This chapter discusses the atomistic account of motion, as an example of the first reactions to the Eleatic challenge by succeeding natural philosophers. The atomists are shown to change the logical basis by implicitly employing a different conception of negation that allows them to understand Being and non-Being as on a par. It also enables them to build a different ontological basis in which non-Being qua void plays a central role in natural philosophy. This new ontological basis allows the atomists to integrate the phenomenal world into their philosophy and to deal with the mereological problems bequeathed by Zeno’s paradoxes. The starting point for this development is the idea that what truly is must in some way also be responsible for the appearances of the phenomenal world. Generation on the phenomenal level is now understood as the combination and separation of aggregates of atoms, while change consists in the rearrangement of some parts of the aggregate. Although the atomists’ notion of the void can be seen as a predecessor to a notion of space, they do not in fact react to the spatio-temporal paradoxes of Zeno.

The main object of this book is to study how the understanding of physical motion in ancient Greek thought developed before and up to Aristotle. It investigates which logical, methodological, and mathematical foundations had to be in place to establish a fully fledged concept of motion that also allows for comparing and measuring speed.1 Given that physical motion is the core concept of natural philosophy, this study thereby also seeks to reconstruct in rough outlines how natural philosophy came to be established as a proper scientific endeavour in ancient Greece.2

The basis of Aristotle’s strategy for bringing together time and distance covered in an account of motion is his understanding time, distance, and motion as continua. Against the background of Parmenides’ notion of continuity and the atomistic understanding of magnitudes, this chapter investigates Aristotle’s notion of continuity. It demonstrates the extent to which Aristotle adopts a mathematical notion of continuity according to which divisibility without end is crucial, and it expounds his appropriation of this mathematical notion for the physical realm. The main characteristics of Aristotle’s account of continuity turn out to be a new part-whole relation (in which the whole is prior to the parts since it is only by dividing the whole that we gain parts), a new account of limits, a new understanding of infinity, and a careful distinction between potential divisibility and actual division. We see how this new understanding of continuity helps counter the mereological problems of Zeno’s motion paradoxes by making it illegitimate to define time, space, and motion in terms of an additive part-whole-relation.

In the third chapter I show how Zeno takes up and advances Parmenides’s criteria for philosophy by developing the genre of paradoxes. The paradoxes are based on Parmenides’s understanding of the principle of non-contradiction but allow Zeno to start with the position of his opponent in order to show how this position will yield inconsistencies. The mereological problems raised by the plurality paradoxes will be discussed, but the main focus will be on Zeno’s paradoxes of motion which seem to show motion to be self-contradictory. They confront natural philosophers with two kinds of problems, mereological ones and spatio-temporal ones. I argue against viewing the paradoxes as simply awaiting their solutions in modern mathematics to be solved. Instead, I interpret them as questioning the very consistency of the notions of time, space, and motion. In this way Zeno’s paradoxes will be shown to constitute one of the severest attacks on any project of conceptualizing motion. The paradoxes will therefore act as a touchstone for whether natural philosophy can develop in such a way as to meet Parmenides’s challenge.

Chapter 5 examines the development of the logical basis required for natural philosophy in Plato. In particular it shows how Plato in the Sophist develops further understanding not only of negation and the connection operator, but also, in connection with this, the principle of non-contradiction. These developments allow for connecting Being and non-Being, which is necessary for making sense of motion without falling into inconsistencies. The chapter then examines Plato’s employment of the principle of sufficient reason and the criterion of rational admissibility in the Timaeus. He develops the principle of sufficient reason further by distinguishing for the first time between necessary and rational reasons. And rational admissibility is taken up by Plato in the way used by the atomists: that is, the basic ontological constituents not only have to be testable by our own reason, but they also have to explain the phenomena. These requirements together emerge as Plato’s standards for natural philosophy and cosmology by being the positive criteria an eikôs mythos has to fulfil.

This monograph is the first study to assess in its entirety the fourth-century CE Latin translation of and commentary on Plato's Timaeus by the otherwise unknown Calcidius.The first part examines the authorial voice of the commentator and the overall purpose of the work; the second part provides an overview of the key themes; and the third part reassesses the commentary's relation to Stoicism, Aristotle, potential sources, and the Christian tradition.

This chapter examines the role of matter as an independent principle in the universe, and shows how Calcidius' borrows elements from Aristotle, the Stoics, and the "Pythagorean" Numenius to posit a minimal dualism.

This chapter examines Calcidius' position vis-à-vis and use of Stoicism, focusing on the themes of Providence and fate, the human soul, and matter, and argues that the Stoic influence is much stronger than commonly assumed, despite an overt polemic.

This chapter examines the extent to which matter can be said to have being, the role of the Platonic Forms, and the methods for discovering the metaphysical principles of the universe.

This chapter looks at the manner in which Calcidius presents allusions to Christian views (in comparison with known Christian authors of the era), his use of the "Hebrews," and his minimal reliance on Origen.

This chapter examines Calcidius' use of Aristotle, focusing on the topics of fate, the human soul, and matter.

This chapter examines Calcidius’ doxographical method, his view of the composition of the human soul, and the latter’s relation to the World Soul

This chapter examines how Calcidius sees his role as commentator in relation to his own translation, and his posiiton vis-à-vis the Platonist tradition.

This chapter reassesses the role of the divine and matter in Calcidius' commentary in comparison with views attested for Christian authors of this era, in order to highlight the incompatibility between the two worldviews.