Pythagoras of Samos (ca 570 – 495 BCE)
In the ancient tradition Pythagoras (Grk. Puthagoras) is presented as a philosopher, scientist,
religious reformer and politician. The old debate on the reliability of this image is still
unresolved. Some scholars accept evidence for Pythagoras’ scientific and philosophical
activities, but disagree on what can be safely ascribed to him; others regard him only as a
religious leader and moral reformer. Like T and So ̄crate ̄s, Pythagoras wrote nothing,
whereas his pupils and followers, unlike So ̄crate ̄s’ pupils, did not take care to expose his
ideas. Absence of direct sources is only partially compensated by a very extensive indirect
tradition, which can be used only as far as it goes back to the 5th/4th centuries.
Pythagoras left Samos ca 530 because of Polukrate ̄s’ tyranny and moved to Kroto ̄n.
Owing to his talents and charisma he found here many supporters and founded a political
community. A special way of life and cultivation of friendship contributed to the rallying of
the Pythagoreans; many of Pythagoras’ ethical rules had a religious basis and were sup-
ported by belief in his god-like nature. The Pythagoreans’ influence increased after the
defeat of Subaris by a Krotonian army under Pythagorean command (ca 510). Shortly after
this, an opposing faction of the Krotonian elite organized an anti-Pythagorean revolt;
Pythagoras fled to Metapontion, where he soon died.
Pythagoras’ teaching has to be considered in a context of the Ionian natural philosophy
and science. A cosmogony that might go back to him explains the origin of the world by the
interaction of two principles, “limit” and “unlimited.” The “unlimited” is identified with an
empty space and with an infinite pneuma that surrounds kosmos. It is inhaled into the
kosmos and, limited by “limit,” begins to separate individual things from each other.
Opposite principles of a different kind play a further and important role both in the
Pythagoreans (A, M, P) and in other Italian philosophers
(P, E).
Pythagoras’ contributions to cosmology and astronomy are hard to discern. Such import-
ant discoveries as the sphericity of the Earth, a division of heavenly and terrestrial spheres
into zones, an identification of the Evening and Morning star with Venus, are ascribed both
to Pythagoras and Parmenide ̄s. Independent planetary movement from west to east and on
circular orbits are first attested in the Pythagorean Alkmaio ̄n (24 A4, 12 DK). It is possible
that relying on A’ concept of “geometrical kosmos,” Pythagoras trans-
ferred to the planets the circular motion inherent in the Sun, the Moon and stars in
Anaximandros’ system. According to the early Pythagorean theory of “heavenly har-
mony,” the circular motions of all the heavenly bodies produce sounds; their pitch depends
on the speed of motion, which, in turn, corresponds to the relative positions of the heavenly
bodies: the farther from the Earth the greater speed of rotation. The speeds correspond to
each other as the harmonious intervals, so that common circular movement of all the
bodies generates harmonious sound.
The search for the heavenly harmony was undoubtedly prompted by Pythagoras’ dis-
covery of the numerical expression of harmonic intervals: octave (2:1), fourth (4:3) and
fifth (3:2). Most probably, he obtained these results by dividing the string of a monochord;
further scientific experiments in acoustics were carried out by Pythagoras’ student
H. Pythagoras’ discovery laid the foundations of the mathematical harmonics and
contributed to the formation of the mathematical quadrivium: geometry, arithmetic,
astronomy and harmonics (A 47 B1 DK). The theory of proportions valid for
commensurable magnitudes became a link between all the four sciences. It is very probable
PYTHAGORAS OF SAMOS