The Role of Stereometry in Plato’s Republic

Abstract

It is in the Republic that stereometry is referred to as one of the mathematical subjects which constitute the prelude for philosophical dialectic. Plato provides stereometry with a number of remarks which need careful investigation. Some of these can be taken as eulogies on stereometry: its marvellous growth (Rep.528c3); its inherent charm (Rep.528c7); its usefulness for contemplating an unchanging reality (Rep.528c5-6). The other remarks, however, relate to stereometry’s handicaps: its being dishonoured by cities (Rep.528b6); its difficulty as a subject (Rep.528b6); the lack of a director for the study of stereometry (Rep.528b7); the arrogant investigators of stereometry who do not want to obey the director’s advice (Rep.528c1); its being held in contempt by the majority of people (Rep.528c4); its being inappropriately investigated by researchers who are unable to give an account of its usefulness (Rep.528c5-6). It is striking that Plato does not straightforwardly give stereometry the kind of eulogy that he usually bestows upon mathemata, (cf. ‘the subject is essential, since it apparently forces the soul to rely purely on the intelligible and to aim for truth in itself’1). Instead he ascribes to it a character less deserving of eulogy. Moreover, it seems worth noting here that Plato seldom provides such specific details concerning other particular branches of mathematics. Therefore, one of the attempts which will be made in this paper is to investigate those puzzling points for clues as to a particular attitude Plato might have taken towards stereometry upon his encounter with it.