Anonymous ID: f4c8da July 26, 2019, 7:21 a.m. No.7199527   🗄️.is đź”—kun   >>9537

>>7199522

 

Pythagoreanism was a philosophic tradition as well as a religious practice. As a religious community they relied on oral teachings and worshiped the Pythian Apollo, the oracular god of Delphic Oracle. Pythagoreans preached an austere life.[26] They believed that the soul was buried in the body, which acted as a tomb for the soul in this life.[27] The highest reward a human could attain was for the soul to join in the life of the gods and thus escaped the cycle of reincarnation in another human body.[28] Like the practitioners of Orphism, a religious tradition that developed in parallel to Pythagorean religious practice, Pythagoreanism believed that the soul was buried in the body as a punishment for a committed offense and that the soul could be purified.[29] Aside from conducting their daily lives according to strict rules Pythagorean also engaged in rituals to attain purity.[30] The 4th century Greek historian and sceptic philosopher Hecataeus of Abdera asserted that Pythagoras had been inspired by ancient Egyptian philosophy in his use of ritual regulations and his belief in reincarnation.[3]

Anonymous ID: f4c8da July 26, 2019, 7:25 a.m. No.7199564   🗄️.is đź”—kun   >>9570

>>7199537

>I Like Beans

 

The practitioners of akousmatikoi believed that humans had to act in appropriate ways. Akousmata (translated as "oral saying") preserved all sayings of Pythagoras as divine dogma. The akousmatikoi tradition resisted any reinterpretation or philosophic evolution of Pythagoras' teachings. Individuals who by their actions attained the most akousmata were regarded as wise. The akousmatikoi philosophers refused to recognize that the continuous development of mathematical and scientific research conducted by the mathēmatikoi practitioners was in line with Pythagoras's intention. Until the demise of Pythagoreanism in the 4th century BC, the akousmatikoi continued to engage in a pious life by practicing silence, dressing simply and avoiding meat, for the purpose of attaining a privileged afterlife. The akousmatikoi engaged deeply in questions of Pythagoras' moral teachings, concerning matters such as harmony, justice,[23] ritual purity and moral behavior.[24]

Anonymous ID: f4c8da July 26, 2019, 7:25 a.m. No.7199570   🗄️.is đź”—kun   >>9602

>>7199564

 

The practitioners of mathēmatikoi acknowledged the religious underpinning of Pythagoreanism and engaged in mathēma (translated as "learning" or "studying") as part of their practice. While their scientific pursuits were largely mathematical, they also promoted other fields of scientific study in which Pythagoras had engaged during his lifetime. A sectarianism developed between the dogmatic akousmatikoi and the mathēmatikoi, who in their intellectual activism became regarded as increasingly progressive. This tension persisted until the 4th century BC, when the philosopher Archytas engaged in advanced mathematics as part of his devotion to Pythagoras' teachings.[23]

 

Today, Pythagoras is mostly remembered for his mathematical ideas, and by association with the work early Pythagoreans did in advancing mathematical concepts and theories on harmonic musical intervals, the definition of numbers, proportion and mathematical methods such as arithmetic and geometry. The mathēmatikoi philosophers claimed that numbers were at the heart of everything and constructed a new view of the cosmos. In the mathēmatikoi tradition of Pythagoreanism the Earth was removed from the center of the universe. The mathēmatikoi believed that the Earth, along with other celestial bodies, orbited around a central fire. This, they believed, resembled a celestial harmony.[25]

Anonymous ID: f4c8da July 26, 2019, 7:28 a.m. No.7199602   🗄️.is đź”—kun   >>9632

>>7199570

>The mathēmatikoi philosophers claimed that numbers were at the heart of everything and constructed a new view of the cosmos.

