Philolaus (/ˌfɪləˈleɪəs/; Ancient Greek: Φιλόλαος, Philólaos; c. 470 – c. 385 BC)[2][3] was a Greek Pythagorean and preSocratic philosopher. He argued that at the foundation of everything is the part played by the limiting and limitless, which combine together in a harmony. He is also credited with originating heliocentrism, the theory that the Earth was not the center of the Universe. According to August Böckh (1819), who cites Nicomachus, Philolaus was the successor of Pythagoras.[4]
Pythagoras "the musician" with his student Philolaus
Biography
Philolaus is variously reported as being born in either Croton,[5] or Tarentum,[6] or Metapontum[7]—all part of Magna Graecia (the name of the coastal areas of Southern Italy on the Tarentine Gulf that were extensively colonized by Greek settlers). It is most likely that he came from Croton.[8][9] He may have fled the second burning of the Pythagorean meetingplace around 454 BC,[10] 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 BC.[11] This would make him a contemporary of Socrates, and agrees with the statement that Philolaus and Democritus were contemporaries.[12]
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 (maybe Oresas), or (as Plutarch calls him) Arcesus.[13] Diogenes Laërtius 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.[14] The pupils of Philolaus were said to have included Xenophilus, Phanto, Echecrates, Diocles, and Polymnastus.[15] As to his death, Diogenes Laërtius reports a dubious story that Philolaus was put to death at Croton on account of being suspected of wanting to be the tyrant;[16] a story which Laërtius even took the trouble to put into verse.[17]
Writings
Philolaus book, (Charles Peter Mason, 1870)
Diogenes Laërtius speaks of Philolaus composing one book,[18] but elsewhere he speaks of three books,[19] as do Aulus Gellius and Iamblichus. It might 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.[20] One of the works of Philolaus was called On Nature,[18] which seems to be the same work which Stobaeus calls On the World, and from which he has preserved a series of passages.[21] Other writers refer to a work entitled Bacchae, which may have been another name for the same work, and which may originate from Arignote. However, it has been mentioned that Proclus describes the Bacchae as a book for teaching theology by means of mathematics.[8]
According to Charles Peter Mason in Sir William Smith's Dictionary of Greek and Roman Biography and Mythology (1870, p. 305):[22]
It appears, in fact, from this, as well as from the extant fragments, that the first book of the work contained a general account of the origin and arrangement of the universe. The second book appears to have been an exposition of the nature of numbers, which in the Pythagorean theory are the essence and source of all things.
Additionally Charles Peter Mason noted (p. 304):[22]
Pythagoras and his earliest successors do not appear to have committed any of their doctrines to writing. According to Porphyrius (Vit. Pyth. p. 40) Lysis and Archippus collected in a written form some of the principal Pythagorean doctrines, which were handed down as heirlooms in their families, under strict injunctions that they should not be made public. But amid the different and inconsistent accounts of the matter, the first publication of the Pythagorean doctrines is pretty uniformly attributed to Philolaus. 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 Philolaus, who was at the time in deep poverty.
Other versions of the story represent Plato as purchasing it himself from Philolaus or his relatives when in Sicily. (Diog. Laert. viii. 15, 55, 84, 85, iii. 9; A. Gellius,iV. iii. 17; lamblichus, Vit. Fyth. 31. p. 172 ; Tzetzes, Chiliad, x. 792, &c. xi. 38, &c.) Out of the materials which he derived from these books Plato is said to have composed his Timaeus. But in the age of Plato the leading features of the Pythagorean doctrines had long ceased to be a secret; and if Philolaus taught the Pythagorean doctrines at Thebes, he was hardly likely to feel much reluctance in publishing them; and amid the conflicting and improbable accounts preserved in the authorities above referred to, little more can be regarded as trustworthy, except that Philolaus was the first who published a book on the Pythagorean doctrines, and that Plato read and made use of it. (Böckh, I.e. p. 22.)
Historians from the Stanford Encyclopedia of Philosophy, Chapter Philolaus' Book: Genuine Fragments and Testimonia, noted the following:[8]
It is implied that these books were not by Philolaus himself, and it seems likely that the statement refers to three spurious works assigned to Pythagoras at D.L. VIII 6 (Burkert 1972a, 224–5). The story of Plato's purchase of these books from Philolaus was probably invented to authenticate the three forged treatises of Pythagoras. Burkert's arguments (1972a, 238–277), supported by further study (Huffman 1993), have led to a consensus that some 11 fragments are genuine (Frs. 1–6, 6a, 7, 13, 16 and 17 in the numbering of Huffman 1993) and derive from Philolaus' book On Nature (Barnes 1982; Kahn 1993 and 2001; Kirk, Raven and Schofield 1983; Nussbaum 1979; Zhmud 1997). Fragments 1, 6a and 13 are identified as coming from the book On Nature by ancient sources. Stobaeus cites fragments 2 and 4–7 as coming from a work On the Cosmos, but this appears to be an alternate title for On Nature, which probably arose because the chapter heading in Stobaeus under which the fragments are cited is 'On the Cosmos.'
Cosmology
Further information: Pythagorean astronomical system
The book by Philolaus begins with the following:[8]
Nature (physis) in the worldorder (cosmos) was fitted together out of things which are unlimited and out of things which are limiting, both the worldorder as a whole and everything in it.
