PITAGORA. — The historical figure of P., philosopher and founder of the school that bears his name, was so distorted by later legends that, amid the accumulation of traditions, it is difficult to distinguish the truth from the fabulous. It is certain that he, born at Samos to Mnesarchus, in the first half of the sixth century B.C. (c. 580), moved in mature age (after perhaps having sojourned in Egypt as a young man) from his island to the Italian city of Croton, and there established a philosophical-religious community that later also became a political party. P. taught only orally: Empedocles celebrates him as ἀνὴρ περιώσια εἰδώς... πάντων δὲ μάλιστα σοφῶν ἐπιήφανος ἔργων (fr. 129), while Heraclitus speaks of his πολυμαθίη (fr. 40, 129); Xenophanes of Colophon attests (fr. 7) P.’s belief in reincarnation, not without reserve. Herodotus (IV, 95) describes him as an eminent σοφιστής. Having carried out
his teaching in Croton, P. emigrated, following the political opposition of part of the Crotoniate citizenry, to Metapontum, where he died (around 500?).
The Pythagoreans formed an association characterized by strict ethical and religious discipline: they observed a practice of prolonged silence (ἐρχιωθία), abstinence at least in part from meat and, apparently, from beans, and various precepts that were partly ethical and partly ritual (the latter too being interpreted later as ethical symbols); and they customarily conducted an examination of conscience every evening. According to later testimonies, the sect supposedly comprised two classes of disciples, the exoteric and the esoteric (the former not admitted to the secrets of the doctrine, that is, simple hearers, ἀκουσματικοί; the latter initiated into wisdom, μαθηματικοί), while others distinguish three categories (ἀκουστικοί, μαθηματικοί, φυσικοί). The master’s views were accepted as indisputable truths (according to the celebrated motto αὐτὸς ἕρα). Extending from Croton to other places in Magna Graecia, the school acquired great political power and governed various cities. But a violent hostility on the part of the democratic parties soon arose against the aristocratic Pythagoreans: the first uprising broke out while P. was still alive (hence his flight from Croton); and further seditions occurred subsequently, until, at an indeterminate date (between 460 and 400), a revolution took place in which the Pythagorean order was utterly destroyed and the members, for the most part, killed. Of the survivors, some moved to Thebes (Lysis and Philolaus), others to Phlius. Some later returned from exile to Tarentum, and in that city Pythagoreanism flourished anew with Archytas, until it died out in the final years of the fourth century B.C. Among the principal ancient Pythagoreans were, besides Philolaus (who was the first to set out the doctrine in a written work), Simmias and Cebes (known through Plato), Ocellus Lucanus, Timaeus of Locri, Lysis, and Archytas (an eminent mathematician and physicist).
How much of the Pythagorean theories goes back to P. himself is difficult to determine; it may be stated with certainty reincarnation (v.), transmitted to his disciples the fundamental core of the ethical-religious precepts destined to constitute the most characteristic patrimony of Pythagoreanism, and initiated those mathematical studies from which the school later derived its greatest glory (it may be that the “theorem of P.” goes back to him personally). In any event, it is preferable to speak, rather than of P., of the Pythagoreans in general. Their metaphysical conception was closely connected with the aforementioned mathematical studies. Observing the importance of numerical relations in the universe, since nothing is knowable without number (πάντα γε μάν τὰ γεγνωσκόμενα ἀριθμὸν ἔγονται: Philolaus, fr. 4), they asserted that the principle of things is precisely number: this seems to be understood, according to the testimony of Aristotle (cf. in particular Met., I, 5, 985 b 23 ff., 986 a 15), in the sense that number is the innermost substance, the ὕλη, of things themselves; nor does the fact that the Pythagoreans at the same time regarded numbers as models of things (ibid., 987 b) conflict with this interpretation. Number has two fundamental categories, the odd (περισσόν) and the even (ἄρτιον), to which Philolaus adds the ἄρτιον-περισσόν, the even-odd, apparently equivalent to the One. The odd is limited (πεπερασμένον) and the principle of limit (πέρας); the even is unlimited (ἄπειρον) and the principle of limitlessness (ἄπειρία). The Universe is a harmony of these contrary principles, with which other antithetical pairs are then connected (cf. the Pythagorean “table” of oppositions in Aristotle, Met., I, 5, 986: πέρας-ἄπειρον; περιτ-τόν-ἄρτιον; ἐν-πλῆθος; δεξιόν-ἀριστερόν;... φῶς-σκάτος; ἀγαθόν-κακόν, etc.). Conflicts are reconciled in an accord that is a numerical accord: thus it follows that “the whole heaven is harmony and number” (cf. Aristotle, Met., I, 5). The Pythagoreans, moreover, by speculating on individual numbers, attributed particular powers and meanings to them; and they attached special importance, besides the One and the Two, respectively the principles of the odd and the even, to the Four and the Ten, perfect numbers. This, so to speak, metaphysical arithmology was nevertheless associated with positive mathematics (the discovery of the incommensurable, successive approximations to V^{-3}, the method of application of areas, etc.).
Pythagorean theology was, apparently, oriented in a monotheistic direction: that is, it admitted a supreme God above the gods; but it is doubtful that this doctrine was philosophically developed in connection with arithmology, and that God was for them identical with the One understood as the original principle (cf. Zeller-Mondolfo, I, 2 [V. BIBLICA.], pp. 457–74). The cosmology of the school, initially akin to the conceptions of the early Ionians, later developed into a system that regarded the earth as revolving, like the sun and a supposed “counter-earth,” around a central fire. Hicetas admitted the rotation of the earth around its own axis and thus explained the alternation of day and night (Cicero, Acad. prior., 2, 39, 123). Another Pythagorean theory is that of the harmony of the spheres.
In psychology, the school regarded the human soul as an eternal substance of divine origin, united with a body as a punishment and destined to transmigrate from body to body, not only into the bodies of human beings but also into those of animals or plants (πληγενεσία, not μεταφύγωσις, is probably the word used by the ancient Pythagoreans). In its union with the body, the soul is enclosed as in a tomb (Philolaus, fr. 14 D; Plato, Gorg., 493 A). The incarnations will continue until the soul itself has been purified and made worthy of returning to its heavenly homeland. How this conception itself (later taken up by Plato) was connected by the Pythagoreans with arithmology is not clear.
Pythagorean ethics, religiously inspired, prescribed for human beings the imitation of Divinity, and inculcated purity of life, measure, and harmony in all activities, as well as the cultivation of wisdom as a means of salvation.
Pythagoreanism had a great influence on Greek thought, Platonism (v.). The school, which died out in the fourth century B.C., later revived, beginning in the first century, in an eclectic form (v. NEO-PYTHAGOREANISM).