The school pythagorician is a philosophical school of the Antiquité founded by Pythagore.
History of the school
Founded by Pythagore (580 - 490 before Jesus-Christ), it lasted nine or ten generations. The last pythagoricians are Xénophile, Phanton de Phlionte, Échécrate, Dioclès and Polymnastos.
Rules of teaching
Teaching pythagorician was divided into two parts: a part for the acousmaticians, not yet initiated, and for the initiates, the mathematicians. This teaching was oral and secret. The transmission of the knowledge between disciples was indissociable compliance with the rules morals of fraternity (philias) as a whole: regulate silence, regards of the rank of initiation of the disciples.
The school pythagorician was thus a brotherhood as well religious as scientific.
Doctrines
Principles
Mathematics seen by Appolos Patrick Kakeu in the work of Plato
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Calculation pythagorician is before a a whole numerical Symbolique. Each number is associated with a figure, from where the restriction on the study of the positive integers:
- 1 represented the divinity,
- 2 the woman,
- 3 the man,
- 10 fraternity pythagorician…
This association number-figure was the support of a mathematical Abstraction, because the number did not rise any more results of mathematical applications - financial, agricultural… - but was consequently posed like principle (in Greek, Arkhê ) of knowledge. It was a question for the pythagoricians of going to more close to the mystic of the numbers, by the establishment of laws between arithmetic.
It is notable that the arithmetic units known by the pythagoricians were it by iterative constructions: that rose in fact from the figuration from the numbers. On the basis of a simple figure, the such formed triangle of three points, one can increase the whole by preserving its form but by increasing its parts, to arrive, for example, with a formed triangle of six points. This not-fixed figuration is an important abstraction for Antiquity, the more so as it related to also certain volumes (pyramids at bases triangular, square, cylinder…). The comparison of the continuations thus built has leads to discovered of relations structural and general between particular units of numbers.
These natural laws are the hard core of the design pythagorician of the Mathématiques, considered as esoteric and sectarian, where the integers are supposed to represent very whole nature. This category of number becomes an end in itself, an immutable principle which has vocation to explain all things. Aristote reports that Pythagore would have endorsed the currency “Any thing is number”. It indicates by this formula that what imports with the pythagoricians is not any more the experimentation, but the theory of the numbers.
Astronomy
Ethics
Policy
The political activity of the pythagoricians was, seems T it, very intense. The social model of fraternity pythagorician would have implied a clear catch of party in favor of the democratic regime where traditionally, an aristocracy holds the capacity, and in fact, the knowledge. Nevertheless, this democratic engagement is contestable, since the example of Archytas de Tarente watch that it was the political balance which was sought by the pythagoricians, which would not imply necessarily a democratic regime.
A popular riot is at the origin of the disappearance of the school pythagorician, but the disciples, then soon the Neo-Pythagoreans, maintained for a long time the doctrines their Master.
Pythagoricians
We present here an exhaustive list of all the known pythagoricians.
Pythagore
-
See article Pythagore
Old pythagoricians
Knowledge that we have of the old pythagoricians is almost null, and it is only starting from Alcméon of Crotona that we have more provided testimonys.
He would have been the rival of
Hésiode. According to a tradition brought back by
Cicéron, Cercops would be the author of the
Poème orphic . He would have written a
Descent into Hell and a
Traité crowned .
He supported the plurality of the worlds laid out in a triangular way. He would have written a book on the number of the world which was according to him of 183.
Independent source:
Plutarque,
Why the Pythie prophetess does not return any more her oracles in worms , 22 and 23.
Originating in
Métaponte, it seems to have been the father (or, certain sources, the husband) of Théanô, woman of
Pythagore. According to certain traditions questioned as of Antiquity (
Diogène Laërce, VIII, 55), it would have had Empédocle for disciple. One allots
to him Péplos ,
the Net and
the Elements of nature (Souda), and a treaty
Of intellect and understanding (
Jamblique,
Of common mathematical science , 8).
