Anna S. Kuznetsova




A paper based upon a MA thesis, defended at Philosophy Department

of Novosibirsk State University in 2005 and received an award of Russian Academy of Sciences in 2006 (cf. pictures)


The complete text (in Russian)



1. The concept of harmony in Early Greek philosophy

1.1. Preliminary remarks

1.2. The harmony of oppositions in Heraclites

1.3. The concept of harmony in Empedocles

1.4. Harmony in Democritus

1.5. Early Pythagoreanism

2. Pythagorean concept of harmony in Ancient philosophic tradition

2.1. Preliminary remarks

2.2. From Plato to Posidonius

2.3. Pythagoreanism in Late Antiquity

2.4. Concluding remarks





The concepts of symmetry, proportion and harmony are already found in the earliest known written sources of different people. Surely the concepts first occur in connection with building techniques. However philosophers started to think of these notions from the very beginning. It should be noticed that the contemporary studies are also mainly concerned with harmony, viewed from the position of Art-historians, often in conjunction with symmetry, proportion and kanōn. Harmony is also much studied by the historians of mathematics and geometry. Researches are continued to be interested in applied aspects of harmony. The concept of harmony as it can be discerned from the fragments and testimonia of Ancient authors still did not receive attention it deserves.

The concept of harmony is commonly associated with Pythagoreanism, but other Early Greek philosophers are of interest in this connection. In Heraclites harmonia is closely connected with the notion kosmos understood in the sense of world order and mundial structure. Things are connected via oppositions (‘a back-stretched connection, as in the bow and the lyre’, fr. 51 DK). This produces Harmony, Beauty and Life. There is no Life without Struggle, according to Heraclites. Fate and Harmony are also connected: Fate is the mind (logos) which creates the world in accordance with Harmony. So Harmony becomes the principle of creation.

Harmony is vital in the processes of world change. But in case with Empedocles we face the problem that his metaphysical foundations are not clearly verbalized in the extant evidence. The Sphere is Harmony embodied. It is a specific form of the elements connection, correct conjunction between them under the influence of Love, achieved as a result of a long evolution. Harmony is the most essential feature of the Sphere. Harmony opens up in Love. As Strife steps back, Love connects separated elements according to Harmony. When Strife is reduced to the utmost limits of Sphere the things ‘stay fast in the close covering of Harmony’ (fr. B 27 DK). We can see therefore that Harmony is a static condition, since in the period of Love dominance the elements ‘fitted together by the divine bonds of Harmony’ (fr. B 26 DK).

Pythagorean concept of harmony developed during a lengthy period of time. The concept of harmony proves to be a key to the entire history of Pythagoreanism over roughly thousand years of its development. In Plato Pythagoreanism acquires new features and certain Pythagorean ideas receive further developments, which opens the way for their new metaphysical applications both in Platonism and Stoicism. The systematic analysis of the history of development of Pythagorean ideas allow to approach a difficult question of identification of the earliest layer of Pythagoreanism.

Among the earliest evidence of Pythagorean acusmatic tradition is the famous oath of Tetractys equated with harmonia (‘sung by Sirens’). This shows that the concept of harmony was already current in Early Pythagorean tradition.

Pythagorean ontology first occurs in Philolaus. Harmony is a law which rules according to limit (peras) and unlimitness (apeiron), thus defining the proportion (logos) in things. Harmony therefore is a necessary condition of worlds existence. Understood both in ethical and epistemological aspects, harmonia in Philolaus is limited, as it were, by ethical frames, which makes it comprehensible. Archytas connected the concept of harmony with social justice. He is also known by his mathematical studies, having defined the harmonic mean for the first time.

The second chapter deals with the so-called Revived Pytagoreanism.  Having discussed briefly such transition figures as Posidonius, we approach the Neopythagoreans properly speaking, such as Moderatus of Gades, Nicomachus of Gerasa, and Numenius of Apamea. Moderatus describes the soul as harmonia in a sense that it produces symmetry and agreement in things quite different in other respects (Jamblichus, De anima, ap. Stobaeus, I p. 364 Wachs.). Nicomachus as Earlier Pythagoreans is sure that the world is harmonized by the Tetractys. In Numenius imagination ‘the Demiurge, binding Matter fast by harmony, so that it may not break loose or wander astray’ (fr. 18 des Places). Here harmony is used by the Demiurge as a mean of establishing the world order.

Having considered the concept of harmony in historical prospective, we have noticed certain important changes. The earliest Pythagorean constructions, although somewhat speculative, in general followed the scientific method. Harmony first played a part in mathematical theories and only than transmitted to other areas of philosophy (being reinterpreted, for instance, as social justice or an ethical concept). Even in Philolaus, whose metaphysical interpretation of harmony breaks with the earlier mathematical tradition, we find, in the given historical context, a more solid justification, than in the later Neopythagorean tradition.  Kosmos of the latter is inhabited by the host of entities of uncertain ontological status, which hardly clarifies the original concept of harmonia (means of joining, fastening).