Pythagoreanism - AbsoluteAstronomy.com

Pythagoreanism was the system of esoteric and metaphysical

Metaphysics

Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

beliefs held by Pythagoras

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

and his followers, the Pythagoreans, who were considerably influenced by mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism

Platonism

Platonism is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In a narrower sense the term might indicate the doctrine of Platonic realism...

. Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism

Neopythagoreanism

Neopythagoreanism was a Graeco-Alexandrian school of philosophy, reviving Pythagorean doctrines, which became prominent in the 1st and 2nd centuries CE...

Two schools

According to tradition, Pythagoreanism developed at some point into two separate schools of thought, the mathēmatikoi Μαθηματικοι ("learners") and the akousmatikoi Ακουσματικοι, ("listeners"). 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

Hippasus

Hippasus of Metapontum in Magna Graecia, was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers.-Life:...

. The mathēmatikoi, on the other hand, allowed that the akousmatikoi were Pythagorean, but felt that their own group was more representative of Pythagoras.

Natural philosophy

Pythagorean thought was dominated by mathematics, but it was also profoundly mystical

Mysticism

Mysticism is the knowledge of, and especially the personal experience of, states of consciousness, i.e. levels of being, beyond normal human perception, including experience and even communion with a supreme being.-Classical origins:...

. In the area of cosmology

Cosmology

Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

there is less agreement about what Pythagoras

Pythagoras

himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul

Metempsychosis

Metempsychosis is a philosophical term in the Greek language referring to transmigration of the soul, especially its reincarnation after death. It is a doctrine popular among a number of Eastern religions such as Hinduism, Buddhism, Jainism and Druzism wherein an individual incarnates from one...

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

Anaximander

Anaximander was a pre-Socratic Greek philosopher who lived in Miletus, a city of Ionia; Milet in modern Turkey. He belonged to the Milesian school and learned the teachings of his master Thales...

's teaching that the ultimate substance of things is "the boundless," or what Anaximander called the "apeiron

Apeiron (cosmology)

Apeiron is a Greek word meaning unlimited, infinite or indefinite from ἀ- a-, "without" and πεῖραρ peirar, "end, limit", the Ionic Greek form of πέρας peras, "end, limit, boundary".-Apeiron as an origin:...

." The Pythagorean account holds that it is only through the notion of the "limit" that the "boundless" takes form.

Pythagoras wrote nothing down, and relying on the writings of Parmenides

Parmenides

Parmenides of Elea was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy. The single known work of Parmenides is a poem, On Nature, which has survived only in fragmentary form. In this poem, Parmenides...

, Empedocles

Empedocles

Empedocles was a Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek city in Sicily. Empedocles' philosophy is best known for being the originator of the cosmogenic theory of the four Classical elements...

, Philolaus

Philolaus

Philolaus was a Greek Pythagorean and Presocratic philosopher. He argued that all matter is composed of limiting and limitless things, and that the universe is determined by numbers. He is credited with originating the theory that the earth was not the center of the universe.-Life:Philolaus is...

and Plato

Plato

Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

(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

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

Anaximander

Anaximander was a pre-Socratic Greek philosopher who lived in Miletus, a city of Ionia; Milet in modern Turkey. He belonged to the Milesian school and learned the teachings of his master Thales...

's ideas about the apeiron

Apeiron (cosmology)

and the peiron, the unlimited and limited, by writing that:
Continuing with the Pythagoreans:
When the apeiron

Apeiron (cosmology)

is inhaled by the peiron it causes separation, which also apparently means that it "separates and distinguishes the successive terms in a series." Instead of an undifferentiated whole we have a living whole of inter-connected parts separated by "void" between them. This inhalation of the apeiron is also what makes the world mathematical, not just possible to describe using maths, but truly mathematical since it shows numbers and reality to be upheld by the same principle. Both the continuum of numbers (that is yet a series of successive terms, separated by void) and the field of reality, the cosmos — both are a play of emptiness and form, apeiron and peiron. What really sets this apart from Anaximander's original ideas is that this play of apeiron and peiron must take place according to harmonia (harmony), about which Stobaeus

Stobaeus

Joannes Stobaeus , from Stobi in Macedonia, was the compiler of a valuable series of extracts from Greek authors. The work was originally divided into two volumes containing two books each...

