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Ancilla to the Pre-Socratic Philosophers, by Kathleen Freeman, [1948], at sacred-texts.com
Philolâus of Tarentum was active in the latter half of the fifth century B.C.
He was said to have written one book, which was the first published account of Pythagoreanism. The fragments attributed to him are in Doric dialect. Their genuineness has been disputed by modern scholars, probably without justification. 1 This work was usually given the title On the Universe. Another work entitled Bacchae was sometimes attributed to him.
1. Nature in the universe was fitted together from the Non-Limited and the Limiting, both the universe as a whole and everything in it.
2. All existing things must necessarily be either Limiting, or Non-Limited, or both Limiting and Non-Limited. But they could not be merely Non-Limited (nor merely Limited). Since however it is plain that they are neither wholly from the Limiting nor wholly from the Non-Limited, clearly then the universe and its contents were fitted together from both the Limiting and the Non-Limited. This is proved also by actual existing things; for those of them which are made of Limiting (elements) impose Limit, whereas those made of both Limiting and Non-Limited (elements) both do and do not impose Limit, and those made of Non-Limited (elements) will appear Non-Limited.
3. For there could not even be an object set before knowledge to begin with, if all things were Non-Limited.
4. Actually, everything that can be known has a Number; for it is impossible to grasp anything with the mind or to recognise it without this (Number).
S. Actually, Number has two distinct forms, odd and even, and a third compounded of both, the even-odd; each of these two forms has many aspects, which each separate object demonstrates in itself.
6. This is how it is with Nature and Harmony: the Being of things is eternal, and Nature itself requires divine and not human intelligence; moreover, it would be impossible for any existing thing to be even recognised by us if there did not exist the basic Being of the things from which the universe was composed, (namely) both the Limiting and the Non-Limited. But since these Elements exist as unlike and unrelated, it would clearly be impossible for a universe to be created with them unless a harmony was added, in which way this (harmony) did come into being. Now the things which were like and related needed no harmony; but the things which were unlike and unrelated and unequally arranged are necessarily fastened together by such a harmony, through which they are destined to endure in the universe. . . .
The content of the Harmony (Octave) is the major fourth and the major fifth; the fifth is greater than the fourth by a whole tone; for from the highest string (lowest note) to the middle is a fourth, and from the middle to the lowest string (highest note) is a fifth. From the lowest to the third string is a fourth, from the third to the highest string is a fifth. Between the middle and third strings is a tone. The major fourth has the ratio 3:4, the fifth 2:3, and the octave 1:2. Thus the Harmony (Octave) consists of five whole tones and two semitones, the fifth consists of three tones and a semitone, and the fourth consists of two tones and a semitone.
7. The first composite (entity), the One, which is in the centre of the Sphere, is called Hearth.
8. The One is the beginning of everything.
9. By nature, not by convention.
10. Harmony is a Unity of many mixed (elements), and an agreement between disagreeing (elements).
11. One must study the activities and the essence of Number in accordance with the power existing in the Decad (Ten-ness); for it (the Decad) is great, complete, all-achieving, and the origin of divine and human life and its Leader; it shares . . . The power also of the Decad. Without this, all things are unlimited, obscure and indiscernible.
For the nature of Number is the cause of recognition, able to give guidance and teaching to every man in what is puzzling and unknown. For none of existing things would be clear to anyone, either in themselves or in their relationship to one another, unless there existed Number and its essence. But in fact Number, fitting all things into the soul through sense-perception, makes them recognisable and comparable with one another as is provided by the nature of the Gnômôn, 1 in that Number gives them body and divides the different relationships of things, whether they be Non-Limited or Limiting, into their separate groups.
And you may see the nature of Number and its power at work not only in supernatural and divine existences but also in all human activities and words everywhere, both throughout all technical production and also in music.
The nature of Number and Harmony admits of no Falsehood; for this is unrelated to them. Falsehood and Envy belong to the nature of the Non-Limited and the Unintelligent and the Irrational.
Falsehood can in no way breathe on Number; for Falsehood is inimical and hostile to its nature, whereas Truth is related to and in close natural union with the race of Number.