 

Arithmetic and numbers

 

Pythagoras in his teachings cultivated mathematics and numbers, engaging in a combination of philosophic theorizing and deductive provable methodology. Numbers were in the Greek world of Pythagoras' days natural numbers - that is positive integers. But unlike their Greek contemporaries, the Pythagorean philosophers represented numbers graphically, not symbolically through letters. Pythagoreans used dots, also known as psiphi (pebbles), to represent numbers in triangles, squares, rectangles and pentagons. This enabled a visual comprehension of mathematics and allowed for a geometrical exploration of numerical relationships. Pythagorean philosophers investigated the relationship of numbers exhaustively. They defined perfect numbers as those that were equal the sum of all their divisors. For example: 28 = 1 + 2 + 4 + 7 + 14.[32] The theory of odd and even numbers was central to Pythagorean arithmetic. This distinction was for the Pythagorean philosophers direct and visual, as they arranged triangular dots so that the even and odd numbers successively alternate: 2, 4, 6, … 3, 5, 7, …[33]

 

Early-Pythagorean philosophers such as Philolaus and Archytas held the conviction that mathematics could help in addressing important philosophical problems.[34] In Pythagoreanism numbers became related to intangible concepts. The one was related to the intellect and being, the two to thought, the number four was related to justice because 2 * 2 = 4 and equally even. A dominant symbolism was awarded to the number three, Pythagoreans believed that the whole world and all things in it are summed up in this number, because end, middle and beginning give the number of the whole. The triad had for Pythagoreans an ethical dimension, as the goodness of each person was believed to be threefold - prudence, drive and good fortune.[35]

Anonymous ID: f4c8da July 26, 2019, 7:31 a.m. No.7199632   🗄️.is đź”—kun   >>9657

>>7199602

>The triad had for Pythagoreans an ethical dimension, as the goodness of each person was believed to be threefold - prudence, drive and good fortune.

 

Geometry

 

The Pythagoreans engaged with geometry as a liberal philosophy which served to establish principles and allowed theorems to be explored abstractly and mentally. Pythagorean philosophers believed that there was a close relationship between numbers and geometrical forms. Early-Pythagorean philosophers proved simple geometrical theorems, including "the sum of the angles of a triangle equals two right angles". Pythagoreans also came up with three of the five regular polyhedra: the tetrahedron, the cube and the dodecahedron. The sides of a regular dodecahedron are regular pentagons, which for Pythagoreans symbolized health. They also revered the pentagram, as each diagonal divides the two others at the golden ratio.[33] When linear geometrical figures replaced the dots, the combination of Babylonian algebra and Pythagorean arithmetic provided the basis for Greek geometric algebra. By attempting to establish a system of concrete and permanent rules, Pythagoreans helped to establish strict axiomatic procedures of solving mathematical problems.[36]

Anonymous ID: f4c8da July 26, 2019, 7:34 a.m. No.7199657   🗄️.is đź”—kun   >>9666 >>9793 >>9884

>>7199632

Music

 

Pythagoras pioneered the mathematical and experimental study of music. He objectively measured physical quantities, such as the length of a string and discovered quantitative mathematical relationships of music through arithmetic ratios. Pythagoras attempted to explain subjective psychological and aesthetic feelings, such as the enjoyment of musical harmony. Pythagoras and his students experimented systematically with strings of varying length and tension, with wind instruments with brass discs of the same diameter but different thicknesses, and with identical vases filled with different levels of water. Early Pythagoreans established quantitative ratios between the length of a string or pipe and the pitch of notes and the frequency of string vibration.[36]

 

Pythagoras is credited with discovering that the most harmonious musical intervals are created by the simple numerical ratio of the first four integer numbers which derive respectively from the relations of string length: the eighth (1/2), the fifth (2/3) and the fourth (3/4).[36] The sum of those numbers 1 + 2 + 3 + 4 = 10 was for Pythagoreans the perfect number, because it contained in itself "the whole essential nature of numbers". Werner Heisenberg has called this formulation of musical arithmetical as "among the most powerful advances of human science" because it enables the measurement of sound in space.[37]

 

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.[38] This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions."[39]

 