commentated:
A musical scale presupposes an unlimited continuum of pitches, which must be limited in some way in order for a scale to arise. The crucial point is that not just any set of limiters will do. One may not simply choose pitches at random along the continuum and produce a scale that will be musically pleasing. The diatonic scale, also known as "Pythagorean," is such that the ratio of the highest to the lowest pitch is 2:1, which produces the interval of an octave. That octave is in turn divided into a fifth and a fourth, which have the ratios of 3:2 and 4:3 respectively and which, when added, make an octave. If we go up a fifth from the lowest note in the octave and then up a fourth from there, we will reach the upper note of the octave. Finally the fifth can be divided into three whole tones, each corresponding to the ratio of 9:8 and a remainder with a ratio of 256:243 and the fourth into two whole tones with the same remainder. This is a good example of a concrete applied use of Philolaus’ reasoning. In Philolaus' terms the fitting together of limiters and unlimiteds involves their combination in accordance with ratios of numbers (harmony). Similarly the cosmos and the individual things in the cosmos do not arise by a chance combination of limiters and unlimiteds; the limiters and unlimiteds must be fitted together in a "pleasing" (harmonic) way in accordance with number for an order to arise.

This teaching was recorded by Philolaus' pupil Archytas in a lost work entitled On Harmonics or On Mathematics, and this is the influence that can be traced in Plato. Plato's pupil Aristotle made a distinction in his Metaphysics between Pythagoreans and "so-called" Pythagoreans. He also recorded the Table of Opposites, and commented that it might be due to Alcmaeon of the medical school at Croton

Crotone

Crotone is a city and comune in Calabria, southern Italy, on the Ionian Sea. Founded circa 710 BC as the Achaean colony of Croton , it was known as Cotrone from the Middle Ages until 1928, when its name was changed to the current one. In 1994 it became the capital of the newly established...

, who defined health as a harmony of the elements in the body.

After attacks on the Pythagorean meeting-places at Croton, the movement dispersed, but regrouped in Tarentum

Taranto

Taranto is a coastal city in Apulia, Southern Italy. It is the capital of the Province of Taranto and is an important commercial port as well as the main Italian naval base....

, also in Southern Italy. A collection of Pythagorean writings on ethics collected by Taylor show a creative response to the troubles.

The legacy of Pythagoras, Socrates and Plato was claimed by the wisdom tradition of the Hellenized Jews of Alexandria, on the ground that their teachings derived from those of Moses. Through Philo of Alexandria this tradition passed into the Medieval culture, with the idea that groups of things of the same number are related or in sympathy. This idea evidently influenced Hegel in his concept of internal relations.

The ancient Pythagorean pentagram was drawn with two points up and represented the doctrine of Pentemychos. Pentemychos means "five recesses" or "five chambers," also known as the pentagonas — the five-angle, and was the title of a work written by Pythagoras' teacher and friend Pherecydes of Syros

Pherecydes of Syros

Pherecydes of Syros was a Greek thinker from the island of Syros, of the 6th century BC. Pherecydes authored the Pentemychos or Heptamychos, one of the first attested prose works in Greek literature, which formed an important bridge between mythic and pre-Socratic thought.- Life :Very little is...

Cosmology

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 souls to achieve a higher rank among the gods. Much of their mysticism concerning the soul seems 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

Pherecydes of Syros

, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherecydes was Pythagoras's most "intimate" teacher. Pherecydes 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

Pentagram

A pentagram is the shape of a five-pointed star drawn with five straight strokes...

, used by them as a symbol of recognition among members and as a symbol of inner health (eugieia Eudaimonia

Eudaimonia

Eudaimonia or eudaemonia , sometimes Anglicized as eudemonia , is a Greek word commonly translated as happiness or welfare; however, "human flourishing" has been proposed as a more accurate translation...

"Wheel of Birth" and scientific contemplation

The Pythagoreans believed that a release from the "wheel of birth" was possible. They followed the Orphic traditions and practices to purify the soul but at the same time they suggested a deeper idea of what such a purification might be. Aristoxenus

Aristoxenus

Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...

said that music was used to purify the soul just like medicine was used to purge the body. But in addition to this, Pythagoreans distinguished three kinds of lives: Theoretic, Practical and Apolautic. Pythagoras is said to have used the example of Olympic games to distinguish between these three kind of lives. Pythagoras suggests that the lowest class of people who come to the games are the people who come to buy or sell. The next higher class comprises people who come to participate in the games. And the highest class contains people who simply come to look on. Thus Pythagoras suggests that the highest purification of a life is in pure contemplation. It is the philosopher who contemplates about science and mathematics who is released from the "cycle of birth." The pure mathematician's life is, according to Pythagoras, the life at the highest plane of existence.

Thus the root of mathematics and scientific pursuits in Pythagoreanism is also based on a spiritual desire to free oneself from the cycle of birth and death. It is this contemplation about the world that forms the greatest virtue in Pythagorean philosophy.

