Pythagore (Encyclopédie de la philosophie de Stanford) | solides de Platon spirituel

Quelle était la croyance et la pratique de la Pythagore historique?
Cette question apparemment simple est devenue les effrayants Pythagoriciens
questions pour plusieurs raisons. Premièrement, Pythagore n'a rien écrit,
donc notre connaissance des vues de Pythagore est entièrement tirée de
rapports d'autres personnes. Deuxièmement, il n'était pas exhaustif ou faisant autorité
récit contemporain de Pythagore. Personne n'a fait pour Pythagore quoi
Platon et Xénophon l'ont fait pour Socrate. Troisièmement, seuls des fragments de
premiers récits détaillés de Pythagore, écrits environ 150 ans plus tard
sa mort, a survécu. Quatrièmement, il est clair que ces comptes
étaient en désaccord sur des points importants. Ces quatre points
rendrait déjà le problème de la détermination philosophique de Pythagore
Croyez plus que de décider presque tout le monde
philosophe ancien, mais un cinquième facteur complique encore les choses
plus. Au troisième siècle après JC, lorsque les premiers récits détaillés de
Pythagore survivant intact était écrit, Pythagore était né
considéré dans certains cercles comme le maître philosophe, dont tous
c'était vrai dans la tradition philosophique grecque. À la fin
au premier siècle avant JC. une grande collection de livres avait été forgée
au nom de Pythagore et d'autres premiers Pythagoriciens, comme
prétendait être les textes originaux de Pythagore tels que Platon et
Aristote a proposé ses idées les plus importantes. Une thèse forgée en
le nom Timée de Locri était le modèle supposé de Platon
Timée, tout comme les fausses thèses attribuées à Archytas
le modèle supposé d'Aristote Catégories. Pythagoras
lui-même a été beaucoup présenté comme prévu plus tard par Platon
métaphysique, où l'unique et la dyade indéfinie sont les premières
des principes. Ainsi, non seulement la première preuve de
Les vues de Pythagore sont maigres et contradictoires, elles sont éclipsées par
présentation hagiographique de Pythagore, devenue dominante
antiquité tardive. Dans ces circonstances, la seule approche fiable
répondre à la question de Pythagore, c'est commencer par le plus tôt
preuve, qui est indépendante des tentatives ultérieures de glorifier
Pythagore, et d'utiliser l'image de Pythagore provenant de
cette première preuve en tant que norme, on peut évaluer ce qui peut
être accepté et ce qui doit être rejeté plus tard
tradition. Suivant une telle approche, Walter Burkert, dans son
livre d'époque (1972a), a révolutionné notre compréhension de
Les questions de Pythagore et toutes les bourses modernes à Pythagore,
y compris cet article, se tient sur vos épaules. Pour un détail
discussion des problèmes sources qui génèrent pythagoricienne
Questions voir 2. Sources ci-dessous.

2.1 Aperçu chronologique des sources de Pythagore

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300 CE Iamblichus
(vers 245–325 après JC)
Sur la vie pythagoricienne (existant)
Porphyre
(234 – ca 305 CE)
La vie de Pythagore (existant)
Diogène Laertius
(environ 200-250 après JC)
La vie de Pythagore (existant)
200 CE Sextus Empiricus
(vers 200 après JC)
(résumé de Pythagore '
philosophie i Adversus Mathematicos (Vers
Théoriciens
), cité ci-dessous comme M.)
100 CE Nicomachus
(vers 50-150 après JC)
Introduction à l'arithmétique
(existant), La vie de Pythagore (fragments cités dans Iamblichus
etc.)
Apollonius de Tyane
(décédé vers 97 après JC)
La vie de Pythagore
(fragments cités dans Iamblichus, etc. Il est possible que ce travail soit d'un autre Apollonius autrement inconnu.)
Modéré de Gades
(50–100)
Conférences sur le pythagorisme
(fragments cités en porphyre)
Aetius
(premier siècle après JC)
Opinions des philosophes (reconstruit
par H. Diels de Pseudo-Plutarque, Opinions de
Les philosophes
(2e CE) et Stobaeus, Choix (5.
CE))
Textes pseudo-pythagoriciens
forgé
(commence dès 300 avant JC mais
le plus courant au premier siècle avant JC)
100 avant JC Alexander Polyhistor
(f. 105 avant notre ère)
son extrait de Souvenirs de Pythagore est
cité par Diogène Laertius
200 avant JC Souvenirs de Pythagore
(200 avant notre ère)
un texte pseudo-pythagoricien (sections citées dans Diogène Laertius)
300 avant JC Timée de Tauromène
(350-260 avant notre ère)
(historien de la Sicile)
Académie Héraclides
(environ 380–310)
Xénocrate
(vers 396–314)
Speusippus
(vers 410–339)
Lycée Dicaearchus
(environ 370–300)
Aristoxène
(environ 370–300)
Eudemus
(environ 370–300)
Théophraste
(372-288)

Aristote
(384-322)

400 avant JC Platon
(427–347 avant notre ère)
500 avant JC Pythagoras
(570–490 avant notre ère)

2.2 Sources post-aristotéliciennes pour Pythagore

Les problèmes avec les sources de la vie et la philosophie de
Pythagore est assez compliqué, mais il est impossible de comprendre
Les questions de Pythagore sans une compréhension exacte d'au moins
la nature générale de ces problèmes. Il vaut mieux commencer par
preuves ultérieures complètes mais problématiques et remontées dans le passé
preuves fiables. Le plus détaillé, le plus étendu et donc le plus
les récits influents de la vie et de la pensée de Pythagore datent du troisième
cent ans après sa mort. Diogène Laertius
(vers 200–250 après JC) et le porphyre (vers 234–305 après JC) ont chacun écrit
une La vie de Pythagore, mens Iamblichus (vers 245–325 après JC)
a écrit Sur la vie pythagoricienne, qui comprend une petite biographie
mais se concentre davantage sur le style de vie que Pythagore a établi pour son
suiveurs. Tous ces ouvrages ont été écrits à une époque où Pythagore
la performance avait été considérablement exagérée. Diogène peut avoir
certains prétendent être objectifs, mais Iamblichus et Porphyre l'ont tous deux
des programmes forts qui n'ont pas grand-chose à voir avec l'histoire
précision. Iamblichus présente Pythagore comme une âme envoyée par les dieux
pour éclairer l’humanité (O’Meara 1989, 35–40). Travail d'Iamblichus
n'était que le premier d'un volume de dix, qui en fait
Néoplatonisme pythagoranisé, mais le pythagorisme impliqué était
Le point de vue d'Iamblique sur Pythagore est particulièrement préoccupant
avec les mathématiques plutôt qu'un compte du pythagorisme basé sur
première preuve. Le porphyre met également l'accent sur les aspects divins de Pythagore
et peut l'installer comme un rival de Jésus (Iamblichus 1991,
14). Ces trois récits de Pythagore du IIIe siècle furent tour à tour
basé sur des sources précédentes, qui sont maintenant perdues. Certains d'entre eux dans le passé
les sources ont été fortement polluées par la vision néopythagoricienne de
Pythagore comme source de toute vraie philosophie, dont les idées Platon,
Aristote et tous les philosophes grecs ultérieurs ont plagié. Iamblichus
cite des biographies de Pythagore par Nicomachus de Gérasa et un certain
Apollonius (VP 251 et 254) et semblent les avoir utilisés
exhaustifs même lorsqu'ils ne sont pas cités (Burkert 1972a, 98
ff.). Nicomachus (vers 50 – vers 150 après JC) attribue à Pythagore un
métaphysique qui est évidemment platonicienne et aristotélicienne et que
utilise des terminologies platoniciennes et aristotéliciennes distinctives
(Introduction à l'arithmétique EN 1). Si Apollonius cité par
Iamblichus est Apollonius de Tyane (1ère CE), son compte sera
influencé par sa vénération pour Pythagore comme modèle pour son
vie ascétique, mais certains savants affirment qu'Iamblique en utilise un
Apollonius autrement inconnu (Flinterman 2014, 357). Porphyre
(VP 48–53) cite explicitement le Moderatus of Gades comme un
de ses sources. Modéré était un "agressif"
Néopythagore du premier siècle après JC, qui rapporte que Platon,
Aristote et leurs élèves Speusippus, Aristoxenus et Xenocrates
a pris pour lui tout ce qui était fécond dans le pythagorisme,
ne laisse à attribuer que ce qui était superficiel et trivial
école (Dillon 1977, 346). Diogène Laertius, qui semble avoir moins
l'allégeance personnelle à la légende pythagoricienne, fonde sa
récit de la philosophie de Pythagore (VIII. 24–33) sur
la Souvenirs de Pythagore extrait d'Alexandre Polyhistor,
qui est un faux datant d'environ 200 avant JC. et qui sont attribués
idées non seulement platoniciennes mais aussi stoïciennes de Pythagore (Burkert 1972a,
53; Kahn 2001, 79-83).

DANS Souvenirs de Pythagore, Pythagore aurait
a adopté la Monade et la Dyade Indéfinie comme principes incorporés,
d'où proviennent d'abord les nombres, puis les figures planes et solides et
enfin les corps du monde rationnel (Diogène Laertius VIII, 25).
C'est le système philosophique le plus souvent attribué
Pythagore dans la tradition post-aristotélicienne, et il se trouve dans
Récits détaillés de Sextus Empiricus (IIe siècle après JC) sur le pythagorisme
(par exemple. M. X.261) et surtout dans l'influent
manuel sur les différentes opinions des philosophes grecs, qui
a été recueilli par Aetius au premier siècle de notre ère. et est basé sur
la Les principes des philosophes naturels de l'élève d'Aristote
Théophraste (par exemple H. Diels, Doxographes grecs I. 3.8). le
le témoignage d'Aristote, cependant, montre très clairement que c'était
le système philosophique de Platon dans ses dernières années et non celui de
Pythagore ou même les derniers Pythagoriciens. Aristote est explicite que
bien que le système de Platon soit similaire à celui de Pythagore antérieur
philosophie des limiteurs et illimitée, la dyade indéfinie est unique
à Platon (Métaphysique 987b26 et suiv.) Et les Pythagoriciens
n'a reconnu que le monde sensible et ne l'a donc pas obtenu de
principes immatériels. DANS Philebus, Dit à Platon un
histoire qui est tout à fait en accord avec le rapport d'Aristote. Tandis que
reconnaître une dette envers la philosophie des limiteurs et illimités,
trouvé dans les récits d'Aristote sur le pythagorisme et dans
fragments du Philolaus de Pythagore du Ve siècle, Platon fait
c'est clairement une philosophie du passé importante car il est
refonte complète à des fins personnelles (16c et suiv.; voir Huffman 1999a
et 2001). Comment expliquer l'écart par rapport à la tradition postérieure
ce témoignage d'Aristote et de Platon? La proposition la plus convaincante
met en évidence des éléments de preuve qui, pour des raisons qui ne sont pas tout à fait claires,
Les successeurs de Platon à l'académie, Speusippus, Xenocrate et
Heraclides a choisi de présenter le pythagorisme non seulement comme un précurseur
la métaphysique platonicienne tardive, mais comme prévu, la
thèses. Ainsi la tradition qui attribue à tort à la fin de Platon
la métaphysique de Pythagore ne commence pas par la néopythagore en
premiers siècles avant JC et CE, mais déjà au quatrième siècle avant JC. parmi
Les propres élèves de Platon (Burkert 1972a, 53–83; Dillon 2003,
61–62 et 153–154). Cette vision du pythagorisme trouve sa
loin dans la doxographie d'Aetius, soit parce que Théophraste a suivi
la première académie à la place du professeur Aristote (Burkert 1972a,
66) ou parce que la doxographie théophrastane de Pythagore a été réécrite
au premier siècle avant JC. sous l'influence du néopythagorisme
(Diels 1958, 181; Zhmud 2012a, 455). Aristote distingue soigneusement
entre Platon et Pythagorisme du Ve siècle, ce qui rend excellent
le bon sens en ce qui concerne le développement général de la philosophie grecque est
largement ignoré dans la tradition postérieure en faveur de la plus
attribution sensationnelle du platonisme mature à Pythagore. Éprouvé
car la première académie, cependant, est très limitée, et certains rejettent
thèse à laquelle les membres ont décerné la métaphysique platonicienne tardive
Pythagore (Zhmud 2012, 415–432). Le texte clé se trouve dans
Proclus ' Commentaire sur Parménide (pages 38,32 à 40,7
Klibansky). Proclus cite un paragraphe dans lequel Speusippus attribue
les anciens, qui dans ce contexte sont les pythagoriciens, l'un et l'autre
la dyade indéterminée. Certains chercheurs affirment que ce n'est pas vrai
fragment de Speusippus, mais plutôt une fabrication ultérieure (voir Zhmud
2012a, 424–425 et pour une réponse Dillon 2014, 251). Si l'académie
n'a pas assigné l'un et la dyade à Pythagore, mais ce sera
moins clair comment ces principes ont été attribués
lui. Théophraste les attribue aux Pythagoriciens
(Métaphysique 11a27), mais puisque Aristote se sépare
Pythagoriciens de Platon sur ce point, proposition de Zhmud (2012a, 455)
qu'il suit son professeur et ne fait que "l'étape suivante"
ne marche pas. Les preuves de Theophrastus ont le meilleur sens si nous acceptons
point de vue traditionnel et supposer que c'est sous l'autorité de Platon
successeurs de l'académie qu'il fonde son départ de son
la vue du professeur, Aristote.

