Abstract

In his commentary on Euclid, Proclus develops what he takes to be an important Platonic critique of the epistemology of abstraction. As I argue, his argument closely reflects terminology and concepts from Plato’s Philebus. Both emphasize the priority—in reality and in our awareness—of the precise over the imprecise. Specifically, Proclus’s famous notion of the psychical “projection” of intermediate mathematical entities, while having no technically exact precedent in Plato, finds a conceptual neighbor in the Philebus’s suggestion that philosophical arithmeticians “posit” pure units for counting. Likewise, for both our self-engagement in mathematical thinking serves to clarify the independence of the precise sciences—both in their content and in their practice—from perception. Thus, as I argue, Plato and Proclus, with their different terms and nuances, develop a shared conception scientific inquiry in which an activity of “creative discovery” plays a central role.