12. The bodies (physical Elements) of the Sphere are five: the Fire in the Sphere, and the Water, and Earth, and Air, and, fifth, the vehicle(?) 2 of the Sphere.
13. (The Four Elements of the rational animal are: Brain, Heart, Navel, Genital Organ). The Head is the seat of the Mind, the
[paragraph continues] Heart of the Soul and of feeling, the Navel of the Rooting and Growth of the original (embryo), the Genital Organ of the emission of Seed and of Creation. The Brain (indicates) the ruling factor of Man, the Heart that of the animal, the Navel that of the plant, and the Genital Organ of them all; for they all derive their life and growth from a seed.
14. The ancient theologians and seers also bear witness that because of certain punishments the soul is yoked to the body and buried in it as in a tomb.
15. (Socrates to Cebes in the 'Phaedo': The theory that we are in a sort of watch-tower which we must not desert is difficult; but I agree that we are one of the possessions of the gods). 1
16. There are certain thoughts which are stronger than ourselves.
Attributed to a prose work called 'Bacchae'
17. (Stobaeus: paraphrase). The universe is one, and it began to come into being from the centre, and from the centre upwards at the same intervals (of distance) as those below. For the parts above from the centre are in inverse relationship to those below; for the centre is to what is below as it is to what is above, and so with all the rest; for both stand in the same relationship to the centre, except in so far as their positions are reversed.
18. (Stobaeus: quotation on the Sun has fallen out).
19. (Proclus: Plato, Pythagorean doctrine and Philolaus in the 'Bacchae' teach theology through mathematical figures).
Doubtful fragments
20. (The Number Seven is like) Nikê (i.e. Athena), the Motherless and Virgin . . . for it is ruler and teacher of all things; it is God, One ever-existing, stable, unmoving, itself like to itself, different from the rest.
20a. The Dyad (Two-ness) is the Bride of Cronos.
Spurious fragments
21. (Quoted by Stobaeus from a work attributed to Philolaus entitled 'On the Soul').
Therefore it (the universe) endures both indestructible and indomitable for endless time. For neither within it will there be found any cause more powerful than itself, nor outside it any cause able to destroy it. But this universe was from eternity and will endure till eternity, One, steered by One, akin to it and most powerful and unsurpassable. The universe, being one and continuous and inspired by the breath of Nature and carried round, has also the beginning of motion and change from its first beginning. And part of it is unchanging and part changing. And the unchanging part has its bounds from the Soul which encloses the Whole as far as the moon; and the changing part from the moon to the earth. But since the moving part circles from everlasting to everlasting, and the part that is moved is disposed in whatever way the moving part carries it, it follows necessarily that one is ever in motion and the other ever passive. And the one is wholly the dwelling (?) of Mind and Soul, and the other of Becoming and Change; and the one is first in power and superior, and the other is second and inferior. But that which is made of both these, namely the ever-running (circling) Divine and the ever-changing Mortal, is the universe.
It is well that the universe should be an everlasting activity of God and Becoming, according to the attendance (on God) of changeable Nature. And he remains One for ever in the same position and condition, but particular existences are coming into being and perishing in vast numbers. And they, when given over to destruction, yet keep their natures and forms, and in birth they reproduce the same form as their father and creator who gave them birth . . .
22. (Claudianus Mamertus (5th century A.D.) purporting to quote from the third volume of a treatise of Philolaus 'On Rhythm and Metre').
The soul is joined to the body through Number and the immortal and likewise incorporeal Harmony . . . The body is loved by the soul, because without it it cannot use the senses. When the soul has been separated from the body by death, it lives an incorporeal existence in the world.
23. (Iamblichus) Number is the ruling and self-created bond which maintains the everlasting stability of the contents of the universe.
73:1 See Companion, pp. 228-9.
75:1 Gnômôn: here, a figure used in solving geometrical problems. Heath, Greek Mathematics, I. p. 78; and Newbold, Philolaus, in Arch. für Gesch. der Phil. (1906) P. 176 sqq.
75:2 ὁλκάς, 'hull of a ship'; some emend to ὁλκός, 'roll' or 'envelope', an unlikely meaning.
76:1 Plato does not name Philolaus here; but his name is applied by Athenagoras (second century A.D.) to a similar statement.