Famous Philosophers

THALES OF MILETUS
(Θαλῆς ὁ Μιλήσιος (pronounced /ˈθeɪliːz/ or "THEH-leez") , ca. 624 BC–ca. 546 BC), was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition.[2] According to Bertrand Russell, "Philosophy begins with Thales."[3]
Life: Thales lived around the mid 620s–547 BCE and was born in the city of Miletus. Miletus was an ancient Greek Ionian city on the western coast of Asia Minor (in what is today the Aydin Province of Turkey) near the mouth of the Maeander River.
Background: The dates of Thales' life are not known precisely. The time of his life is roughly established by a few dateable events mentioned in the sources and an estimate of his length of life. According to Herodotus, Thales once predicted a solar eclipse which has been determined by modern methods to have been on May 28, 585 BC.[4] Diogenes Laërtius quotes the chronicle of Apollodorus as saying that Thales died at 78 in the 58th Olympiad, and Sosicrates as reporting that he was 90 at his death.
As for his origin, the majority opinion considers Thales to have been a Milesian by descent,[1][5] though Herodotus,[6] Duris of Samos and Democritus, according to Diogenes Laërtius,[7] and others[8] suggest that his parents were Phoenician. After repeating a story that Thales had been naturalized, or recently enrolled as a citizen, Diogenes Laërtius informs us that "a more common statement is that he was a native Milesian, of noble extraction."[7] Diogenes Laërtius and others further suggested that Thales was the son of Examyas and Cleobulina and that they were of the Thelidae family (hence Thales), who were of noble descent from Agenor and Cadmus of ancient Thebes, Greece.
Diogenes Laërtius reports two stories about Thales' family life, one that he married and had a son, Cybisthus or Cybisthon, or adopted his nephew of the same name. The second is 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.
Thales involved himself in many activities, taking the role of an innovator. Some say that he left no writings, others that he wrote "On the Solstice" and "On the Equinox". Neither have survived. Diogenes Laërtius quotes letters of Thales to Pherecydes and Solon, offering to review the book of the former on religion, and offering to keep company with the latter on his sojourn from Athens. Thales identifies the Milesians as Athenians.[9]

Politics: Thales’ political life had mainly to do with the involvement of the Ionians in the defense of Anatolia against the growing power of the Persians, who were then new to the region. A king had come to power in neighboring Lydia, Croesus, who was somewhat too aggressive for the size of his army. He had conquered most of the states of coastal Anatolia, including the cities of the Ionians. The story is told in Herodotus.[11]
The Lydians were at war with the Medes, a remnant of the first wave of Iranians in the region, over the issue of refuge the Lydians had given to some Scythian soldiers of fortune inimical to the Medes. The war endured for five years, but in the sixth an eclipse of the sun (mentioned above) spontaneously halted a battle in progress (the Battle of Halys).

Ethics: The ethics of Thales can be estimated from the sayings attributed to him, reported in Diogenes Laertius.[13] First, he recognizes a transcendental God, who has neither beginning nor end. He believes that God is just and expects men to behave justly. Neither men being unjust (ἄδικος) nor thinking injustice escape the notice of the Gods (θεοί). In this form of polytheism the transcendental god expresses himself through gods, so that a man can say θεοί and mean God.
Thales’ idea of justice includes both the letter of the law and the spirit of the law. Concerning the former, he advises that adultery and perjury about it in court are equally bad. His value of civic law is supplemented by some practical advice. Expect the same support from your children that you give to your parents. Do not let talk influence you against those whom you have come to trust. Be rich, yes, for success is sweet. However, do not be rich badly (κακῶς).
As to the spirit of the law, we find Thales expressing a now well-known principle for leading the best (ἄριστα) and most just (δικαιότατα) life:
ἃ τοῖς ἄλλοις ἐπιτιμῶμεν, αὐτοὶ μὴ δρῶμεν
“That for which we blame others, let us not do ourselves”
This rejection of hypocrisy is found in many major world religions. For example, one of the foundational principles of Jewish law is, “Do not unto thy neighbor what is hateful to thyself.” His view of enemies is somewhat more severe than the Old Testament, which supports an equal exchange of penalties: an eye for an eye, tooth for a tooth etc (Exodus 21:23–25). According to Thales, a man can better bear adversity if he sees that his enemies are worse off.
