Philolaus, aka Philolaus of Croton

Philolaus, aka Philolaus of Croton
c. 470 B.C.
c. 385 B.C.

Greek Pythagorean and Pre-Socratic Philosopher, Mathematician and Physicist postulating all matter is composed of limiting and limitless things, the universe is determined by numbers and credited with originating theory the earth was not the center of the universe

Author Quotes

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 Gn“m“n, 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.

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.

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 of the Sphere.

The first composite (entity), the One, which is in the centre of the Sphere, is called Hearth. The One is the beginning of everything. By nature, not by convention.

The Four Elements of the rational animal are: Brain, Heart, Navel, Genital Organ. The Head is the seat of the Mind, the 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.

The universe is made of two things, limiters and unlimiteds. The unlimited are undefined and include earth, air, fire, water, space, and time. Limiters can be structures like shape. Unlimiteds and limiters fit together harmonically or mathematically. A musical scale is an example where the sound is limited by ratios. [paraphrase]

There are certain thoughts which are stronger than ourselves.

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 recognized 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.

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.

Everything that can be known has a Number; for it is impossible to grasp anything with the mind or to recognize it without this (Number).

For there could not even be an object set before knowledge to begin with, if all things were Non-Limited.

Harmony is a Unity of many mixed (elements), and an agreement between disagreeing (elements).

Nature in the universe was fitted together from the Non-Limited and the Limiting, both the universe as a whole and everything in it.

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.

The head [is the seat] of intellect, the heart of soul (psychê) and sensation, the navel of rooting and first growth, the genitals of the sowing of seed and generation. The brain [contains] the origin of man, the heart the origin of animals, the navel the origin of plants, the genitals the origin of all (living things). For all things both flourish and grow from seed.

Number, indeed, has two proper kinds, odd and even, and a third from both mixed together, the even-odd. Of each of these two kinds there are many forms, of which each thing itself gives signs.

Were it not for number and its nature, nothing that exists would be clear to anybody either in itself or in its relation to other things...You can observe the power of number exercising itself ... in all acts and the thoughts of men, in all handicrafts and music.

Since these beginnings [i.e. limiters and unlimiteds] preexisted and were neither alike nor even related, it would not have been possible for them to be ordered, if a harmony had not come upon them… Like things and related things did not in addition require any harmony, but things that are unlike and not even related … it is necessary that such things be bonded together by a harmony, if they are going to be held in an order.

Nature (physis) in the world-order (cosmos) was fitted together out of things which are unlimited and out of things which are limiting, both the world-order as a whole and everything in it.

All things that can be known contain number; without this nothing could be thought or known.

Author Picture
First Name
Philolaus, aka Philolaus of Croton
Birth Date
c. 470 B.C.
Death Date
c. 385 B.C.

Greek Pythagorean and Pre-Socratic Philosopher, Mathematician and Physicist postulating all matter is composed of limiting and limitless things, the universe is determined by numbers and credited with originating theory the earth was not the center of the universe