The Pythagorean brotherhood developed ideas about knowledge that influenced classical Greek philosophers and lasted more than one thousand years. Pythagoras’s mathematical theorems were intended to show the relation between the abstract, mystical concept of number and the physical universe.

The doctrines espoused by the Pythagorean brotherhood were repeated by a number of thinkers. For example, the final conversations of Socrates with his friends as described in the Phaedōn (c. 388-368 b.c.e.; Phaedo, 1675) reveal Plato’s immense debt to Pythagoras and his school. In addition, the Pythagoreans stand out in the history of science as precursors to the later understanding of the structure of the universe in terms of mathematics. Even Nicolaus Copernicus and Johannes Kepler incorporated the mystical importance of “number” in their heliocentric theories of the sixteenth and seventeenth centuries c.e. It is unfortunate, then, that the facts about Pythagoras and his brotherhood are shrouded in legends that began in his own lifetime and grew more colorful during the millennium after his death. Adding to the confusion is the fact that the followers of Pythagoras usually signed his name to their own writings, which did not necessarily contain orthodox Pythagorean philosophy. Archytas of Tarentum
Philolaus of Croton
Pythagoras

Although reliable information is scant, it can be stated that Pythagoras was born about 580 b.c.e. and lived until maturity on the Ionian island of Samos during the period when it was economically and culturally prominent. He had already acquired fame as a sage well versed in the learning of his age and also as an exponent of doctrine about the immortality of the soul when he left Samos about 540 b.c.e. According to tradition, he left Samos because he was opposed to the tyranny of Polycrates. He then settled in Croton, one of the Greek cities in southern Italy and Sicily that made up the region known as Magna Graecia. In Croton, he organized a secret society of mixed religious, philosophic, and political interests that had become dominant by 510, and he played a leading role in the war between Croton and Sybaris, which established the hegemony of Croton over the other cities of Magna Graecia. In 509 b.c.e., a democratic rebellion expelled the Pythagorean party from power in Croton, and Pythagoras moved to Metapontum, where he died about 500 b.c.e.

Pythagoras addresses a group of people.

(F. R. Niglutsch)

His followers founded a number of Pythagorean societies of an oligarchic nature. These groups played a leading role in several cities of Magna Graecia until about the middle of the fifth century b.c.e., when they were expelled in a violent upheaval. Afterward, several survivors migrated to the Greek mainland and established communities in Thebes and in Phlius. The foremost of these Pythagoreans was Philolaus of Croton. He is referred to in the Phaedo even though he wrote only one genuine book. In this work, he argued that “unlimited” and “limiting” substances were bound together through harmony to form the natural world. After the beginning of the fourth century, Pythagorean influence in southern Italy was reestablished with its center at Tarentum under the leadership of Archytas. This philosopher is noted for his collection of a variety of evidence in an attempt to prove that there is a relationship between the pitch of a musical note and its “speed,” or measure.

It is a matter of debate which doctrines may reasonably be attributed to Pythagoras and the society that he founded. The most prevalent view is that the society’s activities were based on a curious fusion of religious belief and speculative cosmology dominated by mathematics. The religious doctrine shared an affinity with so-called Orphic conceptions of the transmigration of souls. The soul, according to this doctrine, is distinct in origin from the body, in which it is imprisoned during a person’s lifespan. Originally akin to the fires of heaven, it has entered at birth into a body from which it is released at death, only to enter anew into another body in a continuing cycle of successive reincarnations. The soul cannot free itself permanently from the cycle of reincarnation until it has successfully purified itself of the corruption to which its bodily imprisonment has subjected it. The distinctive element of the Pythagorean concept of purification is that, although one must engage in ascetic practices of bodily denial, the primary purifying activity is the intellectual endeavor to understand the nature of the heavenly bodies and their harmony.