Thales' view was that men are better than women and Greeks are better than barbarians. (He stated this despite the fact that his proudest ancestor was dethroned in Thebes for being a barbarian.)
Thales was not Democratic. One story has him living with Thrasybulus, tyrant of Miletus. In his letter to Solon he offers to live elsewhere with him, seeing that Solon finds tyranny so offensive. Ancient philosophers in general tended to support benign tyranny, such as Plato’s ideal philosopher-king. Unquestionably, sages were more at home with absolutism than with democratic forms of government. They could not resist undertaking to reform the morals of the citizens, with well-known results. Philosophers' support of tyrants generally had poor results; the outcome was generally the expulsion or murder of the tyrant and the massacre of the philosophers.
According to Thales, a happy man is defined as one
ὁ τὸ μὲν σῶμα ὑγιής, τὴν δὲ ψυχὴν εὔπορος, τὴν δὲ φύσιν εὐπαίδευτος
“Who is healthy in body, resourceful in soul and of a readily teachable nature”
which is similar to the Roman “Mens sana in corpore sano”, our “sane mind in a healthy body.” Perhaps Thales did exercise, but he did not cultivate the body, as he preached not beautifying the appearance (ὄψις) but practicing the good, not the bad.
Theories: Before Thales, the Greeks explained the origin and nature of the world through myths of anthropomorphic gods and heroes. Phenomena such as lightning or earthquakes were attributed to actions of the gods.
Nature as the principles in the form of matter
In contrast to these mythological explanations, Thales attempted to find naturalistic explanations of the world, without reference to the supernatural. He explained earthquakes by hypothesizing that the Earth floats on water, and that earthquakes occur when the Earth is rocked by waves.
Thales, according to Aristotle, asked what was the nature (Greek physis, Latin natura) of the object so that it would behave in its characteristic way. Physis (φύσις) comes from phyein (φύειν), "to grow", related to our word "be".[17] (G)natura is the way a thing is "born",[18] again with the stamp of what it is in itself.
Aristotle[19] characterizes most of the philosophers "at first" (πρῶτον) as thinking that the "principles in the form of matter were the only principles of all things", where "principle" is arche, "matter" is hyle ("wood") and "form" is eidos.
"Principle" translates arche, but the two words do not have precisely the same meaning. A principle of something is merely prior (related to pro-) to it either chronologically or logically. An arche (from αρχειν, "to rule") dominates an object in some way. If the arche is taken to be an origin, then specific causality is implied; that is, B is supposed to be characteristically B just because it comes from A, which dominates it.
The archai that Aristotle had in mind in his well-known passage on the first Greek scientists are not necessarily chronologically prior to their objects, but are constituents of it. For example, in pluralism objects are composed of earth, air, fire and water, but those elements do not disappear with the production of the object. They remain as archai within it, as do the atoms of the atomists.
What Aristotle is really saying is that the first philosophers were trying to define the substance(s) of which all material objects are composed. As a matter of fact, that is exactly what modern scientists are trying to do in nuclear physics, which is a second reason why Thales is described as the first scientist.
Water as a first principle: Thales' most famous belief was his cosmological doctrine, which held that the world originated from water. Aristotle considered this belief roughly equivalent to the later ideas of Anaximenes, who held that everything in the world was composed of air.
The best explanation of Thales' view is the following passage from Aristotle's Metaphysics.[20] The passage contains words from the theory of matter and form that were adopted by science with quite different meanings.
"That from which is everything that exists (ἅπαντα τὰ ὄντα) and from which it first becomes (ἐξ οὗ γίγνεται πρῶτου) and into which it is rendered at last (εἰς ὃ φθείρεται τελευταῖον), its substance remaining under it (τῆς μὲν οὐσίας ὑπομενούσης), but transforming in qualities (τοῖς δὲ πάθεσι μεταβαλλούσης), that they say is the element (στοιχεῖον) and principle (ἀρχήν) of things that are."
