Philolaus ( / ˌ f ɪ l ə ˈ l eɪ ə s / ; Ancient Greek : Φιλόλαος , Philólaos ; c. 470 – c. 385 BC ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pythagorean tradition and the most outstanding figure in the Pythagorean school. Pythagoras developed a school of philosophy that was dominated by both mathematics and mysticism. Most of what is known today about the Pythagorean astronomical system is derived from Philolaus's views. He may have been the first to write about Pythagorean doctrine. According to Böckh (1819) , who cites Nicomachus , Philolaus was the successor of Pythagoras.
64-634: He argued that at the foundation of everything is the part played by the limiting and limitless , which combine in a harmony. With his assertions that the Earth was not the center of the universe ( geocentrism ), he is credited with the earliest known discussion of concepts in the development of heliocentrism , the theory that the Earth is not the center of the Universe , but rather that the Sun is. Philolaus discussed
128-564: A Central Fire as the center of the universe and that spheres (including the Sun) revolved around it. Various reports give the birthplace of Philolaus as either Croton , Tarentum , or Metapontum —all part of Magna Graecia (the name of the coastal areas of Southern Italy on the Tarentine Gulf that were colonized extensively by Greek settlers). It is most likely that he came from Croton. He migrated to Greece , perhaps while fleeing
192-606: A book on the Pythagorean doctrines, and that Plato read and made use of it. Historians from the Stanford Encyclopedia of Philosophy , Chapter Philolaus' Book: Genuine Fragments and Testimonia , noted the following: 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
256-557: 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 Diogenes Laërtius even chose to put into verse. 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
320-415: A gap between the existing mythical and the new rational way of thought ( rationalism ). But if we follow the course, we will see that there is not such an abrupt break with the previous thought. The basic elements of nature, water , air , fire , earth , which the first Greek philosophers believed composed the world, represent in fact the mythical primordial forces. The collision of these forces produced
384-474: A high level of abstraction. It adopted apeiron as the origin of all things, because it is completely indefinite. This is a further transition from the previous existing mythical way of thought to the newer rational way of thought which is the main characteristic of the archaic period (8th to 6th century BC). This shift in thought is correlated with the new political conditions in the Greek city states during
448-467: A limit to his most violent ambitions, that arrogance-injustice ( hubris or adikia ) could disturb the harmony and balance. In that case justice ( dike ) would destroy him to reestablish the order. These ideas are obvious in later Greek philosophers. Philolaus (5th century BC) mentions that nature constituted and is organized with the world from unlimitable ( Ancient Greek : ἄπειρα apeira , plural of apeiron ) and limitable. Everything which exists in
512-513: A pessimist and that he viewed all coming to be as an illegitimate emancipation from the eternal being, a wrong for which destruction is the only penance. In accordance to this the world of the individual definite objects should perish into the indefinite since anything definite has to eventually return to the indefinite. His ideas had a great influence on many scholars including Martin Heidegger . Werner Heisenberg , noted for his contributions to
576-529: A tendency to confound the dogmas of the early Ionian philosophers, and in his accounts, he occasionally mixes up Platonism with Pythagoreanism. Apeiron Apeiron ( / ə ˈ p aɪ ˌ r ɒ n / ; ἄπειρον ) is a Greek word meaning '(that which is) unlimited; boundless; infinite; indefinite' from ἀ- a- 'without' and πεῖραρ peirar 'end, limit; boundary', the Ionic Greek form of πέρας peras 'end, limit, boundary'. The apeiron
640-491: A tenth. However, Greek scholar George Burch asserts his belief that Aristotle was lampooning Philolaus's addition. The system that Philolaus described predated the idea of spheres by hundreds of years, however. Nearly two-thousand years later, Nicolaus Copernicus would mention in De revolutionibus that Philolaus already knew about the Earth's revolution around a central fire. It has been pointed out, however, that Stobaeus betrays
704-450: A tree. When it broke, it created the Sun, the Moon and the stars. The first animals were generated in the water. When they came to Earth they were transmuted by the effect of sunlight. The human being sprung from some other animal, which originally was similar to a fish. The blazing orbs, which have drawn off from the cold earth and water, are the temporary gods of the world clustering around
