With his Commentary to the I book of Euclid’s Elements, Proclus aims at sharing to the philosophy in its whole: the neoplatonics philosophers, heirs of Plato and Aristotle, as well as of the neopythagorian tradition, attributed in fact to the mathematics a role of the first rank in the philosophy. The Proclus’ interest toward Euclid, that he quite considered a Platonic, is not exclusively mathematical, but, as I said, philosophical. In this general perspective, Aristotle, and especially Aristotelian logic, plays an important role in the Commentary, also for the fact that, according to Proclus, Aristotle doesn’t constitute an alternative to Plato, with which, he is substantially in accord. Aristotle is so used by Proclus at the aim of elaborating his own philosophical-mathematical theories. In this study, particularly, are examined the theories of abstraction and motion of mathematical objects, of infinity, of imagination (phantasia) as metaphysical matter in which the reason marks numbers and geometric figures, and still the distinction between definitions and hypothesis and between arithmetic and geometry, with a view to determine what is precisely Aristotle’s role in the Proclus’ Commentary to Euclid.

Considerazioni critiche sulla presenza di Aristotele nell'In Euclidem di Proclo

GIARDINA, GIOVANNA RITA
2008-01-01

Abstract

With his Commentary to the I book of Euclid’s Elements, Proclus aims at sharing to the philosophy in its whole: the neoplatonics philosophers, heirs of Plato and Aristotle, as well as of the neopythagorian tradition, attributed in fact to the mathematics a role of the first rank in the philosophy. The Proclus’ interest toward Euclid, that he quite considered a Platonic, is not exclusively mathematical, but, as I said, philosophical. In this general perspective, Aristotle, and especially Aristotelian logic, plays an important role in the Commentary, also for the fact that, according to Proclus, Aristotle doesn’t constitute an alternative to Plato, with which, he is substantially in accord. Aristotle is so used by Proclus at the aim of elaborating his own philosophical-mathematical theories. In this study, particularly, are examined the theories of abstraction and motion of mathematical objects, of infinity, of imagination (phantasia) as metaphysical matter in which the reason marks numbers and geometric figures, and still the distinction between definitions and hypothesis and between arithmetic and geometry, with a view to determine what is precisely Aristotle’s role in the Proclus’ Commentary to Euclid.
Proclus; Aristotle; Euclid; mathematical objects; infinity; principles
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/31796
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