prior Analytics ascribed to Ammonius (CAG 4.1). 70. For another tenuous accusation of astronomical ignorance against Philoponus see 71,7-19. 71. What Simplicius says in his response suggests that Philoponus may also have invoked, as he does at 71,25-6, Aristotle’s thought experiment at 4.3, 310b3-5 about how the earth would move if it were taken away from the centre of the universe. 72. For Xenarchus’ argument see 50,21-4. 73. Following Philoponus Simplicius quotes two passages from Alexander’s description of the motion of the hupekkauma at 37,13-15 and 37,21-4. Alexander’s notion of the mixed character of that motion comes up again at 51,5. 74. cf. 38,25-6. 75. Simplicius accuses Philoponus of confusing limit (peras) and end at 43,2244,3, where Simplicius says that a finite straight line has a limit, but not an end, because it can be added to while preserving its form; see also 49,10-19, where Simplicius excoriates ‘the grammarian’ for not taking into account the etymology of telos. 76. e.g. 42,20-27, where Simplicius invokes his doctrine of hypernaturalness to distinguish heaven from the four elements. 77. Same kind of exchange at 44,15-45,2. 78. Simplicius makes this same point at 45,29-46,4 when Philoponus invokes the fact that the entireties of the four elements are spherical and so not different in this respect from heaven. In this case Simplicius also points out that the four elements get their sphericity from heaven’s sphericity and, indeed, get it hypernaturally. 79. At 48,14 Philoponus argues that even if a linear circle is complete in the sense of having beginning, middle, and end, it is still incomplete because it lacks one dimension. Simplicius mockingly insists that this sense of completeness is irrelevant with respect to circles. 80. Simplicius gives a curious account of the length, breadth, and depth of a sphere as great circle, surface, and radius, respectively. 81. cf. 57,14-58,1, where Simplicius invokes against a criticism by Philoponus a form of the principle of charity in interpretation. 82. It is not clear to me how Alexander addressed this problem, but he is apparently content with calling circular motion unnatural for fire. He relies on his claim that the motion of the hupekkauma is mixed rather than simple to get out of the difficulty raised by what Aristotle says.

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83. See 66,11-17. 84. cf. 67,5-19 and 72,18-24. 85. I pass over 66,17-33, where Philoponus raises a weak objection to Aristotle’s account of heavy and light at 260b20-9, which Simplicius turns aside. 86. See also Philoponus’ objection at 84,15-22 with Simplicius’ response. 87. Simplicius gives a fuller account of the views of Plato and Aristotle on the makeup of the heavens at 84,30-87,28, where he also explains the harmony of Plato and Aristotle on the question of Forms; see also 90,25-91,3 and 91,7-17. 88. See, e.g., 17,18-33, 24,24-17, 85,7-31, and 86,28-87,1. 89. At 69,11-70,2 Simplicius explains that the difference between Plato and Aristotle on weight and lightness, up and down, is merely linguistic: Plato is speaking about the nature of things, whereas Aristotle is following ordinary ways of speaking about them. 90. Aristotle invokes this ‘fact’ later at 270b11-16, on which see also 142,7143,31. Simplicius uses it against Philoponus again at 87,29-88,8. 91. At 74,4-11 Simplicius makes a confused ‘grammatical’ counterargument according to which if what is unaffectable is imperishable, what is less affectable must be so as well, citing the alleged fact that what is more F is a fortiori F. 92. Simplicius gives a less than illuminating discussion of these ideas at 77,23-31. Philoponus apparently explained the fact that heaven loses none of its parts in terms of its rigidity (sterrotês) and resistance (antitupia). Why then, Simplicius asks, does the earth lose its parts? Moreover, Simplicius says, Philoponus is wrong to make antiperistasis responsible for a fluid’s remaining complete when it loses some part of itself because antiperistasis is not sufficient for this; the missing part must be replaced. 93. Simplicius gives his own account of how the sun warms us at 88,8-28. 94. There is an analogous discussion at 83,30-84,10, where Simplicius points out that what is relevant is the natural, e.g. warmth of air, not the fact that it might be artificially cooled or heated. 95. Simplicius also manages (90,19-20) to bring in the fact that Christians believe that god took on a human nature. 96. I mention only the mss. cited in my notes. 97. A fact first noticed by Peyron (1810). 98. cf. Bergk (1883), p. 143, n. 1 and p. 148.

Translation of the text commented on (On the Heavens 1.2-3.270a12) Since in this work the ratio of commentary to text commented on is unusually high, I give here a translation of the text of Aristotle broken down in accordance with the lemmas in Simplicius. I indicate the pages in the commentary where the lemma is discussed directly and, sometimes, salient features of the discussion, notably where Xenarchus is mentioned. I also indicate the passages which Simplicius devotes to criticism of John Philoponus. Chapter 2 268b11-14 Later we should investigate whether the entire mass of the nature of the universe is infinite in magnitude or finite, but let us now speak about its formal portions, beginning as follows. (10,26-11,30) 268b14-20 For we say that all natural bodies and magnitudes can change place on their own, since we say that nature is a starting point of motion for them. For every change of place — we call change of place motion — is either straight or in a circle or mixed from these. For only these two are simple, the reason being that also only these two magnitudes are simple, the straight and the circular . (10,31-14,29, including some material on Xenarchus) 268b20-6 Motion around the centre is in a circle, motion up or down is straight. I call motion from the centre up, and motion to the centre down. Consequently it is necessary that any simple motion be from the centre or to the centre or around the centre. And this seems to follow reasonably from what was said originally,1 since body is completed in three , and so is its motion. (14,30-15,31) 268b26-269a2 Since some bodies are simple and some are composites of them (I mean by simple bodies those which have a starting point of motion naturally, for example, fire and earth and their species and the things which are akin to them), it is necessary that there also be simple motions and motions which are in some way mixed, and that the motions of the simple bodies be simple, those of the composites mixed, but occurring in accordance with what predominates. (16,1-17,33) 1

In ch. 1. Simplicius rejects Aristotle’s claim here at 15,27-31.

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269a2-7 So since there is a simple motion, and motion in a circle is simple, and the motion of a simple body is simple, and a simple motion attaches to a simple body (since if it attached to a composite one it would be in accordance with what predominates), it is necessary that there is a simple body which is of such a nature as to move in a circle by its own nature. (18,1-19) 269a7-9 For it is possible that something move with the motion of some other different thing by constraint, but it is impossible that it do so naturally since there is a single natural motion for each of the simple bodies. (18,20-19,8; cf. 34,21-32) 269a9-18 Furthermore, if unnatural motion is contrary to natural, and for a single thing there is a single contrary, then since motion in a circle is simple, if it is not natural for a moving body it is necessary that it be unnatural for it. So if fire or some other body of this sort is what moves in a circle, its natural motion would be contrary to motion in a circle. But for a single thing there is a single contrary. And up and down are contrary to one another. And if there is some other body which moves in a circle unnaturally, it has some other motion naturally. But this is impossible, since if its natural motion is up it will be fire or air, and if down, water or earth. (19,9-25,21, including material on Xenarchus, Ptolemy, Plotinus; cf. 34,33-38,2) 25,23-38,5 Against Philoponus 269a18-30 But it is also necessary that this sort of motion be primary. For the complete is prior by nature to the incomplete, and the circle is complete, but no straight line is, neither an infinite one (for if it were complete it would have a limit and end) nor any finite one (for there is something outside of every finite straight line, since any can be increased). So, since a prior motion attaches to a body which is prior by nature, and motion in a circle is prior to straight, and motion in a straight line attaches to simple bodies (since fire moves up in a straight line and earthen things move down toward the centre), it is also necessary that motion in a circle attach to some simple body. For we said1 that the motion of mixed bodies is in accordance with what predominates in the mixture of simple bodies. (38,6-42,16, including material on Xenarchus) 42,17-49,25 Against Philoponus 269a30-2 It is evident from these things that some bodily substance exists in nature which is different from the things in our world and more divine and prior to all of them. (49,26-50,4) 1

at 269a4-5.

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269a32-b2 And if someone takes it that every motion is either natural or unnatural and that a motion which is unnatural for one thing is natural for another, as is the case with motion up and down (since one of them is natural for fire or earth, and one of them is unnatural). Consequently it is necessary that, since motion in a circle is unnatural for these things, it is natural for something else. (50,5-52,18) 269b2-10 In addition, if motion in a circle is natural for something, it is clear that there will be some simple primary body which is constituted to move in a circle naturally in the way that fire moves up and earth down. But if the things which move in a circle move unnaturally, it is amazing and entirely unreasonable that only this motion, being unnatural, is continuous and everlasting, since in the case of other things what is unnatural is observed to perish most quickly. (52,19-53,18) 269b10-13 Consequently if fire were the thing which moves , as some people say, this motion would be no less unnatural for it than motion down; for we see that the motion of fire is from the centre in a straight line. (53,19-54,33) 269b13-17 Therefore, someone arguing on the basis of all these things would be confident that, in addition to the bodies here around us, there is something which is different and separate from them and has a nature which is as much more valuable than they as it is more distant from them. (55,1-56,25, including material on Xenarchus) 56,26-59,23 Against Philoponus Chapter 3. 269b18-270a12 (59,24-91,20) 269b18-20 Since some of the things we have said are hypotheses and some have been demonstrated, it is evident that not every body has lightness or weight. (59,24-60,34) 269b20-9 It is necessary to hypothesise what we mean by heavy and light, now in a way that is sufficient for our present needs, but again more accurately when we investigate their substance. So let what is naturally constituted to move to the centre be heavy, what is naturally constituted to move from the centre be light; and let what sinks to the bottom of everything that moves down be heaviest, and what rises to the top of everything which moves up be lightest. It is necessary that everything which moves up or down have either lightness or weight or both, but not both in relation to the same thing; for these things are heavy and light relative to one another, for

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example, air relative to water and water relative to earth. (61,1-62,2; cf. 66,17-70,33) 269b29-270a3 It is impossible for the body which moves in a circle to have either weight or lightness, since it cannot move to the centre or from the centre either naturally or unnaturally. For rectilinear motion is not natural for it, since of each of the simple bodies is single, so that it would be the same as one of the bodies which move in a straight line. But if it moved unnaturally, if motion down were unnatural , motion up would be natural , and if motion up were unnatural , motion down would be natural . For we have posited that, of contrary , if one is unnatural for something, the other is natural for it. (62,363,24) 270a3-12 Since whole and part move to the same thing naturally, for example, all earth and a small chunk, it results first that has no lightness and no weight, since if it did it could move either toward the centre or from the centre because of its own nature. And second it results that it cannot change place by being dragged either up or down, since it is not possible for it to move naturally in another way or unnaturally – not it nor any part of it; for the argument is the same for the whole and for the part. (63,2566,3) 66,4-91,20 Against Philoponus

SIMPLICIUS On Aristotle On the Heavens 1.2-3 Translation

Simplicius on the first book of Aristotle’s On the Heavens

268b11 From ‘Later … of the nature of the universe’ to ‘beginning as follows’.1 Having said2 in what way each body, both the part and the whole is complete, and said that the whole is complete because it has nothing outside it, he realised that he needed the demonstration of this and of whether it is as infinite that it has nothing outside of it or as finite. And perhaps he also thought he should speak about the nature of the universe next after the discussion of the nature of body without qualification3 and then speak about its parts. But since, as I believe, he includes the discussion of the universe in with the discussion of heaven (for if he proves that heaven is finite, he has the result that the universe is finite), he postpones the discussion of the universe4 and proposes to speak first about its parts, what they are and how many they are. (He is right to say ‘infinite in magnitude’ because it is infinite in the extendedness of its existence and also in time.) Alexander says that the discussion of the whole cosmos is primary for but that it brings with it the discussion of the everlasting body which moves in a circle, which is concluded in the second book, and in addition to these he presents the discussion of the four elements in the two final books. But5 since intended to complete what he has to say about the body which moves in a circle in relation to the discussion of the whole cosmos (that it is not infinite and that it is spherical and does not come to be or perish), he proves first that there is a body of this kind and then teaches about the universe. One should pay attention to whether the things said about the universe (that it is not infinite, that it is spherical, and that it does not come to be or perish) are said primarily about the whole cosmos and the universe is not said to have these because of heaven. For in beginning the second book and stating the conclusion that the whole heaven has not come to be and does not perish, he makes clear that, even if he is speaking about the whole cosmos, he is saying that the cosmos has these properties because of heaven, by what he has written shortly after the beginning, namely,6 ‘Therefore it is well to be persuaded that the ancient accounts which are especially a part of our patrimony are true: that there is something

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immortal and divine included among the things which have motion, and have the kind of motion of which there is no limit’ and so on – so as not to quote a lot. He is calling the formal portions of the universe the ones which differ from each other in form, heaven, fire, air, water, earth, since these are the immediate parts of the universe. And, being homoiomerous, the parts of earth and of each of the others are also parts of the universe, but they are not immediate parts but parts of parts , and they are not portions in the strict sense but parts.7 And so these immediate parts of the universe are the ones which differ in form. 268b14 From ‘For … all natural bodies’ to ‘For only these two are simple, the reason being that also only these two magnitudes are simple, the straight and the circular ’.

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Beginning his discussion of the heavenly body and wanting to prove that it is everlasting, he first establishes that it is different from the four elements, making his argument on the basis of the natural motions. For, if for natural things being natural lies in possessing a nature, but nature is a starting point of motion, a demonstration based on natural motion is at the same time based on clearer things because it is based on activities; for activities are more evident than substances. At the same time it will be based on more authoritative things because based on causes. For the argument based on motions, he assumes in advance these six things: 1. There are two simple motions, in a circle and in a straight line;8 2. a simple motion attaches to a simple body;9 3. the motion of a simple body is simple; 4. one natural motion attaches to one thing;10 5. for a single thing there is a single contrary;11 6. heaven moves in a circle, as perception indicates.12 Plotinus also referred to these hypotheses in On the Cosmos. For wanting to demonstrate in accordance with Plato that heaven is everlasting, he says,13 ‘There would be no issue for Aristotle if one accepted his hypotheses about the fifth body’, meaning these hypotheses, because if these hold, the everlastingness in number14 of the cosmos follows. But Plato also seems to assign a different substance to heaven . For if he thinks that the five figures give form to five bodies and says that the universe was figured at the bounded heaven by the dodecahedron, which is different from the pyramid, octahedron, icosahedron, and cube, it is clear that, also

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according to him, the substance is different. And Xenocrates,15 the most authentic of his disciples, provides sufficient attestation that Plato thinks that there are five simple bodies corresponding to the five figures when he writes in his life of Plato: So he divided up living things in this way into forms and parts in every way until he reached the five elements of living things (which he called five figures and bodies), the five elements being aithêr, fire, water, earth, and air. So, according to Plato, the dodecahedron was also the shape of a simple body, that of heaven, which he calls aithêr. But if he says that heaven is made of fire, he means that it is made of light, since he also says that light is a form of fire. But the stars are made of the four , not the ones involved in coming to be, but of fire insofar as they shine, of earth insofar as they have resistance to sensation, and of the intermediates insofar as they have intermediate . So if Aristotle also agrees that they are visible and tangible, he too does not decline to construct heavenly things from these highest forms , in which the perfection of the elements also is; for he thinks that heaven completely transcends the four sublunary elements, which move in a straight line and are imperfect. Similarly, if he also says it is simple, it is reasonable for him to deny that it is a composite of these . We will learn that he says16 it is a living thing with a soul, and he thinks that living things have composite bodies. That natural bodies do not just change but, most of all, change place is clear because change of place is the primary kind of change in all the senses of ‘primary’, as he proved in the last book of the Physics17 and because nature, being a starting point of change, is most of all a starting point and cause of the primary kind of change. Dividing the natural motions, Aristotle says that some are simple and some are not. And when he has proved that there are simple motions, he will have as an easy result that they attach to simple bodies and that the motions of simple bodies are simple. And it is immediately clear that motion in a circle and motion in a straight line are simple since neither of them is composed from different motions. He proves that only these are simple by setting out lines. For every motion occurs on some linear interval; so if there are only two simple lines, there are also two simple motions. He does not set out the magnitudes18 as causes which produce motions, but as material causes and as playing the role of ‘that without which’,19 as Alexander says; for if motion exists, it is impossible that magnitude does not exist, but if magnitude exists it is not necessary that motion exist (this is proper to matter). But one should realise that perhaps the form of the underlying magnitude is sometimes a cause

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of the form of the motion and the form of the motion is a cause of the form of the underlying magnitude.20

Xenarchus21 argued against many things said in this context in his Against the Fifth Substance, including the words ‘the reason being that also only these two magnitudes are simple, the straight and the circular ’. He says,

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The cylindrical helix22 is also a simple line because any part of it coincides with any part which is equal . But if there is a simple magnitude in addition to the two, there will also be a simple motion in addition to the two and a simple body which moves with that motion in addition to the five. Alexander gives two responses to Xenarchus, the first being an indirect counterargument.23 Agreeing that the cylindrical helix is simple, he says that Aristotle did not set out magnitudes as causes which produce motions. For if it is true that a simple body moves with a simple motion along a simple line, it is not thereby true that, as Xenarchus maintains, for any simple line there is a simple natural body which moves with a simple motion along it; Aristotle does not posit this.24 But perhaps Aristotle’s own response has more force, since he says clearly that the reason is that ‘also only these two magnitudes are simple, the straight line and the circular arc’.25 For even if he does say that magnitudes are material causes and for this very reason if there is another simple magnitude it is not necessary that there also be another simple motion; nevertheless, his clear assertion that there are only these simple magnitudes is overthrown if there is also another simple magnitude. So Alexander’s direct26 response is better, namely that the cylindrical helix is not a simple line since it is generated out of two dissimilar motions, one circular, one in a straight line. For the cylindrical helix is generated when a straight line is drawn around the surface of a cylinder and some point on it moves uniformly. Xenarchus himself accepts this when he writes, Let there be a rectangle (tetragônon) and let it be rotated in a circle with one of its sides (the axis of the cylinder) remaining fixed. Let a point move on the side which is parallel to this side and is revolving, and let this point traverse this line in a time equal to that in which the parallelogram returns to the same position as it started to move from. In this way the parallelogram produces a cylinder, and the point moving on the straight line produces a helix, which (as he says) is simple because homoiomerous.

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However, even if it is homoiomerous, it is not simple. For although a simple line is always also homoiomerous, a homoiomerous line is not always simple, unless it is also of a single kind and unless, if it is generated by a motion, the motion is also of a single kind or rather single. For the helix of the solar motion is generated by two circular motions, that of the sun on the zodiac and that of the sphere of the fixed stars, since each of these motions occurs around different poles; and the helix has a mixed nature. ‘Furthermore’, Alexander says, ‘the simple motions possess their simplicity because of their relation to the centre of the universe,27 since one is around the centre and the others are from the centre or toward the centre. But the helix is not like this’.

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Having said that there are two simple motions, straight and in a circle, he defines each, saying that motion around the centre of the universe is in a circle. According to Alexander, he is indicating the centre of the universe by using the definite article in saying ‘around the centre’;28 consequently the motion of wheels, which does not take place around the centre of the universe, is not simple motion in a circle, since in a way it includes an up and a down in each of its parts, which are up at one time and down at another. He says that the simple straight motions are up or down, and he makes clear what each of these is by saying that motion from the centre is up and motion to the centre is down. And he makes clear that he is assuming the same centre for motion in a circle and the motions in a straight line by saying ‘Consequently it is necessary that any simple motion,’ and so on. He wanted to present all the simple motions in terms of the one relation to the centre. And when motion to the right or to the left or forward or backward is simple, it is either upward or to the centre (for the motions of animals which occur by the bending and stretching of limbs are not simple); consequently lateral movements which are in a straight line are up or down. So Alexander.29 But perhaps motions to the right or to the left or forward or backward are not simple natural motions; rather they are the motions of animals30 which have a right and a left and a front and a back, whereas earth and fire and any of the other do not move with this kind of motion except by constraint when they are thrown or pushed or struck by other things. Having assumed as clearly true that there are two simple lines, the straight and the circular, and that simple motions occur along simple lines, he has implicitly reasoned in the following way: Simple motions occur along simple lines; motions which occur along simple lines occur along a straight line or a circle.

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And the conclusion is clear. And then again, in my view, he has taken it as clearly true that in a sphere what is, most of all, a determinate straight line is the one from the centre to the circumference, so that there are also two determinate rectilinear motions in a sphere, motion up, which is from the centre, and motion down, which is to the centre. Therefore there are three simple motions with a relation to the centre, one from the centre, one to the centre, and one around the centre. It seems to me that the inference that there are three motions, which is said to be reasonable in relation to body being three-dimensional, is a divergence from Aristotle’s precision unless there is an argument to prove some commonality between the motions and the dimensions. 268b26 From ‘Since some bodies’ to ‘but occurring in accordance with what predominates’. Having established the first hypothesis which says that there are three simple motions, that from the centre, that toward the centre, and that about the centre, he turns to the second and third and proves that the motion of a simple body is simple and that a simple motion attaches to a simple body. He proves these things by now dividing bodies into simple and composite as previously31 he divided motions into simple and mixed. And having defined simple bodies, he assigns the simple motions as proper to the simple bodies, the mixed motions as proper to the composites. For every change of place attaches to some body. He says that simple bodies are those which have a starting point only of natural motion. For animals and plants have a starting point of motion, but, qua animals and plants, they do not have a starting point of natural motion, but of psychic motion, and so they move differently at different times. For composites are not restricted to things which are homoiomerous;32 they also possess organic 33 because they have in addition a soul which uses the body as a tool. But nature is a starting point of simple motion, and so things which have only a nature have a motion which is simple. He says what things have a simple motion when he adds ‘for example, fire and earth and their species and the things which are akin to them’, meaning by species of earth sandy earth, stony earth, chunky earth, white earth, black earth, and so on; the species of fire are coals, flame, and light, as Plato says.34 Alexander also explains this well35 in the following way. He says, Having said ‘for example, fire and earth’, he adds ‘and their species’, meaning universally all fire and not just this particular fire, and universally all earth and not just this particular earth,

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that is, the form of earth and fire because of which it is fire or earth. But air is akin to fire, and water to earth, even if there is, as he will prove, another simple body, the fifth; for this too is natural.36

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Alexander says, If what it is to be a natural body lies in having in oneself a starting point of motion, and some things which have a starting point of motion in themselves are simple and others are composites of these, then it will follow that the motions of simple bodies are simple, and those of composite bodies are composite. But perhaps Aristotle is using the term ‘simple bodies’ more precisely, meaning whatever has a natural starting point of motion; for composites,37 insofar as they are composites, do not have a natural starting point of motion, but they have a psychic one and so also possess organic parts. A simple motion is also single. For a simple motion attaches to a simple body. But, since it is simple, a simple body has in itself the starting point of a single motion. For if it had a starting point for many motions, even simple ones, it would no longer be simple, but would be a composite of as many bodies as it had starting points of motion; for a composite body differs from a simple one by having in itself starting points for many simple motions. But a single motion is not always simple. For the motion of animals which results from the stretching and bending of limbs is not, I think, single in the strict sense, whereas an oblique motion like that of shooting stars is single, but not simple, since it is composed from motion up and motion down; and helical motion is composed from straight and circular motion. Alexander says, He says ‘in some way mixed’ because motions are not mixed in the same way as bodies are. For simple bodies exist together with one another in a mixture, but in the case of motion the prior motion does not survive the second one in such a way that we can say that this has been mixed with this. But perhaps in the case of motions which are mixed because they succeed one another, as in the case of the stretching and bending of limbs, it is true that the prior motion does not endure, but I do not think this is true in the case of oblique motions in which up and down have been mixed in a single form or in the case of helical motion. Instead one should understand the phrase ‘in some way’ as appropriate to motion.

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The natural motion of composite bodies occurs in accordance with what predominates: if someone throws a human body it moves down because the earthen predominates in it. However, I think that when Aristotle adds ‘occurring in accordance with what predominates’, he is focusing on those four things which are called elements by us; these are not simple in the strict sense, but they move with their simple motions in accordance with what predominates. For the simple bodies would not be cut off in regions, since they have been made for the composition of the universe. And perhaps heaven is also composed from the highest forms of the four elements (since it is visible and tangible) but the highest form of fire predominates in it,38 and it is also said to be simple, just as these four are said to be simple by comparison with composites.39 Every body which has a simple motion is either simple or it has this motion in accordance with some simple thing in it which predominates. If this is true, then, even if the body which moves in a circle is composite, it would have this simple motion in accordance with something simple which predominates in it. For the composite does not have a simple motion insofar as it is composite. 269a2 From ‘So since there is a simple motion’ to ‘by its own40 nature’. He has proved that motion in a circle is simple on the basis of the fact that the magnitude on which it occurs is simple; and he has also proved that a simple motion attaches to a simple body and that the motion of a simple body is simple. And he produces the following syllogism for what comes next: Since motion in a circle is simple, and a simple motion attaches to a simple body, and the motion of a simple body is simple, ‘it is necessary that there is a simple body which is of such a nature as to move in a circle by its own nature’; but the antecedent holds because it has been proved; therefore the consequent holds. Alexander says,

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It is reasonable that he has not presented this hypothetically by saying ‘if (ei) motion in a circle is simple’ and so on, but he has used the causal connective ‘since’ (eiper), because he has already demonstrated all the lemmas. But perhaps eiper is still hypothetical and does not mean the same thing as epeidêper; for the addition of per to the hypothetical ei does not change its force, just as its addition to the causal connective

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epeidê does not change its force either. Perhaps Aristotle has presented this hypothetically because of philosophical caution.41 But it is clear that the hypothetically expressed lemmas, which have been demonstrated, can also be presented categorically as follows:

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Motion in a circle is simple; a simple motion attaches to a simple body; therefore motion in a circle attaches to a simple body; therefore, the body which moves in a circle naturally is a simple body. 269a7 From ‘For it is possible that something’42 to ‘natural … for each of the simple bodies’. Having proved that there is ‘a simple body which is of such a nature as to move in a circle by its own nature’ (269a6-7), he next proves43 that none of the four is the body which moves in a circle either naturally or unnaturally. He proves that none do so naturally as follows. If the natural motion of each of the simple bodies is single (for the natural motion of the simple bodies is simple, and a simple motion is also single), it is clear that, since each of the four elements is simple, its natural motion is simple and single. So if their natural motion is in a straight line, it is clear that motion in a circle would not be natural for them, but – if there were such a motion – it would be constrained for them. For it is possible that the constrained motion of some other different thing be the same , and it is possible that something move by constraint with the motion of some other thing and not just one other thing but more than one (for fire can move down or in a circle by constraint). But it is impossible for something to move with the motion of something else naturally, since the natural motion of each thing is single. And just as he proved earlier that even if what moves in a circle is something composite, since its motion is simple, it moves in accordance with something simple which predominates in it,44 so now he proves that even if something does move in a circle by constraint, since its motion is simple, there is always something which moves in a circle naturally. 269a9 From ‘Furthermore, if unnatural motion is contrary’ to ‘if down, water or earth’. Next he proves that if motion in a circle does not belong to one of the four elements naturally but it is nonetheless hypothesised to belong to it, it is necessary that it be unnatural for it. And so if it is proved

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that it does not belong to it unnaturally either, then, since it has been proved that it does not belong to it naturally, it follows that it does not belong at all.45 He proves that if is not natural it is unnatural on the basis of the fact that unnatural is contrary to natural, so that if the natural is not present it is necessary that the unnatural belong, and that unnatural and nothing else is the contrary of natural, since for a single thing there is a single contrary. For nature is not unjust – it does not set many things in opposition (antitattein) to one thing. And so if the natural is not present, the contrary itself, the unnatural, is present, since the unnatural is contrary to the natural, and for a single thing there is a single contrary. He states in a remarkable way that the reason why, if motion in a circle were not natural it would be unnatural, is that it is simple. For if it were not simple, it would be possible that it be neither a contrary nor unnatural, but just non-natural. However, if what has a simple motion moves, it is necessary that it move either naturally or unnaturally or with an intermediate motion which is not simple. But motion in a circle is simple. He proves that what revolves in a circle is not one of the four elements unnaturally, using once again the fact that for a single thing there is a single contrary. For if moving up is natural for fire, and down is contrary to up, and for a single thing there is a single contrary, motion in a circle would not be unnatural for fire, and for the same reason neither would it be unnatural for any of the three. He proves that motion in a circle isn’t unnatural for any other simple body on the basis of the fact that there would have to be some other simple motion for that body, since it is simple. But only motion up and motion down are simple, and if something has one of those motions, it would be one of the four and not something else. Although there are two simple motions in a straight line, motion up and motion down, there are not just two elements which move in a straight line, but four. He will state the reason for this in his discussion of heavy and light:46 earth is absolutely heavy because it sinks to the bottom of everything, and fire is absolutely light because it rises to the top of everything, but air and water share in both properties, since each of them is both heavy and light, but not in relation to the same thing.47 Therefore, there are two elements which are simple in the strict sense, fire and earth. One should know that both Ptolemy in his book on the elements48 and in his optics49 and the great Plotinus50 and Xenarchus in his work on difficulties for the fifth substance say that motion in a straight line attaches to the elements when they are still coming to be and are in an unnatural region, when they have not yet taken on their natural

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one. And Aristotle seems to agree with this both in the fourth book of this treatise when he says51 that ‘the motion of each thing into its own place is its motion into its own form’ and in On Coming to be;52 and so too Alexander in his commentary on this work, as will be said.53 For, in fact, if the elements move from an alien place and an unnatural condition because they desire their proper places and their proper entirety, it is clear that they do not move when they are in a completely natural condition, but, as the men I have previously mentioned, Ptolemy, Xenarchus, and Plotinus, say, when the elements are in a natural condition and in their proper places, they either rest or move in a circle. Earth, water, and the air which is stagnant54 clearly rest, but fire and the air which is luminous move in a circle, revolving with heaven in accordance with their close relation to it. If this is true – and Aristotle himself says in the Meteorology55 that the hupekkauma moves in a circle, giving as evidence the fact that comets and other appearances arising in the hupekkauma rise and set with the stars – how, first of all, can he try to prove here the superiority of the heavenly body to sublunary things and its transcendence over them somehow on the basis of the unnatural movement of sublunary things? I will dissolve this difficulty, as put forward by Xenarchus, shortly.56 But now the difficulty should be raised how he says that neither fire nor any of the other elements moves in a circle either naturally, if there is one natural motion for each of them and that in a straight line, or unnaturally, if for a single thing there is a single contrary and the contrary of up is down, not in a circle.57 It is perhaps worth noting that Aristotle does not say without qualification that none of the four elements move in a circle, but only that they do not move in a circle either naturally or unnaturally. For he has demonstrated that there is something which moves in a circle naturally and it is neither fire nor any other of the four elements. For if one hypothesised that it was fire, it would not have this motion naturally, since the natural motion of fire is in a straight line, and there is a single natural motion for each thing. Nor would fire have this one motion unnaturally, since the unnatural motion of fire is downward, and for a single thing there is a single contrary. And he has proved in this way that none of the four elements is what moves with this motion in a circle.58 And he proves that this motion in a circle does not belong to any other body which moves unnaturally with this motion which is simple on the basis of the fact that it would be necessary for that body to also have some natural simple motion, and obviously that would be in a straight line; for there is no other simple motion besides motion in a circle, and so this body would again be one of the four elements, which is impossible.

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Let these considerations have a certain reasonableness. But since even according to Aristotle fire does move in a circle, does it do so naturally or unnaturally? If it does so naturally there is no longer one natural motion for one thing, since fire moves upward naturally; but if it moves in a circle unnaturally, there is no longer a single contrary for a single thing, since motion downward is unnatural for fire. So perhaps motion in a circle does not belong to fire either naturally as its own (since it is carried around with the sphere of the fixed stars, and motion from the east is not natural for the spheres of the planets either) or unnaturally in the sense that is contrary to what is natural (since unnatural motion is harmful and does not last). But is different from natural motion because it belongs to something better which dominates it. And perhaps for this reason Aristotle does not say59 that it is possible that something move with the motion of some other different thing naturally, but that it is possible for it to move by constraint. For there is a beneficial constraint which should not be called unnatural but hypernatural. But someone might reasonably ask us this: if the entirety of fire has its motion in a circle, which we see, from something else and hypernaturally, does it have an everlasting natural motion, or, insofar as it is up to them, do the elements up act like earth and water and rest when they have taken on their proper place? I reply that the impulsion of the entirety of fire is toward heaven just as that of earth is toward the centre, but I will say this more fully in the sequel when Aristotle says that the part and the whole move to the same thing.60

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In his work on difficulties for the fifth substance Xenarchus raises a second difficulty after the one concerning simple lines;61 it is directed against the assertion that the natural motion of a simple body is simple. He says, Motion in a straight line is not natural for any of the four elements when it already is, but only when it is coming to be. But what is coming to be does not exist without qualification, but it is between being and not being, just like what is moving, since what is moving is between the place that it is going to occupy and the one that it occupied previously (and coming to be is akin to motion since it is also a kind of change). And for this reason we do not say that fire which is said to be moving up is fire in the strict sense, but that it is coming to be fire; and when it has reached its proper place and lies above the others and is at rest it has come to be in the strict sense; for it is given

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form by this position insofar as it is light. And earth is earth in the strict sense when it lies below the others and occupies the central region. And similarly for water and air, water when it lies above earth and below air, air when it lies above water and below fire. And so it is false that the natural motion of a simple body is simple. For it has been proved that motion attaches to what is coming to be, not what is. So if one has to assign some simple motion to things which already are, one should assign circular motion if there are only these two simple motions, in a circle and in a straight line, and motion in a straight line belongs to the four elements when they are coming to be, not when they are. So it would not be absurd if someone were to assign circular motion to fire, and rest to the other three.62 In dissolving this difficulty Alexander agrees that motion in a straight line does not attach to things which are complete in every way, Aristotle having accepted this in On Coming to be and in this treatise. says clearly that it would not be possible for them to move if there were not some potentiality in them63 since motion is the actualisation of what is potentially.64 And he agrees that they are complete in every way when they are in the regions which are natural for them. But he says that what moves up is not deficient in being fire but in being in the place which is natural for fire itself, to which it moves; and similarly in the case of the other elements. He says that the fact that the previously mentioned motions are natural for things which are already complete in form is made clear by the fact that if someone, by raising earth, takes it away from the lower region in which it, being actual, is already earth, it moves downward in the same way ; for it does not cease from being what it is because it is taken away from its proper place. Furthermore, he says, if earth is heavy, fire light, and motions of this sort are natural for them, the doctrine is not shaken unless someone were to define not what moves upward but what lies at the top of everything as light, and not what moves downward but what lies at the bottom of everything as heavy. (And Plato’s Timaeus also demonstrated that up and down are relative rather than absolute).65 Now if Aristotle also accepts that what moves to its proper place moves to its form, and Alexander that what is complete in every way occupies its proper place, they should certainly give definitions of these things, but the person who wants to argue on the basis of the motions does not need these definitions. So perhaps Aristotle also knows that motion in a straight line belongs to incomplete and deficient elements which are coming to be and perishing, and, wanting to separate heavenly things from them, he argued on

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the basis of motion to prove that the motion suitable to coming to be and perishing belongs to them, while the motion which admits of everlastingness belongs to what is heavenly.66 Xenarchus raises another difficulty when he says: It is not necessary, if nature has assigned simple proper motions of the same kind to the simple natural bodies, that thereby it has also assigned the simple natural bodies to the simple motions. For it did not assign a composite body to composite motions; if it did, the number of bodies would be infinite, since the composite motions are infinite.67 I think it should be said in response to this difficulty that composite natural bodies have been assigned to the composite motions, but not that the bodies are infinite.68 For the composite motions are not infinite in their forms either, unless it is because they occur again and again, as bodies do. For even if each composite body has many composite motions, they are not infinite in form; but, if they are infinite, they are infinite in number because they occur to infinity; and this does not require that moving things be infinite in number, unless they are infinite because they occur to infinity. It seems to me that Alexander either understands this objection of Xenarchus in a different way or he is thinking of and responding to another objection of the following sort: if a composite is one thing and the motion of one thing is single, a simple thing and a composite one will have the same motion, since the motion of a simple thing is also single. And Alexander dissolves this objection as follows: Even if the motion of a composite thing is single, it is nevertheless not simple; for although a simple motion is also single, a single motion is not always simple; for also a body is not simple just because it is one. Consequently the motion of a composite is single, but it is not simple, and if it is also simple, that is not because it is a composite but because it occurs in accordance with what predominates; for there is more than one starting point of motion in a composite and so it is also composite. Here is more Xenarchus:

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Let it be granted that there are two simple lines, the circular and the straight, and that whenever any of the four elements, earth, water, air, and fire, exists, it has motion along a straight line naturally in the strict sense. Even with these assumptions, what prevents it being the case that circular motion is also natural for one or more or even all of these elements? For we did

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not add the assumption that the natural motion of each of them is single. And it is not possible to add this assumption, since it is evidently false; for each of the intermediate two elements has two natural motions: water moves naturally up from earth and in the contrary direction away from fire and air, and air moves down from fire and up from water. But it is clear that we have also assumed69 that the natural notion of the simple bodies is single, since Aristotle says,70 ‘For it is possible that something move with the motion of some other different thing by constraint, but it is impossible that it do so naturally since there is a single natural motion for each of the simple bodies’. The following makes clear that the intermediate elements do not have two starting points of motion per se. Air is light, but it is less light than fire; and water is heavy, but it is less heavy than earth. Motion downward for air or upward for water is constrained, not natural, and more and less do not change the species of something.71 But if someone wanted to say that one thing is less light and another less heavy because of a mixture of a contrary, he would be saying that these things are not simple in the strict sense (as Aristotle also thinks), but they move for the most part in accordance with what predominates, and sometimes they move in both directions. For what separates a simple body from a non-simple one is having a principle of a single nature (and it is perhaps for this reason that Aristotle often speaks as if he were discussing two simple bodies). Alexander sets down and dissolves these objections of Xenarchus on these subjects. Xenarchus also states another objection as follows: It is impossible that motion in a circle belong naturally to a simple body, since in the case of the simple bodies, which are homoiomerous, all their parts move with equal speed, but in the case of a circle, things toward the centre always move more slowly than things toward the circumference, since they move a lesser distance in the same time. But also in a sphere the circles around the pole move more slowly than those further away, and the greatest of the parallel circles moves fastest of all. I think it should be said in response to this difficulty that Aristotle is calling simple the motion in a circle of one thing which occurs along one circular line. The argument raising the difficulty takes many circles in a sphere which move at unequal speeds and, again in the case of a plane circle, takes circles toward the centre and circles toward the circumference and tries to prove that the motion composed of all of these taken as one is composite and not simple. The argument did not refute the assertion that the motion on each individual circle in the sphere and of each of the circles in a circular

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plane figure is simple; for a motion which occurs on the arctic circle and a motion on the equator are equally simple, even if one is slowest and the other fastest, and the motion of each of the circles drawn in the planes of these circles is equally simple and belongs to the simple body which is associated with that part. For Aristotle did not say that the many circular motions are one simple motion or belonged to simple body, but that a simple motion, which is also single, always belongs to a simple body, and that the motion of one simple body is simple and single. Consequently because Aristotle’s argument is applicable to the whole heaven taken as one undivided thing, and even if someone should divide heaven into parts it is also applicable to each one of them, one should take the hypothesis as concerned with a single motion on one circle.72 Finally in this connection Xenarchus complains that, while talking about natural things we give mathematical demonstrations, since we have used kinds of lines in making the causes of the simple motions depend on the simple lines. However, if we used lines mathematically we would have really deviated from our purpose. But, if every motion occurs on a linear distance, a simple motion on a simple distance, a composite one on a composite one, and we have set out the kinds of distances in order to show the different kinds of motions, how can we be said to prove results about nature mathematically? For if both the physicist and the mathematician use lines as well as surfaces and solids, simply using lines is not mathematical; using them mathematically is.

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Xenarchus has made these objections against the hypotheses accepted by Aristotle. One of our contemporaries,73 who is, it seems, in search of a reputation, has presented some of Xenarchus’ objections as his own progeny and assembled others of the same kind and emerged as a prosecutor of Aristotle, setting as his goal, as he says, to demonstrate that the whole cosmos is perishable – as if he was going to receive some great prize from the creator if he could demonstrate that he created only perishable things and nothing imperishable. Because of this desire he proposes to argue against what Aristotle says here in lengthy books, not just hoping to astound the ignorant with their length, but also, I think, turning away most people and especially refined people from reading his endless babble. The result is that, since his writings remain unexamined, a reputation for wisdom has accrued to the author just because he has written so many pages against Aristotle. I know that these sorts of adventures are like the so-called gardens of Adonis:74 they are thought by the ignorant to blossom, but they die in a few days. And I, having proposed to elucidate Aristotle’s treatise On the Heavens as well as I

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can, have thought it best not to disregard this man’s objections, which, although they do not trouble anyone with an education, among the uneducated75 do stir up those who always rejoice in something novel and are burdened by the renown of the men of old, and further those who think that they honour god if they affirm that heaven, which they say came into being to be of service to human beings, has no transcendence over sublunary things and which they assume is perishable like them. For these people, thinking that these objections provide support for their view of god, hold them in great esteem, knowing nothing about them, and even more knowing nothing about Aristotle’s doctrines, against which they dare to raise these objections, chattering to each other and childishly bragging to us that the doctrines of the philosophers have been overturned. And so, for the sake of these and of those who are more ready to listen, and so that Aristotle’s treatise On the Heavens and its reverential conception of the universe remains unrefuted with its ancient renown, it has seemed best to me to set forth these objections and dissolve them to the best of my ability. For it seemed to me to be more appropriate to combine the objections and their dissolutions with the commentary on the treatise. One should not take offence if I may somehow seem to let out rather rough words against this man; for I am not motivated by the desire for victory over him, whom, so far as I know, I’ve never seen.76 But first of all, it is appropriate to impose a deserved punishment on this person who [i] has learned from Aristotle and his commentators (if indeed he has learned anything about these matters) – he did not come to us from Menander and Herodian77 and the like having learned the truth about the nature of things more accurately than Aristotle – and who [ii] nevertheless is also not ashamed to write about Aristotle, a person whom one would not go wrong in calling an icon or rather the father of cleverness (deinotês) itself, both that he has been clever in obscuring the truth with the mist of fallacies and that the clever Aristotle has also obscured the truth by expressing himself in a variety of ways (and frequently he puffs himself up as wiser than Aristotle and his commentators). And secondly, it seemed to me good to help people who have been led to disdain Aristotle’s writings because of this person’s rashness by showing them that his empty-headed lack of education is worthy to be spit upon. This man has laid down as his first objection against the hypotheses assumed in advance by Aristotle one taken from Xenarchus78 in a debased form. It runs as follows. If different motions are brought about by different natures it would be arbitrary if one and the same nature were not attached to the same motions. Now since earth and water both move to the centre, they would be of the same nature and form; and similarly fire and air both move upward. And so a syllogism of the following kind results for him:

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Translation Since earth and water are simple bodies, and both move to the centre, they should, according to Aristotle, be moved by the same nature; but things moved by the same nature are of the same nature and form; therefore, according to this, earth and water are of the same form.

He says that this is clearly absurd since one is dry, the other moist. In connection with these things it is worth understanding first what is the value of the weight of his arbitrary chatter, when Aristotle clearly says that a single simple motion attaches to a body which is simple and single in nature, from which it follows that different motions are produced by different natures. But this person, taking this as agreed upon, says that it is arbitrary that the same nature does not attach to the same motions, which he adduces as an absurdity. So great is his understanding of what follows in argument! Next, one should understand that even if downward motion is one in genus and so is upward motion, nevertheless the motion of earth and of water are different in species. For earth moves toward the centre and wants to grow around it and lie below all the other elements, but water does not have a desire for the centre but wants to rise above earth and ride on it. And fire and air are related to one another similarly. For there are not, as this person thinks, just two limits, above and below, of motion in a straight line, but each of above and below is divided into two. Accordingly there are also four things which move in a straight line, motion down being divided into motion to the centre and motion to the surface of the earth, motion upward into motion to the concave limit of heaven and motion to the concave limit of the hupekkauma. Consequently water and earth do not have the same motion, and neither do air and fire. But if someone were to say that insofar as they move downward or upward they have the same motion, then these elements would also have the same nature. For if Aristotle is now taking nature as the starting point of change, and not any change but change of place (as he makes clear when he says,79 ‘For we say that all natural bodies and magnitudes can change place on their own, since we say that nature is a starting point of motion in80 them. For every change of place … is either straight or in a circle or mixed from these’), it is clear that things with the same motion would also have the same nature, according to what is now being said, but dry things do not have the same nature in the same way, nor do moist ones. For, insofar as it was a question of differences of this sort, a stone would be different in nature from a stone, and a chunk of earth from a chunk of earth, and one body of water from another.81 But if all things82 followed from different motions being generated by different natures, and this was

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instead true of everything, how can the resulting absurdities follow, since a falsehood does not follow from a truth, as we have learned?83 But this person, taking it as agreed both that water and earth are different in nature, one being moist, the other dry (even though nature is not being understood in terms of such things), and that they move downward with the same motion (even though they do not have this feature in the same respect), adduces a second syllogism, which he also misuses later,84 namely: If it is possible for things of a different nature, such as earth and water, to have the same motion, then, ‘converting with antithesis’ (as he says), you will say: nothing prevents different things which do not have the same motion from being of the same nature, so that, even if heaven moves in a circle, but sublunary things move in a straight line, nothing prevents heaven from being of the same nature as sublunary things and perishable like them. For him what he writes always strives for this . And the absurdity of his argument is already clear from what has been said, if nature is a principle of change of place (as even he agrees). But since he makes much use of conversion with antithesis, perhaps there is nothing to prevent us from showing that he does not understand the way it works.85 For he presents the argument thus:

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If it is possible for things different in nature to have the same motion, then nothing prevents it being the case that (i.e. it is possible that) things which do not have the same motion do not have different natures. However, first of all, he does not add the negating particle to the modal operator in the assumption of the contradictory denial of the affirmative consequent, as the dialectical rule requires. For he says ‘it is possible … to have the same motion’ and, wanting to take the contradictory denial of this affirmation, he does not say ‘it is not possible … to have the same motion’86 as he ought to say in adding the negating particle to the modal operator; rather he says, ‘It is possible that things which do not have the same motion do not have different natures’. So how is it possible for a person who does not know the denial which is contradictory of the consequent of the affirmation of the antecedent to understand conversion with antithesis? And what do I mean by conversion with antithesis? How is it possible for the person who does not know how denials are produced from affirmations to understand any kind of syllogism whatsoever? And he is also ignorant of this very thing: that, in the case of something asserted to be possible, for which what is asserted to follow

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does not follow any more than its contradictory, the result of conversion with antithesis is not necessarily true. But this type took the consequent in such a way that its contradictory rather than the assumption itself followed from the antecedent. For what follows for things which differ in nature is that they do not have the same motion but a different one, rather than that they move in the same way.87 And if this is the way things are, the contradictory of the antecedent will not follow necessarily from the contradictory of the consequent, as conversion with antithesis requires; rather the antecedent itself will. For that they are different in nature rather than that they are the same follows from their not moving in the same way. And perhaps it is not inappropriate to add a few things for the sake of those who have learned later.88 One should understand the following in the case of possible propositions. If the consequent is taken as following from all the antecedent and as possibly holding or not holding (as if we were to say, ‘If it is a human being it is possible that it is literate’), and then the contradictory denial of the affirmative consequent is taken correctly in this way (‘if it is not possible for it to be literate’), then the contradictory of the antecedent (‘it is not a human being’) follows. But if the consequent is taken to follow contingently in the sense of following from some of the antecedent (and these things are also said to follow contingently, as when one says ‘if it is an animal it is possible for it to move its upper jaw’ (a crocodile is an animal which can do this), then the conversion is not preserved, even if one takes the contradictory of the consequent correctly; for ‘it is not an animal’ does not follow from ‘it is not possible for it to move its upper jaw’ (and this is the contradictory of ‘it is possible for it to move its upper jaw’); for most animals move their lower jaw, not their upper one. And this is the sort of conditional proposition which this person has taken. For even if it were correct to hypothesise that things different in nature have the same motion, this does not hold of all things which are different in nature, but, if it holds at all, it holds of extremely few and the contrary holds of more. Therefore, the contradictory of the consequent (‘it is not possible that they have the same motion’) belongs more to the antecedent than to its contradictory; for ‘things not able to have the same motion’ follows more from ‘things different in nature’ than from the contradictory of this, ‘things not different in nature’. And so, if I say, ‘If it is even, it is possible that it is not divisible down to the monad’ (as is the case with what are called even times odd numbers or odd times even ones) and then I take the contradictory of the consequent ‘it is not possible that it is not divisible down to the monad’, and I infer the contradictory of the antecedent, ‘it is not even’, I will be mistaken, since an even times even number89 is even most of all, and it is not possible that it not be divisible down to the monad. But also if it is possible for things which are different in species to fall under the

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same genus (as human being and horse fall under animal), then by the ‘conversion with antithesis’ of this , things which cannot fall under the same genus are not different in species, or, as this person puts forward unsystematically, it is possible that things which are not in the same genus be the same in species,90 so that, according to him, human being and fig-tree, which belong to different genera, namely animal and plant, are of the same species (and what could be more impossible than this, since there is a prior necessity that things of the same species be of the same genus, since the species is composed from the genus and differentiae?). And thus, even if the consequent is taken truly but as possible, the necessity of conversion with antithesis is not preserved. However, this person has also taken the antecedent91 falsely by taking nature in terms of heat and coldness, but not in terms of change of place, as Aristotle thinks proper. And he takes a false consequent. For earth and water do not move the same way, since one moves to the centre, the other to earth. But he has also taken the conditional falsely. For if earth and water are different in nature and nature is a starting point and cause of change and most of all of change of place, it is necessary that they have different motions and not, as he thinks, the same. For if the starting point and cause of motion is different, it is clear that the motion will be different as well. But let us also take a look at the result of conversion, which he calls the second conditional, not even knowing the customary words for these syllogisms; for they do not call the result of conversion the second conditional;92 rather, they call the taking of the contradictory of the consequent the additional assumption93 and the taking of the contradictory of the antecedent the conclusion. And so understandably the conversion (‘It is possible that things which move in different and not the same ways have the same nature’) is mistaken, not only because in prefixing the negating particle negatively he has not attached it to the modal operator ‘it is possible’ and also because in general he proceeds on the basis of this sort of possible subject matter,94 but also because it is impossible that things which have different natural motions have the same nature, since nature is a starting point of motion. So isn’t it laughable that this man makes use of conversion with antithesis and is so ignorant of it? Next, having agreed that heaven has neither weight nor lightness, he tries to show that nothing prevents it from having heat and cold. He writes the following (it is necessary for me also to babble): For if light bodies are always in fact hot, and similarly if heavy bodies are always cold, it will not necessarily follow that things which are neither light nor heavy transcend cold and heat, since conversion of the antecedent is not sound. For look! If something

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Translation is a human being it is always also an animal, but it is not the case that if something is not a human being it is true that it is not an animal.

