This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The book connects the Aristotelian model, which represents spatial magnitude, time, and motion as infinitely divisible and continuous, with the standard ancient geometrical conception of extended magnitude: it is a model which represents the marriage of physical theory and mathematical orthodoxy. In the second half the book discusses two ancient alternatives to the Aristotelian model: ‘quantum’ models, and a Stoic model according to which limit entities such as points, (one-dimensional) ... More

This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The book connects the Aristotelian model, which represents spatial magnitude, time, and motion as infinitely divisible and continuous, with the standard ancient geometrical conception of extended magnitude: it is a model which represents the marriage of physical theory and mathematical orthodoxy. In the second half the book discusses two ancient alternatives to the Aristotelian model: ‘quantum’ models, and a Stoic model according to which limit entities such as points, (one-dimensional) edges, and (two-dimensional) surfaces do not exist in (physical) reality. Both these alternative models deny the applicability of standard ‘Euclidean’ ancient geometry to the physical world. A unique feature of the book is the discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments. A basic assumption of the book's approach is that such a contemporary perspective can deepen our understanding not only of ancient philosophy, physics, and mathematics, but also of later developments in the content and methodology of these disciplines.