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Thales of Miletus

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Thales of Miletus(/ˈθeɪliːz/THAY-leez;‹See Tfd›Greek:Θαλῆς;c. 626/623– c. 548/545 BC) was anAncient Greekpre-SocraticphilosopherfromMiletusinIonia,Asia Minor.Thales was one of theSeven Sages,founding figures ofAncient Greece.

Thales of Miletus
Posthumous portrait of Thales by Wilhelm Meyer, based on a bust from the 4th century
Bornc.626/623 BC
Miletus,Ionian League
(modern-dayBalat,Didim,Aydın,Turkey)
Diedc.548/545 BC (agedc.78)
EraPre-Socratic philosophy
RegionWestern philosophy
SchoolIonian/Milesian
Main interests
Notable ideas

Many regard him as the first philosopher in theGreek tradition,breaking from the prior use ofmythologyto explain the world and instead usingnatural philosophy.He is thus otherwise referred to as the first to have engaged inmathematics,science,anddeductive reasoning.[1]

The first philosophers followed him in explaining all ofnatureas based on the existence of asingle ultimate substance.Thalestheorizedthat this single substance waswater.Thales thought the Earth floated on water.

In mathematics, Thales is the namesake ofThales's theorem,and theintercept theoremcan also be known as Thales's theorem. Thales was said to have calculated the heights of thepyramidsand the distance of ships from the shore. In science, Thales was an astronomer who reportedlypredicted the weatherand asolar eclipse.The discovery of the position of the constellationUrsa Majoris also attributed to Thales, as well as the timings of thesolsticesandequinoxes.He was also anengineer,known for having diverted theHalys River.[1]

Life

The Ionic Stoa on the Sacred Way inMiletus.

The main source concerning the details of Thales's life and career is thedoxographerDiogenes Laërtius,in his third-century-AD workLives and Opinions of the Eminent Philosophers.[2]While it is all we have, Diogenes wrote some eight centuries after Thales's death and his sources often contained "unreliable or even fabricated information".[3][a]It is known Thales was fromMiletus,a mercantile city settled at the mouth of theMaeander river.

The dates of Thales's life are not exactly known, but are roughly established by a few datable events mentioned in the sources. According to the historianHerodotus,writing in the 5th century BC, Thales predicted asolar eclipsein 585 BC.[5]Assuming one'sacme(orfloruit) occurred at the age of 40, the chronicle ofApollodorus of Athens,written during the 2nd century BC, therefore placed Thales's birth about the year 625 BC.[6][7]

Ancestry and family

Map of Phoenician (in yellow) and Greek colonies (in red) around 8th to 6th century BC.

While the probability is that Thales was as Greek as most Milesians,[8]Herodotusdescribed Thales as "aPhoenicianby remote descent ".[9]Diogenes Laërtius references Herodotus,Duris,andDemocritus,who all agree "that Thales was the son of Examyas and Cleobulina, and belonged to the Thelidae who are Phoenicians and amongst the noblest descendants ofCadmusandAgenor"who had been banished from Phoenicia and that Thales was enrolled as a citizen in Miletus along withNeleus.[10][11]

However,Friedrich Nietzscheand others interpret this quote as meaning only that his ancestors wereseafaringCadmeiansfromBoeotia.[12][13]It is also possible that he was of mixed ancestry, given his father had aCarianname and his mother had a Greek name.[13][14][15]Diogenes Laërtius seems to also reference an alternative account: "Most writers, however, represent him as a genuine Milesian and of a distinguished family".[16]Encyclopedia Britannica(1952) concluded that Thales was most likely a native Milesian of noble birth and that he was certainly a Greek.[14]

Diogenes continues, by delivering more conflicting reports: one that Thales married and either fathered a son (Cybisthus or Cybisthon) or adopted his nephew of the same name; the second that he never married, telling his mother as a young man that it was too early to marry, and as an older man that it was too late.[b]Plutarchhad earlier told this version:Solonvisited Thales and asked him why he remained single; Thales answered that he did not like the idea of having to worry about children. Nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus.[18]

Travels

The culture ofArchaic Greecewas heavily influenced by those of theLevantandMesopotamia.[19]It is said Thales was engaged in trade and visited eitherEgyptorBabylonia.[20]However, there is no strong evidence that Thales ever visited countries in theNear East,and the issue is disputed among scholars.[21]Visits to such places were a commonplace attribution to various philosophers by later writers, especially when these writers tried to explain the origin of their mathematical knowledge, such as with Thales orPythagorasorEudoxus.[22][1]

Egypt

Thales may have been educated in Egypt.

