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.

The subject of Aristotle's On the Heavens, Books 3-4, is the four elements of earth, air, fire and water, which exist below the heavens. Book 3, in chapters 1 to 7, frequently criticizes the Presocratic philosophers. Because of this, Simplicius' commentary is one of our main sources of quotations of the Presocratics. Ian Mueller's translation of this commentary gains added importance by enabling us to see the context which guided Simplicius' selection of Presocratic texts to quote. Simplicius also criticizes the lost commentary of the leading Aristotelian commentator, Alexander, and thereby gives us important information about that work. The English translation in this volume is accompanied by a detailed introduction, extensive commentary notes and a bibliography.

In chapter 1 of On the Heavens Aristotle defines body, and then notoriously ruptures dynamics by introducing a fifth element, beyond Plato's four, to explain the rotation of the heavens, which, like nearly all Greeks, Aristotle took to be real, not apparent. Even a member of his school, Xenarchus, we are told, rejected his fifth element. The Neoplatonist Simplicius seeks to harmonise Plato and Aristotle. Plato, he says, thought that the heavens were composed of all four elements but with the purest kind of fire, namely light, predominating. That Plato would not mind this being called a fifth element is shown by his associating with the heavens the fifth of the five convex regular solids recognised by geometry. Simplicius follows Aristotle's view that one of the lower elements, fire, also rotates, as shown by the behaviour of comets. But such motion, though natural for the fifth elements, is super-natural for fire. Simplicius reveals that the Aristotelian Alexander of Aphrodisias recognised the need to supplement Aristotle and account for the annual approach and retreat of planets by means of Ptolemy's epicycles or eccentrics. Aristotle's philosopher-god is turned by Simplicius, following his teacher Ammonius, into a creator-god, like Plato's. But the creation is beginningless, as shown by the argument that, if you try to imagine a time when it began, you cannot answer the question, 'Why not sooner?' In explaining the creation, Simplicius follows the Neoplatonist expansion of Aristotle's four 'causes' to six. The final result gives us a cosmology very considerably removed from Aristotle's.

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.

One of the arguments in Aristotle's On the Heavens propounds that the world neither came to be nor will perish. This volume contains the pagan Neoplatonist Simplicius of Cilicia's commentary on the first part of this this important work. The commentary is notable and unusual because Simplicius includes in his discussion lengthy representations of the Christian John Philoponus' criticisms of Aristotle along with his own, frequently sarcastic, responses. This is the first complete translation into a modern language of Simplicius' commentary, and is accompanied by a detailed introduction, extensive explanatory notes and a bibliography.

The commentary attributed to Simplicius on Aristotle's On the Soul appears in this series in three volumes, of which this is the first. The translation provides the first opportunity for a wider readership to assess the disputed question of authorship. Is the work by Simplicius, or by his colleague Priscian, or by another commentator? In the second volume, Priscian's Paraphrase of Theophrastus on Sense Perception, which covers the same subject, will also be translated for comparison. Whatever its authorship, the commentary is a major source for late Neoplatonist theories of thought and sense perception and provides considerable insight into this important area of Aristotle's thought. In this first volume, the Neoplatonist commentator covers the first half of Aristotle's On the Soul, comprising Aristotle's survey of his predecessors and his own rival account of the nature of the soul.

Simplicius' commentary on Aristotle's Categories is the most comprehensive philosophical critique of the work ever written, representing 600 years of criticism. In his Categories, Aristotle divides what exists in the sensible world into ten categories of Substance, Quantity, Relative, Quality and so on. Simplicius starts with a survey of previous commentators, and an introductory set of questions about Aristotle's philosophy and about the Categories in particular. The commentator, he says, needs to present Plato and Aristotle as in harmony on most things. Why are precisely ten categories named, given that Plato did with fewer distinctions? We have a survey of views on this. And where in the scheme of categories would one fit a quality that defines a substance - under substance or under quality? In his own commentary, Porphyry suggested classifying a defining quality as something distinct, a substantial quality, but others objected that this would constitute an eleventh. The most persistent question dealt with here is whether the categories classify words, concepts, or things.

To open a newspaper or turn on the television it would appear that science and religion are polar opposites - mutually exclusive bedfellows competing for hearts and minds. There is little indication of the rich interaction between religion and science throughout history, much of which continues today. From ancient to modern times, mathematicians have played a key role in this interaction. This is a book on the relationship between mathematics and religious beliefs. It aims to show that, throughout scientific history, mathematics has been used to make sense of the 'big' questions of life, and that religious beliefs sometimes drove mathematicians to mathematics to help them make sense of the world. Containing contributions from a wide array of scholars in the fields of philosophy, history of science and history of mathematics, this book shows that the intersection between mathematics and theism is rich in both culture and character. Chapters cover a fascinating range of topics including the Sect of the Pythagoreans, Newton's views on the apocalypse, Charles Dodgson's Anglican faith and Gödel's proof of the existence of God.