Si nous nous retirons un instant et comparons les sources de Pythagore
avec ceux disponibles pour d'autres premiers philosophes grecs, l'étendue de
les difficultés inhérentes à la question pythagoricienne deviennent apparentes.
Lorsque nous essayons de reconstruire la philosophie d'Héraclite, par exemple,
les chercheurs modernes s'appuient avant tout sur les citations
Le livre d'Héraclite est conservé chez les auteurs ultérieurs. Puisque Pythagore n'a pas écrit
livres, c'est la plus fondamentale de toutes les sources qui nous a refusé. À son tour
avec Héraclite, le savant moderne se tourne à contrecœur à côté
la tradition doxographique, la tradition représentée par Aetius dans
premier siècle après JC, qui conserve dans le manuel, forme une
explique les croyances des philosophes grecs sur une variété de sujets
a à voir avec le monde physique et ses premiers principes. Aetius '
l'œuvre a été reconstruite par Hermann Diels sur la base de deux
les œuvres qui en ont été prises,
Choix de Stobaeus (5ème siècle après JC) et Des avis
des philosophes
du pseudo-Plutarque (IIe siècle après JC). Savant
La croyance en ces preuves repose en grande partie sur l'hypothèse que la plupart des
il remonte à l'école d'Aristote et surtout à
Theophrastus » Les principes des philosophes naturels. Encore ici
Le cas de Pythagore est exceptionnel. Pythagore est représenté dans
cette tradition, mais comme nous l'avons vu, Théophraste dans ce cas plutôt
a adopté le point de vue, contre toute probabilité historique, attribue
La métaphysique ultérieure de Platon de la doxographie de Pythagore ou de Théophraste sur
Les pythagoriciens ont été réécrits au premier siècle avant JC. Ainsi c'est
la deuxième source standard de preuves pour la philosophie grecque primitive est, en
le cas de Pythagore, détruit. Tout ce que Pythagore regarde
a été remplacée par la métaphysique platonicienne tardive
tradition doxographique.

Une troisième source de preuves pour la philosophie grecque primitive est considérée
grand scepticisme de la plupart des savants et, dans le cas de la plupart des premiers Grecs
philosophes, utilisés avec beaucoup de prudence. Ceci est la biographie
tradition représentée par La vie des philosophes
écrit par Diogène Laertius. Dans ce cas, nous semblons à première vue
avoir de la chance, au moins en termes de quantité de preuves
Pythagore, puisque, comme nous l'avons vu, deux récits principaux de la vie
Pythagore et le mode de vie pythagoricien survivent aussi
La vie de Diogène. Malheureusement, ces deux vies supplémentaires sont écrites
par des auteurs (Iamblichus et Porphyry) dont les buts sont explicites
non historique, et les trois vies dépendent fortement des auteurs
la tradition néopythagoricienne, dont le but était de la montrer plus tard
La philosophie grecque, dans la mesure où elle était vraie, a été volée à
Pythagoras. Cependant, il y a quelques sections dans ces trois vies
provenant de sources qui vont au-delà de l'influence déformante
du néopythagorisme, aux sources du IVe siècle av.
qui sont également indépendants des tentatives de la première académie d'attribuer
Métaphysique platonicienne aux pythagoriciens. Le plus important d'entre eux
sources sont les fragments des traités perdus d'Aristote sur
Pythagoriciens et fragments d'œuvres sur le pythagorisme ou d'œuvres
qui a agi en accord avec le pythagorisme écrit par Aristote
étudiants Dicaearchus et Aristoxenus, dans la seconde moitié de la quatrième
siècle avant JC L'historien Timée de Tauromène (vers 350-260
BCE), qui a écrit une histoire sur la Sicile, qui comprenait du matériel sur
Le sud de l'Italie, où Pythagore était actif, est également important. Dans certaines
dans les cas où les fragments de ces premières œuvres sont clairement identifiés
les vies tardives, mais dans d'autres cas, nous pouvons soupçonner qu'ils sont eux
source d'un passage donné sans pouvoir être sûr. Gros
des problèmes persistent même dans le cas de ces sources. Ils étaient tous
écrit 150-250 ans après la mort de Pythagore; donné
Absence de preuves écrites pour Pythagore, elles sont largement basées sur
traditions orales. Aristoxenus, qui a grandi dans la ville du sud de l'Italie
de Tarente, où les architectes de Pythagore étaient les politiciens dominants
figure, et qui était lui-même pythagoricien avant de rejoindre Aristote
l'école possédait sans aucun doute un riche ensemble de traditions orales qu'ils pouvaient utiliser
dessiner. Il est néanmoins clair que 150 ans après sa mort
des traditions contradictoires concernant la foi de Pythagore avaient surgi
même les questions les plus centrales. Ainsi, Aristoxène est catégoriquement si
Pythagore n'était pas un végétarien strict et mangeait une variété de types
viande (Diogène Laertius VIII.20), tandis que le contemporain d'Aristoxène,
le mathématicien Eudoxus, le dépeint non seulement comme évitant toute chair
mais qui refuse même de s'associer aux bouchers (Porphyre, VP
sept). Même parmi les écrivains du quatrième siècle qui au moins en avaient
prétentions à l'exactitude historique et qui avait accès au meilleur
informations disponibles, les présentations sont très différentes,
simplement parce que de telles contradictions étaient endémiques aux preuves
disponible au quatrième siècle. De quoi pouvons-nous espérer
preuves présentées par Aristote, Aristoxenus, Dicaearchus et Timaeus
n'est donc pas une image de Pythagore cohérente à tous égards
mais plutôt une image qui définit au moins les principaux domaines de son
réussite. Cette image peut ensuite être testée par le plus basique
des preuves pour tous, des témoignages d'écrivains ayant mené à Aristote et y compris,
témoignage dans certains cas provenant de Pythagore
simultané. Ce témoignage est extrêmement limité, une vingtaine
références courtes, mais ce manque de preuves n'est pas propre à
Pythagoras. Le témoignage pré-aristotélicien de Pythagore est plus
complet que pour la plupart des autres premiers philosophes grecs et est donc
témoignage de sa renommée.

2.3 Platon et Aristote comme sources de Pythagore

En reconstruisant l'idée des premiers philosophes grecs, les savants
renvoie souvent aux récits d'Aristote et de Platon sur ses prédécesseurs,
bien que les récits de Platon soient intégrés dans la structure littéraire de
ses dialogues et ne prétendent donc pas être l'exactitude historique, alors que
La présentation apparemment plus historique d'Aristote masque un
interprétation significative des vues de son prédécesseur dans
expression de sa propre pensée. Dans le cas de Pythagore, ce qui est frappant
est l'accord essentiel entre Platon et Aristote dans le leur
présentation de sa signification. Aristote débat souvent
philosophie aux pythagoriciens, qu'il date du milieu et d'autres
moitié du 5ème siècle et qui a posé comme limitant et illimité
premiers principes. Parfois, il se réfère à ces pythagoriciens
«Soi-disant pythagoriciens», ce qui indique qu'il avait des
sous réserve de l'application du label
«Pythagore» pour eux. Aristote ne peut étonnamment jamais
fait référence à Pythagore lui-même dans ses écrits existants
(Métaph. 986a29 est probablement une interpolation; Rh.
1398b14 est une citation d'Alcidamas; MM 1182a11 ne peut pas
d'Aristote, et si c'est le cas, cela pourrait bien être un cas là-bas
«Pythagoriciens» a été transformé en
"Pythagore" dans le transfert). Dans les fragments de son
maintenant perdu la thèse de deux boîtes sur les Pythagoriciens, Aristote discute
Pythagore lui-même, mais les références sont toutes à Pythagore comme un
fondateur d'un mode de vie qui interdit de manger des haricots (fr.195),
et à Pythagore comme un fils prodigue, qui avait une cuisse dorée et en mordit une
serpent mort (Fr.191). Zhmud (2012a, 259-260) affirme cela dans un
place Aristote décrit aussi Pythagore comme un mathématicien (Fr.191)
et dans une autre étude de la nature (Protrepticus Fr.20), mais dans aucune
cas sont les mots qui appartiennent probablement à Aristote (voir Huffman 2014b,
281, n ° 7). Si Aristote n'a trouvé que des preuves de Pythagore comme un
travailleur émerveillé et fondateur d'un style de vie, il devient clair pourquoi il
ne mentionne jamais Pythagore dans son récit de sa philosophie
prédécesseurs et pourquoi il utilise le terme «soi-disant
Pythagoriciens »pour désigner le pythagorisme des
cinquième siècle. Car Aristote n'appartenait pas à Pythagore
l'ordre des penseurs à commencer par Thales, qui a tenté de le faire
expliquer les principes de base du monde naturel, et ainsi il pourrait
pas voir ce que signifiait d'appeler un penseur du Ve siècle qui
Philolaus, qui a rejoint l'héritage en fixant des limites et
illimité comme les premiers principes, un Pythagore. On pense souvent à Platon
être lourdement redevable aux Pythagoriciens, mais il est presque égal
parcimonieux dans ses références à Pythagore comme Aristote et mentionne
lui une seule fois dans ses écrits. La seule référence de Platon à Pythagore
(R. 600a) le traite comme le fondateur d'un style de vie, tout comme
Aristote fait, et quand Platon retrace l'histoire de la philosophie avant
à son temps en Sofist, (242c-e), il n'y a aucune allusion à
Pythagoras. DANS Philebus, Décrit Platon
philosophie des limiteurs et illimités, à laquelle Aristote assigne
soi-disant pythagoriciens du cinquième siècle et trouvés dans
fragments de Philolaus, mais comme Aristote il n'attribue pas cela
philosophie à Pythagore lui-même. Des chercheurs, anciens et modernes,
sous l'influence de la glorification ultérieure de Pythagore, a
On pense que Prométhée, que Platon décrit comme un casting
système aux hommes, était Pythagore (par exemple Kahn 2002: 13-14), mais
une lecture attentive du passage montre que Prométhée est juste
Prométhée et que Platon, comme Aristote, attribue le
système à un groupe d'hommes (Huffman 1999a, 2001). Les fragments de
Philolaus montre qu'il était le personnage principal de ce groupe. Quand
Platon fait référence à Philolaus dans Phaedo (61d-e), il ne
identifiez-le comme un Pythagore, de sorte que Platon accepte de nouveau
Aristote en éloignant les soi-disant pythagoriciens
le cinquième siècle de Pythagore lui-même. Pour Platon et
Aristote, puis Pythagore ne fait pas partie du cosmologique et
tradition métaphysique de la philosophie présocratique ni n'est-elle dense
connecté au système métaphysique présenté par le Ve siècle
Pythagoriciens comme Philolaus; il est plutôt le fondateur d'un moyen de
la vie.