Several ancient authors assume that Thales, at one point in his life, visitedEgypt,where he learned about geometry.[23]It is considered possible that Thales visited Egypt, since Miletus had a permanent colony there (namelyNaucratis). It is also said Thales had close contacts with the priests ofThebeswho instructed him, or even that he instructedthemin geometry.[24][25]It is also possible Thales knew about Egypt from accounts of others, without actually visiting it.[26]

Babylon

Aside from Egypt, the other mathematically advanced, ancient civilization before the Greeks was Babylonia, another commonplace attribution of travel for a mathematically-minded philosopher.[27]At least one ancient historian,Josephus,claims Thales visited Babylonia.

Historians Roger L. Cooke andB.L. Van der Waerdencome down on the side of Babylonian mathematics influencing the Greeks, citing the use of e. g. thesexagesimal system(orbase60).[27]Cooke notes "This relation, however, is controversial."[27]Others historians, such as D. R. Dicks, take issue with the idea of Babylonian influence on Greek mathematics. For until around the time ofHipparchus(c. 190–120 BC) their sexagesimal system was unknown.[28]

Herodotus wrote the Greeks learnt thegnomonfrom the Babylonians. Thales's follower Anaximander is credited with introducing thegnomonto the Greeks.[29]Herodotus also wrote that the practice of dividing the day into 12 parts, and thepolos,came to the Greeks from the Babylonians.[c]Yet this too is disputed, for example by historian L. Zhmud, who points out thegnomonwas known to both Egyptians and Babylonians, the division of the day into twelve parts (and by analogy the year) was known to the Egyptians already in the2nd millennium BC,and the idea of thepoloswas not used outside of Greece at this time.[31]

Sagacity

Thales,Nuremberg Chronicle.

Thales is recognized as one of the Seven Sages of Greece, semi-legendary wisestatesmenand founding figures of Ancient Greece. While which seven one chooses may change, the seven has a canonical four which includes Thales, Solon of Athens,Pittacus of Mytilene,andBias of Priene.Diogenes Laërtius tells us that the Seven Sages were created in thearchonshipof Damasius atAthensabout 582 BC and that Thales was the first sage.[32][d]

The sages were associated with theDelphic maxims,a quote or maxim attributed to each one inscribed on theTemple of ApolloatDelphi.Thales has arguably the most famous of all,gnothi seautonorknow thyself.According to the 10th-century Byzantine encyclopedia theSuda,the proverb is both "applied to those whose boasts exceed what they are" and "a warning to pay no attention to the opinion of the multitude."[33][e]

Golden tripod

Diogenes Laërtius relates several stories of an expensive, gold tripod or bowl that is to go to the mostwise.In one version (that Laërtius credits toCallimachusin hisIambics) Bathycles of Arcadia states in his will that an expensive bowl"'should be given to him who had done most good by his wisdom.' So it was given to Thales, went the round of all the sages, and came back to Thales again. And he sent it toApollo at Didyma,with this dedication...'Thales the Milesian, son of Examyas [dedicates this] to Delphinian Apollo after twice winning the prize from all the Greeks.'"[39]

Diplomacy

According to Diogenes Laërtius, Thales gained fame as a counselor when he advised the Milesians not to engage in a symmachia, a "fighting together", with the Lydians. This has sometimes been interpreted as an alliance.[40]

Croesuswas defeated before the city ofSardisbyCyrus the Great,who subsequently spared Miletus because it had taken no action. Cyrus was so impressed by Croesus’ wisdom and his connection with the sages that he spared him and took his advice on various matters.[citation needed]The Ionian cities should be demoi, or "districts".

He counselled them to establish a single seat of government, and pointed outTeosas the fittest place for it; "for that," he said, "was the centre ofIonia.Their other cities might still continue to enjoy their own laws, just as if they were independent states. "[41]

Miletus, however, received favorable terms from Cyrus. The others remained in an Ionian League of twelve cities (excluding Miletus), and were subjugated by the Persians.[citation needed]

Theories and studies

Early Greeks, and other civilizations before them, often invokedidiosyncraticexplanations of natural phenomena with reference to the will ofanthropomorphicgodsandheroes.Instead, Thales aimed to explain natural phenomena via rational hypotheses that referenced natural processes themselves—[42]Logosrather thanmythos.Many, most notably Aristotle, regard him as the first philosopher in theGreek tradition.[43][44]Rather thantheologoiormythologoi,Aristotle referred to the first philosophers asphysiologoi,or natural philosophers, and Thales as the first among them. Also, while the other Seven Sages were strictly law-givers and statesmen and not speculative philosophers, Plutarch noted "it would seem that Thales was the only wise man of the time who carried his speculations beyond the realm of the practical."[45]

Water as thearche

See also:Classical element § Hellenistic philosophy
Thales depicted at theBaths of the Seven Sages.

Thales's most famous idea was his philosophical andcosmologicalthesis that all is water, which comes down to us through a passage fromAristotle'sMetaphysics.[43]In the work, Aristotle reported Thales's theory that thearcheor originating principle of nature wasa single material substance:water. Aristotle then proceeded to proffer a number of conjectures based on his own observations to lend some credence to why Thales may have advanced this idea (though Aristotle did not hold it himself).