Robert Scoon explained Philolaus' universe in 1922:[23]
Philolaus is trying to show how the ordered universe that we know came into its present condition. It arose, he says, by the action of harmony on a basic substance, which we do not know but must infer. This substance consisted of different primary elements, and harmony fitted these together in such a way that nature φύσις turns out to be an ordered world κόσμος.
Stobaeus' account
Philolaus did away with the ideas of fixed direction in space, and developed one of the first nongeocentric 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
In Philolaus's system a sphere of the fixed stars, the five planets, the Sun, Moon and Earth, all moved around his Central Fire. According to Aristotle writing in Metaphysics, Philolaus added a tenth unseen body, he called CounterEarth, as without it there would be only nine revolving bodies, and the Pythagorean number theory required a tenth. However, according to Greek scholar George Burch, Aristotle was lampooning Philolaus's ideas. In reality, Philolaus' ideas predated the idea of spheres by hundreds of years.[24] Nearly twothousand years later Nicolaus Copernicus would mention in De revolutionibus that Philolaus already knew about the Earth's revolution around a central fire.
However, it has been pointed out that Stobaeus betrays a tendency to confound the dogmas of the early Ionian philosophers, and he occasionally mixes up Platonism with Pythagoreanism.[25]
Philosophy
See also: Pythagoreanism § Music and harmony
Philolaus argued at the foundation of everything is the part played by the ideas of limit and the unlimited. One of the first declarations in the work of Philolaus was that all things in the universe result from a combination of the unlimited and the limiting;[26] for if all things had been unlimited, nothing could have been the object of knowledge.[27] 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, Fragment DK 44B 6a.
See also
Alcmaeon of Croton
Apeiron
Nicomachus
Parmenides
Protrepticus (Aristotle)
Pythagoreans
Notes
Gaffurius, Franchinus (1492). Theorica musicae.
Huffman, Carl (2020), "Philolaus", The Stanford Encyclopedia of Philosophy
"The most likely date for Philolaus' birth would then appear to be around 470, although he could have been born as early as 480 or as late as 440. He appears to have lived into the 380s and at the very least until 399." Carl A. Huffman, (1993) Philolaus of Croton: Pythagorean and Presocratic, pages 5–6. Cambridge University Press
Böckh, August (1819). Philolaos des Pythagoreers Lehren nebst den Bruchstücken seines Werkes. In der Vossischen Buchhandlung. p. 14. "Pythagoras Lehren nebst den Bruchstücken seines Werkes."
Iamblichus, Vita Pythagorica, p. 148
Iamblichus, Vita Pythagorica, p. 267; Diogenes Laërtius, viii, p. 46
Iamblichus, Vita Pythagorica, pp. 266–67
Carl Huffman. "Philolaus". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
Carl A. Huffman, (1993) Philolaus of Croton: Pythagorean and Presocratic, p. 6. Cambridge University Press
Not to be confused with the first burning of the meeting place, in the lifetime of Pythagoras, c. 509 BC
Plato, Phaedo, 61DE
Apollodorus ap. Diogenes Laërtius, ix. 38
Iamblichus, Vita Pythagorica; comp. Plutarch, de Gen. Socr. 13, though the account given by Plutarch involves great inaccuracies
Diogenes Laërtius, iii. 6
Diogenes Laërtius, viii. 46
"The story at D.L. 84 that Philolaus was killed because he was thought to be aiming at a tyranny is clearly a confusion with Dion who is mentioned in the context and did have such a death." Carl A. Huffman, (1993) Philolaus of Croton: Pythagorean and Presocratic, p. 6. Cambridge University Press
Diogenes Laërtius, iii. p. 84; cf. Suda, Philolaus
Diogenes Laërtius, viii. 85
Diogenes Laërtius, iii. 9, viii. 15
Diogenes Laërtius, viii. 15, 55, 84, 85, iii. 9; Aulus Gellius, iii. 17; Iamblichus, Vita Pythagorica; Tzetzes, Chiliad, x. 792, xi. 38
DK 44 B 2, 3, 4, 5, 6, 7
Smith, Sir William (1870). Dictionary of Greek and Roman biography and mythology. p. 305.
Scoon, Robert (1922). Philolaus, Fragment 6, Diels. Stobaeus i. 21. 460.
Burch, George Bosworth. The CounterEarth Archived 20131029 at the Wayback Machine. Osirus, vol. 11. Saint Catherines Press, 1954. p. 267294
One or more of the preceding sentences incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). "Stobaeus, Joannes". Encyclopædia Britannica (11th ed.). Cambridge University Press.
Fragment DK 44B 1
Fragment DK 44B 3
References
Laërtius, Diogenes (1925). "Pythagoreans: Philolaus" . Lives of the Eminent Philosophers. 2:8. Translated by Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.

Aglaonice Agrippa Anaximander Andronicus Apollonius Aratus Aristarchus Aristyllus Attalus Autolycus Bion Callippus Cleomedes Cleostratus Conon Eratosthenes Euctemon Eudoxus Geminus Heraclides Hicetas Hipparchus Hippocrates of Chios Hypsicles Menelaus Meton Oenopides Philip of Opus Philolaus Posidonius Ptolemy Pytheas Seleucus Sosigenes of Alexandria Sosigenes the Peripatetic Strabo Thales Theodosius Theon of Alexandria Theon of Smyrna Timocharis

Ancient Greek and Hellenistic mathematics (Euclidean geometry)
Mathematicians
(timeline)
Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner
Problems
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction
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