Références à Pythagore par Xénophane (vers 570–475 avant notre ère) et
Heraclitus (fl. C. 500 BC) montre qu'il était une figure célèbre dans
fin du sixième et début du cinquième siècle. Pour les détails de sa vie, nous
doit s'appuyer sur des sources du quatrième siècle comme Aristoxène,
Dicaearchus et Timaeus de Tauromenium. C'est beaucoup
controverse sur ses origines et ses débuts, mais il y a accord
qu'il a grandi sur l'île de Samos, près du berceau du grec
philosophie, Milet, sur la côte d'Asie Mineure. Il y a un certain nombre
rapporte qu'il a beaucoup voyagé au Moyen-Orient tout en vivant
Samos, par exemple en Babylonie, en Phénicie et en Égypte. Dans une certaine mesure, des rapports
de ces visites sont une tentative d'affirmer l'ancienne sagesse de l'Orient
pour Pythagore et certains chercheurs les rejettent complètement (Zhmud 2012,
83–91), mais des sources relativement anciennes comme Hérodote (II. 81) et
Isocrate (Busiris 28) reliant Pythagore à l'Égypte, donc
qu'un voyage là-bas semble tout à fait plausible. Aristoxenus dit qu'il est parti
Samos à l'âge de quarante ans, lorsque la tyrannie de Polycrate, qui
puissance env. 535 avant JC, est devenu insupportable (Porphyre, VP 9). Ce
la chronologie suggère qu'il est né environ. 570 avant notre ère Han da
émigré vers la ville grecque de Croton dans le sud de l'Italie env. 530 BCE;
c'est à Croton qu'il semble avoir attiré pour la première fois un grand nombre
des adeptes de son style de vie. Il y a un certain nombre d'histoires sur
sa mort, mais la preuve la plus fiable (Aristoxène et
Dicaearchus) suggère que la violence contre Pythagore et
ses disciples à Croton ca. 510 BCE, peut-être à cause de l'exclusivité
la nature du mode de vie pythagoricien, l'a amené à fuir vers un autre
Ville grecque du sud de l'Italie, Metapontum, où il mourut vers 490 avant notre ère
(Porphyre,
VP 54–7; Iamblichus, VP 248 et suiv.; Sur la chronologie,
voir Minar 1942, 133–5). Il n'y a pas grand-chose d'autre dans sa vie
nous pouvons être en sécurité.

Les preuves suggèrent que Pythagore n'a écrit aucun livre. non
source simultanément avec Pythagore ou dans les deux premiers cent
ans après sa mort, y compris Platon, Aristote et leur
successeurs de l'académie et du lycée, citations d'une œuvre de Pythagore
ou donne toute indication que les œuvres écrites par lui étaient en
existence. Plusieurs sources ultérieures affirment explicitement que Pythagore
n'a rien écrit (par exemple Lucian (Conversation, 5),
Josèphe, Plutarque et Posidonius dans DK 14A18; voir Burkert 1972,
218–9). Diogène Laertius a tenté de contester cette tradition en
cite l'affirmation d'Héraclite selon laquelle «Pythagore, fils de
Mnesarchus, a pratiqué l'enquête la plupart de tous les hommes, et en choisissant ces
des choses écrites, se sont fait une sagesse, une
polymathie, une mauvaise conspiration »(Fr. 129). Ce fragment montre
juste que Pythagore a lu les écrits des autres, et dit
rien de lui n'écrivant rien de lui-même. Sagesse et méchanceté
la conspiration que Pythagore construit à partir de ces écrits n'a pas besoin
a été écrite, et la description d'Héraclite en tant qu'un
"Evil conspiracy" suggère plutôt que ce n'était pas le cas (car
traduction et interprétation du P. 129, voir Huffman 2008b). DANS
tradition plus tard, plusieurs livres ont été attribués à Pythagore, cependant
une telle preuve qui existe pour ces livres indique qu'ils étaient
forgé au nom de Pythagore et appartient au grand nombre
traités pseudo-pythagoriciens forgés au nom des premiers Pythagoriciens
comme Philolaus et Archytas. Au troisième siècle avant notre ère Un groupe
trois livres ont circulé au nom de Pythagore, Sur
éducation
, À propos de l'état, et Dans la nature
(Diogène Laertius, VIII. 6). Une lettre de Platon à Dion dans laquelle on lui a demandé
pour acheter ces trois livres à Philolaus a été forgé pour
«Authentifiez-les» (Burkert 1972a,
223–225). Heraclides Lembus au deuxième siècle avant JC. en donne un
liste de six livres attribués à Pythagore (Diogène Laertius, VIII. 7;
Thesleff 1965, 155–186 fournit une collection complète de
fausses écritures attribuées à Pythagore). L'autre de ces derniers est
une Discours sacré, dont certains ont voulu remonter
Pythagore lui-même. L'idée que Pythagore a écrit une telle chose saint
Discours
semble provenir d'une mauvaise lecture des premiers éléments de preuve.
Hérodote dit que les Pythagoriciens n'étaient pas d'accord avec les Égyptiens
que les morts soient enterrés dans la laine et prétendent ensuite que c'est
un discours sacré à ce sujet (II. 81). Hérodote se concentre ici sur
Égyptiens et non pythagoriciens, qui sont présentés comme grecs
parallèle, de sorte que Discours sacré auquel il se réfère est
Égyptien et non pythagoricien, comme des passages similaires ailleurs dans le livre II
de l'exposition Herodotus (par exemple II.62; voir Burkert 1972a, 219). différentes lignes
du vers hexamètre déjà circulé au nom de Pythagore en
troisième siècle avant JC et a ensuite été combiné dans une collection connue sous le nom de
la Vers d'or, qui marque le point culminant de
tradition pour un Discours sacré attaché à Pythagore
(Burkert 1972a, 219, Thesleff 1965, 158-163, et dernier
Thom 1995, bien que sa datation de la collection avant 300 avant JC. est
discutable). Le manque de texte écrit viable qui peut être
raisonnablement attribué à Pythagore est le plus clairement montré par
les écrivains ultérieurs ont tendance à citer Empédocle ou Platon, quand
ils devaient citer "Pythagore" (par exemple Sextus Empiricus,
M. IX. 126–30; Nicomachus, Introduction à
Arithmétique
I. 2). Quel intéressant, mais finalement peu convaincant
tente de faire valoir que le Pythagore historique a écrit des livres, voir
Riedweg 2005, 42–43 et la réponse de Huffman 2008a, 205–207.

L'une des manifestations de la tentative de glorifier Pythagore en
la tradition postérieure est le rapport qu'il a réellement inventé le mot
philosophie. Cette histoire remonte à la première académie, car elle est
trouvé pour la première fois à Heraclides of Pontus (Cicero, Toscane. V 3,8;
Diogène Laertius, Préface). La précision historique de
l'histoire est remise en cause par le fait qu'elle n'apparaît pas dans un
texte biographique, mais plutôt dans un dialogue qui raconte Empédocle »
la renaissance d'une femme qui avait cessé de respirer. D'ailleurs, l'histoire
dépend de l'idée qu'un philosophe n'a aucune connaissance mais
être placé entre l'ignorance et la connaissance et lutter pour
connaissance. Cependant, une telle vision est tout à fait platonique (voir,
par exemple. Symposium 204A), et Burkert a démontré qu'il pouvait
n'appartient pas à l'historique Pythagore (1960). Pour un essai récent
pour défendre au moins l'exactitude partielle de l'histoire, voir Riedweg
2005: 90–97 et la réponse de Huffman 2008a: 207–208; voir
également Zhmud 2012a, 428–430.

Même s'il n'a pas inventé le mot, que dire de
philosophie sur Pythagore? Pour les raisons exposées au point 1. Pythagore
Questions et 2. Sources ci-dessus, tout compte rendu responsable de Pythagore »
la philosophie doit fondamentalement se fonder sur les preuves avant
Aristote et deuxièmement sur la preuve que nos sources
identifier explicitement comme dérivé des livres d'Aristote sur
Pythagoriciens ainsi que des livres de ses élèves comme
Aristoxenus et Dicaearchus. Il y a accord sur ce
les preuves pré-aristotéliciennes sont, bien qu'il y ait des différences
interprétation de celui-ci. Il y a moins d'accord sur ce qui devrait être
inclus dans les preuves d'Aristote, Dicaearchus et Aristoxenus. Quoi
L'un comprend les preuves de ces auteurs qui auront un
effet sur l'image de Pythagore. Un particulièrement pressant
la question est de savoir si les chapitres 18 et 19 de Porphyry La vie à
Pythagoras
doit être considéré comme dérivant de Dicaearchus, car
l'éditeur le plus récent propose (Mirhady Fr.40), ou si seulement
le chapitre 18 devrait être inclus, comme dans l'édition précédente de Wehrli
(Fr 33). Il est crucial de trancher cette question avant de développer un
image de la philosophie de Pythagore depuis le chapitre 19, si c'est par
Dicaearchus, est notre premier résumé de Pythagore
philosophie. Porphyre est très fiable pour citer ses sources. Il
cite explicitement Dicaearchus au début du chapitre 18 et les noms
Nicomachus comme sa source au début du chapitre 20. Le matériel
au chapitre 19 suit de façon transparente le chapitre 18: la description du
discours que Pythagore prononça à son arrivée à Croton au chapitre 18
est suivi au chapitre 19 d'un récit des disciples qu'il
acquis à la suite de ces discours et d'une discussion sur ce qu'il
enseigné à ces disciples. Ainsi, la responsabilité incombe à quiconque prétendrait
que Porphyre change de source avant le changement explicite au
début du chapitre 20. Le chapitre 19 présente un récit très restreint
de ce que l'on peut savoir de manière fiable sur les enseignements de Pythagore et que
une très grande retenue est l'un des arguments les plus solides pour
étant basé sur Dicaearchus, puisque Porphyre ou quiconque dans le
on s'attendrait à ce que la tradition plus tardive donne beaucoup plus
présentation expanisve de Pythagore conformément à la
Vue néopythagoricienne de lui (Burkert 1972a, 122–123). Wehrli ne donne pas
reason for not including chapter 19 and the great majority of scholars
accept it as being based on Dicaearchus (see the references in Burkert
1972a, 122, n.7). Zhmud (2012a, 157) following Philip (1966, 139)
argues that the passage cannot derive from Dicaearchus, since it
presents immortality of the soul with approval, whereas Dicaearchus
did not accept its immortality. However, the passage merely reports
that Pythagoras introduced the notion of the immortality of the soul
without expressing approval or disapproval. Zhmud lists other features
of the chapter that he regards as unparalleled in fourth-century
sources (2012a, 157) but, since the evidence is so fragmentary, such
arguments from silence can carry little weight. Nothing in the chapter
is demonstrably late or inconsistent with Dicaearchus’ authorship so
we must follow what is suggested by the context in Porphyry and regard
it as derived from Dicaearchus.

In the face of the Pythagorean question and the problems that arise
even regarding the early sources, it is reasonable to wonder if we can
say anything about Pythagoras. A minimalist might argue that the early
evidence only allows us to conclude that Pythagoras was a historical
figure who achieved fame for his wisdom but that it is impossible to
determine in what that wisdom consisted. We might say that he was
interested in the fate of the soul and taught a way of life, but we
can say nothing precise about the nature of that life or what he
taught about the soul (Lloyd 2014). There is some reason to believe,
however, that something more than this can be said.