While Aristotle's conjecture on why Thales held water as the originating principle of matter is his own thinking, his statement that Thales held it as water is generally accepted as genuinely originating with Thales. Writing centuries later, Diogenes Laërtius also states that Thales taught "Water constituted (ὑπεστήσατο,'stood under') the principle of all things. "[46][f]

According to Aristotle:[43]

That from which is everything that exists and from which it first becomes and into which it is rendered at last, its substance remaining under it, but transforming in qualities, that they say is the element and principle of things that are.…For it is necessary that there be some nature (φύσις), either one or more than one, from which become the other things of the object being saved... [The first philosophers] do not all agree as to the number and the nature of these principles. Thales the founder of this type of philosophy says that it is water.

Aristotle further adds:

Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption from this; and also from the fact that the seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things. "[48][g]

The 1870 bookDictionary of Greek and Roman Biography and Mythologynoted:[44]

In his dogma that water is the origin of things, that is, that it is that out of which every thing arises, and into which every thing resolves itself, Thales may have followedOrphiccosmogonies, while, unlike them, he sought to establish the truth of the assertion. Hence, Aristotle, immediately after he has called him the originator of philosophy brings forward the reasons which Thales was believed to have adduced in confirmation of that assertion; for that no written development of it, or indeed any book by Thales, was extant, is proved by the expressions which Aristotle uses when he brings forward the doctrines and proofs of the Milesian. (p. 1016)

Most agree that Thales's stamp on thought is the unity of substance. Not merely the empirical claim that all is water, but the deeper philosophical claim that all is one. For example,Friedrich Nietzsche,in hisPhilosophy in the Tragic Age of the Greeks,wrote:[49]

Greek philosophy seems to begin with an absurd notion, with the proposition thatwateris the primal origin and the womb of all things. Is it really necessary for us to take serious notice of this proposition? It is, and for three reasons. First, because it tells us something about the primal origin of all things; second, because it does so in language devoid of image or fable, and finally, because contained in it, if only embryonically, is the thought, "all things are one."

Mathematics

Megiston topos: apanta gar chorei
(Μέγιστον τόπος· ἄπαντα γὰρ χωρεῖ.)

The greatest is space, for it holds all things.

—attributed to Thales[50]

Thales was known for introducing the theoretical and practical use ofgeometryto Greece, and has been described as the first person in the western world to apply deductive reasoning to geometry, making him the West's "first mathematician."[7][51][52]He is also credited with the West's oldest definition ofnumber:a "collection of units", "following the Egyptian view".[53][54]

The evidence for the primacy of Thales comes to us from a book byProclus,who lived a thousand years afterward but is believed to have had a copy ofEudemus's lost bookHistory of Geometry(4th century BC).[h]Proclus wrote that Thales was the first to visit Egypt and bring the Egyptian study of mathematics to Greece, and that Thales "himself discovered many propositions and disclosed the underlying principles of many others to his successors, in some case his method being more general, in others more empirical."[52]In addition to Proclus,Hieronymus of Rhodes(3rd century BC) also cites Thales as the first Greek mathematician.

Proclus attributes to Thales the discovery that a circle isbisectedby its diameter, that thebase angles of an isosceles triangle are equaland thatvertical anglesare equal.[55]Two fundamentaltheoremsof elementary geometry are customarily calledThales's theorem:one of themhas to do with a triangle inscribed in a circle and having the circle's diameter as one side;[55]the other, also called theintercept theorem,is about an angle intercepted by two parallel lines, forming a pair ofsimilar triangles.

Modern scholars are skeptical that anyone in Thales's time was producing mathematical proofs to the standard of later Greek mathematics, though not enough direct evidence remains to draw firm conclusions. While Thales may have discovered some basic geometric relations and provided some justification for them, attribution to him of formal proofs is now thought to represent speculative rationalization and reconstruction by later authors, rather than concrete accomplishments of Thales himself or his contemporaries.[56]

Vertical angles

According to one author, while visiting Egypt,[23]Thales observed that when the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal.[57]Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.

Right triangle inscribed in a circle

Main article:Thales's theorem
Thales's theorem: ifACis a diameter andBis a point on the diameter's circle, the angle∠ABCis a right angle.

Pamphilasays that, having learnt geometry from the Egyptians, Thales was the first to inscribe in a circle a right-angled triangle, whereupon hesacrificed an ox.[52]This is sometimes cited as history's first mathematical discovery.[58]Due to the variations among testimonies, such as the story of the ox sacrifice being accredited to Pythagoras upon discovery of thePythagorean theoremrather than Thales, some historians (such as D. R. Dicks) question whether such anecdotes have any historical worth whatsoever.[28]

It is believed the Babylonians knew the theorem for special cases.[59][60] The theorem is mentioned and proved as part of the 31st proposition in the third book ofEuclid'sElements.[61]Dante'sParadisorefers to Thales's theorem in the course of a speech.[62]

Similar triangles

Main article:Intercept theorem
The intercept theorem:DE/BC=AE/AC=AD/AB.

