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PHILOLAUS (b. c. 480), Greek philosopher of the Pythagorean school, was born at Tarentum or at Crotona[1] (so Diog. Laert. viii. 84). He was said to have been intimate with Democritus, and was probably one of his teachers. After the death of Pythagoras great dissensions prevailed in the cities of lower Italy. According to some accounts, Philolaus, obliged to flee, took refuge first in Lucania and then at Thebes, where he had as pupils Simmias and Cebes, who subsequently, being still young men (νεανίσκοι), were present at the death of Socrates. Before this Philolaus had returned to Italy, where he was the teacher of Archytas. He entered deeply into the distinctively Pythagorean number theory, particularly dwelling on the properties inherent in the decad-the sum of the first four numbers, consequently the fourth triangular number, the tetractys (see Vit. Pythag. ap. Phot. Bibl. p. 712)-which he called great, all-powerful, and all-producing. The great Pythagorean oath was taken by the sacred tetractys. The discovery of the regular solids is attributed to Pythagoras by Eudemus, and Empedocles is stated to have been the first who maintained that there are four elements. Philolaus, connecting these ideas, held that the elementary nature of bodies depends on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to water, and the cube to earth; the dodecahedron he assigned to a fifth element, aether, or, as some think, to the universe (see Plut. de Pl. Ph. ii. 6, ἐκ δὲ τοῦ δωδεκαέδρου τὴν τοῦ παντὸς σφαῖραν and Stob. Ecl. Phys. i. 10, ὁ τᾶς σφαίρας ὁλκός). This theory, however superficial from the standpoint of observation, indicates considerable knowledge of geometry and gave a great impulse to the study of the science. Following Parmenides, Philolaus regarded the soul as a "mixture and harmony" of the bodily parts; he also assumed a substantial soul, whose existence in the body is an exile on account of sin.

Philolaus was the first to propound the doctrine of the motion of the earth; some attribute this doctrine to Pythagoras, but there is no evidence in support of their view. Philolaus supposed that the sphere of the fixed stars, the five planets, the sun, moon and earth, all moved round the central fire, which he called the hearth of the universe, the house of Zeus, and the mother of the gods (see Stob. Ecl. Phys. i. 488); but as these made up only nine revolving bodies he conceived, in accordance with his number theory, a tenth, which he called counter-earth, ἀντίχθων. He supposed the sun to be a disk of glass which reflects the light of the universe. He made the lunar month consist of 29½ days, the lunar year of 354, and the solar year of 365½ days. He was the first who published a book on the Pythagorean doctrines, a treatise of which Plato made use in the composition of his Timaeus. This work of the Pythagorean, to which the mystical name Βάκχαι is sometimes given, seems to have consisted of three books: (1) Περὶ κόσμον, containing a general account of the origin and arrangement of the universe; (2) Περὶ φύσεως, an exposition of the nature of numbers; (3) Περὶ ψυχῆς, on the nature of the soul.

See Boeckh, Philolaus des Pythagoreers Lehren nebst den Bruchstucken seines Werkes (Berlin, 1819); Schaarschmidt, Die angebliche Schriftstellerei des Philolaus (1864); also Fabricius, Bibliotheca graeca; Zeller, History of Greek Philosophy; Chaignet, Pythagore et la philosophie pythagoricienne, contenant les fragments de Philolaus et d'Architas (1873); Th. Gomperz, Greek Thinkers (Eng. trans. (1901), i. 123 sqq., 543 sqq. and authorities there quoted; also art. Pythagoras. For fragments see Ritter and Preller, Hist. Philosoph. ch. ii.

  1. Boeckh places his life between the 70th and 95th Olympiads (496-396 B.C.). He was a contemporary of Socrates and Democritus, but senior to them, and was probably somewhat junior to Empedocles, so that his birth may be placed at about 480.