Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and Platonism.
Later resurgence of ideas similar to those held by the early Pythagoreans are collected under the term Neopythagoreanism.
Two Rival SchoolsAccording to tradition, Pythagoreanism developed at some point into two separate schools of thought, the akousmatikoi ("listeners") and the mathēmatikoi ("learners"). The mathēmatikoi were supposed to have extended and developed the more mathematical and scientific work begun by Pythagoras, while the akousmatikoi focused on the more religious and ritualistic aspects of his teachings. The akousmatikoi claimed that the mathēmatikoi were not genuinely Pythagorean, but followers of the "renegade" Pythagorean Hippasus. The mathēmatikoi, on the other hand, allowed that the akousmatikoi were Pythagorean but felt that they were more representative of Pythagoras.
Pythagorean natural philosophyPythagorean thought was dominated by mathematics, but it was also profoundly mystical. In the area of cosmology there is less agreement about what Pythagoras himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul is too central to have been added by a later follower of Pythagoras. The Pythagorean conception of substance, on the other hand, is of unknown origin, partly because various accounts of his teachings are conflicting. The Pythagorean account actually begins with Anaximander's teaching that the ultimate substance of things is "the boundless," or what Anaximander called the "apeiron." The Pythagorean account holds that Pythagoras wrote nothing down, and relying on the writings of Parmenides, Empedocles, Philolaus and Plato (people either considered Pythagoreans, or whose works are thought deeply indebted to Pythagoreanism) results in a very diverse picture in which it is difficult to ascertain what the common unifying Pythagorean themes were. Relying on Philolaus, whom most scholars agree is highly representative of the Pythagorean school, one has a very intricate picture. Aristotle explains how the Pythagoreans (by which he meant the circle around Philolaus) developed Anaximander's ideas about the apeiron and the peiron, the unlimited and limited, by writing that:
Continuing with the Pythagoreans:
The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods. Much of their mysticism concerning the soul seem inseparable from the Orphic tradition. The Orphics included various purifactory rites and practices as well as incubatory rites of descent into the underworld. Apart from being linked with this, Pythagoras is also closely linked with Pherecydes of Syros, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherekydes was Pythagoras's most intimate teacher. Pherekydes expounded his teaching on the soul in terms of a pentemychos ("five-nooks," or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a symbol of recognition among members and as a symbol of inner health (eugieia).
Pythagorean vegetarianismThe Pythagoreans were well-known in antiquity for their vegetarianism, which they practised for religious, ethical and ascetic reasons. "Pythagorean diet" was a common name for the abstention from eating meat and fish, until the coining of "vegetarian" in the nineteenth century.
The Pythagorean code further restricted the diet of its followers, prohibiting the consumption or even touching any sort of bean. The reason is unclear: perhaps the flatulence they cause, perhaps as protection from potential favism, but most likely for magico-religious reasons, such as the belief that beans and humans were created from the same material.
Pythagorean view of womenWomen were given equal opportunity to study as Pythagoreans; however, they learned practical domestic skills in addition to philosophy. Women were held to be different from men, but sometimes in good ways.
Sentiments similar to Neo-Pythagoreanism can be found in modern philosophy, such as Hilary Putnam's Realist thesis, "Internal Realism," whereby one could be a Pythagorean in this way.
- The Pythagorean idea that whole numbers and harmonic (pleasing) sounds are intimately connected in music, must have been well known to lute-player and maker Vincenzo Galilei, father of Galileo Galilei. While possibly following Pythagorean modes of thinking, Vincenzo is known to have discovered a new mathematical relationship between string tension and pitch, thus suggesting a generalization of the idea that music and musical instruments can be mathematically quantitated and described. This may have paved the way to his son's crucial insight that all physical phenomena may be described quantitatively in mathematical language (as physical "laws"), thus beginning and defining the era of modern physics.
- Pythagoreanism has had a clear and obvious influence on the texts found in the hermetica corpus and thus flows over into hermeticism, gnosticism and alchemy.
- The Pythagorean cosmology also inspired the Arabic gnostic Monoimus to combine this system with monism and other things to form his own cosmology.
- The pentagram (five-pointed star) was an important religious symbol used by the Pythagoreans, which is often seen as being related to the elements theorized by Empedocles to comprise all matter.
- The Pythagoreans were advised to "speak the truth in all situations," which Pythagoras said he learned from the Magi of Babylon.
- O'Meara, Dominic J. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity , Clarendon Press, Oxford, 1989. ISBN 0-19-823913-0
- Riedweg, Christoph Pythagoras : his life, teaching, and influence ; translated by Steven Rendall in collaboration with Christoph Riedweg and Andreas Schatzmann, Ithaca : Cornell University Press, (2005), ISBN 0-8014-4240-0
Pythagoreanism in Belarusian (Tarashkevitsa): Пітагарэйская школа
Pythagoreanism in Czech: Pythagoreismus
Pythagoreanism in German: Pythagoreer
Pythagoreanism in Modern Greek (1453-): Πυθαγορισμός
Pythagoreanism in Spanish: Pitagóricos
Pythagoreanism in Basque: Eskola pitagorikoa
Pythagoreanism in French: École pythagoricienne
Pythagoreanism in Italian: Scuola pitagorica
Pythagoreanism in Hebrew: האסכולה הפיתגוראית
Pythagoreanism in Latvian: Pitagoriešu skola
Pythagoreanism in Hungarian: Püthagoreusok
Pythagoreanism in Dutch: Pythagorisme (Pythagoras)
Pythagoreanism in Japanese: ピュタゴラス教団
Pythagoreanism in Polish: Pitagorejczycy
Pythagoreanism in Romanian: Şcoala pitagoreică
Pythagoreanism in Russian: Пифагореизм
Pythagoreanism in Slovak: Pytagoreizmus
Pythagoreanism in Slovenian: Pitagorejstvo
Pythagoreanism in Serbo-Croatian: Pitagorejci
Pythagoreanism in Swedish: Pythagoréerna
Pythagoreanism in Turkish: Pisagorculuk
Pythagoreanism in Ukrainian: Піфагореїзм