The story is told inDiogenes Laërtius,Pliny the Elder,andPlutarch,[52][63]sourced fromHieronymus of Rhodes,that when Thales visitedEgypt,[23]he measured the height of thepyramidsby their shadows at the moment when his own shadow was equal to his height.[i]According to Plutarch, it pleased the pharoahAmasis.More practically, Thales was said to have the ability to measure the distances of ships at sea.

These stories indicate familiarity with the intercept theorem, and for this reason the 26th proposition in the first book of Euclid's Elements was attributed to Thales.[65]They also indicate that he was familiar with the Egyptianseked,orseqed,the ratio of the run to the rise of aslope(cotangent).[66][j]According to Kirk & Raven,[8]all you need for this feat is three straight sticks pinned at one end and knowledge of your altitude. One stick goes vertically into the ground. A second is made level. With the third you sight the ship and calculate thesekedfrom the height of the stick and its distance from the point of insertion to the line of sight.[67]

Astronomy

Urania, the Muse of Astronomy, Reveals to Thales the Secrets of the Skies

Thales was also a noted astronomer, acknowledged in antiquity for describing the position ofUrsa Minor,and he thought the constellation might be useful as a guide for navigation at sea. He calculated the duration of the year and the timings of theequinoxesandsolstices.He is additionally attributed with calculating the position of thePleiades.[8]

Plutarchindicates that in his day (c. AD 100) there was an extant work, theAstronomy,composed in verse and attributed to Thales.[68]While some say he left no writings, others say that he wroteOn the SolsticeandOn the Equinox.TheNautical Star-guidehas also been attributed to him, but this was disputed even in ancient times.[8][k]No writing attributed to him has survived. Lobon of Argus asserted that the writings of Thales amounted to two hundred lines.[69]

Cosmological model

Worldview of Thales (left) and pupil Anaximander (right).

Thales thought theEarthmust be a flat disk or mound of land and dirt which is floating in an expanse of water.[70]Heraclitus Homericusstates that Thales drew his conclusion from seeing moist substance turn into air, slime and earth. It seems likely that Thales viewed the land as coming from the water on which it floated and the oceans that surround it, perhaps inspired by observingsiltdeposits.[71]

He thought the stars were balls of dirt on fire.[72]He seemed to correctly gather that the moon reflects the Sun's light.[73]Acrateron the Moon is named in his honor.

Meteorology

Rather than assuming thatearthquakeswere the result of supernatural whims, Thales explained them by theorizing that the Earth floats on water and that earthquakes occur when the Earth is rocked by waves.[74][42]He is attributed with the first observation of theHyades,supposed by the ancients to indicate the approach of rain when they rose with the Sun.[75]According toSeneca,Thales explained the flooding of theNileas due to the river being beaten back by theetesianwind.[76]

Olive presses
An olive mill and an olive press dating from Roman times inCapernaum, Israel.

A story, with different versions, recounts how Thales achieved riches from an olive harvest byprediction of the weather.In one version, he bought all theolive pressesin Miletus after predicting the weather and a good harvest for a particular year. Another version of the story has Aristotle explain that Thales had reserved presses in advance, at a discount, and could rent them out at a high price when demand peaked, following hispredictionof a particularly good harvest. This first version of the story would constitute the first historically known creation and use offutures,whereas the second version would be the first historically known creation and use ofoptions.[77]

Aristotle explains that Thales's objective in doing this was not to enrich himself but to prove to his fellow Milesians that philosophy could be useful, contrary to what they thought,[78]or alternatively, Thales had made his foray into enterprise because of a personal challenge put to him by an individual who had asked why, if Thales was an intelligent famous philosopher, he had yet to attain wealth.

Prediction of solar eclipse

Main article:Eclipse of Thales

As mentioned above, according to Herodotus, Thales predicted a solar eclipsewhich occurred during a battlebetween theLydiansand theMedes.[5]Among eclipses of the era, only the eclipse of 28 May 585 BC reached totality inAnatoliawhere the war took place. American writerIsaac Asimovdescribed this battle as the earliest historical event whose date is known with precision to the day, and called the prediction "the birth of science". As well as first mathematician and first philosopher, Thales is often given the label of the first western scientist and the "father of science".[79][80]but some contemporary scholars reject this interpretation.[81]

Totaleclipseof theSun

Herodotuswrites that in the sixth year of the war, the Lydians under KingAlyattesand the Medes underCyaxareswere engaged in an indecisive battle when suddenly day turned into night, leading to both parties halting the fighting and negotiating a peace agreement. Herodotus also mentions that the loss of daylight had been predicted by Thales. He does not, however, mention the location of the battle.[82]