4.1 The Fate of the Soul—Metempsychosis

The earliest evidence makes clear that above all Pythagoras was known
as an expert on the fate of our soul after death. Herodotus tells the
story of the Thracian Zalmoxis, who taught his countrymen that they
would never die but instead go to a place where they would eternally
possess all good things (IV. 95). Among the Greeks the tradition arose
that this Zalmoxis was the slave of Pythagoras. Herodotus himself
thinks that Zalmoxis lived long before Pythagoras, but the Greeks’
willingness to portray Zalmoxis as Pythagoras’ slave shows that they
thought of Pythagoras as the expert from whom Zalmoxis derived his
teaching. Ion of Chios (5th c. BCE) says of Phercydes of
Syros that “although dead he has a pleasant life for his soul,
if Pythagoras is truly wise, who knew and learned wisdom beyond all
men.” Here Pythagoras is again the expert on the life of the
soul after death. A famous fragment of Xenophanes, Pythagoras’
contemporary, provides some more specific information on what happens
to the soul after death. He reports that “once when he
(Pythagoras) was present at the beating of a puppy, he pitied it and
said ‘stop, don’t keep hitting him, since it is the soul of a
man who is dear to me, which I recognized, when I heard it
yelping’” (Fr. 7). Although Xenophanes clearly finds the
idea ridiculous, the fragment shows that Pythagoras believed in
metempsychosis or reincarnation, according to which human souls were
reborn into other animals after death. This early evidence is
emphatically confirmed by Dicaearchus in the fourth century, who first
comments on the difficulty of determining what Pythagoras taught and
then asserts that his most recognized doctrines were “that the
soul is immortal and that it transmigrates into other kinds of
animals” (Porphyry, VP 19). Unfortunately we can say
little more about the details of Pythagoras’ conception of
metempsychosis. According to Herodotus, the Egyptians believed that
the soul was reborn as every sort of animal before returning to human
form after 3,000 years. Without naming names, he reports that some
Greeks both earlier and later adopted this doctrine; this seems very
likely to be a reference to Pythagoras (earlier) and perhaps
Empedocles (later). Many doubt that Herodotus is right to assign
metempsychosis to the Egyptians, since none of the other evidence we
have for Egyptian beliefs supports his claim, but it is nonetheless
clear that we cannot assume that Pythagoras accepted the details of
the view Herodotus ascribes to them. Similarly both Empedocles (see
Inwood 2001, 55–68) and Plato (e.g., Republic X and
Phaedrus) provide a more detailed account of transmigration
of souls, but neither of them ascribes these details to Pythagoras nor
should we. Did he think that we ever escape the cycle of
reincarnations? We simply do not know. The fragment of Ion quoted
above may suggest that the soul could have a pleasant existence after
death between reincarnations or even escape the cycle of reincarnation
altogether, but the evidence is too weak to be confident in such a
conclusion. In the fourth century several authors report that
Pythagoras remembered his previous human incarnations, but the
accounts do not agree on the details. Dicaearchus (Aulus Gellius
IV. 11.14) and Heraclides (Diogenes Laertius VIII. 4) agree that he
was the Trojan hero Euphorbus in a previous life. Dicaearchus
continues the tradition of savage satire begun by Xenophanes, when he
suggests that Pythagoras was the beautiful prostitute, Alco, in
another incarnation (Huffman 2014b, 281–285).

It is not clear how Pythagoras conceived of the nature of the
transmigrating soul but a few tentative conjectures can be made
(Huffman 2009). Transmigration does not require that the soul be
immortal; it could go through several incarnations before perishing.
Dicaearchus explicitly says that Pythagoras regarded the soul as
immortal, however, and this agrees with Herodotus’ description of
Zalmoxis’ view. It is likely that he used the Greek
word psychê to refer to the transmigrating soul, since
this is the word used by all sources reporting his views, unlike
Empedocles, who used daimon. His successor, Philoalus,
uses psychê to refer not to a comprehensive soul but
rather to just one psychic faculty, the seat of emotions, which is
located in the heart along with the faculty of sensation (Philolaus,
Fr. 13). Dette psychê is explicitly said by Philolaus to
be shared with animals. Herodotus uses psychê in a
similar way to refer to the seat of emotions. Thus it seems likely
that Pythagoras too thought of the
transmigrating psychê in this way. If so, it is
unlikely that Pythagoras thought that humans could be reincarnated as
plants, since psychê is not assigned to plants by
Philolaus. It has often been assumed that the transmigrating soul is
immaterial, but Philolaus seems to have a materialistic conception of
soul and he may be following Pythagoras. Similarly, it is doubtful
that Pythagoras thought of the transmigrating soul as a comprehensive
soul that includes all psychic faculties. His ability to recognize
something distinctive of his friend in the puppy (if this is not
pushing the evidence of a joke too far) and to remember his own
previous incarnations show that personal identity was preserved
through incarnations. This personal identity could well be contained
in the pattern of emotions, that constitute a person’s character and
that is preserved in the psychê and need not presuppose
all psychic faculties. In Philolaus this psychê
explicitly does not include the nous (intellect), which is
not shared with animals. Thus, it would appear that what is shared
with animals and which led Pythagoras to suppose that they had special
kinship with human beings (Dicaearchus in Porphyry, VP 19) is
not intellect, as some have supposed (Sorabji 1993, 78 and 208) but
rather the ability to feel emotions such as pleasure and pain.

There are significant points of contact between the Greek religious
movement known as Orphism and Pythagoreanism, but the evidence for
Orphism is at least as problematic as that for Pythagoras and often
complicates rather than clarifies our understanding of Pythagoras
(Betegh 2014; Burkert 1972a, 125 ff.; Kahn 2002, 19–22; Riedweg
2002). There is some evidence that the Orphics also believed in
metempsychosis and considerable debate has arisen as to whether they
borrowed the doctrine from Pythagoras (Burkert 1972a, 133; Bremmer
2002, 24) or he borrowed it from them (Zhmud 2012a,
221–238). Dicaearchus says that Pythagoras was the first to introduce
metempsychosis into Greece (Porphyry VP 19). Moreover, while
Orphism presents a heavily moralized version of metempsychosis in
accordance with which we are born again for punishment in this life so
that our body is the prison of the soul while it undergoes punishment,
it is not clear that the same was true in Pythagoreanism. It may be
that rebirths in a series of animals and people were seen as a natural
cycle of the soul (Zhmud 2012a, 232–233). One would expect that the
Pythagorean way of life was connected to metempsychosis, which would
in turn suggest that a certain reincarnation is a reward or punishment
for following or not following the principles set out in that way of
life. However, there is no unambiguous evidence connecting the
Pythagorean way of life with metempsychosis.

It is crucial to recognize that most Greeks followed Homer in
believing that the soul was an insubstantial shade, which lived a
shadowy existence in the underworld after death, an existence so bleak
that Achilles famously asserts that he would rather be the lowest
mortal on earth than king of the dead (Homer, Odyssey
XI. 489). Pythagoras’ teachings that the soul was immortal, would have
other physical incarnations and might have a good existence after
death were striking innovations that must have had considerable appeal
in comparison to the Homeric view. According to Dicaearchus, in
addition to the immortality of the soul and reincarnation, Pythagoras
believed that “after certain periods of time the things that
have happened once happen again and nothing is absolutely new”
(Porphyry, VP 19). This doctrine of “eternal
recurrence” is also attested by Aristotle’s pupil Eudemus,
although he ascribes it to the Pythagoreans rather than to Pythagoras
himself. (Fr. 88 Wehrli). The doctrine of transmigration thus seems
to have been extended to include the idea that we and indeed the whole
world will be reborn into lives that are exactly the same as those we
are living and have already lived.

4.2 Pythagoras as a Wonder-worker

Some have wanted to relegate the more miraculous features of
Pythagoras’ persona to the later tradition, but these
characteristics figure prominently in the earliest evidence and are
thus central to understanding Pythagoras. Aristotle emphasized his
superhuman nature in the following ways: there was a story that
Pythagoras had a golden thigh (a sign of divinity); the Pythagoreans
taught that “of rational beings, one sort is divine, one is
human, and another such as Pythagoras” (Iamblichus, VP
31); Pythagoras was seen on the same day at the same time in both
Metapontum and Croton; he killed a deadly snake by biting it; as he
was crossing a river it spoke to him (all citations are from
Aristotle, Fr. 191, unless otherwise noted). Aristotle reports that
the people of Croton called Pythagoras the “Hyperborean Apollo” and
Iamblichus’ report (VP 140) that a priest from the land of
the Hyperboreans, Abaris, visited Pythagoras and presented him with
his arrow, a token of power, may well also go back to Aristotle
(Burkert 1972a, 143). Kingsley argues that the visit of Abaris is the
key to understanding the identity and significance of
Pythagoras. Abaris was a shaman from Mongolia (part of what the Greeks
called Hyperborea), who recognized Pythagoras as an incarnation of
Apollo. The stillness of ecstacy practiced by Abaris and handed on to
Pythagoras is the foundation of all civilization. Abaris’ visit to
Pythagoras thus beomces the central moment when civilizing power is
passed from East to West (Kingsley 2010).

Whether or not one accepts this account of Pythagoras and his relation
to Abaris, there is a clear parallel for some of the remarkable
abilities of Pythagoras in the later figure of Empedocles, who
promises to teach his pupils to control the winds and bring the dead
back to life (Fr. 111). There are recognizable traces of this
tradition about Pythagoras even in the pre-Aristotelian evidence, and
his wonder-working clearly evoked diametrically opposed reactions.
Heraclitus’ description of Pythagoras as “the chief of the
charlatans” (Fr. 81) and of his wisdom as “fraudulent
art” (Fr. 129) is most easily understood as an unsympathetic
reference to his miracles. Empedocles, on the other hand, is clearly
sympathetic to Pythagoras, when he describes him as “ a man who
knew remarkable things” and who “possessed the greatest
wealth of intelligence” and again probably makes reference to
his wonder-working by calling him “accomplished in all sorts of
wise deeds”(Fr. 129). In Herodotus’ report, Zalmoxis,
whom some of the Greeks identified as the slave and pupil of
Pythagoras, tried to gain authority for his teachings about the fate
of the soul by claiming to have journeyed to the next world
(IV. 95). The skeptical tradition represented in Herodotus’ report
treats this as a ruse on Zalmoxis’ part; he had not journeyed to the
next world but had in reality hidden in an underground dwelling for
three years. Similarly Pythagoras may have claimed authority for his
teachings concerning the fate of our soul on the basis of his
remarkable abilities and experiences, and there is some evidence that
he too claimed to have journeyed to the underworld and that this
journey may have been transferred from Pythagoras to Zalmoxis (Burkert
1972a,154 ff.).

4.3 The Pythagorean Way of Life

The testimony of both Plato (R. 600a) and Isocrates
(Busiris 28) shows that Pythagoras was above all famous for
having left behind him a way of life, which still had adherents in the
fourth century over 100 years after his death. It is plausible to
assume that many features of this way of life were designed to insure
the best possible future reincarnations, but it is important to
remember that nothing in the early evidence connects the way of life
to reincarnation in any specific fashion.

One of the clearest strands in the early evidence for Pythagoras is
his expertise in religious ritual. Isocrates emphasizes that “he
more conspicuously than others paid attention to sacrifices and
rituals in temples” (Busiris 28). Herodotus gives an
example: the Pythagoreans agree with the Egyptians in not allowing the
dead to be buried in wool (II. 81). It is not surprising that
Pythagoras, as an expert on the fate of the soul after death. should
also be an expert on the religious rituals surrounding death. A
significant part of the Pythagorean way of life thus consisted in the
proper observance of religious ritual. One major piece of evidence for
this emphasis on ritual is the symbola or acusmata
(“things heard”), short maxims that were handed down
orally. The earliest source to quote acusmata is Aristotle,
in the fragments of his now lost treatise on the Pythagoreans. It is
not always possible to be certain which of the acusmata
quoted in the later tradition go back to Aristotle and which of the
ones that do go back to Pythagoras. Most of Iamblichus’ examples in
sections 82–86 of On the Pythagorean Life, however,
appear to derive from Aristotle (Burkert 1972a, 166 ff.), and many are
in accord with the early evidence we have for Pythagoras’ interest in
ritual. Thus the
acusmata advise Pythagoreans to pour libations to the gods
from the ear (i.e., the handle) of the cup, to refrain from wearing
the images of the gods on their fingers, not to sacrifice a white
cock, and to sacrifice and enter the temple barefoot. A number of
these practices can be paralleled in Greek mystery religions of the
day (Burkert 1972a, 177). Indeed, it is important to emphasize that
Pythagoreanism was not a religion and there were no specific
Pythagorean rites (Burkert 1985, 302). Pythagoras rather taught a way
of life that emphasized certain aspects of traditional Greek
religion.

