Difference between revisions of "Pythagoras and Pythagoreans" - New World Encyclopedia

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'''Pythagoras''' (c. 570 BC – 496 B.C.E., [[Greek language|Greek]]:
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'''Pythagoras''' ([[580s B.C.E.|582 BC]] – [[496 B.C.E.]], [[Greek language|Greek]]:
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Πυθαγόρας) was a Greek [[Pre-Socratic philosophy|pre-Socratic philosopher]], [[mystic]], and [[mathematician]], known best for the [[Pythagorean theorem]].
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Πυθαγόρας) was an [[Ionians|Ionian]] [[mathematician]] and [[philosopher]], known best for formulating the [[Pythagorean theorem]].
 
  
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Earliest Greek philosophers in [[Ionia]], known as [[Ionians]], such as [[Thales]], [[Anaximander]], and [[Anaximenes]], inquired into the origin of beings, and developed theories of nature in order to explain natural processes of the formation of the world. Pythagoras, born in an island off coast of Ionia and moved into Southern Italy, inquired into the question of the salvation of human beings, tried to answer it by clarifying the essence of beings, and developed a mystic religious philosophy. Pythagoras developed both theoretical foundations and practical methodology, and formed ascetic religious community. Followers of Pythagoras were known as Pythagoreans.
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Pythagoras approached the question of being from a different angle from early Ionian philosophers. While Ionians tried to find the original stuff or the original matter out of which the world is made of, Pythagoras inquired into the principle that gives order and harmony to the original stuff or element of the world. In other words, Pythagoras found the essence of being not in “what is to be determined” but in “what determines.” From Pythagoras’ perspective, Ionians’ answers, such as Thales’ “water” and Anaximander’s “indefinite,” were equally beings that were determined, and they did not explain why and how the world was orderly structured and maintained rhythm and harmony.
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Pythagoras found the “[[number]]” or the mathematical as the principle that gave the order, harmony, rhythm, and beauty to the world. The harmony keeps a balance both in the cosmos and the soul. For Pythagoras, “numbers” are not abstract concepts but embodied entities manifested as norms, cosmos, sensible natural objects.
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The mathematical order in beings is perceivable not by physical senses but by senses of the soul. Unlike modern conception of mathematical exercises, Pythagoras conceived them as the method of liberating the soul from the bondages of bodily senses and conceived them as religious trainings. For Pythagoras, the soul is [[Immortality of the soul|immortal]] and the cultivation of soul is achieved by the studies of truth and ascetic life. Aristotle noted that Pythagoras was the first person who took up the issue of “[[virtue]]” in philosophy (DK. 58B4).
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Pythagoras opened a new path to early Greek [[ontology]] by turning people’s attention to the soul, virtue, and ascetic life. He presented a new integral model of thought where the mystic and the mathematical or the scientific and the religious (as well as the aesthetic) are uniquely integrated. This type of thought is uncommon in mainstream philosophy today. Like other wise men of antiquity, Pythagoras had a broad knowledge encompassing medicine, music, cosmology, astronomy, mathematics and others. His thought gave strong impacts on Plato.
  
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Known as "[[List of people known as the father or mother of something|the father of numbers]]", he made influential contributions to [[philosophy]] and religious teaching in the late [[6th century B.C.E.]]. Because legend and obfuscation cloud his work even more than with the other [[pre-Socratic]]s, one can say little with confidence about his life and teachings. Pythagoras and his students believed that everything was related to [[mathematics]], and felt that everything could be predicted and measured in rhythmic [[cycles]].
 
 
==Biography==
 
==Biography==
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Pythagoras was born on the island of [[Samos]], off the coast of [[Ionia]] ([[Asia Minor]]). He was born to Pythais (a native of Samos) and Mnesarchus (a merchant from [[Tyre]]). As a young man he left his native city for [[Crotona]] in Southern [[Italy]], to escape the [[tyranny|tyrannical]] government of [[Polycrates]]. Many writers credit him with visits to the sages of [[Egypt]] and [[Babylon]] before going west; but such visits feature stereotypically in the biographies of many Greek wise men, and are likely more legend than fact.
  
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Pythagoras was born on the island of [[Samos]], off the coast of [[Asia Minor]]. He was born to Pythais (a native of Samos) and Mnesarchus (a merchant from [[Tyre]]). As a young man he left his native city for [[Crotona]] in Southern [[Italy]], to escape the [[tyranny|tyrannical]] government of [[Polycrates]]. Many writers credit him with visits to the sages of [[Egypt]] and [[Babylon]] before going west; but such visits feature stereotypically in the biographies of many Greek wise men, and are likely more legend than fact.  
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Upon his migration from Samos to Crotona, Pythagoras established a secret religious society similar to, and possibly influenced by, the earlier [[Orphism]].
  