The fact that mathematics could explain the human sentimental world had a profound impact on the Pythagorean philosophy. Pythagoreanism became the quest for establishing the fundamental essences of reality. Pythagorean philosophers advanced the unshakable belief that the essence of all thing are numbers and that the universe was sustained by harmony.[37] According to ancient sources music was central to the lives of those practicing Pythagoreanism. They used medicines for the purification (katharsis) of the body and, according to Aristoxenus, music for the purification of the soul. Pythagoreans used different types of music to arouse or calm their souls.[40]

Anonymous ID: f4c8da July 26, 2019, 7:35 a.m. No.7199666   🗄️.is đź”—kun   >>9672 >>9683

>>7199657

Harmony

 

For Pythagoreans harmony signified the "unification of a multifarious composition and the agreement of unlike spirits". In Pythagoreanism numeric harmony was applied in mathematical, medical, psychological, aesthetic, metaphysical and cosmological problems. For Pythagorean philosophers the basic property of numbers was expressed in the harmonious interplay of opposite pairs. Harmony assured the balance of opposite forces.[41] Pythagoras had in his teachings named numbers and the symmetries of them as the first principle, and called these numeric symmetries harmony.[42] This numeric harmony could be discovered in rules throughout nature. Numbers governed the properties and conditions of all beings and were regarded the causes of being in everything else. Pythagorean philosophers believed that numbers were the elements of all beings and the universe as a whole was composed of harmony and numbers.[35]

Anonymous ID: f4c8da July 26, 2019, 7:36 a.m. No.7199672   🗄️.is đź”—kun   >>9676

>>7199666

Cosmology

 

The philosopher Philolaus, one of the most prominent figures in Pythagoreanism,[44] was the precursor of Copernicus in moving the earth from the center of the cosmos and making it a planet.[44] According to Aristotle's student Eudemus of Cyprus, the first philosopher to determine quantitatively the size of the known planets and the distance between them was Anaximander, a teacher to Pythagoras, in the 6th century BC. Historic sources credit the Pythagorean philosophers with being the first to attempt a clarification of the planet sequence.[45] The early-Pythagorean philosopher Philolaus believed that limited and unlimited things were the components of the cosmos and these had existed ever since. The center of the universe, according to Philolaus, was the number one (hēn), which equated to the unity of Monism. Philolaus called the number one an "even-odd" because it was able to generate both even and odd numbers. When one was added to an odd number it produced an even number, and when added to an even number it produced an odd number. Philolaus further reasoned that the fitting together of the earth and the universe corresponded to the construction of the number one out of the even and the odd. Pythagorean philosophers believed that the even was unlimited and the odd was limited.[46]

 

Aristotle recorded in the 1st century BC on the Pythagorean astronomical system:

 

It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape. As to its position, there is some difference of opinion. Most people–all, in fact, who regard the whole heaven as finite–say it lies at the center. But the Italian philosophers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the center. They further construct another earth in opposition to ours to which they give the name counterearth.[47]

 

It is not known whether Philolaus believed Earth to be round or flat,[48] but he did not believe the earth rotated, so that the Counter-Earth and the Central Fire were both not visible from Earth's surface, or at least not from the hemisphere where Greece was located.[44] But the conclusion of Pythagorean philosophers that the universe is not geocentric was not based on empirical observation. Instead, as Aristotle noted, the Pythagorean view of the astronomical system was grounded in a fundamental reflection on the value of individual things and the hierarchical order of the universe.[45]

 

Pythagoreans believed in a musica universalis. They reasoned that stars must produce a sound because they were large swiftly moving bodies. Pythagoreans also determined that stars revolved at distances and speeds that were proportional to each other. They reasoned that because of this numerical proportion the revolution of the stars produced a harmonic sound.[45] The early-Pythagorean philosopher Philolaus argued that the structure of the cosmos was determined by the musical numerical proportions of the diatonic octave, which contained the fifth and fourth harmonic intervals.[46]

Anonymous ID: f4c8da July 26, 2019, 7:36 a.m. No.7199676   🗄️.is đź”—kun   >>9708

>>7199672

Justice

 