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#1732776717188768-423: A way that nature φύσις turns out to be an ordered world κόσμος . The book by Philolaus begins with the following: Nature ( physis ) in the world-order (cosmos) was fitted together out of things which are unlimited and out of things which are limiting, both the world-order as a whole and everything in it. According to Stobaeus, Philolaus did away with the ideas of fixed direction in space and developed one of
832-492: 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. Out of the materials which he derived from these books Plato is said to have composed his Timaeus . But in
896-400: Is apeiron . Because only then genesis and decay will never stop. Therefore, it seems that Anaximander argued about apeiron and this is also noticed by Aristotle : The belief that there is something apeiron stems from the idea that only then genesis and decay will never stop, when that from which is taken what is generated is apeiron . Friedrich Nietzsche claimed that Anaximander was
960-403: Is an ancient Near Eastern unit of weight for silver or gold, equivalent to approximately 1.25 pounds (0.57 kg), which was divided into 60 shekels . The mina, like the shekel, eventually also became a unit of currency . From earliest Sumerian times, a mina was a unit of weight. At first, talents and shekels had not yet been introduced. By the time of Ur-Nammu (shortly before 2000 BCE),
1024-417: Is central to the cosmological theory created by Anaximander , a 6th-century BC pre-Socratic Greek philosopher whose work is mostly lost. From the few existing fragments, we learn that he believed the beginning or ultimate reality ( arche ) is eternal and infinite, or boundless ( apeiron ), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we can perceive
1088-442: Is contrasted with hubris (arrogance). Arrogance was considered very dangerous because it could break the balance and lead to political instability and finally to the destruction of a city-state . Aetius (1st century BC) transmits a different quotation: Everything is generated from apeiron and there its destruction happens. Infinite worlds are generated and they are destructed there again. And he says (Anaximander) why this
1152-585: Is derived. Apeiron generated the opposites (hot–cold, wet–dry, etc.) which acted on the creation of the world ( cf. Heraclitus ). Everything is generated from apeiron and then it is destroyed by going back to apeiron , according to necessity. He believed that infinite worlds are generated from apeiron and then they are destroyed there again. His ideas were influenced by the Greek mythical tradition and by his teacher Thales (7th to 6th century BC). Searching for some universal principle, Anaximander retained
1216-671: Is described in Genesis . In the Hindu cosmogony which is similar to the Vedic ( Hiranyagarbha ) the initial state of the universe was an absolute darkness. Hesiod made an abstraction, because his original chaos is a void, something completely indefinite. In his opinion the origin should be indefinite and indeterminate. The indefiniteness is spatial in early usages as in Homer (indefinite sea). A fragment from Xenophanes (6th century BC) shows
1280-630: Is mentioned in the Bible, where Solomon is reported to have made 300 shields, each with 3 "mina" of gold (Hebrew: מָנֶה , romanized: mane ), or later after the Edict of Cyrus II of Persia the people are reported to have donated 5000 minas of silver for the reconstruction of Solomon's Temple in Jerusalem . In the Code of Hammurabi which is considered one of the first examples of written law,
1344-400: Is metaphysical (and can lead to monism ), while the second one dealing with mutual changes and the balance of the opposites as central to reality is physical. The same paradox existed in the Greek way of thought. The Greeks believed that each individual had unlimitable potentialities both in brain and in heart, an outlook which called a man to live at the top of his powers. But that there was
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#17327767171881408-464: Is no return to the real world. Everything generated from apeiron must return there according to the principle genesis-decay. There is a polar attraction between the opposites genesis-decay, arrogance-justice. The existence itself carries a guilt. The idea that the fact of existence by itself carries along an incurable guilt is Greek ( Theognis 327) and anybody claims that surpasses it, commits arrogance and therefore he becomes guilty. The first half of
1472-617: The Akkadian period, 2 mina was equal to 1 sila of water (cf. clepsydra , water clock). In ancient Greece , the mina was known as the μνᾶ ( mnâ ). It originally equalled 70 drachmae but later, at the time of the statesman Solon (c. 594 BC), was increased to 100 drachmae. The Greek word mna ( μνᾶ ) was borrowed from Semitic. Different city states used minae of different weights. The Aeginetan mina weighed 623.7 g (22.00 oz). The Attic mina weighed 436.6 g (15.40 oz). In Solon's day, according to Plutarch ,
