Abstract

This chapter examines whether space and extended bodies are ultimately composed of points (and point‐masses) or spatial regions (and voluminous bodies). It focuses on three positions: Pointillism, according to which only points and point‐sized bodies are fundamental; Voluminism, according to which the only fundamental things are regions and voluminous bodies; and Volume‐Boundary Dualism, according to which both points and regions really exist and are equally fundamental. The first prima facie problem for Voluminism concerns continuous variation. The chapter looks at the idea of constructing points from regions and concerns whether points or regions are fundamental. It lays out three arguments against Pointillism, the thesis that points are the only fundamental entities, namely, the arguments from Finitism, from mathematical paradoxes, and from the nature of contact. Aristotelian Finitists can explain why some sets of points have measurable volume and why some do not.