See also: Théano (mathematician)
Perhaps these two names nominate the same person. According to Jamblique ( pythagoric Life , 132), it was the wife of Brontin, and was a remarkable Femme as well by her Sagesse as by its personality:
- “the woman must offer a sacrifice to the moment even where it leaves the bed of her husband. ”
It was made the spokesperson of the women of
Crotona who asked Pythagore “to maintain their husbands the respect due to the wife. ” (ibid) We know indeed that the rules of life pythagoricians prohibited the husbands from beating their wife, and that the husband was held to observe an absolute fidelity (
Aristote,
Économiques , I, IV 1344 has 8).
Doctor pythagorician, originating in
Crotona and father of Démocédès.
- Démocédès
- Parméniscos or Parmicos
Rich person citizen of Métaponte, one reports that it lost the faculty of Rire after being gone down in the cave from Trophonios, and that it sought to find it by consulting the Pythie. It would have sold, with Orestadas, the philosopher Xénophane like slave.
Average period
Iccos of
Tarente, wire of Nicolaïodas,
Doctor, victorious Athlete of the Pentathlon to the
Olympic Games and Gymnastic Master of
. Its acme is dated from the 77ème Olympiade (472 - 469).
Plato reports that its lifestyle during its career was very strict (
the Laws , VIII, 839, E - 840 a), in particular with regard to the trade with the Femme S and the Adolescent S, and the food mode (the expression
meal of Iccos became proverbial to indicate a perfect mode which does not include/understand anything superfluity), which seems well to make a pythagorician way of life of it. But it was perhaps actually a Sophiste (
Plato,
Protagoras , 316 d).
We do not know almost anything of this philosopher, if it is not that he considered, while being opposed to Simonide, the Temps like a place of lapse of memory,
all-ignoramus (
Aristote,
Physique , IV, XIII, 222 B 17).
Another source:
Simplicius de Cilicie,
Comment on the Physics of Aristote , 754,9.
Wire of Diochètas and friend of
Parménide with which it inspired the taste of the study; honest man, it lived in poverty, and Parménide made him build a tomb after its Mort (
Diogène Laërce, IX, 21).
There was also a bearing Athénien this name and which was archonte towards 438 - 435 avt. J.C., and a Lacédémonien (
Thucydide,
History of the Peloponnesian War ). We do not know if Aminias the pythagorician can be identified with one of these two homonyms.
Recent Pythagoricians
Originating in
Sybaris, he is the founder of the Botanique. We know its theories only by
Théophraste (
Of the causes of the plants ).
Originating in Crotona, it supported that the principles are the rare one and the dense one, assumption which leads to the assertion of the
Existence Vide, because, without these principles and the vacuum, there would be no movement (
Aristote,
Physique , IV, IX, 216 B 22). But, according to him, the world undulates, while swelling and while decreasing like the Mer (
Simplicius de Cilicie,
Commentaire on the Physics of Aristote , 683,24).
It is possible that this pythagorician is in fact Ion of Tap-hole, since this last was called Xouthos.
In its " Life pythagorique" Jamblique specifies that Eurytos of Crotona is a disciple of Philolaos.
In " Métaphysique" , Aristote explains why Eurytos assigned a number to the people, to the animals, the plants and the geometrical figures (the triangle and the square).
The commentators of Aristote (Alexandre d' Aphrodise) and his successor with the head of the College (Théophraste) described the taste of Eurytos for stones. Thus, Eurytos took number 250 for measurement of the man and sought for this purpose 250 stones of all the colors; then it reconstituted the silhouette of the man with these stones, to represent the face, the body, the members, until all the stones are used.
According to
Jamblique, Archippos is the only pythagorician with
Lysis to be had escaped with the fire lit by the men of
Cylon after the banishment of fraternities pythagoriciennes.
Plutarque says that the survivors are Philolaos and
Lysis. After the fire, Archippos turned over to Tarence and
Lysis to Thèbes.
Occelos (or Ocelos) of Lucanie, brother of the pythagorician Byndaco, supported that mankind had always existed. One allots a
to him nature of the universe , in which it affirms that the world is inengendré and incorruptible (
Philon of Alexandria,
Of the eternity of the world ). This work would have inspired
Aristote for its
Of the generation and corruption (Syrianos reports that he would have plagiarized it, cf
Commentaire on the Metaphysics of Aristote , 175,7).
Occelos thought that the triad is the origin of all, from where the gods proceed and from where they hold their eternal position: “It is the triad which, the first, fixed beginning, medium and end” (Jean of Lydie,
Of the months , II, 8).