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Upon his migration from Samos to Crotona, Pythagoras established a secret religious society very similar to, and possibly influenced by, the earlier Orphic cult.
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Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue, and formed a circle of followers around him. Very strict rules of conduct governed this cultural center. He opened his school to men and women students alike. They called themselves the ''Mathematikoi''; a secret society of sorts.
  
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Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an [[elite]] circle of followers around himself. Very strict rules of conduct governed this cultural center. He opened his school to men and women students alike. They called themselves the ''Mathematikoi''; a secret society of sorts.
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According to [[Iamblichus (philosopher)|Iamblichus]], the [[Pythagoreans]] followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. We may infer from this that participants required some degree of wealth and leisure to join the inner circle. [[Music]] featured as an essential organizing factor of this life because musical harmony was believed to be effective to the harmony of the soul : the disciples would sing hymns [[Apollo]] together regularly; they used the [[lyre]] to cure illness of the soul or body; [[poetry]] recitations occurred before and after sleep to aid the memory.
  
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According to [[Iamblichus (philosopher)|Iamblichus]], the [[Pythagoreans]] followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. We may infer from this that participants required some degree of wealth and leisure to join the inner circle. [[Music]] featured as an essential organizing factor of this life: the disciples would sing hymns [[Apollo]] together regularly; they used the [[lyre]] to cure illness of the soul or body; [[poetry]] recitations occurred before and after sleep to aid the memory.
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The [[Pythagorean theorem]] that bears his name was known much earlier in [[Mesopotamia]] and [[Egypt]], but no proofs have been discovered before the proofs offered by the [[Greeks]].  Whether Pythagoras himself proved this theorem is not known as it was common in the ancient world to credit to a famous teacher the discoveries of his students.  
  
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The [[Pythagorean theorem]] that bears his name was known much earlier in [[Mesopotamia]] and [[Egypt]], but no proofs have been discovered before the proofs offered by the [[Greeks]].  Whether Pythagoras himself proved this theorem is not known as it was common in the ancient world to credit to a famous teacher the discoveries of his students.
 
 
==Pythagoreans==
 
==Pythagoreans==
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''Main articles: [[Pythagoreans]], [[Pythagoreanism]]''
 
  
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Pythagoras' followers were commonly called "Pythagoreans." They were mostly philosophers, mathematicians and geometricians who had an influence on the beginning of Euclidian geometry.  
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===History===
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Pythagoras' followers were commonly called "Pythagoreans." The early Pythagorean brotherhood was formed in Croton by Pythagoras and dissolved by the second half of the fifth century B.C.E. The group was re-formed in [[Tarentum]] soon after, and it lasted until the end of fourth century B.C.E. The teachings and theories of Pythagoreans were customarily ascribed to the founder Pythagoras. It is difficult to discern clearly ideas of Pythagoras and those of Pythagoreans. Around the first century B.C.E., concern for Pythagoreanism revived in Rome, and a number of forgeries were written under the name of Pythagoras and Pythagoreans until the first century.
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===Transmigration of souls===
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The Pythagoreans were known for their teachings of the [[transmigration of souls]], and also for their theory that numbers constitute the true nature of things. The doctrine of transmigration of souls is constituted of a set of beliefs: souls are immortal; a soul migrates from a living thing to another upon its birth and death; human body is like a prison of a soul, and bodily desires detain the freedom of a soul (“body is a tomb”).
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This doctrine led Pythagoreans to a number of prescriptive rules concerning killing and eating of animals and plants.
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They had performed purification rites and followed ascetic, dietary and moral rules which they believed would enable their soul to achieve a higher rank among the gods. Consequentially, they expected they would be set free from the [[wheel of life]. Religious training included: studies of philosophy and mathematics (cultivate the sense of the soul); exercises of music (musical harmony enhances the balance and harmony of human beings); and physical exercises (training of bodily control).
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===Cosmology===
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Harmony and balance, for Pythagoreans, was the principle that determined the order of cosmos. Numerical and geometrical ratios represented this orderly construction of the world. Pythagorean [[numerology]] contained the principle of dual characteristics of masculinity and femininity, comparable to the principle of [[yin and yang]] in ancient Chinese thought. Pythagoreans divided all numbers into a pair of odd and even, and associated odd with masculinity, and even with femininity. Hippolytus, a second and third century [[Doxography|doxographist]], described Pythagorean principle of dual characteristics:
  