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It ought to be realised that if light things are hot, then even more will hot things be light, since what is hot has fine parts, and lightness is a consequence of having fine parts. And for the same reasons cold things are heavy because of the condensing principle (logos) of coldness. So if these things are equivalent, there is nothing to prevent also making the conversion from the antecedent. For if a human being then risible, and if not risible then not a human being, then it is also true to say that if not a human being then not risible because both are equivalent. So here again he obviously does not understand the specific features of conversion with antithesis and emptily judges heaven to be cold or hot. And he brings in something else to his discussions of simple motions: Just as in the case of the four elements, even if motion in a straight line is one in genus, nevertheless since motion from the centre is different in species from motion to the centre, there is a resulting difference in species between fire and earth; so too, since motion from the east is different from motion from the west in species, the moving bodies are also different. And since the spheres of the planets differ naturally from one another in speed (just as earth and water even though they have the same impulsion downward), they differ in species because of being faster and slower. Therefore there are not just five simple bodies, but they are equal in number to the spheres plus the four elements.95 In this case too I think this man has not attended to Aristotle’s purpose. For Aristotle would not deny that the heavenly spheres differ in species, just as the sublunary elements also do. And consequently he inferred96 the number of unmoving causes (obviously causes differing in species or form, since they do not differ in matter)97 on the basis of the heavenly spheres. But just as he considers motion in a straight line to be the cause and sign of coming to be and perishing in the case of all sublunary things, so too in the case of heavenly things he thinks that circular motion is a suitable recipient of everlastingness; so, whether it is from the east or from the west, whether it is faster or slower, the motion is circular and consequently always complete98 and unceasing and everlasting, as has been proved.99 And again, whether it is from the centre or to the centre and whether it is faster or slower, motion in a straight line is limited and consequently involved in coming to be. And I think the cause of

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Aristotle’s dividing sublunary things into four and leaving heavenly things undivided for the time being is that he wants to distinguish the principles of things which come to be and perish (the subject of much of the study of nature) – principles on the basis of which he also explains the causes of what happens among sublunary things. For the distinction between motion in a straight line as one thing and motion in a circle as one thing suffices as far as the difference between heaven and sublunary things is concerned. And so Aristotle also discusses most things not as if there were four sublunary , but as if there were two; but in the next book he also distinguishes the sphere of the fixed stars from that of the planets. In his seventh chapter, this person says: If Alexander was correct100 in pointing out that Aristotle says that the kind of motion which takes place around the centre of the universe is in a circle in the strict sense, but that those motions which do not take place around the centre of the universe are neither in a circle in the strict sense nor simple, and the stars have their own motion apart from the spheres, as the astronomers hold, and move around distinct centres of their own and are not homocentric with the universe, then clearly neither the stars themselves nor their epicycles nor the socalled eccentric spheres have a circular motion in the strict sense or a simple motion, since both motion downward and motion upward are seen in them (for even if this goes against Aristotle’s hypotheses, the stars are clearly observed to reach perigees and apogees). I say that here Aristotle says only that motion in a circle is around the centre, since this is appropriate for every circular motion. If he says elsewhere that bodies which move in a circle move around the centre of the universe, one should understand that he is speaking in terms of the hypotheses of the earlier astronomers. For the associates of Eudoxus and Callippus and those up until Aristotle hypothesised counterrevolving spheres homocentric with the universe and tried to preserve the phenomena by means of them; and they said that all the spheres move around the centre of the universe, but they were not able to give in terms of those hypotheses the explanation of apogees and perigees and the apparent progressions and retrogressions and the apparent anomalies in the motions. That’s why, to be sure, the associates of Hipparchus (and perhaps some before him)101 and after him Ptolemy, hypothesised eccentric spheres and epicycles. Because of these hypotheses they disregarded the that the heavenly bodies all move around the centre of the universe, and in terms of these hypotheses they gave the causes of the I have just mentioned, which were left out by .

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And so Aristotle says nothing about these matters here, and when he does discuss them he obviously follows the hypotheses of his predecessors.102 But it is clear that the disagreement about these hypotheses is no reproach . The issue is on what hypothesis the phenomena might be preserved, and so there is nothing surprising if different people tried to preserve the phenomena on the basis of different hypotheses. However, if the stars move around their own centres,103 they nevertheless also move by being carried by spheres around the centre of the universe. From what astronomer did this person find out that the stars move around their own centres? Was it from hearing what is written in the Tables of Ptolemy, that the numbers of the centre of the epicycle are different from the numbers of the star itself104 that he thought that these were the numbers of the motion of a star around its own centre, not understanding that the numbers apply to the passage of the star and that the motion of the star around its centre does not relate to its passage, but that rather the numbers of the centre of the epicycle show the motion of the homocentric or eccentric on which the epicycle is carried, the numbers of the star showing the motion of the epicycle on which the star is carried? However, it is impossible to apprehend the time of a complete rotation of the star itself around its own centre, since it doesn’t pass from place to place in making this motion. Consequently none of the astronomers tried to calculate the time of a complete rotation of a star around its centre; for it could not be apprehended. But Plato also knows of this motion of the stars. And in the second book of this treatise Aristotle will say what he thinks about the motion of stars.105 This person says, Furthermore, Aristotle has not made the comparison of the elements and heaven on the basis of the same things: in the case of heaven he took the whole moving in its proper place, but in the case of the elements he took a part which had left its proper place and come to be in an unnatural one.

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Here again106 I say briefly that Aristotle’s purpose is to show on the basis of the difference in motions that heavenly things are of a different nature from the four elements. So since the parts of the four elements move away both from what is unnatural and with the motion which is involved in coming to be, motion in a straight line, but the whole heaven moves with the motion which is akin to everlastingness, circular motion, it is reasonable that he inferred from these things that the four elements come to be and perish, but heaven is everlasting. And it was not absurd for Aristotle to make the hypothesis107 that the whole earth was away from the centre, so that he could prove that the impulsion of the whole converges toward the

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centre; for it is immediately clear that whatever piece of it you take, it has an impulsion to the centre. And so it is not necessary for the person who is inferring difference of substance from motion to take things which are moving naturally.108 But even if one thing is a part and the other is a whole, and the one is in an unnatural and the other always in a natural one (for these things show even more clearly the difference, namely that the parts of the one are naturally constituted to separate, the parts of the other are not; and the parts of the one are naturally constituted to be coming to be in an unnatural place, those of the other to be always in a natural one) and even if the entireties of the elements either rest or move in a circle, nevertheless it also suffices to grasp the difference in nature on the basis of the parts themselves, and most of all when all the parts obviously have similar natures to one another, as with the parts of earth, which move toward the centre, and those of water, which rise above earth. But if the entireties of the elements, which do not move in a straight line, are everlasting, and their parts, which come to be and perish, do move in a straight line, it is reasonable that the difference with regard to parts shows most of all the transcendence of heaven. Wanting to show that heaven is also perishable, this person also tries hard to prove that it is of the same nature as the elements on the basis of their also having the same motion. He says: For both the hupekkauma and air, which have the same motion, move in a circle because of their own nature, just as heaven does. For is either natural or constrained and unnatural, but it is better not to exist at all than to be in an unnatural forever. But if the parts of a whole are in an unnatural , the whole will be as well. He wastes time, making this banquet for himself and speaking the same nonsense many times in this text.109 I have spoken against this ‘difficulty’ before110 and, I think, very explicitly. But let me say again now that the motion in a circle of fire is not its own since it is carried around with the sphere of the fixed stars, just as the motion from the east of the planets is not their own either. But that does not mean that it is unnatural in such a way as to be harmful, but in such a way as to be hypernatural insofar as it is dominated by what is better, and it is of such a nature as to have the motion of what is better, just as the soul is of such a nature as to be divinely inspired, but it does not have this divine motion on its own. But how can he think that the circular motion of fire is its own when it is transmitted by the sphere of the fixed stars and the spheres moved by it? Furthermore, he also objects to the statement that it is possible

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that the motion be of some other and different thing by constraint but it is impossible that it be natural,111 since for earth and water motion to the centre of the universe is natural. However, he is incorrect in thinking that water has this impulsion to the centre rather than112 that of rising above earth. And so even if water proceeds as far as the centre when earth is taken away ,113 it does proceed because it reaches earth at some point, on which it will float; and if someone took the earth away from the centre, I think the water would go past the centre, seeking earth. This is made clear by the fact that water naturally rests when there is earth lying under it and does not need to flow downward unless, insofar as earth is taken away from under it, it is necessary for it to flow to more hollow places, since it is liquid and flows. But if, as this person thinks, motion to the centre of the universe is natural for both earth and water, each does not move naturally with the motion of another thing but with its own motion. And he adds the text which says, ‘Furthermore if unnatural motion is contrary to natural’, and so on,114 in which Aristotle proves that circular motion is not only not natural for some element, it isn’t unnatural either. And he utters what I think is a lot of nonsense, trying to prove that motion in a circle is not unnatural for fire. Aristotle also says the same thing, but he says that it is neither natural nor unnatural. However, this person wants it to hold naturally, and he first proves that it is not unnatural, using Aristotle’s demonstration: if for a single thing there is a single contrary, and downward motion is contrary to the natural motion of fire, motion in a circle will not also be contrary to it; and so it will not be unnatural either, since what is unnatural is contrary . Therefore, , motion in a circle is natural for fire in its proper place. However, in using the Aristotelian demonstration he ought rather to have been stirred to investigate the question why in the world Aristotle chose to say what is apparently incongruous, namely that fire moves in a circle neither naturally nor unnaturally, although it does move in a circle. But, as I have said,115 how can anyone assert that the motion which is not fire’s own motion is natural for it? And so, since the motion is entirely simple, it is better to say that it is hypernatural, so that the natural motion of a single thing is single. He debases this too by saying that fire has two natural motions: one, which belongs to its parts which have been detached from the entirety, being upward, the other, which belongs to the entirety, being in a circle. The result is that nothing prevents heaven, which moves in a circle, from being fire, nor will motion in a circle be unnatural for fire. And in all of this it is clear that his downfall was thinking that the motion in a circle of heaven does not belong to fire hypernaturally, but naturally.

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Alexander has said correctly116 that in there is also a rectilinear motion which is fire’s own motion, since some parts of it rise and sink and become rarer and denser. He said this when he proved that the motion is mixed, not simple, and in this way inferred that circular motion was neither natural nor unnatural for fire. And as a result of this the same thing does not have two natural motions nor are there two contraries for a single thing, but rather, since there is some circular and some rectilinear motion in fire, as was said, it should be said that circular motion is bestowed upon it by heavenly things in a hypernatural way and that rectilinear motion belongs to its parts. But this contentious person, although he earlier117 does not even accept that heavenly things have this kind of motion, continues to argue that the entirety of the hupekkauma has its own simple circular motion. The reason is that he thinks that he can infer from this that, even if heaven has a simple circular motion, nothing prevents it having the same nature as sublunary things and being perishable in the way they are. It would suffice against this impious and irrational purpose to invoke what was proved earlier, namely that the hupekkauma does not move in a circle on its own, but its motion is bestowed hypernaturally by the revolution of the heavenly sphere, as is made clear by the appearances which are constructed there and also rise and set together with the stars for several days. And it would also suffice to note that even if heaven were fiery, it would be everlasting because it has a simple circular motion, and it would be everlasting not just as a whole, as fire is, but also in its parts, since none of its parts would separate from their proper entirety and again be attached to it. So in this respect, if in no other, it would be of a different nature than the sublunary elements; because of its nature it does not come to be in time or perish, not only with respect to its entirety (as is the case with the elements) but also with respect to its parts. Since he has said a lot against Alexander’s proving that the motion of the hupekkauma is not simple but mixed, it is right to put a few of the things he says to the test. He says: Even if some parts of the hupekkauma and the air go up and some go down, and some become denser, some rarer, and it is clear that one part moves faster, another slower,118 nevertheless the circular motion of the whole is simple. For it is also possible that when fire moves upward and water downward, some of its parts are thrown here and there by some wind, but nevertheless the whole has a simple motion from the centre or to the centre.119 However, who would say that the motion of that fire or that water is simple in the strict sense, if what moves is composed of dissimilar

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parts and one draws up, the other down, when in the case of things which move in a straight line the motion is probably oblique? And he says: While the sphere of the Morning Star is rotating, the Morning Star itself is moving on its own epicycle and sometimes coming closer to earth and sometimes further away. And the same is true of the other planets, but nevertheless the whole heaven has a single simple motion.

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One should note that he accepts these things now when he thinks he can overturn other things on the basis of them; and one should also note that he is sounding off in this way out of unfamiliarity with astronomical hypotheses. What person who has been educated to any extent does not know that the astronomers’ hypotheses have this purpose: to demonstrate by means of them in what way the additions and subtractions and moving away from and toward the earth and the progressions and retrogressions and the phases and all the heavenly phenomena come about, with all the circular and uniform motions of heavenly things being preserved? For the motion of each of the things in heaven is simple and uniform. And even if more partial things are carried around by bigger wholes, the motion of the bigger wholes does not become composite: it remains simple and transmits to the things more partial than itself; and the motion of the more partial things is not composite, but it remains simple, and they take on another more divine and simpler motion from the bigger wholes. He says: And even if some part of the air or the hupekkauma becomes rarer or denser, this does not make the motion of the whole not simple. For in general, rarefaction and condensation are qualitative changes, not changes of place. For also if it happened that a chunk of earth became warmer or colder while moving to the centre, this is not a reason why the motion is not simple. Notice how unintelligible what he says is, since he does not understand that what becomes rarer becomes lighter and what becomes denser becomes heavier, and as a result the parts120 also change place at unequal speeds. But also when water moves down and becomes ice, it does not keep its motion downward simple,121 as this person believes. But he again sets out a passage from Alexander. It says: It is necessary that at the same time as it is carried around it also move in accordance with its proper impulsion, up if it is a

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light thing or down if it is a heavy one, and accordingly that its motion be a mixture of straight and circular. This person mischievously distorts the passage, understanding ‘up’ and ‘down’ in relation to the whole , and he tries to prove that the hupekkauma cannot move either up (because it touches the lunar sphere) or down naturally. But it is clear that Alexander is saying that when the whole is moved in a circle by heaven, some parts of it move up and some move down, as is made clear by the passage of Alexander which this person set out earlier.122 It says:

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For fire and air do not move simply in a circle with this motion nor simply in a straight line, but they have a mixed motion. For some of their proceed above and become lower in a revolution of this kind; and in addition they are rarefied and condensed. Consequently Alexander said that some of them (not their wholes) are rarefied or condensed. And, since these things produce a difference in motion, he does not agree that the motion remains simple. Since he frequently brings in the claim that if circular motion is not natural for the hupekkauma and air, it would not last long since it would be unnatural (for Aristotle also says123 what is unnatural perishes most quickly), it should be mentioned [i] that the motion of those things is not entirely simple, as Alexander proved on the grounds that the motion in a straight line of things which rise and sink has been woven in, and [ii] that they have circular motion hypernaturally, and this better preserves the things sharing in it. So even if Ptolemy, Plotinus, Proclus, and Aristotle himself say that the hupekkauma moves, they do not say that it has this motion on its own because it keeps pace with the sphere of the fixed stars, but they say that it is naturally related to the sphere of the fixed stars so that it is not dragged by constraint, although it is moved along by something else, just as the sphere of the planets are moved by the sphere of the fixed stars. And this motion of the hupekkauma is not its own, but it is not constrained either; it is hypernatural. So these are the things relating to these discussions spoken against Aristotle by this person. I think they have been dissolved. We should return and go on to what comes next. 269a18 But it is also necessary that this sort of motion124 be primary … He has proved that there is another simple natural motion beside motion in a straight line, namely motion in a circle, and that a simple

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motion attaches to a simple body; and he has inferred from these things that there is another simple body beside the four elements which move in a straight line, for which motion in a circle is natural. And having also proved that none of the four elements can move in a circle either naturally125 or unnaturally, he next proves that the body which moves in a circle is prior to those which move in a straight line, and more divine126 than they. He proves this by proving that motion in a circle is naturally prior to the other motions, which he proves by proving that a circular line is prior by nature to a straight one, which he proves by showing that a circular line is complete, a straight one incomplete, just as he also established that there is a simple body which moves in a circle naturally from the fact that motion in a circle is simple,127 and that motion in a circle is simple from the fact that a circular line is simple.128 And he establishes simplicity together with priority;129 for primary things are always simple because simple things are prior by nature to composites. In the eighth book of the Physics130 Aristotle also proved that motion in a circle is prior to motion in a straight line. There he proved it on the grounds that motion in a circle is complete, simple, and continuous in the strict sense, and here the demonstration depends upon its being complete. For it is immediately clear that what is complete is prior by nature to what is incomplete, since incomplete things are derivative from (ek) complete ones. He proves that motion in a circle is complete on the basis of the fact that a circle is complete, and this on the basis of the fact that a circle is limited and has an end (these are appropriate to complete things) and, furthermore, the fact that, if a circle is added to, its form does not remain (since addition occurs with respect to a deficiency). He does not prove these things in terms of the circle, but he proves that the circle is complete through the fact that the opposites of the things through which he proves the straight line to be incomplete and not the things themselves are present in the circle. He proves that every straight line is incomplete by first making a division into infinite and finite since every straight line is either infinite or finite. He does not do this because he thinks that there is an infinite straight line131 (since the universe is finite) but because some people think there is; and, even if there isn’t, the division includes the line which is continually increased in imagination, and the division does away with any refutation. For132 an infinite straight line is not complete because it does not have an end or boundary but is indeterminate (for what already has an end and boundary and lacks none of the things belonging to it is complete); and a finite straight line has something outside it and so can be increased, but what can be increased is incomplete, since it has not yet taken on everything belonging to it. However, a circle is limited and has an end and has nothing outside it, and it cannot be increased with its form remaining.

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Alexander proves that the circle is complete on the basis of the fact that it has a beginning, middle, and end: ‘at least’, he says, ‘if the centre is its beginning, the outermost line its limit, and the plane between these two its middle’. But I think it should be noticed that Aristotle is perhaps now taking the linear circle on which a motion is completed and not the plane circle, and so he does not think it right to give a demonstration in the way Alexander does, but on the basis of the fact that a circle is limited and does not admit being added to. And it may have a beginning, middle, and end, but each of them is everywhere, since anything you take which belongs to it can be beginning or middle or end. And this, I think, would be evidence that the circle is absolutely complete since it reveals completeness in everything belonging to it. But why is it true that there is something outside of every finite straight line? The diameter of the universe is also finite, but what could there be outside it since there is nothing outside the cosmos? And how is it not absurd to say that every straight line is incomplete? For there is a form of straight line and it is necessary that it participate in completeness just like the other forms, so that, even if there are incomplete straight lines, there must nevertheless always also be a complete one. (Alexander understands that we can extend any straight line which is taken in theory (logos), not meaning that the straight line is increased but that a line which is of any given size is).133 Consequently the form of straight line insofar as it is straight is everywhere complete, both in a small straight line and in a large one, whereas the magnitude is complete in the straight line which takes on the whole measure of the cosmic straight line. The completeness of this cosmic straight line is also deficient with respect to form relative to the circular form and its completeness, because it does not converge into itself but flows out as far as it is able toward unmeasuredness and infinity, but its quantity is bounded by demiurgic measures. So this is what is meant by there being something outside of every finite straight line: that, insofar as it is up to it and its indefinite flow, it always has something deficient and can be added to. So, having also assumed that a more complete motion is prior (he says ‘for the complete is prior by nature to the incomplete’), and having demonstrated that the circle is prior by nature to the straight line because it is more complete, and motions are related as the lines on which they occur, he has as conclusion that motion in a circle is prior to motion in a straight line. And again, taking in addition to this proposition another clear one which says that a prior motion attaches to a body which is prior by nature, he has as conclusion that motion in a circle attaches to a body which is prior by nature to bodies which move in a straight line, a conclusion which he has left out as clear, since he has set out the two premisses which directly imply it.

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And then, wanting to prove that this body which is prior by nature and moves in a circle exists and is simple and different from the four elements, he does so, I believe, in the following way. If there are two simple motions which attach to simple bodies, motion in a straight line and motion in a circle, and motion in a straight line attaches to the simple sublunary bodies, which move up and down, it is necessary that motion in a circle also attach to some simple body which is different from the sublunary bodies. For motion always attaches to a moving body, and simple motion always attaches to a simple body. For even if a mixed body sometimes moves with a simple motion, as a human being who falls from a roof moves toward the centre, he too has this motion in accordance with the predominant simple body in the mixture, that is the earthen body.134 However, Alexander says that it is proved that this body which is prior by nature is simple with an argument from the less and more135 in the following way (to put it briefly): If, in the case of motions for which it is less reasonable that the moving bodies be simple, the bodies are simple, then, in the case of motion in a circle for which it is more reasonable that the moving body be simple, it would be more that this body is simple. But perhaps it is not immediately evident that it is absolutely more reasonable that a body which moves in a circle is simple; rather, if anything is immediately obvious, it is that the body which has a motion which is prior by nature is simple; for simple things are prior to composite ones. So perhaps the argument should rather be presented as follows:

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If, it is less reasonable that the substance of things which are posterior by nature (that is, the things which move in a straight line – for this has been proved)136 be simple, and their substance is simple, and it is more reasonable that the substance of things which are prior by nature (that is, things which revolve in a circle) be simple, then it would be more that their substance be simple. Let these things be said for the clarification of Aristotle’s words. But, as Alexander says, some people raise a difficulty for the doctrine which we have stated, according to which what is more complete is prior by nature and what is prior is simpler. For if the cosmos is more complete than each of the things of which it is composed, and what is more complete is prior and what is primary is also simple, the cosmos will also be prior to and simpler than the things of which it is composed. But, as Alexander says, the cosmos does not exist before

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its parts, nor is what is composed of them thought to be simpler. Alexander concedes these things and tries to dissolve the difficulty with the assertion that the cosmos is said to be more complete in the sense that it contains more, but motion in a circle and the circle are not said to be more complete than motion in a straight line and the straight line in the sense of containing them, but in the sense of being more complete with respect to form. He says that in the case of these which have been separated it is true that what is more complete is both prior and simpler, but it is not true in the case of wholes and parts. For, he says, the whole is both more complete than its parts by nature and prior in substance, but it is not also prior in time; for what is prior in time is complete and, in addition, simple. But Aristotle proved in the eighth book of the Physics137 that motion in a circle is prior to motion in a straight line not only in substance but also in time. This is what Alexander says. But perhaps the word ‘prior’ has not been used to mean ‘prior in time’; for there was no time at which there was circular motion but not motion in a straight line, even if circular motion is always the cause of motion in a straight line; and it is even more true that there never was a time when there was a circle but not a straight line. Rather the word ‘prior’ has been used to mean ‘prior by nature’; at least Aristotle clearly says, ‘For the complete is prior by nature to the incomplete’ and again ‘So, since a prior motion attaches to a body which is prior by nature’. And so the cosmos, which is more complete than its parts, is prior to them by nature, as Alexander also agrees. And I think it is simpler; for if it is prior by nature it is more unified, and what is more unified is more akin to the One, and what is more akin to the One is simpler. But we do not attend to the unified entirety of the cosmos in terms of which a single living thing is an image of the Intelligible Living Thing, but rather we attend to its separated plurality, and, talking about this cosmos, we think that the part is simpler than the whole and that the parts are prior. But, in fact, the whole introduces the appropriate separation into itself from its own unity. Aristotle has demonstrated together not only that motion in a circle attaches to a more complete and primary body, but also that it attaches to a simple body because it is simple. And in order that the argument be more general, whether the heavenly body is simple or mixed, he adds ‘For we said that the motion of mixed bodies is in accordance with what predominates in the mixture of simple bodies’ and so on, as if he said ‘For we said that the motion of mixed bodies is also in accordance with what predominates …’. So, even if heaven were composite and moved in a circle, there would always be something simple in it in accordance with the predominance of which it would move in a circle.138

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Here too Xenarchus again raises the same difficulties: first, that the argument makes use of mathematical premisses, the straight line and the circle; second, that there is no simple natural body which moves along a circular line, because the things toward the centre and toward the circumference and in between these which move have motions of unequal speed; third, that even if there is a body which moves in a circle, it is not different from the four elements since some of them rest and the others move in a circle when they are complete – this feature belongs especially to fire (for, as Aristotle also thinks, when they are still incomplete they move in a straight line, a motion which is incomplete). Alexander did not even think it worth while to set out these objections since they had already been put forward and dissolved,139 and in the sequel I will try to pass over things of this sort.

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But this young crow of ours – or rather jackdaw – who, as the magniloquent Pindar140 puts it, ‘chatters emptily against the divine bird of Zeus’, sneaks out against what Aristotle says here and adduces a first objection, presenting as his own progeny Xenarchus’ third objection. He says: Even if what moves in a circle is first, it is not thereby different from the four elements since resting or moving in a circle also attach to them when they are complete.

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However, it has been said many times before141 that motion in a circle does not belong to the hupekkauma on its own, but it moves with the motion which it has hypernaturally, being carried along with heaven. Consequently, in the strict sense motion in a circle belongs to heaven. And since what moves in a circle naturally is first by nature, heaven would be first and different from the hupekkauma, which we say is fire. Then, conceding ‘for the time being’ that a circle is complete because it has a beginning, a middle, and an end, he says: Why is it necessary that motion on a circle also be complete? If it is because it has a beginning, a middle, and an end (as Alexander but not Aristotle says142), then motion on a finite straight line also has a beginning, middle, and end. However, if he has conceded ‘for the time being’ that a circle is complete, but that obviously the straight line is incomplete, as Aristotle hypothesises, how can a straight line have an end (telos) when it is incomplete (atelês), if, indeed, one should understand an end as what makes the thing which has it complete and in need of no

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addition, and one should not understand an end as just a limit (to perainon), since a limit also attaches to things which admit of an addition? Consequently, someone who hypothesises that a circle is complete, a straight line incomplete – as this person has done ‘for the time being’ – has no room for saying that motion in a straight line is complete since a straight line does not have an end, and, if it doesn’t have an end, it doesn’t have a middle (in the sense of a middle relative to an end) either. He says, Furthermore, since they hypothesise that circular motion is everlasting because it has neither a beginning nor a limit, it is clear that it will be incomplete because it is infinite, but motion on a finite straight line will be complete. For they say that an infinite straight line is incomplete because it does not have a beginning, middle, and end, even if it does not admit further increase. I think that this difficulty has been raised in a reasonable way, no matter who raised it. But it is worth noting that on this ground a circle will be completely complete because every part of it has143 a beginning, a middle, and an end. And even if motion on a circle is infinite in the sense of proceeding to infinity, it is not infinite in the sense that it has infinity and indefiniteness as something completed at the present time; rather it, too, always has a finite form, since any of it which is taken is the beginning of some revolution, the middle of some revolution, and the end of some revolution, so that, while always being complete, it advances its completeness to infinity. For, in general, if it were to be incomplete, it could not proceed to infinity, since, if it were incomplete, it could not have infinite power; and if it ever were completed and took on a beginning and acme in a part of time, it could not fail to also decline from its acme in some time. He says, But since there is no infinite straight line in reality, it is clear that any motion in a straight line will have a beginning and a limit and what is between them; and therefore, as far as the definition of ‘complete’ is concerned, the motion will be complete. This is again of a piece with the other difficulties raised by this man. He takes144 the limit (peras) of a straight line as an end (telos), although even he knows that what is said an end is what does not admit another addition as if it previously were deficient. And this belongs to the circle and motion in a circle, but it does

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not belong to the straight line. For even if each bit of circular motion is not just the limit of another motion but also the beginning of one, it is not as if the preceding motion lacked something for completeness; rather, the same motion, which is complete in form, occurs again and again. But motion on a finite straight line is itself added to when the straight line is added to, there being145 one form of what comes to be after the addition. However, if it is not possible to take a natural straight line which is greater than the diameter of the universe, why isn’t the diameter146 complete relative to an end in the strict sense, since, having received its own form, it cannot receive any addition? In fact I have spoken about this difficulty when147 I tried to make clear Aristotle’s reasoning but did not defend Alexander’s idea that one should understand that we can increase any given straight line in theory; but rather asserted that Aristotle was looking to the form itself of circle and of straight line, the one converging by its own nature, the other flowing out into indefiniteness as far as is in its power, even if the demiurgic logos with the help, I think, of the circular figure gave it bounds and measures; for the circle converges toward itself; and the straight lines in it, although they desire infinity as far as it is in their power, have taken on the limit which is appropriate. He says, Furthermore if the motion of heaven and the time which measures it are complete, then they have a beginning, a middle, and an end, and they are not infinite or unceasing, as Aristotle thinks. But if they are unceasing they are not complete, since they do not have a beginning, a middle, and an end. Since this person is again turning the same difficulties up and down, it is necessary for me also to say the same things, namely that just as in the case of the circle, so too each revolution and the time measuring it always have a beginning, middle, and end. For just as every point in a circle is a beginning, middle, and end, so too every bit of motion in the whole motion and every moment in the time of the motion is a beginning, middle, and end; but they are unceasing because again and again.148 The form is, then, what has a beginning, middle, and end everywhere and does not admit an addition; but it is not unceasing, since what is unceasing has a different completeness, infinite power, and it perhaps has this hypernaturally, since it appears to be true that every finite body has a finite power by its own logos.149 So, whether one begins the inference from the magnitude and says ‘as is the magnitude, so is the motion and the time’ or begins from the time and moves in the reverse direction, it is clear that one should understand in terms of form the fact that a circular magnitude and the

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recurrent motion and the time measuring it are complete and have a beginning, middle, and end; for the form of all of them has a beginning, middle, and end, and has these three appearing everywhere, and they accept no addition as if they were deficient in some way. However, the proof is not, as thinks, circular. He says, For if Aristotle is maintaining that motion on a circle is complete on the ground that a circle is complete, and if the motion is on a natural circle, that is, the heavenly body, and he also takes it that what moves in a circle, that is, heaven, is complete on the ground that motion in a circle is complete, then the argument is circular and not a demonstration. Here I have set out the very words of the man for the attention of the competent so that they can witness his state on the basis of a few words. And so, first of all, he thinks that circular motion occurs on some circle and that the motion of heaven occurs on the heavenly body, not realising [i] that it is the motion which is circular but that it is possible for what is not circular to move in a circle (for it is possible for a cube to move about an axis in a circle although it does not contain a circle), 150 or [ii] that heaven itself and the circles in it move in a circle.151 So, how is it possible for the moving body and that on which it moves to be the same? Moreover, Aristotle has not made use of the sphericity of heaven up to now (for he demonstrates it later),152 but rather he has used the circular motion of the stars, which is proved by the revolution of the stars from and to the same point at an equal distance from the earth.153 Consequently he has not proved that circular motion is complete on the basis of the heavenly body taken as a circle, but on the basis of the very form of its motion; for because a motion has some extension, it also has a shape, sometimes straight and sometimes circular. And taking this circle as complete because the form of the circle is everywhere , he has demonstrated from this that the motion which is configured by it is complete; and from this motion as something more evident (since activities are more evident than substances) he has inferred that the substance of the heavenly body (or body which moves in a circle) is absolutely complete. Consequently this proof is not circular in the way this good fellow thinks. He says, But if the heavenly body is complete because it is spherical, it would not differ in at least this respect from the other elements, the entireties of which Aristotle himself also thinks154 are spherical.

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And so once again I am constrained to say the same thing: Aristotle has not yet demonstrated that heaven is spherical, nor has he said up to now that it is complete because it is spherical, but he has said that it is complete because it moves in a circle, thinking that because motion in a circle is complete, it is appropriate to complete things. So, even if the other elements are also spherical, firstly he has not here proved on the basis of sphericity that the heavenly body is different from the four elements, and secondly the sphericity in the four elements is not precise, but that which they have they have from being held together by heaven (and perhaps they also receive this hypernaturally). But again, as if regretting that he has accepted that the circle is more complete than the straight line,155 he tries to show the opposite. He says: If, as Alexander thinks,156 a circle were being taken as a plane figure, it would not have its centre in actuality (if it did, a circle would no longer be continuous because divided by its centre), and so it would not have a beginning . But the extremities of either a natural or mathematical finite line are actual. And so to the extent that the actual is more complete than the potential, to that extent a straight line will be more complete than a circle. Now if he had put this forward as an exercise for kids, it would perhaps have some not distasteful rationale. But since he is offering these things as opinions about the blessedness of heaven and what he says is unsound, he is rightly to be pitied and so are those who encounter his words and are deceived. For how can he say that the centre of the universe, around which the whole heaven moves with an everlasting motion, exists potentially – and obviously he also thinks that the poles of heaven only exist potentially? The reason for which he chose to say these things exposes his mindlessness even more. For he says that the centre of a circle does not exist actually, so that the continuity of the circle is not interrupted. However, since, according to the definition which has been given of the continuous (‘that of which the extremities are one’),157 and the centre is one and is common to the straight lines drawn from it to the circumference, why would it destroy continuity if it existed actually? ‘But if’, he says, ‘the circle is linear, first of all it will be mathematical and not natural, and second it is impossible to take as actual not only the centre of this kind of circle but also what is between the circumference and the centre’. But who, hearing of a linear circle, would still seek something between the circumference and the centre? However, in the case of a linear circle, which, as I have said,158 is what Aristotle is arguing in terms of (for the circle the extension of the motion is linear), every part is beginning, middle, and end, and so the circle is through and through complete. Next he also objects to the possibility of increasing a finite straight line, bringing in the diameter of the cosmos and the interpretation of Alexander,159 according to which there is nothing to prevent increasing any finite straight line in theory. And he defends himself with empty ideas. However, I said160 that Aristotle was looking to the nature of the straight line, which does not converge into itself as the circle does, but which, insofar as it is in its own power, flows out into indefiniteness, just like this man’s talk. ‘For,’ he says, ‘if a body is spread around and assimilated to a circle (if a circle were a body), or even more around a sphere, from outside everywhere equally, it makes the circle or sphere greater.’ Notice that this person does not know the definition of circle, since he hypothesises that it is a body.161 (Moreover, I do not think that Alexander gave an interpretation in harmony with Aristotle when he hypothesised a plane circle.)162 But how can he say that what is spread around a circle or sphere from outside is added to it without the previous surface of the circle or sphere being eliminated? Just as in the case of the straight line when we increase it, we eliminate its original limit and make a single three-foot straight line in place of a two-foot one, so too in the case of a circle when we put a circle around a circle or a sphere around a sphere.163 He says,

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However, many circular and spherical things in the bodies of animals grow because of the nourishment which enters them, for example, the circle164 of the head of a human being or the circle of the cornea in the eye. People who raise these difficulties have not touched Aristotle’s conception of these things at all. He says that a finite straight line is incomplete because there is something outside it to which it extended while remaining itself and only losing its determination. But the circle or sphere which grows because of nourishment grows from within and not because an addition accrues to it from outside, as in the case of a straight line. Therefore something is also said to be outside . But the whole form increases, and so the which enters is not said to be added to what grows, since what receives the addition does not endure, as it does in the case of the straight line. And so, even if the diameter of the universe were to increase, the spherical surface would not increase in the same way as the diameter. Rather, the earlier part of the straight line which receives the addition remains (and that is why the part is thought to be incomplete), but nothing of the previous spherical surface or the circle remains; for the circuit of

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the circumference becomes different. Consequently one should not conceive of increase in the same way in the case of the circle and of the straight line, but in the one case where there is addition, the addition is related to a deficiency, whereas in the other case something complete and determinate comes to be again out of something complete. He also finds fault with the definition of ‘complete’ which has been given and says that the person who tries to divide the arm or tongue or earth or fire or any other part into beginning, middle, and extremity is wasting his time.165 However, even if one did not think that completeness is having a beginning, middle, and extremities, nevertheless any body from which nothing is missing would always be filled out by these things. The first part of an arm would be the part where it is attached to the whole , the extremity would be at the fingers, and the middle would be the elbow, and similarly with the tongue. And in one way spheres have their beginning in their centres, and in another in their circumferences; and homoiomerous things, if they are complete, certainly have them, and so do other things. And in the case of a body, which has three dimensions, we will not be puzzled, as this person thinks, which dimension has the role of beginning, which that of middle, and which that of end. For it is clear that the dimension related to line and length is the beginning, that related to surface is the middle, that related to depth the end. And if, because its three dimensions are equal, the cube makes one raise the question which is beginning, which middle, and which end, I will say again that we will take the dimension defined as length as beginning, even if it is indifferent which dimension one takes. And in the case of a sphere a great circle in it defines length, the whole surface defines breadth, and the distance reaching from the surface to the centre defines depth. But the gentleman has thought of an additional kind of sophism.166 He says: If the linear circle is complete insofar as it has beginning, middle, and end, it is incomplete insofar as it is not three-dimensional, so that it is complete in one way and incomplete in another. So if circular motion occurs on a circular line and not in three dimensions, it, too, is incomplete. So, if wanted to demonstrate that motion in a circle is prior to rectilinear on the ground that motion in a circle is complete, he should have defined the idea of completeness universally, and proved that the definition applies to every circle and to no straight line. Let everyone who reads with care excuse me if I choose to quote so many things he says in his very words. For I do this in the hope of

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preventing it ever being doubted that this person with such ideas dared to write against Aristotle. He clearly says that since a linear circle does not have the completeness of a body (and it is clear that it doesn’t have the completeness of a human body either, since it doesn’t have a head, a chest, or feet; nor does it have the completeness of a lawyer’s address, since it does not contain a prologue, an epilogue, and what comes between them), it is not complete in the strict sense, since it has not gathered together the completenesses of all forms and distinguished them as a single form. But according to this argument a linear circle is not a whole either, since it does not have the wholeness of a horse. Nevertheless, with respect to its own form the circle does have the common characteristic of completeness, that is, having a beginning, middle, and end, just as a body has the common characteristic of completeness with respect to its proper form. And it is amazing that, when he has heard Aristotle say,167 ‘For end, middle, and beginning contain the number of the universe’ and ‘All and what is complete do not differ from one another as far as form is concerned’ and when he has used the word ‘complete’ in this way up to this point, and when immediately afterward he objects to this conception by saying ‘Why is what has beginning and limit and what comes between them complete at all?’, he nevertheless still demands that Aristotle give a universal definition of the idea of completeness168 (unless he means by ‘universal’ not what is common but what is collected together from all the particulars by reference to their differentiae; but this would be impossible). But he does ask, ‘Why is what has beginning and limit and what comes between them complete at all, and not rather what does not have either beginning or end, as an infinite line does not, since even in thought it does not admit addition or increase?’ It is also amazing that although he signs his works as a grammarian he never asks about the etymology of ‘complete’ (teleios), a word which wholly derives from ‘end’ (telos). For what has an end of the things which fill it out and are proper to it always also has a middle and beginning, but what has just a beginning or a beginning and a middle (but not in the sense of a middle ) has not thereby also received an end in every case. And because of this, Aristotle also says that all and what is complete do not differ as far as form is concerned. And if we were to call the most complete good an end, the thing which is filled with all of its own goods, first, middle, and last, (and filled with all of the parts contributing to it if the thing were a magnitude) would be complete. But as for the infinite straight line, first of all it doesn’t even exist, so that our grammarian decrees that of magnitudes only what does not exist169 should be called complete in the absolutely strict sense. Moreover, even if it does exist, its existence and the conception of its existence are indefinite and impossible to grasp, but

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wants the complete to be defined and encompassed by the things which fill it out. So with these arguments this person, whoever he is, thought that he could also make trouble for this passage of Aristotle with a lot of nonsense. But we should turn to what comes next in the text. 269a30 From ‘It is evident from these things that some bodily substance exists in nature’ to ‘and prior to all of them’.

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He adduces a common conclusion from the things he has said. For when those things were posited, there clearly resulted from them that there is another simple body, the one which revolves in a circle, apart from the four elements, more divine than they and prior by nature. For if it has been proved that motion in a circle is simple and prior by nature to motion in a straight line, but the simple motion which is prior to motion in a straight line attaches to a body which is simple and prior by nature to bodies which move in a straight line, and the simple and prior by nature is also more divine, then it is clear that this conclusion follows from the premisses. 269a32 From ‘And if someone takes it that every motion’ to ‘it is natural for something else’. He does not infer that the body which moves in a circle is different from the four elements just from what has been said already. He also infers it from the arguments which he now adds.170 I believe that the first is the following according to Alexander:

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Every simple natural motion is either natural or unnatural for the simple body which moves with it; but a motion which is unnatural is natural for another (for this is what it is for a thing to move unnaturally with a natural motion: to move with the motion which is in accordance with the nature of something else but not in accord with the thing’s own nature; for every natural motion is in accordance with the nature of some moving thing); so, if motion in a circle is natural, and if natural motion is unnatural it is natural for something else, it is clear that even if motion in a circle is posited to be unnatural for the four elements, there will nonetheless be a body besides these for which moving in a circle is natural. Alexander mentions a difficulty for this , since Aristotle says171 of the hupekkauma that the body next to the one which moves in a circle is always carried around in a circle by it, and Xenarchus raises an objection. 172 says:

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It should be asked whether motion in a circle is natural or unnatural for . And if someone says that it is unnatural, some motion, motion upward, will be natural for it. So since motion downward is unnatural for it, two things will be contrary to one. Consequently air and fire173 move in a circle naturally. And first raises the difficulty in connection with a wooden or clay sphere. If someone were to move it in a circle and ask whether the motion in a circle is unnatural for it, it could be proved that it is not unnatural. For there will be some motion which is natural for it and it will be either up or down, since there are no simple motions other than those. But whichever one says it is, the other will be contrary to it. But unnatural motion in a circle will also be contrary to it. And therefore a single thing will have two contraries. In order that this not follow, it is necessary to say that motion in a circle is also natural for such a sphere. However, I think that it was not necessary for him to hypothesise a sphere. For up to this point Aristotle is not making his argument as applying to a spherical heaven; rather he is arguing on the basis of motion in a circle. But a cube or, in general, non-circular bodies can move in a circle.174 Alexander dissolves the difficulty by saying that the body which is carried around by heaven175 does not move in a circle, since its motion is not simple. For if something in it is light, then when it is carried around it is necessary that the something move up; and if something is heavy it is necessary that it move down, and so the motion is mixed. But, he says, neither the stone sphere nor the wooden one moves in a circle, but rather they move up and down, if, indeed, from the centre of the universe is up and toward it is down.176 However, I think it would be easier to dissolve this difficulty by saying that a movement of this kind177 is not natural and does not attach to a simple body, but rather it is artificial (tekhnêtên) and attaches to a composite body. And as a result it does not belong to the sphere (or to anything else) naturally and so not unnaturally either, since it does not belong to something else naturally. In addition to dissolving the difficulty concerning the hupekkauma, we should ask about the sphere of the planets which moves178 in the opposite direction from it. For it is also carried around by the sphere of the fixed stars, and it is clear that it contains nothing light or heavy, nothing which rises or sinks.179 And would not be natural for it since it has another motion, that from the west, naturally; and there is one natural motion for each one of the simple bodies. Nor would Aristotle agree that is unnatural since shortly hereafter180 he says quite rightly that it

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would be ‘amazing and entirely unreasonable’ that a motion which is continuous and everlasting be unnatural, since what is unnatural perishes most quickly. But it was said earlier181 that this sort of motion is neither natural nor unnatural for either the hupekkauma or the sphere of the planets; rather, it is hypernatural and ‘unnatural’ in the sense that it derives from the vital nature of something else which is better and bestows the motion in accordance with superior measures of life. But what is unnatural in this way is not a contrary, since it does not exist in terms of contrary qualities such as up and down, nor do conflict with one another, since the natural is, rather, preserved by the hypernatural. But we should investigate what Aristotle actually says. How can he say that motion in a circle belongs unnaturally to the sublunary elements (he mentions earth and fire)? For motion in a circle does not belong unnaturally to earth or water or the lower portion of air. However Alexander also says:182 Motion in a circle is unnatural for the four elements, and it seems that the argument is to be taken as saying that ‘a motion which is unnatural for one thing is natural for another’, and giving as examples the motion up and down of fire and earth, and saying that of these two motions one is natural for fire, the other for earth, and one is unnatural for fire, the other for earth. Perhaps the words ‘since motion in a circle is unnatural for these things, it is natural for something else’183 are not said because earth and the other sublunary elements are moving unnaturally when they move in a circle, but because he is taking ‘unnatural’ as the denial of ‘natural’. It is as if he said, ‘Since the motion in a circle which is natural and simple is not natural for the four elements (either because [i] they don’t move this way at all – it would not be true to say that motion in a circle was natural for such things – or [ii] because, although they do move in a circle, they do not do so because of their own nature but because of that of something else),184 it is necessary that it belong to something else naturally, since motion belongs to something which moves’. In this way we can dissolve the objection which emerges and asks, ‘How, when he has said earlier185 that motion in a circle attaches to the four elements neither naturally nor unnaturally, can he say here it is unnatural for them?’ The reason is that there ‘unnatural’ was taken as the privative opposite186 of ‘natural’ so that there it followed187 that for a single thing there would be two contraries, but here ‘unnatural’ is taken as the denial of natural.188

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269b2 From ‘In addition, if motion in a circle is natural for something’ to ‘what is unnatural … to perish most quickly’. He again proves that the body which moves in a circle is something other than the four elements, and he does so by division. He makes the tacit assertion that since motion in a circle is a natural and simple motion, it certainly belongs to some natural simple body either naturally or unnaturally. Here he uses division superfluously since it is immediately clear that if the motion is natural it certainly belongs to something naturally, but he uses it because the division is inescapable. And at the same time he establishes what is proposed in many ways by adding this argument. He says that if motion in a circle, which (as has been proved)189 is simple and primary, is natural, and every motion always attaches to a body which moves, ‘there will be some simple primary body which is constituted’ to move in this way and is different from those which move in a straight line; for this body moves in a circle just as those move in a straight line. But if motion in a circle attaches unnaturally to what it attaches to (which is to say, if the things which move in a circle move in a circle unnaturally), it is amazing and entirely unreasonable that only motion in a circle, being unnatural, is continuous and everlasting, as was proved in the eighth book of the Physics.190 This is ‘amazing’ because it deviates so much from the ordinary nature of things – that’s what amazing things are like. And it is ‘entirely unreasonable’ that what is unnatural is the cause of a continuous and everlasting motion, ‘since in the case of other things, what is unnatural is observed to perish most quickly’. For anything which does not act in accordance with its own form wears out. For things which move naturally move by themselves (autophuôs) because of an active power which exists together with their existence, and so they act without difficulty. But things which move unnaturally are acted on more than they act, since they are not moved by a natural power but are pushed by an external force. Therefore natural bodies do not need a rest period, because they act in accordance with their own nature. But bodies of animals always need to rest because the animal movements of their bodies are not natural but, as things which are moved by something else, they are moved by their souls, which use them as tools.

