A Trivial Source of Wonder: Some Mathematical Examples in Plato’s Dialogues

The purpose of this paper is to reassess some mathematical examples in Plato's dialogues which at a first glance may appear to be nothing more than trivial puzzles. In order to provide the necessary background for this analysis, I shall begin by sketching a brief overview of Plato's mathematical passages and discuss the criteria for aptly selecting them. Second, I shall explain what I mean by 'mathematical examples,' and reflect on their function in light of the discussion on pi alpha rho alpha delta epsilon iota gamma mu alpha tau alpha outlined in the Sophist and the Statesman. Against this framework, I shall move to a close examination of specific examples drawn from the Theaetetus (154c-55d), the Republic (523c-24d), and the Phaedo (96d-97b, 100e-101d). By placing these examples in the broader context of pre-Euclidean mathematics, I shall show that their mathematical content is often less elementary than might appear at first sight. Moreover, by placing emphasis on the specific philosophical concerns that motivated their introduction, I shall argue that the examples are not merely nonsensical jokes. Even if their illustrative purpose is not always immediately clear, and even if they can sound playful and bizarre, they in fact fulfil an important function: by virtue of their power to generate wonder or confusion, they serve as exercises and act as a trigger with respect to the difficult philosophical issues they are intended to clarify.