Pythagoreans equated justice with geometrical proportion, because proportion ensured that each part receives what it is due.[49] Early-Pythagoreans believed that after the death of the body, the soul would be punished or rewarded. Humans could accomplish, through their conduct, that their soul was admitted to another world. The reincarnation in this world equated to a punishment. In Pythagoreanism life in this world is social[50] and in the realm of society justice existed when each part of society received its due. The Pythagorean tradition of universal justice was later referenced by Plato. For Pythagorean philosophers the soul was the source of justice and through the harmony of the soul, divinity could be achieved. Injustice inverted the natural order. According to the 4th century BC philosopher Heraclides Ponticus, Pythagoras taught that "happiness consists in knowledge of the perfection of the numbers of the soul.[49] A surviving fragment from the 3rd century BC by the late-Pythagorean philosopher Aesara reasoned that:

 

I think human nature provides a common standard of law and justice for both the family and the city. Whoever follows the paths within and searches will discover; for within is law and justice, which is the proper arrangement of the soul.[51]

Anonymous ID: f4c8da July 26, 2019, 7:38 a.m. No.7199708   🗄️.is đź”—kun   >>9726 >>9869 >>0127

>>7199676

Body and soul

 

Pythagoreans believed that body and soul functioned together, and a healthy body required a healthy psyche.[52] Early Pythagoreans conceived of the soul as the seat of sensation and emotion. They regarded the soul as distinct from the intellect.[53] However, only fragments of the early Pythagorean texts have survived and it is not certain whether they believed the soul was immortal. The surviving texts of the Pythagorean philosopher Philolaus indicate that while early Pythagoreans did not believe that the soul contained all psychological faculties, the soul was life and a harmony of physical elements. As such the soul passed away when certain arrangements of these elements ceased to exist.[54] However, the teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body.

Anonymous ID: f4c8da July 26, 2019, 7:40 a.m. No.7199726   🗄️.is đź”—kun   >>9742

>>7199708

Vegetarianism

 

Some Medieval authors refer to a "Pythagorean diet", entailing the abstention from eating meat, beans or fish.[61] Pythagoreans believed that a vegetarian diet fostered a healthy body and enhanced the search for Arete. The purpose of vegetarianism in Pythagoreanism was not self-denial, instead it was regarded as conductive to the best in a human being. Pythagoreans advanced a grounded theory on the treatment of animals. They believed that any being that experienced pain or suffering should not have pain inflicted on it unnecessarily. Because it was not necessary to inflict pain on animals for humans to enjoy a healthy diet, they believed that animals should not be killed for the purpose of eating them. The Pythagoreans advanced the argument that unless an animal posed a threat to a human, it was not justifiable to kill an animal and that doing so would diminish the moral status of a human. By failing to show justice to the animal, humans diminish themselves.[52]

 

Pythagoreans believed that human beings were animals, but with an advanced intellect and therefore humans had to purify themselves through training. Through purification humans could join the psychic force that pervaded the cosmos. Pythagoreans reasoned that the logic of this argument could not be avoided by killing an animal painlessly. The Pythagoreans also thought that animals were sentient and minimally rational.[62] The arguments advanced by Pythagoreans convinced numerous of their philosopher contemporaries to adopt a vegetarian diet.[52] The Pythagorean sense of kinship with non-humans positioned them as a counterculture in the dominant meat-eating culture.[62] The philosopher Empedocles is said to have refused the customary blood sacrifice by offering a substitute sacrifice after his victory in a horse race in Olympia.[45]

 

Late-Pythagorean philosophers were absorbed into the Platonic school of philosophy and in the 4th century AD the head of the Platonic Academy Polemon included vegetarianism in his concept of living according to nature.[63] In the 1st century AD Ovid identified Pythagoras as the first opponent to meat-eating.[62] But the fuller argument Pythagoreans advanced against the maltreatment of animals did not sustain. Pythagorean had argued that certain types of food arouse the passions and hindered spiritual ascent. Thus Porphyry would rely on Pythagorean's teachings when arguing that abstinence from eating meat for the purpose of spiritual purification should be practiced only by philosophers, whose aim was to reach a divine state.[64]

 

>>7199537

Anonymous ID: f4c8da July 26, 2019, 7:42 a.m. No.7199742   🗄️.is đź”—kun   >>9765

>>7199726

Women philosophers

 

The biographical tradition on Pythagoras holds that his mother, wife and daughters were part of his inner circle.[65] Women were given equal opportunity to study as Pythagoreans and learned practical domestic skills in addition to philosophy.[66]

Illustration from 1913 showing Pythagoras teaching a class of women.