Afterwards, on the refusal of Alyattes to give up his suppliants when Cyaxares sent to demand them of him, war broke out between the Lydians and the Medes, and continued for five years, with various success. In the course of it the Medes gained many victories over the Lydians, and the Lydians also gained many victories over the Medes. Among their other battles there was one night engagement. As, however, the balance had not inclined in favour of either nation, another combat took place in the sixth year, in the course of which, just as the battle was growing warm, day was on a sudden changed into night. This event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing for it the very year in which it actually took place. The Medes and Lydians, when they observed the change, ceased fighting, and were alike anxious to have terms of peace agreed on.[41]

However, based on the list ofMedian kingsand the duration of their reign reported elsewhere by Herodotus, Cyaxares died 10 years before the eclipse.[83][84]

D. R. Dicks joins other historians (F. Martini, J. L. E. Dreyer,O. Neugebauer) in rejecting the historicity of the eclipse story.[28]Dicks links the story of Thales discovering the cause for a solar eclipse with Herodotus' claim that Thales discovered the cycle of the sun with relation to the solstices, and concludes "he could not possibly have possessed this knowledge which neither the Egyptians nor the Babylonians nor his immediate successors possessed."[28]

Falling into a well

See also:The Astrologer who Fell into a Well

Plato, Diogenes Laertius, and Hippolytus all relay the story that Thales was so intent upon watching the stars that he failed to watch where he was walking, and fell into a well.[85][86][l]

"Thales was studying the stars and gazing into the sky, when he fell into a well, and a jolly and witty Thracian servant girl made fun of him, saying that he was crazy to know about what was up in the heavens while he could not see what was in front of him beneath his feet."[88]

Engineering

The Halys River

In addition to astronomy, Thales involved himself in other practical applications of mathematics, includingengineering.[89]Another story by Herodotus is thatCroesussent his army to the Persian territory. He was stopped by the riverHalys,then unbridged. Thales then got the army across the river by digging a diversion upstream so as to reduce the flow, making it possible to cross the river.[90]While Herodotus reported that most of his fellow Greeks believe that Thales did divert the river Halys to assist King Croesus' military endeavors, he himself finds it doubtful.[28]Plato praises Thales along withAnacharsis,who is credited as the originator of the potter's wheel and the anchor.[91]

Divinity

Thales (Electricity),a sculpture from "The Progress of Railroading" (1908), located at the main façade ofWashington Union Station

According to Aristotle, Thales thought "all things are full of gods",[8][92]i. e.lodestoneshadsouls,because iron is attracted to them (by the force ofmagnetism).[93]The same applied toamberfor its capacity to generatestatic electricity.The reasoning for suchhylozoismororganicismseems to be if something moved, then it was alive, and if it was alive, then it must have a soul.[94][95]

As well as gods seen in the movement caused by what came to be known asmagnetism and electricity,it seems Thales also had a supreme God which structured the universe:

"Thales", saysCicero,[96]"assures thatwateris the principle of all things; and that God is that Mind which shaped and created all things from water. "

According toHenry Fielding(1775),Diogenes Laërtius(1.35) affirmed that Thales posed "the independent pre-existence of God from all eternity, stating" that God was the oldest of all beings, for he existed without a previous cause even in the way of generation; that the world was the most beautiful of all things; for it was created by God. "[97]

Nicholas Molinari has recently argued that Thales was influenced by the archaic water deityAcheloios,who was equated with water and worshipped in Miletus during Thales's life. For evidence, he points to the fact thathydormeant specifically "fresh water", and also that Acheloios was seen as a shape-shifter in myth and art, so able to become anything. He also points out that the rivers of the world were seen as the "sinewsof Acheloios "in antiquity, and this multiplicity of deities is reflected in Thales's idea that" all things are full of gods. "[98]

Death and legacy

Diogenes Laërtius quotes Apollodorus as saying that Thales died at the age of 78 during the 58thOlympiad(548–545 BC) and attributes his death toheat strokeand thirst while watching the games.[99]

Influence

Detail of Thales fromThe Beginnings of Science(1906) byVeloso Salgado

As the first philosopher and mathematician, Thales had a profound influence on other Greek thinkers and therefore onWesternhistory. However, due to the scarcity of sources concerning Thales and the discrepancies between the accounts given in the sources that have survived, there is a scholarly debate over the extent of the influence Thales had and on which of the Greek philosophers and mathematicians that came after him.[m]

The first three philosophers in the Western tradition were allcosmologistsfrom Miletus, and Thales was the very first, followed byAnaximander,who was followed in turn byAnaximenes.They have been dubbed theMilesian school.According to theSuda,Thales had been the "teacher and kinsman" of Anaximander.[101]Rather than water, Anaximander held all was made ofapeironor the unlimited; while Anaximenes, the successor of Anaximander, perhaps more like Thales with water, held that everything was composed ofair.[102]

John Burnet(1892) noted[103]

Lastly, we have one admitted instance of a philosophic guild, that of thePythagoreans.And it will be found that the hypothesis, if it is to be called by that name, of a regular organisation of scientific activity will alone explain all the facts. The development of doctrine in the hands of Thales,Anaximander,andAnaximenes,for instance, can only be understood as the elaboration of a single idea in a school with a continuous tradition.