Vegetarianism

The Pythagoreans were well-known in antiquity

Classical antiquity

Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome, collectively known as the Greco-Roman world...

for their vegetarianism

Vegetarianism

Vegetarianism encompasses the practice of following plant-based diets , with or without the inclusion of dairy products or eggs, and with the exclusion of meat...

, which they practised for religious, ethical and ascetic reasons, in particular the idea of metempsychosis

Metempsychosis

– the transmigration of souls into the bodies of other animals. "Pythagorean diet" was a common name for the abstention from eating meat and fish, until the coining of "vegetarian

Vegetarianism

Vegetarianism encompasses the practice of following plant-based diets , with or without the inclusion of dairy products or eggs, and with the exclusion of meat...

" in the nineteenth century.

The Pythagorean code further restricted the diet of its followers, prohibiting the consumption or even touching of any sort of bean

Bean

Bean is a common name for large plant seeds of several genera of the family Fabaceae used for human food or animal feed....

. It is probable that this is due to their belief in the soul, and the fact that beans obviously showed the potential for life. Some, for example Cicero, say perhaps the flatulence

Flatulence

Flatulence is the expulsion through the rectum of a mixture of gases that are byproducts of the digestion process of mammals and other animals. The medical term for the mixture of gases is flatus, informally known as a fart, or simply gas...

beans cause, perhaps as protection from potential favism, perhaps because they resemble the genitalia, but most likely for magico-religious reasons, such as the belief that beans and human beings were created from the same material. Most stories of Pythagoras' murder revolve around his aversion to beans. According to legend, enemies of the Pythagoreans set fire to Pythagoras' house, sending the elderly man running toward a bean field, where he halted, declaring that he would rather die than enter the field – whereupon his pursuers slit his throat.

Views on women

Women were given equal opportunity to study as Pythagoreans, and learned practical domestic skills in addition to philosophy. Women were held to be different from men, but sometimes in good ways. The priestess, philosopher and mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

Themistoclea

Themistoclea was a priestess, philosopher and mathematician at Delphi.. According to surviving sources she was Pythagoras’ teacher, although she may also have been his sister...

is regarded as Pythagoras' teacher; Theano

Theano

Theano was the priestess of Athena in Troy. She was the daughter of the Thracian king Cisseus and Telecleia, wife of Antenor, and mother of many sons and a daughter Crino. The household of Antenor and Theano advocated peace and advised Helen's return to the Greeks. Because of their support , the...

, Damo and Melissa

Melissa (philosopher)

Melissa was a Pythagorean philosopher and mathematician from the 6th century. Her name derives from the Greek word melli meaning honey.Little is known about her life and works, although remaining letters point to a neo-Pythagorean thought....

as female disciples. Pythagoras is also said to have preached that men and women ought not to have sex during the summer, holding that winter was the appropriate time.

Neopythagoreanism

Neopythagoreanism was a revival in the 2nd century BC—2nd century AD period of various ideas traditionally associated with the followers of Pythagoras, the Pythagoreans. Notable Neopythagoreans include Nigidius Figulus

Nigidius Figulus

Among his contemporaries, Nigidius's reputation for learning was second only to that of Varro. Even in his own time, his works were regarded as often abstruse, perhaps because of their esoteric Pythagoreanism, into which Nigidius incorporated Stoic elements...

, Apollonius of Tyana

Apollonius of Tyana

Apollonius of Tyana was a Greek Neopythagorean philosopher from the town of Tyana in the Roman province of Cappadocia in Asia Minor. Little is certainly known about him...

and Moderatus of Gades

Moderatus of Gades

Moderatus of Gades was a Greek philosopher of the Neopythagorean school, who lived in the 1st century AD,...

. Middle and Neo-Platonists such as Numenius

Numenius of Apamea

Numenius of Apamea was a Greek philosopher, who lived in Apamea in Syria and flourished during the latter half of the 2nd century AD. He was a Neopythagorean and forerunner of the Neoplatonists.- Philosophy :...

and Plotinus

Plotinus

Plotinus was a major philosopher of the ancient world. In his system of theory there are the three principles: the One, the Intellect, and the Soul. His teacher was Ammonius Saccas and he is of the Platonic tradition...

also showed some Neopythagorean influence.

They emphasized the distinction between the soul

Soul

A soul in certain spiritual, philosophical, and psychological traditions is the incorporeal essence of a person or living thing or object. Many philosophical and spiritual systems teach that humans have souls, and others teach that all living things and even inanimate objects have souls. The...

and the body

Body

With regard to living things, a body is the physical body of an individual. "Body" often is used in connection with appearance, health issues and death...

