_ Source: _Volume 61, Issue 1, pp 43 - 59 Contemporary debate on Plato’s cosmogony often assumes that the ‘literal’ reading of the _Timaeus_ yields an account of creation, while the view that the cosmos always existed is non-literal. In antiquity, Taurus has been seen as a forerunner of the ‘non-literal’ interpretation. This paper shows, on the contrary, that Taurus’ argument for the sempiternity of the cosmos is a literalist one, relying on a strict linguistic analysis of _Timaeus_ 28b6-8.

In Archytas of Tarentum, Carl Huffman reconstructs Archytas’ theory of definition by linking definitions to the mathematical study of ratios and proportions. This paper considers whether and how Archytas used definitions and whether he possessed a theory of definition. Our evidence does not support the claim that Archytas has a theory of definition, and his approach to the science of harmonics suggests that he relied on analogies and proportions in the practice of inquiry. We understand sounds and other entities by (...) placing them in a network of relations governed by mathematical proportions. Although he does not seem to have formulated definitions of sound, Archytas pursued inquiry into motion and rest by formulating definitions in such a way that they fit into a larger network of causal explanations. (shrink)

The Euclidean ‘Division of the canon’ and Pythagorean harmonics: The article presents the first Polish translation of a short Ancient Greek treatise entitled The division of the canon, which is commonly dated to the 3rd century BC, with a doubtful assumption that the author of the treatise is Euclid himself. It is the oldest surviving text derived from the mathematical school of harmonics, which combined the mathematical theory of proportion with the musical laws of harmony. The main purpose of this (...) Euclidean treatise is to describe the instrument called canon, which consists in determining the successive notes of the Greek musical system by means of mathematical principles. The treatise essentially consists of two distinct parts: an introduction and twenty propositions in the style of Euclid’s Elements. To bring this highly esoteric text closer to the modern reader, the translation is preceded by a brief introduction, which deals with the basic issues of the transmission of the text, its structure, and the problem of authorship. The philosophical problems of the treatise and its basic concepts are also discussed. An underlying idea of both the introduction and the work on the translation is that The division of the canon is an eminently Pythagorean text, which both expressed and proved their conviction about the mathematical structure of the universe. (shrink)

In this paper, I reconstruct the reasons why Aristotle thinks that musical education is important for moral education. Musical education teaches us to enjoy appropriately and to recognize perceptually fine melodies and rhythms. Fine melodies and rhythms are similar to the kind of movements fine actions consist in and fine characters display. By teaching us to enjoy and recognise fine melodies and rhythms, musical education can train us to recognize and to take pleasure in fine actions and characters. Thus, musical (...) education can, up to a point, lead us toward the actions and character dispositions a virtuous life requires. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

Plato treats of the topic justice in the Republic, offering the concept of harmony as a perspective from which to examine this difficult concept. An ideal existing in a realm that is separate from the human and physical cosmos, justice is difficult to explain and even more so to achieve. Plato's disenchantment with his beloved city urges him on in this difficult task, especially difficult because the word harmony refers to tuning patterns for lyres and not to agreeable blending of (...) musical notes. Does he achieve his goal? (shrink)

This paper examines the relation between Pythagorean and Heraclitean political views. I argue that for Pythagoras, Heraclitus, and Archytas the cosmological and musical notions of harmony (ἁρμονία) and the related notion of concord (ὁμόνοια) have an intrinsic political significance. These thinkers variously reflect upon political harmony and concord, and agree that a crucial condition for it is law (νόμος), which according to Pythagoras and Heraclitus has a divine origin. I begin with the Heraclitean fragments 22 B51, 54, 72, and 114 (...) DK, in which social and political reflection is connected with the theory of the harmony of opposites. In the case of Pythagoras and early Pythagoreanism, the intense, albeit indirect political influence in Magna Graecia—as transmitted by Iamblichus and Porphyry—offers evidence for social and political ideas determined by a reflection on the cosmological role of harmony and number. Finally, Archytas’ political application of rational calculation in fragment 47 B3 DK, which aims at producing concord by establishing the just measures of wealth in the city, together with the testimony on Archytas’ intense and fruitful political activity, can be taken as confirmation that the thinker’s wider cosmological views were indeed intertwined with his political reflection and action. (shrink)

This thesis regards the ancient Pythagorean-Platonic idea of heavenly harmony as a philosophical paradox: stars are silent, music is not. The idea of ‘star music’ contains several potential opposites, including imagination and sense perception, the temporal and the eternal, transcendence and theophany, and others. The idea of ‘star music’ as a paradox can become a gateway to a different understanding of the universe, and a vehicle for a shift to a new – and yet very ancient – form of consciousness. (...) The ancient Greeks had a holistic form of consciousness, which was continually intermingling with a transpersonal dimension. This ancient state of consciousness was related to a musical understanding of the world, the Pythagorean-Platonic experience of the universe as an ordered cosmos. My research is approached from two angles, namely from the history of ideas and from musicianship, exploring how music is reflected in the world of thought. By reflexive re-reading of the sources, new insights into the nature of musical consciousness are explored. The idea of ‘star music’ can be found throughout the history of music and thought in the West, including Plato’s works and that of other ancient philosophers, through the Middle Ages, the Renaissance, the Romantic era and the twentieth century up to contemporary New Age music. As a conclusion, the paradox of ‘star music’ is connected to an experience of a shared transcendent meaning of music, which can be present in the moment of a musical performance. ‘Star music’ is a living paradox. (shrink)