And again:
"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... Thales the founder of this type of philosophy says that it is water."[21]
Aristotle's depiction of the change problem and the definition of substance is clear. If an object changes, is it the same or different? In either case how can there be a change from one to the other? The answer is that the substance "is saved", but acquires or loses different qualities (πάθη, the things you "experience").
A deeper dip into the waters of the theory of matter and form is properly reserved to other articles. The question for this article is, how far does Aristotle reflect Thales? He was probably not far off, and Thales was probably an incipient matter-and-formist.
The essentially non-philosophic Diogenes Laertius states that Thales taught as follows:
"Water constituted (ὑπεστήσατο, 'stood under') the principle of all things."[22]
Heraclitus Homericus[23] states that Thales drew his conclusion from seeing moist substance turn into air, slime and earth. It seems clear that Thales viewed the Earth as solidifying from the water on which it floated and which surrounded Ocean.
Beliefs in divinity: Thales applied his method to objects that changed to become other objects, such as water into earth (he thought). But what about the changing itself? Thales did address the topic, approaching it through magnets and amber, which, when electrified by rubbing, attracts also. A concern for magnetism and electrification never left science, being a major part of it today.
How was the power to move other things without the mover’s changing to be explained? Thales saw a commonality with the powers of living things to act. The magnet and the amber must be alive, and if that were so, there could be no difference between the living and the dead. When asked why he didn’t die if there was no difference, he replied “because there is no difference.”
Aristotle defined the soul as the principle of life, that which imbues the matter and makes it live, giving it the animation, or power to act. The idea did not originate with him, as the Greeks in general believed in the distinction between mind and matter, which was ultimately to lead to a distinction not only between body and soul but also between matter and energy.
If things were alive, they must have souls. This belief was no innovation, as the ordinary ancient populations of the Mediterranean did believe that natural actions were caused by divinities. Accordingly, the sources say that Thales believed all things possessed divinities. In their zeal to make him the first in everything they said he was the first to hold the belief, which even they must have known was not true.
However, Thales was looking for something more general, a universal substance of mind. That also was in the polytheism of the times. Zeus was the very personification of supreme mind, dominating all the subordinate manifestations. From Thales on, however, philosophers had a tendency to depersonify or objectify mind, as though it were the substance of animation per se and not actually a god like the other gods. The end result was a total removal of mind from substance, opening the door to a non-divine principle of action. This tradition persisted until Einstein, whose cosmology is quite a different one and does not distinguish between matter and energy.
Classical thought, however, had proceeded only a little way along that path. Instead of referring to the person, Zeus, they talked about the great mind:
"Thales", says Cicero,[24] "assures that water is the principle of all things; and that God is that Mind which shaped and created all things from water."
The universal mind appears as a Roman belief in Virgil as well:
"In the beginning, SPIRIT within (spiritus intus) strengthens Heaven and Earth,
The watery fields, and the lucid globe of Luna, and then --
Titan stars; and mind (mens) infused through the limbs
Agitates the whole mass, and mixes itself with GREAT MATTER (magno corpore)"[25]

ANAXIMANDER
(Ancient Greek: Ἀναξίμανδρος) (c. 610 BC–c. 546 BC) was a pre-Socratic Greek philosopher who lived in Miletus, a city of Ionia. He belonged to the Milesian school and learned the teachings of his master Thales. He succeeded him and became the second master of that school where he counted Anaximenes and Pythagoras amongst his pupils.
Little of his life and work is known today. According to available historical documents, he is the first philosopher known to have written down his studies[2], although only one fragment of his work remains. Fragmentary testimonies found in documents after his death provide a portrait of the man.
Anaximander was one of the earliest Greek thinkers at the start of the Axial Age, the period from approximately 700 BC to 200 BC, during which similarly revolutionary thinking appeared in China, India, Iran, the Near East, and Ancient Greece. He was an early proponent of science and tried to observe and explain different aspects of the universe, with a particular interest in its origins, claiming that nature is ruled by laws, just like human societies, and anything that disturbs the balance of nature does not last long.[3] Like many thinkers of his time, his contributions to philosophy relate to many disciplines. In astronomy, he tried to describe the mechanics of celestial bodies in relation to the Earth. In physics, he postulated that the indefinite (or apeiron) was the source of all things. His knowledge of geometry allowed him to introduce the gnomon in Greece. He created a map of the world that contributed greatly to the advancement of geography. He was also involved in the politics of Miletus as he was sent as a leader to one of its colonies.
