Aristotle argues in On the Heavens 1.5-7 that there can be no infinitely large body, and in 1.8-9 that there cannot be more than one physical world. As a corollary in 1.9, he infers that there is no place, vacuum or time beyond the outermost stars. As one argument in favour of a single world, he argues that his four elements: earth, air, fire and water, have only one natural destination apiece. Moreover they accelerate as they approach it and acceleration cannot be unlimited. However, the Neoplatonist Simplicius, who wrote the commentary in the sixth century AD (here translated into English), tells us that this whole world view was to be rejected by Strato, the third head of Aristotle's school. At the same time, he tells us the different theories of acceleration in Greek philosophy.

Commenting on the end of Aristotle's On the Heavens Book 3, Simplicius examines Aristotle's criticisms of Plato's theory of elemental chemistry in the Timaeus. Plato makes the characteristics of the four elements depend on the shapes of component corpuscles and ultimately on the arrangement of the triangles which compose them. Simplicius preserves and criticizes the contributions made to the debate in lost works by two other major commentators, Alexander the Aristotelian, and Proclus the Platonist. In Book 4, Simplicius identifies fifteen objections by Aristotle to Plato's views on weight in the four elements. He finishes Book 4 by elaborating Aristotle's criticisms of Democritus' theory of weight in the atoms, including Democritus' suggestions about the influence of atomic shape on certain atomic motions. This volume includes an English translation of Simplicius' commentary, a detailed introduction, extensive commentary notes and a bibliography.

Aristotle believed that the outermost stars are carried round us on a transparent sphere. There are directions in the universe and a preferred direction of rotation. The sun moon and planets are carried on different revolving spheres. The spheres and celestial bodies are composed of an everlasting fifth element, which has none of the ordinary contrary properties like heat and cold which could destroy it, but only the facility for uniform rotation. But this creates problems as to how the heavenly bodies create light, and, in the case of the sun, heat. The value of Simplicius' commentary on On the Heavens 2,1-9 lies both in its preservation of the lost comments of Alexander and in Simplicius' controversy with him. The two of them discuss not only the problem mentioned, but also whether soul and nature move the spheres as two distinct forces or as one. Alexander appears to have simplified Aristotle's system of 55 spheres down to seven, and some hints may be gleaned as to whether, simplifying further, he thinks there are seven ultimate movers, or only one.

This is the first English translation of Simplicius' responses to Philoponus' Against Aristotle on the Eternity of the World. The commentary is published in two volumes: Ian Mueller's previous book in the series, Simplicius: On Aristotle On the Heavens 1.2-3, and this book on 1.3-4. Philoponus, the Christian, had argued that Aristotle's arguments do not succeed. For all they show to the contrary, Christianity may be right that the heavens were brought into existence by the only divine being and one moment in time, and will cease to exist at some future moment. Simplicius upholds the pagan view that the heavens are eternal and divine, and argues that their eternity is shown by their astronomical movements coupled with certain principles of Aristotle. The English translation in this volume is accompanied by a detailed introduction, extensive commentary notes and a bibliography.

Aristotle believed that the outermost stars are carried round us on a transparent sphere. There are directions in the universe and a preferred direction of rotation. The sun, moon and planets are carried on different revolving spheres. The spheres and celestial bodies are composed of an everlasting fifth element, which has none of the ordinary contrary properties like heat and cold which could destroy it, but only the facility for uniform rotation. But this creates problems as to how the heavenly bodies create light, and, in the case of the sun, heat. The topics covered in this part of Simplicius' commentary are: the speeds and distances of the stars; that the stars are spherical; why the sun and moon have fewer motions than the other five planets; why the sphere of the fixed stars contains so many stars whereas the other heavenly spheres contain no more than one (Simplicius has a long excursus on planetary theory in his commentary on this chapter); discussion of people's views on the position, motion or rest, shape, and size of the earth; that the earth is a relatively small sphere at rest in the centre of the cosmos.

An astounding project of analysis on more than one hundred translations of ancient philosophical texts, this index of words found in the Ancient Commentators on Aristotle series comprises some 114,000 entries. It forms in effect a unique dictionary of philosophical terms from the post-Hellenistic period through to late antiquity and will be an essential reference tool for any scholar working on the meaning of these ancient texts. As traditional dictionaries have usually neglected to include translation examples from philosophical texts of this period, scholars interested in how meanings of words vary across time and author have been ill served. This index fills a huge gap, therefore, in the lexical analysis of ancient Greek and has application well beyond the reading of ancient philosophical commentaries. Bringing together the full indexes from 110 of the volumes published in Bloomsbury's Ancient Commentators on Aristotle series, McKirahan has combined each word entry and analysed how many times particular translations occur. He presents his findings numerically so that each meaning in turn has a note as to the number of times it is used. For meanings that are found between one and four times the volume details are also given so that readers may quickly and easily look up the texts themselves.

The third volume of this invaluable sourcebook covers three main subject areas. First, the metaphysics of Aristotle's logical works: the concepts of universal and particular underwent surprising transformations in this period, which gave rise to debates, still raging today, on personal survival after an interruption such as death. Second, logic in a more conventional sense: perhaps the most impressive debate was on the existence of the subject in singular and universal statements. There was also debate about the very different Aristotelian and Stoic conceptions of syllogism, of modal logic, of induction, of the nature of mathematics, and of philosophy of language. Third, the higher metaphysics of the Neoplatonists taught Augustine, and indirectly Descartes, to look for truth within themselves. The Neoplatonists struggled with the question whether our higher intellectual selves have distinct individuality, and thus they fed both sides in the great medieval debate between Aquinas and the followers of Averroes on individual human immortality. All sources appear in English translation and are carefully linked and cross-referenced by editorial comment and explanation. Bibliographies are provided throughout.