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269b10 Consequently if fire were the thing which moves … Alexander asserts that what is said here follows from what was proved above. For it follows for those who say that fire moves in a circle that this motion is no less unnatural for it than motion downward, since motion upward is natural for it and one thing has a single natural motion. But perhaps Aristotle is not saying that motion in a circle is

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unnatural for fire, since he has said this several times. Rather, having proved that since motion in a circle is continuous and everlasting it is not unnatural for the body which moves in a circle,191 he next uses what he has previously demonstrated (that motion in a circle is not unnatural for the body which moves in a circle) to prove that the body which moves in a circle is not fire. And he proves it in the following way:

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If the body which moves in a circle is fire, it follows that circular motion is no less unnatural for it than motion downward; but motion in a circle is not unnatural for the body which moves in a circle, since that motion is continuous and everlasting; therefore the body which moves in a circle is not fire.

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If we understand what is said in this way, we will not claim that something is missing in the text, as Alexander does.192 He also adds that those193 who say that the body which moves in a circle is emaciated and undernourished and moves in a circle around its nourishment, since the nourishment no longer reaches it because of its elevation up in a straight line, also agree that it moves unnaturally since it is drawn forcefully by the nourishment. But motion which is constrained is unnatural, and the unnatural is posterior to the natural, so that motion in a circle would not be primary if the body which moves in a circle were fire. In this connection Alexander uses many dense arguments to prove that motion in a circle is not natural for fire. He says, It is not reasonable to say that, of the natural bodies, only fire has two natural motions (however, they say that not just fire but also the luminous air moves in a circle), but it is absurd that fire, which is simple, should have two starting points of motion naturally; for it is clear that it will also keep its motion upward, since if it were dragged down it would move up again. But perhaps, if it were dragged down, it would become incomplete and take on motion in a straight line in place of motion in a circle. But when it has come to be above and reached completion, it casts off motion in a straight line, which suits incomplete things, just as it

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casts off incompleteness, and takes on the motion which is appropriate to complete things, because it has become akin to the most complete thing.194 It does not take on motion in a circle from its location but from the body which moves in a circle and adjoins it at that time. Nor does it change its form absolutely when it takes on motion in a circle, since motion in a straight line belongs to what is becoming fire, motion in a circle to fire which has been brought to completion. For we do not say that earth changes its form when, having reached bottom, it rests, but we assign motion in a straight line to it when it is incomplete, and rest when it has been completed. So the person who says that fire insofar as it is fire moves upward and earth insofar as it is earth moves downward, and does not make a distinction between their incomplete and complete conditions, and the motions or rest which are appropriate to each of these would say what Alexander says, and that Alexander speaks well in some respects. 269b13 Therefore, someone arguing (sullogizomenos) on the basis of all these things would be confident … There are two kinds of confidence.195 One is reached irrationally, apart from demonstration; some people hold fast to this kind of confidence even in the case of the most absurd things. The other involves demonstration and demonstrative argument; it is secure, irrefutable and naturally allied with the truth of things. So since he has said what he has said with demonstration, it is reasonable for him to speak of someone who argues being confident. This sort of confidence goes beyond scientific knowledge because of its vital sympathy. And so Aristotle now uses the term ‘be confident’ philosophically and appropriately because vital sympathy is stirred up, together with the unshakeable understanding of more divine things. It is also possible that he says ‘be confident’ because he has argued on the basis of hypotheses, and it is clear that as the hypotheses are in certainty, so their consequences will be in confidence. However, I think it is better to say that everywhere, but especially in discussions of divine things, he espouses that one add to demonstrative necessities the sympathy derived from confidence which implants not only the warrant of true understanding which supervenes after demonstration but also unification with the knowable, which is the end of human blessedness. For Love (erôs), which elevates, takes the lead, awakening the desire for divine beauty in souls, and there follows for those who are worthy the true manifestation of that beauty, and in these people confidence furnishes a firm foundation in that beauty and a unification with it. And it should be immediately clear that however more distantly heavenly things are separated spatially from things which come to be and perish, so much and even more are they superior to them in substantial value; for heavenly things have been thrust away into the

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extremity of the universe, and heaven has been assigned the highest form of corporeality.

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In connection with the words which have already been set out, Xenarchus also raises objections to other things which have already been discussed, and especially against the statement that for a single thing there is a single contrary.196 He says, It is easy for those who use force to move fire on any form of line, simple or variegated, whatsoever. And we say in the ethical treatises197 that there are two contraries to each virtue, as knavery and goodheartedness are contrary to wisdom, and rashness and cowardice are contrary to courage, and similarly with the other virtues. Against the first point it should be said that it is also necessary that unnatural motions be proper to each thing, since they are also natural and not artificial. And variegated forms of lines have no weight against the doctrine, since the lines for simple motions are simple; and, furthermore, unnatural motions must be such as to be natural for something else. And against the second point it should be said that since each of the virtues is a balance, the two on each side of it are opposed as a single imbalance to a balance, since the one is an excess, the other a deficiency, and imbalance is common to both. And, in proceeding, recognises that knavery is opposed to goodheartedness, and cowardice to rashness, but neither knavery nor goodheartedness is opposed to wisdom; rather, what is common to them both is; and what is common to rashness and cowardice is opposed to courage. In the same way, the deficient is opposed to the excessive, and what is common to both of them, inequality, is opposed to equality. He says, But if these things are true, it is not necessary that heaven be made of some fifth body on the grounds that two things (in this case the motion in a circle of fire and its downward motion) cannot be opposed to one thing (its upward motion). For upward motion is opposed to downward motion in the way excess and deficiency are opposed, and the motion common to both, that is, motion in a straight line, is opposed to motion in a circle in the way inequality is opposed to equality. These things are stated elegantly, but I don’t think they relate to the contrariety Aristotle is talking about. For Aristotle is not opposing

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motion up and motion down as a pair to motion in a circle but motion in a circle and motion down to motion up. But as regards the hypothesis which says that what moves in a circle is fire, if it is expressed198 with the conception of this fire in our world, which does move up naturally, it is not absurd for Aristotle to have said199 that motion in a circle is no less unnatural for fire than motion down, since he opposed them in this way earlier.200 And so, taking the unnatural as two while the natural is one, he reasonably inferred that for a single thing there two contraries.

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In this connection the grammarian has not shrunk from calling his own dull-wittedness and rashness ignorance and contradiction in the statements of Aristotle, since he says, In the second argument,201 when he wanted to prove that what moves in a circle is not one of the four elements, he said that motion in a circle is neither natural nor unnatural for the four elements because the unnatural motion for them is in a straight line, and for a single thing there is a single contrary. But now wanting to prove in turn that it is necessary for motion in a circle to be natural for something other than the four elements, he has taken as agreed that motion in a circle is unnatural for the four elements, but since it is a natural and simple motion, it would be entirely necessary for it to belong to something naturally. But if motion in a circle attaches to the four elements unnaturally, then – since there is also a motion in a straight line which is unnatural for them, namely the one which is opposite to their natural motion – for a single thing there will be two contraries according to this hypothesis. So either Aristotle made a false assumption earlier, namely that heaven cannot be one of the four elements moving unnaturally in a circle, or he has now incorrectly hypothesised that motion in a circle is unnatural for the four elements. He said that the absurdity that, for a single thing, there are two contraries follows from this hypothesis, but now it has been proved to follow from what he has posited. In connection with these things which I have set out in practically his very words, albeit more concisely, one should first attend to what is said directly and see if in each of the arguments the same absurdity is inferred. It is agreed that there the argument was a reduction to an absurdity, namely the denial of the principle that, for a single thing, there is a single contrary. But here it is inferred that motion in a circle, since it is unnatural for sublunary things, must belong to something else naturally. Because it was not out of

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ignorance or self-contradiction that Aristotle said before that motion in a circle belongs neither naturally nor unnaturally to the elements, and now that it belongs to them unnaturally, we should, I think, be constrained202 to assert that Aristotle does not say opposite things in close proximity in this way, and rather seek the explanation of what he has said. Since this person inclines toward what is worse while assuming that he is glorifying himself, it is necessary for me to say again what I said a little while ago in my exegesis of these passages.203 There took ‘unnatural’ as the contrary of ‘natural’ and so inferred that, for a single thing, there would be two contraries because both motion in a circle and motion downward would be unnatural for fire. But here he has taken the negative ‘not natural’ as ‘unnatural’. ‘Not natural’ can apply to the privative ‘unnatural’, and it can also be true of what does not hold at all, and it can also be understood in the case of the hypernatural. And this is reasonable since some sublunary elements, earth and water and the stagnant air, don’t move in a circle at all; others do move in a circle, but with the motion of something else, so that their motion is unnatural in the sense that it is hypernatural. Therefore, he has not inferred here that, for a single thing, there are two contraries, but he says that since motion in a circle is unnatural for these things, it is natural for something else. But in general, why, if he is now taking unnatural as holding privatively, would he say that motion in a circle is unnatural for these things and mention immediately fire and earth, when he does not think that earth moves in a circle at all? He says, But if thinks that none of the elements can move in a circle unnaturally, nevertheless he says that motion in a circle is ‘no less unnatural’ for them,204 and so again, for a single thing, there will be two contraries. (In what way two, good sir, if motion in a circle does not belong to any element unnaturally?)205 But nothing prevents us from converting the statement and saying that motions in a straight line are unnatural for what Aristotle thinks is a fifth body, which moves in a circle, even if it never moves in a straight line unnaturally;206 for these motions are also simple. And so again the two motions in a straight line which are unnatural for the fifth body will be contrary to the one motion, motion in a circle, which is natural for it. However, if these motions in a straight line never belong to the fifth body in such a way as to be contrary to its natural motion, but ‘unnatural’ can be said as a denial which is equivalent to ‘not natural’ (which is also true of what isn’t unnatural),207 there is nothing absurd about speaking of the unnatural in this way, since, for a single thing, there will not be two contraries either.

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Being unable to turn his eyes away from this very frenzy of contradiction toward the truth, he also brings into battle the following, thinking that Aristotle posits motion in a straight line as contrary to motion in a circle although, as he says, in a little while208 stretches out long arguments in which he tries to prove that there is no motion which is contrary to motion in a circle. He says, The rectilinear motions are natural and simple, and they are not natural for the fifth body. Therefore they will necessarily be unnatural for it. But the unnatural is contrary to the natural. Therefore the rectilinear motions, which are simple, are contrary to motion in a circle. Here again he has taken motions which are not natural (here the denial of ‘natural’) as contrary unnatural motions, an affliction which has obviously befallen him in all of these contradictions, since he does not know in what sense Aristotle says that motion in a circle is unnatural for the sublunary elements, namely that it does not belong to some of them, earth, water and the stagnant air, at all, and it belongs hypernaturally to others which are carried around by heaven, the hupekkauma and the luminous air. So these things will not stand in the way of what is subsequently proved about there not being a motion contrary to motion in a circle. It has been said against Aristotle (in the way this person also sets out briefly) and against many other philosophers that they say that motion in a straight line belongs naturally to pieces of the elements since it leads them to their natural form, which they will possess because they take on their proper place and proper entirety.209 However, it is worth investigating whether motion in a circle belongs naturally to the hupekkauma and the upper air as their own motion if they are carried around with the fixed heaven. And I think it is better to say that this motion is hypernatural because it belongs to things which are clearly naturally constituted to share in it. And if someone says that the motion is natural in this sense, I do not think he will be speaking absurdly or contradicting Aristotle, since Aristotle finds the difference between the heavenly body and the sublunary elements, most of all, on the basis of the parts of the sublunary elements, since the heavenly parts do not undergo anything of this kind.210 But this person thinks he has set something very important straight by showing that other people have also spoken against the fifth substance. But he does not notice that none of them wrote against it thinking that the everlastingness of the cosmos was being undermined; rather, they were doing exercises in arguments containing some novelty against the teachings of earlier philosophers. And

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some of them, such as this drimakòs,211 entirely misunderstand what Aristotle thinks. But others, having mastered it, confront Aristotle’s view with the phenomena and try to prove that heaven is not simple. And others devise some other piece of cleverness. But none of these people are frivolous the way this person is; they do not make use of the paltry ideas concerning the creator of the cosmos which are dominant,212 and only pay attention to seeming to be in opposition to those who demonstrate that the cosmos is everlasting. It is worth noticing that in everything which this man says he is fighting against the fifth substance and striving to prove that heaven has the same nature as the entireties of the four elements. And so he has still not demonstrated even from these considerations that heaven is perishable, since it is possible that the entireties of the elements are everlasting even if they have parts which come to be and perish and move in a straight line. But if the parts of heaven are not observed to undergo these things, it is clear that, as far as the things this person says are concerned, nothing prevents heaven from being everlasting, not only as a whole but also in its parts.

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269b18 Since some of the things we have said are hypotheses and some have been demonstrated, it is evident that not every body213 has lightness or weight. Since all intellectual teaching and learning proceed from pre-existing cognition,214 as Aristotle has taught us in the Analytics, it is necessary that some things be laid down in advance of demonstrations, some of them as trustworthy in themselves, others as either previously demonstrated or as to be proved. And so here he has laid down in advance certain lemmas and demonstrated some of them. He has laid down in advance that: [i] There are two simple lines, the straight line and the circle;215 [ii] motion from the centre is up;216 [iii] motion to the centre is down;217 [iv] motion around the centre is circular;218 [v] for a single thing there is a single contrary;219 [vi] there is a single natural motion for each of the simple bodies.220 Of the lemmas it has been demonstrated that:

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[vii] There are two simple motions, the circular and the rectilinear;221 [viii] the motions of simple bodies are simple;222

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[ix] the simple motions attach to simple bodies (for I think that this has also been proved on the basis of the division of motions and the division of bodies and their proper co-ordination (epharmogê)).223 It has also been demonstrated224 from the lemmas which have been hypothesised and those which have been demonstrated that, beside the four sublunary simple bodies, there is another fifth body for which motion in a circle is natural, and that this body is prior to and more complete and honourable in nature than the other bodies. He says that it follows from these things which have been assumed and demonstrated that not every body has weight or lightness. For if heavy and light are shown by their very definition to be propria of things which move in a straight line,225 and it has been proved226 that the thing which moves in a circle is different from the things which move in a straight line, and different in the sense that motion in a straight line cannot attach to it either naturally or unnaturally, it clearly follows that not every body has weight or lightness. And so in this way too the heavenly is proved to differ from sublunary things in having neither weight nor lightness. For him this will contribute toward proving227 that the heavenly body does not come to be or perish, does not increase or diminish, and does not change in quality. For if it had weight or lightness there would be a motion contrary to its motion; but if this were the case there would be something contrary to it, namely what moves naturally with the contrary motion;228 but if this were the case, it would also come to be from a contrary and perish into it. But if it has neither weight nor lightness and does not move in a straight line at all (and there is a contrariety in the case of motion in a straight line), but it only moves in a circle; and if it has been proved229 there is no motion contrary to motion in a circle, it is clear that what moves in a circle will not have any contrary, and so it will not come to be from something or perish into something. And so he assumes in advance that necessarily having neither weight nor lightness is the same as moving neither up nor down,230 which is the same as to say what does not move in a way which involves a contrariety. And so, having proved that there is no motion contrary to the motion in a circle with which it moves, he will have as a consequence that there is no contrary to , from which it follows necessarily that it neither comes to be nor perishes; and the other things231 follow from this. 269b20 It is necessary to hypothesise what we mean by heavy and light … He shows clearly by what he says that for him the discussion of light and heavy is not of primary importance at the present, as it is in the fourth book where he discusses these things in a primary way, but

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that at the moment he needs them for proving that the body which moves in a circle does not come to be or perish on the basis of the fact that it does not have either weight or lightness. Having in a way already announced the conclusion of what will be proved by saying,232 ‘It is evident that not every body has lightness or weight’ (for the conclusion is that it is impossible that what moves in a circle have either weight or lightness233), he defines what heavy and light and heaviest and lightest are. For since of things which move down, one, earth, proceeds as far as the centre, that is to say, as far as what is lowest, the other as far as earth, and of those which move up one, fire, moves as far as what is highest, that is, the lunar sphere, the other as far as fire, it is reasonable that the one is heavy, the other heaviest, and that the one is light, the other lightest. So if what moves down is heavy and what moves up is light, and these are the definition of heavy and light, it is clear that the definitions necessarily convert,234 so that what moves up has lightness and what moves down heaviness. And since of the upper region there is some, such as the region under fire, which is not completely up but also contains some down, and of the lower region there is some which is not completely down, things which go to these regions are rightly said to have both weight and lightness, but not in relation to the same thing; for it is not possible to be lighter and heavier than the same thing at the same time. But for these things heavy and light are relative. For air is light relative to water, but not relative to fire; and water is light relative to earth, but not relative to air – it is heavy relative to air. Therefore these things are neither light in the strict sense nor heavy in the strict sense nor simple in the strict sense. Fire is light and simple in the strict sense, and earth is heavy and simple in the strict sense, the one rising to the top of everything which moves up, the other sinking to the bottom of everything which moves down. Consequently, if the intermediate are not entirely simple, the account of simples would not apply to them in the strict sense, nor is it good that some people tried on the basis of these things to undermine the demonstrations given for the simples.235 269b29 From ‘… the body236 which moves in a circle’ to ‘the other is natural for it’.

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Making use of the definitions of heavy and light which have been given – or rather of their conversions – he proves that it is impossible for the body which moves in a circle to have weight or lightness, since if it has them, it has them either naturally or unnaturally, but it will be demonstrated that neither alternative is possible. He proves this using two of his axioms, that the natural motion of each of the simple bodies is single,237 and that ‘of contrary if one is unnatural for something, the other is natural for it’.

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Alexander and Themistius say that he proves this in the following way: [i’] What moves in a circle does not move up or down naturally; [ii’] what does not move up or down naturally is neither light nor heavy; [iii’] 238 Here the minor premiss [i’] is not negative, since, if it is, the conclusion does not follow from two negative premisses. Rather, the predicate in the minor premiss is indefinite, as if one were saying, ‘What moves in a circle moves neither up nor down because of its own nature’.239 But perhaps, retaining the idea that the predicate is indefinite, the syllogism is rather this: [i] The body which moves in a circle cannot move from the centre or to the centre either naturally or unnaturally (this is equivalent to ‘The body which moves in a circle is such240 that it cannot move from the centre or to the centre either naturally or unnaturally’); [ii] such a thing can have neither weight nor lightness; and the conclusion is clear. But it is clear from the conversion of the definitions that what moves neither to the centre nor from the centre has neither weight nor lightness. For if what is naturally constituted to move to the centre is heavy and what is naturally constituted to move from the centre is light, it is clear that what moves neither to the centre nor from the centre is neither heavy nor light. He proves the minor premiss241 tacitly in the following way: What moves in a circle, since it is simple and has a simple motion, has a single natural motion, which is in a circle; such a thing does not move in a straight line naturally.

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But , rather, gives the following syllogism in the second hypothetical mode:242 If motion in a straight line belongs naturally to what moves in a circle, it will be the same as one of the things which move in a straight line; but it is not the same, as has been proved several times; therefore, motion in a straight line does not belong naturally to the thing which moves in a circle.

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He reminds us that the conditional (‘If is natural for , it is the same as one of the things which moves ’) is true by saying ‘since of each of the simple bodies is single’. And I think that he proves that the body which moves in a circle does not move in a straight line unnaturally either with the same kind of argument, : If motion in a straight line of any kind is unnatural for the thing which moves in a circle, the opposite of that motion will be natural for it;

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And he adds the reason why this conditional with the words ‘For we have posited that of contrary if one is unnatural for something the other is natural for it’. And he has carried out the syllogism only this far, leaving out the rest on the grounds that it is clear from what has already been said. But to complete there is need of one other conditional: If either of the opposite motions, motion up or motion down, is natural , it will be the same as one of the things which moves this way, that is, the same as one of the sublunary bodies; but this has been proved impossible; therefore, neither is either of the motions in a straight line unnatural for the thing which moves in a circle. So if is neither natural nor unnatural (and clearly it is not hypernatural either since motion in a straight line is inferior to motion in a circle), it will not move up or down at all. Consequently it will be neither light nor heavy, since what moves up is light and what moves down is heavy. However, Themistius does not think that the syllogism proceeds this way, but as follows:243

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If moved down unnaturally, the contrary of this motion, motion up, would be natural for it; but circular motion is also natural for what moves in a circle; therefore, for a single thing there are two contraries. And if it moved up unnaturally, again, motion down would be natural for it; and the same absurdity, that for a single thing there are two contraries, would follow. And this interpretation is also reasonable.

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270a3 Since whole and part move to the same thing244 … Having proved that the body which moves in a circle has neither weight nor lightness, he next proves that not only is the whole of it this way, its parts are as well; for since the parts have the same motion as the whole, they have neither weight nor lightness. In my opinion he first proves this as follows. He assumes that whole and part move naturally to the same thing and gives the following syllogism:

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If the whole does not move up or down, neither will the part; but if this is so, the part will have neither lightness nor weight; but the antecedent; therefore the consequent. He has proved245 that the axiom he has assumed to start – that ‘whole and part move to the same thing naturally’ – is true on the basis of the words ‘for example, all earth and a small chunk’.246 For if the whole is all the parts and all the parts have the same impulsion, it is clear that the whole also has that impulsion. And I think that he next also proves in this way the same thing generally for the whole and the parts , namely that it is impossible for them to change place either by being drawn up or dragged down. And he gives a proof using the demonstration which has just been given for the whole,247 recalling it briefly. He says, ‘since it is not possible for it to move naturally in another way’ than in a circle (since the natural notion of each of the simple bodies is single) ‘or unnaturally’ with one of the motions in a straight line (for the opposite motion would be natural for it, and it would no longer be true that the natural motion of each thing is single, but rather, two natural things would be contrary to one unnatural thing). It is clear that this demonstration also requires it to be agreed in advance that ‘whole and part move to the same thing naturally’, if this is going to be true of the parts. This whole argument about the parts was also in itself necessary for what was already said: it adds the assumption that the parts have the same nature as the whole and proves that the entireties of the sublunary elements also do not have heaviness and lightness, as they are thought to have, but only the parts which are detached from the entireties do.248 And so he has also assumed this in advance directly, that ‘whole and part move to the same thing naturally’. Moreover he also responds to objections, the one which says that the comparison of heaven with the sublunary elements is not based on similar things, but rather, the parts of the which are disposed unnaturally outside their proper regions were taken, but the whole of heaven was taken.249 And furthermore he responds to those who think that even heaven is similar to sublunary things because it is also everlasting as a whole, but comes to be and

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perishes in its parts. For if in the case of the sublunary elements the parts are observed to be detached from their proper entirety, and to be disposed unnaturally, and to have an impulsion for motion in a straight line, but, according to the record handed down from one person to another, in all past time nothing heavenly has been observed to have changed either as a whole or in its parts,250 then it is clear that heaven is rightly said to be of a different nature from the four elements, and our confidence seems to be drawn from perception which has been handed down from eternity. But how, does he confirm the claim that the part moves the same way as the whole on the basis of the fact that all earth and a small chunk of it move to the same thing? For all earth is settled around the centre and doesn’t move in any way. Or perhaps he is speaking of all earth viewed in terms of all its parts, as I have said,251 but not in terms of its entirety, and that is why he says ‘all earth’ and not ‘the whole earth’; it is as if someone were to say that all earth comes to be and perishes because all its parts do so and none of them is everlasting, although it is not true to say this of the entirety. Secondly,252 the whole earth as a whole has a total convergence and impulsion toward the centre even if it does not change place. And that is why the whole has the form of a sphere around the centre and each of the parts strives to be near the centre when it is not already occupied by another part; for the desire of both the whole and its parts is for the centre, and they want to be kept at the centre and be held together, although they have a constitution which naturally scatters away from it; and in the same way the whole of fire and its parts desire the divine body as something of the same kind as they, and strive toward it from every direction, and so the whole is formed into a sphere under the divine body, and all its parts want to be next to it and to enjoy its vital motion. And each of the intermediate elements has a desire to be near something because of its own impulsion. Water desires to be near earth because by its own nature it flows and is seated on earth, and so it, too, flows around earth and is formed into a sphere around it, and is held together because the earth is central and water enjoys its continuity with the centre. But the whole of air and its parts go toward fire, wanting to be freed from their own turbid thickness and made bright. But heaven, because it is more divine than and superior to all bodies in the cosmos, has no desire for anything else and does not go in the direction of anything else, but converges into itself and desires itself and its own soul and mind; it does not move in a straight line with the motion which is deficient and incomplete, and joined with much that is potential, and proceeds toward something external; rather it moves with the circular motion, which is always complete and active and contains the good in itself. And if in saying these things I am saying anything, Aristotle was correct to say that whole253 ‘and part move to the same thing natu-

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rally’ and that some things desire what is outside themselves and, because their wholes and parts desire that, they have an impulsion to move in a straight line, and therefore have some impulsion254 because what they desire is external, and externality is spatial. And if (hypothetically) heaven were to be raised higher than where it is now located, fire would follow it; for it seems to me that the four elements do not desire either a place255 or their entirety256 so much as they desire contact with what is better,257 and the whole desires this no less than its parts.

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If what I have said is correct Aristotle’s theories are freed from a lot of bother. And I know that, since Plato and Aristotle posited different things about heavy and light,258 it was necessary to say something about this passage, but, so that I not say the same thing twice, I am protecting these things from refutation. But since it is necessary to swim, even if one falls into the wide sea or into a pool or rather into a filthy swamp, let us turn aside and look at what our Telkhin259 says. He says,

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If demonstrated that what is heavenly is neither heavy nor light, using that it is not one of the four elements, and the arguments establishing this have been dissolved,260 it is clear that what is established using them, that it is neither heavy nor light, is also refuted. This is the self-satisfied way in which this good fellow has confirmed his own imaginings. But what human being would dispute what Aristotle has proved in moving forward to this point, namely that what is heavenly is different in substance? Next he says,

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If Aristotle correctly defined what is lightest as ‘what rises to the top of everything which moves up’,261 and heaven lies on top of everything, it would be the lightest of all things. Here he has not noticed what the words ‘which moves up’ and epipolazein mean, but he thinks that they mean the same thing as ‘be on top’ (epikeisthai). ,262 having said that what from the centre, that is, what moves up, is light, says that what moves up most, that is, what rises from below and floats on top of everything, is lightest. For olive oil, ceding the lower place to water, also lies on top of it.263 But if what lies on top of everything is taken to be different from everything which moves up,264 it is clear that what lies below everything which moves down should be taken as different from the things which move down, and there should be some body lower than earth. But this person does not have the strength to

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be guided by the similar account nor by the definitions of heavy and light. For if what moves downward is heavy and what moves upward light, it is clear that the thing which of all the things which move down is furthest down would be heaviest; and this is what Aristotle himself has explained more strictly when he said that what sinks below everything which moves down is heaviest, and explained ‘lightest’ in a similar way. This person thinks he is following Plato, who says that heaven is made of fire, but he does not know what Plato means by fire,265 and that this is not the thing which Aristotle says moves up and is therefore light, and rises above all the things which move up and is therefore lightest, and that Plato distinguishes one form of fire, light (phôs), and thinks that the heavenly fire is only light.266 And again he stretches out a lot of talk trying to prove that the entireties of the elements do not move in a straight line. But he needed most of all to understand that what has a desire always has an impulsion toward what it desires; and that if both are bodies, then, even if they touch one another, they continue to have the impulsion, because of which they do not just lie together, but they lie together while clinging to what they desire and blending with it as much as possible. Accordingly the entirety of the hupekkauma also desires proximity to heaven and, preserving its impulsion toward it, it always endures more than its parts do, so that if one were to move heaven – hypothetically, of course, – the hupekkauma would follow it.267 As I have said, he should have understood this most of all. But if this is too much for this man, who has been made blind by the goal of his book, nevertheless it should be immediately clear that, even if the entireties268 of the elements do not have an impulsion and, as he thinks, heaven does not differ from them at all in this respect, nevertheless, the parts of the elements do move in a straight line whereas the parts of heaven undergo no such thing, and at least in this respect the difference between the two is defined.269 But since this treatise of his has been put forward as refutation, and he neither knows nor wants to learn the truth, he wanders about gathering information about whether someone else somewhere thought it right to argue against the same things. And he does not figure out the purpose of these people, but just because some well-known person has spoken against , he acts childishly and brings him forward. But come, let us investigate the doctrines of those who provide him support. The most divine Plato observed that all things in the cosmos are living, and have a desire for the good things proper to them, and consequently also have an impulsion for their proper entireties or the nearby bodies270 of the same nature which are useful, an impulsion which did not come by choice; and he recognised similarly that earth

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and fire moved toward things for which they had a proper desire, and therefore he says that each thing is ‘weighed down’ toward its own ; for we say that a thing is weighed down toward what it has an impulsion for. But since these are incomplete, they move naturally to these things and not because of choice. However, because the other ‘fall’ (as it were) in the same way as earth, he calls the place into which such things move ‘down’, and he writes the following:271 One ought to notice one thing about all of them: it is the passage of each thing to what is of the same kind which makes what moves heavy and makes the region to which it moves down. For this reason he does not think that the difference between heavy and light is natural, since he thinks that everything is heavy by nature and, moreover, that in a universe which is spherical, up and down are not attached to periphery and centre. And he says that heavy is thought to be what moves downward, light what moves upward.272 But since he did not understand what Plato said, this person calls on Themistius for help, setting out a long passage from his paraphrase of the fourth book of On the Heavens, as if Themistius along with Plato objected to the idea that something was light or heavy in its proper region.273 However, I do not think that Plato says this directly; rather he says that heavy and light are not natural. For since the universe is spherical, there is no up and down, but we judge them relative to our head and our feet. And so he sets out the image of someone having his head in the air and his feet on the sphere of fire, and dragging a balance up into the air, and placing two portions of fire, one greater, the other less, on the disks. He says274 that if the person standing in this way, … lifted the balance up and dragged the fire by force into air, which is unlike fire, it is clear that a lesser amount of fire will be forced into the air more easily than a greater; for if two things are raised up together by one force, it is necessary that the lesser yield to the force more when pulled and the greater do so less, and that the large amount be said to be heavy and move down, and the small one be said to be light and to move up. We should notice that we do the same thing in our region. We stand on earth and separate earthen things and sometimes earth itself and drag them into the dissimilar air by force and against nature (since both cling to things of their own kind). The smaller one yields more easily than the greater to what forces them into what is dissimilar, and so we call the smaller one ‘light’ and the region into which we force it ‘up’, and we call the contrary of these ‘heavy’ and ‘down’.

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These are the words of Plato, and just before this he says,275

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Since the whole heaven is spherical, things which, being equally distant from the centre, are extremities must be equally of such a nature as to be extremities. And one should think that the centre, which is equally distant from the extremities, lies in what is opposite to all the extremities. And, since the cosmos is of this nature, which of the things we have referred to could one posit as above or below, without being justly thought to use an entirely inappropriate word? For it is not right to say that its central region is by nature either above or below, but only that it is central; and the periphery is certainly not central, and there is no difference in it by which one part of it or one of the opposite parts is closer to the centre than another part. And what sort of contrary names could someone apply to what is by nature similar everywhere, and in what way could he be thought to speak correctly? And so Plato does not think that up and down are used in the strict sense in the case of the universe, and therefore also denies that light and heavy are as well. And Themistius, although in most matters he adheres to the Peripatetic school, in this case seems rather to adopt the views of Plato. However, I think that one should also attend to the purpose as well as at the words and recognise that the difference between the two philosophers on these questions is not about things but about words: Plato rejects the ordinary use of words in the name of precision, but Aristotle makes use of the ordinary use of words on the grounds that the truth is not at all harmed by this. For Plato proposed to articulate the nature of heavy and light, but Aristotle does not now have this purpose, but that whereas some of the sublunary elements move to the centre and some move from it, heaven in itself as a whole and in its parts is superior to such an impulsion. But since it was customary to call the centre ‘down’, the extremity ‘up’ and what has an impulsion to go down ‘heavy’ and what has an impulsion to go up ‘light’, in accordance with custom he defined heaviness as the impulsion to the centre and lightness as the impulsion from the centre. And Plato makes clear that he is aware of this impulsion when he says,276 ‘it is the movement of each thing to what is of the same kind which makes what moves heavy and makes the region to which it moves down.’ That Aristotle uses words in agreement with predominant custom is also clear since he says here,277 ‘Let what is naturally constituted to move to the centre be heavy’ and not ‘what is naturally constituted to move is heavy’. If he says ‘Let be’, but does not himself make that supposition, it is clear that he speaks in agreement with those who do make it. And in the fourth book he

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says278 that it is necessary first to be explicit about them and to posit what is obvious to everyone and is agreed to by them, that ‘what sinks to the bottom of everything is absolutely heavy, and (conversely) what rises to the top of everything ’. How could he show more clearly than this that he is using words in the ordinary way? However, he has also departed a little from ordinary usage when, speaking against Plato, he straightforwardly defines heavy and light not as what has impulsion downward or upward, but as what has an impulsion to the centre or from it.279 However, even though Themistius, whom this person brings in as evidence, does away with heavy and light especially in the case of things in their proper regions, he does say that an impulsion attaches to elements when they are in alien regions when he says,280 ‘It would be more reasonable and would agree with the phenomena concerning these things to rather assign impulsions to the elements when they are in alien regions’. And so he clearly agrees that impulsions do not attach to heaven.281 Now what does this grand quotation from Themistius, a man who, in agreement with Aristotle, thinks that heaven both as a whole and in its parts transcends all impulsion, contribute to this person’s own purpose? For if the entireties of the elements do not have an impulsion (if indeed they do not have it282) it is not the case that thereby heaven, which has no impulsion not just as a whole but also in its parts, has the same nature as they do; when, even if heaven were shown to have the same nature as the entireties of the elements, it would not thereby be perishable as a whole, as this person desires, but, if it were perishable, it would be in its parts, just as the elements are. What, then, is the point of his bringing together in mindless contentiousness283 these many arguments, which have an impious purpose, from arguments which do not have the same purpose? Xenarchus says that it is incorrect to say that what lies at the top of everything is light because when fire is down it does not yet lie at the top, so that it is not yet light, and, not being light, it will not move upward. Against this it should, I think, be readily said that talks about what is naturally constituted to lie at the top of everything; he adds this in the case of things which move up and down when he says,284 ‘So let what is naturally constituted to move to the centre be heavy, what is naturally constituted to move from the centre be light’. But if we combine into one the two definitions of light, the one which says that what is of a nature to always move up is light, the other which says that what lies at the top of everything is light, there will be one complete definition which says, ‘what, always moving up, lies at the top of everything is light’. But perhaps also the lightest thing which is in any given region lies at the top of everything in its vicinity; for example, since fire is upward-moving, the fire under earth, even if it at some time had air and earth and water

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above it, always overtakes the things above it in its vicinity and lies at the top of all of them. The grammarian says, 71,1

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But since, according to Aristotle, there are only two differences and contrarieties relating to place, up and down, every body which is in place is either in the place which is up or in that which is down. So since the heavenly spheres other than the sphere of the fixed stars are in place, namely in the limit of the surrounding sphere (the lunar sphere in the limit of the sphere of Venus, the sphere of Venus in the limit of the sphere of Mercury, and so on), it is necessary, that these spheres be up, since they certainly aren’t down; and so they will share in lightness. Notice how much of this man’s ignorance and also lack of education is shown at the same time in a few words and especially if he is, as he signs himself, a ‘grammarian’. First of all he thinks that ‘up’ (anô) and ‘upward’ (epi to anô) are the same. Consequently, even though Aristotle says not that what is up is light, but that what upward is and what rises to the top of what moves up is , this person thinks that Aristotle must agree that heaven is light, since it is up. Moreover, what moves up – or at least what moves up in the strict sense and directly – is said to move toward heaven; for fire moves because it desires to be near heaven.285 Furthermore, : he thinks that according to Aristotle there are only two spatial contrarieties, up and down, and he calls this two contrarieties, when the contrariety of up and down is one antithesis.286 What is amazing is that a person who is still ignorant of the fact that the sphere of Mercury is directly above the moon and the sphere of Venus is above that287 dares to speak against Aristotle. He stretches out many words in the belief that Themistius also gives support to his view that, when the elements are in their proper places, they do not share in either weight or lightness, but that weight and lightness accrue to them when they are in an unnatural position; and he thinks that he can infer from this that the entirety of fire (and he would also say of the other elements) does not share in weight or lightness, just as heaven does not, with the result that heaven has the same nature as the elements. He says, Just because if the earth were removed hypothetically from its proper place and released it would move to the same place, one should not think that the whole earth has weight. For if, making a similar hypothesis, one were to change the position of the whole cosmos, if it were released, it would return again to its own place. However, it is not possible that the whole cosmos

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have either weight or lightness since it contains everything in itself. Perhaps there is nothing to prevent it from moving in accordance with what predominates in it, but288 someone could not say whether it was moving upward or downward, since up and down are inside it. So, since he says these things and others of the same kind, one should first notice that the absurdity concerning the cosmos follows from the absurdity of the hypothesis. For how can what contains and embraces the difference of up and down inside itself move upward or downward? And if it has no up or down outside itself, how can it be heavy or light? And I am not saying that one should not hypothesise an impossibility. For I know that a person who has the earth move outside its proper place makes an impossible hypothesis, but no absurdity follows from the impossibility of the hypothesis. For it is not absurd that the earth move to its proper place, the place at the centre, just as it is not absurd that if the cosmos is moved outside of its proper place, it would move back to it again; however it is impossible for the cosmos to move to the centre or the extremity or down or up, since it embraces these things inside itself.289 I say these things against the eloquent Themistius, since this person has furnished himself with this support from Themistius and uses it for a worse purpose. He says, Even if someone will not agree to hypothesising that the cosmos is made to change position, what is to prevent it being hypothesised that a star falls down from its proper abode to the interior ? If this star were conceived to go up again to its natural region, it is clear that it would move in a straight line. But nevertheless Aristotle thinks that nothing heavenly shares in either weight or lightness. Against this it should be said that if something fell and moved upward naturally it would share in lightness. And what is absurd about that? If not only portions of the elements but also their entireties desire to be near what is like them and better than them and to enjoy what comes from it, earth desiring the centre and being held together by it, fire the purity of heaven and, of the intermediate elements, air desiring fiery fineness and water its seat in earth, it is clear that the entireties also have impulsions for these things. And so Aristotle says290 that ‘whole and the part move to the same thing naturally’. But there is nothing better than heaven – either as a whole or in its parts – toward which it could move, so that one should not assert the same things in the case of the entirety of the elements and of heaven. And heavy and light are in some ways different because of the different impulsion , even if in the case of

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everything the impulsions are thought to be cases of heaviness, as Plato says.291 But, as I have said many times (since I am constrained to say the same things), I think that nothing useful for his own goal comes to him from showing that the entireties of the elements have neither weight nor lightness and are similar to heaven in this respect; for it is not the case that heaven is perishable because of this similarity, but rather, if there is a similarity, the entireties of the elements are also everlasting because of their similarity to heaven. The difference with respect to the parts (since the parts of the elements are observed to become detached from their whole and to come to be and perish, but, according to the truth which has been handed down, in all past time no portion of heaven has been observed to be detached from the entirety or to have changed)292 provides an easy objection against those who say that heaven has the same nature as the sublunary elements; accordingly the grammarian, thinking to dissolve this objection, says that the more authoritative and governing parts of animals, such as the heart, are less easily affected, and yet they are composed of the same elements. And, agreeing that heaven is more authoritative than the bodies inside the cosmos, he says that heaven is much less affected than the other bodies and that therefore its parts have clearly not undergone the same things as the parts of the elements. Now here too I think that this person is ignorant of many true things: first, that it is not even true that more authoritative things are less easily affected, since the least authoritative things of all, hair and nails, are least easily affected, and bones are less easily affected than the brain or the heart; and secondly that, even if the heart is said to endure, it does not usually survive293 when the animal has already perished, but it is always affected first by fever and transmits it to the rest of the body. However, although it is true that the more authoritative parts of an animal attain more foresight, nevertheless an animal has perception, and perception is a matter of being affected, so that the parts of the body which are less easily affected are less able to perceive and less authoritative. But let these remarks suffice, since, even if he thinks he knows something more in these matters, I think that he is more ignorant of them than even uneducated amateurs. However, it is amazing that he does not understand that it is impossible for what has a temporal beginning of coming to be and an end to remain the same from beginning to end, whether it is inanimate or animate, an animal or a plant; but rather that, beginning from what is less complete, it proceeds toward what is more complete until it reaches its acme, and after that it wastes away little by little and makes its way to perishing. So if heaven is observed never to vary at all, either as a whole or in its parts, but to have its own completeness, not just previously but also now and until the ‘last days’ – as this person clearly believes294

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– how, by its very nature, can it perish when it is at its own acme, although no animal or plant or even any other of the lowliest perishable things in the cosmos, which is still at its acme, is destroyed unless some force ? But let this person, who has completely blinded the eyes of his own soul by his victory-loving outlook, not see these things. However, he says he is a grammarian. So how can he say that heaven is less affected than anything else and still suppose it is perishable? For if what cannot be affected does not perish, how can what is less affected perish? For the comparative contains an increase of the positive, since what is more white is whiter, and if it is true that what is white cannot be black, it is even more true that what is whiter cannot be black. Similarly too what is unaffected cannot suffer, and much more can what is more unaffected not suffer. But enough of this! If the parts of the elements are clearly observed to come to be and perish and change in all sorts of ways, but no part of heaven has ever been observed to vary from its own completeness (as the motions of all the parts, which remain the same, also make clear), who will not accept and reverence the substantial superiority of heaven over sublunary things? He also cites Aristotle, who says in the fourth book of this treatise295 that fire is light everywhere and earth heavy everywhere, but water is light in earth and heavy in the other elements, while air is light in water and earth, but heavy outside of them, as is made clear by the fact that an inflated bag weighs more than an empty one. And from this this person infers that heaviness and lightness do not belong per se to the elements. He says, For if they did the same things with respect to the same powers and taking on nothing from outside but only from their relation to one another, they would not be light in one place and heavy in another, and light in relation to one thing, heavy in relation to another. For at least white and black and hot do not depart from their own ordering, however they might be related to other things. He says these things in these very words, and I am amazed that he does not realise that in this passage Aristotle is also saying that fire is lightest and only light, and earth is only heavy, whereas the two intermediate elements share in both in relation to different ones296 … of their own activities. For in relation to people who have a discriminating eye, what is grey acts like white, but for those who have a synthesising eye it acts as black, because it shares in both white and black.297 But in general how does the fact that the intermediate elements are both heavy and light undermine the argument which proves that

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heavenly things do not share in either lightness or heaviness? For whether heavy and light are natural or relational, or per se or relative to something else, they have been proved to be present in sublunary things because those things move in a straight line. However, at least on the basis of what has been said, there is nothing to prevent fire from being light per se (since it is absolutely light) and earth from being heavy per se (since it is absolutely heavy). And even if heavy and light belong to things which leave their proper places,298 nevertheless both leaving places and becoming heavy or light on leaving them are features specific to sublunary things, and the difference in this respect would also be sufficient to prove that heavenly things have a different nature. Having come across something else of the man’s, which I think is excessively mindless, it is necessary for me to quote his absurdities themselves so that those who read299 what I write do not disbelieve that someone who attempts to write has such unintelligent and inconsistent ideas. In the thirteenth chapter of his second book, he says, But let it have been agreed that not only do the elements have weight or lightness in alien places, but also that they are given form by such powers when they are in their own places. I do not think that, even if this is agreed, there will be an argument capable of proving that only the heavenly body is free of these powers since Aristotle inferred that it does not share in weight or lightness, from the that it is not naturally constituted so as to move in a straight line. For he assumed that heaven is different from the substance of the bodies which move in a straight line in order to demonstrate that it is not of a nature to move in a straight line; and he inferred that it does not share in weight or lightness from its not moving in a straight line. So, if there were some argument to prove that, even if heaven shared in weight or lightness or even if it were a composite of heavy and light bodies, it would nonetheless still be impossible for it to move in a straight line, it would be completely clear, I think, that it is not necessary that heaven be free of weight and lightness just because it does not move in a straight line. Let the starting point of the demonstration be the following: … And then he assumes that heaven is a solid body which offers resistance and is incapable of yielding in the way water and air do, and that if some part of it is detached, it does not remain continuous, as water and air do because other parts of them move in to replace the torn-away part. And he asserts that the spherical shape of heaven is the cause of its solidity,300 and says,

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Therefore, if heaven were light, then just for that very reason it would not move in a straight line since it would be occupying its own place (the outermost one), just as the whole earth cannot move lower either since it occupies its natural place. But if it were heavy it would again be impossible for it to move in a straight line outside, since there is no void outside. And, in addition, the natural motion of heavy things is to the centre, but heaven cannot move to the centre because there is no void between it and the centre (and, if there were, the smaller space could not receive the greater body), and because it is held together in a spherical shape at every point by its own parts, being indivisible or difficult to divide. For, in the case of things which are moist and easy to divide and yield readily to things which come against them, if some part of the whole withdraws, the remaining parts mutually replace one another and make the whole continuous again, as happens with the elements other than earth; but if some part of things which have resistance and are difficult to divide falls away, it destroys the shape of the whole. Consequently, as long as it is necessary that heaven remain with its natural shape and the whole cosmos exist, it is impossible that some part of heaven fall away from the continuity of the whole, so that we should not ask why some parts of the other elements fall out , but this does not happen in the case of heaven; for if some part of those other elements is detached, the continuity and natural shape of the whole is still preserved because of the mutual replacement of the remaining parts, and no harm accrues to the whole as a result; but it would be impossible for this to happen in the case of heaven; and so, as long as it is necessary for it and the universe to be preserved, it is necessary that no part of heaven fall away. The fact that heaven is like this demonstrates that some form which is different from the simple accrues to it, but not one which is alien to the nature of the elements; for frozen water also can become ice or snow, but these are not therefore considered to be bodies of a fifth nature.

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In conclusion he says, Therefore, if even when we hypothesised that heaven shares in weight and lightness, we found that motion in a straight line is impossible for it, it is not the case that if it does not move in a straight line it is thereby free from lightness and weight. Now here notice first that, although he agrees that what moves to the centre naturally is heavy and (obviously) that what moves from the

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centre is light, and although he demonstrates that it is impossible for heaven to move in a straight line, he nevertheless hypothesises that it is either heavy or light, and thinks he proves on the basis of this that, even if heaven does not move in a straight line, nothing prevents it from having weight or lightness. How does he infer this, if what is heavy moves in a straight line and what does not move in a straight line is not heavy? For to hypothesise that heaven301 is heavy or light and never moves in a straight line is not to demonstrate that, even if it does not move in a straight line, it is heavy or light. Rather, someone who says the sort of thing this person does seems to me to be saying something like the person who says that if I demonstrate that a human being does not have wings and I hypothesise that it flies, I will have proved that, even if it does not have wings, it is not prevented from flying just because it does not have wings. However, a human being does not fly because it does not have wings, just as heaven is neither heavy nor light because it does not move in a straight line. Consequently an inference of this sort is no inference at all. Turning to particulars, how can he declare that it is not possible to prove that heaven is free from weight and lightness if it is clear that it moves in a circle and not in a straight line? And how can he say that Aristotle has assumed that heaven is different from the substance of the bodies which move in a straight line in order to demonstrate that it is not of such a nature as to move in a straight line? For, on the contrary, he demonstrated that heaven is different in substance from the fact that it moves in a circle, taking as agreed that there is some body which moves in a circle.302 For he says, ‘So since there is a simple motion, and motion in a circle is simple, … it is necessary that there is a simple body which is of such a nature as to move with a circular motion by its own nature’. And everywhere he infers that there is some substance other than those in our world from the fact that there is motion which is not in a straight line but in a circle. And it is immediately clear that, even if heaven doesn’t have solidity or resistance, it does not move up or down or outside its proper place at all, and that it moves naturally in a circle and not in a straight line, and that there is nothing outside it which is better, toward which it can move, and so it moves in a circle. And this person gives an amazing reason why no part of heaven is detached even if it has the same nature as the sublunary elements, namely its solidity. ‘For’, he says, ‘the parts would not grow together if they were detached because of the resistance of heaven and the difficulty of dividing it, and it would remain incomplete’. And yet he considers the earth to have resistance. Why then are parts detached from it? And in the case of moist things he incorrectly makes mutual replacement responsible for their not remaining incomplete if some

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part of them withdraws. For mutual replacement can make such things continuous, but it cannot make them whole unless something is introduced to replace what has departed. But, in general, if parts of the sublunary elements are detached, but parts of heaven are not of a nature to be detached because of their solidity and the strength with which they are endowed by the spherical body, who would not say that heaven is of another nature and substance? And why is it not necessary that heaven last for a much longer time if it is by nature so much stronger? For look! Even if the bones of animals are also perishable, they nevertheless have a more solid structure and are much more long-lasting than flesh and veins and sinews and other parts of the body. And so for this person who desires to destroy the cosmos, there is time to allow heaven to escape for a certain sufficient time after the perishing of sublunary things. However, since he thinks that heaven and earth came to be on the same day,303 it follows that they perish on the same day. And why, my good sir, if these things follow from what you say, do you not urge investigation of why parts of the other elements, but not those of heaven, fall out, even though heaven is equally perishable and subject to affection as the others and to have a constitution of the same age? In what follows, up to the end of the second book, he obviously does not say anything relevant to either the subjects under discussion or, it seems, to his own purpose, but he only strives to entangle Aristotle in contradiction. And thus this man attends only to counterargument, and … .304 He proves with many arguments, which are, he says, in agreement with Plato, that the circular motion of heaven is both natural and bestowed by soul, because heaven is a living thing; and I think that he has spoken correctly, albeit longer than necessary. But he censures Aristotle for what he believes is his denial in the second book of this treatise305 that the circular motion is caused by soul, as Plato thought it is, and for saying that if it were caused by soul it would be unnatural and would need rest and pressure, like other living things. He says, However, even Aristotle himself says that ‘heaven has a soul and a starting point of motion’, and that one should not think about the stars as if they were just bodies and ordered monads but entirely without soul; rather, one should conceive them as sharing in action and life.306 However, if heaven has a soul and a starting point of motion, in what other way will it be changed by soul than by changing place, if it does not come to be or perish or increase or diminish or change in quality?307 And if he has also proved in the eighth book of the Physics308 that the heavenly body is finite and that what is finite has a finite power, but

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circular motion is infinite, it is necessary that the circular motion is given to heaven by an infinitely powerful cause. But since nature is in a finite substrate, it is also finite. Therefore, even according to Aristotle, what causes heaven to move in a circle is something other . How then can he think it right to say here that the circular motion is derived from nature alone?