As two of the first Greek mathematicians, Thales is also considered an influence on Pythagoras. According to Iamblichus, Pythagoras "had benefited by the instruction of Thales in many respects, but his greatest lesson had been to learn the value of saving time."[104]Early sources[which?]report that Pythagoras, in this story a pupil of Anaximander, visited Thales as a young man, and that Thales advised him to travel to Egypt to further his philosophical and mathematical studies.

Thales was also considered the teacher of the astronomer Mandrolytus of Priene.[105]It is possible he was also the teacher ofCleostratusof Tenedos.[106]

Notes

  1. ^This use of hearsay and a lack of citing original sources leads some historians, like Dicks and Werner Jaeger, to view the whole idea of pre-Socratic philosophy as a construct from a later age, "fashioned during the two or three generations from Plato to the immediate pupils of Aristotle".[4]
  2. ^In addition, his supposed mother, Cleobulina, has also been described as his companion instead of his mother.[17]
  3. ^The exact meaning of this use of the wordpolosis unknown, current theories include: "the heavenly dome", "the tip of the axis of the celestial sphere", or a spherical concave sundial.[30]
  4. ^The same story, however, asserts that Thales emigrated to Miletus; and that he did not become a student of nature until after his political career. This story has to be rejected if one is to believe that Thales was a native of Miletus, and other typical things about him like his prediction of the eclipse.
  5. ^The aphorism has also been attributed to various other philosophers.Diogenes Laërtiusattributes it to Thales[34][35]but notes that Antisthenes in hisSuccessions of Philosophersattributes it instead toPhemonoe,a mythical Greek poet. The Roman poetJuvenalquotes the phrase in Greek and states that the precept descendede caelo(from heaven).[36]Other names of potential includePythagoras[37]andHeraclitus.[38]
  6. ^Historian Abraham Feldman wrote that for Thales "...water united all things...all whatness is wetness".[47]
  7. ^Feldman notes "The social significance of water in the time of Thales induced him to discern through hardware and dry-goods, through soil and sperm, blood, sweat and tears, one fundamental fluid stuff...water, the most commonplace and powerful material known to him."[47]
  8. ^While some historians, such as Colin R. Fletcher, note there could have been a precursor to Thales named by Eudemus, without the work "the question becomes mere speculation."[52]Fletcher grants there is no other viable contender to the title of first Greek mathematician, and that Thales qualifies as a practitioner in the field. "Thales had at his command the techniques of observation, experimentation, superposition and deduction... he has proved himself mathematician."[52]
  9. ^A right triangle with two equal legs is a 45-degree right triangle, all of which are similar. The length of the pyramid's shadow measured from the center of the pyramid at that moment must have been equal to its height.[64]
  10. ^Thesekedis at the base of problems 56, 57, 58, 59 and 60 of theRhind papyrus— an ancient Egyptian mathematical document.
  11. ^According to Diogenes Laertius, the Nautical Astronomy attributed to Thales was written byPhocusof Samos.
  12. ^The Scottish philosopherAdam Smithonce similarly, absent-mindedly fell into atannerypit.[87]
  13. ^Edmund Husserl[100]attempts to capture the new movement as follows. Philosophical man is a "new cultural configuration" based in stepping back from "pregiven tradition" and taking up a rational "inquiry into what is true in itself;" that is, an ideal of truth.

