The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics by Barbara M. Sattler (review)

A large part of the difficulty of writing "conceptual history"—to borrow a term from Reviel Netz (The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History [Cambridge: Cambridge University Press, 1999])—is that once an illuminating new conceptual framework is articulated, it begins to seem self-evident and commonsensical to later thinkers. The historian's task of problematizing the obvious, and showing us the moves by which commonsense came to be created historically, is an arduous and challenging one, requiring resources of imagination, patience, and attention to detail. Sattler displays all those qualities in this dense and demanding study, and a review needs to begin by acknowledging the sheer hard work that lies behind a book of this kind. It is an achievement.

It is nonetheless necessary to clarify the skopos of this book: it is not a general treatment of the concept of motion in ancient Greek thought, nor even in ancient Greek philosophy. It stops with Aristotle—and only some of Aristotle—leaving many issues aside. The reason for the breadth implied in the title may simply be that the book encompasses two distinct projects. The second is an inquiry into the conceptual equipment required for applying quantitative analysis to the speed of moving bodies in the natural world, heaving closer to the territory the title suggests. The first project is much more ambitious: it is an account of the struggle to articulate the presuppositions necessary for an account of change in early natural philosophy more generally, retelling the traditional account of the response by early atomists, Plato, and Aristotle to the challenge posed by Parmenides. Whatever the merits of the first project, much of its work seems separable from the second. In a book of four hundred pages, it is worth asking whether, despite some overlap, the two projects really belong in a single volume.

The second project is, in my view, the book's stronger suit: it problematizes much that may seem commonsensical and offers a brilliant account of the intellectual background to Aristotle's articulation of the notions of time and space. It addresses the conceptual equipment required for applying quantitative analysis to the locomotion of bodies in the natural world. Sattler highlights Aristotle's achievement in conceptualizing both time and space as continua. The central idea is that a notion of speed requires a new way of approaching measurement that is distinct from counting units, and that would allow for the compounding of two distinct dimensions. Aristotle does not completely realize this task in his Physics, and Sattler argues that central commitments in Greek mathematics at the time impeded the development of an adequate account of speed that can be distinguished from either the measure of distance or the measure of time. It is a fascinating story, and the last three chapters include much careful reflection on the conceptual tools required for thinking about measuring speed, including some discussion of the problem of angular velocity in astronomy. There are other topics in the vicinity that might complement this work—Strato's attempts to measure acceleration, the Mechanica method for summing speeds in different directions, the use by some mathematicians of a moving point to define the notion of a line—and the planned successor volumes on space and time suggest that we can hope to hear more from Sattler on these themes.

The analysis of motion is somewhat crowded out by the former project, which is a broader story about the possibility of rational inquiry into change in the natural world. Sattler traces a narrative from the Eleatics through the atomists to Plato's Sophist. Her analysis is expressed in a terminology of operands and operator, rather than different senses of Being, and whether or not this furthers our understanding of Parmenides is an issue I will leave for others to assess. Sattler wants to change the terms...