Plato’s Philosophy of Mathematics: ἀριθμητική (Arithmetic), λογιστική (Logistikē) and γεωμετρία (Geometry) as ‘Spiritual’ Mathematics

Sammanfattning

This thesis examines the nature and purpose of the Greek sciences ἀριθμητική, λογιστική and γεωμετρία in the texts of Plato. The statements of some other ancient authors are also mentioned, and the relevant modern research is consulted. ἀριθμός is at any instance, as Klein has already noted, ‘a definite number of definite objects’. In Plato’s philosophical ἀριθμητική, ἀριθμός seems to always consist of ‘the odd and even’, or it is the ‘multitude of the μονάδων/units’, just as in Euclid. Many of the key concepts of Plato’s mathematics appear to have a hierarchical order, or a duality (perhaps later called ‘προποδισμός’ process, progression). Plato seems to employ a peculiar ‘oracular/religious vocabulary’ which is only recognized in the original Greek sources. There is an obvious form of ‘spirituality’ in the entire philosophy of Plato’s mathematics. The source of the mathematical concepts, and of the ‘Forms’, is from a god (Prometheus?). The concept of the soul’s purification and ‘σωτηρία’ (salvation) is probably one of the ultimate purposes of Plato’s mathematics, along with the aim of reaching the ‘Good’ and ‘Being’. ἀριθμητική, λογιστική and γεωμετρία draw the soul towards ‘Truth’ (“πρὸς ἀλήθειαν”), and this is one of their purposes and an oft-mentioned theme by Plato. It is concluded that Plato’s mathematics is in its broadest extent an all-encompassing study of the very things (τῶν ὄντων) of nature and existence, in the background of a spiritual philosophy.