The Senses of Apeiron in Philebus 16b–27c

Abstract

Abstract Scholars debate whether ‘apeiron’ (unlimited) is univocal or multivocal in Plato’s Philebus. Offering a ‘middle path,’ I argue that the term is univocal, but used with respect to two senses of unlimited continua. The term appears early in two dense passages on ontological structure: the descriptions of the ‘god-given method’ (16b–18d) and ‘the fourfold division of beings’ (23c–27c). I consider each passage and argue that they respectively concern the eidetic continua of being that the knower comes to understand and the fluxing continua of opposed and co-constitutive bodily elements from which spatiotemporal objects derive their natures. They also indicate two major influences on Plato, respectively the Pythagorean and Heraclitean as recorded in Aristotle’s Metaphysics, and I draw on these resources to develop my account. I conclude by considering some important Platonic lessons that we learn from thinking through this distinction between the related senses of the unlimited.