1536-466: The Bacchae as a book for teaching theology by means of mathematics. 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. He composed
1600-541: The Pythagoreans (in particular, Philolaus ), the universe had begun as an apeiron , but at some point it inhaled the void from outside, filling the cosmos with vacuous bubbles that split the world into many different parts. For Anaxagoras , the initial apeiron had begun to rotate rapidly under the control of a godlike Nous (Mind), and the great speed of the rotation caused the universe to break up into many fragments. Since all individual things had originated from
1664-472: The Pythagoreans : [...] for they [the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit. Greek philosophy entered a high level of abstraction making apeiron the principle of all things and some scholars saw
1728-439: The 6th century BC. In the mythical Greek cosmogony of Hesiod (8th to 7th century BC) the first primordial god is Chaos , which is a void or gap. Chaos is described as a gap either between Tartarus and the Earth's surface (Miller's interpretation) or between earth's surface and the sky (Cornford's interpretation). One can name it also abyss (having no bottom). Alternately, Greek philosopher Thales believed that
1792-457: The 6th century is a period of great social instability in Miletus, the city state where Anaximander lives. Any attempt of excess leads to exaggerations and each exaggeration must be corrected. All these have to be paid according to the debt. The things give justice to one another with the process of time. Justice has to destroy everything which is born. There is no external limit that can restrict
1856-424: The Earth, which to the ancient thinker is the central figure. In the commentary of Simplicius on Aristotle's Physics the following fragment is attributed direct to Anaximander: From where things have their origin, there their destruction happens as it is ordained [Greek: kata to chreon means 'according to the debt']. For they give justice and compensation to one another for their injustice according to
1920-429: The activities of men, except the destruction. Arrogance is an expression of the chaotic element of human existence and in a way a part of the rebounding mechanism of order, because pushing it to exertions causes destruction which is also a reestablishment. We may assume that the contradiction in the different interpretations is because Anaximander combined two different ways of thought. The first one dealing with apeiron
1984-417: 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
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2048-510: 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.' Philolaus argued at the foundation of everything is the part played by the ideas of limit and the unlimited. One of
2112-430: The cosmic harmony according to the Greek cosmogony (Hesiod). Anaximander noticed the mutual changes between these elements, therefore he chose something else (indefinite in kind) which could generate the others without experiencing any decay. There is also a fragment attributed to his teacher Thales: "What is divine? What has no origin, nor end." This probably led his student to his final decision for apeiron , because
2176-426: The different and inconsistent accounts of the matter, the first publication of the Pythagorean doctrines is pretty uniformly attributed to Philolaus. In one source, Diogenes Laërtius speaks of Philolaus composing one book, but elsewhere he speaks of three books, 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. Later, it
2240-423: The divinity applied to it implies that it always existed. The notion of the temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality and Anaximander's description was in terms appropriate to this conception. This arche is called "eternal and ageless" (Hippolitus I,6,I;DK B2). The apeiron has generally been understood as a sort of primal chaos . It acts as
2304-533: The earth, in which are found generation and change, he calls the sky. In Philolaus's system a sphere of the fixed stars , the five planets , the Sun , Moon , and Earth, all moved around a Central Fire. According to Aristotle , writing in Metaphysics , Philolaus added a tenth unseen body, he called Counter-Earth , as without it there would be only nine revolving bodies, and the Pythagorean number theory required
2368-420: 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; for if all things had been unlimited, nothing could have been the object of knowledge. Limiters and unlimiteds are combined 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,
2432-469: The first non-geocentric views of the universe and in his new way of thinking, the universe 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
2496-449: The foundation of quantum mechanics , arrived at the idea that the elementary particles are to be seen as different manifestations, different quantum states, of one and the same "primordial substance". Because of its similarity to the primordial substance hypothesized by Anaximander, his colleague Max Born called this substance apeiron . Scholars in other fields, e.g. Bertrand Russell and Maurice Bowra , did not deny that Anaximander