He thought that the whole of the things is composed of five elements: he added indeed to the traditional elements, the ether of which the sky and the celestial bodies are made up (Sextus Empiricus,
Against the professors , X, 316). He would have also written
Of the law , the royalty
, Of holiness ,
Of the origin of the universe .
Hicétas of Syracuse would be the inventor of the assumption pythagorician of the anti-Ground (Aétius,
Opinions , III, IX, 1 - 2). It supported that the vault of heaven is fixed, and that only the
Ground is moving and turns around its axis; this movement explained according to him the illusion of the movement of all the stars (
Cicéron,
First academic , II, XXXIX, 123).
Ecphantos of Syracuse supported that the principles are the indivisible bodies and the vacuum; Aétius considers that it is the first to have said that the monades pythagorician are body (
Opinions , I, III, 19). The world thus consists of Atome of infinite number, distinguished by the size, the form and the power, and are the matter of sensitive (Hippolyte,
Réfutation of all the heresies , I, 15). They are driven by a divine principle, Intellect and Heart, kind of
providence whose world is the idea. This world is one and has a spherical form. It placed the Earth in the center of the world, and thought that it rotated of west in est.
Since we do not know at which time it lived, we cannot say if it is a precursor pythagorician of the Atomisme, where if it adapted on the contrary the atomism to the thought pythagorician.
Xenophile of Chalcis, main Musicien of Aristoxène which died at the 105 years age with
Athens (without to have ever been sick, cf Macrobe,
Saturnales , 18) was one of the last pythagoricians (
Diogène Laërce, VIII, 46). We do not know anything else.
Echecrat of Tarente (or Locres, according to
Cicéron,
Of the ends , V, XXIX, 87) is known to us by the
Phédon , a dialog of
Plato. This last makes him support the thesis phytagorician of the harmony of the heart:
- “Indeed, the theory according to which our heart would be a harmony captivates me, each time I intend it to expose, as it is the case aujourd' ui; and to hear it, it, so to speak, returned to me in memory that such was my first opinion, to me too. ” (88 d)
- Polymnasto
- Phanton
- Arion
- Proros
- Amyclas
- Clinias
- Damon
- Phintias
- Myonide
- Euphranor
- Lycon
Lycon (or Lycos) of Tarente,
Botanist and author of a
Life of Pythagore (, II, 69 E and X, 418 E). It seems to have compiled rather whimsical anecdotes on certain philosophers (
Aristoclès, in
Eusèbe de Césarée,
evangelic Préparation , XV, II, 8).
List pythagoricians according to Jamblique
Here a catalog established by Jamblique ( pythagoric Vie , 267), which includes/understands names of philosophers of which we do not know absolutely anything.
Crotona
Hippostrate, Dymas, Égon, Hémon, Syllos, Cléosthène, Agélas, Épysylos, Phyciadas, Ecphantos, Timée, Bouthos, Ératos, Itanée, Rhodippos, Bryas, Énadros, Myllias, Antimédon, Agéas, Léophron, Agylos, Onatas, Hipposthène, Cléophron, Alcméon of Crotona, Damocles, Milon, Ménon.
Métaponte
Brontin, Parmicos, Orestadas, Leon, Damarménos, Énée, Chilas, Mélésias, Aristée, Laphaon, Évandre, Agésidamos, Xenocade, Euryphémos, Aristomène, Agésarque, Alcias, Xénophante, Trhaséos, Eurytos, Épiphron, Iriscos, Mégistas, Léocyde, Trasymède, Euphémos, Proclès, Antimène, Lacritos, Damotagès, Pyrrhon, Rhexibios, Alopécos, Astylos, Dacidas, Aliochos, Lacratès, Glycinos.
Agrigente
Élée
Tarente
The women pythagoricians
Jamblique gives us the names of 16 Femme S which followed the doctrines of Pythagore: Timicha (woman of Myllias of Crotona), Philtys (girl of Théophris of Crotona), Byndaco, Chilonis, Cratésicléia, Théano, Mya, Lasthénéia, Habrotéléia, Échécratéia, Tyrrhénis, Pisirrhodè de Tarénte, Nisthéadousa de Sparte, Boio and Babélyca d' Argos, Autocharidas.