 

Many of the surviving texts of women Pythagorean philosophers are part of a collection, known as pseudoepigrapha Pythagorica, which was compiled by Neopythagoreans in the 1st or 2nd century. Some surviving fragments of this collection are by early-Pythagorean women philosophers, while the bulk of surviving writings are from late-Pythagorean women philosophers who wrote in the 4th and 3rd century BC.[12] Female Pythagoreans are some of the first female philosophers from which texts have survived.

 

Theano of Croton, the wife of Pythagoras, is considered a major figure in early-Pythagoreanism. She was noted as distinguished philosopher and in the lore that surrounds her, is said to have taken over the leadership of the school after his death. Text fragments have also survived from women philosophers of the late-Pythagorean period. These include Perictione I, Perictione II, Aesara of Lucania and Phintys of Sparta.[14]

 

Scholars believe that Perictione I was an Athenian and contemporary of Plato, because in On the Harmony of Woman she wrote in Ionic and used the same terms of virtues as Plato had done in his Republic - andreia, sophrosyne, dikaiosyne and sophia.[14] In On the Harmony of Woman Perictione I outlines the condition that enable women to nurture wisdom and self-control. These virtues will, according to Perictione I, bring "worthwhile things" for a woman, her husband, her children, the household and even the city "if, at any rate, such a woman should govern cities and tribes". Her assertion that a wife should remain devoted to her husband, regardless of his behavior, has been interpreted by scholars as a pragmatic response to the legal rights of women in Athens.[67] The woman Pythagorean philosopher Phyntis was Spartan and is believed to have been the daughter of a Spartan admiral killed in the battle of Arginusae in 406 BC.[14] Phyntis authored the treatise Moderation of Women, in which she assigned the virtue of moderation to women, but asserted that "courage and justice and wisdom are common to both" men and women. Phyntis defended the right of women to philosophize.

Anonymous ID: f4c8da July 26, 2019, 7:44 a.m. No.7199765   🗄️.is đź”—kun   >>9800 >>9803

>>7199742

 

In the Jewish communities the development of the Kabbalah as esoteric doctrine was periated with numerology. It was only in the 1st century that Philo of Alexandria, developed a Jewish Pythagoreanism. In the 3rd century Hermippus popularised the belief that Pythagoras had been the basis for establishing key dates in Judaism. In the 4th century this assertion was further developed by Aristobulus. The Jewish Pythagorean numerology developed by Philo held that God as the unique One was the creator of all numbers, of which seven was the most divine and ten the most perfect. The medieval edition of the Kabbalah focused largely on a cosmological scheme of creation, in reference to early Pythagorean philosophers Philolaus and Empedocles, and helped to disseminate Jewish Pythagorean numerology.

Anonymous ID: f4c8da July 26, 2019, 7:48 a.m. No.7199803   🗄️.is đź”—kun   >>9846 >>9848

>>7199765

(I'm having fun with this, sorry for the huge post count)

 

In the Middle Ages various classical texts that discussed Pythagorean ideas were reproduced and translated. Plato’s Timaeus was translated and republished with commentary in the Arab and Jewish worlds. In the 12th century the study of Plato gave rise to a vast body of literature explicating the glory of God as it reflected in the orderliness of the universe. Writers such as Thierry of Chartres, William of Conches and Alexander Neckham referenced not only Plato but also other classical authors that had discussed Pythagoreanism, including Cicero, Ovid and Pliny. William of Conches argued that Plato was an important Pythagorean. In this medieval Pythagorean understanding of Plato, God was a craftsman when he designed the universe.