With his assertion that physical forces, rather than supernatural means, create order in the universe, Anaximander can be considered the first true scientist. He is known to have conducted the earliest recorded scientific experiment.[4]
Apeiron: Main article: Apeiron (cosmology)
The bishop Hippolytus of Rome (I, 5), and the later 6th century Byzantine philosopher Simplicius of Cilicia, attribute to Anaximander the earliest use of the word apeíron (ἄπειρον/infinite or limitless) to designate the original principle. He was the first philosopher to employ, in a philosophical context, the term arkhế (ἀρχή), which until then had meant beginning or origin. For him, it became no longer a mere point in time, but a source that could perpetually give birth to whatever will be.
Aristotle writes (Metaphysics, I III 3-4) that the Pre-Socratics were searching for the element that constitutes all things. While each pre-Socratic philosopher gave a different answer as to the identity of this element (water for Thales, air for Anaximenes, fire for Heraclitus), Anaximander understood the beginning or first principle to be an endless, unlimited primordial mass (apeiron), subject to neither old age nor decay, that perpetually yielded fresh materials from which everything we perceive is derived.[8] He proposed the theory of the apeiron in direct response to the earlier theory of his teacher, Thales, who had claimed that the primary substance was water.
For Anaximander, the principle of things, the constituent of all substances, is nothing determined and not an element such as water in Thales' view. Neither is it something halfway between air and water, or between air and fire, thicker than air and fire, or more subtle than water and earth.[9] Anaximander argues that water cannot embrace all of the opposites found in nature — for example, water can only be wet, never dry — and therefore cannot be the one primary substance; nor could any of the other candidates. He postulated the apeiron as a substance that, although not directly perceptible to us, could explain the opposites he saw around him.
Anaximander explains how the four elements of ancient physics (air, earth, water and fire) are formed, and how Earth and terrestrial beings are formed through their interactions. Unlike other Pre-Socratics, he never defines this principle precisely, and it has generally been understood (e.g., by Aristotle and by Saint Augustine) as a sort of primal chaos. According to him, the Universe originates in the separation of opposites in the primordial matter. It embraces the opposites of hot and cold, wet and dry, and directs the movement of things; an entire host of shapes and differences then grow that are found in "all the worlds" (for he believed there were many).
Anaximander maintains that all dying things are returning to the element from which they came (apeiron). The one surviving fragment of Anaximander's writing deals with this matter. Simplicius transmitted it as a quotation, which describes the balanced and mutual changes of the elements:[10]
Whence things have their origin, Thence also their destruction happens, According to necessity; For they give to each other justice and recompense For their injustice In conformity with the ordinance of Time.
This concept of returning to the element of origin was often revisited afterwards, notably by Aristotle,[11] and by the Greek tragedian Euripides: "what comes from earth must return to earth."[12] Strangely, it also finds a parallel in the book of Genesis, in the phrase, "For dust you are and to dust you will return".
Cosmology: Map of Anaximander's universe
Anaximander's bold use of non-mythological explanatory hypotheses considerably distinguishes him from previous cosmology writers such as Hesiod. It confirms that pre-Socratic philosophers were making an early effort to demythify physical processes. His major contribution to history was writing the oldest prose document about the Universe and the origins of life; for this he is often called the "Father of Cosmology" and founder of astronomy. However, pseudo-Plutarch states that he still viewed celestial bodies as deities.[13]
Anaximander was the first to conceive a mechanical model of the world. In his model, the Earth floats very still in the centre of the infinite, not supported by anything. It remains "in the same place because of its indifference", a point of view that Aristotle considered ingenious, but false, in On the Heavens.[14] Its curious shape is that of a cylinder[15] with a height one-third of its diameter. The flat top forms the inhabited world, which is surrounded by a circular oceanic mass.
