Abstract

In his Euclid commentary, Proclus states that mathematical objects have a status in between Platonic forms and sensible things. Proclus uses geometrical examples liberally to illustrate his theory but says little about arithmetic. However, by examining Proclus’s scattered statements on number and the traditional sources that influenced him, I argue that he maintains an analogy between geometry and arithmetic such that the arithmetical thinker projects a “field of units” to serve as the bearers of number forms. I argue that this conception of a “multitude,” wherein each unit differs in no way from the others, implies that Platonists need not recognize unqualifiedly what would become the principle of the identity of indiscernibles. I argue that Cratylus 432c in particular provides support for a reading of Plato as consistently thinking beyond the principle of identity. I conclude by drawing out an important epistemological and ethical lesson from this reading.