References

  1. ^abcRussell, Bertrand(1945).A History of Western Philosophy.Simon & Schuster.
  2. ^Translation of his biography on Thales:ThalesArchived9 February 2008 at theWayback Machine,classicpersuasion site; original Greek text, underΘΑΛΗΣ,the Library of Ancient Texts Online site.
  3. ^SeeMcKirahan, Richard D. Jr. (1994).Philosophy Before Socrates.Indianapolis: Hackett. p.5.ISBN978-0-87220-176-7.
  4. ^Jaeger, Werner (1948).Aristotle(2nd ed.). p. 454.
  5. ^abHerodotus,1.74.2,and A. D. Godley's footnote 1; Pliny,2.9 (12)and Bostock's footnote 2.
  6. ^Cohen, Mark S.; Curd, Patricia; Reeve, C. D. C. (2011).Readings in Ancient Greek Philosophy (Fourth Edition): From Thales to Aristotle.Indianapolis, Indiana: Hackett Publishing. p. 10.ISBN978-1603846073.
  7. ^abFrank N. Magill,The Ancient World: Dictionary of World Biography,Volume 1,Routledge, 2003ISBN1135457395
  8. ^abcdeKirk, G. S.; Raven, J. E. (1957)."Chapter II: Thales of Miletus".The Presocratic Philosophers.Cambridge University Press. pp. 74–98.
  9. ^Freely, John (2012).The Flame of Miletus: The Birth of Science in Ancient Greece (And How It Changed the World).London: I. B. Tauris & Co. Ltd. p. 7.ISBN978-1-78076-051-3.Retrieved1 October2017.
  10. ^Lawson, Russell M. (2004).Science in the Ancient World: An Encyclopedia.Santa Barbara, California; Denver, Colorado; and Oxford, England: ABC CLIO. pp. 234–235.ISBN978-1-85109-534-6.
  11. ^Thatcher, Oliver J. (2004).The Library Of Original Sources: The Greek World.The Minerva Group, Inc. p. 138.ISBN978-1-4102-1402-7.
  12. ^Nietzsche, Friedrich (2001).The Pre-Platonic Philosophers.University of Illinois Press. p. 23.ISBN978-0252025594.
  13. ^abAlexander Herda. Burying a sage: the heroon of Thales in the agora of Miletos: With remarks on some other excavated Heroa and on cults and graves of the mythical founders of the city. 2èmes Rencontres d'archéologie de l'IFEA: Le Mort dans la ville Pratiques, contextes et impacts des inhumations intra-muros en Anatolie, du début de l'Age du Bronze à l'époque romaine., Nov 2011, Istanbul, Turkey. pp. 67–122
  14. ^abYust, Walter (1952).Encyclopaedia Britannica: A New Survey of Universal Knowledge.Encyclopaedia Britannica.p. 13.
  15. ^Guthrie, W. K. C. (1978).A History of Greek Philosophy: The Earlier Presocratics and the Pythagoreans.Vol. 1. Cambridge University Press. p. 50.ISBN978-0-521-29420-1.
  16. ^Goodman, Ellen (1995).The Origins of the Western Legal Tradition: From Thales to the Tudors.Federation Press. p. 9.ISBN978-1-86287-181-6.
  17. ^Plant, I. M. (2004).Women Writers of Ancient Greece and Rome: An Anthology.Norman: University of Oklahoma Press. pp. 29–32.
  18. ^Plutarch (1952). "Solon". In Robert Maynard Hutchins (ed.).Lives.Great Books of the Western World. Vol. 14. Chicago: William Benton. p. 66.
  19. ^Riedweg, Christoph (2005) [2002],Pythagoras: His Life, Teachings, and Influence,Ithaca, New York: Cornell University Press,ISBN978-0-8014-7452-1p. 7
  20. ^Plutarch, Life of Solon § 2.4
  21. ^O'Grady, Patricia F. (2017).Thales of Miletus: The Beginnings of Western Science and Philosophy.Taylor & Francis. p. 263.ISBN978-1-351-89537-8.
  22. ^Hamlyn, David W. (2002).Being a Philosopher: The History of a Practice.Routledge. p. 7.ISBN978-1-134-97101-5.
  23. ^abcRusso, Lucio (2013).The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn.Translated by Levy, Silvio. Springer. p. 33.ISBN978-3642189043.
  24. ^Harrison, Frederic(1892).The new calendar of great men: biographies of the 558 worthies of all ages.London and New York: MacMillan & Co. p. 92.
  25. ^Plutarch,On Isis And Osiris,ch. 10.
  26. ^Ferguson, Kitty(2011).Pythagoras: His Lives and the Legacy of a Rational Universe.Icon Books Ltd. p. 28.ISBN978-1-84831-250-0.
  27. ^abcCooke, Roger L. (2005).The History of Mathematics: A Brief Course.John Wiley & Sons, Inc.
  28. ^abcdeDicks, D. R. (November 1959). "Thales".The Classical Quarterly.9(2): 294–309.doi:10.1017/S0009838800041586.S2CID246881067.
  29. ^Diogenes Laertius (II, 1)
  30. ^"LacusCurtius • Ancient Astronomy: Polus (Smith's Dictionary, 1875)".penelope.uchicago.edu.
  31. ^Zhmud, Leonid (2006).The Origin of the History of Science in Classical Antiquity.Die Deutsche Bibliothek.
  32. ^Diogenes Laërtius 1.22
  33. ^"SOL Search".www.cs.uky.edu.
  34. ^LivesI.40
  35. ^"SOL Search".www.cs.uky.edu.
  36. ^Satires11.27
  37. ^Vico, Giambattista; Visconti, Gian Galeazzo (1993).On humanistic education: (six inaugural orations, 1699–1707).Six Inaugural Orations, 1699–1707 From the Definitive Latin Text, Introduction, and Notes of Gian Galeazzo Visconti. Cornell University Press. p.4.ISBN0801480876.
  38. ^Doctoral thesis, "Know Thyself in Greek and Latin Literature," Eliza G. Wilkens, U. Chi, 1917, p. 12 (online).
  39. ^Laërtius 1925,§ 28
  40. ^Diogenes Laërtius1.25
  41. ^abHerodotus.The Histories.Translated by Rawlinson, George.
  42. ^abO'Grady, Patricia F.(2017).Thales of Miletus: The Beginnings of Western Science and Philosophy.Taylor & Francis. p. 102.ISBN978-1-351-89536-1.
  43. ^abcAristotle,MetaphysicsAlpha, 983b.http://data.perseus.org/citations/urn:cts:greekLit:tlg0086.tlg025.perseus-eng1:1.983b
  44. ^abSmith, William,ed. (1870)."Thales".Dictionary of Greek and Roman Biography and Mythology.p. 1016.
  45. ^Plutarch, Life of Solon, 3.5
  46. ^Diogenes Laërtius.Lives of the Eminent Philosophers.Book 1, paragraph 27.
  47. ^abFeldman, Abraham (October 1945). "Thoughts on Thales".The Classical Journal.41(1): 4–6.ISSN0009-8353.JSTOR3292119.
  48. ^Aristotle."Book I 983b".Aristotle, Metaphysics.Perseus Project.
  49. ^§ 3
  50. ^Laërtius 1925,§ 35
  51. ^Boyer 1989,p. 43 (3rd ed.)
  52. ^abcdefFletcher, Colin R. (December 1982). "Thales – our founder?".The Mathematical Gazette.66(438): 267.doi:10.2307/3615512.JSTOR3615512.S2CID125626522.
  53. ^Nicomachus of Gerasa (1926)."Introduction to Arithmetic".Macmillan.
  54. ^A History of Greek Mathematics, Heath, p. 70
  55. ^abBulmer-Thomas, Ivor(1939)."Thales".Selections Illustrating the History of Greek Mathematics.Vol. 1. Harvard University Press. pp. 164–169.
  56. ^Sidoli, Nathan (2018)."Greek mathematics"(PDF).In Jones, A.; Taub, L. (eds.).The Cambridge History of Science: Vol. 1, Ancient Science.Cambridge University Press. pp. 345–373.
  57. ^Shute, William George; Shirk, William W.; Porter, George F. (1960).Plane and Solid Geometry.American Book Company.pp. 25–27.
  58. ^Boyer 1989,p. "Ionia and the Pythagoreans" p. 43.
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  60. ^Boyer, Carl B. andMerzbach, Uta C.(2010).A History of Mathematics.John Wiley and Sons, Chapter IV.ISBN0-470-63056-6
  61. ^Heath, Thomas L. (1956).The Thirteen Books of Euclid's Elements.Vol. 2 (Books 3–9) (2nd ed.). Dover. p. 61.ISBN0486600890.Originally published by Cambridge University Press. 1st edition 1908, 2nd edition 1926.
  62. ^canto 13, lines 101–102
  63. ^Plutarch, Moralia, The Dinner of the Seven Wise Men,147A
  64. ^J J O'Connor and E F Robertson
  65. ^"Ars Quatuor Coronatorum: Being the Transactions of the Quatuor Coronati Lodge No. 2076, London".W. J. Parre H, Limited. 10 June 1897.
  66. ^History of Astronomy, by Richard Perason, p. 65
  67. ^Proclus,In Euclidem,352
  68. ^Plutarch,De Pythiae oraculis,18.
  69. ^D.L. I.34
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  71. ^Harris, Roy (2005).The Semantics of Science.Continuum International. p. 31.
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  85. ^Theaetetus (174 A)
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Works cited