. God

God

God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....

must be worshipped spiritually by prayer

Prayer

Prayer is a form of religious practice that seeks to activate a volitional rapport to a deity through deliberate practice. Prayer may be either individual or communal and take place in public or in private. It may involve the use of words or song. When language is used, prayer may take the form of...

and the will to be good. The soul must be freed from its material surroundings by an ascetic habit of life. Bodily pleasures and all sensuous impulses must be abandoned as detrimental to the spiritual purity of the soul. God is the principle of good; Matter the groundwork of Evil. The non-material universe was regarded as the sphere of mind or spirit.

In 1915, a subterranean basilica where 1st century Neo-Pythagoreans held their meetings was discovered near Porta Maggiore

Porta Maggiore

The Porta Maggiore , or Porta Prenestina, is one of the eastern gates in the ancient but well-preserved 3rd-century Aurelian Walls of Rome....

on Via Praenestina

Via Praenestina

The Via Praenestina was an ancient Roman road of central Italy.It was initially called Via Gabina, from Gabii, the ancient city of Latium where it ended...

, Rome

Rome

Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...

. The groundplan shows a basilica with three naves and an apse similar to early Christian basilicas that did not appear until much later, in the 4th century. The vaults are decorated with white stuccoes symbolizing Neopythagorean beliefs but its exact meaning remains a subject of debate.

Influences

The Pythagorean idea that whole numbers and harmonic (euphonic) sounds are intimately connected in music, must have been well known to lute-player and maker Vincenzo Galilei
Vincenzo Galilei
Vincenzo Galilei was an Italian lutenist, composer, and music theorist, and the father of the famous astronomer and physicist Galileo Galilei and of the lute virtuoso and composer Michelagnolo Galilei...

, father of Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

. 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 quantified 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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

.
Pythagoreanism has had a clear and obvious influence on the texts found in the hermetica
Hermetica
The Hermetica are Greek wisdom texts from the 2nd and 3rd centuries CE, mostly presented as dialogues in which a teacher, generally identified with Hermes Trismegistus or "thrice-greatest Hermes", enlightens a disciple...

corpus and thus flows over into hermeticism
Hermeticism
Hermeticism or the Western Hermetic Tradition is a set of philosophical and religious beliefs based primarily upon the pseudepigraphical writings attributed to Hermes Trismegistus...

, gnosticism
Gnosticism
Gnosticism is a scholarly term for a set of religious beliefs and spiritual practices common to early Christianity, Hellenistic Judaism, Greco-Roman mystery religions, Zoroastrianism , and Neoplatonism.A common characteristic of some of these groups was the teaching that the realisation of Gnosis...

and alchemy
Alchemy
Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher's stone possessing powers including the capability of turning base...

.
The Pythagorean cosmology also inspired the Arab gnostic
Gnosticism
Gnosticism is a scholarly term for a set of religious beliefs and spiritual practices common to early Christianity, Hellenistic Judaism, Greco-Roman mystery religions, Zoroastrianism , and Neoplatonism.A common characteristic of some of these groups was the teaching that the realisation of Gnosis...

Monoimus
Monoimus
Monoimus was an Arab gnostic , who was known only from one account in Theodoret until a lost work of anti-heretical writings by Hippolytus was found...

to combine this system with monism
Monism
Monism is any philosophical view which holds that there is unity in a given field of inquiry. Accordingly, some philosophers may hold that the universe is one rather than dualistic or pluralistic...

and other things to form his own cosmology.
The pentagram
Pentagram
A pentagram is the shape of a five-pointed star drawn with five straight strokes...

(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
Empedocles
Empedocles was a Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek city in Sicily. Empedocles' philosophy is best known for being the originator of the cosmogenic theory of the four Classical elements...

to comprise all matter.
The Pythagorean school doubtless had a monumental impact on the development of numerology
Numerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...

and number mysticism, an influence that still resonates today. For example, it is from the Pythagoreans that the number 3 acquires its modern reputation as the noblest of all digits.
The Pythagoreans were advised to "speak the truth in all situations," which Pythagoras
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

said he learned from the Magi
Magi
Magi is a term, used since at least the 4th century BC, to denote a follower of Zoroaster, or rather, a follower of what the Hellenistic world associated Zoroaster with, which...

of Babylon
Babylon
Babylon was an Akkadian city-state of ancient Mesopotamia, the remains of which are found in present-day Al Hillah, Babil Province, Iraq, about 85 kilometers south of Baghdad...

.
The Pythagorean theory of harmonic ratios is basis of studies on music theory in Islamic world, for example the al-Farabi
Al-Farabi
' known in the West as Alpharabius , was a scientist and philosopher of the Islamic world...

's Kitab al-Musiqa al-kabir.

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Two schools

Natural philosophy

Cosmology

"Wheel of Birth" and scientific contemplation

Vegetarianism

Views on women

Neopythagoreanism

Influences

See also

Further reading

External links