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So here this person makes these accusations, and he says that it is not impossible for the same motion to come to be both because of soul and because of nature. He says, ‘It is as if one conceived of a bird flying in a straight line to the centre since in this case the desire of the soul works together with the natural impulsion of the body’. However, he thinks that Aristotle is not of this opinion here, and he argues against the interpretation of Alexander which says Aristotle is of this opinion.309 And so we should attend to the text of Aristotle in relation to which this person has written all these things. It goes as follows:310

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Who, hearing Aristotle say that the motion in a circle is natural and also that heaven has a soul would not recognise that he is directing these words against those who say that motion in a circle is only due to soul without also factoring in that it is natural? For in the Timaeus Plato at least first assigns circular motion to heaven as natural and then says it involves soul. He speaks about its natural motion as follows: 311 It had no need of hands to grasp things or keep them away, and thought that it would be pointless to attach them; nor did it have need of feet or in general anything with which to walk. He assigned it the motion appropriate to its body, the one most related to mind and thinking. And so he made it revolve and move in a circle, making it turn in a self-contained way uniformly in the same place, but he deprived it of the other six 312 and caused it not to wander. Later, but not immediately after, he wrote the following about the motion which is due to soul: 313

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When the whole psychic structure had come to be in the way its maker intended, he next fashioned inside it everything corporeal, and he brought them together, fitting centre to centre. And the soul, being interwoven from the centre to the last heaven and surrounding it in a circle, revolved within itself and made the divine beginning of an unceasing, intelligent life … . But Aristotle says314 that what is moved by some soul which constrains it – obviously if it were constrained to move against its own nature in a way other than that in which it is naturally constituted to move – would not remain fixed forever, and he says that one should not accept that the life of the cause of this motion is ‘painless and blessed’. And the addition by Aristotle of the word ‘constrains’ suffices to dissolve everything that this man has said. And if motion in a circle is natural for the body and intellectual soul, it is reasonable that both what moves and what is moved are everlasting and blessed. This person is remarkably full of the writings of Plato, just as he is full of those of Aristotle. For although Plato gave heaven its circular motion before adding a soul to it, this person still defends Plato as if he says that the motion were only due to soul. He says that its circular motion is not unnatural for the body , since it does not have any other motion naturally, just as no motion is unnatural for the whole cosmos, since it doesn’t move naturally either. One should also say these things against him when he asks315 whether the motion in a circle of the whole hupekkauma is unnatural or natural for it. For, since, if the hupekkauma does not have this motion naturally, it doesn’t have a natural motion, it should be said that motion in a circle is neither natural nor unnatural for it; it is hypernatural, as has been said.316 It is his goal, as he himself admits, to oppose what is said about the everlastingness of heaven, and he has not been satisfied with writing against what has been written in On the Heavens, but he spends his third book writing against Aristotle’s statement in the Meteorology317 that heaven is not fiery. And so there is nothing to prevent us from setting out the unsoundness of what he says, especially because as a result we will learn what sort of fire Aristotle denies that heaven is, and what Plato indicates the fieriness of heaven is like, and what this person, who does not realise that agrees with Plato, says it is like. When Aristotle says in the first book of the Meteorology318 that if the whole heaven including the stars were made of fire, ‘each of the other elements would have vanished long ago’, this person says first that the hupekkauma raises the same difficulty since it is greater than the things it surrounds. However, he says, neither the fire of the hupekkauma nor the heavenly fire burns; what burns is the fire around us, since, according to Aristotle,319 it is an excess of fire.

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In this connection one should notice that for him the whole argument is again aimed at proving that the heavenly body has the same nature as sublunary things, with the result that it is demonstrated that it is also perishable in the same way as they are. Now, if sublunary things are naturally constituted to act on one another and to be affected by one another and to change into one another, it is clear that if the heavenly body were fire or something of the same nature as fire, it would be necessary for it to be affected by sublunary things and act on them and to be equal in strength to them.320 Now if in terms of size the excess of heavenly things to sublunary ones is as great as astronomy proves it is (and it proves that the earth has the ratio of a point or centre to what is above the sun), then if we were to add the hupekkauma to heaven321 in the entirety of fire, how could any of the sublunary elements possibly be equal in strength to it? And why wouldn’t other things easily be overpowered by it and vanish322 entirely, not by being burned – Aristotle did not bring in burning in this context – but by being changed into that, whatever it was? In this connection he has pointlessly wasted many arguments proving that the qualities of the elements do not increase in proportion to the mass of the bodies in which the qualities exist; for example, ten thousand times as much water does not have ten thousand times as much cold, but a cup of water from the sea is equally cold as the whole sea. For he does not understand that, even if the form does not increase in such a way as to become colder, nevertheless it is magnified along with the quantity of the mass, so that more has more effect than less, and the cold air in a large house cools more than that in a smaller one, even if there is the same quality of coldness in both cases. And a greater quantity is less affected than a smaller one, as even this person agrees. For even if a quality which impinges from outside is sometimes more intense in a smaller magnitude, nevertheless a natural quality is proportional to the magnitude and does not itself become greater or more intense, but expands along with the magnitude in which it is present.323 Accordingly, greater magnitudes are less easily affected with respect to a quality, because the quality is greater in greater things. For things do not undergo qualitative change in relation to mass but in relation to quality. Consequently, if the heavenly body together with the hupekkauma is practically infinitely many times the size and its power is as many times the power, how would it not be the case that ‘each of the other elements would have vanished long ago’, as Aristotle says,324 when it had been changed by the hupekkauma and heaven? (And there is a reason why Aristotle said ‘each’, namely, so that the excess of the excess325 would increase.) This person is satisfied that the fire does not burn, but he does not also take into account that are of the same nature, and change into one

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another. Such are the things which this person, who has, unfortunately, heard philosophical arguments, puts forward. But since I also think that some people will not believe that someone who tries to write could be so badly educated as to be ignorant of these matters, it is necessary for me to once again quote his very words: Because the sun heats most the things to which it has come nearer, it shows clearly that the great distance of heavenly things and especially of the stars – which earlier people thought were more of the substance of fire – makes the heat which comes from them to things here weaker. So what qualitative effect can the heat in the sphere of the fixed stars (if it has a hot nature) bring about in things on earth, since it is so far away? For the outermost sphere could not have a qualitative effect on the next ones, since it is similar to them, nor could those affect the hupekkauma, since like is not of a nature to be affected by like. And so the hupekkauma would retain its own nature, not undergoing anything because of the heat in the heavenly spheres; nor would the hupekkauma itself have any more effect on what is inside it than it does now, even if everything around it were fiery; and this is especially true because, as we have said many times, that fire is hypothesised not to be a flame which burns. Here it is clear that this person thinks that the sun heats us more in summer because it is nearer to us then; and it is clear that he thinks that it is nearer to us at noon than when it is rising or setting, since it heats us more at noon. And he is not aware that the earth has practically the ratio of a point to the sphere of the sun, so that the difference326 between its precise position and its apparent position is minimal. But then how can the sun become so much nearer to or further away from us that the difference in heat between the summer and the winter becomes as great as it is? But he is also unaware of the fact that, just as, although the sun is at the same distance from us every day, no matter what position it is in, it heats us more at noon because the rays are reflected back into themselves more, so too, the sun produces the difference between the seasons with regard to hot and cold not because it is nearer to us in summer but because it is nearer to our zenith point and again further away from it in winter.327 But you hear him say, in the belief that the heavenly body is hot328 and has a heat like that of sublunary fire, that it is the only body in the cosmos which does not act, since the sphere of the fixed stars has no effect on the heavenly spheres below it, and the whole heaven has no effect on the hupekkauma. He says, ‘Like is not of a nature to be affected by like, but only the hupekkauma acts on what is below it’.329 And it is clear that even if the heavenly heat is vital (as this person thinks), it does not transmit a share of itself330 to sublunary things.

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But how can he hypothesise that the fixed heaven is hot and say that it does not act at all, but that the sun heats us? For, according to his own statement, the fixed heaven cannot have any effect on the heavenly spheres since, as he says, ‘like is not of a nature to be affected by like’, nor can it affect the hupekkauma, and so it cannot affect things here. But, then, does heaven not have any effect on sublunary things because of its own qualities although it is affected by them, or does this good fellow say that, although it neither acts nor is affected, it has the same qualities and nature as sublunary things? But it is clear that according to what he has said, except for the last part of it which is next to the air, the hupekkauma does not have any effect on the air, and again that, except for its last parts, the air does not have any effect. But how can someone who earlier agreed331 that heaven is more solid and stronger and more authoritative now declare that it has less effect than everything else?332 Alexander having said333 that the reason why the elements are preserved and endure together and are not destroyed by one another is the equality of their powers, but that air would exceed them greatly if it extended up to heaven, this person argues against this and says that ‘it is possible for a small amount of air to be cooled down or heated greatly and for a large amount to be less so’. And it is clear that nothing prevents qualities which enter from outside from being more intense in a small amount, as has been said,334 and being less intense in a large one; but it is necessary that the qualities which attach to air naturally extend along with its size, and that one understand the natural powers of air in terms of these natural qualities and not in terms of the ones which enter from outside. And one should understand the equality of the elements as the equality of these powers.335 So if air were simply everything above earth extending up to heaven, how would it be an element co-ordinate with the others? And how could the other elements have a power equal to it when it exceeds them so much in size? For even if the elements are not equal in size, they must have some harmonious ratio to one another. But if the whole heaven and the hupekkauma were fire, what would the ratio in size of the other elements to them be, and what would the ratio of earth to the mass of air between earth and heaven be? The views of Plato seem to appeal to this person. I don’t know how, since, as they say,336 he has found no teachers in these matters, and he has not sought to find out Plato’s views in an intellectually serious way (philomathôs). As a result he sometimes thinks that Plato’s views harmonise with his own imaginings and sometime that they contradict Aristotle’s. So let us now watch him as he sets out some of Plato’s views. He says,

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Plato hypothesised that the heavenly bodies are not composed of just fire, but above all share most in that sort of fire which also makes the mixture of the other elements more temperate. And he thinks that for the composition of the heavenly bodies there was chosen from all the elements the whole of the most pure substance, and the one which has fine parts and which has the role of form in relation to the other , and that the more material and, so to speak, sludgy portions of these things exist in this world. And Plato also thinks that the stars and the sun are made from that sort of fire. Now if heaven is composed from the purest substance of the elements, a substance having fine parts and having the role of form in relation to the matter or ‘sludge’ which is the substance of the elements here, how can he think that heavenly things have the same nature as things in our world and are perishable like them, especially, perhaps, since the totality of them is proved to be imperishable? For if the perishing of one element is its change into and coming to be of another, how is it possible for such an arrangement to perish? But let the disdain of heaven be a just retribution for those who have sinned against god! Plato says the following things. The whole cosmos is composed from the four elements: visibility coming from fire, tangibility from earth, the intermediate elements having come into being for binding the extremes in a harmonious way. But heaven is composed of the purest of the elements, which also has337 the role of form, and it possesses the highest kind of corporeal nature. Therefore, it is both everlasting and divine, because the highest kinds of all things are everlasting and divine, since they are dedicated to the gods,338 the highest of all things; and accordingly the first minds are divine, and so are the first souls, and so too are the first bodies.339 And consequently, change of place being the first , heaven was assigned the first motion, circular motion, and came to be the cause of change in other things. And Plato says that heaven is composed mainly of fire because, there being, according to him, three kinds of fire, coals, flame, and light, heaven is mostly composed of the purest and brightest light; for just as each of the so-called sublunary elements is composed of the four simple elements, which are truly elements, but they are given substance and characterised and named by reference to the predominance of one of the four, so too heaven, which is composed of the highest forms of the four elements, is given substance by the best of the highest forms, having been brought to completion as brightest and shining everywhere, and is therefore proclaimed as Olympus.340 And it is also clear from perception that the so-called sublunary elements, as wholes and in their parts, are not simple in the strict sense. For earth holds together and is not

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broken into pieces because of the water it contains, it has colour and burns because of fire, it is always full and provides no room for void because, even if it decays, air enters into it, this air causing it to stand upright and hold itself up and not collapse; and one can see the same thing in the case of the other elements. And what I am saying is also clear from the nature of an element: elements, insofar as they are elements, never exist independently but give rise to what is composite because they always spread through one another, just like the twenty-four elements of speech, the letters. For the parts of speech do exist but, since they are parts, they cannot exist independently. In the same way the elements of a composite also exist and always spread through one another and never have an independent existence; but only after they have first been mixed together and given form by the predominance of one thing do they combine to make animals and plants and their parts in a second synthesis in which the ‘elements’ determined by predominance function like simple things; and they strive to preserve the original unity in their causes by always blending together with one another. But in what way does this person think that Aristotle has a position contrary to Plato on the substance of the heavenly body and does not accept either that the heavenly body is composite or that it is simple in the way that fire and any other of the four so-called elements are?341 Perhaps Aristotle foresaw the gigantesque rebellion of these impious humanoids against heavenly things and therefore, since he wanted people to recognise the complete transcendence of heaven over sublunary things and its divine superiority to them, he refrained from the words of those who try to drag heaven down into similarity , and so placed heaven above both the composite and the simple things in our world. Moreover, it is possible to see that in these ideas Aristotle is not in disagreement with Plato, if one recognises that would readily accept that heaven is completely visible and tangible, since it is immediately clear to those of us who value342 vision that heaven is visible, and it is also immediately clear that the heavenly bodies touch one another. So if heaven is visible because of colours, and colours are effluxes of something bright, and if heaven is tangible because of the resistance provided by earth, how could Aristotle not agree that there is fire and earth in heaven and obviously also what is intermediate between them, since fire and earth are extremes and in every way require a mean? But they are not at all this earth and this fire, of which portions become detached and become arranged in an unnatural way and are naturally constituted to move in a straight line because they are incomplete. Accordingly, on the basis of their difference with respect to these incomplete motions, Aristotle accepted the superiority of heavenly things to sublunary ones, and so separated heavenly things from this earth and this fire, portions of which are

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sometimes arranged unnaturally, even though the entireties of them remain in a natural condition. …343 It is then reasonable for him to agree that heaven is not composed of much fire, dismissing that fire which changes the other elements into itself. And that is why he says344 that if heavenly things were made of fire, ‘each of the other would have vanished long ago’. It is clear that Aristotle also believes that the things which we call elements in our world are also given form because of the predominance of one of the simple bodies (and I think that he believes this of heaven as well); and because of these bodies he frequently says that not just the simple bodies but also the composites move with simple motions (and for him the discussion is about simple motions) in accordance with what predominates in their mixture;345 so how can we say that in these matters he says things contrary to Plato when he does not say the ‘contrary’ things about the same subject? And now I will express my own view. I think that Aristotle has undergone the same experience in these matters as he has in the case of the ideas. For in the case of the forms he has obviously accepted that the causes of all things are in god, and that these causes are separate, since he says that there is a double order, one in this world and one in the creator, from which the first order derives in just the way that there is a double order , one in the general and one in the army, the latter deriving from the former. And there is always a separation where there is an order. But he has asked to be allowed to refer to the causes with the same words as are used in our world, ‘man’, ‘horse’, and so on, because the imaginations of most people move along easily with words.346 So too in the case of heaven he would also say that it is composed of bright and tangible substance, with the bright predominating, but not of what is bright and tangible in our world but from the highest forms of these things, as he makes clear by calling it ‘divine’ and ‘first’ when he says,347 ‘So if there is something divine, as there is, what we have just said about the first substance of bodies is correct.’ As a result he saw that he should call this divine thing a fifth substance, so that we might put forward our conceptions of it as completely transcendent over things in our world. And I also mentioned earlier348 that this is not incompatible with what Plato has taught, because Plato says that the creator painted sublunary things with certain figures and the heavenly body with a different one. And this is also clear from what Xenocrates has recounted about these matters. It would not be a bad thing to recall them now. In what he has written about the life of Plato he says, So he divided up living things again in this way into forms and parts in every way, until he reached the five elements of living things (which he called five figures and bodies), the five elements being aithêr, fire, water, earth, and air.

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Let these things suffice concerning the views of Plato and Aristotle on the present subject, if god has granted us some understanding of the views of those divine men. Against this person, who is striving contentiously to place heat and coldness, dryness and moistness, softness and hardness, and the other tangible and affective qualities in heaven, one should again ask: If such qualities of heaven are of a nature to act on things here and to be acted on by them, why has no qualitative change deriving from things here been observed to occur in heaven up to now? For even if heaven is less easily affected than things here, nevertheless since it is already the last days (as they349 say) and the completion of time is expected any moment now, certainly something ought to have appeared differently in heaven and its motion by now. But if things here are affected by heaven, and nothing here is of a nature to act on it, how can we dare to say that heaven has the same nature as things here? And how can we bring in Plato as a witness for this on the grounds that he says heaven is composed of the four elements? And how does this person think, on the basis of the fact that the sun heats things here, that heaven is hot in quality and shares in a great deal of fire (something he also infers from its colour)? For look! The other stars are also said to share in a great deal of fire and to have, as he says, a fiery colour, but Saturn is believed to make things here cold350 and to combine them; and it is clear that by the same argument it would be cold and not fiery but, rather, watery. However, the sun does not heat things because it is the fire which we accept, nor does Saturn make them cold because it is watery. Rather, in a way which is common all of them use their incorporeal powers to turn bodies here to their own specific features, just as when the soul feels ashamed or is concentrating on something, the incorporeal activity of the soul makes the body blush or frown. On the other hand, because of this power and the rubbing of its rays, the sun makes the air warm and heats other things through the air; this is clear from the fact that the sun heats more when its rays are reflected back into themselves. And so one should not think that things heated by the sun are heated because they receive a similar heat which is in the sun in the way that things which are heated by fire are heated because they receive what flows out from the fire. For if they were it would be necessary that the sun flow out as the fire in our world does, and that it not only heat but also become cooler, since the heat in us also becomes cooler when it is separated from the heat in the sun. But further, this person does not shrink from committing unrestrained – or rather mad – blasphemy against heaven and obviously against the god who gives it existence and sustains it in existence. He clearly shouts that heavenly things are not of a different nature from the things in our world, and says, ‘For there is practically nothing which we see in heavenly things which does not also belong to the

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bodies around us’. And he brings in transparency, which is observed similarly in heaven and air and water and glass and certain stones. Nor does he refrain from adding the word ‘similarly’, and he calls the different colours in the stars not just similar to but also the same as the colours in our world. He says, And the colour called bright and light, and all the accompanying affections in light attach to many bodies in our world, to fire, to fire-flies, to the heads and scales of certain fish, and to other such things.

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Can he be in his right mind and say that the light of heavenly things and their brightness attaches to fire-flies and fish-scales? He says, And spherical shape does not just attach to heavenly bodies but also to all the other elements and, moreover, to some composites. And circular (enkuklios) motion also attaches to fire and to some parts of the air.351 In this way he shamelessly or perhaps ignorantly obscures the fact that the hupekkauma is made to move with a circular (kuklikos) – this is what he means352 – motion by heaven, as is made clear by comets and other appearances in the hupekkauma which rise and set together with the fixed stars. After having said other similar things, he next adduces that, being visible, heaven is certainly tangible; and being tangible, it also has the tangible qualities, hardness, softness, smoothness, roughness, dryness, moistness, and things similar to these, and also what embraces all of these, heat and cold. It is also clear from what I said earlier353 that heaven is tangible. But this person, who also frequently brings in the heat of the sun, is obviously contending that heavenly things are tangible to us. And finally he says that the three-dimensionality of heavenly things and of things in our world is the same, because, qua three-dimensional, one three-dimensional thing does not differ from another, since, qua body, one body does not differ from another either. And it is clear that this argument would not only make heaven have the same nature as things here, it would also do the same to anything intelligible and to god himself.354 Let this argument and what follows from it be his, not mine, if, indeed, he thinks that both those things and these exist, and that existence is the same for each of them. It was not pointless for Aristotle to pass over this universal which exists in us by abstraction, on the basis of which this person has also treated the other specific features and that of three-dimensionality; and indeed this person for his own use asks to identify the use of words in first things and later ones.355 For if the light and the brightness of

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heaven differed from the light and brightness in our world by so much that they were not referred to with the same words there and in our world, this person would not have dared to say that the light of heaven also inheres in fire-flies and fish-scales. And if he had contemplated the procession from the One which bestows commonality with difference (diaphoroumenê koinotês) from first things to intermediate and last ones, he would not have dared to say that last things have the same nature as first ones, or to be angry with those who demonstrate that the substance of heavenly things transcends that of sublunary ones. However, having heard that both ‘this’ and ‘that’ are light and transparent and bright, he thought that ‘these’ have the same nature as ‘those’ because of his own uneducated rashness. But why should I blame his lack of education when it seems to me that this person, whoever he is, has corrupted senses, since he supposes that the heavenly light is similar to and the same as the light of fire-flies? Because of his empty-headed contentiousness he does not notice that he is arrayed in opposition to that ‘David’ whom he absolutely admires. For David makes clear that he does not think that heavenly things have the same nature as sublunary ones when he says356 that heaven – not fire-flies! – declares the glory of god, and the firmament – not fish-scales – proclaims the work of his hands. But here, too, the words of Aristotle357 are apropos: ‘if one absurdity is granted, the others follow’. For if someone thinks that god has the same nature as he himself does,358 why would he shrink from childishly puffing himself up with respect to the best and most beautiful of god’s creations? In concluding this discussion he seems to express anger at those who (he says) introduce for the heavenly bodies a nature which is alien and foreign to the elements and has nothing in common with them. And he says these things even though everyone who is celebrated in philosophy supposes heaven is made of the four elements! But it is immediately clear that if those people359 who said that heavenly things are made of the four elements had supposed that some people would so impiously misinterpret them as to think that, as a consequence, heavenly things have the same nature as sublunary ones, they would not have presented their doctrine in this way. And it is also immediately clear that those360 who said that there is a fifth substance did not say that it is alien and foreign to sublunary things and has nothing in common with them; but they said, in the same way as those who said that heaven is made of the four elements, that the fifth substance transcends sublunary things in substance and power, but is the immediate cause of their coming to be and existence and of their shape and motion and of their acting and being acted on. For even god would not be said to be alien and foreign to what he produces and to have nothing in common with them because he is superior to the things which he produces.

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At the end of his arguments of this kind he says that the heavenly body is composite according to Aristotle as well, because he says in De Anima that every body which has a soul is a composite of the elements, but in this treatise in the second book361 he says clearly that heaven has a soul. So do we still need some further argument to prove that Aristotle thinks the same things as Plato about the constitution of the heavenly body, but that he has presented more unshakeable arguments?362 For wanting to hymn the praise of the transcendent nature of heaven vis-à-vis sublunary things, Aristotle fled from the sameness of words and said that it is simple in the way that the sublunary things which are determined by predominance are called simple; but he proved that heaven is of a different nature from these things on the basis of the fact that it is composed from the highest forms . And he proved that they are different in substance on the basis of the difference of their motions: rectilinear motion indicating that parts come to be and perish and change toward the natural and the unnatural; circular motion that both whole and parts are always complete. It is worth noting that this person, in contrast to others of his sect,363 also thinks heaven has a soul, even though he is obviously no less impious than the most mindless of them. But now let us go on to the next of Aristotle’s considerations.

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Notes 1. For the whole text on which Simplicius will now comment see pp. 37-40. 2. In the preceding chapter. 3. Not reading haplou with Hankinson. The reference is to the discussion in chapter 1 of body as three-dimensional. 4. Until chapter 5. 5. Rescigno includes only the first sentence of this paragraph as his text 5b, but the second should probably be taken as expressing Alexander’s view as well; cf. Moraux (2001), p. 189. Alexander believes that book 1 of De Caelo is primarily about the whole cosmos and book 2 is primarily about heaven. Simplicius is inclined to see the two topics as more mixed together. 6. 2.1, 284a2-5; see also the continuation of the passage and Simplicius’ comment at 373,25-8. 7. merê as opposed to moria; see Hankinson ad loc. The distinction is not one to which Simplicius adheres. 8. ‘Established’ at 268b20-6, which is taken to show that there are three simple motions, up, down, and around the centre. 9. This and the next hypothesis are said to be ‘established’ at 268b20-269a2; asserted at 269a2-4. 10. cf. 269a8-9. 11. Asserted at 269a14. 12. For the importance of this assumption for Simplicius see 45,17-19 and 77,11-23. 13. Enneads 2.1.2,12-14 (Wilberding (2006)); on this quotation see Wilberding (2006), ad loc; for another list of Aristotle’s ‘hypotheses’ see Proclus’ commentary on the Timaeus (Diehl (1903-6)) 1, 237,27-238,1). Simplicius now goes on to argue for the harmony of Aristotle’s conceptions of heaven and what Plato says in the Timaeus. 14. i.e. eternity as a single thing. 15. What follows is Xenocrates fragment 265 (Isnardi Parente (1982)), on which see her commentary. The same passage from Xenocrates is quoted by Simplicius again at 87,23-6 and at 1165,35-8 of his commentary on the Physics (CAG 10). 16. cf. 2.12, 292a18-21. 17. 8.7, 260a26-261a28. 18. i.e. the lines. 19. i.e. as necessary conditions. For the reason why Alexander makes this point see 13,22-14,3. 20. For one explanation of this obscure remark see Hankinson, ad loc. (I mention that the footnote numbers in Hankinson’s text diverge from those in the notes by 1, with 77-134 in the text corresponding to 78-135 in the notes.) 21. Late first century BC; see note 83 (82) in Hankinson, or for more detail Moraux (1973), pp. 197-212. 22. hê epi tou kulindrou helix, described below at 14,14-21. 23. antiparastasis, a counterargument based on a hypothesis (in this case that

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the helix is simple) accepted by one’s opponent; see, for example, Hermogenes, On Invention (Rabe (1913)) 3.6. An enstasis (see below 14,9-10) is an objection to the hypothesis. 24. Simplicius goes on to reject this interpretation of Alexander because for him it is incompatible with Aristotle’s second hypothesis (12,8-9), and Aristotle himself argues (269a2-7) for the existence of a simple body which moves in a circle on the basis of the fact that circular motion is simple, itself a consequence of the fact that a circular line is simple. 25. Simplicius substitutes periphereian for Aristotle’s peripherês. 26. kata enstasin; see the note on 13,29. 27. cf. the beginning of the commentary on the next lemma. 28. This is a crucial point for the question whether Aristotle is doing physics or mathematics in this part of De Caelo. For Philoponus’ follow-up to Alexander’s claim here see 32,1-14, where Simplicius also backs away from Alexander’s position. 29. For an attempt to explain this apparently strange position of Alexander see Hankinson ad loc. 30. On animal motion see further 16,11-17. 31. cf. 268b17-19. 32. Bracketing monôn merôn with Moerbeke, who has only omiomeris. 33. Inserting moria in line with line 33 below. 34. Timaeus 58C. 35. Although Simplicius commends what Alexander says, some commentators (e.g. Stocks (1922) ad loc.) distinguish between Alexander’s taking Aristotle’s phrase ‘fire and earth and their species’ to mean ‘fire in general and earth in general’ and Simplicius’ taking it to mean ‘fire and earth and also their species’, of which he lists some. 36. This sentence is not included in the quotation by Heiberg or Hankinson, but it would apparently be by Rescigno (see p. 186). 37. Here Simplicius takes composites as living things; other composites, including for Simplicius the things we ordinarily call elements, have the natural motion of their dominant component. 38. This is, of course, Plato’s doctrine, which Simplicius now tries to harmonise with Aristotle’s claim that heaven is a simple body distinct from the four sublunary elements. 39. That is, the things that we ordinarily call composites. 40. Moraux prints heautou, Heiberg hautou with an apparatus reporting that autou is the reading of A, heautou that of E and Karsten. In a citation at 18,8 Heiberg prints hautou agreeing with a correction of Bessarion, noting that ABCDE have autou, Karsten heautou. Moerbeke has ipsius in the lemma and suam at 18,8. The situation is quite the same in another citation at 18,23 except that there C has heautou. 41. This seems a tempest in a teapot, since Simplicius does think Aristotle has proved the antecedent. 42. The subject of this sentence is not made explicit. Most translators and commentators take it to be the body which moves in a circle naturally, but, as Simplicius’ discussion shows, he takes it to be the sublunary elements. He may be influenced by the fact that it is impossible for heaven to move in any way other than the way it does. 43. In this lemma and the next. 44. cf. 17,25-33.

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45. Aristotle’s argument is vitiated here because it is false that if something doesn’t belong to a subject its contrary (enantion, to be distinguished from its denial (apophasis)) does; see Hankinson’s notes on this section of the commentary. In the case at hand the contraries are natural circular motion and unnatural circular motion, and Aristotle assumes that if something doesn’t move in a circle naturally it does so unnaturally. In what comes next Simplicius struggles to justify Aristotle’s reasoning. Later (e.g., at 52,5-18) he will say that Aristotle sometimes uses ‘unnatural’ as the denial of ‘natural’. 46. In De Caelo 4.5, on which see Simplicius’ commentary. Here Simplicius makes his first pass at another major problem for the De Caelo, the attempt to correlate two simple rectilinear motions with four elements. 47. That is, water is heavy in relation to air (and fire) but light in relation to earth, whereas air is light in relation to water (and earth) and heavy in relation to fire. On the other hand fire is light in relation to all the other elements and earth is heavy in relation to all the others. 48. Ptolemy’s book on the elements is lost. Simplicius may be citing it at 37,33-4, where the topic is the hupekkauma. In his commentary on the Timaeus (Diehl (1903-6) 3, 114,31-115,2) Proclus assigns to Ptolemy and Plotinus the view that ‘every body which is in its proper region either rests or moves in a circle, and what moves up or down are things which are not in their proper regions but desire to achieve their proper region’. And Simplicius himself accepts this view. 49. A truncated version of Ptolemy’s Optics survives in a Latin translation from Arabic (Lejeune (1989)). In his summary of physical subjects (Delatte (1939), p. 73,11-13) Symeon Seth says that, according to Ptolemy in his optics, optical pneuma is something ethereal made of the fifth substance. Lejeune (p. 14) suggests that this passage and the one referred to by Simplicius are based on a part of the Optics, book 1, which is no longer extant. 50. On Plotinus’ theory of elemental motion and its ancient interpretation see Wilberding (2006), pp. 62-8. 51. 3, 310a33-4. 52. I take the reference to be to On Coming to be and Perishing 2.8, 335a18-21: ‘For only fire or fire most of all belongs with form because it is naturally constituted to move toward the boundary (horos). For each moves into its own region, and the shape and form of everything lies in the boundaries.’ For another view see Hankinson ad loc. 53. cf. 22,18-33. 54. limnazon, a characteristic of the air extending up to the height of the highest mountains; above this is the luminous air and fire, the hupekkauma, which revolves in the same direction as the sphere of the fixed stars. 55. 1.7, 344a8-14. 56. See 21,33-33,10. 57. In the next paragraph Simplicius addresses this difficulty, repeating his exegesis of 269a7-18 (18,20-20,4), but now stressing that in that passage Aristotle did not show that, e.g., fire cannot move in a circle but only that it cannot do so either naturally or unnaturally (here, contrary to nature). Simplicius is concerned about the hupekkauma, which does move in a circle, but – according to Simplicius – does so neither naturally nor unnaturally, but ‘hypernaturally’. 58. That is, with a natural or unnatural circular motion. 59. At 269a7-9. 60. See chapter 3, 270a3-12 with Simplicius’ discussion starting at 63,26. 61. See 13,22-8 above.

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Notes to pages 55-59

62. Note that just above (20,18-25) Simplicius has assigned to Xenarchus and others a distinction between two kinds of air in this respect. 63. I adopt Rescigno’s (p. 194) punctuation of 22,18-21 which removes the comma before the first kai and places it after entautha. Like him I also take autos in line 20 to be Alexander rather than Aristotle. With this material see also 20,10-25. 64. cf. Physics 3.1, 201a10-11. 65. cf. Timaeus 62C3-63E8. The point of this remark is not clear to me; perhaps Simplicius is suggesting that if up and down are relative they cannot have a bearing on the form of the elements. 66. In other words, Aristotle recognises that sublunary elements in their proper places do not move in a straight line, but he is stressing their rectilinear motion to underline the distinction between the sublunary world and heaven. 67. Xenarchus assumes that if every simple motion attaches to a simple body, then every composite motion attaches to a composite body. He argues that the latter is impossible because the number of composite motions is infinite, the number of bodies finite. Simplicius denies that either motions or bodies are infinitely many in form, but sees no problem in their being infinitely many in number (over time). Alexander appears to construe what Xenarchus says as an argument that since a composite has a single motion it has a simple motion. Alexander denies that a single motion has to be simple. But Simplicius admits that Alexander may be responding to a different argument; cf. 24,20-1. 68. The text here is problematic, as Heiberg’s apparatus shows. What Heiberg prints (ou tôi apeira einai) should mean ‘not because the bodies are infinite’. I have chosen to translate loosely. 69. Reading prosüpethemetha instead of the proüpethemetha printed by Heiberg. The reading is also Hankinson’s, but his note 138 is inaccurate. 70. 269a7-9. 71. And so, e.g., even if air is less light than fire, it is still light. 72. Here Simplicius tries to finesse the fact that heaven is not, in fact, a circle or a surface but a body with thickness. 73. tis tôn eph’ hêmôn, i.e., John Philoponus, whom Simplicius never names and most often refers to as houtos (‘this person’). 74. Gardens of Adonis were baskets of quickly growing and quickly dying plants used in the Athenian festival for Adonis in classical times. They are mentioned by Plato at Phaedrus 276B3. A scholium on that passage (Greene (1938), p. 88) says that ‘gardens of Adonis’ was a proverbial expression for things out of season which are short-lived and not firmly rooted. See Simms (1997-8). 75. Simplicius expresses his view of the Christians. 76. Simplicius’ assertion has been doubted by some (see, for example, Verrycken (1990), pp. 263-4), but, even if it is true, one need not conclude that he and Philoponus were not living in Alexandria at the same time; cf. p. 13 of the Introduction. 77. Aelius Herodianus was a grammarian of the second century AD. Philoponus composed an epitome of one or more of his works on accentuation; see Dickey (2007), pp. 75-7 and 81-2. The name ‘Menander’ is more problematic. In his extant works Philoponus does cite the comic poet once in his commentary on book 1 of the Meteorology (CAG 14.1, 94,6-7), but so does Simplicius in his commentary on the Physics (CAG 9, 384,14). Perhaps Simplicius is referring to the third-century AD rhetorician Menander of Laodicea (on whom see Russell and Wilson (1981)), but I know of nothing in Philoponus’ works to substantiate the claim of any connection.

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78. cf. 23,31-24,7. 79. 268b14-18. 80. Simplicius inserts an en which is not in our texts of Aristotle; he does the same thing at 132,24. 81. That is, e.g., one stone can be hot, another cold. 82. i.e. all kinds of characteristics. 83. i.e. Philoponus’ premisses can’t be true since they imply a false conclusion. But, of course, Philoponus is trying to extract an absurdity from premisses he assigns to Aristotle. 84. Since nothing ascribed to Philoponus by Simplicius in the rest of the commentary is really the same as this syllogism, it is simplest to assume that Simplicius is referring to something he does not discuss. 85. The logical discussion which follows from here to 31,6 is badly marred by its lack of formality. I have tried to explain what I think is the basic (and not profound) issue here on p. 17 of the Introduction. Philoponus is wrong to say that he is applying conversion with antithesis, but Simplicius’ attempts to explain why he is wrong are unhelpful, to say the least. 86. Simplicius’ formulation here is loose, but his point (not clearly relevant to Philoponus’ argument) is clear enough: the negation of ‘It is possible that …’ is ‘It is not possible that …’ and not ‘It is possible that not …’. 87. Here it seems that Simplicius is attacking Philoponus’ assumption about things of different natures possibly moving in the same way. 88. cf. Plato, Sophist 251B7. We might paraphrase Simplicius’ point in what follows by saying that if all As are possibly Bs, then what is not possibly B is necessarily not A; but if only some As are possibly Bs, then what is not possibly B is not necessarily not A. I would like here to record my gratitude to the vetter of CAG pp. 29-50 for very thoughtful comments and suggestions. 89. In later writers (but not in Euclid) an even times even number is one which can only be represented as the product of two even numbers; see Heath (1956), pp. 281-2. These numbers are all the powers of 2 and thus only they are ‘divisible down to the monad’. 90. It seems highly unlikely that Philoponus made any such assertion. Simplicius is arguing that he is committed to such a claim, given his use of what he calls conversion with antithesis. 91. Simplicius is referring to the argument at 28,6-11. 92. Philoponus’ vocabulary here is certainly unusual, but he may not have been using the phrase ‘second conditional’ in a technical sense, rather, simply as a way of referring to the result of applying ‘conversion with antithesis’ to a (first) conditional. Simplicius indicates that Philoponus means to be talking about the second unprovable (modus tollens) of the Stoics. 93. Reading proslêpsin with A, D, and E rather than the prolêpsin of B, printed by Heiberg. Moerbeke has proslipsim. 94. I take Simplicius to be saying that, whereas the conversion with antithesis of ‘if p then q’ to ‘if not q, then not p’ is straightforward, Philoponus’ introduction of possible propositions makes his argument problematic, as indeed it does. 95. This last sentence presumably does not express Philoponus’ opinion but his view of what Aristotle is committed to because he distinguishes elements by motions. It is possible that the sentence is Simplicius’ own assignment of a conclusion to Philoponus. 96. In Metaphysics 12.8. 97. Since the ‘unmoved movers’ are immaterial.

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Notes to pages 64-70

98. cf. 307,19 in Simplicius’ commentary on the Categories (CAG 8). 99. In Physics 8.7-9. 100. cf. 14,31-15,4, where Simplicius apparently endorsed Alexander’s view, which he now appears to back away from. 101. The origins of theories of eccentrics or epicycles are not clear, but Apollonius (d. c. 190 BC) was already aware of the equivalence of the two types of theory well before Hipparchus (d. c. 120 BC); see DSB 1, pp. 189-90. 102. Simplicius shows a good historical sense here, but it is only his instrumentalist conception of astronomical ‘hypotheses’ which enables him to avoid saying that Aristotle was wrong. 103. Simplicius now switches from the view that heavenly bodies move around centres other than the centre of the cosmos (which for him is an astronomical hypothesis) to the view that the (spherical) stars rotate on their own axis (which for him is a physical truth). He claims that Philoponus has confused the two motions. 104. The reference is to the Handy Tables (Halma (1822)), and the distinction is between the periods of the centre of the epicycle and of the star on the epicycle; see pp. 112-33. and see also van der Waerden (1953). 105. See 454,23-456,27 of Simplicius’ commentary on book 2. 106. cf. 31,16-32,1. 107. As he does at 4.3, 310b3-5. 108. Here, unusually, Simplicius takes the motion of the elements when they are outside their proper place as unnatural. 109. epi tês lexeôs. The anonymous reader of these pages suggests translating ‘verbatim’. 110. See 20,32-21,25. 111. cf. 269a7-9, the relevant part of which (‘since there is a single natural motion for each of the simple bodies’) is not cited here. Philoponus’ position is again that, just as earth and water have the same natural motion, so too do heaven and the hupekkauma. 112. Reading mê to with Karsten rather than the to of Heiberg, who notes that B has to mê. 113. For this doctrine see 4.4, 312b2-7. 114. 269a9-18. 115. cf. 34,14-21. 116. Although Simplicius commends Alexander’s view here in the context of disputing with Philoponus, later at 54,12-33 he implies that fire has no rectilinear motion when it is in the hupekkauma. 117. Simplicius is perhaps referring to Philoponus’ mention (32,1-11) of epicycles and eccentrics and also rotations of the stars on an axis as evidence that heavenly things do not move in a circle around the centre of the cosmos. 118. That is, parts closer to the centre move more slowly than those higher up. 119. The sequence of argument here is not entirely clear. Philoponus starts by considering the hupekkauma and the upper air as a unit, and argues that, even if there are variations inside of it, the whole moves uniformly in a circle. As confirmation he (apparently) invokes a compound of fire and water and argues that, even though it has parts moving up or down or to the side, as a whole it has a simple motion up or down. Simplicius responds that the motion of Philoponus’ compound is not simple and that in the case he describes, the motion would probably be oblique rather than up or down. 120. e.g. lumps of earth.

Notes to pages 70-79

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121. Rather, it moves faster. 122. But here for the first time in Simplicius. 123. At 269b9-10. 124. i.e. circular motion. 125. Retaining, with Hankinson, the oude kata phusin bracketed without explanation by Heiberg; see, e.g., 18,22-4. The point is, of course, central to Simplicius’ interpretation. 126. This is ‘proved’ at 269a30-2. 127. At 269a2-7. 128. At 268b14-20. 129. This is not a remark about Aristotle’s procedure since for Simplicius Aristotle has already established the simplicity of circular motion. All Simplicius is saying is that the simplicity of circular motion implies its priority over composite motions. 130. In chapter 9. 131. cf. 49,19-23. 132. Reading hê men gar with Bessarion rather than the ei oun hê men printed by Heiberg. 133. This sentence, which I have put in parentheses, is difficult, and it interrupts Simplicius’ own interpretation, which he clearly thinks of as incompatible with the claim that Aristotle has in mind the fact that any finite straight line can be extended in theory; see below 44,3-15 and 46,33-47. 134. The sentence is anacoluthic, but Simplicius’ meaning is clear. 135. On such arguments see Aristotle, Topics 2.10, 114b37-115a14. 136. In the present lemma. 137. Aristotle argues that circular motion is prior to rectilinear in chapter 9. What he says at 265a22-4 implies that it is prior in nature, logos, and time. 138. Again Simplicius strains to harmonise Plato’s and Aristotle’s views of the composition of heaven. 139. For the first, see 25,11-21, for the second 24,20-25,10, and for the third 21,33-23,10. 140. Simplicius quotes lines 157-8 of Pindar’s second Olympian Ode (Maehler (1987)). 141. See, e.g., 35,12-20. 142. cf. 39,11-21. I take this contrast between Alexander and Aristotle to be Simplicius’ rather than Philoponus’. 143. i.e. is. For Simplicius’ claim here cf. 39,18-21. 144. Reading labôn with A, B, E, and Karsten rather than the labon of D printed by Heiberg. 145. Inserting ontos after eidous with Karsten. Simplicius is here stressing that a straight line added to from outside in the standard way remains a straight line, but an ordinary addition to a circle or sphere changes its shape; cf. 38, 26-39,11. 146. Reading autê with B, D, E, and Karsten rather than the hautê printed by Heiberg; A has autêi, Moerbeke hec. 147. cf. 39,21-40,1. 148. Simplicius’ expression is opaque here; he presumably means only that bits of motion and moments of time occur forever. 149. cf. Physics 8.10, 266a24-b6. 150. That is, Philoponus does not realise that heaven could revolve without itself being a circle or sphere. 151. That is, according to Simplicius, Philoponus thinks Aristotle is arguing

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Notes to pages 79-86

that the heavens move in a circle, whereas for Aristotle this is known from perception. 152. In 2.4. 153. Of course, Aristotle himself makes no mention of the stars here, but see 12,10-11. 154. cf. 2.4, 287a30-b4. 155. cf. 42,27-8. 156. With this see 39,11-21, where Simplicius presents and rejects Alexander’s interpretation. 157. Physics 5.4, 228a29-30 and 6.1, 231a22. 158. See 39,11-21. 159. For Alexander’s interpretation and Simplicius’ rejection of it see 39,2140,1. 160. At 39,30-40,1. 161. But obviously counterfactually: eiper sôma eiê (47,1). 162. cf. 39,11-21. 163. Simplicius pursues this nebulous line of argument in what immediately follows. 164. I translate following Moerbeke, who has circulus (ho kuklos), where Heiberg prints to with A and B, remarking that to is omitted in D and E and that Karsten prints ho. 165. ekpiptein psukhrotêta, on which see Wildberg (1987), p. 54. In raising this objection Philoponus is focusing on Alexander’s account of completeness; see 39,11-13. 166. Replacing Heiberg’s comma with a raised dot and moving the quotation mark to before ei. 167. Simplicius quotes 268a11-12 (with a missing ton) and 268a20-1, both from chapter 1. 168. Dropping the period after horizasthai and placing parentheses around ei mê … ên. Simplicius thinks that Aristotle has provided a clear enough general account of ‘complete’ and that an attempt to give a definition which said for any kind of thing why it is complete would be an impossible task. 169. i.e. the infinite straight line. 170. In this lemma and the next. 171. See Meteorology 1.3, 340b32-341a3. 172. The assignment of this argument and the material in the next paragraph to Xenarchus is controversial. For discussion see pp. 234-5 of Rescigno, who assigns both to Alexander. 173. i.e. the pure air and the hupekkauma. 174. cf. 45,2-27. 175. i.e. the pure air and the hupekkauma. 176. For the view expressed here by Alexander see 14,31-15,4. 177. The revolution of a stone or wooden sphere, which is Simplicius’ only concern in this paragraph. 178. Reading, with Hankinson, parapheromenon, a correction of Bessarion, in place of the parapheronta printed by Heiberg. 179. As the hupekkauma does, according to Alexander. This difference means that Alexander’s solution for the hupekkauma will not work for the planets. 180. cf. 269b7-10. 181. e.g., at 34,13-21. 182. Simplicius gives Alexander’s obviously correct explication of Aristotle’s

Notes to pages 86-93

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opaque words hê men gar tôi puri, he de têi gêi para phusin kai kata phusin (translated ‘since one of them is natural for fire or earth, and one of them is unnatural’), but he wants to bring out that Alexander apparently endorses Aristotle’s problematic assertion that circular motion is unnatural for the four elements. 183. Simplicius writes heterôi where Aristotle has heterou tinos einai. 184. The second case here is obviously the hupekkauma; the first is the stagnant air, water, and earth at the centre of the cosmos; cf. 57,22-9. 185. See 269a9-18 with Simplicius’ commentary (starting at 19,11) and the notes on it. 186. In this commentary Simplicius uses ‘privative’ (sterêtikos) to mean ‘contrary’; see also 57,24 and 31. 187. From the assumption that circular motion was unnatural for, e.g., fire. 188. i.e. it simply means ‘not natural’ and so leaves open the possibility that circular motion is hypernatural for the hupekkauma. Simplicius repeats this line of argument in responding to an objection of Philoponus; see 56,26-58,1. 189. At 268b14-20. 190. In chs 7-9. 191. Here (and elsewhere) it is important to realise that, although the hupekkauma moves in a circle, ‘the body which moves in a circle’ is a term which refers to heaven for Simplicius; cf. 45,25-6. 192. Alexander perhaps thought that the text was missing the premiss that one thing has a single natural motion. 193. The people Alexander has in mind are most likely to be Stoics; for discussion and references see pp. 239-242 of Rescigno, to whom I owe my translation of this sentence. 194. i.e. heaven. 195. pistis, the standard word for ‘faith’ in the Christian tradition, frequently used in philosophical contexts for an unreliable form of cognition. Simplicius goes on to describe the role of a good kind of pistis in Neoplatonist terms. On this whole passage and the role of pistis in Neoplatonism see Hoffmann (2000). 196. 269a14. 197. Xenarchus’ two examples are taken from Eudemian Ethics 2.3, the first from 1221a12, the second from 1220b39 (and for the latter cf. Nicomachean Ethics 2.7, 1107a33-b4). 198. Reading legetai for Heiberg’s legei. 199. At 269b11. 200. At 269a32-b2. 201. 269a9-18. In the next stretch of text this passage is referred to with words such as ‘the second argument’ or ‘there’ and 269a32-b2 with words such as ‘here’ or ‘now’. 202. Reading dusôpêthênai to with Karsten (D also has dusôpêthênai) where Heiberg prints dusôpêthenta tou. 203. See 52,5-18. 204. cf. 269b11. 205. Here in Simplicius’ interjection ‘unnaturally’ is the contrary of ‘naturally’. 206. Because it never moves in a straight line. 207. That is, what isn’t contrary to the natural. 208. In chapter 4. 209. The point of the objection is that the natural motion of a thing should not be its motion when it has not obtained its proper form; see 20,10-25.

