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Chapter 13 - Harmonia in Philoponus’ Commentary on Nicomachus’ Introduction to Arithmetic

Published online by Cambridge University Press:  27 November 2020

Francesco Pelosi
Affiliation:
Università degli Studi, Pisa
Federico M. Petrucci
Affiliation:
Università degli Studi di Torino, Italy
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Summary

In his commentary on Nicomachus’ Introduction to Arithmetic, John Philoponus explains the role that mathematics, and hence harmonics, play in Platonic philosophy, as redefined by the Neoplatonists. There are two main issues regarding harmonics. The first issue: harmonics is one of the mathematical sciences that lead to the knowledge of divine and absolutely immaterial entities; but harmonics also concerns other mathematical disciplines, because there is an astronomical harmony, that is, the harmony of the revolution of the stars, and there is a geometric harmony, that is, the cube, one of the Platonic solids that are the constitutive elements of the physical world as a geometric model of equality. The second issue: there exists a harmonic proportion, already known to the Pythagoreans, Plato and Aristotle. Both these aspects in Philoponus’ study of harmonics have a common denominator, namely the fact that, as Plato teaches in the Timaeus, the universe, its soul and human souls have a numerical structure based on the relationship between two principles, that is, equality and inequality. But harmonics is precisely the mathematical science of relationship. Therefore, harmonics has a privileged place in the Neoplatonic philosophical system, as Philoponus’ commentary worthily testifies.

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Publisher: Cambridge University Press
Print publication year: 2020

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