A second characteristic of the Pythagorean way of life was the
emphasis on dietary restrictions. There is no direct evidence for
these restrictions in the pre-Aristotelian evidence, but both
Aristotle and Aristoxenus discuss them extensively. Unfortunately the
evidence is contradictory and it is difficult to establish any points
with certainty. One might assume that Pythagoras advocated
vegetarianism on the basis of his belief in metempsychosis, as did
Empedocles after him (Fr. 137). Indeed, the fourth-century
mathematician and philosopher Eudoxus says that “he not only
abstained from animal food but would also not come near butchers and
hunters” (Porphyry, VP 7). According to Dicaearchus,
one of Pythagoras’ most well-known doctrines was that “all
animate beings are of the same family” (Porphyry, VP
19), which suggests that we should be as hesitant about eating other
animals as other humans. Unfortunately, Aristotle reports that
“the Pythagoreans refrain from eating the womb and the heart,
the sea anemone and some other such things but use all other animal
food” (Aulus Gellius IV. 11. 11–12). This makes it sound
as if Pythagoras forbade the eating of just certain parts of animals
and certain species of animals rather than all animals; such specific
prohibitions are easy to parallel elsewhere in Greek ritual (Burkert
1972a, 177). Aristoxenus asserts that Pythagoras only refused to eat
plough oxen and rams (Diogenes Laertius VIII. 20) and that he was fond
of young kids and suckling pigs as food (Aulus Gellius
IV. 11. 6). Some have tried to argue that Aristoxenus is refashioning
Pythagoreanism in order to make it more rational (e.g., Kahn 2001, 70;
Zhmud 2012b, 228), but Aristoxenus, in fact, recognizes the
non-rational dimension of Pythagoreanism and Pythagoras’ eating of
kids and suckling pigs may itself have religious motivations (Huffman
2012b). Moreover, even if Aristoxenus’ evidence were set aside
Aristotle’s testimony and many of the
acusmata indicate that Pythagoras ate some meat. Certainly
animal sacrifice was the central act of Greek religious worship and to
abolish it completely would be a radical step. De acusma
reported by Aristotle, in response to the question “what is most
just?” has Pythagoras answer “to sacrifice”
(Iamblichus, VP 82). Based on the direct evidence for
Pythagoras’ practice in Aristotle and Aristoxenus, it seems most
prudent to conclude that he did not forbid the eating of all animal
food. The later tradition proposes a number of ways to reconcile
metempsychosis with the eating of some meat. Pythagoras may have
adopted one of these positions, but no certainty is possible. For
example, he may have argued that it was legitimate to kill and eat
sacrificial animals, on the grounds that the souls of men do not enter
into these animals (Iamblichus, VP 85). Perhaps the most
famous of the Pythagorean dietary restrictions is the prohibition on
eating beans, which is first attested by Aristotle and assigned to
Pythagoras himself (Diogenes Laertius VIII. 34). Aristotle suggests a
number of explanations including one that connects beans with Hades,
hence suggesting a possible connection with the doctrine of
metempsychosis. A number of later sources suggest that it was believed
that souls returned to earth to be reincarnated through beans (Burkert
1972a, 183). There is also a physiological explanation. Beans, which
are difficult to digest, disturb our abilities to concentrate.
Moreover, the beans involved are a European vetch (Vicia
faba
) rather than the beans commonly eaten today. Certain people
with an inherited blood abnormality develop a serious disorder called
favism, if they eat these beans or even inhale their
pollen. Aristoxenus interestingly denies that Pythagoras forbade the
eating of beans and says that “he valued it most of all
vegetables, since it was digestible and laxative” (Aulus Gellius
IV. 11.5). The discrepancies between the various fourth-century
accounts of the Pythagorean way of life suggest that there were
disputes among fourth-century Pythagoreans as to the proper way of
life and as to the teachings of Pythagoras himself.

De acusmata indicate that the Pythagorean way of life
embodied a strict regimen not just regarding religious ritual and diet
but also in almost every aspect of life. Some of the restrictions
appear to be largely arbitrary taboos, e.g., “one must put the
right shoe on first” or “one must not travel the public
roads” (Iamblichus, VP 83, probably from Aristotle). On
the other hand, some aspects of the Pythagorean life involved a moral
discipline that was greatly admired, even by outsiders. Pythagorean
silence is an important example. Isocrates reports that even in the
fourth century people “marvel more at the silence of those who
profess to be his pupils than at those who have the greatest
reputation for speaking” (Busiris 28). The ability to
remain silent was seen as important training in self-control, and the
later tradition reports that those who wanted to become Pythagoreans
had to observe a five-year silence (Iamblichus, VP
72). Isocrates is contrasting the marvelous self-control of
Pythagorean silence with the emphasis on public speaking in
traditional Greek education. Pythagoreans also displayed great
loyalty to their friends as can be seen in Aristoxenus’ story of Damon
who is willing to stand surety for his friend Phintias, who has been
sentenced to death (Iamblichus, VP 233 ff.). In addition to
silence as a moral discipline, there is evidence that secrecy was kept
about certain of the teachings of Pythagoras. Aristoxenus reports that
the Pythagoreans thought that “not all things were to be spoken
to all people” (Diogenes Laertius, VIII. 15), but this may only
apply to teaching and mean that children should not be taught all
things (Zhmud 2012a, 155). Clearer evidence is found in Dicaearchus’
complaint that it is not easy to say what Pythagoras taught his pupils
because they observed no ordinary silence about it
(Porphyry, VP 19). Indeed, one would expect that an exclusive
society such as that of the Pythagoreans would have secret doctrines
and symbols. Aristotle says that the Pythagoreans “guarded among
their very secret doctrines that one type of rational being is divine,
one human, and one such as Pythagoras” (Iamblichus, VP
31). That there should be secret teachings about the special nature
and authority of the master is not surprising. This does not mean,
however, that all Pythagorean philosophy was secret. Aristotle
discusses the fifth-century metaphysical system of Philolaus in some
detail with no hint that there was anything secret about it, and
Plato’s discussion of Pythagorean harmonic theory in Book VII of the
Republic gives no suggestion of any secrecy. Aristotle
singles out the acusma quoted above (Iamblichus, VP
31) as secret, but this statement in itself implies that others were
not. The idea that all of Pythagoras’ teachings were secret was used
in the later tradition to explain the lack of Pythagorean writings and
to try to validate forged documents as recently discovered secret
treatises. For a sceptical evaluation of Pythagorean secrecy see Zhmud
2012a, 150–158.

There is some controversy as to whether Pythagoras, in fact, taught a
way of life governed in great detail by the acusmata as
described above. Plato praises the Pythagorean way of life in
the Republic (600b), but it is hard to imagine him admiring
the set of taboos found in the acusmata (Lloyd 2014, 44;
Zhmud 2012a). Although acusmata were collected already by
Anaximander of Miletus the younger (ca. 400 BCE) and by Aristotle in
the fourth century, Zhmud (2012a, 177–178 and 192–205) argues that
very few of these embody specifically Pythagorean ideas and that it is
difficult to imagine anyone following this bewildering set of rules
literally as Burkert argues (1972a, 191). However, the early evidence
suggests that Pythagoras largely constructed the acusmata out
of ideas collected from others (Thom 2013; Huffman 2008b: Gemelli
Marciano 2002), so it is no surprise that many of them are not
uniquely Pythagorean. Moreover, Thom suggests a middle ground between
Zhmud and Burkert whereby, contra Zhmud, most of the acusmata
were followed by the Pythagoreans but contra Burkert, they were
subject to interpretation from the beginning and not followed
literally, so that it is possible to imagine people living according
to them (Thom, 2013). It is true that there is little if any fifth-
and fourth-century evidence for Pythagoreans living according to
the acusmata and Zhmud argues that the undeniable political
impact of the Pythagoreans would be inexplicable if they lived the
heavily ritualized life of the acusmata, which would
inevitably isolate them from society (Zhmud 2012a, 175–183). He
suggests that the Pythagorean way of life differed little from
standard aristocratic morality (Zhmud 2012a, 175). If, however, the
Pythagorean way of life was little out of the ordinary, why do Plato
and Isocrates specifically comment on how distinctive those who
followed it were? The silence of fifth-century sources about people
practicing acusmata is not terribly surprising given the very
meager sources for the Greek cities in southern Italy in the
period. Why not suppose that the vast majority of names in
Aristoxenus’ catalogue of Pythagoreans, who are not associated with
any political, philosophical or scientific accomplishment, who are
just names to us, are preceisely those who were Pythagoreans because
they followed the Pythagorean way of life? We would then have lots of
people who followed the acusmata (166 of the 222 name in the
catalogue appear nowhere else). This suspicion is confirmed by the
fact that one of the names from Arsitoxenus’ catalogue (Hippomedon of
Argos) is elsewhere (Iamblichus, On the Pythagorean Life, 87)
explicitly said to belong the acusmatici. Moreover, other
scholars argue that archaic Greek society in southern Italy was
pervaded by religion and the presence of similar precepts in authors
such as Hesiod show that adherence to taboos such as are found in
the acusmata would not have caused a scandal and adherence to
many of them would have gone unobserved by outsiders (Gemelli Marciano
2014, 133–134).

Once again a problem of source criticism raises its head. Zhmud argues
that the split between acusmatici who blindly followed
the acusmata and the mathematici who learned the
reasons for them (see the fifth paragraph of section 5 below) is a
creation of the later tradition, appearing first in Clement of
Alexandria and disappearing after Iamblichus (Zhmud 2012a,
169–192). He also notes that the term acusmata appears first
in Iamblichus (On the Pythagorean Life 82–86) and suggests
that it is also a creation of the later tradition. The Pythagorean
maxims did exist earlier, as the testimony of Aristotle shows, but
they were known as symbola, were originally very few in
number and were mainly a literary phenomena rather than being tied to
people who actually practiced them (Zhmud 2012a, 192–205). However,
several scholars have argued that the passages in which the split
between the acusmatici og mathematici is described
as well as the passage in which the term acusmata is used, in
fact, go back to Aristotle (Burkert 1972a, 196; see Burkert 1998, 315
where he comments that the Aristotelian provenance of the text is “as
obvious as it is unprovable”) and even Zhmud recognizes that a large
part of the material in Iamblichus is derived from Aristotle (2012a,
170). Indeed, the description of the split in what is likely to be the
original version (Iamblichus, On General Mathematical Science
76.16–77.18 Festa) uses language in describing the Pythagoreans that
is almost an Aristotelian signature, “There are two forms of the
Italian philosophy which is called Pythagorean”
(76.16). Aristotle famously describes the Pythagoreans as “those
called Pythagoreans” and also describes them as “the
Italians” (e.g., Mete. 342b30, Cael.
293a20). So the question of whether Pythagoras taught a way of life
tightly governed by the acusmata turns again on whether key
passages in Iamblichus (On the Pythagorean Life 81–87, On
General Mathematical Science
76.16–77.18 Festa) go back to
Aristotle. If they do, we have very good reason to believe that
Pythagoras taught such a life, if they do not the issue is less
clear.