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Notes to pages 93-97

210. i.e. rectilinear motion. 211. An unknown word which Heiberg prints with D, noting that E has drímakos and A, B and Karsten dramikòs. Moerbeke has cervicosus (stubborn). Heiberg also refers to the story of the Chian slave Dramikos, retailed by Athenaeus (Olson (2008), 265d-266e), citing Nymphodorus, and mentions Diels’ suggestion that drimakos might be related to drimus (meaning ‘sharp’ or ‘keen’) as platukos is to platus. 212. A reference to the prevalence of Christianity. 213. Heiberg prints pan sôma where Moraux has sôma hapan. Simplicius uses pan sôma in a citation at 61,8. 214. An expansion of the opening sentence of the Posterior Analytics. 215. 2, 268b19-20. 216. 2, 268b21-2. 217. 2, 268b22. 218. 2, 268b20. 219. 2, 269a14. 220. 2, 269a8-9. 221. 2, 268b18-20. derived from [i]. 222. 2, 269a1; cf. 16,8-11. 223. 2, 268b26-269a2. 224. At 269a2-b17. 225. See the next lemma. 226. At 269a2-b17. 227. Starting at 270a12. 228. Not translating autôi, which it would seem should be autêi, if it is anything at all. The sense is not in question. 229. For Simplicius this is assumed at 270a19-20 and demonstrated in chapter 4. 230. See the next lemma. 231. i.e. that it does not change in quality or size. 232. In the previous lemma. 233. cf. the beginning of the next lemma. 234. At 62,5-7 Simplicius explains that Aristotle makes use of the ‘conversions’ of his definitions. 235. cf. 74,16 ff., where Philoponus tries to use the relative heaviness and lightness of air and water to argue that none of the elements are heavy or light in themselves. 236. Heiberg prints dê here, a correction in A. Moraux prints de. 237. cf. 12,10 and 60,3-4 with the notes. Aristotle mentions the second ‘axiom’ at the end of the lemma as something which has been posited, but it is not clear where it has been posited. 238. The discussion of this lemma in Themistius’ paraphrase of De Caelo (CAG 5.4), 12,1-13,3 contains toward its end an argument like this one and gives a remark about the first premiss not being negative. However, Themistius’ argument does not include the word ‘naturally’, and it is preceded by reasoning very like Aristotle’s and Simplicius’ own reconstruction of it (62,30-63,16) to show that what moves in a circle does not move up or down either naturally or unnaturally. I do not know what to make of this apparent misrepresentation by Simplicius. It may be that Alexander saw that Aristotle only needed to consider natural motion because only natural motion is relevant to weight. Simplicius is, however, concerned to follow Aristotle, and so replaces the argument he ascribes to Themistius

Notes to pages 97-101

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and Alexander with the one at 62,18-23. To fill in the details he now needs proofs for both [i’] and [ii’] What moves in a circle does not move up or down unnaturally. He gives a proof of [i’] at 62,27-63,6, and a proof of [i”] at 63,6-16. He concludes his discussion by giving Themistius’ proof of [i”]. 239. In his notes Hankinson explains what Simplicius has in mind here. 240. The reformulation is intended to make more explicit that the premiss is not negative. 241. Simplicius is here concerned with [i’] in the argument he has assigned to Alexander and Themistius. Since Simplicius offers an alternative proof, which corresponds closely to the second sentence of the lemma, it seems that this first argument may be due to Alexander. There is no trace of it in Themistius. 242. Modus tollens. 243. cf. Themistius’ paraphrase of De Caelo (CAG 5.4), 12,11-17. 244. Heiberg prints tauton, Moraux to auto. Simplicius mentions this passage several times using tauton (63,30, 64,13 and 18, 65,21 and 29); at 64,1 Heiberg prints tauto, noting that B has tauton; tauto also occurs at 65,1 and 72,24. 245. Simplicius raises a question about this ‘proof’ starting at 64,31. 246. It seems best to follow D, Karsten and Hankinson, and change the text to make an exact fit with the text of Aristotle, reading pasa gê kai mikra bôlos for Heiberg’s pasan gên kai mikran bôlon. 247. In the preceding lemma. 248. For Simplicius the entireties of the sublunary elements either rest (earth, water, and stagnant air) or move in a circle (pure air and fire) and so have no weight or lightness in the sense in which detached pieces of them do. But Simplicius will go on to argue that, even when in their proper places, the elements have certain ‘desires’ which give them a kind of weight or lightness. 249. For this objection of Philoponus and Simplicius’ response see 33,17-34,5. It is not clear who might have held the position underlying the second objection; see Hankinson ad loc. 250. A close paraphrase of 270b13-16. 251. cf. 64,2. 252. And this is the more important consideration for Simplicius. 253. Simplicius now substitutes pan for holon. 254. Whereas heaven does not have any impulsion. 255. As Aristotle emphasises. 256. As Plato emphasises. 257. Here, unusually, a view which is neither Aristotle’s nor Plato’s. 258. For Simplicius’ account of the (alleged) difference between Plato and Aristotle on weight see 67,24-70,2 below, and also 679,2-687,8 of his commentary on book 4 and the Introduction to Mueller (2009). 259. The Telkhins were a mythological race of dwarves who invented the art of metalworking and who became proverbial for their spiteful and jealous evil-doing. 260. See, e.g., 28,1-11, 34,33-35,20, 35,28-36,9, 42,17-27, 45,27-46,4. 261. 269b25-6. The discussion here concerns 269b20-9. Here and elsewhere I translate epipolazein as both ‘rise to the top’ and ‘lie on top’; similarly with huphistasthai and ‘sink to the bottom’ and ‘lie at the bottom’. At 70,20 Simplicius mentions an objection of Xenarchus to the definition of light, which apparently plays on the double meaning of epipolazein: fire, he says, will not be light when it does not lie at the top.

138

Notes to pages 101-108

262. Wildberg ((1987), p. 59, (1988), pp. 148-9) takes the person in question to be Philoponus, who also makes the remark about olive oil. 263. But olive oil is not light, just lighter than water. 264. As heaven is different from the four elements. 265. Philoponus’ view is more nuanced than this (see 84,15-22), but the nuance is not relevant to Simplicius’ criticism here. 266. For Simplicius’ conception of Plato’s and Aristotle’s view of the composition of heaven and the stars see 12,26-13,3. 267. With this paragraph cf. 65,7-66,3. 268. Reading holotêtes with Wildberg. Moerbeke also has the plural totalitates, so that Heiberg’s singular holotêtos is probably a misprint. 269. cf. 64,25-31. 270. Heiberg brackets the word ‘bodies’ with no explanation. 271. Timaeus 63E4-7. 272. But for Plato down and up are toward and away from one’s like. 273. For Themistius’ assertion that Plato held this see his paraphrase of De Caelo (CAG 5.4), 244,21-3. Simplicius is only concerned to say that Themistius was wrong. 274. Timaeus 63B5-D4. 275. Timaeus 62C8-D12. 276. Timaeus 63E4-6. Simplicius’ point is apparently that Plato is aware that he is abandoning ordinary usage. 277. 269b23. 278. 4.4.311a16-18. 279. See 4.1.308a13-33 with Simplicius’ comments starting at 678,15. 280. I am unable to provide a source for this quotation. Wildberg’s ((1987), p. 61, n. 37) reference to 221,28-30 in Themistius’ paraphrase of De Caelo (CAG 5.4) does not seem apposite. 281. ‘He’ here is houtos, normally Simplicius’ way of referring to Philoponus. Simplicius presumably thinks that Themistius agrees that impulsions do not attach to heaven because heaven is never in an alien place, and perhaps chooses to assign acceptance of this to Philoponus on the grounds that he cites Themistius. 282. For Simplicius the entireties do have an impulsion, but only in an extended sense, which he calls ‘desire’; see, e.g., 65,7-66,3. 283. Reading philoneikounta for the philoneikountôn printed by Heiberg. 284. 269b23-4. 285. cf., e.g., 65,12-16. 286. Simplicius criticises Philoponus for speaking of two contrarieties (enantiôseis) when he should be speaking of two contraries (enantia). 287. Simplicius accuses Philoponus of ignorance of the order of the planets. On this topic see Neugebauer (1975), pp. 690-3. The order espoused by Simplicius is that adopted by Ptolemy; see DSB 11, pp. 197, 205. 288. I have followed Karsten in omitting hoti. 289. It is perhaps surprising that Simplicius does not object to hypothesising that the cosmos might change place (even though it has no place), but only to hypothesising that it could move up or down or toward the centre or the periphery. 290. 270a4-5. 291. cf. 67,24-69,10. 292. cf. 270b13-16. 293. Reading, instead of the phlegmainein oukh hupomenêi printed by Heiberg, the words menein legetai oukh hupomenei written in the margin by Bessarion and

Notes to pages 108-113

139

translated by Moerbeke, who has dicatur manere non sustinet. A and B have mê phlegmainein oukh hupomenei. Heiberg ascribes hupomenêi to D with a question mark, but I cannot determine from Heiberg’s apparatus what the full reading of D or E is. Karsten prints men phlegmonên oukh hupomenei (‘even if the heart endures when it suffers inflammation, it does not usually survive …’). The anonymous vetter of CAG pp. 70-91, to whom I am grateful for many valuable corrections and suggestions, offers the following translation of Heiberg’s text: ‘Secondly, the heart, even if it does not sustain inflammation, because the animal often dies first , nevertheless it is always affected first by fever …’. 294. cf. Simplicius’ commentary on the Physics (CAG 10), 1335,5-7. 295. 4.4, 311b6-13, with which see Simplicius’ discussion at 709,8-712,17. 296. That is, Philoponus doesn’t realise that his criticism applies only to water and air, which are in fact only relatively heavy and light. The words which follow are kai ou dêpou touto poiei mê metekhein to pros allo kai allo kai kat’ allo kai allo tôn heautou energein, and I have chosen to follow E, which lacks all but the last three. I have also changed energein to energeiôn (and, if necessary, heautou to heautôn). The anonymous vetter of these pages accepts this last emendation, but suggests translating what is otherwise Heiberg’s text as ‘And surely this variation in relation to different things does not prevent their participating in their own activities’. 297. eudiakritos. I do not know what distinction Simplicius is making between a discriminating and a synthesising eye, and the way they perceive the black and white components of grey, but he obviously is giving an example of something’s being F in one context and non-F in another. 298. As Philoponus believes, but Simplicius does not; see, e.g., 68,6-10. 299. enteuxomenous, indicating that Simplicius’ intended audience is readers not auditors; for other such references see Golitsis (2008), p. 13n.36. 300. This apparently means that heaven always retains its spherical shape whereas fluids take on the shape of their container. 301. The word ‘heaven’ is not in Heiberg’s text, but is supplied by Moerbeke (celum). 302. For this assumption cf. 12,10-11. Simplicius goes on to cite 2, 269a2-7. 303. cf. Genesis 1.1 (Septuagint (Rahlfs (1935))). 304. As Heiberg’s apparatus suggests, the next words are apparently unintelligible, and Wildberg ((1987), p. 65) does well to pass them over. Heiberg’s text runs hôste kai anô potamôn anastellesthai, to legomenon, kai pro tou ton Aristotelên legein, haper enantia legein heautôi nomizei, propêdan ep’ auton. The hôste is omitted in all mss., which have pro where Heiberg prints anô. So the hôste should go and so should the anô since pro potamôn anastellesthai is proverbial; see von Leutsch (1851), p. 768 (Mantissae Proverbiorum 2.70). So Simplicius is comparing Philoponus’ speaking against Aristotle (I would read pro tou Aristotelous legein) with a fool’s standing up against rivers. The next words suggest a charge of self-contradiction against Philoponus, but the nomizei is difficult. So perhaps one should read autôi for heautôi and understand Simplicius to be saying that Philoponus confronts Aristotle with anything he thinks contradicts him. 305. See 2.1, 284a27-35, and compare the discussion here with what Simplicius says on this passage at 374,34-382,19. As Simplicius indicates at 79,14-20, Philoponus is now focused on this Aristotelian passage. 306. Philoponus cites 2.2, 285a29-30 and 2.12, 292a18-21. 307. As Aristotle will argue at 270a12-35.

140

Notes to pages 113-118

308. In chapter 10. 309. Alexander’s position is more complex than the formulation here suggests, since Alexander holds that in the case of the heavenly bodies, soul and nature are identical; see Moraux (2001), p. 176. 310. 2.1, 284a27-32. 311. Timaeus 33D3-34A6. 312. Simplicius omits the word kinêseis, found in our mss. of Plato. 313. Timaeus 36D8-E5. 314. cf. 2.1, 284a27-8, quoted above. 315. cf. 34,7-11 with the discussion of Simplicius which follows and the notes. 316. This paragraph is difficult. Simplicius has already commended Philoponus for recognising that Plato ascribed heavenly motion to both nature and soul (78,17-21). But he now says that Philoponus defends Plato as if Plato says that the motion is only due to soul, and then gives a reason for thinking that the heavenly motion is due to nature (the motion can’t be unnatural, because heaven has no other natural motion). When Simplicius says that one should say ‘these things’ when Philoponus asks whether the motion of the hupekkauma is natural or unnatural, one would expect the answer to be that its motion is natural; but, of course, Simplicius’ answer is that it is hypernatural, certainly not something he would say about heaven. 317. 1.3, 339b16-340a3. 318. 1.3, 340a1-3. 319. Aristotle actually says that the fire in our world is an excess of heat; see, e.g., Meteorology 1.4, 340b19-23. 320. Without ‘equality of strength’ there would be destruction of one by the other; cf. 83,30-84,10 with the notes. 321. The position adopted by Philoponus entails the elimination of a substantive distinction between heaven and the hupekkauma, so that the word ‘sublunary’ in this sentence and elsewhere should really refer only to air, water and earth. 322. phrouda, the word used by Aristotle at 1.3, 340a2 of the Meteorology. 323. That is, although we can, for example, warm up a cup of water to any temperature, the ‘natural temperature’ is not higher in a larger quantity of water, even though it contains ‘more’ of the natural temperature; see also below at 83,34-84,4. 324. Meteorology 1.3, 340a1-3. 325. That is, heaven is greater than any single element by more than it is greater than more than one element. 326. parallaxin, the difference in the apparent position of an object (in this case, the sun) viewed from different positions (in this case, on the earth). Solar parallax is too small to have been observed in antiquity. 327. On this topic see also 438,30-444,15 in Simplicius’ commentary on book 2. 328. This is only a hypothesis for Philoponus (82,18-19), not a belief; his case would be stronger if heaven were not hot. 329. Accepting Wildberg’s ((1987), p. 61) identification of the end of the quotation. 330. Reading hautês (or heautês with Karsten) for the autês printed by Heiberg; Moerbeke has ex ipsa. 331. cf. 77,31-78,1 and 73,12-13. 332. For Simplicius’ account of how heaven affects things in our world see below 88,8-28. 333. See 9,16-18 of Alexander’s commentary on the Meteorology (CAG 3.2),

Notes to pages 118-121

141

where Alexander is discussing 1.3, 340a3-8. Where, according to Simplicius, Philoponus spoke of ‘equality of power’, Aristotle speaks of ‘equality of shared proportionality’, which Alexander paraphrases with ‘equality with respect to proportionality’. As Simplicius makes clear at the end of this paragraph, the claim involved is not that the elements are equal (in size or power), but that they have a relationship which makes the world orderly. 334. 81,31-2. 335. So air is naturally warm and the power of its warmness is proportional to its size, but it can be heated or cooled and the heat or coolness need not be proportional to its size. 336. This sentence is a source of great perplexity. I note that Moerbeke has ‘he says’ (dicit), and that Karsten does as well (phêsi). The claim that no one taught Philoponus about Plato could be true if, as some scholars hold, but I and others do not, Ammonius’ agreement with the bishop of Alexandria (see Introduction, p. 6) involved renouncing the teaching of Plato. Otherwise it seems certain that Philoponus had a good education in Platonism. If we read ‘he says’, we might hold that Philoponus was dissociating himself from or denigrating the teaching of Ammonius, presumably because of Ammonius’ paganism. Verrycken ((1990, p. 264) characterises ‘they say’ as very possibly ‘a rather transparent attempt to hide the truth’. And perhaps the best we can do is to dismiss Simplicius’ remark as a falsehood; the claim about Philoponus’ lack of seriousness is certainly an assessment rather than a report. 337. Reading ekhontos with D rather than the ekhontôn printed by Heiberg. 338. cf. Proclus, The Elements of Theology, 139 (Dodds (1963), 122,25). 339. i.e. the heavenly bodies. 340. cf. [Aristotle], De Mundo 6, 400a7-8. 341. That is, really a compound with a predominant component in the way that what we call elements are. 342. Reading Bessarion’s axiousin for the axioumenois of E printed by Heiberg; Moerbeke has volentibus. 343. The next sentence, which is called a ‘locus desperatus’ by Heiberg, says something about Aristotle making something clear about rectilinear motion in the final parts of De Caelo and in On Coming to be and Perishing, and it mentions the incompleteness of the sublunary bodies and speaks of ‘falling upon (epipiptôn) appropriate things and things better than themselves’: hôs atelôn tôn hupo selênên sômatôn kai hôs tois oikeiois kai tois heautôn kreittosin epipiptontôn tên kat’ eutheian legei kinêsin, kai en tois teleutaiois tautês tês pragmateias kai en tois Peri geneseôs dêloi. 344. Meteorology 1.3, 340a1-3. 345. Heiberg’s full stop after mixei should be a comma. 346. I take Simplicius to be saying that although Aristotle recognised the existence of separate forms, he referred to, e.g. the form of man as ‘man’ rather than, e.g., ‘man itself’ because the ordinary vocabulary is easier for ordinary people; cf. 69,13-15. 347. Later at 270b10-11. Simplicius’ quotation includes an oun here which is not in our text of Aristotle. 348. See 12,16-27, where the same passage (without a palin which is in this quotation) from Xenocrates is quoted. 349. The Christians. 350. cf. Ptolemy, Apotelesmatika (Tetrabiblios, Hübner (1998)) 1.4.3, where other references are given. Ptolemy also says that Saturn has a moderate drying effect.

142

Notes to pages 123-125

351. Translating Karsten’s meresi tisi tou aeros (Moerbeke has aliquibus partibus) instead of Heiberg’s tisi tou aeros. Philoponus is, of course, referring to the pure air above the mountain-tops. 352. I do not know why Simplicius remarks on Philoponus’ use of enkuklios, a word he himself uses frequently enough. 353. See 84,30-2 and 86,8-16. 354. Because, as Simplicius goes on to point out for the case of ‘being’, there are predicates shared by everything. 355. This sentence is difficult. I take Simplicius to be saying that Philoponus’ argument relies on an ordinary notion of universal, and that he fails to understand the Neoplatonic hierarchy of entities with the same names. 356. Psalm 18.2 (Septuagint (Rahlfs (1935))). 357. Physics 1.2, 185a11-12. 358. Presumably a crack at the incarnation and perhaps at Philoponus’ Monophysitism. 359. e.g. Plato; with this sentence see also 59,6-15. 360. e.g. Aristotle. 361. For the references see what Philoponus says at 78,24-8 with the note on 78,28. As far as I know, Aristotle does not say in De Anima that every body with soul is a composite of the four elements, but there is no reason to doubt that he would accept such a claim. 362. Replacing Heiberg’s raised dot with a question mark, as in Bossier’s edition of Moerbeke. 363. cf. 78,17-21 where Philoponus is said to offer many arguments that the motion of the heavens is due both to nature and to soul. However, in On the Creation of the World (Reichardt (1897)) 6.2, Philoponus argues that ‘there is no evidence capable of showing that heavenly things have souls, and no testimony in holy scripture …’. It is perhaps surprising that Simplicius purports to know what Christians believe on a subject for which we have very little clear-cut evidence about their beliefs. It is, however, striking that among the documents relating to the controversies about Origen, which may have ended in his condemnation in 553, there is a letter written by the Emperor Justinian to the bishop of Alexandria in which Origen is anathematised for believing, among other things, that ‘heaven, sun, moon, and the waters above the heavens have souls and are certain rational powers’ (Denzinger (1976), 408); cf. 2,1,3 of Origen’s On Principles (Koetschau (1913)). I am grateful to Stephen Menn for help with this note.

Appendix 1 The ‘fragments’ of Philoponus, Against Aristotle I give here the correlation between passages translated in Wildberg (1987) and their location in the text translated here. I also indicate where a passage is discussed in Wildberg (1988). Wildberg attaches an asterisk to indicate that a ‘fragment’ includes no direct citation or paraphrase of an argument in Against Aristotle. Simplicius in Cael. 25,22-26,31 26,31-27,4 28,1-11 30,26-34 31,6-16 32,1-11 33,17-20 34,5-11 34,21-4,30-2 34,33-35,8 35,12-20 35,28-33 36,9-18 36,21-5 37,3-12 37,12-29 42,17-22 42,27-31 43,8-12 43,22-5 44,15-18 45,2-7 45,27-9 46,4-11 46,17-25 46,29-47,3 47,10-13 47,27-30 48,5-11

Wildberg (1987) fragment Prologue 1* 4 5 6 7 8 9 10* 11* 12* 13* 14 15 16 17* 18 19 20 21 22 23 24 25 26 27* 28 29* 30*

Wildberg (1988) discussion — pp. 108-11 111-17 117-19 120-1 121-3 123-4 124-5, 131 131 131 132 131 133 133 133 133 136 137-8 138 — 138-9 139-40 140 140-1 141-2 142 142 143 143

144

Appendices 48,14-22 48,35-49,12 56,26-57,8 58,1-10 58,14-22 59,6-10 66,8-14 66,17-24 66,33-67,19 68,6-10 70,2-8 70,34-71,6 71,19-33 72,10-16 73,4-15 74,16-26 75,16-76,29 77,23-7 78,12-79,14 80,13-23 80,23-81,11 81,22-6 82,8-83,30 83,30-84,4 84,15-22 87,29-88,2 88,8-14 88,28-89,26 90,13-25 91,3-7,17-19

31 32 33 34 35 36* 37 38 40* 41* 42* 39 43 44* 45* 46 47 48 49 51* 52 53* 54 55 56 57* 58 59 60* 61*

143-4 — 145 — — 145 147-8 148-9 150 150-1 150-1 149 151-2 152-3 154-5 155-6 156-9 158 159-64 164-5 166-8 168-9 169-70 171 171 181 182, 184 182-4 — 163

Appendix 2 The ‘fragments’ of Alexander’s commentary on De Caelo I give here the correlation between passages translated in Rescigno (2004) and their location in the text translated here. Simplicius in Cael.

Rescigno fragment

Aristotle text where relevant

11,7-15 5a (pp. 165-7) Alexander says that the whole cosmos is the primary subject of De Caelo, but that this entails the discussion of heaven, which is concluded in book 2, and is followed by the discussion of the sublunary elements in books 3 and 4; Simplicius mildly disagrees. 13,15-18 6a (167-9) 268b14-20 Alexander’s first response to Xenarchus’ claim that the ‘cylindrical helix’ is a simple line disapproved of Simplicius. 13,22-14,29 7 (169-76) His second response is approved of by Simplicius.

268b14-20

14,31-15,13 8a (177-82) 268b20-6 Alexander says that Aristotle defines circular, up, and down with respect to the centre of the universe. Simplicius’ position is less than clear (see fragment 8c, 32,1, below) but he disagrees with Alexander’s characterisation of animal motion. 16,11-30 9a (182-6) 268b26-8 Simplicius commends Alexander’s explanation of the text, but disagrees with his statement that composite natural bodies have a composite natural motion because for Simplicius ordinary animal motion is psychic rather than natural. 17,9-13 10 (187-91) 268b26-8 Simplicius disagrees with Alexander’s claim that motions are not ‘mixed’ in the same way bodies are.

146

Appendices

18,9-12 11 (191-3) 269a2-7 Alexander thinks that the eiper at 269a2 means ‘since’, but Simplicius thinks it means ‘if’. 20,10-25;21,33-23,6 12 (193-200) Alexander (Simplicius refers to his lost commentary on On Coming to be and Perishing), Ptolemy, Plotinus, Xenarchus, Simplicius, and apparently Aristotle all agree that the sublunary elements move in a straight line when they are not in a natural condition. 23,11-24,21 13 (200-5) 269a2-7 Alexander’s response to Xenarchus’ claim that there could be a simple motion for which there was no simple body is perplexing to Simplicius. At 24,20-1 Simplicius indicates that Alexander is his source for Xenarchus’ objections. 32,1-11 8c (178-82) Philoponus cites Alexander (see 8a, 14,31, above) for the view that for Aristotle circular motion in the strict sense is motion around the centre of the universe; Simplicius now separates himself from Alexander on this question. 35,20-8 14a (205-10) Here Simplicius commends Alexander’s view that the hupekkauma has a mixed motion, a view disputed by Philoponus; however, at 54,12-33 Simplicius implies that the motion of the hupekkauma is not mixed. 36,9-11 14b (206-10) A reference to Philoponus’ rejection of Alexander’s view that the motion of the hupekkauma is mixed. 37,12-33 14c (206-10) This passage gives the fullest account of Alexander’s conception of the motion of the hupekkauma. 39,11-17,26-8 15a (211-15) 269a18-30 Simplicius disputes Alexander’s claim that a circle is complete because it has a beginning (its centre), an end (its circumference), and a middle (the space between centre and circumference). He also mentions Alexander’s view, which he thinks is unsatisfactory, that any straight line (including a diameter of the cosmos) is incomplete because it can be extended in theory (logos). 40,21-5 16a (215-17) 269a18-30 Alexander finds in 269a23-8 an argument ‘from the less and the more’ that heaven is simple. Simplicius disagrees with Alexander’s analysis.

Appendices

147

41,2-25 17 (217-27) 269a18-30 Alexander’s attempt to resolve a difficulty about priority and completeness disputed by Simplicius. 42,6-16 18 (227-9) Alexander’s disregard of certain objections of Xenarchus. 42,29-31 15c (212-15) 269a18-30 Philoponus uses Alexander’s characterisation of the completeness of a circle (see 15a, 39,11). 44,6-13 19a (229-31) 269a18-30 Simplicius explains his disagreement with Alexander’s claim that any finite straight line can be extended in logos (see 15a, 39,11). 46,4-8 15d (212-15) 269a18-30 Philoponus disputes Alexander’s account of the completeness of a circle (see 15a, 39,11). 46,29-47,6 19b (230-31) 269a23 Philoponus invokes Alexander’s claim that any finite straight line can be extended in logos and refers to the diameter of the cosmos (see 15a, 39,11). 47,1-6 15e (212-15) 269a18-30 Simplicius remarks on his disagreement with Alexander about the completeness of the circle (see 15a, 39,11). 50,7-51,10 20 (232-5) 269a32-b2 In response to an objection of Xenarchus that the motion of the hupekkauma is natural, Alexander says that the motion of the hupekkauma is mixed (cf. 14c, 37,12). Simplicius invokes his alternative, hypernatural motion. 51,32-52,5 21 (236) 269a32-b2 Simplicius rejects Alexander’s acceptance of the view that circular motion is unnatural (para phusin) for the sublunary elements, invoking the idea that para phusin sometimes means ‘other than natural’ and sometimes means ‘counternatural’. 53,20-3 22 (237) 269b10-13 Alexander takes this passage to be an argument that if heaven were fire, its circular motion would be unnatural for it, whereas Simplicius thinks Aristotle is proving that heaven is not fire. It appears from 54,5-6 in 23, 54,5 that Alexander thought there was a lacuna in the text.

148

Appendices

54,5-19,29-33 23 (238-42) 269b10-13 The first two lines of this passage really go with the preceding fragment. In the next six lines Simplicius tells us that Alexander also criticised thinkers, perhaps Stoics, who held that heavenly fire moves in a circle around its nourishment. Simplicius goes on to give one of Alexander’s arguments that fire does not move in a circle naturally. But for Simplicius Alexander’s position (cf. 14a,35,20) that the hupekkauma contains upwardly moving fire is incompatible with his own view that the hupekkauma has a simple hypernatural motion. 62,11-17 24a (243-52) 269b29-270a3 Simplicius presents Alexander’s (and Themistius’) representation of the argument in this passage and offers an insignificant variation. 64,23-31 25b (248-52) 270a3-12 Simplicius says that in this passage Aristotle responds to people who say that heaven, like the sublunary elements, is everlasting as a whole but comes to be and perishes in its parts. He cites the fact that heaven has never been observed to change (cf. 270b13-16). Simplicius does not mention Alexander. 79,8-14 not in Rescigno Philoponus says that the same motion, in particular the motion of heaven, can be due to both nature and soul. He thinks that Aristotle denies this at 2.1, 284a27-35, and argues against Alexander’s contrary interpretation of Aristotle. 83,30-34 26 (252-3) A dispute between Philoponus and Alexander over the relationship between the size of an elementary mass and its power to heat or cool, be heated or be cooled.

Bibliography Abbadi, Mostafa el (1988), ‘The Grain Supply of Alexandria and its Population in Byzantine Times’, in Basil G. Mandilaras (ed.), Proceedings of the XVIII International Congress of Papyrology, Athens: Greek Papyrological Society. Ambjörn, Lena (tr.) (2008), The Life of Severus by Zachariah of Mytilene, Piscataway: Gorgias Press. Athanassiadi, Polymnia (ed. and tr.) (1999), Damascius, The Philosophical History, Athens: Apamea. Baltussen, Han (2008), Philosophy and Exegesis in Simplicius, London: Duckworth. Bergk, Theodor (1883), Fünf Abhandlungen zur Geschichte der griechischen Philosophie und Astronomie, Leipzig: Fues’s Verlag. Bernard, Hildegund (tr.) (1997), Hermeias von Alexandrien, Kommentar zu Platons Phaidros, Tübingen: Mohr Siebeck. Bossier, F. (ed.) (2004), Simplicius, Commentaire sur le Traité Du Ciel d’Aristote, Traduction de Guillaume de Moerbeke, vol. 1 (Corpus Latinum Commentariorum in Aristotelem Graecorum 8,1). Louvain: Leuven University Press. Brooks, E.W. (tr.) (1910), Eliae Metropolitae Nisibeni, Opus Chronologicum 1 (Corpus Scriptorum Christianorum Orientalium, Scriptores Syri, 3. series, 7 (Versio), now reprinted as Corpus Scriptorum Christianorum Orientalium 63*, Scriptores Syri 23). Chabot, J.-B. (tr.) (1901), Chronique de Michel le Syrien, vol. 2, Paris: Ernest LaRue (reprinted Brussels: Culture et Civilisation, 1963). Chabot, J.-B. (tr.) (1933), Documenta ad Origines Monophysitarum Illustrandas (Corpus Scriptorum Christianorum Orientalium, Scriptores Syri, 2. series, 37 (Versio), now reprinted as Corpus Scriptorum Christianorum Orientalium 103, Scriptores Syri 52). Colonna, Maria Minniti (ed. and tr.) (1973), Zacaria Scolastico, Ammonio, Naples: La Buona Stampa. Delatte, A. (ed.) (1939), Anecdota Atheniensia et Alia, v. 2 (Bibliothèque de la Faculté de Philosophie et Lettres de l’Université de Liége 88). Denzinger, Heinrich (ed.) (1976), Enchiridion Symbolorum, 36th edn, Barcelona, Freiburg im Breisgau, and Rome: Herder. Dickey, Eleanor (2007), Ancient Greek Scholarship, Oxford: Oxford University Press. Diehl, Ernst (ed.) (1903-6), Procli Diadochi in Platonis Timaeum Commentaria, 3 vols, Leipzig: Teubner. Dillon, John and O’Meara, Dominic (trs) (2006), Syrianus, On Aristotle Metaphysics 13-14, London: Duckworth. Dodds, E.R. (ed. and tr.) (1963), Proclus, The Elements of Theology, 2nd edn, Oxford: Clarendon Press. Ebied, R.Y., Roey, A. van, and Wickham, L.R. (1981), Peter of Callinicum, AntiTritheist Dossier (Orientalia Lovaniensia Analecta 10). Fox, Robin Lane (2005), ‘Harran, the Sabians, and the late Platonist “movers”’, in

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Textual Questions Listed here are places where I have translated a text different from the one printed by Heiberg. In many cases notes on the lines in the translation provide more information. 16,15 22,20 24,7 30,18 34,25 38,11 39,5 43,27 44,3 44,5 47,12 48,14 49,5 51,15 56,21 57,17 60,24 64,1 67,16 67,27 70,19 71,31 73,19

Bracket monôn merôn with Moerbeke. Insert before organika; cf. line 33. Remove the comma after geneseôs and place it after entautha with Rescigno. Read, with Hankinson, prosüpethemetha for the proüpethemetha printed by Heiberg. Read, with A, D, E, and Moerbeke, proslêpsin rather than the prolêpsin of B printed by Heiberg. Read, with Karsten, mê to rather than the to printed by Heiberg. Retain, with Hankinson, the oude kata phusin bracketed by Heiberg. Read, with Bessarion, hê men gar rather than the ei oun hê men printed by Heiberg. Read, with A, B, E, and Karsten, labôn for the labon of D printed by Heiberg. Insert ontos after eidous with Karsten. Read, with B, D, E, and Karsten, autê rathern than the hautê printed by Heiberg. Read, with Moerbeke, ho kuklos for the to printed by Heiberg with A and B; one might read simply ho with Karsten. Replace the comma after gennadas with a raised dot. Begin the quotation with the next word, ei, rather than after it. Drop the period after horizasthai, and place the next sentence in Heiberg’s text in parentheses. Read, with Hankinson, the parapheromenon of Bessarion for the parapheronta printed by Heiberg. For Heiberg’s legei read legetai. Read, with Karsten, dusôpêthênai to for the dusôpêthenta tou printed by Heiberg. Bracket autôi. Read, with D, Karsten and Hankinson, pasa gê kai mikra bôlos for the pasan gên kai mikran bôlon printed by Heiberg. Read, with Wildberg, holotêtes for the holotêtos in Heiberg (probably a misprint). Retain the sômatôn bracketed by Heiberg. Read philoneikounta for the philoneikountôn printed by Heiberg. Omit hoti with Karsten. Read, instead of the phlegmainein oukh hupomenêi printed by

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74,29-30 75,1 75,15 75,16 75,17 83,18

85,1 86,11 86,33 91,9

Textual Questions Heiberg, menein legetai oukh hupomenei, a marginal correction of Bessarion, which also corresponds to Moerbeke’s translation. Bracket kai ou dêpou … allo kai allo, following E. For Heiberg’s heautou energein read heautôn energôn. For Heiberg’s hôste kai anô read kai pro with all the mss. For Heiberg’s ton Aristotelên read tou Aristotelous. For Heiberg’s heautôi read autôi. Move the close quotation mark back to after drai in line 16 with Wildberg. Read hautês (or heautês with Karsten) for the autês printed by Heiberg. Read ekhontos with D for the ekhontôn printed by Heiberg. Read Bessarion’s correction axiousin for the axioumenois of E printed by Heiberg. Replace Heiberg’s period after mixei with a comma. Replace Heiberg’s raised dot after logous with a question mark, as in Bossier’s edition of Moerbeke.

Here I bring together places where Simplicius apparently read a text in De Caelo different from that printed by Moraux or a lemma in Heiberg differs from the corresponding text in Moraux. I have paid no attention to the numerous differences regarding elision (e.g. de vs. d’) or minor variations in spelling (e.g., hauton vs. heauton or teleiotaton vs. teleôtaton). Moraux 268a12 ton tou 269b2 heterou tinos einai 269b20 sôma hapan 269b30 de 270a4 to auto 270b10 hôsper esti

Heiberg 48,36 ton 59,5 heterôi 59,25 pan sôma (lemma) 62,3 dê (lemma) 63,25 tauton (lemma) 87,14 hôsper oun esti

I mention also that at 79,31 in a quotation of the Timaeus Heiberg omits a kinêseis printed at 34A5 in Rivaud (1925).

English-Greek Glossary This glossary is derived from the Greek-English Indices for this volume and for Mueller (forthcoming 2011) and gives standard Greek equivalents for many nouns, verbs, adjectives, adverbs, and a few prepositions in the translation. It does not include equivalents for words which have no relatively simple equivalent in English, and it does not always attend to the difference in meanings between active, middle, and passive forms of a verb. The reader will get a better sense of the range of a Greek word by looking at the Greek-English Index for the word and ones closely related to it. The letter ‘n’ indicates that an English word is a noun or nominalization, ‘v’ that it is a verb or deverbative. abiding (n.): aiôn abode (n.): hedra above: anô, epanô absence: apousia absolutely: haplôs absolutely complete: panteleios abstraction (n.): aphairesis absurd: atopos absurdity (n.): atopia, lêrêma accept (v.): apodekhomai, homologeô, hupodekhomai, hupolambanô, paradekhomai, paralambanô, prosiêmi, sunginôskô, sunkheô accidental: sumbebêkôs accompany (v.): parepomai, sunedreuô account (n.): apodosis, logos accrue (v.): epiballô, epiginomai, paraginomai, proseimi, prosginomai accurate: akribês accuse (v.): enkaleô acme (n.): akmê act (n.): poiêsis act (v.): draô, energeô, poieô act childlishly (v.): neanieuomai acting (n.): drasis activate (v.): energeô active: drastikos, energêtikos activity (n.): energeia actual: energeiai actualization (n.): entelekheia add (v.) epagô, epipherô, prostithêmi addition (n.): prosthêkê, prosthesis

addition and subtraction (n.): prosthaphairesis additional assumption (n.): proslêpsis adduce (v.): epagô adhere to (v.): proiskhô admire (v.): timaô admit (v.): dekhomai, epidekhomai admitting: dektikos advance (v.): prokoptô adventure (n.): tolmêma affection (n.): pathos affirm (v.): episêmainô affirmation (n.): kataphasis again: palin agree (v.): homologeô, sumphôneô, sunaidô, sunkheô, suntithêmi agree in advance (v.): proomologeô agreeing: sumphônos air (n.): aêr aithêr (n.): aithêr akin to: sunêthês alien: allotrios allege (v.): proiskhô alone: monos already: hêdê alter (v.): alloioô alteration (n.): alloiôsis always: aei, diolou, pantakhou, pantôs amazing: thaumastos analyze (v.): analuô ancient: arkhaios, palaios animal (n.): zôion announce (v.): epangellô

156

English-Greek Glossary

announce previously (v.): proaphôneô anomaly (n.): anômalia antecedent (n.): hêgoumenon antithesis (n.): antithesis antithetical: antithetos apogee, at: apogeios appear (v.): anaphainô, phainô appearance (n.): phasma apply (v.): epharmottô apportion with (v.): sundiaireô apprehend (v.): katalambanô apprehensible: katalêptos approach (v.): plêsiazô appropriate: emmelês, oikeios apropos: eukairos arbitrary chatter (n.): apoklêrôsis arc (n.): periphereia argue (v.): epikheireô, sullogizô argue against (v.): antilegô, aposkeuazô argument (n.): ephodos. epikheirêma, epikheirêsis, kataskeuê, logos, sullogismos aribitrary: apoklêrôtikos arm (n.): kheir army (n.): stratopedon arrange (v.): diatattô, diatithêmi arrangement (n.): mêkhanêma articulate (v.): diarthroô artifact (n.): kataskeusma artifice (n.): epitekhnêsis artificial: tekhnêtos ask (v.): erôtaô, zêteô ask also (v.): epaporeô ask for (v.): aiteô assemble (v.): athroizô assert (v.): episêmainô assign (v.): apodidômi, didômai, klêroô assign the same rank (v.): suntassô assimilate (v.): proskrinô assume (v.): hupolambanô, lambanô assume in addition (v.): proslambanô, prosupotithêmi assume in advance (v.): prolambanô assumption (n.): lêpsis astound (v.): kataplêttô astronomer (n.): astronomos astronomical: astronomikos astronomy (n.): astronomia attach (v.): exaptô, huparkhô, prosêkô, prosphuô attach oneself to (v.): prosekhô attain (v.): tunkhanô attend (v.): apoblepô, blepô

attention (n.): epistasis attentive: prosektikos authoritative: kurios awaken (v.): enegeirô awareness (n.): sunaisthêsis axiom (n.): axiôma axis (n.): axôn babble (n.): phlênaphos babble utter nonsense (v.): lêreô back: opisthen, opisthios backward: opisthen bad: kakos badly educated: anagôgos bag (n.): askos balance (n.): summetria banquet (n.): thoinê be (v.): eimi, huparkhô, tunkhanô be in (v.): eneimi bear witness (v.): martureô beautiful: kalos beauty (n.): kallos begin (v.): arkhô beginning (n.): arkhê beginningless: anarkhos being held together (n.): susphinxis belief (n.): dogma, doxa believe (v.): hêgeomai, nomizô, pisteuô belong (v.): huparkhô, prepô below: katô bending (n.): kampsis beneficial: epôphelês beside the point: para thuras bestow (v.): endidômi better: kreittôn between: metaxu binding (n.): sundesis binding: sunektikos bitterness (n.): pikrotês black: melas blame (v.): aitiaomai blaspheme (v.): blasphêmeô blending (n.): sumphusis blessed: makarios blessedness (n.): makariotês blind: tuphlos blind (v.): ektuphlô blossom (v.): antheô blush (v.): eruthrainomai body (n.): sôma bond (n.): desmos bone (n.): osteon book (n.): biblion, sungraphê both: amphô, amphoteros

English-Greek Glossary bother (v.): enokhleô boundary (n.): horos brag childishly (v.): neanieuomai brain (n.): enkephalos breadth (n.): platos break (v.): klaô, periklaô break into pieces (v.): katathrauô brief: brakhus, suntomos bright: lampros, phôteinos brighten (v.): exaitheroô brightness (n.): lamprotêta bring about (v.): epiteleô bring down (v.): hupopherô bring forward (v.): parapherô, proagô bring in (v.): epagô, epeisagô, paragô, prosagô bring into existence (v.): paragô bring to completion (v.): epiteleô bronze (n.): khalkos burden (v.): barunô burn (v.): anazôpureô, kaiô burning: kaustikos business (n.): askholia call (v.): kaleô, onomazô call on (v.): paristêmi care (n.): epistasis, eulabeia careless: atalaiporos carry along with (v.): sumpherô carry around (v.): periagô, peripherô, sumperiagô, sumperipherô carry down (v.): hupopherô, katapherô cool down (v.): katapsukhô carry out (v.): proagô carve (v.): gluphô carver (n.): hermogluphos cast off (v.): apoballô categorical: katêgorikos category (n.): katêgoria causal: parasunaptikos cause (n.): aitia, aition caution (n.): eulabeia cease (v.): lêgô, pauô cede (v.): parakhôreô celebrate (v.): diaboaô censure (v.): memphomai central: kentrikos centre (n.): kentron, meson certainly: pantôs certainty (n.): enargeia chance: apoklêrôtikos change (n.): kinêsis, metabolê, metastasis

157

change (v.); allassô, ameibô, metaballô, metalambanô change in quality (v.): alloioô change position (v.): methistêmi changing: kinêtos, metabatikos chapter (n.): kephalaion characteristic (n.): kharaktêr characterize (v.): kharaktêrizô charge (v.): enkaleô chatter (v.): thruleô chest (n.): sternon choice (n.): proairesis choose (v.): apokrinô, haireô chunk of earth (n.): bôlos circle (n.): kuklos circuit (n.): periagôgê circular: diallêlos, enkuklios, kuklikos, peripherês circular arc (n.): periphereia circumference (n.): periphereia cite as evidence (v.): martureô clarification (n.); saphêneia clarify (v.): diasapheô, saphênizô clear: dêlos, enargês, saphês clearly: dêlonoti clever: deinos cleverness (n.): deinotês, phronêsis close: engus close to earth: perigeios coals (n.): anthrax cognition (n.): gnôsis coincide (v.): epharmottô cold (n.): psuxis cold: psukhros coldness (n.): psukhrotês, psuxis collect together (v.): sunagô colour (n.): khrôma colour (v.): khrôizô colourless: akhrômatos combination (n.): sumplokê, sunthesis combine (v.): sunkrinô, suntassô, suntithêmi combining (n.): sunagôgê come (v.): erkhomai come across (v.): empiptô, entunkhanô come against (v.): antibainô come (into existence) (v.): parerkhomai come from (v.): exerkhomai come to be (v.): ginomai come together (v.): suntrekhô comet (n.): komêtês coming to be (n.): genesis coming to be: genêtos commentary (n.): hupomnêma

158

English-Greek Glossary

commentator (n.): exêgêtês common: koinos common feature (n.): koinotêta commonality (n.): koinônia, koinotêta comparative: sunkritikos compare (v.): sunkrinô comparison (n.): parexetasis, sunkrisis complain (v.): memphomai complete (v.): apoteleô, sumplêroô, sunteleô, teleô, teleiô complete: teleios, telikos completely: pampan, pantelôs, panu, pantapasi completeness (n.): teleiotês completion (n.): sunteleia compose (v.): sunistêmi composite: sunthetos composition (n.): sunkrima, sunthesis concave: koilos concede (v.): didômai, endidômi, sunkheô conceive (v.): epinoeô, noeô concentrate (v.): sunneuô concept (n.): epinoia conception (n.) ennoia, hupolêpsis, prolêpsis conclude (v.): diaperainô, sumperainô conclusion (n.): epiphora, sumperasma condensation (n.): puknôsis condense (v.): puknoô condition (n.): diathesis, katastasis confidence (n.): pistis configuration (n.): skhêmatismos configure (v.): skhêmatizô confirm (v.): pistoô confirmation (n.): marturia, pistis conflict (n.): makhê conflict (v.): makhomai conflicting: makhêtikos confuse (v.): sunkheô connect (v.): sunaptô consequent (n.): hepomenon, lêgon consider (v.): apeidon, episkopeô, hêgeomai, theôreô constitute (v.): sunistêmi constitution (n.): diathesis, sustasis constitutive: sustatikos constrain (v.): anankazô, biazô, dusôpeô constrained: biaios constraint (n.): bia construct (v.): kataskeuazô, paraskeuô contact (n.): epaphê contain (v.): periekhô, perilambanô

containing: periektikos contend (v.): diateinô contentious: philoneikos contentiousness (n.): philoneikia continue (v.): epimenô continuity (n.): sunekheia, sunokhê continuous: sunekhês contract (v.): sunaireô contradict (v.): enantioomai contradiction (n.): enantiologia, enantiologos contradictory: diaphônos contrariety (n.): enantiôsis, enantiotês contrary: enantios, hupenantios contribute (v.): epiballô, sumballô, sunteleô converge (v.): sunneuô convergence (n.): sunneusis conversion (n.): antistrophê convert (v.): anastrephô, antistrephô convex: kurtos cool (v.): psukhô co-operate (v.): sunergeô co-ordinate: isostoikhos, sustoikhos co-ordination (n.): epharmogê cornea (n.): keratoeidês khitôn correct: alêthês, hugiês, kalos, orthos corroborate (v.): martureô corrupt (v.): diaphtheirô cosmic: kosmikos cosmos (n.): kosmos count (v.): aparithmeô counterargument (n.): antilogia counterrevolve (v.): anelittô courage (n.): andreia cow (n.): bous cowardice (n.): deilia crap (n.): kopros create (v.): dêmiourgeô create life (v.): zôipoieô creation (n.): dêmiourgêma, dêmiourgia creator (n.): dêmiourgos criticism (n.): enklêma crocodile (n.): krokodeilos crow (n.): korax cube (n.): kubos cup (n.): kuathos curved: peripherês custom (n.): ethos, sunêtheia customary: sunêthês cylinder (n.): kulindros cylindrical: kulindrikos

