This chapter is concerned with the foundations of Hobbes’s natural philosophy, notably his account of space and time, as well as an inertial law the author terms the “persistence principle” and a mechanistic principle of action by contact. The author argues that these foundational concepts and principles serve as a framework that places constraints upon the kinds of hypotheses that may figure in the explanation of phenomena, but they do not uniquely determine how natural philosophy is to be developed. In particular, the author shows that (contra Descartes and Thomas White) Hobbes took questions about the infinitude and uniqueness of the world as unanswerable in principle, although he regarded the question of the vacuum as an empirical matter that could be settled by experiment. Hobbes did, however, hold that certain doctrines (notably the Aristotelian theory of rarefaction and condensation) were incoherent and should be rejected on a priori grounds.