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In 1915 a subterranean basilica was discovered near Porta Maggiore on Via Praenestina, Rome where Neo-Pythagoreans held their meetings in the 1st century. The groundplan shows a basilica with three naves and an apse similarly to early Christian basilicas that appeared only 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.^[1]

Sentiments similar to Neopythagoreanism can be found in modern philosophy, such as Hilary Putnam's Realist thesis, "Internal Realism," whereby one could be a Pythagorean in this way.^{[clarification needed]}

Influences

The Pythagorean idea that whole numbers and harmonic (pleasing) sounds are intimately connected in music, must have been well known to lute-player and maker Vincenzo Galilei, father of Galileo Galilei. While possibly following Pythagorean modes of thinking, Vincenzo is known to have discovered a new mathematical relationship between string tension and pitch, thus suggesting a generalization of the idea that music and musical instruments can be mathematically quantitated and described. This may have paved the way to his son's crucial insight that all physical phenomena may be described quantitatively in mathematical language (as physical "laws"), thus beginning and defining the era of modern physics.
Pythagoreanism has had a clear and obvious influence on the texts found in the hermetica corpus and thus flows over into hermeticism, gnosticism and alchemy.
The Pythagorean cosmology also inspired the Arabic gnostic Monoimus to combine this system with monism and other things to form his own cosmology.
The pentagram (five-pointed star) was an important religious symbol used by the Pythagoreans, which is often seen as being related to the elements theorized by Empedocles to comprise all matter.
The Pythagoreans were advised to "speak the truth in all situations," which Pythagoras said he learned from the Magi of Babylon.^{[citation needed]}

References

^ Ball Platner, Samuel. "Basilicae". penelope.uchicago.edu.

External links

Pythagoreanism Web Article
Pythagoreanism Discussion Group
Pythagoreanism Web Site
Pythagoreanism Web Site
Carl Huffman. "Pythagoreanism". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.

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[1] Ball Platner, Samuel. "Basilicae". penelope.uchicago.edu.