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The Pythagoreans well known for their teachings of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They had performed purification rites and followed ascetic, dietary and moral rules which they believed would enable their soul to achieve a higher rank among the gods. Consequentially, they expected they would be set free from the wheel of birth.  
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<blockquote>
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Number is the first principle, a thing which is undefined, incomprehensible, having in itself all numbers which could reach infinity in amount. And the first principle of numbers is in substance the first monad, which is a male monad, begetting as a father all other numbers. Secondly the dyad is female number, and the same is called by the arithmeticians even. Thirdly the triad is male number; this the arithmeticians have been wont to call odd. Finally the tetrad is a female number, and the same is called even because it is female.  
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</blockquote>
  
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The Pythagoreans had also believed that sexes as equal; all slaves were treated humanely, and to respect animals as creatures with souls. The highest purification of the soul was "philosophy," Pythagoras has been credited with the first use of the term.
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Pythagorean perspective on duality was extended to paired elements in the world: finite and infinite; one and many, light and darkness, and others. In Metaphysics (985 b 23-986 b 8.), Aristotle explained this Pythagorean perspective:
  
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They had discovered the relationship between musical notes could be expressed in numerical ratios. The Pythagoreans elaborated on a theory of numbers. Ironically, the exact meaning is still disputed by scholars. For a short while, they taught that all things were numbers. Essence of everything is a number. All relationships, even the abstract concepts, could be expressed numerically.
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<blockquote>
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the first principles are ten, named according to the following table: -finite and infinite, even and odd, one and many, right and left, male and female, rest and motion, straight and crooked, light and darkness, good and bad, square and oblong.
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</blockquote>
  
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==Literary works==
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In Pythagorean numerology, the number ten is the perfect and sacred number, which is the sum of four numbers: one, two, three, and four. These four numbers and their sum (the number ten) were conceived as the fundamental units of all numbers and the world. Hippolytus recorded Pythagorean number theory:
  
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No texts by Pythagoras survive, although forgeries under his name &mdash; a few of which remain extant &mdash; did circulate in [[classical antiquity|antiquity]]. Critical ancient sources like [[Aristotle]] and [[Aristoxenus]] cast doubt on these writings. And ancient Pythagoreans usually quoted their master's doctrines with the phrase ''autos ephe'' ("he himself said") &mdash; emphasizing the essentially oral nature of his teaching. Pythagoras appears as a character in the last book of [[Ovid]]'s ''[[Metamorphoses (poem)|Metamorphoses]]'' , where Ovid has him expound upon his philosophical viewpoints.
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<blockquote>
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All numbers, then, taken by classes are fours (for number is undefined in reference to class), of which is composed the perfect number, the decad. For the series, one two three and four, becomes ten, if its own name is kept in its essence by each of the numbers. Pythagoras said that this sacred tetraktys is 'the spring having the roots of ever-flowing nature in itself, and from this numbers have their first principle.
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</blockquote>
  
 
==Scientific contributions==
 
==Scientific contributions==
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Some consider Pythagoras the pupil of [[Anaximander]] and some ancient sources tell of his visiting, in his twenties, the philosopher [[Thales]], just before the death of the latter. No account exists of the specifics of the meeting, other than the report that [[Thales]] recommended that Pythagoras travel to [[Egypt]] in order to further his philosophical and mathematical training. Evidence certainly suggests that the Egyptians had advanced further than the Greeks of their time in [[mathematics]] and [[astronomy]], and many scholars now believe that the [[Egyptians]] used the [[Pythagorean theorem]] in some of their architectural projects before the [[6th century B.C.E.]]. [[India]]n mathematicians were aware of special cases (at least) of the theorem as early as the [[8th century B.C.E.]] (see: [[Baudhayana]]).
 
  
 
[[Image:450px-Pythagoras Bust Vatican Museum.jpg|thumb|Bust of Pythagoras, Vatican Museum, Rome]]
 
[[Image:450px-Pythagoras Bust Vatican Museum.jpg|thumb|Bust of Pythagoras, Vatican Museum, Rome]]
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Whether or not we attribute the [[Pythagorean theorem]] to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the [[musical scale]], since this plays a key role in many other areas of the Pythagorean tradition, and since no evidence remains of earlier Greek or Egyptian musical theories. Another important discovery of this school — which upset Greek mathematics, as well as the Pythagoreans' own belief that [[whole numbers]] and their ratios could account for geometrical properties — was the incommensurability of the diagonal of a square with its side. This result showed the existence of [[irrational number]]s.
 