Further reading

  • Couprie, Dirk L. (2011).Heaven and Earth in Ancient Greek Cosmology: from Thales to Heraclides Ponticus.Springer.ISBN978-1441981158.
  • Luchte, James (2011).Early Greek Thought: Before the Dawn.London: Bloomsbury Publishing.ISBN978-0567353313.
  • O'Grady, Patricia F. (2002).Thales of Miletus: The Beginnings of Western Science and Philosophy.Western Philosophy Series. Vol. 58. Ashgate.ISBN978-0754605331.
  • Mazzeo, Pietro (2010).Talete, il primo filosofo.Bari: Editrice Tipografica.
  • Molinari, Nicholas J. (2022).Acheloios, Thales, and the Origin of Philosophy: A Response to the Neo-Marxians.Archaeopress.ISBN9781803270869.
  • Priou, Alex (2016). "'...Going Further On Down the Road...': The Origin and Foundations of Milesian Thought."The Review of Metaphysics70, 3–31.
  • Russell, Bertrand (1947).A History of Western Philosophy.Traditio Praesocratica. US: Simon & Schuster publisher.ISBN0-415-32505-6.
  • Wöhrle, Georg., ed. (2014).The Milesians: Thales. Translation and additional material by Richard McKirahan.Traditio Praesocratica. Vol. 1. Walter de Gruyter.ISBN978-3-11-031525-7.
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