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

Kalyvas, Thomas LU (2024) SPVR01 20241
Greek (Ancient and Byzantine)
Master's Programme: Language and Linguistics
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
Kalyvas, Thomas LU
supervisor
organization
course
SPVR01 20241
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Plato’s philosophy of mathematics, ἀριθμητική, λογιστική, γεωμετρία, oracular vocabulary, spirituality, σωτηρία, ἀριθμός, ἀλήθεια, προποδισμός
language
English
id
9171076
date added to LUP
2024-08-21 12:57:27
date last changed
2024-08-21 12:57:27
@misc{9171076,
  abstract     = {{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.}},
  author       = {{Kalyvas, Thomas}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Plato’s Philosophy of Mathematics: ἀριθμητική (Arithmetic), λογιστική (Logistikē) and γεωμετρία (Geometry) as ‘Spiritual’ Mathematics}},
  year         = {{2024}},
}