Whether or not we attribute the [[Pythagorean theorem]] to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the [[musical scale]], since this plays a key role in many other areas of the Pythagorean tradition, and since no evidence remains of earlier Greek or Egyptian musical theories. Another important discovery of this school — which upset Greek mathematics, as well as the Pythagoreans' own belief that [[whole numbers]] and their ratios could account for geometrical properties — was the incommensurability of the diagonal of a square with its side. This result showed the existence of [[irrational number]]s.
  
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The influence of Pythagoras has transcended the field of mathematics, and the [[Hippocratic Oath]] &mdash; with its central commitment to '''First do no harm''' &mdash; has its roots in the oath of the Pythagorean Brotherhood [http://www.nlm.nih.gov/hmd/greek/greek_oath.html].
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==References==
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===Texts===
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==See also==
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*Diels, H. and Kranz, W. (eds), ''Die Fragmente der Vorsocratiker'' (Berlin: Weidmannsche Verlagsbuchhandlung, 1960) (This is the standard text for pre-Socratics; abbr. DK)
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*[[Hippasus]]
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*Freeman, K. (ed), ''Ancilla to the pre-Socratic philosophers'' (Cambridge:Harvard University Press, 1983)( a complete translation of the fragments in Diels and Kranz.)
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*[[Pythagoreans]]
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*Kirk, G. S., Raven, J. E. and Schofield, M. ''The Presocratic Philosophers'', 2nd ed. (Cambridge: Cambridge Univ. Press, 1983).  (Notes: quotes in the article are taken from this text.)
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*[[Pythagoreanism]]
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*Hicks, R. D., ''Diogenes Laertius, Lives of Eminent Philosophers'', 2 vols., The Loeb Classical Library, 1925)
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*[[Pythagorean comma]]
 
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*[[Pythagorean theorem]]
 
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*[[Sacred geometry]]
 
  
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==References==
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===General===
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*Barnes, Jonathan. ''The Presocratic Philosophers'', vol. 1 (London: Routledge, 1979)
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*Bell, Eric Temple. ''The Magic of Numbers'' (New York: Dover, 1991) ISBN 0486267881
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* Burkert, Walter. ''Lore and Science in Ancient Pythagoreanism'' (Cambridge: Harvard University Press, 1972), ISBN 0674539184
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*Dominic J. O'Meara, ''Pythagoras Revived'' (Oxford: Clarendon Press, 1989) Paperback ISBN 0198239130, Hardcover ISBN 0198244851
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*Furley, David. and Allen, R. E. (ed), ''Studies in Presocratic Philosophy'', vol. I (New York: Humanities Press, 1970)
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*Emlyn-Jones, C. ''The Ionians and Hellenism'' (London: Routledge, 1980)
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*Furley, David. and Allen, R. E. (ed), ''Studies in Presocratic Philosophy'', vol. I (New York: Humanities Press, 1970)
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*Gorman, P. ''Pythagoras: a life'' (London: Routledge, 1979)
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*Guthrie, K. L. (Ed.), ''The Pythagorean Sourcebook and Library'', (Grand Rapids: Phanes, 1987) ISBN 0-933999-51-8
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*Guthrie, W.K.C., ''A History of Greek Philosophy'', 6 vol. (Cambridge: Cambridge University Press, 1986)
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*Maziarz, J.E. & Greenwood. ''Greek mathematical philosophy'' (New York: Frederick Ungar, 1968)
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* O'Meara, Patrick J. ''Pythagoras Revived'' (Oxford: Clarendon Press, 1989)
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*Raven, J.E. ''Pythagoreans and Eleatics''  (Cambridge: Cambridge University Press, 1948)
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*Stokes, M.C. ''One and many in presocratic philosophy'' (Langham, MD: University Press of America, 1986)
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*Taylor, A.E. ''Aristotle on his predecessors'' (La Salle: Open Court, 1977)
  
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===[[Primary source]]s:===
 
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''Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information from these four books.''
 
