Philolāus in Harpers Dictionary of Classical Antiquities (1898)
（Φιλόλαος). A distinguished Pythagorean philosopher. He was a native of Croton or Tarentum, a contemporary of Socrates, and the instructor of Simmias and Cebes at Thebes, where he appears to have lived many years. Pythagoras and his earliest successors did not commit any of their doctrines to writing, and the first publication of the Pythagorean doctrines is pretty uniformly attributed to Philolaüs. He composed a work on the Pythagorean philosophy in three books, which Plato is said to have procured at the cost of 100 minae through Dion of Syracuse, who purchased it from Philolaüs, who was at the time in deep poverty (Gell. iii. 17). Other versions of the story represent Plato as purchasing it himself from Philolaüs or his relatives when in Sicily. Plato is said to have derived from this work the greater part of his Timaeus.
Philolaus in Wikipedia
Philolaus (Greek: Φιλόλαος; c. 470–c. 385 BCE) was a Greek Pythagorean and Presocratic philosopher. He argued that all matter is composed of limiting and limitless things, and that the universe is determined by numbers. He is credited with originating the theory that the earth was not the center of the universe.
Philolaus is variously reported as being born in either Croton, Tarentum, or Metapontum. All three places were located in southern Italy. He may have fled the second burning of the Pythagorean meeting-place around 454 BCE, after which he migrated to Greece. According to Plato's Phaedo, he was the instructor of Simmias and Cebes at Thebes, around the time the Phaedo takes place, in 399 BCE. This would make him a contemporary of Socrates, and agrees with the statement that Philolaus and Democritus were contemporaries. The various reports about his life are scattered among the writings of much later writers and are of dubious value in reconstructing his life. He apparently lived for some time at Heraclea, where he was the pupil of Aresas, or (as Plutarch calls him) Arcesus. Diogenes Laertius is the only authority for the claim that Plato, shortly after the death of Socrates, traveled to Italy where he met with Philolaus and Eurytus. The pupils of Philolaus and were said to have included Xenophilus, Phanto, Echecrates, Diocles and Polymnastus. As to his death, Diogenes Laertius reports a dubious story that Philolaus was put to death at Croton on account of being suspected of wanting to be the tyrant; a story which Laertius even took the trouble to put into verse.
Diogenes Laertius speaks of Philolaus composing one book, but elsewhere he speaks of three books, as do Aulus Gellius and Iamblichus. It may have been one treatise, divided into three books. Plato is said to have procured a copy of his book, from which, it was later claimed, Plato composed much of his Timaeus. One of the works of Philolaus was called On Nature, which seems to be the same work which Stobaeus calls On the World, and from which he has preserved a series of passages. Other writers refer to a work entitled Bacchae, which may have been another name for the same work.
Philolaus did away with the ideas of fixed direction in space, and developed one of the first non-geocentric views of the universe. His new way of thinking quite literally revolved around a hypothetical astronomical object he called the Central Fire.
Philolaus says that there is fire in the middle at the centre ... and again more fire at the highest point and surrounding everything. By nature the middle is first, and around it dance ten divine bodies - the sky, the planets, then the sun, next the moon, next the earth, next the counterearth, and after all of them the fire of the hearth which holds position at the centre. The highest part of the surrounding, where the elements are found in their purity, he calls Olympus; the regions beneath the orbit of Olympus, where are the five planets with the sun and the moon, he calls the world; the part under them, being beneath the moon and around the earth, in which are found generation and change, he calls the sky.
-Stobaeus, i. 22. 1d
A popular misconception about Philolaus is that he supposed that a sphere of the fixed stars, the five planets, the Sun, Moon and Earth, all moved round his Central Fire, but as these made up only nine revolving bodies, he conceived in accordance with his number theory a tenth, which he called Counter-Earth. This fallacy grows largely out of Aristotle's attempt to lampoon his ideas in his book, Metaphysics. In reality, Philolaus' ideas predated the idea of spheres by hundreds of years. He never recognized the fixed stars as any kind of sphere or object.
His ideas about the nature of the Earth's place in the cosmos was influential. Nicolaus Copernicus mentions in De revolutionibus that Philolaus already knew about the Earth's revolution around a central fire.
Philolaus argued that all matter is composed of limiters and unlimiteds. Limiters set boundaries, such as shape and quantity. Unlimiteds are universal forms and rules such as the four elements of earth, air, fire and water and the continua of space and time. Limiters and unlimiteds are combined together in a harmony (harmonia):
This is the state of affairs about nature and harmony. The essence of things is eternal; it is a unique and divine nature, the knowledge of which does not belong to man. Still it would not be possible that any of the things that are, and are known by us, should arrive to our knowledge, if this essence was not the internal foundation of the principles of which the world was founded, that is, of the limiting and unlimited elements. Now since these principles are not mutually similar, neither of similar nature, it would be impossible that the order of the world should have been formed by them, unless the harmony intervened . . .
-Philolaus, Frag. 6a.
This harmony can be described mathematically (similar to the combinations of elements in modern chemistry). Philolaus used the musical scale to illustrate his philosophy, whereby whole number ratios limit pleasing sounds (e.g., the octave, fifth, and fourth are defined by the ratios 2 : 1, 4 : 3 and 3 : 2). Philolaus also regarded the soul as a "mixture and harmony" of the bodily parts.