A Likely Account of Necessity: Plato’s Receptacle as a Physical and Metaphysical Foundation for Space

Abstract

This paper aims to show that—and how—Plato’s notion of the receptacle in the Timaeus provides the conditions for developing a mathematical as well as a physical space without itself being space. In response to the debate whether Plato’s conception of the receptacle is a conception of space or of matter, which presupposes some vague notion of space, I suggest employing criteria from topology and the theory of metric spaces as the most basic ones available. I show that the main task of the receptacle consists in allowing the elements qua images of the Forms to exist as sensible things, since the receptacle is that in which the elements appear, change and move. The receptacle guarantees this possibility by virtue of being pure continuity, while all further qualifications of this continuity required for a full notion of space are derived solely from the content of the receptacle.