  
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*[[Diogenes Laertius]], ''[[Lives and Opinions of Eminent Philosophers|Vitae philosophorum VIII]]'' (''Lives of Eminent Philosophers'', which in turn reference the [[lost work]] ''[[Successions of Philosophers]]'' by [[Alexander Polyhistor]]) &mdash; [http://classicpersuasion.org/pw/diogenes/dlpythagoras.htm ''Pythagoras'', Translation by C.D. Yonge]
 
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*[[Porphyry (philosopher)|Porphyry]], ''Vita Pythagorae'' (''Life of Pythagoras'')
 
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*[[Iamblichus (philosopher)|Iamblichus]], ''De Vita Pythagorica'' (''On the Pythagorean Life'')
 
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*[[Apuleius]] also writes about Pythagoras in ''Apologia'', including a story of him being taught by [[Babylon|Babylonian]] disciples of [[Zoroaster]]
 
  
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===[[Secondary source]]s:===
 
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*[[Eric Temple Bell]], ''The Magic of Numbers'', Dover, New York, 1991 ISBN 0486267881
 
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*Walter Burkert, ''Lore and Science in Ancient Pythagoreanism'', Harvard University Press (June 1, 1972), ISBN 0674539184
 
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*K. L., Guthrie (Ed.), ''The Pythagorean Sourcebook and Library'', Phanes, Grand Rapids, 1987 ISBN 0-933999-51-8
 
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*Dominic J. O'Meara, ''Pythagoras Revived'', Clarendon Press, Oxford, 1989, Paperback ISBN 0198239130, Hardcover ISBN 0198244851
 
  
 
== External links ==
 
== External links ==
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*[http://plato.stanford.edu/entries/pythagoras/ Stanford Encyclopedia of Philosophy entry]
 
*[http://plato.stanford.edu/entries/pythagoras/ Stanford Encyclopedia of Philosophy entry]
  
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'''Pythagoreanism''' is a term used for the [[esoteric]] and [[metaphysics|metaphysical]] beliefs held by [[Pythagoras]] and his followers the Pythagoreans, much influenced by [[mathematics]] and probably a main inspiration source to [[Plato]] and [[platonism]].
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== External links ==
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* [http://users.ucom.net/~vegan Pythagoreanism Web Site]
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* [http://cyberspacei.com/jesusi/inlight/philosophy/western/Pythagoreanism.htm Pythagoreanism Web Article]
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* [http://groups.yahoo.com/group/Pythagorean-L Pythagoreanism Discussion Group]
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* [http://www.ivu.org/faq/definitions.html Vegetarianism and Pythagoreanism]
  
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One main subject that is part of pythagoreanism is [[musica universalis]], the ''music of the spheres''. Some [[Surat Shabd Yoga|Surat Shabda Yoga]], [[Satguru]]s considered the music of the spheres to be a term synonymous with the Shabda or the Audible Life Stream in that tradition, because they considered Pythagoras to be a Satguru as well.
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http://history.hanover.edu/texts/presoc/pythagor.htm
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Pythagoras and the Pythagoreans,  
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Fragments and Commentary, Hanover Historical Texts Project
  
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The '''Pythagoreans''' were a [[Hellenic Greece|Hellenic]] [[organization]] of [[astronomer]]s, [[musician]]s, [[mathematician]]s, and [[philosopher]]s who believed that all things are, essentially, [[number|numeric]]. The group strove to keep the discovery of [[irrational number]]s a secret, and legends tell of a member being [[drowning|drowned]] for breaching this secrecy (see [[Hippasus]]).
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==External links==
  
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Later resurgence of the same ideas are collected under the term '''neopythagoreanism'''.
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* "http://www.iep.utm.edu/a/anaximen.htm" Anaximenes from The Internet Encyclopedia of Philosophy.
  
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==Influence==
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* "http://history.hanover.edu/texts/presoc/anaximen.htm " Anaximenes: Fragments and Commentary, Hanover Historical Texts Project
  
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The word '[[vegetarian]]' was coined in 1847 when the British Vegetarian Society was formed. Before this, vegetarians were known as Pythagoreans.
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===General Philosophy Sources===
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*[http://www.epistemelinks.com/  Philosophy Sources on Internet EpistemeLinks]
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The [[pentagram]] (five-pointed star) was an important religious symbol used by the Pythagoreans. It was called "health".
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*[http://plato.stanford.edu/ Stanford Encyclopedia of Philosophy]
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*[http://www.bu.edu/wcp/PaidArch.html Paideia Project Online]
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*[http://www.iep.utm.edu/ The Internet Encyclopedia of Philosophy]
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*[http://www.gutenberg.org/ Project Gutenberg]
  
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==Pythagorean cosmology==
 
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Pythagorean 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 [[reincarnation|transmigration of the soul]] is too central to have been added by a later follower of Pythagoras. On the other hand it is impossible to determine the origin of the Pythagorean account of substance. It seems that the Pythagorean account begins with [[Anaximander]]'s account of the ultimate substance of things as "the boundless." Another of Anaximander's pupils, Anaximenes, who was a contemporary of Pythagoras, gave an account of how Anaximander's "boundless" took form, through condensation and refraction. On the other hand, the Pythagorean account says that it is through the notion of the "limit" that the "boundless" takes form.
 