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-[[Image:Kapitolinischer Pythagoras.jpg|160px|thumb|Bust of [[Pythagoras]]]]
-'''Pythagoreanism''' is a term used for the [[esoteric]] and [[metaphysics|metaphysical]] beliefs held by [[Pythagoras]] and his followers, the Pythagoreans, who were much influenced by [[mathematics]] and probably a very inspirational source for [[Plato]] and [[Platonism]].
-Later resurgence of ideas similar to those held by the early Pythagoreans are collected under the term [[Neopythagoreanism]].
-==Two schools==
-According to tradition, Pythagoreanism developed at some point into two separate schools of thought, the ''akousmatikoi'' ("listeners") and the ''mathēmatikoi'' ("learners").  The ''mathēmatikoi'' were supposed to have extended and developed the more mathematical and scientific work begun by Pythagoras, while the ''akousmatikoi'' focused on the more religious and ritualistic aspects of his teachings. The ''akousmatikoi'' claimed that the ''mathēmatikoi'' were not genuinely Pythagorean, but followers of the "renegade" Pythagorean [[Hippasus]].  The ''mathēmatikoi'', on the other hand, allowed that the ''akousmatikoi'' were Pythagorean but felt that ''they'' were ''more'' representative of Pythagoras.<ref>On the two schools and these differences, see Charles Kahn, p. 15, ''Pythagoras and the Pythagoreans'', Hackett 2001.</ref>
-==Pythagorean natural philosophy==
-Pythagorean thought was dominated by mathematics, but it was also profoundly [[mysticism|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 [[Metempsychosis|transmigration of the soul]] is too central to have been added by a later follower of Pythagoras. The Pythagorean conception of substance, on the other hand, is of unknown origin, partly because various accounts of his teachings are conflicting.  The Pythagorean account actually begins with [[Anaximander]]'s teaching that the ultimate substance of things is "the boundless," or what Anaximander called the "[[Apeiron (cosmology)|apeiron]]." 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]], [[Empedocles]], [[Philolaus]] and [[Plato]] (people either considered Pythagoreans, or whose works are thought deeply indebted to Pythagoreanism) results in a very diverse picture in which it is difficult to ascertain what the common unifying Pythagorean themes were. Relying on [[Philolaus]], whom most scholars agree is highly representative of the Pythagorean school, one has a very intricate picture. Aristotle explains how the Pythagoreans (by which he meant the circle around Philolaus) developed [[Anaximander]]'s ideas about the [[Apeiron (cosmology)|apeiron]] and the peiron, the unlimited and limited, by writing that:
-{{quotation|... for they [the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.}}
-Continuing with the Pythagoreans:
-{{quotation|The Pythagoreans, too, held that void exists, and that it enters the heaven from the unlimited breath – it, so to speak, breathes in void. The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature.}}
-[[Image:Bronnikov gimnpifagoreizev.jpg|thumb|left|350px|''Pythagoreans celebrate sunrise'' by [[Fyodor Bronnikov]] ]]
-When the [[apeiron (cosmology)|apeiron]] 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]] commentated:
-{{quotation|About nature and harmony this is the position. The being of the objects, being eternal, and nature itself admit of divine, not human, knowledge – except that it was not possible for any of the things that exist and are known by us to have come into being, without there existing the being of those things from which the universe was composed, the limited and the unlimited. And since these principles existed being neither alike nor of the same kind, it would have been impossible for them to be ordered into a universe if harmony had not supervened – in whatever manner this came into being. Things that were alike and of the same kind had no need of harmony, but those that were unlike and not of the same kind and of unequal order – it was necessary for such things to have been locked together by harmony, if they are to be held together in an ordered universe.}}
-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 [[Crotone|Croton]], 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 [[Taranto|Tarentum]], 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]].<ref>This is actually a lost book whose contents are preserved in [[Damascius]], ''[[de principiis]],'' quoted in Kirk and Raven, ''The Pre-Socratic Philosophers'', Cambridge Univ. Press, 1956, page 55.</ref>
-The Pythagorean symbols are central to the  mystery in the novel ''The Oxford Murders'' (Crímenes imperceptibles, 2003) by [[Guillermo Martinez]].
-==Pythagorean cosmology==
-{{details|Iamblichus of Chalcis}}
-[[Image:Monad.svg|thumb|The [[Monad (symbol)|Monad]] was a symbol referred by the Greek philosophers as "The First," "The Seed," "The Essence," "The Builder," and "The Foundation"]]
-The Pythagoreans are known for their theory of the [[transmigration]] of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods. Much of their mysticism concerning the soul seem inseparable from the [[Orphic]] tradition. The Orphics included various purifactory rites and practices as well as incubatory rites of descent into the underworld. Apart from being linked with this, Pythagoras is also closely linked with [[Pherecydes of Syros]], the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherekydes was Pythagoras's most "'''''intimate'''''"teacher. 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]], used by them as a symbol of recognition among members and as a symbol of inner health (eugieia [[Eudaimonia]]).
-==Pythagorean vegetarianism==
-The Pythagoreans were well-known in [[classical antiquity|antiquity]] for their vegetarianism, which they practised for religious, ethical and ascetic reasons, in particular the idea of [[metempsychosis]] - the transmigration of souls into the bodies of other animals.<ref>{{citation|url=http://www.oup.com/us/brochure/0195154371/samples/vegetarianism.pdf|title=The Oxford Encyclopedia of Food and Drink|chapter=Vegetarianism|publisher=OUP|year=2004}}</ref> "Pythagorean diet" was a common name for the abstention from eating meat and fish, until the coining of "[[vegetarianism|vegetarian]]" in the nineteenth century.<ref>See for instance the popular treatise by Antonio Cocchi, ''Del vitto pitagorico per uso della medicina'', Firenze 1743, which initiated a debate on the "Pythagorean diet".</ref>
-The Pythagorean code further restricted the diet of its followers, prohibiting the consumption or even touching of any sort of bean. The reason is unclear: perhaps the [[flatulence]] they cause, perhaps as protection from potential [[favism]], perhaps because they resemble the genetalia,<ref>Seife, Charles. ''Zero'' p 26</ref> but most likely for magico-religious reasons,<ref>Gabrielle Hatfield, ''review'' of Frederick J. Simoons, ''Plants of Life, Plants of Death'', University of Wisconsin Press, 1999. ISBN 0-299-15904-3.  In ''Folklore'' '''111''':317-318 (2000). </ref> such as the belief that beans and human beings were created from the same material.<ref>Riedweg, Christoph, ''Pythagoras: his life, teaching, and influence''. Ithaca : Cornell University Press, pp. 39, 70. (2005), ISBN 0-8014-4240-0</ref> 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.<ref>Seife, p 38</ref>
-==Pythagorean view of women==
-Women were given equal opportunity to study as Pythagoreans; however, they learned practical domestic skills in addition to philosophy.<ref name=glenn>Glenn, Cheryl, ''Rhetoric Retold: Regendering the Tradition from Antiquity Through the Renaissance''. Southern Illinois University, 1997. 30-31.</ref>  Women were held to be different from men, but sometimes in good ways.<ref name=glenn/> 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.<ref>Seife, Charles. ''Zero'' p. 27</ref>
-==Neo-Pythagoreanism==
-{{main article|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 first century [[Apollonius of Tyana]] and [[Moderatus of Gades]].  Middle and Neo-Platonists such as [[Numenius of Apamea|Numenius]] and [[Plotinus]] also exhibited some Neo-Pythagorean influence.
 In 1915 a subterranean basilica was discovered near [[Porta Maggiore]] on [[Via Praenestina]], [[Rome]] where Neo-Pythagoreans held their meetings in the 1st century. The groundplan shows a basilica with three naves and an apse similarly to early Christian basilicas that appeared only 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.<ref>{{cite web |url=http://penelope.uchicago.edu/Thayer/E/Gazetteer/Places/Europe/Italy/Lazio/Roma/Rome/_Texts/PLATOP*/basilicae.html|title=Basilicae|author=Ball Platner, Samuel|publisher=penelope.uchicago.edu}}</ref>

Pythagoreanism: Difference between revisions

Revision as of 14:46, 6 February 2009

Influences

References

Further reading

See also

Pythagorean symbols

External links