English-Greek Glossary dark: melas darken (v.): melainô, skotizô darkening (n.): melansis darkness (n.): skotos day (n.): hêmera deal with (v.): hupantaô debase (v.): parakharattô, paraphtheirô decay (n.) phthisis decay (v.): aporreô, phthinô deceive (v.): apataô deception (n.): apatê declare (v.): anangellô, apophainô decline (n.): parakmê decline (v.): apaxioô, parakmazô decree (v.): nomotheteô defend (v.): amunô, apologeomai deficiency (n.): elleipsis deficient: ellipês define (v.): diorizô, horizô definition (n.): horismos, horos demand (v.): apaiteô, axioô demiurgic: dêmiourgikos demonstrate (v.): apodeiknumi demonstrate previously (v.): proapodeiknumi demonstrate together (v.): sunapodeiknumi demonstration (n.): apodeixis demonstrative: apodeiktikos denial (n.): apophasis dense: puknos deny (v.): anaireô, apophaskô, paraiteomai depart (v.): apeimi, apokhôreô, exerkhomai, existêmi depend upon (v.): exartaô depth (n.): bathos descend (v.): katabainô desire (n.): ephesis, hormê, prothumia desire (v.): ephiêmi, epithumeô, hormaô, oregô desire for victory (n.): philoneikia desired: ephetos destroy (v.): anaireô, apollumi, diaphtheirô, phtheirô detach (v.): apospaô determination (n.): diorismos determine (v.): horizô, tithêmi development (n.): agôgê deviate (v.): ekbainô deviation (n.): parallaxis dialectical: dialektikos diameter (n.): diametros

159

die (v.): aposbennumi differ (v.): diapherô difference (n.): diaphora, heterotês, parallaxis different: alloios, allos, diaphoros, heteros differentia (n.): diaphora differently qualified: alloios difficult: aporos difficulty (n.): aporêma, aporia dimension (n.): diastasis diminish (v.): meioô, phthinô diminishing (n.): meiôsis, phthisis diminution (n.): meiôsis direct (v.): apoteinô direct: prosekhês directly: autothen disagree (v.): diapherô, diaphôneô disagreement (n.): antirrêsis disciple (n.): akroatês discriminating: eudiakritos discuss (v.), dialegô discussion (n.): logos disdain (n.): kataphronêsis disharmony (n.): anarmostia disk of a balance (n.): plastinx dispose (v.): diatithêmi disposition (n.): diathesis dispute (v.): amphisbêteô disregard (v.): pareidon dissimilar: anomoios dissoluble: lutos dissolution (n.): dialusis, lusis dissolve (v.): dialuô, luô distance (n.): apostasis, diastasis distasteful: akharis distinction (n.): diairesis distinguish (v.): antidiaireô, aphorizô, diaireô, diakrinô, diorizô distinguish together (v.): sundiaireô distort (v.): diaspaô divide (v.): diaireô divide (into parts) (v.): merizô divided: meristos divine: theios division (n.): diairesis, diakrisis, merismos do away with (v.): atheteô doctrine (n.): dogma, logos dodecahedron (n.): dôdekaedron dominate (v.): krateô doubt (v.): amphiballô down: katô drag (v.): helkô

160

English-Greek Glossary

drag down (v.): kataspaô, kathelkô drag up (v.): anelkô draw (v.): agô, graphô, helkô, perigraphô draw down (v.): kathelkô draw things out (v.): mêkunô draw up (v.): anelkô drimakos: drimakos dry (v.): xêrainô dry: xêros dryness (n.): xerotês due measure (n.): summetria dull-wittedness (n.): dussunesia dung (n.): kopros duration (n.): paratasis eager to learn: philomathês earlier: emprosthen early: arkhaios, presbus earth (n.): gê earthen: geôdês east (n.): anatolê easy: hetoimos, prokheiros, rhaidios easy to divide: eudiairetos eccentric: ekkentros educate (v.): paideuô efficient: poiêtikos efflux (n.): apaugasma elbow (n.): ankôn elegant: glaphuros element (n.): stoikheion elemental: stoikheiôdês elevating: anagôgós elevation (n.): anatasis, hupsos eliminate (v.): aphanizô elucidate (v.): saphênizô embrace (v.): periekhô embracing: periektikos emerge (v.): anadunô emplant (v.): empoieô empty: kenos empty (v.): kenoô empty-headed: kenodoxos empty-headedness (n.): kenodoxia encounter (v.): entunkhanô, hupantaô end (n.) teleutê, telos end up (v.): teleutaô endless: diôlugios endure (v.): anekhô, diateleô, hupomenô, menô endure together (v.): summenô enjoy (v.): apolauô enjoyment (n.): apolausis enough: halis

enquire (v.): zêteô entailment (n.): akolouthia entangle in (v.): periballô entire: holos entirely: pampan, pantelôs, pantapasi entirety (n.): holotês entrance (n.): pareisdusis enumerate (v.): aparithmeô envelop (v.): perikaluptô epicycle (n.): epikuklos epilogue (n.): epilogos equal: isos equal in age: isokhronios equal in number: isarithmos equal in size: isomegethês equality (n.): isotês equally: homoiôs equally powerful: isodunamos equally strong: isosthenês equator (n.): isêmerinos (kuklos) err (v.): hamartanô escape notice (v.): lanthanô especially: malista espouse (v.): paraineô establish (v.): bebaioô, kataskeuazô establishing: kataskeuastikos esteem (n.): timê eternal: aiônios, diaiônios eternity (n.): aiôn etymology (n.): etumologia even: artios even times: artiakis everlasting: aidios everlastingness (n.): aidiotêta everywhere: pantakhothen, pantakhou evidence (n.): marturia, tekmêrion evident: phaneros, prophanês examine (v.): basanizô example (n.): paradeigma exceed (v.): huperballô excess (n.): huperbolê, huperokhê excessively: lian exchange (n.): metadosis exchange (v.): metadidômi excuse (v.): sunginôskô exegesis (n.): exêgêsis exercise (n.): gumnasia exercise (v.): gumnazô exist (v.): huparkhô, eimi, huphistêmi exist before (v.): prouparkhô exist together (v.): suneimi, sunuparkhô, sunuphistêmi existence (n.): hupostasis expand along with (v.): sunauxanô

English-Greek Glossary expect (v.): prosdokeô explain (v.): apologeomai, diarthroô, exêgeomai, hermêneuô explain in detail (v.): dierkhomai explainer (n.): exêgêtês explanation (n.): aitia, exêgêsis explicitly: diêrthrômenôs expose (v.): dielenkhô extend (v.): diêkô, prosauxanô extend along with (v.): sumparateinô extended: diastatos extendedness (n.): paratasis extension (n.): diastasis, ektasis external: ektos, exô, exôthen, heterôthen extreme: akros, eskhatos eye (n.): omma, ophthalmos fact (n.): pragma factor in (v.): proslogizomai faculty (n.): dunamis fair: dikaios fall (v.): piptô fall away (v.): apopiptô fall down (v.): apopiptô fall from (v.): ekpiptô fall into (v.): empiptô fallacy (n.): paralogismos false: pseudos famous: onomastos far away: prosô fast: takhus fate (n.): moira fever (n.): puretos few: oligos fiery: purios fight (v.): makhomai fig-tree (n.): sukê figure (n.): skhêma figure (v.): diazôgrapheô figure out (v.): anikhneuô fill (v.): korennumi, plêroô fill out (v.): sumplêroô filthy: borborôdês final: teleutaios, telikos find (v.): heuriskô find fault (v.): memphomai fine: leptos fineness (n.): leptotês fine parts, having (n.): leptomereia fine-parted: leptomerês finger (n.): daktulos fire (n.): pur fire-fly (n.): pugolampis

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firm: bebaios firmament (n.): stereôma first: prôtos fish (n.): ikhthus fit (v.): epharmottô fit together (v.): harmozô fitting (n.): epharmogê fixed: aplanês flame (n.): phlox flat: epipedos flavour (n.): khumos flesh (n.): sarx flight (n.): ptêsis float (v.): epinêkhomai flow (n.): khusis flow (v.): khôreô, rheô flow around (v.): perirreô flow out (v.): aporreô, ekkheô flowing: rheustos follow (v.): akoloutheô, epakoloutheô, hepomai, sumbainô following: akolouthos, ephexês foot (n.): pous force (n.): bia force (v.): biazô forceful: biaios foreign: xenos foresee (v.): promanteuomai foresight (n.): pronoia forever: aei, aidios forget (v.): epilanthanô form (n.): eidos, idea form (v.): eidopoieô form into a sphere (v.): sphairoô forming: eidopoios forward: emprosthen foundation (n.): hidrusis free: eleutheros frenzy (n.): lutta frequently: pollakhou, pollakis frivolous: kakoskholos front: emprosthen, prosthen, prosthios frown (v.): sunophruoomai full: diakorês, plêrês furnish (v.): khorêgeô, parekhô, porizô further increase (n.): prosauxêsis furthest down: katôtatô gather (v.): sullegô gather together (v.): sullambanô general (n.): stratêgos general: katholikos generate (v.): gennaô generated: genêtos

162

English-Greek Glossary

generative: gonimos generic: genikos genesis (n.): genesis gentle: êremaios gentleman (n.): gennadas genuinely: ontôs genus (n.): genos gigantesque: gigantikos give (v.): apodidômi, didômai give as evidence (v.): tekmairomai give existence (v.): huphistêmi, sunistêmi give life (v.): zôipoieô give light (v.): phôtizô give shape (v.): skhêmatizô give substance (v.): ousioô giving existence: hupostatikos glass (n.): hualos glorify (v.): semnunô go (v.): bainô, eimi go after (v.): apeimi go beyond (v.): pleonazô go down (v.): kateimi go on (v.): diateleô go on at length (v.): mêkunô go past (v.): parekhô go through (v.): dierkhomai, eperkhomai go up (v.): aneimi go up again (v.): epanerkhomai goal (n.): skopos god (n.): theos good: agathos, kalos good fellow (n.): khrêstos good sir!: beltiste goodheartedness (n.): euêtheia goodness (n.): agathotêtos governing: arkhikos grammarian (n.): grammatikos grand: diôlugios grant (v.): didômai, sunkheô grasp (v.): haireô great: megas greater: meizôn grey: phaios grow (v.): anaphuô, auxanô, prosauxanô grow around (v.): periphuô grow together (v.); sumphuô growth (n.): auxêsis guide (v.): ithunô, kheiragôgeô hair (n.): thrix hand (n.): kheir

hand down (v.): diadidomai, paradidômi happen (v.) sumbainô happen to be (v.): tunkhanô hardness (n.): sklêrotês harm (v.): blaptô harmful: blaberos harmonious: enarmonios harmonize (v.): harmozô, sumphôneô, sunaidô harmonizing: sumphônos harmony (n.): harmonia have (v.): ekhô, epekhô, iskhô, have the strength to (v.): iskhuô head (n.): kephalê hear (v.): akouô hearing (n.): akoê heart (n.): kardia heat (n.): thermotês, thermasia heat (v.): thermainô heaven (n.): ouranos heavenly: ouranios heavens (n.): ouranos heaviness (n.): barutês heavy: barus helix (n.): helix help (v.): boêtheô, sunergeô helping: boêthos hemisphere (n.): hêmisphairion high: meteôros higher: anôterô highest: akros, anôtatô highest form (n.): akrotês hold (v.): huparkhô hold oneself up (v.): anekhô hold together (v.): sunekhô holding together: sunektikos hollow: koilos holy: hieros homocentric: homokentros homoiomerous: homoiomerês honour (v.): timaô honour god (v.): theosebeô honourable: timios hope (v.): elpizô horse (n.): hippos hot: thermos hour (n.): hôra house (n.): oikêma, oikia human being (n.): anthrôpos human: anthrôpeios, anthrôpinos humanoid: anthrôpiskos hupekkauma (n.): hupekkauma hymn praises of (v.): anumneô

English-Greek Glossary hypernatural: huper phusin, huperphuês hypothesis (n.): hupothesis hypothesize (v.): hupotithêmi hypothetical: hupothetikos ice (n.): krustallos icon (n.): aphidruma icosahedron (n.): eikosaedron idea (n.): ennoia, epibolê, epinoia, idea ignite (v.): exaptô ignorance (n.): agnoia, agnômosunê ignorant: agnômôn, anoêtos illuminate (v.): phôtizô image (n.): eikôn imagination (n.): phantasia imagining (n.): phantasia imbalance (n.): asummetria imitate (v.): mimeomai imitation (n.): mimêsis immaterial: aülos immediate: amesos, prosekhês immediately clear: prodêlos immortal: athanatos immortality (n.): athanasia imperishable: aphthartos impinge (v.): epeiseimi impious: asebês impose (v.): epitithêmi impossible: adunatos impulsion (n.): rhopê inanimate: apsukhos incline (v.): apoklinô include (v.): perilambanô, sullambanô incomplete: atelês incomplete condition (n.): ateleia inconsistent: anakolouthos incorporeal: asômatos incorrect: kakos increase (n.): auxêsis, epitasis increase (v.): auxanô, epauxanô, epididômi, epiteinô, prosauxanô indefinite: aoristos indefiniteness (n.): aoristia indeterminate: aoristos indicate (v.): dêloô, emphainô, endeiknumi, hupodeiknumi, sêmainô indication (n.): tekmêrion indifferent: adiaphoros indisputable: anamphilektos indivisible: adiairetos inequality (n.): anisotês inescapable: aphuktos

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infer (v.): epagô, sullogizô, sumperainô, sunagô, tekmairomai inference (n.): akolouthia, sunagôgê infinite: apeiros infinite power (n.): apeirodunamia infinitely many times: apeiroplasiôn infinitely many: apeiros infinitely powerful: apeirodunamos infinity (n.): apeiria inflate (v.): phusaô inhere (v.): enuparkhô injure (v.): blaptô inner: entos inside: endothen, entos instantaneous: exaiphnês intellectual: dianoêtikos, noeros intelligible: noêtos intense: sphodros intensify (v.): epiteinô intermediate: mesos, metaxu interpretation (n.): exêgêsis interrupt (v.): diakoptô interval (n.): apostêma introduce (v.): epeisagô, paragô, prosagô investigate (v.): episkeptomai, episkopeô, meteimi, zêteô investigation (n.): zêtêsis life (n.): zôê invisible: aphanês irrational: alogistos, alogos irrefutable: anelenktos issue (n.): pragma jackdaw (n.): koloios jaw (n.): genus join (v.): epizeugnumi, sunaptô judge (v.): hêgeomai, katakrinô, krinô just: dikaios justice (n.): dikê knavery (n.): panourgia katamênia (n.): katamênion keeping pace together (n.): sunapokatastasis kind (n.): eidos, idea kinship (n.): sungeneia know (v.): ginôskô, gnôrizô, noeô, oida knowable: gnôstos knowledge (n.): eidêsis lack (n.): sterêsis lack (v.): elleipô, stereô last (v.): diamenô

164

English-Greek Glossary

last: eskhatos lasting: monimos later: husteros lateral: plagios lawyer-like: dikanikos lay down in advance (v.): proupotithêmi lead (v.): agô, hupagô lead back (v.): epanagô learn (v.): ginôskô, gnôrizô, manthanô learning (n.): mathêsis learning late: opsimathês least: elakhistos, hêkistos leave (v.): eaô, existêmi leave out (v.) aphaireô, paraleipô, pariêmi left: aristeros leisure (n.): skholê lemma (n.): lêmma length (n.): mêkos lengthy: makros less: elattôn, hêttôn let out (v.): aporriptô lie (v.): keimai lie above (v.): epipolazô, huperkeimai lie at the bottom (v.): huphizô lie at the top (v.): epipolazô lie on top (v.): epikeimai lie together (v.): parakeimai lie under (v.): hupokeimai life (n.): bios light (n.): phôs light: kouphos, leukos light colour (n.): leukotês lighten (v.): leukainô lightening (n.): leukansis lightness (n.): kouphotês like: homoios limb (n.): kôlon limit (n.): peras limit (v.): peratoô line (n.): grammê, epos linear: grammikos link with (v.): sunartaô listener (n.): akroatês literate: grammatikos live (v.): zô living: zôos living thing (n.): zôion long: makros long ago: palai long-lasting: polukhronios look (v.): eidon look!: idou

look at (v.): blepô look to (v.): apeidon lose (v.): apollumi love (n.): erôs loving learning: philomathês low: tapeinos lower: katô, katôterô lowest: katôtatô lowly: eutelês luminous: euagês lunar: selêniakos mad: maniôdês made of clay: plinthinos magnify along with (v.): sumpleonazô magniloquent: megalorrêmôn magnitude (n.): megethos maintain (v.): axioô, phulattô major (premiss): meizôn make (v.): ergazomai, poieô make cold (v.): psukhô make depend (v.); apartaô make fall down (v.): sphallô man (n.): anêr manifestation (n.): ekphansis many: polus mass (n.): khuma, onkos master (n.): didaskalos master (v.): krateô material: enulos, hulikos mathematical: mathêmatikos mathematical thing (n.): mathêma matter (n.): hulê mean (n.): mesotês mean (v.): sêmainô mean the same thing (v.): isodunameô meaning (n.): ennoia measure (n.): metron measure (v.): katametreô, metreô measuring: metrêtikos measuring stick (n.): pêkhus meet (v.): hupantaô, sumballô member of the same sect (n.): sustasiôtês mention (v.): erô, hupomimnêskô, mnêmoneuô, onomazô middle (n.): mesotês mind (n.): noos mindless: anoêtos mindlessness (n.): anoia minor (premiss): elattôn mischief (n.): panourgia mischievous: kakoskholos misinterpret (v.): parakouô

English-Greek Glossary mist (n.): akhlus misunderstand entirely (v.): diamartanô misunderstanding (n.): agnoia, parakoê misuse (v.): katakhraomai mix (v.): mignumi mix together (v.): sunanakerannumai mixed: miktos mixture (n.): mixis mode (n.): tropos moist: hugros moisten (v.): hugrainô moistness (n.): hugrotês monad (n.): monas moon (n.): selênê mortal: thnêtos most of all: malista motion (n.): kinêsis, phora motion in a circle (n.): kuklophoria motion in reverse directions (n.): antikinêsis motion up (n.): anabasis mountain (n.): oros move (v.): erkhomai, hiêmi, khôreô, kineô, pherô move along with (v.): sunektrekhô, sunkineô move closer (v.): prokoptô move down (v.): huperkhomai move forward (v.): probainô move in a circle (v.): kuklophoreomai move in a straight line (v.): euthuporeô move in both directions (v.): epamphoterizô move in reverse directions (v.): antikineô, antipherô move in the opposite direction (v.): parapherô move together (v.): suneimi moved by something else: heterokinêtos moving: kinêtos moving down (n.): katabasis moving in a circle: kuklophorêtikos moving in a straight line: euthuporos moving with equal speed: isotakhês much: polus multiply (v.): pollaplasiazô mutual replacement (n.): antiperistasis name (n.): onoma name (v.): onomazô natural: phusikos, kata phusin

165

nature (n.): phusis near: plêsios nearness (n.): plêsiasmos necessitate (v.): anankazô necessity (n.): anankê necesssary: anankaios need (n.): khreia negating: arnêtikos negative: apophatikos new: neos next: ephexês, hexês, loipos no longer: mêketi, ouketi nonsense (n.): phlênaphos, phluaria noon (n.): mesêmbria note (v.); ephistêmi notice (v.): ephistêmi, suniêmi nourish (v.): trephô nourishment (n.) trophê novel: kainoprepês, xenos number (n.): arithmos, plêthos nutritive: threptikos object (v.): enistêmi, enkaleô, memphomai objection (n.): antirrhêsis, enstasis oblique: loxos obscure (v.): apokruptô, suskiazô observe (v.): theaomai obviously: dêlonoti occupy (v.): epekhô, epilambanô, episkhô occupy previously (v.): prokatekhô occur (v.): aphikneomai, ginomai. sumbainô octahedron (n.): oktahedron odd: perittos odd times even: perissartios old: palaios olive oil (n.): elaion omit (v.): pariêmi only: monos opinion (n.): dogma, doxa oppose (v.): antitithêmi order (n.): taxis order (v.): diakosmeô, euthetizô ordinary: sunêthês ordinary use (n.): sunêtheia organic: organikos original: arkhegonos other: allos, heteros, loipos outer: ektos outermost: exôtatô outside: ektos, exô overbearingness (n.): pleonexia

166

English-Greek Glossary

overpower (v.): krateô overtake (v.): hupertrekhô overthrow (v.): anastrephô, anatrepô overturn (v.): anatrepô page (n.): selis paltry: eutelês paradigm (n.): paradeigma parallel: parallêlos parallelogram (n.): parallêlogrammon paraphrase (n.): paraphrasis part (n.): meros, morion partial: merikos participate in (v.): metekhô participation (n.): metalêpsis, methexis particular: merikos pass (v.): metabainô pass over (v.): diaballô, eaô, paratrekhô passage (n.): khôrion, lexis, rhêsis passive: pathêtikos perceive (v.): aisthanomai, sunaisthanomai perceptible: aisthêtos perception (n.): aisthêsis, sunaisthêsis perfection (n.): teleiotês perfective: telesiourgos perhaps: isôs, mêpote, takha perimeter (n.): perimetros peripheral: perix perishable: phthartos perishing (n.): phthora perishing: phthartos phase (n.): phasis philosopher (n.): philosophos philosophical: philosophos philosophize (v.): philosopheô philosophy (n.): philosophia pitiable: eleeinos place (n.): khôra, topos place above (v.): huperedrazô plane: epipedos plant (n.): phuton please (v.): areskô plurality (n.): plêthos point (n.): sêmeion, skopos pointless: mataios, matên pool (n.): kolumbêthra portion (n.): moira, morion posit (v.): tithêmi position (n.): epokhê, thesis possess in addition (v.): prosktaomai possible: dunatos posterior: husteros

postpone (v.): anaballô postulate (v.): aiteô potentiality (n.): dunamis power (n.): dunamis practically: skhedon precede (v.): proêgeomai, prouparkhô preceding: prosthen precise: akribês precision (n.): akribeia preconception (n.): prolêpsis predicate (n.): katêgoroumenon predominance (n.): epikrateia predominate (v.): epikrateô pre-exist (v.): prouparkhô premiss (n.): lêmma, protasis prepare (v.): paraskeuô presence (n.): parousia present (v.): paradidômi, proagô present as one’s own progeny (v.): hupoballô preserve (v.): diasôzô, sôzô, phulattô pressure (n.): antereisis prevent (v.): kôluô previous: prosthen, proteros primary: prôtos principle (n.): arkhê, logos prior: proteros, prôtos privation (n.): sterêsis privative: sterêtikos prize (n.): epathlon probable: eikos problem (n.): problêma proceed (v.): eimi, proeimi, proerkhomai procession (n.): proodos, propodismos proclaim (v.): aneuphêmeô, diêgeomai produce (v.): apergazomai, paragô, poieô producing motion: poiêtikos production (n.): poiêsis progression (n.): propodismos prologue (n.): prooimion prone to scatter: skedastos proof (n.): deixis proper: idios, oikeios proportion (n.): analogia proportional: analogos proposal (n.): epibolê, problêma propose (v.): proballô, propherô, protithêmi proposition (n.): logos, protasis proprium (n.): idion prosecutor (n.): katêgoros prove (v.): deiknumi

English-Greek Glossary provide (v.): parekhô proving: deiktikos proximity (n.): plêsiasis punishment (n.): dikê pure: eilikrinês, katharos purity (n.): katharotês purpose (n.): skopos pursue (v.): meteimi push (v.): ôtheô put around (v.): periballô put forward (v.): diateinô, proballô, propherô, proteinô putrefaction (n.): sêpsis pyramid (n.): puramis qualitative change (n.): alloiôsis quality (n.): poion, poiotês qualityless: apoios quantity (n.): plêthos, poson, posotês quick: takhus quote (v.): paragraphô raise (v.): anateinô, exairô, meteôrizô rank (n.): taxis rarefaction (n.): manôsis rarefy (v.): manoô rash: propetês rashness (n.): propeteia, thrasutês ratio (n.): logos ray (n.): aktis reach (v.): aphikneomai, katalambanô, kathêkô reach a conclusion (v.): perainô read (v.): anagignôskô, entunkhanô reading (n.): enteuxis ready: eukolos, prokheiros reality (n.): huparxis realize (v.): ennoeô, ginôskô reason (n.): aitia, aition reasonable: eikos, eulogos, metrios reasonably: eikotôs reasoning (n.): dianoia rebellion (n.) aponoia recall (v.): hupomimnêskô, mimnêsko receive (v.): apolambanô, dekhomai, epidekhomai, hupodekhomai, lankhanô receive in advance (v.): prolambanô receptacle (n.): hupodokhê reception (n.): metalêpsis receptive: dektikos, khôrêtikos recognize (v.): ennoeô record (n.): mnêmê record (v.): anagraphô

167

recount (v.): historeô rectangle (n.): tetragônon recycle (v.): anakukleô reduce (to an absurdity): apagô reductio ad impossibile (n.): apagôgê eis adunaton refer (v.): anapempô, hupargoreuô refined: katharos reflect back (v.): anaklaô reflection back (n.): anaklasis refutation (n.): antilogia, elenkhos refute (v.): dielenkhô, elenkhô refute as well (v.): sunapelenkhô region (n.): khôra, topos regret (v.): metamelomai reject (v.): aporrapizô, aporriptô rejoice (v.): khairô relation (n.): skhesis release (v.): aphiêmi remain (v.): epimenô, leipô, menô, perileipomai remaining: loipos remarkable: thaumasios, thaumastos remember (v.): mimnêsko remind (v.): hupomimnêskô remove (v.): aphaireô, exaireô renown (n.): eukleia renowned: kleinos replace mutually (v.): antiperiistêmi replace with (v.): anteisagô report (v.): historeô reproach (n.): enklêma reputation (n.): doxa require (v.): anankazô, apaiteô resist (v.): antitupoô resistance (n.): antitupia resolve (v.): analuô respond (v.): hupantaô response (n.): hupantêsis rest (n.): anapaula, êremia, monê, stasis rest (v.): anapauô, êremeô, menô rest period (n.): anapausis restrict (v.): sunaireô result (v.); sumbainô retribution (n.): timôria retrogression (n.): hupopodismos return (v.): apokathistêmi reveal (v.): apokaluptô, emphainô reverence (v.): sebomai reverential: theosebês reverse: anapalin, empalin revolution (n.): periagôgê, periodos, periphora

168

English-Greek Glossary

revolve (v.): anakukleô, peridineô, peristrephô revolve with (v.): sumperipoleô ride (v.): okheô right: dexios, dikaios, kalos, orthos rigorous: akribês rise (v.): anabainô, anatellô rise above (v.): epipolazô rise to the top (v.): epipolazô rise together with (v.): sunanatellô risible: gelastikos role (n.): logos roof (n.): tegos room (n.): khôra rough: trakhus roughness (n.): trakhutês rub (v.): paratribô rubbing (n.): paratripsis rule (n.): nomos rule (v.): krateô run (v.): theô run together (v.) sunkheô sacred: hieros said previously: proeirêmenos sameness (n.): tautotês sandal (n.): hupodêma sandy: ammôdês say (v.): eipon, legô, erô saying (n.): paroimia scale (of a fish) (n.): lepis scientific: epistêmonikos scorn (v.): duskherainô sea (n.): pelagos, thalatta searcher (n.): thêratês season (n.): hôra seat (n.): hedra seat (v.): hedrazô see (v.): eidon, horaô, sunêgoreô, theaomai, theôreô see in (v.): entheôreô seed (n.): sperma sphere (n.): sphaira seek (v.) zêteô, epizêteô seem (v.): dokeô, eoika segment (n.): tithêmi self-moving: autokinêtos self-satisfied: eukolos self-substantiating: authupostatos semicircle (n.): hêmikuklion separate (v.): apomerizô, diakrinô, dialambanô, khôrizô separation (n.): diakrisis, diastasis service (n.): hupêresia

set (v.): duô set aside (v.): eaô set out (v.): ektithêmi, paratithêmi, protithêmi set straight (v.): katorthoô set together (v.) sundunô setting out (n.): parathesis settle (v.): hidruô shake (v.): saleuô shameless: anaidês shape (n.): morphê, skhêma shapelessness (n.): askhêmosunê share in (v.): koinôneô, metekhô shining: phôteinos shining everywhere: hololampês ship (n.): naus shooting star (n.): diaittôn short: brakhus shout (v.): boaô show (v.): deiknumi, dêloô, epideiknumi show oneself (v.): anaphainô showing (n.): deigma shrink from (v.): okneô side (n.): pleura sign (n.): tekmêrion sign (of the zodiac) (n.): zôidion sign (v.): epigraphô signal (v.): episêmainô similar: homoios, paraplêsios similarity (n.): homoiotês simple: haplous simplicity (n.): haplotês simply: haplôs simultaneous: hama sin (v.): asebeô sinew (n.): neuron sink (v.); katabainô size (n.): megethos, poson slow: bradus sludge (n.): trugê sludgy: trugôdês small: mikros smaller: elattôn smoothness (n.): leiotês, malakotês sneak out (v.): parekduomai snow (n.): khiôn solar: hêliakos solid: sterros, stereos solidity (n.): sterrotês sometimes: eniote soul (n.): psukhê sound (n.): phônê, psophos sound: hugiês

English-Greek Glossary sound (off) (v.): phthengomai sound out (v.): perikrouô space (n.): khôra, topos spatial: topikos speak against (v.): anteipon, anterô, antilegô speak nonsense (v.): phluareô species (n.): eidos specific feature (n.): idion speech (n.): logos speed (n.): takhos spend (v.): dapanaô spend time: endiatribô spherical: sphairikos spread (v.): khôreô spread around (v.): perikheô stable: monimos stand (v.): bainô, kathistêmi stand in the way (v.): empodizô stand still (v.): histêmi standard (n.): kritêrion star (n.): astêr, astron start (v.): arkhô, hormaô starting point (n.): arkhê state (n.): hexis statement (n.): logos stir up (v.): anakineô stir up together (v.): sunanakineô stone (n.): lithos stony: lithôdês stop (v.): histêmi stopping (n.): stasis straight: euthus straight-edge (n.): kanôn strange: atopos strength (n.): iskhus stretch out (v.): apoteinô, katateinô stretching (n.): ektasis strict: kurios strife (n.): neikos strike (v.): antikoptô strike into perplexity (v.): kataplêttô strive (v.): speudô, spoudazô strive for victory (v.): philoneikeô strong: iskhuros structure (n.): sustasis study of nature (n.): phusiologia stupid: anepistatos stupidity (n.): anepistasia sublunary: hupo selênên substance (n.): ousia substantial: ousiôdês suffer (v.): eaô suffering: pathêtos

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suffice (v.): arkeô, diarkeô sufficient: hikanos suitability (n.): epitêdeiotês suitable: epitêdeios suited: epitêdeios summer (n.): theros sun (n.): hêlios superficial: epipolaios superfluity (n.): periousia superfluous: perittos superior: huperteros superiority (n.): huperokhê supervene (v.): epiginomai, paraginomai supply (v.): parekhô support (n.): sunêgoria support (v.): sunêgoreô support also (v.): summartureô supportive: sunêgoros suppose (v.): hupolambanô, huponoeô, tithêmi surface (n.): epiphaneia surprising: thaumastos surround (v.): periekhô surrounding: perix sustain (v.): sunekhô swamp (n.): telmation sweetness (n.): glukutês swim (v.): nêkhô syllogism (n.): sullogismos symmetric: summetros symmetry (n.): summetria sympathy (n.): sumpatheia synthesis (n.): sunthesis synthesizing: eusunkritos take (v.): lambanô, paralambanô take as a pair (v.): sunduazô take away (v.): aphaireô, aphiêmi, huphaireô take away from under (v.): hupospaô take into account (v.): logizomai take offense (v.): nemesaô take on (v.): apolambanô, metalambanô take on in addition (v.): proslambanô taking (n.): lêpsis tangible: haptos teach (v.): didaskô teacher (n.): didaskalos teaching (n.): didaskalia, paradosis temperate: eukraês temple (n.): naos term (n.): horos

170

English-Greek Glossary

test (v.): basanizô text (n.): lexis, rhêsis theory (n.): logos thereby: hêdê thesis (n.): thesis thickness (n.): pakhutês thin (v.): leptunô thing (n.): pragma think (v.): boulomai, dianoeô, doxazô, epinoeô, noeô, oiomai, nomizô think of (v.): mnêmoneuô think of in addition (v.): prosennoeô thinking (n.): phronêsis thought (n.): epinoia, noêsis thoughtless: aperiskeptos threaten (v.): anateinô three-dimensional: trikhê diastatos three-foot: tripêkhus throw (v.): exakontizô, rhiptô thrust away (v.): apôtheô time (n.): aiôn, hôra, khronos together: hama, homou tongue (n.): glôtta tool (n.): organon touch (v.): ephaptô, ephikneomai, haptô trace back (v.): anikhneuô train (v.): gumnazô transcend (v.): exaireô transcendence (n.): exairesis transcendent: exairetos transcending impulsion: arrepês transfer (v.): metapherô transference (n.): metalêpsis transform (v.): metabainô transformation (n.): metabasis, tropê transition (n.): metabasis transmission (n.): metadosis transmit (v.): diadidomai, diapempô, metadidômi, paradidômi transparent: diaphanês treatise (n.): logos, pragmateia triangle (n.): trigônon trouble (n.): askholia trouble (v.): enokhleô true: alêthês trust (v.): pisteuô trustworthiness (n.): piston truth (n.): alêtheia try (v.): epikheireô, peiraô try hard (v.): spoudazô tune (v.): harmozô turbid: thôlôdês

turn (v.): anakamptô, meteimi, strephô, trepô turn aside (v.): ektrepô turn away (v.): apotrepô, apoklinô twist (v.): diastrephô twisted: diastrophos unaffected: apathês unbroken: aklastos unceasing: anekleiptos unchanging: akinêtos, ametablêtos undemonstrated: anapodeiktos undergo (v.): hupomenô, paskhô underlie (v.): hupokeimai undermine (v.): diasaleuô, parapodizô, saleuô understand (v.): akouô, apodekhomai, ekdekhomai, ennoeô, ephistêmi, epistamai, ginôskô, parakoloutheô, sunaisthanomai, suniêmi, sunnoeô understand in addition (v.): prosennoeô understanding (n.): gnôsis, noêsis, sunaisthêsis undivided: adiairetos, askhistos uneducated: apaideutos uneducated amateur (n.): idiôtês unequal: anisos unexamined: anepikritos unextended: adiastatos unfamiliarity (n.): apeiria unfortunate: dustukhês ungraspable: aperilêptos unification (n.): henôsis uniform: homalês, monoeidês unify (v.): hênoô unintelligible: asunetos unity (n.): henôsis universal: katholikos, katholou unjust: adikos unmeasuredness (n.): ametria unmoving: akinêtos unmusical: amousos unnatural: para phusin unreasonable: alogos unrefuted: anelenktos unshakable: asphalês, bebaios unsound: sathros unsystematic: amethodos up: anô upper: anô urge (v.): parangellô use (n.): khreia, ophelos use (v.): apokhraomai, khraomai,

English-Greek Glossary paralambanô, proskhraomai, sunkhraomai useful: khrêsimos valuable: timios value (n.): axiôma, timiotês vanishing: phroudos variegated: poikilos vary (v.): paralattô vein (n.): phleps verse (n.): epos vice (n.): kakia victory-loving: philoneikos view (n.): doxa virtue (n.): aretê visible: horatos vision (n.): opsis visual: optikos vital: zôtikos void: kenos wander (v.): planaô wander about (v.): perinosteô want (v.): boulomai, ethelô warm (v.): thermainô warm: thermos warrant (n.): bebaiôsis waste (v.): dapanaô waste away (v.): marainô water (n.): hudôr watery: hudatinos way (n.): tropos weak: asthenês weaken (v.): kamnô wear out (v.): kamnô weave in (v.): paraplekô weave together (v.): prosuphainô weigh (v.) helkô weigh down (v.): bareô weight (n.): baros well-known: epiphanês west (n.): dusis, dusmai

171

wheel (n.): trokhos white: leukos whiteness (n.): leukotês whole (n.): holotês whole: holos whiten (v.): leukainô will (n.): boulêsis will (v.): ethelô wind (n.): pneuma winged: ptênos winter (n.): kheimôn wisdom (n.): phronêsis, sophia wise: sophos wish (v.): boulomai, ethelô withdraw (v.): hupexerkhomai without difficulty: aponos without leisure: askholos without qualification: haplôs without restraint: anedên witness (n.): martus witness (v.): epiginôskô wonder (v.): thaumazô wood (n.): xulon wooden: xulinos word (n.): onoma words (n.): lexis, logos, rhêmata work (n.): ergon, poiêsis, sungramma work together (v.): suntrekhô worse: kheirôn worth: axios worthy to be spit upon: kataptustos write (v.): graphô write against (v.): antigraphô write in addition (v.): epigraphô writing (n.): gramma year (n.): etos yield (v.): hupeikô young: nearos, neos zenith (n.): koruphê zodiac (n.): zôidiakos (ho)

Greek-English Index This index, which is based on Heiberg’s text plus the variants I have adopted (see pp. 153-4) and covers all of the commentary on 1.2-4, indicates the English translations of many nouns, verbs, adjectives, and some adverbs used by Simplicius more than one time. For the most part, words are given in the form which serves as the basis of an entry in LSJ. There will be an index of words which Simplicius uses only once in Mueller (forthcoming 2011). Certain very common words (e.g., einai, ekhein, and legein) and number words are omitted, as are words which occur only in quotations (or apparent quotations) of Aristotle and earlier authors. When a word occurs no more than ten times, its occurrences are listed; in other cases only the number of occurrences is given; an expression such as ‘62+6’ means that there are 62 occurrences in the text of Simplicius and 6 in De Caelo 1.2-4, and one such as ‘62’ means there are 62 occurrences in Simplicius and none in De Caelo 1.2-4. Occurrences in lemmas and as part of a book title are ignored. Sometimes comparatives, superlatives, and adverbs are included under the positive form of an adjective, sometimes they are treated separately. The expression ‘m/p’ indicates that a verb occurs in the middle or passive tense. There is a separate index of names. adiairetos, undivided, indivisible, 25,8; 76,9; 145,7; 179,1 adiaphoros, not different, indifferent, 28,18.25; 29,27.35; 48,11; 164,6 adiastatos, unextended, 95,4; 138,23; 178,36 adranês, not acting, without effect, 83,12.19.29 adunateô, to be unable, 58,15; 105,25 adunatos, impossible, 62+6 aei, always, forever, 68+2 aêr, air, 109+3 aganakteô, to be angry, 90,8.22 agathos, good, 12 agathotêtos, goodness, 12 agenêtos, not coming to be, not generated, 64+2 agnoeô, to be ignorant of, not understand, be unaware, 32 agnoia, ignorance, misunderstanding, 171,23; 177,19; 182,28 agô, to lead, draw, 26,8; 54,10; 142,25; 180,24 agôgê, development, 28,15; 92,12; 170,28; 194,18

aideomai, to be ashamed, 26,24; 88,17; 112,27 aidios, everlasting, forever, 64+3 aidiotêta, everlastingness, 18 aiôn, time (88,3; 93,27; 195,22; 196,15), eternity (94,15; 105,22; 141,29 (2, both Septuagint) 142,1.2 (2, both Septuagint); abiding 141,4.8 (both Empedocles) aiônios, eternal, 93,28; 95,21; 105,26.30; 107,13; 116,28; 138,17; 141,8; 143,18.23 aiskhunomai, to be ashamed, 56,27; 105,27; 184,28 aisthanomai, to perceive, 81,3; 103,26; 194,24 aisthêsis, perception, 15+1 aisthêtos, perceptible, 111,8; 133,29; 135,19; 140,27.29; 142,31 aiteô, to postulate, ask for, 108,17.31 aithêr, aithêr, 12,25.27; 87,25; 116,14; 188,18.21; 119,2.5 aitia, cause, reason, explanation, 41 aitiaomai, to blame, make responsible, 77,28; 79,9; 119,2; 133,20; 158,17; 166,13; 180,23.25 aition, cause, reason, 58+1

Greek-English Index akhrômatos, without colour, 124,17; 130,17.29 akinêsia, absence of motion, 122,7.13 akinêtos, unmoving, unchanging, 26 aklastos, unbroken, 145,24; 171,3.10.28.29; 172,12 akmazô, to be or reach an acme, 74,3; 118,2; 142,32; 143,5 akmê, acme, 43,21; 73,29; 74,2; 142,28; 188,1.6(2) akoê, hearing, 26,12; 137,1; 201,2 akoinônêtos, having nothing in common, 90,23.29; 91,3 akoloutheô, to follow, 26+2 akolouthia, inference, entailment, 15,28; 27,11; 44,29; 77,9; 162,32; 170,11; 176,30 akolouthos, following, 10,31; 78,8; 89,27; 142,6; 152,16; 163,10; 182,20; 183,16; 189,15 akouô, to hear, understand, 38 akribês, precise, accurate, rigorous, 16,20; 26,22; 46,2; 69,13; 83,2; 110,3.26; 114,29; 176,30 akroasis, see phusikos akroatês, disciple, listener, 12,22; 131,31 akros, extreme, highest; 16 akrotês, highest form, 12,32; 17,26.27; 55,24; 85,13; 87,13; 91,13 aktis, ray, 83,7; 88,20.22; 113,18 akuros, without authority, 73,17.23 alêtheia, truth, 15 alêthês, true, correct, 68 alêtheuô; to be true, to speak truly, 29,32; 57,25; 64,13; 121,12; 131,20; 162,15; 165,29; 166,10.12 allakhou, in another place, 74,23.24 allassô, to change (form), 54,25.27 alloioô, to alter, change in quality, 22 (all m/p) alloios, different, differently qualified, 88,4; 99,4; 100,21; 117,28; 137,26 alloiôsis, alteration, qualitative change, 28+1 allos, other, different, 385+9 allote, at different times, 18 allotrios, alien, 12 alogistos, irrational, 35,34; 91,19 alogos, irrational, unreasonable, 10+1 alutos, indissoluble, 105,16.18.19; 106,3.9.12.27; 109,5; 143,12

173

ameibô, to change, 18,14; 24,14; 100,19 ameiôtos; not diminishing, 60,21; 109,22; 111,5; 144,8 amerês, without parts, 95,4; 104,13 ameristos, having no parts, 97,7; 140,15 amesos, immediate, 127,33; 137,17.19.24; 138,16.28 ametablêtos, unchanging, 95,29; 96,17; 105,6; 107,3; 109,3; 184,30 amousos, unmusical, 121,17; 122,25.27; 125,1.6 (all 4 Aristotle); 128,21.24; 168,14 amphiballô, to doubt, 134,12; 159,11.12 amphisbêteô, to dispute, 66,17; 133,25 amphô, both, 56+1 amphoteros, both, 12+1 amunô, to defend, 46,33; 79,27 (Plato) (both m/p) anabainô, to rise, 35,21; 37,32; 51,17; 66,23; 155,25; 161,12 anaballô, to postpone, 11,4; 108,18 (both m/p) anagignôskô, to read, 123,3; 131,29(2) anagraphô, to record, 107,24; 182,31 anaidês, shameless, 89,12, 107,5; 125,24; 180,26 anaireô, to do away with, destroy, deny, 24,24; 39,5; 78,22; 119,22; 120,16; 129,2; 147,23; 175,25; 184,29 anakamptô, to turn 102,1.2; 132,1; 154,4.5 anakineô, to stir up, 35,9; 119,11 anakolouthos, inconsistent 75,15; 77,8 anakukleô, to recycle, revolve, 119,1; 140,30; 141,9; 155,18 analloiôtos, not altering, not changing in quality, 13+4 analuô, to analyze, resolve, 107,19; 110,14; 123,21; 132,6; 135,30, 152,3 (all but last m/p) anamphilektos, indisputable, 103,15; 116,8; 176,2 anankaios, necesssary, 22+4 anankazô, to constrain, require, necessitate, 11 anankê, necessity, it is necessary, 97+7

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anapalin, in reverse directions, 11 anapempô, to refer, 92,9; 108,19; 124,24; 131,25; 136,17; 144,10 anaphainô, to appear, show oneself, 93,16; 95,24; 97,6; 138,2 anaphuô, to be produced, grow, 93,17; 130,28 (both m/p) anapodeiktos, undemonstrated, 92,27; 102,20; 108,14; 163,25; 164,10 anarkhos, without beginning, 132,15.34; 141,17 anarmostia, disharmony, 102,30; 121,18; 125,19 (last 2 Aristotle) anastrephô, to convert, overthrow, 164,24; 170,8 anateinô, to raise, threaten, 141,17; 170,22 anatellô, to rise, 20,28; 82,29; 155,16 anatolê, east, 14 anatrepô, to overturn, overthrow, 14,8; 26,11; 36,26; 157,20 anauxês, not increasing, 60,21; 91,26; 92,1; 112,4; 116,18; 144,8; 170,13; and 270a13 anauxêtos, not increasing, not growing, 111,3.4; and 270a25 andreia, courage, 55,20; 56,10 anekhô, to hold oneself up, endure, 85,20; 165,5 (both m/p) anekleiptos, unceasing, 31,25; 44,17.18.24.26; 138,21.24; 142,2; 143,25; 194,4; 200,1 anelenktos, irrefutable, unrefuted, 26,14; 55,5; 199,21 anelittô (anelissô in LSJ), to counterrevolve, 32,17; 156,1 anelkô, to draw up, drag up, 64,5; 68,14 anepistasia, stupidity, 163,35; 172,36; 191,9 anepistatos, ignorant, mindless, 71,7; 89,12; 157,11; 183,34 anêr, man, 30; Simplicius refers to Philoponus with phrases like ‘this man’ (houtos ho anêr) 21 times. anikhneuô; to trace back, figure out, 67,22; 160,23 anisos, unequal, 177,29(2); 187,14 anisotakhês, at unequal speed, 24,30; 37,9; 42,9 anisotês, inequality, 56,12.16; 173,7.9 anô, up, upper, above, 180+14; epi to

anô translated ‘upward’; see also anôtatô and anôterô anoêtos, mindless, ignorant, 11 anoia, mindlessness, 46,18; 133,19.20; 156,27; 163,35; 182,18 anomoios, dissimilar, 14,11; 36,19; 68,17.23.24; 109,30; 110,19 anôphoros, moving up, 66,22(2); 70,31 anôtatô, highest, 61,13; and 270b6,22 anôterô, higher, 52,14; 169,5 anôthen, from above, 117,24; 197,20 anteipon, to speak against, 13,22.23; 25,33; 31,17; 59,7; 121,8; 188,26 anterô, to speak against, 25,22; 38,4; 67,23; 157,14 anthrax, coals, 16,20; 85,8 anthrôpinos, human, 17,19; 55,17; 135,9; and 270b13 anthrôpos, human being, human, 59+1 (plural often translated ‘people’) antidiaireô, to distinguish, 95,8; 103,31 (both m/p) antigraphô, to write against, 48,25; 59,8; 80,26; 198,11 antikeimai, to be opposite, be opposed, be contradictory, 124+3 antikineô, to move in reverse directions, 149,21; 152,17; 153,29.31; 154,23; 197,11.23 (all m/p) antikinêsis, motion in the reverse direction, 179,25; 186,23 antilegô, to speak against, argue against, 16 antilogia, counterargument, refutation, 12 antiparastasis, indirect counterobjection, 13,29; 149,15 antiperiistêmi, to replace mutually, 75,33; 76,11 antiperistasis, mutual replacement, 76,19; 77,28.29; 161,13 antipherô, to move in reverse directions, 151,3.10; 156,6; 180,33; 193,27 (all m/p) antirrêsis, disagreement, objection, 170,9.13 antistrephô, to convert, 12 antistrophê, conversion, 23 antitattô (antitassô in LSJ), to set in opposition, 19,18; 59,14; 80,25 antithesis, antithesis, 33

Greek-English Index antithetos, antithetical, 128,7.8; 166,3.7.9; 192,5 antitithêmi, to oppose, be antithetical, 56,19.24; 125,30; 165,22; 177,3 antitupia, resistance, 86,14; 130,22 antitupos, having resistance, 75,31; 76,13; 77,21.26.27 aoristia, indefiniteness, 44,11; 46,35; 94,29 aoristos, indefinite, indeterminate, 18 apagô, to reduce (to an absurdity), 57,11; 136,28; 137,11; 177,2; 178,7 apagôgê eis adunaton, reductio ad impossibile, 150,24; 194,17 apaideusia, lack of education, 26,31; 90,11 apaideutos, uneducated, 26,13; 71,7; 90,10 apaidô, to be out of tune, be incompatible, 87,18; 183,30 apaiteô, to demand, require, 10,30; 29,5; 49,4; 138,16; 182,26.27; 183,15; 195,18 apallassô, to be freed, to be free, 65,21; 66,5; 75,20.29; 77,10; 79,20; 118,9 (all m/p) aparithmeô, to enumerate, count, 119,31; 120,20 apataô, to deceive, 46,14; 162,33; 165,6 apatê, deception, 182,18.27.28; 183,16 apathês, unaffected, without affection, 17+1 apeidon, to look to, consider, 46,34; 187,26 apeimi, to depart, go after, 110,18.19.20; 148,20 apeirakis, infinitely many times, 93,7; 171,31; and 270b19 apeiria (B), infinity, 39,33; 44,14 apeiros, infinite, infinitely many (ep’apeiron translated ‘to infinity’), 62+3 apekhô, to be distant, be separated, 86,7; 148,2; 181,9.20.32; 182,16; and 271a13 apergazomai, to produce, 80,1; 83,11; 106,24; 107,14 (last 3 Plato) aperiskeptos, thoughtless, 134,27; 136,12 aphaireô, to take away, remove, leave out, 22,29; 34,27; 71,25; 79,31; 117,16; 158,16