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[[Diogenes Laërtius|Diogenes Laertius]] (about AD 200) quotes [[Alexander Polyhistor]]'s (about 100 B.C.E.) book ''[[Successions of Philosophers]]'' (and according to Diogenes, Alexander had access to a book called ''The Pythagorean Memoir'') in his account of how the Pythagorean cosmology was constructed (Diogenes Laertius, ''[[Lives and Opinions of Eminent Philosophers|Vitae philosophorum VIII]]'', 24):
 
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:The principle of all things is the [[monad]] or unit; arising from this monad the undefined dyad or two serves as material substratum to the monad, which is cause; from the monad and the undefined dyad spring numbers; from numbers, points; from points, lines; from lines, plane figures; from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four, fire, water, earth and air; these elements interchange and turn into one another completely, and combine to produce a universe animate, intelligent, spherical, with the earth at its centre, the earth itself too being spherical and inhabited round about. There are also antipodes, and our &#8216;down' is their &#8216;up'.
 
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This cosmology also inspired the Arabic [[gnosticism|gnostic]] [[Monoimus]] to combine this system with [[monism]] and other things to form his own cosmology.
 
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==Reference==
 
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* '''Pythagoras Revived''', Patrick J. O'Meara, Clarendon Press, Oxford, 1989.
 
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==See also==
 
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* [[Pythagoras]]
 
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*[[Neo-Pythagoreanism]]
 
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* [[Pythagorean tuning]]
 
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* [[Esoteric cosmology]]
 
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== External links ==
 
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* [http://users.ucom.net/~vegan Pythagoreanism Web Site]
 
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* [http://cyberspacei.com/jesusi/inlight/philosophy/western/Pythagoreanism.htm Pythagoreanism Web Article]
 
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* [http://groups.yahoo.com/group/Pythagorean-L Pythagoreanism Discussion Group]
 
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* [http://www.ivu.org/faq/definitions.html Vegetarianism and Pythagoreanism]
 
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[[Category:582 B.C.E. births]]
 
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[[Category:496 B.C.E. deaths]]
 
 
[[Category:Ancient Greek mathematicians]]
 
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[[Category:Vegetarians]]
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[[Category:Philosophy and religion]]
  
 
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Revision as of 11:33, 3 January 2006

File:Pythagoras von Samos.png

Pythagoras (c. 570 B.C.E. – 496 B.C.E., Greek: Πυθαγόρας) was a Greek pre-Socratic philosopher, mystic, and mathematician, known best for the Pythagorean theorem.

Earliest Greek philosophers in Ionia, known as Ionians, such as Thales, Anaximander, and Anaximenes, inquired into the origin of beings, and developed theories of nature in order to explain natural processes of the formation of the world. Pythagoras, born in an island off coast of Ionia and moved into Southern Italy, inquired into the question of the salvation of human beings, tried to answer it by clarifying the essence of beings, and developed a mystic religious philosophy. Pythagoras developed both theoretical foundations and practical methodology, and formed ascetic religious community. Followers of Pythagoras were known as Pythagoreans.

Pythagoras approached the question of being from a different angle from early Ionian philosophers. While Ionians tried to find the original stuff or the original matter out of which the world is made of, Pythagoras inquired into the principle that gives order and harmony to the original stuff or element of the world. In other words, Pythagoras found the essence of being not in “what is to be determined” but in “what determines.” From Pythagoras’ perspective, Ionians’ answers, such as Thales’ “water” and Anaximander’s “indefinite,” were equally beings that were determined, and they did not explain why and how the world was orderly structured and maintained rhythm and harmony.

Pythagoras found the “number” or the mathematical as the principle that gave the order, harmony, rhythm, and beauty to the world. The harmony keeps a balance both in the cosmos and the soul. For Pythagoras, “numbers” are not abstract concepts but embodied entities manifested as norms, cosmos, sensible natural objects.

The mathematical order in beings is perceivable not by physical senses but by senses of the soul. Unlike modern conception of mathematical exercises, Pythagoras conceived them as the method of liberating the soul from the bondages of bodily senses and conceived them as religious trainings. For Pythagoras, the soul is immortal and the cultivation of soul is achieved by the studies of truth and ascetic life. Aristotle noted that Pythagoras was the first person who took up the issue of “virtue” in philosophy (DK. 58B4).