Anonymous ID: f4c8da July 26, 2019, 7:51 a.m. No.7199848   🗄️.is đź”—kun   >>9894

>>7199803

 

Christianity in the 1st century was influenced by a Christianized form of Platonism, which had been set out in the four books of the Corpus Areopagiticum or Corpus Dionysiacum - The Celestrial Hierarchy, The Ecclesiastical Hierarchy, On Divine Names and The Mystical Theology. Having been attributed to Pseudo-Dionysius the Areopagite, the books explained the relationship among celestrial beings, humans, God and the universe. At the heart of the explanation were numbers. According to The Celestrial Hierarchy the universe consisted of a threefold division - heaven, earth and hell. Sunlight lit up the universe and was proof of God’s presence.[75] In the Middle Ages this numerological division of the universe was credited to the Pythagoreans, while in the 1st century it was regarded as an authoritative source of Christian doctrine by Photius and John of Sacrobosco. The Corpus Areopagiticum or Corpus Dionysiacum was to be referenced in the late Middle Ages by Dante and in the Renaissance a new translation of it was produced by Marsilio Ficino.[76]

 

Early Christian theologians, such as Clement of Alexandria, adopted the ascetic doctrines of the neopythagoreans.[73] The moral and ethical teachings of Pythagorean influenced early Christianity and assimilated into early Christian texts. The Sextou gnomai (Sentences of Sextus), a Hellenistic Pythagorean text modified to reflect a Christian viewpoint, existed from at least the 2nd century and remained popular among Christians well into the Middle Ages. The Sentences of Sextus consisted of 451 sayings or principles, such as injunctions to love the truth, to avoid the pollution of the body with pleasure, to shun flatterers and to let one’s tongue be harnessed by one’s mind. The contents of the Sentences of Sextus was attributed by Iamblichus, the 1st century biographer of Pythagoras, to Sextus Pythagoricus. The assertion was repeated subsequently by Saint Jerome. In the 2nd century many of the Sentences of Sextus were cited by Plutarch as Pythagorean aphorisms. The Sentences of Sextus were translated into Syriac, Latin and Arabic, then the written language of both Muslims and Jews, but only in the Latin world did they become a guide to daily life that was widely circulated.[77]

Anonymous ID: f4c8da July 26, 2019, 7:55 a.m. No.7199894   🗄️.is đź”—kun   >>9935

>>7199848

>Sentences of Sextus

 

The work is similar to the sayings gospels called the Gospel of Phillip and the Gospel of Thomas in that it is purely a collection of sayings, with no bridging framework. Unlike the Christian sayings gospels, the wisdom comes from a man named Sextus rather than Jesus. Sextus appears to have been a Pythagorean. Some of the 451 sentences are:

 

The soul is illuminated by the recollection of deity

Bear that which is necessary, as it is necessary

Be not anxious to please the multitude

Esteem nothing so precious, which a bad man may take from you

Use lying like poison

Guard yourself from lying. (Because when you lie) there is a deceiver and the deceived.

Nothing is so peculiar to wisdom as truth

Wish that you may be able to benefit your enemies

A wise intellect is the mirror of God

Cast away any part of the body that would cause you not to live abstinently. For it is better to live abstinently without this part than ruinously with it.

Anonymous ID: f4c8da July 26, 2019, 7:59 a.m. No.7199935   🗄️.is đź”—kun

>>7199894

 

Ye Gods, what strength and spirit one finds in him! This is not the case with all philosophers; there are some men of illustrious name whose writings are sapless. They lay down rules, they argue, and they quibble; they do not infuse spirit simply because they have no spirit. But when you come to read Sextius you will say: "He is alive; he is strong; he is free; he is more than a man; he fills me with a mighty confidence before I close his book." I shall acknowledge to you the state of mind I am in when I read his works: I want to challenge every hazard; I want to cry: "Why keep me waiting, Fortune? Enter the lists! Behold, I am ready for you!"