Philolaus (ca. 480 BC – ca. 385 BC, _el. Φιλόλαος) was a Greek Pythagorean and Presocratic. He argued that all matter is composed of limited and unlimited 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. He also thought that the immortal soul was imprisoned as a punishment from former lives.


As is the case with most other Presocratic thinkers, "any chronology constructed for his life is a fabric of the loosest possible weave." Huffman, Carl. "Philolaus of Croton Pythagorean and Presocratic: A Commentary on the Fragments and Testimonia With Interpretive Essays". New York: Cambridge University Press, 1993. p. 1–16.] But that should not diminish the importance of establishing such a chronology, which helps scholars see his relationship to other Pre-Socratics. A passage out of Plato's "Phaedo" reveals his influence on two of the characters within the dialogue:

cquote|"What, Cebes? Have you and Simmias not heard about such things in your association with Philolaus?"
"Nothing definite, at least, Socrates... Why ever then do they deny that it is unlawful to kill oneself Socrates? For, to answer the question that you were just now asking, I already heard from Philolaus, when he was spending time with us, and before that from some others as well, that it was not right to do this."

This passage makes clear that Philolaus had spent time in Thebes and was heard by Simmias and Cebes around the time the "Phaedo" takes place, in 399 BC. The dates of his birth and death are culled from his known association with other Pre-Socratics, as well as the date of the burning of the Pythagorean meeting-place (which he fled from), around 454 BC. Besides this chronological outline the details of Philolaus' life are unknown to us.

Diogenes Laertius reports that Philolaus and Eurytus are two of the Pythagoreans that Plato met when he traveled to Italy shortly after the death of Socrates. The pupils of Philolaus and Eurytus were:

* Xenophilus of Chalcis, Thrace
* Phanto of Phlius
* Echecrates of Phlius
* Diocles of Phlius
* Polymnastus of Phlius

Philolaus was a contemporary of Socrates and Democritus, but senior to them, and was probably somewhat junior to Empedocles, and a contemporary of Zeno of Elea, Melissus and Thucydides, so that his birth may be placed at about 480 BC.

Philolaus is variously reported as being born in either Croton, [Iamblichus, "Vita Pythagorica", 148] Tarentum, [Iamblichus, "Vita Pythagorica", 267; Diogenes Laertius, VIII 46] or Metapontum. [Iamblichus, "Vita Pythagorica", 266-67] Croton, Tarentum and Metapontum were all located in southern Italy.

He was said to have been intimate with Democritus, and was probably one of his teachers. Philolaus was the first Pythagorean to write and disseminate any philosophical treatise at all; he published a book, of which the only extant fragments are found in other philosophers and doxographers. 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 (Crito), all three of whom were subsequently present at the death of Socrates in 399 BC. Before this Philolaus had returned to Italy, where he was the teacher of Archytas (428–347 BC). Philolaus was perhaps also connected with the Pythagorean exiles at Phlius mentioned in Plato's "Phaedo".

Philolaus spoke and wrote in a Greek Doric dialect and 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 either Pythagoras or the younger Hicetas (ca. 400 – ca. 335 BC) of Syracuse.


Philolaus' ideas about the cosmology of the universe were so drastically different from any previous suppositions about the Earth's place in the cosmos that he simultaneously did away with the ideas of fixed direction in space, and developed one of the first non-geocentric views of the universe. These new ways of thinking quite literally revolved around a hypothetical astronomical object he called the Central Fire.

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, and the Counter-Earth was conceived to explain his revolutionary ideas about the lack of up or down in space to the Pythagorean community. He never recognized the fixed stars as any kind of sphere or object.Burch, George Bosworth. "The Counter-Earth". Osirus, vol. 11. Saint Catherines Press, 1954. p. 267-294 ]

His new ideas about the nature of the Earth's place in the cosmos influenced Aristarchus of Samos dramatically. Nicolaus Copernicus mentions in "De revolutionibus" that Philolaus already knew about the Earth's revolution around a central fire.

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 to publish a book on the Pythagorean doctrines, a treatise of which Plato made use in the composition of his "Timaeus". Philolaus represented the philosophical system of his school in a work "Peri physeos" ("On Nature"). Speusippus, Plato's successor at the Academy summarized Philolaus's work.

Pythagorean Number Theory

Philolaus was deeply involved in the distinctively Pythagorean number theory, dwelling particularly on the properties inherent in the decad – the sum of the first four numbers, consequently the fourth triangular number, the tetractys – 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 classical 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. This theory, however superficial from the standpoint of observation, indicates considerable knowledge of geometry and gave a motivating boost to the study of science.

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), which 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).

Following Parmenides' philosophy, 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.



* Diogenes Laertius, "Life of Pythagoras", VIII, 46.
* Iamblichus, "Vita Pythagorica", 148, 266-67.
* Plato, "Phaedo", 61d-e

External links

* [ Stanford Encyclopedia of Philosophy entry]
* [ Burch, George Bosworth. The Counter-Earth. Osirus, vol. 11. Saint Catherines Press, 1954. p. 267-294 ]

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