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 παραδείγματα outlined (...) in theSophistand theStatesman. Against this framework, I shall move to a close examination of specific examples drawn from theTheaetetus(154c–55d), theRepublic(523c–24d), and thePhaedo(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. (shrink)

This paper aims to gain multiple perspectives on Plato’s ontology through the analysis of the Intermediates. Plato refers to them to provide his cosmos with a dynamic structure, in which every part relates to a whole. Nevertheless, this definition could reverse in an opposite: the Intermediate justifies the sensible world to reach the ideal stability, concerning a mixture of being and nothing that gets purification from the becoming by degrees. In this interpretation, the sensibility absorbs life from the Forms, living (...) as their parasite. According to J. N. Findlay, the metaxy state is parasitical because of his logical exemplification of the Ideas, lacking an ontological substance. On the contrary, the void of the half-nothing takes a different role, necessary to establish a symbolic betweenness. (shrink)