This chapter gives an overview of the problems raised by the concept of motion in the period investigated – specifically, its apparent integration of Being and non-Being, and its combination of Time and Space. It then discusses the central notions employed in the present project: the criteria or standards established for philosophical inquiry (the principles of non-contradiction and of sufficient reason, and a criterion termed “rational admissibility”) and the roles of logic and mathematics in establishing natural philosophy. This chapter lays out broad outlines, systematic and historical, of the issues to be discussed in detail in the ensuing chapters, each of which will deal with one thinker or one school. Thus this opening chapter will serve as a first orientation for the project as well as a reservoir for consultation if questions concerning the basic concepts employed arise during the reading of the whole book.

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.