175

aphairesis, abstraction, 89,29; 178,15 (both ex aphaireseôs) aphanês, invisible, 106,7; 113,5 aphanizô, to eliminate, 47,7.9; 113,14; 155,33 aphiêmi, to take away, release, 22,28; 71,26.28 aphikneomai, to reach, occur, 11+2 aphistêmi, to be at a distance from, depart from, 10+1 aphorizô, to distinguish, 10 aphôtistos, lacking light, 131,1.2 aphthartos, not perishing, imperishable, 36+3 apisteô, to not believe, 75,13; 82,12; 122,1; 163,12; 179,35; 180,26 aplanês, fixed, 44 (hê aplanês sphaira translated ‘sphere of the fixed stars’, to aplanes translated ‘fixed stars’ or ‘sphere of the fixed stars’) apoballô, to cast off, 54,21.22; 127,26; 128,8.10; 134,1 apoblepô, to attend to, 17,22; 31,17; 44,10; 58,15; 59,13; 69,11; 78,15 apodeiknumi, to demonstrate, 69+1 apodeiktikos, demonstrative, 45,7; 55,5.6.13; 116,6 apodeixis, demonstration, 54 apodekhomai, to accept, understand, 17,18; 67,1; 195,10 apodidômi, to assign, give, 29+1 apodosis, account, 66,28.33; 173,23 apogeios, at apogee, far from earth, 32,11.19; 36,23; 113,10 apoios, qualityless, 112,8.10 apokaluptô, to reveal, 165,16; 169,29 apokatastasis, complete rotation, return to the same point, 33,12; 199,26 apokatastatikos, returning to the same point, recurrent, 44,32; 117,30 apokathistêmi, to make a complete rotation, return, 14,18; 33,10; 34,20 apokhraomai, to misuse, 119,6; 134,19 apoklêrôtikos, aribitrary, chance, 26,34; 27,9; 158,4; 161,21; 162,21 apoklinô, to incline, turn away, 57,19; 156,27; 159,8 apolambanô, to take on, receive, 11 apolauô, to enjoy, 65,16.20; 200,4 apoleipô, to leave, allow, 78,6; 114,3; 134,9

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apollumi, to lose (active), be destroyed (m/p), 47,16; 74,4; 98,27; 104,8.17.19.20; 139,4.6 apologeomai, to explain, defend, 31,31; 80,17 apomerizô, to separate, 88,28; 98,14 apophainô, to declare, 77,9; 83,29; 136,12; 158,33 apophasis, denial, 15 apophaskô, to deny, 12 apophatikos, negative 30,21; 57,23; 62,14.15 apopiptô, to fall (down, away), 72,13.17; 76,13.22 aporeô, to raise a difficulty, be perplexed, 21 aporia, difficulty, 14 aporos, difficult, 20,31; 136,11 aporreô, to flow out, decay, 85,19; 88,25(2) aporriptô, to reject, let out, 26,18; 108,32; 200,30 apospaô, to become detached, 16 (all m/p) apostasis, distance 45,18; 113,11; 181,29.30; 184,11 apostêma, interval, 180,13; 181,18 apoteinô, to stretch out, direct, 67,20; 79,15.22; 185,27 apoteleô, to be completed, 85,14; 126,29; and 268b26 (all m/p) apousia, absence, 12 (1 Aristotle) apsukhos, inanimate, without a soul, 73,27; 78,27 areskô, to please, 69,10; 84,11; 87,27 aretê, virtue, 55,29; 56,5; 163,1.4.8 aristeros, left, 11+1 aristos, best, 90,21; 95,26 arithmos, number, 23+1 arkeô, to suffice, to be satisfied, 26 (all m/p) arkhaios, ancient, early, 11,22; 82,15; 118,17; 136,27; and 270b17 arkhê, beginning, starting point, principle, 127+4 arkhikos, governing, being a first principle, 73,11; 130,26 arkhô, to begin, start, 20+1 (all m/p) arnêtikos, negating, 28,19; 30,21 artaô, to depend, 92,22; 144,16 (both m/p) artios, even, 29,28.32(3); 174,22; 175,1 asebês, impious, 35,34; 70,17; 86,3; 90,27; 91,19

askhêmosunê, absence of shape, 125,16; 129,15.18.26 (last 3 Aristotle) askholia, trouble, business, 165,3.5; 201,8 asômatos, incorporeal, 88,16.18; 135,27.29 asphalês, unshakable, 55,5; 91,9 astêr, star, 22 asthenês, weak, 82,16; 197,31 astrôios, of the stars, 117,25; 199,6 astron, star, 12 astronomos, astronomer, 32,6.15.34; 33,11; 36,29 asummetria, imbalance, 56,6.7; 173,8.9 asunetos, without understanding, unintelligible, 37,8; 75,14; 136,27; 178,28; 195,18; 199,22 atalaiporos, careless, 104,17; 143,16 atelês, incomplete, 47+1 athanasia, immortality, 109,7; 143,23 athanatos, immortal, 18+2 atopia, absurdity, 28,12; 71,34 atopos, absurd, strange, 44 aülos, immaterial, 133,28.29.30; 139,9 authupostatos, self-substantiating, 16; cf. huphistêmi autokinêtos, self-moving, 94,4.6.11.30; 95,3.5 autophuês, of the same nature, 53,12; 67,27 autothen, directly, 68,10; 110,25; 113,32; 157,16 auxanô, to increase, cause to grow, 61+3 (mostly m/p) auxêsis, increase, growth, 20+3 axiôma, axiom, value, 63,33; 119,22; 132,4; 154,17; 189,31 axioô, to think right, maintain, demand, 25 axios, worth, 15 axôn, axis, 14,15; 45,13 bainô, to stand, go, 68,22 (Plato); 195,16 barbaros, non-Greek,117,4; 139,29; and 270b7 bareô, to weigh down, 67,29.30 baros, weight, 36+4 barus, heavy, 102+4 barutês, heaviness, 12 basanizô, to examine, put to the test, 36,11; 201,9

Greek-English Index bathos, depth, 48,8.13; 140,8; 179,7.12 bebaioô, to establish, 126,17; 157,13 bebaios, firm, unshakeable, 55,10.20; 141,13 beltiste (see beltistos in LSJ), good sir (addressed to Philoponus), 58,4; 78,9 bia, constraint, force, 20+1 biaios, constrained, forced, forceful, 14,3; 18,30; 38,2; 54,10; 139,23; 154,21 biazô, to force, constrain, 10 (4 Plato, 1 Xenarchus, all m/p) biblion, book, 21 bios, life, 12,23; 80,7; 87,22; 94,16; 106,18 blaberos, harmful, 21,34; 34,17 blaptô, to harm, injure, 69,15; 141,21 (both m/p) blepô, to attend to, look at, 41,28; 157,10; 159,7 boêtheô, to help, 26,30; 184,31; 194,25 bôlos, chunk of earth, 16,20; 27,33(2); 37,6; 64,2; 65,1; 198,24; and 270a5 boulêsis, will, 106,13; 108,34 (both Plato); 143,14 boulomai, to want, wish, think, 63 bous, cow, 98,5.7; 123,20 bradus, slow, 11 brakhus, brief, short, 96,1; 125,24.29; 198,24 brenthumai, to be puffed up, 26,28; 130,14 dapanaô, to spend, waste, 80,28; 81,23; 134,11; 157,2; 172,25; 183,21; 189,28 dei, it is necessary, 32 (often translated with ‘ought’ or ‘should’) deiknumi, to prove, show, 274 deiktikos, proving, 152,26; 175,24 deilia, cowardice, 55,31; 56,9 deinos, clever, 26,25.27 deinotês, cleverness, 26,24; 170,11.12 deixis, proof, 45,3.26; 60,20; 136,17; 144,9 dekhomai, to receive, admit, 24 dektikos, receptive, admitting, 11 dêlonoti, obviously, clearly, 42 dêloô, to make clear, show, indicate, 44 dêlos, clear, 127+2 (mostly dêlon) dêmiourgêma, creation, 90,21; 143,28 dêmiourgeô, to create, 59,15; 106,2; 154,14

177

dêmiourgia, creation, 106,20; 107,12 dêmiourgikos, relating to the creator, demiurgic, 39,34; 44,12; 143,19.26 dêmiourgos, creator, 23 deô (B), to need, 43,3; 86,16; 91,7; 121,25; 124,19; 132,26; 164,21 (all m/p) desmos, bond, 106,13 (Plato).28; 109,4 dexios, right, 11+1 diadidomai, to transmit, hand down, 73,21; 143,1 diaiônios, eternal, 105,20.29 (both Plato); 137,28 diaireô, to divide, distinguish, 32 diairesis, division, distinction, 10 diakeimai, to be disposed, 64,22; 159,25; 197,9; 198,26.31 diakosmeô, to order, 136,7; 138,31 diakrinô, to distinguish, separate, 10 diakrisis, division, separation, 41,32; 87,8; 93,16; 96,30; 107,1 dialambanô, to separate, 172,15; 197,20 (both m/p) dialegô, to discuss, 24,19; 31,35; 61,4 (all m/p) diallêlos, circular (said of an argument), 45,2.7.26 dialuô, to dissolve, 19 dialusis, dissolution, 123,1; 126,20; 131,17; 144,3; 159,27 diamenô, to last, 37,28; 142,15 diametros, diameter, 26+1 dianoeô, to think, 67,33 (Plato); 78,27 dianoia, reasoning, 44,7; and 270a26 diapempô, to transmit, 112,14; 113,18; 114,36 diaphanês, transparent, 89,1; 90,9; 130,16 diapherô, to differ, disagree, 31 diaphôneô, to conflict, contradict, 116,9; 143,15; 158,26; 159,6; 165,11 diaphônos, in conflict, contradictory, 159,4.23 diaphora, difference, differentia, 66+1 diaphoros, different, 62 diaphtheirô, to corrupt, destroy, 90,12; 103,28 (Plato); 142,6 (all m/p) diarthroô, to articulate, explain, 69,16; 102,15; 166,16 diasapheô, to clarify, 92,30; 194,10 diaphulattô (diaphulassô in LSJ), to preserve, 156,1.4

178

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diasôzô, to preserve, 32,32; 67,13; 85,31; 142,17 diastasis, distance, separation, extension, dimension, 85 diastatos, extended, 105,33; 108,33; 179,2; see also trikhê diastatos diastêma, interval, 34 diastrephô, to twist, 182,29; 184,6 diastrophos, twisted, 184,19.27 diatattô (diatassô in LSJ), to be arrayed, have a position, 86,1; 90,15 (both m/p) diateinô, to contend, put forward, 89,21; 173,1; 191,6 diateleô, to endure, go on, 139,33; 198,19 diathesis, arrangement, condition, constitution, disposition, 18+1 diatithêmi, to be disposed, arranged, 14 (all m/p) didaskalia, teaching, 59,9.27 didaskalos, teacher, master, 84,11; 153,17 didaskô, to teach, 11,15; 25,11; 59,28; 123,17; 131,24; 157,34.35; 165,34 didômai, to give, assign, grant, concede, 54,29; 79,5; 85,19; 87,28; 90,19; 106,24; 107,14 (last 2 Plato); 147,25; 157,7.10; 160,9 dielenkhô, to refute, expose, 46,18; 136,16; 201,4 dierkhomai, to go through, explain in detail, 152,7.8; 162,31 diistêmi, to be at a distance, be separated, be extended, 74 dikaios, right, just, fair, 46,14; 61,21; 64,30; 69,3; 84,29; 158,29; 159,3; 181,34; 183,15 dikê, justice, punishment, 26,20; 69,2; 106,22 (last 2 Plato) diôlugios, endless, grand, 25,31; 70,9 diorizô, to distinguish, be explicit, define, 31,33; 32,1; 54,30; 69,29; 105,26; 135,21; 192,14 dôdekaedron (see dôdekaedros in LSJ), dodecahedron, 12,18.26 dogma, doctrine, opinion, belief, 26,11; 46,12; 126,17; 136,9; 140,9; 141,13 dokeô, to seem, be thought, 86+1 doxa, opinion, belief, view, reputation, 16+1 doxazô, to think, 33,15; 91,8 draô, to act, have an effect, 27

drasis, acting, 98,31; 115,19 drastikos, active, 12 dunamai, to be able, be possible, 87+1 dunamis, power, potentiality, faculty, 59 dunatos, possible, 52 duô, dunô, to set, 20,28; 82,30, 155,15 dusdiaretos, difficult to divide, 76,9.13; 77,26 dusis, west, 154,25.26; 155,9.12.14.15.16; see also dusmê duskherainô, to show scorn, 119,9; 135,26 dusmê, west, 31,11.24; 51,18; 155,13; 188,14.15 (always plural); see also dusis duspathês, not easily affected, 73,10.16.17.18.23; 82,1 (always comparative) eaô, to leave, set aside, pass over, suffer, 31,29; 137,4 (Parmenides); 170,24; 201,5 eidon (see eido* in LSJ), to see, look, 13 eidopoieô, to give form, 16 (all but 1 passive) eidopoios, giving form, 12,17; 168,20.30; 169,24 eidos, form, species, kind, 221+2 eikôn, image, 41,28; 68,13; 95,25.27 eikos, probable, reasonable, 13,2; 36,21; 102,16; see also eikotôs eikotôs, reasonably, 29; see also eikos eilikrinês, pure, 97,6; 170,1; 176,1 eimi, to proceed, go, 43,16; 49,25; 61,20; 150,20; 156,9; 160,5; 163,10; 193,27; 197.9 eipon, to say, 36,18; 71,23; 78,1; 87,12; 93,13; 94,18; 134,19; 194,3; 199,5 (always aorist optative) ekei, there, 25 ekkeimai, to be set out, 55,25; 57,9; 108,2; 165,15; 168,22.29; 169,2 ekkentros, eccentric, 32,8.23; 33,7 ekkheô, to flow out, 39,33; 44,11; 46,35 (all m/p) ekphainô, to show (active), 118,18; to appear (m/p), 96,26; 138,7 ekphansis, manifestation, 55,19; 138,5 ekpiptô, to fall from, 40,18; 47,28; 76,16.17; 78,10; 179,18 ekstasis, unfolding, 95,14; 96,20,

Greek-English Index ektasis, stretching, 15,12; 17,6.14 ektithêmi, to set out, 37,20; 40,9; 42,15; 137,7; 144,2.3; 153,17; 182,30; 184,22; 198,8 ektos, outside, external, outer, 17+1 ektuphlô, to blind, 67,15; 74,5; 101,32 elakhistos, least, 23 elattôn, less, smaller, minor (said of a premiss), 36 elenkhô, to refute, 11 elenkhos, refutation, 135,28; 142,26; 181,17 elleipô, to be deficient, lack, 38,30; 39,7.32; 43,31; 47,26.32; 56,11 elleipsis, deficiency, 56,7.15; 171,19; 173,5 ellipês, deficient, 40,1; 43,28; 45,2 empalin, reverse, in reverse direction, 15 emphainô, to reveal, indicate, 39,21; 91,15; 93,21.30; 118,22; 196,29 empiptô, to fall into, come across, 66,19; 75,13; 136,1 empodizô, to stand in the way, put up obstacles, 58,29; 193,32 empoieô, to emplant, 55,16; 99,1.10 emprosthen, forward, front, earlier, 15,10.14.15; 191,3 enantiologia, contradiction, 58,24; 78,14; 188,25 enantiologos (not in LSJ; Simplicius also uses the word at 131,31 of his commentary on the Physics (CAG 9)), contradiction, 57,14; 58,15 enantioomai, to contradict, be contrary, 59,3; 84,14; 92,31; 146,4; 167,8.24; 172,27; 196,5 enantios, contrary, 991+28 enantiôsis, contrariety, 80+3 enantiotês, contrariety, 112,3; 114,14; 151,7; 154,30; 178,6; 196,29 enargeia, clear truth, certainty, 15,18; 55,12; 116,7 enargês, clear, clearly true, 24 enarmonios, harmonious, 84,32; 97,29; 156,24 endeiknumi, to indicate, 13 endekhomai, to be possible, 44+8 endeô (B), to be deficient, be missing, 22,23; 23,7; 54,6; 65,25 endiatribô, to spend time, 34,12; 184,28 endidômi, to bestow, concede, 10

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endothen, from within, inside, 47,17; 173,28 energeia, activity (dative singular translated ‘actual’ or ‘actually’), 31 energeô, to act, activate, be active, 29 energêtikos, active, 12 engus, close, 82,4; 181,31; 185,25; 186,10.11.20.21.27.31 eniote, at some time, 24,17; 48,25; 68,22(Plato); 70,31; 100,13; 180,28 enistêmi, to object, (perfect active participle translated ‘present’), 15 enkaleô, to charge, accuse, object, 165,4; 170,12; 183,16; 194,21 enklêma, reproach, criticism, 32,30; 130,13 enkuklios, circular, 16 ennoeô, to understand, recognize, realize, 28 ennoia, conception, idea, meaning, 20 ennous, possessing mind, 199,35; 200,8.12 enokhleô, to trouble, bother, 26,2; 49,25; 66,4 enstasis, objection, 24 entautha, here, 76+2 (including kantautha) entheôreô, to see in, 32,9; 88,32 entos, inside, inner, 10 entunkhanô, to encounter, come across, read, 46,14; 48,23; 75,13; 102,16; 135,31(2); 194,18 enulos, in matter, material, 133,22.25; 135,11.18; 167,28 enuparkhô, to inhere, 90,5; 127,31; 169,12 (Iamblichus); 183,29 eoika to seem, be like, 21+4 epagô, to bring in, adduce, add, infer, 25 epakoloutheô to follow, 65,33; 182,17 epamphoterizô, to move in both directions, be both heavy and light, 24,17; 75,4 epanagô, to lead back, 58,32; 118,29 epangellô, to announce, 170,25.27; 171,14 epaniteon, we should return or go on, 38,4; 91,20; 107,25 epeisagô, to introduce, bring in, 90,24; 121,24 epeisaktos, from outside, 83,35; 84,3; 94,23.28; 97,3; 106,28 epekhô, to have, occupy, 76,2; 83,1; 84,19; 85,2

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eperkhomai, to go through, 129,6; 194,2 ephaptô, to touch, 67,8; 86,12; 156,9.14; 195,23 epharmogê, co-ordination, fitting, 60,8; 184,21 epharmottô (epharmozô in LSJ), to coincide, fit, apply,18 ephesis, desire, 55,18; 65,10; 67,25 ephetos, desired, 65,17.23.30.32; 67,8.10.29 ephexês, next, following, 27 ephiêmi, to desire, 10 ephistêmi, to notice, note, understand, 40 epiballô, to contribute, accrue, 49,19; 96,23 epibolê, idea, proposal, 44,8; 132,3 epideiknumi, to show, 33,21; 46,6; 143,17; 178,28 epidekhomai, to admit, receive, 38,29; 39,17; 43,12; 44,6; 153,31; 169,14.17 epiginomai (epigignomai in LSJ), to accrue, supervene, 55,16; 76,23; 98,4; 128,7; 129,27; 130,25 epigraphô, to sign, 49,11; 71,8; 119,7; 136,8 epikheirêma, argument, 30 epikheireô, to try, argue, 17 epikheirêsis, argument, 40,22; 146,12; 150,15; 152,22.24.32; 171,9; 176,31; 194,24 epikrateia, predominance, 42,4; 85,12.28.29; 86,29; 91,12 epikrateô, to predominate, 21+3 epikuklos, epicycle, 32,7.24; 33,2.6.7.8; 36,23 epilanthanô, to forget, 135,4; 162,34; 173,17; 193,4; 194,34 epimenô, to continue, remain, 35,28; 98,1; 164,22 epinêkhomai, to float, 34,27; 66,23 epinoeô, to conceive, think, 47,25; 49,25; 79,20 epinoia, idea, thought, concept, 46,33; 49,10; 168,16; 179,2.6.8.18 epipedos, plane, flat, 10 epiphaneia, surface, 16 epipherô, to add, 16,18.22; 37,13; 69,6; 112,15; 152,24 epipolaios, superficial, 111,9; 133,1; 135,15; 140,7; 159,23; 184,31; 196,34

epipolazô, to rise to the top, rise above, lie at the top, lie above, 26+1 (see the note on 66,19) episêmainô, to assert, affirm, signal, 108,23.28; 109,8; 112,12; 163,30 (all m/p) episkeptomai, to investigate, 51,29; 198,12; 199,10; and 268b13 episkopeô, to investigate, consider, 67,24; 123,22; 129,21; 139,13; and 269b20 epistasis, attention, care, 45,8; 48,22; 191,5 epitêdeios, suitable, suited, 13 epitêdeiotês, suitability, 97,30; 98,6; 104,27; 128,4; 138,3; 200,7 epiteinô, to increase, intensify, 81,27; 114,30; 115,11 (all m/p) epiteleô, to be brought to completion, be brought about, occur, 12 (all m/p) epithumeô, to desire, 70,15; 78,5; 200,33 epizeugnumi, to join, 146,28; 148,15; 176,22; 179,4; 180,30; 181,35; 182,11 epôphelês, beneficial, 21,24; 90,1 epos, verse, line, 137,2; 140,31 êremaios, gentle, 83,34; 84,1 êremeô, to rest, 21,29; 22,6; 34,29; 54,28 êremia; rest, 22,17; 158,6; 159,12 ergon, work, 106,9 (Plato); 185,2 erkhomai, to come, move, 22,5; 26,22; 98,12; 103,25.26; 150,20; 194,14 erô, to say, mention, 79+2 (usually m/p); see also rhêteon erôtaô, to ask, 13 eskhatos, last, extreme, 26 (4 Plato)+1 ethelô, to want, wish, will, 27,15; 31,30; 106,8.10.11.22 (all 4 Plato); 108,32; 162,8 ethô, to be accustomed, 137,28; 181,21 ethos, custom, 96,7; 101,30; 140,26; 168,25 etos, year, 105,24; 113,21 (Melissus); 117,26; 118,1; 140,12 euagês, luminous, 20,24; 54,16; 58,29 euêtheia, goodheartedness, 55,30; 56,8.10 eukleia, renown, 26,4.14 eukolos, ready, self-satisfied, 26,12; 66,15 eulabeia, caution, care, 18,15; 48,24 eulogos, reasonable, 15 (1 Aristotle)+2

Greek-English Index eutelês, paltry, lowly, 59,15; 74,3 euthetizô, to order, 95,14.15 euthuporeô, to move in a straight line, 19 (all m/p) euthus, straight, 443+15 exaiphnês, instantaneous, 119,29; 120,1.6.7.18.31; 121,2 exaireô, to remove, 107,29 (active); to transcend, 24 (all m/p) exairesis, transcendence, 20,30; 91,28 exairetos, transcendent, 26,6; 118,20 exaptô, to attach, ignite, 117,17; 131,5 exartaô, to be dependent upon, 137,28; 143,26 (both m/p) exêgeomai, to explain, 16,22; 181,11; 194,10 exêgêsis, interpretation, exegesis, explanation, 46,31; 47,5; 57,20; 79,14; 107,20; 170,24; 176,34; 189,6 exêgêtês, commentator, explainer, 11 exerkhomai, to depart, come from, 77,31; 108,35 exisazô, to be equivalent, 12 existêmi, to depart, leave, 13 exô, outside, external, 13 exôtatô, outermost, 39,13; 76,2; 82,20; 178,21 exôthen, from outside, external, 13 gê, earth, 157+7 gelastikos, risible, 31,3(2).4 genesiourgos, involved in coming to be, 31,28; 33,23; 102,1; 115,12.13 genesis, coming to be, genesis, 128+1 genêtos, coming to be, generated, 57 genikos, generic, 97,22; 131,19.27 gennaô, to generate, 12 genos, genus, 21 genus, jaw, 29,16.18.19.20(2) geôdês, earthen, 17,20; 40,20; 68,22 ginomai (gignomai in LSJ), to come to be, occur, be generated, 540+4 ginôskô (gignôskô in LSJ), to learn, know, realize, understand, 14 glôtta (glôssa in LSJ), tongue, 47,29; 48,2 glukutês, sweetness, 97,25; 174,33 gluphô, to carve, 126,28.30(2) gnôrizô, to know, learn, 67,21; 134,5; 187,22.23 gnôsis, understanding, cognition, 55,10.16; 59,28; 163,2

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gonimos, generative, 96,16; 137,29 gônioomai, to have angles, 129,28; 130,6 grammatikos, literate, 29,10.12; references to Philoponus as a grammarian at 49,10.20; 56,26; 70,34; 71,8; 73,10; 74,5; 119,7; 156,26; 162,20; 166,3 grammê, line, 57+1 grammikos, linear, 11 graphô, to write, draw, 63 gumnazô, to do exercise, train, 59,8; 159,4 haireô, to choose, grasp, 22 halis, enough, 74,11; 103,1 haliskomai, to be caught, 157,34; 165,34 hama, simultaneous, at the same time, together, 33 hamartanô, to go wrong, 26,25; 30,19 haplôs, absolutely, without qualification, simply, 32 haplotês, simplicity, 198,30; 200,6 haplous (haploos in LSJ), simple 353+30; see also haplôs haptô, to be connected to, touch, 37,18; 95,33; 107,32 (all m/p) haptos, tangible, 14 harmonia, harmony, 121,20; 125,12 (both Aristotle); 194,3 harmozô, to harmonize, fit together, tune, 106,10 (Plato); 121,17.18(2); 125,9.10.11 (last 6 Aristotle); 178,23 hêdê, already, thereby, 39 hedra, seat, abode, 72,13.22 hêgeomai, to believe, consider, judge, 69,7 (Plato); 107,6; 116,11.16; 176,31; 185,2; see also hêgoumenon. hêgoumenon (see hêgeomai in LSJ) , antecedent, 20; epi ta hêgoumena translated ‘toward the west’ at 193,14 and 197,3 hêkistos, least, 95,32; 107,32 hêliakos, solar, of the sun, 14,24; 113,3.18.19; 115,7; 135,3 hêlios, sun, 26 helix, helix, 13,25.30; 14,10.13.20.24.26.29; 17,9.17 helkô, to drag, draw, weigh, 36,20; 37,26; 68,16.22; 74,20; 162,4 hêmera, day, 12 hêmikuklion (see hêmikuklios in LSJ), semicircle, 54+3

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hêmisphairion, hemisphere, 155,14; 188,14; 196,1; 197,6 hênoô, to unify, 11 (all m/p) henôsis, unification, unity, 10 hepomai, to follow, 29; hepomenon translated ‘consequent’ 16 times; epi ta hepomena translated ‘toward the east’ at 193,15 and 197,3 hermogluphos, carver, 126,30; 127,1 heteros, other, different, 93+14 (including thateros) heterotês, difference, 109,13; 174,22 heterôthen, external, 94,24; 103,32; 140,14 hetoimos, easy, 51,11; 138,7 hêttôn (hêssôn in LSJ), less, 31+1 heuriskô, to find, 13 hexês, next, 20 hexis, state, 16+1 hiêmi, to move, 34,1; 65,26 (both m/p) hieros, holy, sacred, 141,16.22.25 hikanos, sufficient, 75,11; 106,17; 125,27; 140,20; 170,7; and 269b21, 270b12 hippos, horse, 29,34; 48,32; 87,9; 98,5.7; 123,19 histêmi, to stop, stand still, 138,26; 151,14.31; 154,5.21; 197,13.17(2).18.21.22 historeô, to recount, report, 87,21; 117,28; 139,30 holikoteron (see holikos in LSJ), bigger whole, 36,34(2); 37,2 holôs, in general, (not) at all, 58 holos, whole, entire, 145+5; see also holôs holotês, entirety, whole, 45 homalês, uniform, 14,13; 36,29.33 homoeidês, of the same kind, species, or form, 27,2; 30,3.4; 168,11; 177,10.35; 179,31; 180,3.4 homoiomerês, homoiomerous, 11,28; 14,20.21.22(2); 16,15; 24,23; 48,4; 110,16 homoios, similar, like, 33; see also homoiôs homoiôs, similarly, in the same way, equally, 58+4 homoiotês, similarity, 73,3; 86,7; 95,26; 96,10 homokentros, homocentric, 32,7.17; 33,7 homologeô, to agree, accept, 40

homologoumenôs, by agreement, 57,11; 168,22; 192,18 homophuês, having the same nature, 24 homou, together, at the same time, 48,30; 112,1.2 hopôsoun, to any extent, in every way, 36,28; 93,10.11.19; 130,22; 200,31 hopou, where, 47,26.27; 67,30; 87,7; 131,4; 174,26.28 hôra, hour, season, time, 78,5; 83,11; 118,3; 142,30.33 horaô, to see, 31+2; the imperative hora is translated ‘notice’ 11 times horatos, visible, 10 horismos, definition, 24 horizô, to define, determine, 72 hormaô, to start, desire, 44,14; 102,17; 152,17; 195,6 (all m/p) hormê, desire, 27,15; 79,3 horos, term, definition, boundary, 39,6; 43,25; 47,28; 164,3.12.19.23; 169,20.32 hualos, glass, 89,1; 130,15 hudatinos, watery, 88,14.15 hudôr, water, 96+4 hugiês, sound, correct, 30,32; 70,20; 163,22; 190,30 hugrainô, to moisten, 99,2; 112,32; 160,5 hugros, moist, 15 hugrotês, moistness, 13 hulê, matter, 62+1 hulikos, material, 13,16; 14,6; 84,20; 100,10; 168,1 hupantaô, to meet, encounter, respond to, deal with, 17 hupantêsis, response, 14,4.9; 165,15 huparkhô, to belong, attach, hold, be, exist, 108 huparxis, reality, 43,23; 162,13 hupeikô, to yield, 75,31; 76,10 hupekkauma, hupekkauma, 35 hupenantios, contrary, 153,30; 198,31 huperanekhô, to be superior to, 55,22; 69,19; 86,6; 91,2; 114,38; 118,21; 134,1 huperballô, to exceed, 56,11; 83,32 huperbolê, excess, 56,7.15; 81,9; 82,8; 171,18; 172,36; 173,5 huperekhô, to be superior to, 121,4; 172,19; 176,6; 199,8

Greek-English Index hupêresia, service, 26,5; 79,28 (Plato) huperkeimai, to lie above, 158,16; 161,18; 162,12 huperkhomai, to move down, 94,26; 95,20.27; 97,15; 103,29 huperokhê, superiority, excess, 10 huperphuês, hypernatural, 38,2; 44,27; 46,3; 59,1 huperteros, superior, 51,25; 65,23; 199,29.32 hupertrekhô, to overtake, be superior to, 70,32; 93,21 hupexerkhomai, to withdraw, 76,11; 77,29 huphistêmi, to exist, give existence; to sink below, sink to the bottom, 70+1 hupoballô, to present as one’s own progeny, 25,24; 45,20 (both m/p) hupodekhomai, to accept, receive, 45,2; 94,21; 95,23; 115,8; 200,2 hupodêma, sandal, 151,20; 198,2; and 271a32 hupodokhê, receptacle, 98,10; 141,24 hupokeimai, to underlie, be a substratum, lie under, be assumed, be a hypothesis, 91+4 hupolambanô, to suppose, assume, accept, 16+4 hupolêpsis, conception, 116,13.23; 117,5; and 270b6 hupomenô, to endure, undergo, 19 hupomimnêskô, to recall, remind, mention, 15 huponoeô, to suppose, 140,23; 147,23 hupopherô, to bring or carry down, 102,30; 118,7; 143,9.29 (all m/p) hupopodismos, retrogression, 32,20; 36,31 hupospaô, to take away from under, 34,30; 158,15 (both m/p) hupostasis, existence, 20 hupostatikos, giving existence, 94,11.26(2) hupothesis, hypothesis, 48 hupothetikos, hypothetical, 18,10.12.13.15.16; 62,31 hupotithêmi, to hypothesze, make a hypothesis, 42+1 hupsos, elevation, 37,23; 54,8 husteros, later, posterior, 15+1 idea, form, kind, idea, 10 idios, one’s own, proper (the

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substantive is often translated ‘proprium’ or ‘specific feature’), 36 idiotês, specific feature, specific character, 74,8; 88,17; 89,30; 109,9; 113,19; 135,25; 184,14; 199,3 idou, look! 30,32; 78,2; 88,10; 170,4 ikhthus, fish, 89,7.9; 90,4.18; 200,29 isazô, to be equal to, 106,18; 154,15 iskhô, to have, 37,1.11; 55,4; 102,25; 160,17; 175,1 iskhuô, to be able, have the strength, 32,21; 66,28; 121,9; 183,24; 188,17 iskhuros, strong, 78,2; 83,29; 154,22; 156,2; 197,31 (always comparative) isôs, perhaps, 12 isosthenês, equally strong, 81,15.19; 151,13.14.20; 155,2.31; 196,10; 197,12 isostoikhos, co-ordinate, 196,18.19 isotês, equality, 56,12.15; 83,32; 84,4; 173,7 isteon, one should understand, one should know, 20,10; 27,11; 29,8; 32,15; 120,23; 167,27 ithunô, to guide, 138,34; 142,19; 143,78; 172,22 (all m/p) kaiô, to burn, 81,21; 119,3 kakia, vice, 163,1.4.8 kakos, bad, incorrect, 57,5; 77,28; 106,11; 184,3; see also kheirôn kakoskholos, mischievous, frivolous, 37,16; 59,13; 131,21 (all kakoskholôs) kakourgeô, to be malicious, 122,21; 182,26.28(2); 183,15 kaleô, to call, 46 (1 Plato) +1 kalos, correct, right, good, beautiful, 39+2 kamnô, to wear out, get weaker, 53,10; 98,9 kampsis, bending, 15,12; 17,7.15 kanôn, straight-edge, rule, 139,14;184,5.6.19.25 kardia, heart, 73,11.18(2) katabainô, to sink, descend, 35,21; 37,32; 51,17; 119,13; 155,25 katalambanô, to apprehend, reach, 33,10; 34,26; 183,31 katamênion (see katamênios in LSJ), katamênia, 101,25(2); 102,27; 110,6.7; 127,2 katametreô, to measure, 181,11; 182,32.34; 183,4.5.6.10; 187,21

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kataphasis, affirmation, 28,20.22.27.29; 29,12; 127,21.22; 129,2; 174,1 katapherô, to move down, 37,11; 54,28 (m/p) kataphronêsis, disdain, 26,29; 84,29 kataplêttô (kataplêssô in LSJ), to astound, strike into perplexity, 25,30; 136,8 kataskeuastikos, establishing, 66,13; 144,23 kataskeuazô, to establish, construct, 16 kataskeuê, argument, 12,2.7; 191,22 kataskeusma, artifact, 180,9.10.11; 181,18 kataspaô, to drag down, 54,19.20; 64,6; and 270a9 (all m/p) katastasis, condition, 95,11.19 katateinô, to stretch out, 58,18; 67,6; 68,19; 71,19; 162,20; 179,29; 186,30; 190,19 katêgoria, category, 123,30; 130,11; the plural occurs 18 times as the name of the first treatise in the Aristotelian corpus katêgorikos, categorical, 18,16; 54,2; 111,19 katêgoroumenon (see katêgoreo in LSJ), predicate, 62,15.18 katharos, pure, refined, 25,31; 84,19.23.33; 85,9; 98,14; 119,22; 131,12; 180,23 kathelkô, to drag down, draw down, 86,7; 161,7 kathistêmi, to stand, 96,14.22 katholikos, universal, general, 41,33; 189,8 katholou, universal, 14 katô, down, lower, below,155+16; epi to katô translated ‘downward’; see also katôtatô and katôterô katôtatô, lowest, furthest down, 61,12; 66,30 katôterô, lower, 66,27; 76,3 katôthen, from below, 66,23; 190,9; 197,19 kaustikos, burning, 81,7.8; 82,9.26 keimai, to lie, be a premiss, 50,3; 108,21; 168,26; 182,24; 200,29.30 kenodoxia, empty-headedness, 143,15; 157,9 kenodoxos, empty-headed, 26,31; 90,13; 131,32

kenoô, to empty, 161,7.10 (both m/p) kenos, empty, void, 14 kentron, centre, 50 kephalaion (see kephalaios in LSJ), chapter, 32,1; 75,16; 165,31; 190,21 kephalê, head, 47,12; 48,28; 68,12.13; 89,6; 135,4 khalkos, bronze, 183,26; 184,9.13 kharaktêrizô, to characterize, 85,11; 128,18.23; 130,9; 149,8; 171,31 kheimôn, winter, 83,5.9 kheir, hand, arm, 47,29; 48,1; 79,26; 90,17; 141,17 kheirôn, worse, 57,19; 63,17; 72,11; 87,21; 143,9; 189,7 khôra, space, room, region, place, 43,6; 65,33; 72,14; 85,19; 97,4; 105,3; 158,16.20; 161,9.10 khorêgeô, to furnish, 55,20; 143,25 khôreô, to flow, spread, move, 34,29; 67,10; 85,24.26; 98,11; 127,10; 170,25 khôrion, passage, 57,20; 126,4; 129,15; 194,2 khôrizô, to separate, 23,8; 24,18; 33,32; 41,11; 55,21; 86,21; 143,19; 169,21 khraomai (see khraô in LSJ), use, 33 khreia, need, use, 14+1 khrêstos, good fellow (a way of referring to Philoponus), 45,27; 66,15; 83,25; 170,11; 176,13; 188,2 khrôizô, to colour, 85,18; 126,14 (both m/p) khrôma, colour, 32 khronikos, related to time, 94,16; 95,21; 97,14; 122,16.32 khronos, time, 81+3 khumos, flavour, 11 kinêma, bit of motion, 43,20; 44,23 kineô, to move, cause motion, 403+5, (usually m/p) kinêsis, motion, change, 870+29 kinêtos, moving, changing, 13,4(2); 27,27 (Aristotle); 40,23.25; 132,23; 134,7 (last 2 Aristotle); 135,13,21; 139,10; and 268b15 (usually kinêtos kata topon) klaô, to break, 171,10; 172,12 (both m/p) kleinos, renowned, 140,2; 200,28 klêroô, to assign, 55,24; 85,6 (both m/p) koilos, concave, hollow, 26+1

Greek-English Index koinôneô, to share in, 20,9; 96,19; 105,1 (Plato) koinos, common, 48 koinotêta, common feature, commonality, 90,7; 134,18; 199,4 kôlon, limb, 15,12; 17,7.15 kôluô to prevent, 32 komêtês, comet, 20,27; 89,14; 164,34 kopros, crap, dung, 119,13; 136,1 korax, crow, 42,17; 142,29 korennumi, to fill, 94,7; 155,35 (both m/p) kosmos, cosmos, 80 kouphos, light, 112+5 kouphotês, lightness, 50+3 krateô, to dominate, master, rule, overpower, 24+1 kreittôn (kreissôn in LSJ), better, 13 krinô, to judge, 11 kritêrion, standard, 183,34; 184,1.12.15 krustallos, ice, 37,11; 76,25 kubos, cube, 12,20; 45,12; 48,8; 51,4 kuklikos, circular, 38 kuklophoreomai, to move or be moved in a circle, 32,14; 38,14; 58,7; 199,2.7.34 kuklophorêtikos, moving in a circle, 60 kuklophoria, motion in a circle, 16 kuklos, circle, 513+29 (the dative kukôi often translated ‘in a circle’) kulindrikos, cylindrical, 13,30; 14,13 kulindros, cylinder, 14,15.19 kurios, authoritative, strict, 16; see also kuriôs kuriôs, in the strict sense, 61 kurtos, convex, 21+1 lambanô, to take, assume,129+3 lampros, bright, 89,4; 90,2.10 lankhanô, to receive, 95,33; 138,7.20.27 lanthanô, to escape notice, 90,14; 125,9 lêgô, to cease, 141,5 (Empedocles); lêgon translated ‘consequent’ at 18,9; 63,33; 145,26 leiotês, smoothness, 89,17; 97,25 leipô, to be left, remain,119,19.28; 120,5; 163,33; 174,1 (all m/p) lêmma, lemma, premiss, 18,12.16; 42,7; 59,32; 60,5.9; 115,32; 176,27 lepis, scale (of a fish), 89,7.9; 90,4.18

185

lêpsis, assumption, taking, 28,19; 30,18; 146,22 leptomerês, having fine parts, 30,35; 84,18.23 leptos, fine, 118,22; 161,9; 162,1 leptunô, to thin, 54,7; 161,6 lêreô, to babble, utter nonsense, 30,29; 35,1; 136,14 leukainô, to make white or light, 127,11.13(2).16; 159,24.29; 160,9.10.18 leukansis, becoming light, 158,3; 159,15 leukos, white, light, 26 leukotês, whiteness, light colour, 97,24; 127,12.16; 174,33 lexis, words, text, passage, 24 limnazô, to be stagnant (said of the air in the vicinity of the earth), 20,24; 57,27; 58,27 lithinos, made of stone, 51,9; 137,15 lithos, stone, 27,32(2); 89,1; 126,28.30; 127,1; 137,16; 142,11 logos, argument, discussion, doctrine, theory, account, principle, what is said, words, speech, treatise, statement, proposition, ratio, role, 216+6 loipos, remaining, other, next, 44 loxos, oblique, 17,7.16; 36,21 luô, to dissolve, 17 lusis, dissolution, 26,17; 51,14; 105,16; 109,4; 192,17 lutos, dissoluble, 106,10; 107,2 makarios, blessed, 79,18; 80,9.13; 96,18; 104,33; 140,31; 184,29 makariotês, blessedness, 46,13; 55,17; 104,30 makros, long, lengthy, 49,25; 58,17; 68,7; 78,20; 126,5; 142,25; 169,27; 178,11; 185,27 malakotês, smoothness, 87,30; 89,17 malista, most, most of all, especially, 57+2 manoô, to make rarer, 35,22; 36,13; 37,4.8.24.25; 112,34 (all m/p) manthanô, to learn, 14 martureô, to bear witness, cite as evidence, corroborate, 116,23; 126,11.13; 140,2.4; 199,31; and 270b5 marturia, evidence, confirmation, 70,3; 116,12; 126,12; 140,1

186

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martus, witness, 88,17; 105,28 mataios, pointless, 142,7; 200,27 matên, pointless, 47+4 mathêma, mathematical thing, 178,14 (on which see the note),30 mathêmatikos, mathematical, 25,12.14.18.19.20(2); 42,7; 46,9.23 makhê, conflict, 193,12.26.30 makhêtikos, conflicting, 152,16; 197,9 makhomai, to conflict, fight, 25 megas, great, 22; see also meizôn megethos, magnitude, size, 46+3 meionexia, being overborne, having less than one’s share, 98,6; 171,20 meioô, to diminish, 27 (all but 1 m/p) meiôsis, diminution, diminishing, 13 meizôn, greater, 38 (translated ‘major’ at 92,9.17 and 191,23) mêketi, no longer, not, 12; see also ouketi mêkos, length, 48,7.10.12 mêkunô, to go on at length, draw things out, 122,33; 132,26; 143,31; 169,27 melainô, to make dark, 159,25.29.33; 160,10.11 melansis, becoming dark, 158,3; 159,15 melas, black, dark, 18 mellô, to be going to, 15+1 memphomai, to censure, complain, find fault, object, 25,11; 47,27; 78,21; 90,11; 174,11; 178,11; 188,6 menô, to remain, endure, rest, 67 mêpote, perhaps, 22 merikos, partial, particular, 36,34.35; 37,1; 107,18 merismos, division, being divided, 95,1; 97,6 meristos, divided, having parts, 95,2.5 merizô, to divide (into parts), 94,10; 95,15; 104,14; 140,16; 188,30; 189,4 meros, part, 141+1 mesêmbriazô, to be at noon, 82,29.30 mesos; intermediate, 137+16; to meson translated as ‘centre’ or ‘middle’, apo tou mesou, ‘from the centre’, epi tou mesou, ‘to the centre’, peri tou mesou ‘around the centre’, pros to meson, ‘toward the centre’. mesotês, mean, middle, 48,6; 86,16 metabainô, to transform, pass, 33,5.6.10; 103,26; 105,4; 190,12; 201,2

metaballô, to change, 116+2 metabasis, transformation, transition, 103,25; 131,8; 191,7.8 metabatikos, changing, 200,3.4 metablêtikos, involving change, 114,7; 115,5 metabolê, change, 69+1 metadidômi, to transmit, exchange, 37,1; 83,17; 113,1 metadosis, transmission, exchange, 112,29; 113,1.2; 115,4 metalambanô, to take on, change, 54,20.22.26; 98,29; 127,26; 128,14; 131,23 metalêpsis, reception, participation, 88,23.24; 112,29; 196,17 metapherô, to transfer, 139,7.19 metaxu, between, intermediate, 53 meteimi (B), to turn, investigate, pursue, 16,5; 134,4 (2, both Aristotle); 166,2 metekhô, to share in, participate in, 63 meteôrizô, to raise 22,28; 68,18 (Plato) methexis, participation, 96,23; 97,3; 143,25; 164,32; 165,2 methistêmi, to change position, 71,28; 72,12; 98,17; 161,15 metreô, to measure, 33 metrêtikos, measuring, 44,15.21 metrios, reasonable, 43,13; 155,7; 164,33; 170,10; 184,31; 197,16 metron, measure, 28 mignumi (meignumi in LSJ), to mix, 17,10.13.16; 130,23; 170,2 (all m/p) mikros, small, 39,29; 64,2; 65,1; 68,20.24 (both Plato, smikros); 166,8 (Aristotle); and 270a5 miktos, mixed, 17+4 mimeomai, to imitate, 95,23; 106,20 (Plato) mimêsis, imitation, 105,29 (Plato); 141,23 mimnêsko, to remember, recall, 102,21; 104,32; 191,20 (all m/p) mixis, mixture, 17,12; 24,14; 40,19; 42,2; 84,17; 86,33; 145,9; 269a29 mnêmê, record, 64,28; 116,14; 117,24; 142,13.35; 270b14 mnêmoneuô, to think of, mention, 12,12; 23,23; 37,29; 58,1 moira, portion, fate, 84,21; 106,4.13; 107,4 (last 3 Plato)

Greek-English Index monas, monad, 29,28.32.33; 78,27; 93,15 monê, rest, 54,29.32; 96,2 monimos, stable, lasting, 21,21; 95,30; 111,10 monoeidês, of a single kind, uniform, 14,23(2); 163,6 monos, alone, only, 165+4 morion, part, portion, 74+6 morphê, shape, 126,29.31; 137,15.16 mousikos, musical, 13 (mostly Aristotle) murias, ten thousand, 117,26.27 murioplasios, ten thousand times as much, 81,25(2) murios, multitude, ten thousand, 113,21 (Melissus); 134,21; 174,23 naos, temple, 141,16.22; 142,4; 200,32 naus, ship, 127,2; 136,21 neanieuomai, to act childishly, brag childishly, 26,11; 67,23; 90,21 neazô, to be renewed, 151,29; 152,21 Neikos, Strife, 140,27 (Empedocles); 141,2 (Empedocles), 7 nêkhô, to swim, 66,10; 200,29 neos, new, young, 46,11; 136,10; 201,7 noeô, to think, conceive, know, 58,25; 72,14; 137,5 (Parmenides); 155,18; 165,16 noeros, intellectual, 80,12; 116,28 noêsis, thought, understanding, 104,6 (Plato); 106,6; 121,9; 200,3 noêtos, intelligible, 12 nomizô, to think, believe, 94+2 noos, mind, 13 oida (see eidô B in LSJ), to know, 33; see also isteon oikeios, proper, appropriate, one’s own, 73+1 oikeiotês, close relation, 20,25; 132,9 oikia, house, 125,13.14 (both Aristotle); 129,9.16.17 (last 2 Aristotle); 132,9(2) oiomai, to think, 118 okneô, to shrink from, 88,28; 90,28; 177,17 oligos, few, 33 (frequently in temporal expressions such as ‘a little while ago’ (pro oligou) or ‘shortly hereafter’ (met’ oliga)) omma, eye, 74,5; 75,2; 141,21