The testimony of fourth-century authors such as Aristoxenus and
Dicaearchus indicates that the Pythagoreans also had an important
impact on the politics and society of the Greek cities in southern
Italy. Dicaearchus reports that, upon his arrival in Croton,
Pythagoras gave a speech to the elders and that the leaders of the
city then asked him to speak to the young men of the town, the boys
and the women (Porphyry, VP 18). Women, indeed, may have
played an unusually large role in Pythagoreanism (see Rowett 2014,
122–123), since both Timaeus and Dicaearchus report on the fame of
Pythagorean women including Pythagoras’ daughter
(Porphyry, VP 4 and 19). De
acusmata teach men to honor their wives and to beget children
in order to insure worship for the gods (Iamblichus, VP
84–6). Dicaearchus reports that the teaching of Pythagoras was
largely unknown, so that Dicaearchus cannot have known of the content
of the speech to the women or of any of the other speeches; the
speeches presented in Iamblichus (VP 37–57) are thus
likely to be later forgeries (Burkert 1972a, 115), but there is early
evidence that he gave different speeches to different groups
(Antisthenes V A 187). The attacks on the Pythagoreans both in
Pythagoras’ own day and in the middle of the fifth century are
presented by Dicaearchus and Aristoxenus as having a wide-reaching
impact on Greek society in southern Italy; the historian Polybius
(II. 39) reports that the deaths of the Pythagoreans meant that
“the leading citizens of each city were destroyed,” which
clearly indicates that many Pythagoreans had positions of political
authority. On the other hand, it is noteworthy that Plato explicitly
presents Pythagoras as a private rather than a public figure
(R. 600a). It seems most likely that the Pythagorean
societies were in essence private associations but that they also
could function as political clubs (see Zhmud 2012a, 141–148), while
not being a political party in the modern sense; their political
impact should perhaps be better compared to modern fraternal
organizations such as the Masons. Thus, the Pythagoreans did not rule
as a group but had political impact through individual members who
gained positions of authority in the Greek city-states in southern
Italy. See further Burkert 1972a, 115 ff., von Fritz 1940, Minar 1942
and Rowett 2014.

In the modern world Pythagoras is most of all famous as a
mathematician, because of the theorem named after him, and secondarily
as a cosmologist, because of the striking view of a universe ascribed
to him in the later tradition, in which the heavenly bodies produce
“the music of the spheres” by their movements. It should
be clear from the discussion above that, while the early evidence
shows that Pythagoras was indeed one of the most famous early Greek
thinkers, there is no indication in that evidence that his fame was
primarily based on mathematics or cosmology. Neither Plato nor
Aristotle treats Pythagoras as having contributed to the development
of Presocratic cosmology, although Aristotle in particular discusses
the topic in some detail in the first book of the Metaphysics
and elsewhere. Aristotle evidently knows of no cosmology of Pythagoras
that antedates the cosmological system of the “so-called
Pythagoreans,” which he dates to the middle of the fifth
century, and which is found in the fragments of Philolaus. There is
also no mention of Pythagoras’ work in geometry or of the Pythagorean
theorem in the early evidence. Dicaearchus comments that “what
he said to his associates no one can say reliably,” but then
identifies four doctrines that became well known: 1) that the soul is
immortal; 2) that it transmigrates into other kinds of animals; 3)
that after certain intervals the things that have happened once happen
again, so that nothing is completely new; 4) that all animate beings
belong to the same family (Porphyry, VP 19). Thus, for
Dicaearchus too, it is not as a mathematician or Presocratic writer on
nature that Pythagoras is famous. It might not be too surprising that
Plato, Aristotle and Dicaearchus do not mention Pythagoras’ work in
mathematics, because they are not primarily dealing with the history
of mathematics. On the other hand, Aristotle’s pupil Eudemus did write
a history of geometry in the fourth century and what we find in
Eudemus is very significant. A substantial part of Eudemus’ overview
of the early history of Greek geometry is preserved in the prologue to
Proclus’ commentary on Book One of Euclid’s Elements (p. 65,
12 ff.), which was written much later, in the fifth century CE. At
first sight, it appears that Eudemus did assign Pythagoras a
significant place in the history of geometry. Eudemus is reported as
beginning with Thales and an obscure figure named Mamercus, but the
third person mentioned by Proclus in this report is Pythagoras,
immediately before Anaxagoras. There is no mention of the Pythagorean
theorem, but Pythagoras is said to have transformed the philosophy of
geometry into a form of liberal education, to have investigated its
theorems in an immaterial and intellectual way and specifically to
have discovered the study of irrational magnitudes and the
construction of the five regular solids. Unfortunately close
examination of the section on Pythagoras in Proclus’ prologue reveals
numerous difficulties and shows that it comes not from Eudemus but
from Iamblichus with some additions by Proclus himself (Burkert 1972a,
409 ff.). The first clause is taken word for word from Iamblichus’
On Common Mathematical Science (p. 70.1 Festa). Proclus
elsewhere quotes long passages from Iamblichus and is doing the same
here. As Burkert points out, however, as soon as we recognize that
Proclus has inserted a passage from Iamblichus into Eudemus’ history,
we must also recognize that Proclus was driven to do so by the lack of
any mention of Pythagoras in Eudemus. Even those who want to assign
Pythagoras a larger role in early Greek mathematics recognize that
most of what Proclus says here cannot go back to Eudemus (Zhmud 2012a,
263–266). Thus, not only is Pythagoras not commonly known as a
geometer in the time of Plato and Aristotle, but also the most
authoritative history of early Greek geometry assigns him no role in
the history of geometry in the overview preserved in
Proclus. According to Proclus, Eudemus did report that two
propositions, which are later found in Euclid’s Elements,
were discoveries of the Pythagoreans (Proclus 379 and 419). Eudemus
does not assign the discoveries to any specific Pythagorean, and they
are hard to date. The discoveries might be as early as Hippasus in the
middle of the fifth century, who is associated with a group of
Pythagoreans known as the
mathematici, who arose after Pythagoras’ death (see
below). The crucial point to note is that Eudemus does not assign
these discoveries to Pythagoras himself. The first Pythagorean whom we
can confidently identify as an accomplished mathematician is Archytas
in the late fifth and the first half of the fourth century.

Are we to conclude, then, that Pythagoras had nothing to do with
mathematics or cosmology? The evidence is not quite that simple. De
tradition regarding Pythagoras’ connection to the Pythagorean theorem
reveals the complexity of the problem. None of the early sources,
including Plato, Aristotle and their pupils shows any knowledge of
Pythagoras’ connection to the theorem. Almost a thousand years later,
in the fifth century CE, Proclus, in his commentary on Euclid’s proof
of the theorem (Elements I. 47), gives the following report:
“If we listen to those who wish to investigate ancient history,
it is possible to find them referring this theorem back to Pythagoras
and saying that he sacrificed an ox upon its discovery”
(426.6). Proclus gives no indication of his source, but a number of
other late reports (Diogenes Laertius VIII. 12; Athenaeus 418f;
Plutarch, Moralia 1094b) show that it ultimately relied on
two lines of verse whose context is unknown: “When Pythagoras
found that famous diagram, in honor of which he offered a glorious
sacrifice of oxen…” The author of these verses is variously
identified as Apollodorus the calculator or Apollodorus the
arithmetician. This Apollodorus probably dates before Cicero, who
alludes to the story (On the Nature of the Gods III. 88),
and, if he can be identified with Apollodorus of Cyzicus, the follower
of Democritus, the story would go back to the fourth century BCE
(Burkert 1972a, 428). Two lines of poetry of indeterminate date are
obviously a very slender support upon which to base Pythagoras’
reputation as a geometer, but they cannot be simply ignored. Several
things need to be noted about this tradition, however, in order to
understand its true significance. First, Proclus does not ascribe a
proof of the theorem to Pythagoras but rather goes on to contrast
Pythagoras as one of those “knowing the truth of the
theorem” with Euclid who not only gave the proof found in
Elements I.47 but also a more general proof in
VI. 31. Although a number of modern scholars have speculated on what
sort of proof Pythagoras might have used (e.g., Heath 1956, 352 ff.),
it is important to note that there is not a jot of evidence for a
proof by Pythagoras; what we know of the history of Greek geometry
makes such a proof by Pythagoras improbable, since the first work on
the elements of geometry, upon which a rigorous proof would be based,
is not attested until Hippocrates of Chios, who was active after
Pythagoras in the latter part of the fifth century (Proclus, A
Commentary on the First Book of Euclid’s Elements
, 66). All that
this tradition ascribes to Pythagoras, then, is discovery of the truth
contained in the theorem. The truth may not have been in general form
but rather focused on the simplest such triangle (with sides 3, 4 and
5), pointing out that such a triangle and all others like it will have
a right angle. Modern scholarship has shown, moreover, that long
before Pythagoras the Babylonians were aware of the basic Pythagorean
rule and could generate Pythagorean triples (integers that satisfy the
Pythagorean rule such as 3, 4 and 5), although they never formulated
the theorem in explicit form or proved it (Høyrup 1999, 401–2, 405;
cf. Robson 2001). Thus, it is likely that Pythagoras and other Greeks
first encountered the truth of the theorem as a Babylonian
arithmetical technique (Høyrup 1999, 402; Burkert 1972a,429). It is
possible, then, that Pythagoras just passed on to the Greeks a truth
that he learned from the East. The emphasis in the two lines of verse
is not just on Pythagoras’ discovery of the truth of the theorem, it
is as much or more on his sacrifice of oxen in honor of the
discovery. We are probably supposed to imagine that the sacrifice was
not of a single ox; Apollodorus describes it as “a famous
sacrifice of oxen” and Diogenes Laertius paraphrases this as a
hecatomb, which need not be, as it literally says, a hundred
oxen, but still suggests a large number. Some have wanted to doubt the
whole story, including the discovery of the theorem, because it
conflicts with Pythagoras’ supposed vegetarianism, but it is far from
clear to what extent he was a vegetarian (see above). If the story is
to have any force and if it dates to the fourth century, it shows that
Pythagoras was famous for a connection to a certain piece of
geometrical knowledge, but it also shows that he was famous for his
enthusiastic response to that knowledge, as evidenced in his sacrifice
of oxen, not for any geometric proof. What emerges from this evidence,
then, is not Pythagoras as the master geometer, who provides rigorous
proofs, but rather Pythagoras as someone who recognizes and celebrates
certain geometrical relationships as of high importance.

It is striking that a very similar picture of Pythagoras emerges from
the evidence for his cosmology. A famous discovery is attributed to
Pythagoras in the later tradition, i.e., that the central musical
concords (the octave, fifth and fourth) correspond to the whole number
ratios 2 : 1, 3 : 2 and 4 : 3 respectively (e.g., Nicomachus,
Handbook 6 = Iamblichus, On the Pythagorean Life
115). The only early source to associate Pythagoras with the whole
number ratios that govern the concords is Xenocrates (Fr. 9) in the
early Academy, but the early Academy is precisely one source of the
later exaggerated tradition about Pythagoras (see above). One story
has it that Pythagoras passed by a blacksmith’s shop and heard the
concords in the sounds of the hammers striking the anvil and then
discovered that the sounds made by hammers whose weights are in the
ratio 2 : 1 will be an octave apart, etc. Unfortunately, the stories
of Pythagoras’ discovery of these relationships are clearly false,
since none of the techniques for the discovery ascribed to him would,
in fact, work (e.g., the pitch of sounds produced by hammers is not
directly proportional to their weight: see Burkert 1972a, 375). An
experiment ascribed to Hippasus, who was active in the first half of
the fifth century, after Pythagoras’ death, would have worked, and
thus we can trace the scientific verification of the discovery at
least to Hippasus; knowledge of the relation between whole number
ratios and the concords is clearly found in the fragments of Philolaus
(Fr. 6a, Huffman), in the second half of the fifth century. There is
some evidence that the truth of the relationship was already known to
Pythagoras’ contemporary, Lasus, who was not a Pythagorean (Burkert
1972a, 377). It may be once again that Pythagoras knew of the
relationship without either having discovered it or having
demonstrated it scientifically. The relationship was probably first
discovered by instrument makers, and specifically makers of wind
instruments rather than stringed instruments (Barker 2014,
202). De acusmata reported by Aristotle, which may go back
to Pythagoras, report the following question and answer “What is
the oracle at Delphi? De tetraktys, which is the harmony in
which the Sirens sing” (Iamblichus, On the Pythagorean
Life
, 82, probably derived from Aristotle). De
tetraktys, literally “the four,” refers to the
first four numbers, which when added together equal the number ten,
which was regarded as the perfect number in fifth-century
Pythagoreanism. Here in the acusmata, these four numbers are
identified with one of the primary sources of wisdom in the Greek
world, the Delphic oracle. In the later tradition the
tetraktys is treated as the summary of all Pythagorean
wisdom, since the Pythagoreans swore oaths by Pythagoras as “the
one who handed down the tetraktys to our generation.”
De tetraktys can be connected to the music which the Sirens
sing in that all of the ratios that correspond to the basic concords
in music (octave, fifth and fourth) can be expressed as whole number
ratios of the first four numbers. Dette acusma thus seems to
be based on the knowledge of the relationship between the concords and
the whole number ratios. The picture of Pythagoras that emerges from
the evidence is thus not of a mathematician, who offered rigorous
proofs, or of a scientist, who carried out experiments to discover the
nature of the natural world, but rather of someone who sees special
significance in and assigns special prominence to mathematical
relationships that were in general circulation. This is the context in
which to understand Aristoxenus’ remark that “Pythagoras most of
all seems to have honored and advanced the study concerned with
numbers, having taken it away from the use of merchants and likening
all things to numbers” (Fr. 23, Wehrli). Some might suppose that
this is a reference to a rigorous treatment of arithmetic, such as
that hypothesized by Becker (1936), who argued that Euclid
IX. 21–34 was a self-contained unit that represented a deductive
theory of odd and even numbers developed by the Pythagoreans (see
Mueller 1997, 296 ff. and Burkert 1972a, 434 ff.). It is crucial to
recognize, however, that Becker’s reconstruction is rejected in some
recent scholarship (e.g., Netz 2014, 179) and no ancient source
assigns it even to the Pythagoreans, let alone to Pythagoras
himself. There is, moreover, no talk of mathematical proof or a
deductive system in the passage from Aristoxenus just quoted.
Pythagoras is known for the honor he gives to number and for
removing it from the practical realm of trade and instead pointing to
correspondences between the behavior of number and the behavior of
things. Such correspondences were highlighted in Aristotle’s book on
the Pythagoreans, e.g., the female is likened to the number two and
the male to the number three and their sum, five, is likened to
marriage (Aristotle, Fr. 203).

