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

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

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

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

Synopsis

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.

Excerpt

This book consists of an analysis of three ancient conceptions or 'models' of spatial magnitude, time, and motion: an Aristotelian, a quantum, and a Stoic model. This characterization, I realize, requires its own apologia. Although the nature and extent of the influence of Aristotle on subsequent Hellenistic thought--philosophical and scientific--is a matter of dispute, I am not particularly concerned with that historical issue here. Rather, my aim is to analyse in some detail Aristotle's account of spatial magnitude, time, and motion, and then to examine two Hellenistic conceptions of these basic physical phenomena as conceptual alternatives to the Aristotelian model. I am aware of the lack of parallelism with respect to my designation of the three models. Although I am uncomfortable about this fact, there seemed no easy way to avoid the situation. There is no simple descriptive tag, analogous to 'quantum', for the Aristotelian and Stoic models. and versions of the quantum theory can be associated not only with the Epicurean tradition but also with the 'Dialectical' philosopher Diodorus Cronus, who was a contemporary of Epicurus.

The Aristotelian model receives the most space (roughly the first half of the book) largely because we have much more hard information about it than we do about the other two models. At one level, the Aristotelian model looks very familiar: spatial magnitude, time, and motion have the formal, structural properties of infinite divisibility and continuity. in other words, these phenomena are 'continua' in one sense of this term. Although Aristotle does not have the mathematical apparatus (e.g. the mathematical concept of a function) capable of rigorously expressing these properties in a contemporary form, he does possess the basic formal, structural ideas. and in some cases his own apparatus is sophisticated enough that it is possible to show that what Aristotle had in mind is closely related to contemporary accounts of certain properties of spatial magnitude, time, and motion. For example, with respect to a stretch of local motion, the continuity of the function from time elapsed to distance traversed (since the beginning . . .

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