Pythagoras opened a new path to early Greek ontology by turning people’s attention to the soul, virtue, and ascetic life. He presented a new integral model of thought where the mystic and the mathematical or the scientific and the religious (as well as the aesthetic) are uniquely integrated. This type of thought is uncommon in mainstream philosophy today. Like other wise men of antiquity, Pythagoras had a broad knowledge encompassing medicine, music, cosmology, astronomy, mathematics and others. His thought gave strong impacts on Plato.

Biography

Pythagoras was born on the island of Samos, off the coast of Ionia (Asia Minor). He was born to Pythais (a native of Samos) and Mnesarchus (a merchant from Tyre). As a young man he left his native city for Crotona in Southern Italy, to escape the tyrannical government of Polycrates. Many writers credit him with visits to the sages of Egypt and Babylon before going west; but such visits feature stereotypically in the biographies of many Greek wise men, and are likely more legend than fact.

Upon his migration from Samos to Crotona, Pythagoras established a secret religious society similar to, and possibly influenced by, the earlier Orphism.

Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue, and formed a circle of followers around him. Very strict rules of conduct governed this cultural center. He opened his school to men and women students alike. They called themselves the Mathematikoi; a secret society of sorts.

According to Iamblichus, the Pythagoreans followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. We may infer from this that participants required some degree of wealth and leisure to join the inner circle. Music featured as an essential organizing factor of this life because musical harmony was believed to be effective to the harmony of the soul : the disciples would sing hymns Apollo together regularly; they used the lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to aid the memory.

The Pythagorean theorem that bears his name was known much earlier in Mesopotamia and Egypt, but no proofs have been discovered before the proofs offered by the Greeks. Whether Pythagoras himself proved this theorem is not known as it was common in the ancient world to credit to a famous teacher the discoveries of his students.

Pythagoreans

History

Pythagoras' followers were commonly called "Pythagoreans." The early Pythagorean brotherhood was formed in Croton by Pythagoras and dissolved by the second half of the fifth century B.C.E. The group was re-formed in Tarentum soon after, and it lasted until the end of fourth century B.C.E. The teachings and theories of Pythagoreans were customarily ascribed to the founder Pythagoras. It is difficult to discern clearly ideas of Pythagoras and those of Pythagoreans. Around the first century B.C.E., concern for Pythagoreanism revived in Rome, and a number of forgeries were written under the name of Pythagoras and Pythagoreans until the first century.

Transmigration of souls

The Pythagoreans were known for their teachings of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. The doctrine of transmigration of souls is constituted of a set of beliefs: souls are immortal; a soul migrates from a living thing to another upon its birth and death; human body is like a prison of a soul, and bodily desires detain the freedom of a soul (“body is a tomb”). This doctrine led Pythagoreans to a number of prescriptive rules concerning killing and eating of animals and plants.

They had performed purification rites and followed ascetic, dietary and moral rules which they believed would enable their soul to achieve a higher rank among the gods. Consequentially, they expected they would be set free from the [[wheel of life]. Religious training included: studies of philosophy and mathematics (cultivate the sense of the soul); exercises of music (musical harmony enhances the balance and harmony of human beings); and physical exercises (training of bodily control).

Cosmology

Harmony and balance, for Pythagoreans, was the principle that determined the order of cosmos. Numerical and geometrical ratios represented this orderly construction of the world. Pythagorean numerology contained the principle of dual characteristics of masculinity and femininity, comparable to the principle of yin and yang in ancient Chinese thought. Pythagoreans divided all numbers into a pair of odd and even, and associated odd with masculinity, and even with femininity. Hippolytus, a second and third century doxographist, described Pythagorean principle of dual characteristics:

Number is the first principle, a thing which is undefined, incomprehensible, having in itself all numbers which could reach infinity in amount. And the first principle of numbers is in substance the first monad, which is a male monad, begetting as a father all other numbers. Secondly the dyad is female number, and the same is called by the arithmeticians even. Thirdly the triad is male number; this the arithmeticians have been wont to call odd. Finally the tetrad is a female number, and the same is called even because it is female.

Pythagorean perspective on duality was extended to paired elements in the world: finite and infinite; one and many, light and darkness, and others. In Metaphysics (985 b 23-986 b 8.), Aristotle explained this Pythagorean perspective:

the first principles are ten, named according to the following table: -finite and infinite, even and odd, one and many, right and left, male and female, rest and motion, straight and crooked, light and darkness, good and bad, square and oblong.