What then was the nature of Pythagoras’ cosmos? The doxographical
tradition reports that Pythagoras discovered the sphericity of the
earth, the five celestial zones and the identity of the evening and
morning star (Diogenes Laertius VIII. 48, Aetius III.14.1, Diogenes
Laertius IX. 23). In each case, however, Burkert has shown that these
reports seem to be false and the result of the glorification of
Pythagoras in the later tradition, since the earliest and most
reliable evidence assigns these same discoveries to someone else
(1972a, 303 ff.). Thus, Theophrastus, who is the primary basis of the
doxographical tradition, says that it was Parmenides who discovered
the sphericity of the earth (Diogenes Laertius VIII. 48). Parmenides
is also identified as the discoverer of the identity of the morning
and evening star (Diogenes Laertius IX. 23), and Pythagoras’ claim
appears to be based on a poem forged in his name, which was rejected
already by Callimachus in the third century BCE (Burkert 1972a, 307).
The identification of the five celestial zones depends on the
discovery of the obliquity of the ecliptic, and some of the doxography
duly assigns this discovery to Pythagoras as well and claims that
Oenopides stole it from Pythagoras (Aetius II.12.2); the history of
astronomy by Aristotle’s pupil Eudemus, our most reliable source,
seems to attribute the discovery to Oenopides (there are problems with
the text), however (Eudemus, Fr. 145 Wehrli). It thus appears that the
later tradition, finding no evidence for Pythagoras’ cosmology in the
early evidence, assigned the discoveries of Parmenides back to
Pythagoras, encouraged by traditions which made Parmenides the pupil
of Pythagoras. In the end, there is no evidence for Pythagoras’
cosmology in the early evidence, beyond what can be reconstructed
from acusmata. As was shown above, Pythagoras saw the cosmos
as structured according to number insofar as the tetraktys is
the source of all wisdom. His cosmos was also imbued with a moral
significance, which is in accordance with his beliefs about
reincarnation and the fate of the soul (West 1971, 215–216; Huffman
2013, 60–68). Thus, in answer to the question “What are the
Isles of the Blest?” (where we might hope to go, if we lived a
good life), the answer is “the sun and the moon.” Again
“the planets are the hounds of Persephone,” i.e., the
planets are agents of vengeance for wrong done (Aristotle in
Porphyry VP 41). Aristotle similarly reports that for the
Pythagoreans thunder “is a threat to those in Tartarus, so that
they will be afraid” (Posterior Analytics 94b) and
another acusma says that “an earthquake is nothing
other than a meeting of the dead” (Aelian, Historical
Miscellany
, IV. 17). Zhmud calls these
cosmological acusmata into question (2012a, 329–330), noting
that some only appear in Porphyry, but Porphyry explicitly identifies
Aristotle as his source and we have no reason to doubt him
(VP 41). Pythagoras’ cosmos embodied mathematical
relationships that had a basis in fact and combined them with moral
ideas tied to the fate of the soul. The best analogy for the type of
account of the cosmos which Pythagoras gave might be some of the myths
which appear at the end of Platonic dialogues such as
the Phaedo,
Gorgias or Republic, where cosmology has a primarily
moral purpose. Should the doctrine of the harmony of the spheres be
assigned to Pythagoras? Certainly the acusma which talks of
the sirens singing in the harmony represented by the
tetraktys suggests that there might have been a cosmic music
and that Pythagoras may well have thought that the heavenly bodies,
which we see move across the sky at night, made music by their
motions. On the other hand, there is no evidence for “the
spheres,” if we mean by that a cosmic model according to which
each of the heavenly bodies is associated with a series of concentric
circular orbits, a model which is at least in part designed to explain
celestical phenomena. The first such cosmic model in the Pythagorean
tradition is that of Philolaus in the second half of the fifth
century, a model which still shows traces of the connection to the
moral cosmos of Pythagoras in its account of the counter-earth and the
central fire (see Philolaus).

If Pythagoras was primarily a figure of religious and ethical
significance, who left behind an influential way of life and for whom
number and cosmology primarily had significance in this religious and
moral context, how are we to explain the prominence of rigorous
mathematics and mathematical cosmology in later Pythagoreans such as
Philolaus and Archytas? It is important to note that this is not just
a question asked by modern scholars but was already a central question
in the fourth century BCE. What is the connection between Pythagoras
and fifth-century Pythagoreans? The question is implicit in
Aristotle’s description of the fifth-century Pythagoreans such as
Philolaus as “the so-called Pythagoreans.” This expression
is most easily understood as expressing Aristotle’s recognition that
these people were called Pythagoreans and at the same time his
puzzlement as to what connection there could be between the
wonder-worker who promulgated the acusmata, which his
researches show Pythagoras to have been, and the philosophy of
limiters and unlimiteds put forth in fifth-century Pythagoreanism. De
tradition of a split between two groups of Pythagoreans in the fifth
century, the mathematici and the acusmatici, points
to the same puzzlement. The evidence for this split is quite confused
in the later tradition, but Burkert (1972a, 192 ff.) has shown that
the original and most objective account of the split is found in a
passage of Aristotle’s book on the Pythagoreans, which is preserved in
Iamblichus (On Common Mathematical Science, 76.19 ff). De
acusmatici, who are clearly connected by their name to the
acusmata, are recognized by the other group, the
mathematici, as genuine Pythagoreans, but the
acusmatici do not regard the philosophy of the
mathematici as deriving from Pythagoras but rather from
Hippasus. De mathematici appear to have argued that, while
the acusmatici were indeed Pythagoreans, it was the
mathematici who were the true Pythagoreans; Pythagoras gave
the acusmata to those who did not have the time to study the
mathematical sciences, so that they would at least have moral
guidance, while to those who had the time to fully devote themselves
to Pythagoreanism he gave training in the mathematical sciences, which
explained the reasons for this guidance. This tradition thus shows
that all agreed that the acusmata represented the teaching of
Pythagoras, but that some regarded the mathematical work associated
with the mathematici as not deriving from Pythagoras himself,
but rather from Hippasus (on the controversy about the evidence for
this split into two groups of Pythagoreans see the fifth paragraph of
section 4.3 above). For fourth-century Greeks as for modern scholars,
the question is whether the mathematical and scientific side of later
Pythagoreanism derived from Pythagoras or not. If there were no
intelligible way to understand how later Pythagoreanism could have
arisen out of the Pythagoreanism of the acusmata, the puzzle
of Pythagoras’ relation to the later tradition would be insoluble. De
cosmos of the acusmata, however, clearly shows a belief in a
world structured according to mathematics, and some of the evidence
for this belief may have been drawn from genuine mathematical truths
such as those embodied in the “Pythagorean” theorem and
the relation of whole number ratios to musical concords. Even if
Pythagoras’ cosmos was of primarily moral and symbolic significance,
these strands of mathematical truth, which were woven into it, would
provide the seeds from which later Pythagoreanism grew. Philolaus’
cosmos and his metaphysical system, in which all things arise from
limiters and unlimiteds and are known through numbers, are not stolen
from Pythagoras. They embody a conception of mathematics, which owes
much to the more rigorous mathematics of Hippocrates of Chios in the
middle of the fifth century; the contrast between limiter and
unlimited makes most sense after Parmenides’ emphasis on the role of
limit in the first part of the fifth century. Philolaus’ system is
nonetheless an intelligible development of the reverence for
mathematical truth found in Pythagoras’ own cosmological scheme, which
is embodied in the acusmata.

The picture of Pythagoras presented above is inevitably based on
crucial decisions about sources and has been recently challenged in a
searching critique (Zhmud 2012a). Zhmud argues that the consensus view
of Pythagoras’ cosmos as presented above is based on the faulty
assumption that there was a progression from myth and religion to
reason and science in Pythagoreanism. In many cases, he argues, the
evidence suggests that early Pythagoreanism was more scientific and
that religious and mythic elements only gained in importance in the
later tradition. The consensus picture of Pythagoras’ cosmos assigns
number symbolism a central role and treats the tetraktys, the
first four numbers, which total to the perfect number ten, as a
central concept. Zhmud argues that the tetraktys and the
importance of the number ten do not go back to Pythagoras but flourish
in the Neopythagorean tradition, while having roots in number
speculation in the Academy associated with such figures as Plato’s
successor Speusippus. One of the central pieces of evidence for this
view is that the tetraktys does not first appear until late
in the tradition, in Aetius in the first century CE (DK
1.3.8). However, the tetraktys does appear in one of
the acusmata in a section (82) of Iamblichus’ On the
Pythagorean Life
that is commonly regarded as deriving from
Aristotle. Zhmud himself agrees that sections 82–86 of On the
Pythagorean Life
as a whole go back to Aristotle but suggests
that the acusma about the tetraktys was a post-Aristotelian
addition (2012a, 300–303). Once again source criticism is crucial. If
the acusma in question goes back to Aristotle then there is
good evidence for the tetraktys in early Pythagoreanism. If
we regard it as a later insertion into Aristotelian material, the
early Pythagorean credentials of the tetraktys are less
clear.

Zhmud supports Pythagoras’ position as genuine mathematician rather
than someone interested only in number symbolism by pointing to gaps
in the development of early Greek mathematics. Although there is no
explicit evidence, Pythagoras is the most likely candidate to fill
these gaps. Thus between Thales, whom Eudemus identifies as the first
geometer, and Hippocrates of Chios, who produced the
first Elements, someone turned geometry into a deductive
science (Zhmud 2012a, 256). Similarly, Hippasus’ experiment with
bronze disks to show that the concordant intervals of the octave,
fifth and fourth were governed by whole number ratios is too complex
to be a first attempt so that once again someone must have discovered
the ratios in a simpler way earlier (Zhmud 2012a, 291). In each case
Zhmud suggests that Pythagoras is that someone. Finally, the study of
proportion ties together airthmetic, geometry and harmonics and Zhmud
argues that, although there is no explicit fourth-century evidence,
later reports which assign Pythagoras the discovery of the first three
proportions (Iamblichus, Commentary on Nicomachus’ Introduction to
Arithmetic
100.19–101.11) are likely to go back to Eudemus
(2012a, 265–266). Such speculations have some plausibility but they
highlight even more the puzzle as to why, if Pythagoras played this
central role in early Greek mathematics, no early source explicitly
ascribes it to him. Of course, some scholars argue that the majority
have overlooked key passages that do assign mathematical achievements
to Pythagoras. In order to gain a rounded view of the Pythagorean
question it is thus appropriate to look at the most controversial of
these passages.

