Pythagoras: the philosopher

The eternal essence of number, opposites as a creative force, the table of ten pairs of opposites, the music of the spheres and why Pythagoras called the world cosmos.

The priest and the philosopher Pythagoras cannot be separated. At the centre of his thought stands the eternal essence of number. It is the origin that foresees everything, the origin of heaven, earth and the nature in between, and the root from which gods, daimons and divine human beings endure. Orpheus is said to have revealed these words to Pythagoras through a Thracian priest.

In his manner of speaking in coded sayings, Pythagoras is said often to have declared in public speeches: All things resemble number.

Opposites as a creative force

A central idea of Pythagorean philosophy is polarity as a creative principle. This was new in Greek thought. Opposites already play a part in Anaximander (c. 610 to 546 BC). With the Pythagoreans, however, opposition becomes, in the reading of the philologist Walther Kranz, the force that creates the world: light and dark, good and evil, indeed opposition itself, is seen as a basic feature of the world as it appears to us.

Walther Kranz sees here an intellectual link between Greece and the East, since similar ideas are found in the ancient Iranian teaching of Zoroaster. But the Greeks decisively reshaped what they borrowed. They now found opposition in the series of numbers: the odd number stands for firm limit, the even, being divisible again and again, for the unlimited. The bridge between them is harmony, literally the “fitting together” that creates a definite ratio between numbers. The world law that Anaximander had only sensed is defined more precisely through insight into the meaning of number. The Pythagoreans were the first to look into the mystery of number.

Number in music

This shows most clearly in music. The ratio 1 : 2 gives the octave, in old times called “harmony” in the narrower sense, 2 : 3 the fifth, 3 : 4 the fourth. The first four numbers here form three times the ratio of an odd to an even number and so give the basic intervals.

Instrument makers and musicians had long known that string or pipe length and pitch stand in a fixed relation. Pythagoras was the first to study this dependence of harmony on number scientifically. More on the page Number and sound.

The table of opposites

The four, also the first square number, became sacred to the Pythagoreans, as did the sum of the first four numbers, the ten. That is why later Pythagoreans gathered the opposites of the world into a table of ten pairs, handed down by Aristotle:

limited	unlimited
odd	even
one	many
right	left
male	female
at rest	in motion
straight	curved
light	darkness
good	bad
square	oblong

What male and female mean in this table and why the odd stands on the side of limit is explained on the page The masculine and the feminine.

The music of the spheres

Boldly Pythagoras carried the numerical laws of music over to the cosmos, to the distances of the spheres of stars, sun and moon from the earth. For the Pythagoreans the whole cosmos is pervaded by harmony, by fourth, fifth and octave. When their world picture grew richer in the fifth century, they had the five planets Kronos (Saturn), Zeus (Jupiter), Ares (Mars), Aphrodite (Venus) and Hermes (Mercury) circle between the sphere of fixed stars and the earth, together with sun and moon. This number seven corresponded to the seven notes of the octave.

Here lies the origin of the music of the spheres. The idea lives on in poetry to this day and in science has led to harmonic research, which looks for harmonic basic structures in creation (see Harmony of the spheres).

Late biographers such as Porphyry and Iamblichus report that Pythagoras could hear the sounds of the universe. Today we smile at such reports and read them only figuratively. All the more remarkable is that the philologist Walter Burkert, a leading authority on Pythagoreanism, takes them seriously. He draws parallels with the documented abilities of shamans and thinks it possible that Pythagoras heard heavenly music in ecstatic rapture.

Later Pythagoreans went so far as to equate the human soul itself with harmony. The Pythagoreans, by contrast, had as far as we know only taught that the soul can understand harmony because it is akin to the cosmos.

Beauty, wisdom and philosophy

Closely tied to harmony is the idea of beauty, which decisively influenced Plato and Aristotle. According to Iamblichus the purest way of life was that of those who devote themselves to contemplating the most beautiful things. It is beautiful to look at the universe as a whole and to recognise the order in which the stars move. This beauty comes from the world’s share in a First that can be reached only in thought.

This First was for Pythagoras number and proportion, whose nature runs through all things. By number and proportion the universe is harmoniously joined and ordered. Wisdom is knowledge of this beautiful, first, divine, unmixed and ever-unchanging being. Philosophy is the striving for this vision.

Cosmos

This explains the word cosmos for the universe. It originally means arrangement, order and regularity, but also adornment (hence our word cosmetic). Pythagoras is said to have been the first to call the ordered world “cosmos”. Others consider this tradition uncertain and point to a fragment of his older contemporary Anaximenes in which the word already occurs. Whether its wording is genuine is, however, also disputed.

Sources and further reading

Sources

Aristotle, Metaphysics A 5, 985b to 986b (the table of opposites)
Philolaus, fragments B 1, B 6 and B 11 (B 11 is considered spurious)
Iamblichus, On the Pythagorean Life, around 300 AD