2560-418: 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
2624-483: The mina had a value of 1 ⁄ 60 talent as well as 60 shekels . The weight of this mina is calculated at 1.25 pounds (0.57 kg), or 570 grams of silver (18 troy ounces). The word mina comes from the ancient Semitic root m-n-w / m-n-y 'to count', Akkadian manû , Hebrew : מָנָה ( mana ), Imperial Aramaic : מָנָה / מְנָא ( mana / mena ), Classical Syriac : ܡܢܳܐ ( mena ), Ugaritic : 𐎎𐎐 , romanized: mn . It
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2688-485: The mina is one of the most used terms denoting the weight of gold to be paid for crimes or to resolve civil conflicts. In the Biblical story of Belshazzar's feast , the words mene, mene, tekel, upharsin appear on the wall (Daniel 5:25), which according to one interpretation can mean "mina, mina, shekel, and half-pieces", although Daniel interprets the words differently for King Belshazzar. Writings from Ugarit give
2752-672: The mutual changes between the four elements, he did not demand to make one of them a subject, but something else except these. He considers that genesis takes place without any decay of this element, but with the generation of the opposites by his own movement. Mina (unit) The mina / ˈ m aɪ n ə / ( Akkadian : 𒈠𒈾 , romanized: manû ; Ugaritic : 𐎎𐎐 , romanized: mn ; Imperial Aramaic : מְנֵא , romanized: mənēʾ ; Hebrew : מָנֶה , romanized : māneh ; Classical Syriac : ܡܢܝܐ , romanized: manyāʾ ; Ancient Greek : μνᾶ , romanized : mnā ; Latin : mina )
2816-402: The notion that someone has operated outside of his own sphere, without respecting the one of his neighbour. Therefore, he commits hubris . The relative English word arrogance (claim as one's own without justification; Latin : arrogare ), is very close to the original meaning of the aphorism: "Nothing in excess." Other pre-Socratic philosophers had different theories of the apeiron . For
2880-564: The old mythical language. The Goddess Justice ( Dike ), appears to keep the order. The quotation is close to the original meanings of the relevant Greek words. The word dike (justice) was probably originally derived from the boundaries of a man's land and transmits metaphorically the notion that somebody must remain in his own sphere, respecting the one of his neighbour. The word adikia (injustice) means that someone has operated outside of his own sphere, something that could disturb "law and order" ( eunomia ). In Homer's Odyssey eunomia
2944-447: The order of the world should have been formed by them, unless the harmony intervened [...]. Robert Scoon explained Philolaus' universe in 1922: 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
3008-442: The ordering of time. This fragment remains a mystery because it can be translated in different ways. Simplicius comments that Anaximander noticed the mutual changes between the four elements (earth, air, water, fire), therefore he did not choose one of them as an origin, but something else which generates the opposites without experiencing any decay. He mentions also that Anaximander said all these in poetic terms, meaning that he used
3072-437: The origin is neither water, nor any other of the so-called elements, but something of different nature, unlimited. From it are generated the skies and the worlds which exist between them. Whence things (beings) have their origin, there their destruction happens as it is ordained. For they give justice and compensation to one another for their injustice according to the ordering of time, as he said in poetic terms. Obviously noticing
3136-450: The origin or first principle was water. Pherecydes of Syros (6th century BC) probably called the water also Chaos and this is not placed at the very beginning. In the creation stories of Near East the primordial world is described formless and empty. The only existing thing prior to creation was the water abyss. The Babylonian cosmology Enuma Elish describes the earliest stage of the universe as one of watery chaos and something similar
3200-556: The price of a sheep was one drachma or a medimnos (about 40 kg) of wheat. Thus a mina was worth 100 sheep. The word mina also occurs in Latin literature, but mainly in plays of Plautus and Terence adapted from Greek originals. In Terence's play Heauton Timorumenos , adapted from a play of the same name by the Greek playwright Menander , a certain sum of money is referred to in one place as "ten minae" (line 724) and in another as "1000 drachmas of silver" (line 601). Usually
3264-414: The same apeiron , all things must contain parts of all other things. This explains how one object can be transformed into another, since each thing already contains all other things in germ. Anaximander from Miletus, son of Praxiades student and descendant of Thales, said that the origin and the element of things (beings) is apeiron and he is the first who used this name for the origin (arche). He says that
