Pythagorean School of Ancient Greek Philosophy Texts

Pythagoreanism

Pythagoras (c. 570–c. 490 BCE) founded the school after moving from Samos to Croton in southern Italy around 530 BCE. There he established a secretive community that combined philosophical inquiry, religious practice, and political activity.

Core Teachings

The school prescribed a highly structured way of life. Its central religious doctrine was metempsychosis (μετεμψύχωσις), the transmigration of the soul into a new body after death. This belief in an immortal soul required purification through ascetic practices and intellectual study to achieve liberation.

Pythagoreans held that numbers (ἀριθμοί) are the fundamental essence of reality. They saw mathematical ratios as governing cosmic harmony, most famously in the discovery that harmonious musical intervals correspond to simple whole-number ratios. This principle was extended to describe all natural phenomena as part of a single, intelligible system.

A later development, associated with Philolaus, posited two fundamental principles: limiters (πέρας) and unlimiteds (ἄπειρον). Number was understood as the means by which a limiter structures the unlimited. Another group formulated a table of ten opposing principles, such as limit/unlimited, odd/even, and one/many.

The community lived an ascetic and communal life under the maxim “All things in common among friends.” Members were traditionally divided into two groups: the akousmatikoi (ἀκουσματικοί), who focused on religious rules and teachings, and the mathēmatikoi (μαθηματικοί), who pursued mathematical and scientific inquiry.

Key Figures

Pythagoras (c. 570–c. 490 BCE): The founder and central figure of the school. Philolaus (fl. late 5th century BCE): A Pythagorean who wrote on the principles of limiters and unlimiteds. Archytas (c. 420–c. 350 BCE): A leading figure in Tarentum, known for his work in mathematics, harmonics, and mechanics.

Historical Development

The brotherhood flourished in Croton until the mid-5th century BCE. It faced violent political opposition, including an attack on a meeting house in 510 BCE. Its influence waned in Magna Graecia but was reestablished in the 4th century BCE at Tarentum under Archytas.

By the 4th century BCE, the akousmatikoi tradition largely dissolved or merged with other movements like Cynicism. The mathēmatikoi were increasingly absorbed into the Platonic tradition. After a period of dormancy, Pythagorean ideas saw a revival in the 1st century BCE with the rise of Neopythagoreanism.