187

onkos, mass, 81,24.28; 82,3; 268b12 onoma, word, name, 32+2 (including tounoma) onomastos, famous, 200,31,33 onomazô, to call, name, mention, 12,25 (Xenocrates); 30,18; 51,31; 87,16.25 (Xenocrates); 123,11; 125,9 (Aristotle); 129,26; 151,26; 270b25 ontôs, genuinely, 18 (5 Plato) opheilô, to be necessary, 39,24; 110,25; 152,7; 196,25 ophthalmos, eye, 47,13; 102,1 opisthen, back, backward, 15,10.14.16; 130,3 (Aristotle) opisthios, back, 151,8; 271a27 opsimathês, learning late, 29,7; 140,5; 159,3.7 opsis, vision, 130,17; 144,19 optikos, visual, 184,4.17.23 organikos, organic, 16,15.33; 110,17.29 organon, tool, 16,16; 53,18 oros, mountain, 142,11.13.30 orthos, correct, right, 29,11.17; 66,17; 85,20; 108,28; 132,29; 134,4; 176,10 (last 3 Aristotle); 270a20; all but 85,20 orthôs osteon, bone, 73,18; 78,2; 110,15 ôtheô, to push, 15,17; 53,14 (both m/p) ouketi, not, no longer, 32; see also mêketi ouranios, heavenly, 125 ouranos, heaven, heavens, 283+1 ousia, substance, 222+3 ousiôdês, substantial, 113,26; 127,10.32; 160,19; 163,32; 165,24.28; 167,20 (kat’ ousian also translated ‘substantial’) ousioô, to give substance, 85,11.14; 94,3; 130,18 (all m/p) paideuô, to educate, 26,2.23; 36,28 (all m/p) pakhutês, thickness, 65,21; 135,1 palai, long ago, 81,5; 82,6; 86,28 (all 3 Aristotle); 156,3 palaios, ancient, old, 26,4.14; 136,10 palin, again, 106+1 pampan, completely, entirely, 78,27 (Aristotle); 106,2.12; 107,3.33 (last 3 Plato); 109,2.5 pampolou, very, 185,26; 186,28 panourgia, knavery, 55,30; 56,8.9; 133,19.20

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pantakhothen, in every direction, everywhere, 12 pantakhou, everywhere, always, 19 pantapasi, completely, entirely, 81,20; 96,21; 105,2.5; 136,26; 165,13 pantê (pantêi in LSJ), in any way, in every way, 12 pantelôs (see pantelês in LSJ), completely, entirely, 16 pantôs, always, certainly, 77 panu, completely, very much, 49,20; 83,33; 86,10; 133,25.28; 176,28; 180,32; 183,32 paradeigma, example, paradigm, 52,3; 95,26; 105,20.21 (both Plato); 125,23; 173,6; 177,12; 184,22 paradekhomai, to accept, 12,15; 115,31 (both Plotinus) paradidômi, to transmit, hand down, present, 14+2 paraginomai (paragignomai in LSJ), to accrue, supervene, 102,29; 200,8.9 paragô, to bring in, introduce, bring into existence, produce, 29 paragraphô, to quote, 12 paraiteomai, to deny, ask to be allowed, refrain from, 69,9; 87,9; 89,2; 90,1 parakeimai, to lie together, 67,9.10 parakmazô, to decline, 43,22; 142,33 parakmê, decline, 118,7; 142,28 parakoê, misunderstanding, 135,15; 139,9 parakoloutheô, to understand, 11 parakouô, to fail to understand, misinterpret, 33,2; 90,26 paralambanô, to take, accept, use, 12 paralattô (paralassô in LSJ), to vary, 25,14; 73,31; 74,13; 118,1; 143,2; 174,5 parallaxis, difference, deviation, 83,2; 184,21 parallêlogrammon (see parallêlogrammos in LSJ), parallelogram, 14,18.19 parallêlos, parallel, 14,16; 24,27 parapherô, to bring forward, to move in the opposite direction, 51,15; 107,23 paraphrasis, paraphrase, 68,8; 176,33; 188,30 paraplêsios, similar, 89,18; 122,31 parapodizô, to undermine, 75,4; 110,31

paraskeuô, to construct, prepare, 137,22; 139,34; 193,29 parasunaptikos, causal, 18,11.14; 117,15 paratasis, extendedness, duration, 10 parathesis, setting out, 13,13; 70,9 paratithêmi, to set out, 25 paratribô, to rub, 124,15; 131,5 pareidon, to disregard, 26,2; 32,25 pareimi, to be present,19,16.19(2); 38,31; 61,2; 127,8; 138,9; 269b21 parekhô, to provide, supply, furnish, 25,34; 81,6; 93,27; 94,16; 136,9; 151,20; 156,22; 187,22; 194,5 (all but 136,9 m/p) parerkhomai, to come into existence, go past, 34,28; 64,28; 73,8; 105,13; 120,19; 140,13; 142,8; 270b13 (perfect active participle translated ‘past’) parexetasis (not in LSJ; see Lampe (1961)), comparison, 33,18; 64,20 pariêmi, to leave out, omit, 40,9; 63,11; 133,24; 146,8 paroimia, saying, 142,27; 191,1 parousia, presence, 125,28 (Aristotle); 127,9 paskhô, to undergo, be affected, be acted on, 62+1 pathêtikos, passive, involving being affected, 35 pathêtos, subject to affection, suffering, 74,10; 78,11 pathos, affection, 47+2 pauô, to cease, 22,29; 156,3; 197,9 peiraô, to try, 26 (all m/p) peisis, being acted on or affected, 90,32; 98,31; 115,19; 159,31 pêkhus, measuring stick, 11 perainô, to be finite or limited, reach a conclusion 40+3 (all but 1 m/p) peras, limit, 53+1 peratoô, to limit, 27,21; 31,27; 185,6 (all m/p) periagô, to carry around, 11 periagôgê, revolution, circuit, 37,24; 47,24 periballô, to put around, entangle in, 47,10; 78,14 peridineô, to revolve, 96,4; 109,12 periekhô, to embrace, contain, surround, 41,10; 71,4; 72,1.10; 81,7; 169,19; 173,23

Greek-English Index periektikos, containing, embracing, 41,9; 89,19 perigeios, close to earth, at perigee, 32,11.20; 36,23; 113,10 perigraphô, to draw, 14 (applied to curved lines and pairs of points) perikheô, to spread around, 47,2.7 (both m/p) periklaô, to break, 145,25; 171,3 (both m/p) perikrouô, to sound out, 157,21; 194,7 perilambanô, to contain, include, 39,4; 71,30 perileipomai, to remain, 107,7; 116,9; 165,28 perimetros (hê), perimeter, 180,16.18; 186,12.14 periodos, revolution, 43,18; 44,10 periousia, superfluity, 52,24; 149,25; 186,26; 190,26; 194,9 (all ek periousias) periphereia, arc, circular arc, circumference, 121 peripherês, circular, curved, 21+4 peripherô, to carry around, 19,27; 50,20; 51,7; 142,26; 150,12 periphora, revolution, 36,1; 45,18; 112,14; 191,8; 196,13 perittos (perissos in LSJ), superfluous, odd, 133,26; 134,16; 165,3.8; 174,22.35; 177,12 perix, peripheral, surrounding, 68,4; 69,4 (Plato); 82,25; 177,15.17.27; and 269b7 phainô, to be obvious, to be observed, to appear, 63+4 (all m/p) phaios, grey, 75,1; 127,18 phaneros, evident, 25,1; 49,29; 61,7; 125,13; 129,12; 150,17; 170,10; and 269a30, 269b19, 270b3,26 phantasia, imagination, imagining, 39,4; 66,15; 84,13; 87,11 phasma, appearance, 20,28; 36,2; 89,14; 164,34 pherô, to move, 129+9 (almost all m/p and including 10 occurrences of the imperative phere) philomathês, loving learning, eager to learn, 84,12; 130,4; 131,32; 158,29; 159,2; 166,16; 200,28 philoneikeô (philonikeô in LSJ), to be contentious, strive for victory, 11 philoneikia (philonikia in LSJ),

189

desire for victory, contentiousness, 26,19; 90,13; 157,12; 178,28 philoneikos (philonikos in LSJ), victory-loving, contentious, 74,4; 143,14 philosophia, philosophy, 82,11; 90,24; 140,2; 200,28 philosophos, philosopher, philosophical, 18,15; 26,11; 55,9; 58,34; 69,13; 132,16; 143,17; 176,19 phlênaphos, nonsense, babble, 25,32; 135,31 phlox, flame, 16,21; 82,25; 85,8 phluareô, to speak nonsense, 34,13; 178,11; 186,15; 199,19 phluaria, nonsense 49,25; 131,30; 190,16 phônê, sound, 107,5; 184,5 phora, motion, 70+18 phôs, light, 27 phôteinos, bright, shining, 12,30; 85,9.14; 86,13; 87,11.12 phôtizô, to illuminate, give light, 124,15(2); 131,5(2); 138,1; 199,6.7 phronêsis, wisdom, cleverness, thinking, 55,30; 56,9; 79,29; 133,26 phroudos, vanished, 81,5.20; 82,6.28 (all but 81,20 Aristotle) phthartos, perishable, perishing, 37 phtheirô, to destroy (m/p usually translated ‘perish’), 110+2 phthengomai, to sound (off), 36,27; 134,26; 157,21; 163,11 phthinô, to decay, diminish, 106,25; 107,14.18 (all 3 Plato); 160,10 phthisis, decay, diminishing, 110,29; 158,5; 161,23; and 270a31,34, 270b1 phthora, perishing, 66+1 phulattô (phulassô in LSJ), to preserve, maintain, avoid, 36,29; 54,18; 66,8; 74,14; 96,9; 139,9; 194,31 phuô, to be of a nature, to be naturally constituted, 68+4 (always perfect active) phusikos, natural, 134+2 (in addition there are 18 occurrences of Phusikê akroasis translated Physics) phusis, nature, (i) kata phusin, natural (simpliciter, 254+20; with some additional qualifier, e.g., kata tên heautou phusin), 17); (ii) para phusin, unnatural (167+17, including para tên heautou phusin

190

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at 80,8); (iii) huper phusin, hypernatural (21,15.27; 34,17; 35,13.19.27; 36,1; 37,32; 42,24; 51,24.28; 57,25.29; 58,28; 63,17; 80,23; and huper tên autou phusin at 196,16); (iv) phusei, by nature (49+2); (v) 123+5 other (more ordinary) occurrences. phuton, plant, 10+1 pikrotês, bitterness, 97,25; 174,33 piptô, to fall, 67,32; 85,20 pisteuô, to be confident, trust, believe, 48,24; 55,7.9.11(last 2 Aristotle); 66,15; 74,1; 88,13; 115,28 (Aristotle); 269b14, 270b3 pistis, confidence, confirmation, 14+2 planaô, to wander 35 (all m/p; all but 2 a present participle, which is translated using ‘planets’ ) pleonazô, to go beyond, 55,7; 128,30 pleonexia, overbearingness, having more than one’s share, 98,6.9; 171,19 plêrês, full, 85,18; 141,17 plêrôma, something which contributes to filling out, 49,13.23 plêroô, to fill, 49,17; 158,16; 163,35; 196,17 plêsiasis, proximity, 67,11; 71,14 plêsiazô, to be near or next to, approach, 12 plêsios, near, 82,18; 83,8; 103,25 (Plato) plêthos, plurality, number, quantity, 23 pleura, side, 14,15; 180,21 poieô, to act, make, produce, 115+3 poiêsis, work, act, production, 90,17.32; 98,22; 106,6 poiêtikos, efficient, producing motion, 13,15.30; 136,31.32; 154,8 poikilos, variegated, 26,26; 55,28; 56,2; 124,5; 131,9 poiós, quality, 111,8; 113,31; 270a27,28 (all neuter) poiotês, quality, 112 pollakhou, frequently, 26,27; 37,27; 86,31; 129,26; 165,10; 196,8; 200,26 pollakis, many times, frequently, 21 pollaplasiazô, to multiply, 99,25.26 polueidôs (see polueidês in LSJ), in many ways, 52,27; 74,12; 92,25 polus, many, much, 87 (positive); 31+2 (comparative); 76 (superlative)

porrôthen (see prosôthen in LSJ), from a distance, 24,26; 110,5 posós, quantity, size, 39,34; 81,28; 176,19 (all neuter) posotês, quantity, 100,4.27; 158,7; 190,11 pous, foot, 48,28; 68,12.14; 79,28; 186,13.14 (para podas translated ‘immediately afterward’ or ‘in close proximity’ at 49,2; 57,17; 182,26) pragma, thing, fact, issue, 14 pragmateia, treatise, 11 proagô, to bring forward, present, introduce, carry out, 16 proairesis, choice, 67,28.31; 163,9 proapodeiknumi, to previously demonstrate, 18,11; 53,27; 59,30; 114,32; 198,16 (all aorist or perfect) proballô, to put forward, propose, 10 problêma, problem, what is proposed, 52,27; 91,20; 189,17.18 prodêlos, immediately clear, 18 proêgeomai, to precede, be prior, be primary, 11 proeimi, to proceed, 11 proeirêmenos (see proereô in LSJ), said already or previously, 22,26; 63,11; 124,9; 144,3; 150,16; 152,33; 176,16 proerkhomai, proceed, 12 proiskhô, to allege, adhere to, 69,10; 165,10 prokeimai, to be proposed, 14 prokheiros, easy, ready, 13,9; 70,23; 73,4; 146,19; 163,8 prokoptô, to advance, move closer, 118,6; 181,23 prolambanô, to assume or receive in advance, 12 prolêpsis, conception, preconception, 30,18; 74,4; 116,6; 117,19; 140,3.6; 142,7 proodos, procession, 90,5; 135,26 propeteia, rashness, 56,26; 90,10; 182,18 propetês, rash, 158,23; 173,30 prophanês, evident, 12,5; 24,4; 40,25; 45,23(2) propherô, to put forward, propose, 30,21; 46,12; 133,7; 136,18; 154,9; 164,6 propodismos, progression, procession, 32,20; 36,31; 93,15

Greek-English Index prosagô, to bring in, introduce, 118,16; 133,21; 187,25 prosauxanô, to increase, grow, extend, 39,4.8; 46,30; 47,8.12.15.21; 197,33 prosdokeô, to expect, 88,4; 135,11 proseimi, to accrue, be added, 47,19; 55,14; 84,2; 184,9; and 270a24 prosekhês, direct, immediate, 41 (usually prosekhôs) prosekhô, to attach oneself to, 140,7; 180,25 prosêkô, to be appropriate to, attach to, 19 prosektikos, attentive, 115,1; 143,17 prosennoeô, to think of or understand in addition, 48,14; 114,7 prosginomai (prosgignomai in LSJ), to accrue to, 71,22; 76,20 prosiêmi, to accept, be attached to, 68,4; 172,19 proskeimai, to be added, 64,16; 80,11; 109,5; 125,24; 154,7 proskhraomai, to use, 11 prosktaomai, to possess in addition, 16,15.33 proslambanô, to take on in addition, assume in addition, 16,16; 37,3; 40,1.6; 54,24; 74,23; 100,3; 151,34; 183,9 proslêpsis, additional assumption, 30,18, 145,27; 146,2; 151,33 prosô, far away, 83,4; 186,32 (both comparative) prosphuô, to attach, 36,6; 100,25 prosthêkê, addition, 15 prosthen, preceding, previous, front, 121,24; 126,19; 130,3; 163,10 prosthesis, addition, 47,26(2); 110,28 prosthios, front, 151,7; and 271a27 prostithêmi, to add, 53 prosuphainô, to weave together, 106,24; 107,9 prosupotithêmi, to assume in addition, 24,2.3.7 protasis, premiss, proposition, 20 proteinô, to put forward, 42,15; 46,11 proteros, prior, previous, 114+5 protithêmi, to propose, set out, 28 (including 2 occurrences of protheô (B) at 132,16 and 191,20) prôtos, first, primary, prior, 144+7 prouparkhô, to pre-exist, exist before, precede, 41,6; 59,27;

191

100,30.32; 105,11; 122,22; 136,15; 137,18 proupotithêmi, to lay down in advance, 59,31(2) pseudos, false, 20 psophos, sound, 130,21.25 psukhê, soul, 49 psukhikos, involving soul, due to soul, 79,22; 80,1.16; 100,25 psukhô, to cool, make cold, 18 psukhros, cold, 32 psukhrotês, coldness, 12 psuxis, cold, coldness, becoming cold, 13 pteron, wing, 77,5.6 pugolampis, fire-fly, 89,6.8; 90,4.13.17; 135,5 puknoô, to condense, make denser, 31,1; 35,22; 36,13; 37,4.9.24.35; 112,33; 161,17 (all but 31,1 m/p) puknôsis, condensation, 37,5; 161,12 pur, fire, 273+10 purios, fiery, 31,1; 35,22; 36,13; 37,4.9.24.25; 112,33; 161,17 rhaidios, easy, 11 rhêma, word, 66,10; 68,27; 69,11; 105,5; 156,32; 190,22 (always in plural) rheô, to flow, 34,30; 94,20 rhepô, to have an impulsion, 67,8.30; 69,21; 70,2; 161,6 rhêsis, passage, text, things said, 11 rhêteon, it should be said, 16 rhêtos, said, 53,20; 55,25; 192,16 (always neuter substantive) rheustos, flowing, 34,30; 65,18 rhiptô, to throw, 15,17; 17,20 rhopê, impulsion, 30 saleuô, to shake, undermine, 22,31; 59,8; 139,26 saphêneia, clarification, 41,1; 154,7 saphênizô, to elucidate, make clear, 15,5; 26,1; 44,7; 135,32; 144,4 saphês, clear, 43 (mostly saphôs) sarx, flesh, 78,4; 110,15; 157,30.31 sathros, unsound, 46,13; 80,29; 112,25; 126,16; 157,21; 184,30; 194,24; 199,22 selênê, moon, 105; hupo selênên translated ‘sublunary’ selêniakos, lunar, 37,18; 61,13; 71,4; 173,11; 175,17

192

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sêmainô, to mean, indicate, 25 (sêmainomenon frequently translated ‘sense’) sêmeion, point, 55+1 sêmeiôteos, to be signalled, 111,24; 112,5 sêpsis, putrefaction, 124,4; 131,9 skhedon, practically, 57,8; 83,1; 88,31; 112,24; 142,12 skhêma, figure, shape, 39 skhêmatismos, configuration, 96,22; 101,4; 113,2.7; 138,31 skhêmatizô, to configure, give shape, 45,23; 125,15 (Aristotle); 129,18 (Aristotle) (all m/p) skhesis, relation, 14 skholê, leisure, 180,24; 185,2 sklêrotês, hardness, 87,30; 89,17 skopos, purpose, goal, point, 26 skotizô, to darken, 131,3.6 (both m/p) skotos, darkness, 124,11(2).13; 131,3 sôma, body, 345+25 sophos, wise, 26,28; 48,14; 59,13; 143,15; 158,26; 175,13; 176,34 sôzô, to preserve, 15 sperma, seed, 13 sphaira, sphere, 50 sphairikos, spherical, 22 sphairoeidês, spherical, 11,12.16; 68,4.11.28 (Plato) sphairoô to form into a sphere, 65,8.14.19 (all m/p) sphodros, intense, 81,32; 82,1; 83,35 spoudazô, to strive, try hard, 13 spoudê, something worthy of attention or serious 165,8; 176,31 stasis, rest, stopping, 109,12; 113,4; 171,30.31; 172,15; 174,21; 197,20 stereô, to lack, be exempt from, 101,30.31.32.33; 175,21,22 (all m/p) sterêsis, privation, lack, 87 sterêtikos, privative, 52,16; 57,24.31 sterros, stereos, solid, 75,31.33; 77,21; 78,3; 83,28; 130,1 (Aristotle); 174,8 sterrotês, solidity, 77,24.32 stoikheion, element, 160+1 strephô, to turn, 44,19; 79,31; 80,6 (last 2 Plato) sullambanô, to gather together, include, 11,3; 48,30 sullogismos, syllogism, argument, 14 sullogizô, to argue, infer, give a syllogism, 26+1 (mostly m/p)

sumbainô, to happen, occur, result, follow, 31+2; see also sumbebêkôs sumballô, to meet (active), to contribute (m/p), 116,5; 151,23.25; 152,17; 155,3; 174,24; 196,25.26 sumbebêkôs, accidental, 23 summetria, balance, 56,5.6; 98,4.5; 171,19; 173,8 summetros, balanced, symmetric, 97,29; 141,23; 171,21(2) sumparateinô, to extend along with, 84,2; 142,12 (both m/p) sumpatheia, sympathy, 55,8.10.15 sumperainô, to conclude, infer, 11,18; 76,26; 77,19; 90,21; 116,1 (all m/p) sumperasma, conclusion, 13 sumperiagô, to carry around, 36,34; 51,5; 151,31; 154,22; 155,32 sumperipherô to carry around, 21,19; 34,15; 51,15; 58,28.36; 196,13.14 (all m/p) sumphôneô, to harmonize, agree, 116,7; 159,5; 190,25 sumphônos, in agreement or harmony, 47,5; 70,6.10; 78,18; 81,2; 159,6 sumphuô, to grow together, be attached, 48,1; 55,6; 77,25 sumplêroô, to fill out, complete, 47,32; 97,7; 114,27; 143,3; 151,17 sunagô, to infer, collect together, 49 sunagôgê, inference, combining, 97,29; 150,15 sunaidô, to harmonize, be in agreement, 84,14; 139,14; 158,26; 159,1.20 sunaireô, to contract, restrict, 93,28; 153,16; 199,16.17 sunaisthanomai, to be aware, perceive, understand, 153,11; 179,29; 182,12; 189,21 sunaisthêsis, perception, awareness, understanding, 27,11; 170,10; 184,24 sunanatellô, rise together with, 36,2; 89,15; 164,34 sunaptô, to join, connect; 58,16; 95,28; sunêmmenon translated ‘conditional’ in 12 occurrences sunartaô, to link with, 116,30; 117,2.3; 139,29; and 270b9 (all m/p) sundiaireô, to distinguish together

Greek-English Index with, apportion with, 176,4; 196,7 (both m/p) sunduazô, to take as a pair, 145,31; and 271a1 (both m/p) sundunô (see sunduomai in LSJ), to set together with, 36,2; 89,15; 164,34 sunedreuô, to accompany, 97,23; 112,35 sunêgoreô, to provide support, 26,7; 107,23 suneidon, to see, understand, 56,8; 87,16; 131,12; 177,13.18.23; 188,17.20 suneimi, to exist together, be joined, 65,26; 102,7; 134,15; 156,10; 167,24.28.33 sunekheia, continuity, 46,22; 76,16.18; 153,12; 178,26 sunekhês, continuous, 27 sunekhô, to hold together, sustain, 65,12.19; 76,9; 85,17; 97,31.32; 194,4 sunektikos, holding together, binding, 138,33; 142,18; 172,21 sunergeô, to co-operate, help, 44,12; 99,24 sunêtheia, ordinary use, custom, 69,14(2).26.32.33; 153,13 sunêthês, customary, ordinary, 30,16; 53,7; 69,20.22; 156,10 sungenês, akin, of the same kind, 20+2 sunginôskô (sungignôskô in LSJ), to accept, excuse, 48,22; 88,15; 118,7 (all m/p) suniêmi, to understand, 68,6; 131,29; 157,4; 173,4; 180,28; 183,21; 186,30; 187,7; 191,20 sunistêmi, to compose, constitute, give existence, 31 sunkeimai, to be composed, be put together, 13,12; 36,19; 41,8; 112,22; 125,14; 129,17 (last 2 Aristotle); 162,9 sunkheô, to run together, confuse, 139,17; 161,27 sunkhôreô, to agree, accept, concede, grant, 45 sunkineô, to move along with, 37,36; 164,33.35 (all m/p) sunkrinô, to combine, compare, 88,12; 171,6 sunneuô, to converge, 33,27; 39,32; 44,11.13; 46,34; 65,24

193

sunnoeô, to understand, concentrate, 88,18; 183,19; 186,8 sunokhê, continuity, being held together, 65,20; 72,21 suntassô, to combine, assign the same rank, 26,16; 154,17 sunteleô, to contribute, complete, 11,13; 60,20; 70,9; 157,20; 182,16 sunthesis, composition, combination, synthesis, 13,1; 85,29; 94,28.31; 98,12; 121,20; 125,12.16; 129,18 (last 4 Aristotle); and 271a1 sunthetos, composite, 74+3 suntithêmi, to combine, agree to, 97,18; 145,31; 188,26; see also sunthetos suntomos, brief, 33,20; 40,23; 57,8; 58,33; 64,7; 129,5; 142,27; 196,17 suntrekhô, to come together, work together, 79,12; 97,20 sunuparkhô, to exist together, 37 sunuphistêmi, to exist together, be constituted together, 97,2; 130,20; 169,27 suskiazô, to obscure, 26,25.27 sustasis, structure, constitution, 65,12; 78,3.12; 80,3 (Plato); 91,9; 98,18; 139,31; 157,5(2) sustatikos, constitutive, 167,32; 175,6 sustoikhos, co-ordinate, 84,5; 107,31 takha, perhaps, 19 takhus, fast, quick, 13+1 tautotês, sameness, 89,31; 91,11; 95,26; 109,13; 118,3.8; 142,34; 156,4; 174,22 taxis, order, position, rank, 12 tekhnêtos, artificial, 51,12; 132,10 tekmairomai, to give as evidence, infer, 20,27; 88,10; 152,18; 165,14 tekmêrion, evidence, indication, sign, 31,22; 39,20; 141,15; 157,12 teleios, complete, 133+2 teleiotês, completeness, perfection, 16 teleô, teleiô, to complete, 39,7; 43,21; 54,21.27.29 (all m/p) telesiourgos, perfective, 97,13; 112,28; 113,12.24; 115,3.14 teleutaios, final, 11,11; 25,11; 115,27 teleutaô, to end up, 155,19; 177,16 teleutê, end, 48,7.8.10.35 (Aristotle); 73,27 telikos, final, complete, 49,16; 154,8

194

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têlikosde, telikoutos, of any given size, so many, 39,28; 48,23 telos, end, 47+1 thalatta (thalassa in LSJ), sea, 81,26(2) thaumasios, remarkable, 132,3; 146,24 thaumastos, amazing, surprising, remarkable, 22+1 thaumazô, to be amazed or impressed, wonder, 74,27; 123,3; 176,28; 177,12; 191,10 theaomai, to see, observe, 26,19; 67,25 theios, divine, 39+3 theô, to run, 118,23; and 270b23 theôreô, to see, consider, 10 (all but 1 m/p) theos, god, 60+3 thermainô, to heat, warm, 31 thermansis, being heated, 158,3; 159,15 thermos, hot, warm, 34 thermotês, heat, 35 theros, summer, 82,28; 83,4.8 thesis, position, thesis, 11 thnêtos, mortal, 13 thoinê, banquet, 34,12; 139,34 thrasutês, rashness, 26,29; 55,30; 56,9.10 threptikos, nutritive, 100,25; 110,30; 123,23 thrix, hair, 73,17; 113,21 (Melissus) thuras, para (see thura in LSJ), beside the point, 126,10; 129,5; 157,14; 195,16 timaô, to honour, admire, 90,14; 118,21 timios, honourable, valuable, 60,12; and 269b16 tithêmi, to posit, suppose, determine, 29+4 tmêma, segment, 145,16; 148,14 topikos, spatial (usually modifying

kinêsis, where the phrase is translated ‘motion’ or ‘change of place’), 11 topos, place, region, space, 151+10 trakhutês, roughness, 89,17; 97,25 trephô, to nourish, 100,23; 107,18; 109,29; 110,5.7(2).9.16.29 trepô, to turn, 88,16; 101,13; 106,19; 107,11 (last 2 Plato); 126,19 trigônon (see trigônos in LSJ), triangle, 123,26; 180,20.21 trikhê diastatos, three-dimensional, 12 tropê, transformation, 100,28; 101,2; 107,8; 139,2 trophê, nourishment, 11 tropos, way, mode, 24+1 tunkhanô, to happen to be, be, attain, 43 tuphlos, blind, 123,1; 195,19 xenos (adj.), foreign, novel, 26,3; 90,23.29; 91,2 xêrainô, to dry, 112,31; 160,5; 168,11 xêros, dry, 12 xêrotês, dryness, 16 xulinos, wooden, 50,25; 51,9; 183,26.29 xulon, wood 127,1; 136,21; 184,7 zêteô, to ask, seek, investigate, enquire, 29 zêtêsis, investigation, 35,9; 156,25 zôê, life, 78,28; 79,17 (Aristotle); 80,10; 196,17 zôidion, sign (of the zodiac), 97,16; 181,30.31 zôion, animal, living thing, 63+1 zôipoieô (no iota subscript in LSJ), to create life, give life, 115,3; 163,7 zôos, living, 78,28; 79,17; 80,10; 196,17 zôtikos, vital, 51,25; 55,8.10; 65,16; 83,16

Index of Passages (a) Passages quoted by Simplicius For Philoponus and Alexander see Appendices 1 and 2, and for Themistius, Xenarchus, and Xenocrates the Index of Names. ARISTOTLE

De Caelo (outside 1.2-3.270a12) 1.1, 268a11-12: 48,35-6; 1.1, 268a20-1: 48,36-49,1; 1.3, 270b10-11: 87,14-15; 2.1, 284a2-5: 11,21-4; 2.1, 284a27-32: 79,16-20; 2.2, 285a29-30: 78,26; 4.3, 310a33-4: 20,16-17; 4.4, 311a17-18: 69,30-1 Meteorology 1.3, 340a2-3: 81,4-5; 82,6; 86,27-8 Physics 1.2, 185a11-12: 90,19

PINDAR

Olympian Odes (Maehler (1987)) 2.157-8: 42,17-18 PLATO

Timaeus 33D3-34A6: 79,26-80,1; 36D8-E5: 80,2-7; 62C8-D12: 68,27-69,7; 63B5-D4: 68,16-26; 63E4-6: 69,23-5; 63E4-7: 67,33-68,1 PLOTINUS

Enneads (Wilberding (2006)) 2.1.2.12-14: 12,13-15

(b) Early texts cited in the notes Only passages not cited in (a) are mentioned here. References are to the line in the Greek text where a note number occurs. ALEXANDER OF APHRODISIAS

in Meteor. (CAG 3.2) 9.16-18: 83,30 ARISTOTLE

De Caelo (outside of 1.2-3.270a11 ) 1.3, 270a12: 60,20; 1.3, 270a12-35: 79,2; 1.3, 270a19-20: 60,32; 1.3, 270b13-16; 1.4: 58,17; 60,32; 73,9; 2.1, 284a27-8: 80,7; 2.1, 284a27-35: 78,22; 2.4: 45,17; 2.4, 87a30-b4: 45,29; 2.12, 292a18-21: 13,2; 78,26-8; 4.1, 308a13-33: 70,2; 4.3, 310b3-5: 33,26; 4.4, 311b6-13: 74,17; 4.4, 312b2-7: 34,26; 4.5:20,7 On Coming to be and Perishing 2.8, 335a18-21: 20,17 Eudemian Ethics 2.3, 1220b39: 55,29; 2.3, 1221a12: 55,29 Metaphysics 12.8: 31,20 Meteorology 1.3, 339b16-340a3: 80,26; 1.3, 340a1-3; 81,4; 1.3, 340a2: 81,20; 1.3, 340a3-8: 83,30; 1.3, 340b19-23: 81,9; 1.3, 340b32-341a3: 50,19; 1.7, 344a8-14: 20,26

Nicomachean Ethics 2.7, 1107a33-b4: 55,29 Physics 3.1, 201a10-11: 22,22; 5.4, 228a29-30: 46,20; 6.1, 231a22: 46,20; 8.7-9: 31,26; 53,6; 8.7, 260a26-261a28: 13,6; 8.9: 38,23; 41,17; 8.10: 79,3; 8.10,266a24-b6: 44,28 Posterior Analytics 1.1, 71a1-2: 59,28 Topics 2.10, 114b37-115a14: 40,22 [ARISTOTLE]

De Mundo 6, 400a7-8: 85,15 ATHENAEUS

Learned Banqueteers (Olson (2008)) 265d-266e: 59,11 HERMOGENES

On Invention (Rabe (1913)) 3.6: 13,29 MANTISSAE PROVERBIORUM (von Leutsch (1851)) 2.70: 78,15 ORIGEN

On Principles (Koetschau (1913)) 2.1.3: 91,18 PHILOPONUS

in Meteor. (CAG 14.1) 94,6-7: 26,22

196

Index of Passages

On the Creation of the World (Reichardt (1897)) 6.2: 91,18 PLATO

Phaedrus 276B3: 25,35 Sophist 251B7: 29,8 Timaeus 58C: 16,21; 62C3-63E8: 23,2 PROCLUS

Elements of Theology (Dodds (1963)) 139: 85,3 in Tim. (Diehl (1903-6)) 1.237,27-238,1: 12,13; 3.114,31-115,2: 20,11 PTOLEMY

Handy Tables (Halma (1822)) 112-33: 33,3 Optics (Lejeune (1989)): 20,11 Tetrabiblios (Hübner (1998)) 1.4.3: 88,13 SEPTUAGINT (Rahlfs (1935)) Genesis 1.1: 78,8; Psalms 18.2: 90,16

SIMPLICIUS

in Cael. (CAG 7) (outside of 10,28-201,10) 373,25-8: 11,21; 374,34-382,19: 78,22; 438,30-444,15: 83,11; 454,23-456,27: 33,26; 679,2-687,8: 66,6; 678,15-682,3: 70,2; 709,8-712,17: 74,17; 717,21-729,15: 20,7 in Cat. (CAG 8) 307,19: 31,25 in Phys. (CAG 9 and 10) 384,14: 26,22; 1165,35-8: 12,22; 1335,5-7: 74,1 SYMEON SETH

Summary of Physical Subjects (Delatte (1939)) 73,11-13: 20,11 THEMISTIUS

in Cael. (CAG 5.4) 12,1-13,3: 62,14; 12,11-17: 63,19; 221,28-30: 70,5: 244,21-3: 68,9

Index of Names (a) Names mentioned by Simplicius In many cases information on an item or a reference to where information can be found is provided in a note on a given passage. Page and line numbers indicate where a given name is found. world); 45,16.29; 51,2 (makes no Adonis, gardens of: 25,35 (their use of the sphericity of heaven transcience compared with until he demonstrates it in 2.4); Philoponus’ arguments) 39,14; 46,27; 47,5 ( argues in terms Alexander: 49 occurrences; see of the linear circle); 57,16.18 (does Appendix 2 not contradict himself); 65,29; Analytics (Analytika): 59,28 72,23 (why he says whole and part Aristotle: 12,13 (Plotinus mentions move to the same thing); his ‘hypotheses’ for the proof that 66,6.17.31; 71,1.9.11 (on heavy and heaven is everlasting); 12,31; 67,2; light, up and down); 69,14.25 (uses 80,27; 81,1.3.9.21; 82,7; 85,31; 86, terms in the ordinary way); 70,10; 15; 91,4.8 (on the composition of 72,16; 75,22 (assigns no impulsion heaven; sublunary and heavenly to heaven); 78,21.25; 79,13.15.21; fire); 15,29 (diverges from his usual 80,7 (believes the motion of heaven precision at 268b24-6; 17,21; 24,16 involves soul); 87,2.26 (his belief in (believes what we call elements or forms); 13,31; 14,3.4; 16,31; 21,32; simple bodies are really 24,28; 25,22.25.29.33.36; composites); 20,15; 22,19; 23,2.6; 26,9.12.20.23.24.30.32; 27,2; 42,13 (believes that the sublunary 31,17(2); 32,3; 33,14; 38,4; elements move in a straight line 41,1.17.21; 42,19.30; 43,1; when (and only when) they are in 44,7.9.17; 46,34; 47,14; 48,25.35; an unnatural condition; 20,26.29; 49,4.15.24; 56,18.27; 59,10; 66,4; 37,29.34; 50,19 (on the 71,15.19; 74,16.27; 78,14; 80,14; hupekkauma); 21,1.14.23; 34,34; 84,14;89,29; 90,18; 91,20 (other 35,2.5.9.10; 51,19.29; 56,22; mentions of less interest) 58,16.25.33 (on hypernatural Callippus: 32,16 (he and Eudoxus motion); 24,8; 25,5; 27,6 (believes hypothesized counterrevolving that a simple body has a single concentric spheres, a hypothesis natural motion); 24,19; 31,34 used by Aristotle) (sometimes speaks as if there were David: 90,14 (the Psalms cited against only two simple sublunary bodies); Philoponus) (Themistius’ 26,27 (an icon or father of paraphrase); 80,25 cleverness (deinotês), accused by Eudoxus: 32,16 (he and Callippus Philoponus of obscuring the truth); hypothesized counterrevolving 27,25; 30,8 (is now taking nature concentric spheres, a hypothesis as the starting point of motion used by Aristotle) only); 32,10.12.17.27 (his relation Herodian: 26,22 (apparently referred to astronomical theory); to along with Menander as some 33,17.21.26; 59,3; 69,17 (is focused kind of teacher of Philoponus) on establishing the difference Hipparchus: 32,22 (hypothesized between heaven and the sublunary

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eccentric spheres and epicycles before Ptolemy) Menander: 26,22 (apparently referred to along with Herodian as some kind of teacher of Philoponus) Mercury, sphere of: 71,5.18 (Philoponus mistaken about its position relative to the sphere of Venus) Meteorology: 20,26 (Meteôrologika); 80,26; 81,4 (both Meteôra) Olympus: 85,15 (as name of heaven) On Coming to be and Perishing (Peri geneseôs): 20,17; 22,20; see also 86,25 On the Heavens (Peri ouranou) 26,1.13; 68,7 Optics: 20,11 (in his Optics Ptolemy says that the sublunary elements move in a straight line when they are still coming to be) Peripatetic School (Peripatos): 69,10 (Themistius usually follows it) Physics 13,6; 41,17; 53,6; 79,2; 92,9.26 (all Phusikê Akroasis); 38,23 (Phusikê) Pindar: 42,18 (quoted in a derisive remark about Philoponus) Plato: 12,16.21.23; 16,21; 66,33; 67,2.4; 68,6.8.10.27; 69,7.10; 81,1.2; 84,11.13.14.15(2).22.30; 85,7; 86,1.9.33; 87,18.19.22.26; 88,7; 91,8 (his and Aristotle’s views on the composition of the heavens, and the misunderstandings of Philoponus and Themistius); 12,13 (Plotinus tried to prove that heaven is everlasting in a Platonic way); 23,1; 66,16; 67,25; 69,13.16.23; 70,2; 72,9 (on up and down, heavy and light); 33,13 (recognized the rotation of the stars on their axes) Plotinus: 12,12 (wished to demonstrate that heaven is eternal in a Platonic way, and said there would be no problem if one accepted Aristotle’s hypothesis about the fifth body (Enneads 2.1.2.12-14)); 20,12.21 (like Ptolemy and Xenarchus, said that the sublunary elements move in a straight line when they have not yet taken on their natural form,

and that when they have and are in their proper places they either rest or move in a circle); 37,33 (like Ptolemy, Proclus, and Aristotle himself, says that the hupekkauma has a hypernatural motion) Proclus: 37,34 (like Ptolemy, Plotinus, and Aristotle himself, says that the hupekkauma has a hypernatural motion) Ptolemy: 20,11.21 (like Plotinus and Xenarchus, said that the sublunary elements move in a straight line when they have not yet taken on their natural form, and that when they have and are in their proper places they either rest or move in a circle; mentions his Optics); 32,23 (after Hipparchus, made the hypothesis of eccentric spheres and epicycles); 33,1 (Philoponus misunderstands his distinction between the motion of a star and the motion of the centre of its epicyle); 37,33 (like Plotinus, Proclus, and Aristotle himself, says that the hupekkauma has a hypernatural motion); Saturn: 88,12.15 (cools things but not because it is watery) Telkhins: 66,10 (Philoponus called a Telkhin) Themistius: 62,12; 63,19 (his account of 269b29-270a3); 68,6; 71,20; 72,10 (invoked by Philoponus as believing along with Plato that the elements are light or heavy in their proper regions); 69,9 (although normally a Peripatetic, he agrees with Plato in thinking that up and down are relative); 70,2,9 (quoted by Philoponus for the view that elements have impulsions only outside their natural regions) Timaeus: 23,1 (the character in Plato’s dialogue); 79,24 (the dialogue). Venus, sphere of: 71,4.18 (Philoponus mistaken about its position relative to the sphere of Mercury) Xenarchus: 13,22.29; 14,3,14 (argument that the cylindrical helix is a simple line); 20,12.21 (like Ptolemy and Plotinus, said

Index of Names that the sublunary elements move in a straight line when they have not yet taken on their natural form, and that when they have and are in their proper places they either rest or move in a circle); 20,32 (charges Aristotle with trying to prove the superiority of heaven over the sublunary elements on the basis of their unnatural motion); 21,33 (his argument for his position on the motion of the sublunary elements); 23,11.23 (argument that even if all simple bodies have simple motions it does not follow that for any simple motion there is a simple body which has it); 23,31 (argument that even if rectilinear motion is natural for the sublunary elements, circular motion might also be natural for them); 24,20 (Alexander the source for information about his arguments); 24,21 (argument that revolving

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objects do not move with uniform speed); 25,11 (complaint that Aristotle mixes together mathematics and physics); 25,22.24; 26,33; 42,20 (Philoponus takes over his arguments against Aristotle and represents them as his own); 42,6 (raises the same difficulties a second time); 50,20 (argument that the hupekkauma moves in a circle naturally); 55,20 (arguments that one thing may have more than one contrary); 70,20 (argument — apparently based on a misreading — that Aristotle was wrong to say that what lies at the top of everything is light). Simplicius mentions Xenarchus one more time at 286,2. Xenocrates: 12,22; 87,21 (fragment 285 (Isnardi Parente (1982)) quoted to show that Plato believed in 5 simple bodies) Zeus: 42,18 (mentioned in a quotation from Pindar)

(b) Scholars cited in the Introduction and in the Notes to the Translation This index does not include editors or translators of texts unless they are mentioned for their position on an editorial or interpretive issue; reference to a page and line of the text translated indicates the position of a note in which the scholar in question is mentioned. Abbadi, Mostafa el: Introduction, n. 60 Athanassiadi, Polymnia: Introduction, n. 9 Baltussen, Han: Introduction, n. 58 Bergk, Theodor: Introduction, n. 96 Bernard, Hildigund: Introduction, n. 22 Bessarion, Basilius: p. 30; 18,1; 39,5; 51,15; 73,19; 86,11 Bossier, F.: p. 30; 91,9 Dickey, Eleanor: 26,22 Diels, Hermann: 59,11 Dillon, John: Introduction, n. 7 Ebied, R.Y.: Introduction, n. 50 Fox, Robin Lane: Introduction, n. 61 Golitsis, Pantelis: 75,14 Grillmeier, Alloys: Introduction, n. 43 Hadot, Ilsetraut: Introduction, nn. 18, 58 Hainthaler, Theresia: Introduction, n. 43

Hankinson, R.J.: Introduction, n. 5; 11,1; 13,21.22; 15,13; 16,26; 19,14; 20,17; 24,7; 38,12; 51,15; 62,2.17; 64,2.23 Heath, Thomas L.: 29,32 Heiberg, J.L.: pp. 29, 30, 31; 16,26; 18,1; 23,17; 30,18; 34,25; 38,12; 39,5; 43,27; 44,5; 47,12; 48,14; 51,15; 56,21; 57,17; 59,11.26; 62,3; 63,25; 64,2; 67,16; 70,19; 73,19; 74,29; 77,2; 78,15; 83,18; 85,1; 86,11.33; 89,12; 91,9 Hoffmann, Philippe: 55,3 Karsten, Simon: pp. 30, 31; 18,1; 34,25; 43,27; 44,5; 47,12; 57,17; 59,11; 64,2; 71,31; 73,19; 83,18; 84,12; 89,12 Lejeune, Albert: 20,11 Martin, H.: Introduction, n. 47 Martindale, J.R.: Introduction, n. 13

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Menn, Stephen: 91,18 Moerbeke, William: p. 30; 16,15; 18,1; 30,18; 44,5; 47,12; 67,16; 73,19; 77,2; 83,18; 84,12; 86,11; 89,12; 91,9 Moraux, Paul,: 11,11; 13,22; 18,1; 59,26; 62,3; 63,25; 79,14 Neugebauer, O.: 71,19 O‘Meara, Dominic: Introduction, n. 7 Peyron, Amadeo,: Introduction, n. 95 Pines, Shlomo: Introduction, n. 40 Rescigno, Andrea: Introduction, n. 5, 11,11; 16,26; 22,21; 50,21; 54,7 Roey, A. van: Introduction, n. 50 Russell, D.A.: 26,22 Saffrey, Henri Dominique: Introduction, nn. 6, 8 Schibli, Hermann S.: Introduction, n. 19 Scholten, Clemens: Introduction, nn. 36, 56

Segonds, Alain-Philippe: Introduction, n. 8 Simms, Ronda: 25,35 Sorabji, Richard: Introduction, nn. 3, 36 Stocks, J.L.: 16,22 Tardieu, M.: Introduction, n. 59 Trombley, Frank R.: Introduction, n. 26 Verrycken, Konrad: p. 12; 26,19; 84,12 Waerden, Bartel L. van der: 33,3 Westerink, L.G.: Introduction, n. 6 Wickham, L.R.: Introduction, n. 50 Wilberding, James: 12,13; 20,12 Wildberg, Christian: Introduction, nn. 4, 5, 41, 57, 66; 47,28; 66,21; 67,16; 70,5; 78,15; 83,16 Wilson, N.G.: 26,22 Wipszycka, Ewa: Introduction, n. 30 Wolska, Wanda: p. 11

Subject Index assumptions made by Aristotle: 12,6-16; 59,27-60,8; 62,9-11 completeness of and priority among lines, motions, and bodies: 38,8-39,11; 40,1-41,32; 45,3-46,4; 47,1-27; 48,14-34; Alexander’s notion of completeness as having a beginning, middle, and end, 39,11-21; 42,27-44,3; 44,15-45,2; 46,4-29; 47,4-6; 47,27-48,14; 49,10-19; an alternative proposed by Philoponus: the complete is what has neither beginning nor end, 49,7-10, 19-23; Is a diameter of the cosmos complete? 39,21-40,1; 44,3-15; are infinite straight lines complete? 38,32-39,11; 49,7-10; 49,19-23 contraries: the assertion that for a single thing there is a single contrary (269a14), 19,9-30; 55,25-58,14; circular motion has no contrary, 58,14-30; 60,25-34 conversion with antithesis: 28,1-34,6 De Caelo, subject of: 10,28-11,25 heaven: a distinct fifth element: 18,3-20,4; 30,26-31,6; 49,26-50,18; 52,19-54,32; 56,26-58,1; 74,11-16; 80,23-84,11 (what Aristotle says in the Meteorology); 87,29-90,13; indestructibility; 59,15-23; 72,29-73,4; less easily affected than the rest of the cosmos, 73,4-24; 78,1-12; agreement of Plato and Aristotle on its composition, 12,16-13,3; 66,33-67,5; 84,13-87,28; 91,3-17; Plato and Aristotle’s views on whether heaven’s motion involves soul, 78,17-80,23 heavy and light: heaven is neither, 60,12-63,24; 75,17-77,23; Aristotle’s definition of, 61,1-62,2; 66,17-33; 70,20-71,14; relativity of 74,16-75,12; Plato’s view and

Themistius’ account of it, 67,24-69,10; the relation of Plato’s view to Aristotle’s, 69,11-70,2; do the totalities of the four elements have weight or lightness? 68,6-10; 71,19-72,10 hupekkauma: 20,25-21,32; 34,5-21; 35,20-38,2; 42,20-7; 50,18-51,28; 58,19-59,5; 67,5-14; 80,20-84,10 impulsion and desire of the elements: 27,11-23; 64,31-66,3; 67,5-68,5; 72,18-24 mathematical astronomy: 32,1-33,17 mathematics and physics: 25,11-21 motion: of the elements, 20,10-24; 21,33-23,10; 23,11-31; 42,20-7; 67,5-14; contrast between motions of the totalities of the elements and portions of them, 33,17-34,5; 63,25-66,3; 70,2-19; 72,12-73,4; 77,23-7; hypernatural, 20,32-21,32; 34,5-21; 34,33-35,20; 37,26-38,2; 42,20-7; 50,18-52,18; 56,26-58,1; 58,14-59,5 Philoponus, Simplicius’ attacks on his motives, character, intelligence, and religion: 25,23-26,33; 27,4-11; 28,14-30,25; 30,34-31,6; 32,32-33,16; 34,12-13; 35,1-12; 36,25-33; 37,8-10; 37,16; 42,17-20; 44,19-20; 45,7-9; 46,11-18; 47,3-4; 49,10-12; 49,23-5; 56,26-8; 59,6-18; 66,4-17; 67,14-24; 71,17-19; 72,10-11; 74,4-11; 75,12-16; 78,1-17; 82,8-14; 84,11-14; 88,2-7; 88,28-31; 90,11-28; 91,17-19 pistis (confidence): 55,1-21 simple bodies not genuinely simple: 17,18-33 simple lines: relation to simple motions, 13,8-21; 15,18-27; include only straight lines and circles, 13,22-14,29 simple motions: their relation to

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Subject Index

simple bodies, 16,3-17,33; 20,4-10; 23,31-24,21; 24,21-25,10; 26,31-28,14; 31,6-32,1; 34,21-32;

definitions of motion up, motion down, and motion in a circle, 14,31-15,17