Words have determinable sense only within a complex of unstated assumptions, and all interpretation must therefore go beyond the given material. This book addresses what is man's place in the Aristotelian world. It also describes man's abilities and prospects in managing his life, and considers how far Aristotle's treatment of time and history licenses the sort of dynamic interpretation of his doctrines that have been given. The ontological model that explains much of Aristotle's conclusions and methods is one of life-worlds, (...) in which the material universe of scientific myth is no more than an abstraction from lived reality, not its transcendent ground. (shrink)

Richard Sorabji here takes time as his central theme, exploring fundamental questions about its nature: Is it real or an aspect of consciousness? Did it begin along with the universe? Can anything escape from it? Does it come in atomic chunks? In addressing these and myriad other issues, Sorabji engages in an illuminating discussion of early thought about time, ranging from Plato and Aristotle to Islamic, Christian, and Jewish medieval thinkers. Sorabji argues that the thought of these often negelected philosophers (...) about the subject is, in many cases, more complete than that of their more recent counterparts. “Splendid. . . . The canvas is vast, the picture animated, the painter nonpareil. . . . Sorabji’s work will encourage more adventurers to follow him to this fascinating new-found land.”—Jonathan Barnes, Times Literary Supplement “One of the most important works in the history of metaphysics to appear in English for a considerable time. No one concerned with the problems with which it deals either as a historian of ideas or as a philosopher can afford to neglect it.”—Donald MacKinnon, Scottish Journal of Theology “Unusually readable for such scholarly content, the book provides in rich and cogent terms a lively and well-balanced discussion of matters of concern to a wide academic audience.”— Choice. (shrink)

Available from UMI in association with The British Library. ;Plato's philosophy of mathematics must be a philosophy of 4th century B.C. Greek mathematics, and cannot be understood if one is not aware that the notions involved in this mathematics differ radically from our own notions; particularly, the notion of arithmos is quite different from our notion of number. The development of the post-Renaissance notion of number brought with it a different conception of what mathematics is, and we must be able (...) to see the differences before we can begin to appreciate Plato's views, which must never be seen as applying to a revolutionary notion of mathematics . For this reason the first part of this dissertation must comprise a detailed analysis of these differences, along with some criticisms of those of Plato's modern interpreters who have not taken this point. Much of what will be found here can be found in Jacob Klein's Greek Mathematics and the Origin of Algebra, which will be extensively quoted and interpreted. This book is often quoted, but very seldom understood; or at least, those lessons which should be taken from it are rarely applied to Platonic exegesis. In the second part I attempt a better explanation of Plato's mathematical ontology, beginning with the most extensive passage in the dialogues, the triple image of Sun, Line and Cave in Republic. This reveals a relation between sensibles and forms which is at odds with the traditional view that mathematical objects are never precisely accurate instances of their forms--but this view can be refuted. Plato's view of the nature of mathematical objects will be seen to be a metaphorical way of saying what Aristotle says logically, and is entirely appropriate to the aims and methods of his contemporary mathematicians. Aristotle's criticism of Plato's views is examined and found to make sense and to be appropriate to views which Plato could consistently have held. (shrink)

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

In Book K of the Metaphysics Aristotle raises a problem about a very persistent concern of Greek philosophy, that of the relation between the one and the many , but in a rather peculiar context. He asks: ‘What on earth is it in virtùe of which mathematical magnitudes are one? It is reasonable that things around us [i.e. sensible things] be one in virtue of [their] ψνχ or part of their ψνχ, or something else; otherwise there is not one but (...) many, the thing is divided up. But [mathematical] objects are divisible and quantitative. What is it that makes them one and holds them together?’. (shrink)

This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The Aristotelian model is presented as an application of the ancient, geometrically orthodox conception of extension to the physical world. The other two models, which represent departures from mathematical orthodoxy, are a "quantum" model of spatial magnitude, and a Stoic model, according to which limit entities such as points, edges, and surfaces do not exist in (physical) reality. The book is unique in its (...) discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments. (shrink)