In Pythagorean numerology, the number ten is the perfect and sacred number, which is the sum of four numbers: one, two, three, and four. These four numbers and their sum (the number ten) were conceived as the fundamental units of all numbers and the world. Hippolytus recorded Pythagorean number theory:

All numbers, then, taken by classes are fours (for number is undefined in reference to class), of which is composed the perfect number, the decad. For the series, one two three and four, becomes ten, if its own name is kept in its essence by each of the numbers. Pythagoras said that this sacred tetraktys is 'the spring having the roots of ever-flowing nature in itself, and from this numbers have their first principle.

Scientific contributions

Bust of Pythagoras, Vatican Museum, Rome

In astronomy, the Pythagoreans were well aware of the periodic numerical relations of the planets, moon, and sun. The celestial spheres of the planets were thought to produce a harmony called the music of the spheres. These ideas, as well as the ideas of the perfect solids, would later be used by Johannes Kepler in his attempt to formulate a model of the solar system in his work The Harmony of the Worlds. Pythagoreans also believed that the earth itself was in motion and that the laws of nature could be derived from pure mathematics. It is believed by modern astronomers that Pythagoras coined the term cosmos, a term implying a universe with orderly movements and events.

It is sometimes difficult to determine which ideas Pythagoras taught originally, as opposed to the ideas his followers later added. While he clearly attached great importance to geometry, classical Greek writers tended to cite Thales as the great pioneer of this science rather than Pythagoras. The later tradition of Pythagoras as the inventor of mathematics stems largely from the Roman period.

Whether or not we attribute the Pythagorean theorem to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the musical scale, since this plays a key role in many other areas of the Pythagorean tradition, and since no evidence remains of earlier Greek or Egyptian musical theories. Another important discovery of this school — which upset Greek mathematics, as well as the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties — was the incommensurability of the diagonal of a square with its side. This result showed the existence of irrational numbers.

References
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Texts

  • Diels, H. and Kranz, W. (eds), Die Fragmente der Vorsocratiker (Berlin: Weidmannsche Verlagsbuchhandlung, 1960) (This is the standard text for pre-Socratics; abbr. DK)
  • Freeman, K. (ed), Ancilla to the pre-Socratic philosophers (Cambridge:Harvard University Press, 1983)( a complete translation of the fragments in Diels and Kranz.)
  • Kirk, G. S., Raven, J. E. and Schofield, M. The Presocratic Philosophers, 2nd ed. (Cambridge: Cambridge Univ. Press, 1983). (Notes: quotes in the article are taken from this text.)
  • Hicks, R. D., Diogenes Laertius, Lives of Eminent Philosophers, 2 vols., The Loeb Classical Library, 1925)

General

  • Barnes, Jonathan. The Presocratic Philosophers, vol. 1 (London: Routledge, 1979)
  • Bell, Eric Temple. The Magic of Numbers (New York: Dover, 1991) ISBN 0486267881
  • Burkert, Walter. Lore and Science in Ancient Pythagoreanism (Cambridge: Harvard University Press, 1972), ISBN 0674539184
  • Dominic J. O'Meara, Pythagoras Revived (Oxford: Clarendon Press, 1989) Paperback ISBN 0198239130, Hardcover ISBN 0198244851
  • Furley, David. and Allen, R. E. (ed), Studies in Presocratic Philosophy, vol. I (New York: Humanities Press, 1970)
  • Emlyn-Jones, C. The Ionians and Hellenism (London: Routledge, 1980)
  • Furley, David. and Allen, R. E. (ed), Studies in Presocratic Philosophy, vol. I (New York: Humanities Press, 1970)
  • Gorman, P. Pythagoras: a life (London: Routledge, 1979)
  • Guthrie, K. L. (Ed.), The Pythagorean Sourcebook and Library, (Grand Rapids: Phanes, 1987) ISBN 0-933999-51-8
  • Guthrie, W.K.C., A History of Greek Philosophy, 6 vol. (Cambridge: Cambridge University Press, 1986)
  • Maziarz, J.E. & Greenwood. Greek mathematical philosophy (New York: Frederick Ungar, 1968)
  • O'Meara, Patrick J. Pythagoras Revived (Oxford: Clarendon Press, 1989)
  • Raven, J.E. Pythagoreans and Eleatics (Cambridge: Cambridge University Press, 1948)
  • Stokes, M.C. One and many in presocratic philosophy (Langham, MD: University Press of America, 1986)
  • Taylor, A.E. Aristotle on his predecessors (La Salle: Open Court, 1977)


External links

External links

http://history.hanover.edu/texts/presoc/pythagor.htm Pythagoras and the Pythagoreans, Fragments and Commentary, Hanover Historical Texts Project

External links

General Philosophy Sources

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