Some scholars who regard Pythagoras as a mathematician and rational
cosmologist, such as Guthrie, admit that the earliest evidence does
not support this view (Lloyd 2014, 25), but maintain that the
prominence of Pythagoras the mathematician in the late tradition must
be based on something early. Others maintain that there is evidence in
the sixth- and fifth-century BCE for Pythagoras as a mathematician and
cosmologist. They argue that Herodotus’ reference to Pythagoras as a
wise man (sophistês) and Heraclitus’ description of him
as pursuing inquiry (historiê), show that he was
regarded as practicing rational cosmology (Kahn 2002, 16–17;
Zhmud 2012a, 33–43). The concept of a wise man in Herodotus’
time was very broad, however, and includes poets and sages as well as
Ionian cosmologists; the same is true of the concept of
inquiry. Historiê peri physeos (inquiry concerning
nature) is later used to refer specifically to the inquiry into nature
practiced by the Presocratic cosmologists, but Herodotus’ usage shows
that at Heraclitus’ time historiê referred to inquiry
in a quite general sense and has no specific reference to the
cosmological inquiry of the Presocratics (Huffman 2008b). In one
instance in Herodotus it refers to inquiry into the stories of
Menelaus’ and Helen’s adventures in Egypt (II. 118). Heraclitus may be
thinking of Pythagoras’ inquiry into and collection of the mythical
and religious lore that is found in the acusmata (Huffman
2008b; see also Gemelli Marciano 2002, 96–103). Thus the
description of Pythagoras as a wise man who practiced inquiry is
simply too general to aid in deciding what sort of figure Herodotus
and Heraclitus saw him as being. It is certainly true that Empedocles
shows that the roles of rational cosmologist and wonder-working
religious teacher could be combined in one figure, but this
does not prove these roles were combined in Pythagoras’ case. The only
thing that could prove this in Pythagoras’ case is reliable early
evidence for a rational cosmology and that is precisely what is
lacking.

There is more controversy about the fourth-century evidence. Zhmud
argues that Isocrates regards Pythagoras as a philosopher and
mathematician (2012a, 50). However, it is hard to see how the passage
in question (Busiris 28–29) supports this view. Nowhere in it
does Isocrates ascribe mathematical work or a rational cosmology to
Pythagoras. He reports in general terms that Pythagoras brought
“ other philosophy” to Greece from Egypt but what he
emphasizes is that Pythagoras was “more clearly interested than
others in sacrificial rites and temple rituals.” It is true that
earlier, in a passage that does not mention Pythagoras
(Busiris 22–23), Isocrates had said that some of the Egyptian
priests studied mathematics but if Isocrates thought Pythagoras also
brought mathematical learning from Egypt he has chosen not to say so
explicitly. What Isocrates emphasizes about Pythagoras is what the
rest of the early tradition emphasizes, his interest in religious
rites. Fr. 191 from Aristotle’s lost work on the Pythagoreans reports
that Pythagoras “dedicated himself to the study of mathematical
sciences, especially numbers” and Fragment 20 from
Aristotle’s Proptrepticus says that Pythagoras said that
human beings were born to contemplate the heavens and described
himself as an observor of nature (Zhmud 2012a, 56 and
259–260). Unfortunately, in neither case are the words in question
likely to be Aristotle’s. Fr. 191 comes from a book on marvels by
Apollonius (2nd BCE?). The words in question come before Apollonius
mentions Aristotle and, as Burkert pointed out (1972a, 412), are
overwhelming likely to be by Apollonius himself, since they serve as
the transition sentence between Apollonius’ account of Pherecydes and
his account of Pythagoras. In the face of the huge extant corpus of
Aristotle’s works in which he never ascribes any mathematical work to
Pythagoras, a single sentence that is not ascribed directly to
Aristotle and that, in terms of function, appears to be the work of
Apollonius and not Aristotle cannot with any confidence be used as
evidence that Aristotle regarded Pythagoras as a mathematician. De
same situation arises with Fr. 20 of the Protrepticus. If the
words in question were by Aristotle they would be his sole statement
that Pythagoras was a natural philosopher. The case of Fr. 20 is even
more tenuous than that of Fr. 191. Fr. 20 comes from
Iamblichus’ Protrepticus, large parts of which are likely to
derive from Aristotle’s lost Protrepticus but, as is his
practice, Iamblichus does not make any explicit reference to
Aristotle. The further problem with Fr. 20, as Burkert noted (1960,
166–168), is that the same story is told first about Pythagoras and
then immediately afterwards about Anaxagoras: both are asked why human
beings were born and both answer “to contemplate the
heavens” (Iamblichus, Protrepticus 51.8–15). Dette
awkward repetition of the same story about two different people
immediately suggests that only one story was in the original and the
other was added in the later tradition. This suggestion is strikingly
confirmed by the fact that Aristotle does tell this story about
Anaxagoras in his extant works (Eudemian Ethics 1216a11–16)
but not about Pythagoras. Thus, if the passage in
Iamblichus’ Protrepticus is, in fact, from Aristotle, it is
very likely that only Anaxagoras appeared in Aristotle’s version and
that Pythagoras was added in the later tradition, perhaps by
Iamblichus himself. Since these two passages are unlikely to be from
Aristotle, there are no references to Pythagoras as a mathematician or
as a natural philosopher either in Aristotle’s extant works or in the
fragments of his works. Aristotle only knows Pythagoras as a wonder
working sage and teacher of a way of life (Fr. 191). Aristotle’s
attitude is similar to his predecessors in the earlier fourth century:
Plato’s sole reference to Pythagoras is as the founder of a way of
life and Isocrates emphasizes both the way of life and the interest in
religious ritual.

What about the pupils of Plato and Aristotle? As discussed in the
second paragraph of section 5 above, Eudemus, who wrote a series of
histories of mathematics never mentions Pythagoras by name. Arguments
from silence are perilous but, when the most well-informed source of
the fourth-century fails to mention Pythagoras in works explicitly
directed towards the history of mathematics, the silence means
something. There are only two passages in which Pythagoras is
explicitly associated with anything mathematical or scientific by
pupils of Plato and Aristotle. First, Aristotle’s pupil Aristoxenus
reports that Pythagoras “most of all valued the pursuit
(pragmateia) of number and brought it forward, taking it away
from the use of traders, by likening all things to numbers”
(Fr. 23). Zhmud translates pragmateia as
“science” (2012a, 216) so that he has Aristoxenus
attributing the invention of the science of number to Pythagoras but,
while Aristoxenus does use pragmateia to mean science in some
contexts, it more commonly simply means “pursuit” (Huffman
2014b, 292). Here surely it must mean “pursuit,” because
Pythagoras is presented as taking it away from the traders and we can
hardly suppose that the traders were engaged in the theoretical
science of arithmetic. Moreover, Aristoxenus explains what he means in
the final participial phrase. He is not ascribing rigorous mathematics
with proofs to Pythagoras but rather says that Pythagoras was
“likening all things to numbers”. This is consistent with
the moralized cosmos of Pythagoras sketched above in which numbers
have symbolic significance. The second important passage is Plato’s
pupil Xenocrates’ assertion that Pythagoras “discovered that the
intervals in music, too, do not arise in separation from number”
(Fr. 9). Xenocrates is being quoted here in a fragment of a work by a
Heraclides (Barker 1989, 235–236), perhaps Heraclides of Pontus. There
is controversy whether the quotation of Xenocrates is limited just to
what has been quoted in the previous sentence or whether the whole
fragment of Heraclides is a quotation of Xenocrates. Burkert (1972a,
381) and Barker (1989, 235) argue that it is probably just the first
sentence that Heraclides ascribes to Xenocrates, while Zhmud would
include at least a second sentence in which Heraclides presents
Pythagoras as pursuing a program of research into “the
conditions under which concordant and discordant intervals
arise” (Zhmud 2012a, 258). If the second sentence is accepted
then Xenocrates clearly presents Pythagoras as an acoustic
scientist. It seems most reasonable, however, to accept only the first
sentence as belonging to Xenocrates. If the quotation from Xenocrates
does not break off at that point, there is no other obvious breaking
point in the fragment and the whole two pages of text must be ascribed
to Xenocrates. The problem with ascribing it all to Xenocrates is that
Porphyry introduces the passage as a quotation from Heraclides, which
would be strange if everything quoted, in fact, belongs to
Xenocrates. If just the first sentence comes from Xenocrates, then all
he is ascribing to Pythagoras is the recognition that the concordant
intervals are connected to numbers. It is easy to assume, as Zhmud
does, that Xenocrates is saying that Pythagoras was the first
to discover that the concordant intervals are governed by whole number
ratios but Xenocrates’ remarks need not mean this. Xenocrates’
comments might well come from a context like that in the fragment of
Aristoxenus, above, i.e., a context in which Pythagoras is presented
as likening all things to numbers and arguing that numbers in some
sense explain or control things. In such a context Xenocrates would
not be making the point that Pythagoras discovered the whole number
ratios but rather that he found out that concords arose in accordance
with whole number ratios, perhaps from musicians (who discovered them
first not being the issue), and used this fact as another illustration
of how things are like numbers. Thus, the fragments of Aristoxenus and
Xeoncrates show that Pythagoras likened things to numbers and took the
concordant musical intervals as a central example, but do not suggest
that he founded arithmetic as a rigorous mathematical discipline or
carried out a program of scientific research in harmonics.

Controversy concerning Pythagoras’ role as a scientist and
mathematician will continue. Indeed, Hahn has recently endorsed many
of Zhmud’s arguments and argues that Pythagoras was a rational
cosmologist, who was further developing a project begun by Thales to
contruct the cosmos out of right triangles. Hahn admits, however, that
his thesis is “speculative” and “a circumstantial
case at best” (2017:xi). It should now be clear that decisions
about sources are crucial in addressing the question of whether
Pythagoras was a mathematician and scientist. The view of
Pythagoras’ cosmos sketched in the first five paragraphs of this
section, according to which he was neither a mathematician nor a
scientist, remains the consensus.

Les anciennes cultures néolithiques ont gravé des clichés des composants de la nature sur des boules de pierre pendant un millier d’années avant qu’elles ne soient renommées sous l’appelation de solides platoniques. Les philosophes et les mathématiciens grecs ont analysé l’idée des formes primaires. Certains attribuent leurs origines à Pythagore ( 570-495 av. J. -C. ), Empedocle ( 490-430 av. J. -C. ) ou Theaetetus ( 417-369 av. J. -C. ). Platon ( 424-347 av. J. -C. ), un étudiant de Socrate, en a beaucoup parlé dans son dialogue avec Timée. Il les a décrits comme les composants constituants de la vie représentés par les 4 éléments que sont la terre, l’eau, le feu et l’air. Aristote a identifié un cinquième élément qu’il a nommé Aether. Euclide ( 323-283 av. J. -C. ) les réunit, les nomme les Solides de Platon et leur donne des descriptions mathématiques précises dans son bouqin Elements. Ce vaste corpus de connaissances est passé pratiquement sous terre jusqu’à ce que Johannes Kepler ( 1571-1630 ), un astronome allemand, considère la sphère comme un container pour chacun des cinq robustes de Platon. Il a aussi essayé de rattacher les robustes aux six planètes connues de Mercure, Vénus, Terre, Mars, Jupiter et Saturne. En géométrie euclidienne, un solide de Platon est défini comme un polyèdre fréquent et convexe, dont les faces sont des polygones constants et congruents, avec le même nombre de faces se rencontrant à chaque plus haut qui s’inscrivent dans une sphère. Empedocle voyait l’attachement comme le pouvoir qui attire ces formes ensemble mais la lutte les sépare. Les éléments ont inspiré l’art, la méthode et la compréhension de l’élégance de notre monde. n

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