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#17327767171883328-458: The second burning of the Pythagorean meeting-place around 454 BC. 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. That would make him a contemporary of Socrates , and would agree with the statement that Philolaus and Democritus were contemporaries. The writings of much later writers are
3392-567: The sources of further reports about his life. They are scattered and of dubious value in reconstructing his life. Apparently, he lived for some time at Heraclea , where he was the pupil of Aresas , or (as Plutarch calls him) Arcesus. Diogenes Laërtius is the only authority for the claim that shortly after the death of Socrates, Plato traveled to Italy where he met with Philolaus and Eurytus . The pupils of Philolaus were said to have included Xenophilus , Phanto , Echecrates , Diocles , and Polymnastus . As to his death, Diogenes Laërtius reports
3456-399: The substratum supporting opposites such as hot and cold, wet and dry, and directed the movement of things, by which there grew up all of the host of shapes and differences which are found in the world. Out of the vague and limitless body there sprang a central mass—Earth—cylindrical in shape. A sphere of fire surrounded the air around the Earth and had originally clung to it like the bark round
3520-417: 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
3584-587: The traditional religious assumption that there was a cosmic order and tried to explain it rationally, using the old mythical language which ascribed divine control on various spheres of reality. This language was more suitable for a society which could see gods everywhere; therefore the first glimmerings of laws of nature were themselves derived from divine laws. The Greeks believed that the universal principles could also be applied to human societies. The word nomos (law) may originally have meant natural law and used later to mean man-made law. Greek philosophy entered
3648-468: The transition from chaos to apeiron : "The upper limit of earth borders on air. The lower limit reaches down to the unlimited. (i.e. the Apeiron)". Either apeiron meant the "spatial indefinite" and was implied to be indefinite in kind, or Anaximander intended it primarily 'that which is indefinite in kind' but assumed it also to be of unlimited extent and duration. His ideas may have been influenced by
3712-631: The value of a mina as equivalent to fifty shekels. The prophet Ezekiel refers to a mina ( maneh in the King James Version ) also as 60 shekels, in the Book of Ezekiel 45:12. Jesus of Nazareth tells the " parable of the minas " in Luke 19:11–27, also told as the "parable of the talents" in Matthew 25:14–30. In later Jewish usage, the maneh is equal in weight to 100 denarii . From
3776-404: The word mina referred to a mina of silver, but Plautus also twice mentions a mina of gold. In the 4th century BC, gold was worth about 10 times the same weight of silver. In Plautus, 20 minae is mentioned as the price of buying a slave. It was also the price of hiring a courtesan for a year. 40 minae is given as the price of a house. In classical Latin the approximate equivalent of a mina
3840-496: The world contains the unlimited ( apeiron ) and the limited. Something similar is mentioned by Plato : Nothing can exist if it does not contain continually and simultaneously the limited and the unlimited, the definite and the indefinite. Some doctrines existing in Western thought still transmit some of the original ideas: "God ordained that all men shall die", "Death is a common debt". The Greek word adikia (injustice) transmits
3904-516: Was claimed that Plato composed much of his Timaeus based upon the book by Philolaus. One of the works of Philolaus was called On Nature . It seems to be the same work that 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, and which may originate from Arignote . However, it has been mentioned that Proclus describes
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#17327767171883968-474: 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
4032-477: Was the libra (the word also meant "balance" or "weighing scales"). With a weight of only 328.9 g (11.60 oz), however, the Roman libra was lighter than either a Greek mina or a modern pound of 16 ounces. It was divided into 12 Roman ounces. Sometimes the word libra was used together with the word pondo "in weight", e.g. libram pondo "a pound in weight" (Livy, 3.29); but often pondo
4096-485: Was the first who used the term apeiron , but claimed that the mysterious fragment is dealing with the balance of opposite forces as central to reality being closer to the quotation transmitted by Simplicius. There are also other interpretations which try to match both the previous aspects. Apeiron is an abstract, void, something that cannot be described according to the Greek pessimistic belief for death. Death indeed meant "nothingless". The dead live like shadows and there
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