This endeavor was based on the assumption that understanding the essence of the astral harmony enables the soul to “recollect” its primal astral purity and actualize at last its divine nature. The Pythagoreans believed that the essence of the heavenly bodies and their interrelationships was number: One came to understand the heavens by understanding the geometrical and arithmetical ratios involved in the constitution of the cosmos. They noted that harmonious sounds were in whole number ratios, and they believed that these ratios could be extended to describe all natural objects. The resulting cosmos was a single and nonmaterial system of reality which included a correspondence between inanimate and living objects. The Pythagoreans claimed, however, that only the elite could achieve this mystical process of knowing. Aristotle reported on the Pythagorean view of the ultimate reality in the Metaphysica (335-323 b.c.e.; Metaphysics, 1801), although he on occasion purposely misunderstood them in his works in order to minimize their philosophical influence.

Plato had visited the Pythagoreans and incorporated the concept of number as the essence of reality into his theory of matter. His sharp distinction between the sense-experience mediated by organs of the body and the intellectual awareness of pure concepts is essentially Pythagorean, as is the notion that mathematical relationships are eternal objects of knowledge. Once Plato had taken the step of identifying the eternally valid moral concepts that Socrates sought to define as of the same nature with the Pythagorean eternal mathematical objects of knowledge, the ground was laid for the doctrine of Ideas.

It was probably also through the mediation of the Pythagorean tradition that Plato came to appropriate the notions of the soul’s eternal nature, of its transmigration, and of learning as a process of “recollection” of truths once known by the soul when free from the corrupting influences of the bodily prison.

All these notions find expression in the Phaedo of Plato, a dialogue deliberately fashioned so as to present Socrates as a Pythagorean sage and a paradigm of the disciplined philosophic life of progressive actualization of one’s innate potential divinity through the acquisition of wisdom. Through Plato the influence of the Pythagorean brotherhood continued throughout the history of Western philosophy.

• Barnes, Jonathan. The Presocratic Philosophers. 2 vols. London: Routledge & Kegan Paul, 1979. Single-volume revised reprint, 1982. Pythagorean scholars of the 1980’s and 1990’s, among others, have drawn upon this book for background information and issues to be discussed.
• Furley, David. The Formation of the Atomic Theory and Its Earliest Critics. Vol. 1 in The Greek Cosmologists. New York: Cambridge University Press, 1987. Furley keeps a general audience in mind while discussing the Pythagoreans in terms of the early Greek theories of the universe.
• Guthrie, Kenneth Sylvan, trans. The Pythagorean Sourcebook and Library. Introduction by David Fideler. Grand Rapids, Mich.: Phanes Press, 1991. A voluminous anthology of ancient writings related to Pythagoras and Pythagorean philosophy and practice. Fideler’s introduction places the material in cultural and historical context. Includes a glossary of Pythagorean terms, bibliography, and indexes of proper names and topics.
• Huffman, Carl A. Philolaus of Croton: Pythagorean and Presocratic. New York: Cambridge University Press, 1993. Huffman’s book includes scholarly commentary on the fragments attributed to Philolaus as well as essays on his life and philosophy.
• Kingsley, Peter. Ancient Philosophy, Mystery, and Magic: Empedocles and Pythagorean Tradition. New York: Oxford University Press, 1997. A study of Pythagorean influence on Plato’s philosophy as well as on medieval alchemy and Islamic science.
• Kirk, G. S., J. E. Raven, and M. Schofield. The Presocratic Philosophers. 2d ed. New York: Cambridge University Press, 1983. The landmark work that has been stimulating discussion since the 1960’s and 1970’s.
• Lloyd, G. E. R. Early Greek Science: Thales to Aristotle. New York: W. W. Norton, 1970. The classic textbook for the beginning scholar, providing assistance with placing the Pythagoreans in context in the history of science and with explaining their mathematics.
• Navia, Luis E. Pythagoras: An Annotated Bibliography. New York: Garland, 1990. A reference which contains detailed information on more than eleven hundred journal articles, books, and dissertations on a variety of topics related to Pythagoras.

Alcmaeon; Aristotle; Plato; Pythagoras; Socrates. Pythagorean brotherhood