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.