The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective

An analysis of three ancient models of spatial magnitude, time and local motion. The Aristotelian model is presented as an application of the ancient conception of extension to the physical world. The other two models are a "quantum" model of spatial magnitude and a Stoic model.
The Continuous and the Discrete presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion.

Professor White 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 of the book the author 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 standardEuclidean' 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 author'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.