Such a model allowed the concept that celestial bodies could pass under it. It goes further than Thales’ claim of a world floating on water, for which Thales faced the problem of explaining what would contain this ocean, while Anaximander solved it by introducing his concept of infinite (apeiron).
At the origin, after the separation of hot and cold, a ball of flame appeared that surrounded Earth like bark on a tree. This ball broke apart to form the rest of the Universe. It resembled a system of hollow concentric wheels, filled with fire, with the rims pierced by holes like those of a flute. Consequently, the Sun was the fire that one could see through a hole the same size as the Earth on the farthest wheel, and an eclipse corresponded with the occlusion of that hole. The diameter of the solar wheel was twenty-seven times that of the Earth (or twenty-eight, depending on the sources)[16] and the lunar wheel, whose fire was less intense, eighteen (or nineteen) times. Its hole could change shape, thus explaining lunar phases. The stars and the planets, located closer,[17] followed the same model.[18]
Anaximander was the first astronomer to consider the Sun as a huge mass, and consequently, to realize how far from Earth it might be, and the first to present a system where the celestial bodies turned at different distances. Furthermore, according to Diogenes Laertius (II, 2), he built a celestial sphere. This invention undoubtedly made him the first to realize the obliquity of the Zodiac as the Roman philosopher Pliny the Elder reports in Natural History (II, 8). It is a little early to use the term ecliptic, but his knowledge and work on astronomy confirm that he must have observed the inclination of the celestial sphere in relation to the plane of the Earth to explain the seasons. The doxographer and theologian Aetius attributes to Pythagoras the exact measurement of the obliquity.
Multiple worlds: According to Simplicius, Anaximander already speculated on the plurality of worlds, similar to atomists Leucippus and Democritus, and later philosopher Epicurus. These thinkers supposed that worlds appeared and disappeared for a while, and that some were born when others perished. They claimed that this movement was eternal, "for without movement, there can be no generation, no destruction".[19]
In addition to Simplicius, Hippolytus[20] reports Anaximander's claim that from the infinite comes the principle of beings, which themselves come from the heavens and the worlds (several doxographers use the plural when this philosopher is referring to the worlds within,[21] which are often infinite in quantity). Cicero writes that he attributes different gods to the countless worlds.[22]
This theory places Anaximander close to the Atomists and the Epicureans who, more than a century later, also claimed that an infinity of worlds appeared and disappeared. In the timeline of the Greek history of thought, some thinkers conceptualized a single world (Plato, Aristotle, Anaxagoras and Archelaus), while others instead speculated on the existence of a series of worlds, continuous or non-continuous (Anaximenes, Heraclitus, Empedocles and Diogenes).
Meteorological phenomena: Anaximander attributed some phenomena, such as thunder and lightning, to the intervention of elements, rather than to divine causes.[23] In his system, thunder results from the shock of clouds hitting each other; the loudness of the sound is proportionate with that of the shock. Thunder without lightning is the result of the wind being too weak to emit any flame, but strong enough to produce a sound. A flash of lightning without thunder is a jolt of the air that disperses and falls, allowing a less active fire to break free. Thunderbolts are the result of a thicker and more violent air flow.[24]
He saw the sea as a remnant of the mass of humidity that once surrounded Earth.[25] A part of that mass evaporated under the sun's action, thus causing the winds and even the rotation of the celestial bodies, which he believed were attracted to places where water is more abundant.[26] He explained rain as a product of the humidity pumped up from Earth by the sun.[5] For him, the Earth was slowly drying up and water only remained in the deepest regions, which someday would go dry as well. According to Aristotle's Meteorology (II, 3), Democritus also shared this opinion.
Origin of humankind: Anaximander speculated about the beginnings and origin of animal life. Taking into account the existence of fossils, he claimed that animals sprang out of the sea long ago. The first animals were born trapped in a spiny bark, but as they got older, the bark would dry up and break.[27] As the early humidity evaporated, dry land emerged and, in time, humankind had to adapt. The 3rd century Roman writer Censorinus reports:
“ Anaximander of Miletus considered that from warmed up water and earth emerged either fish or entirely fishlike animals. Inside these animals, men took form and embryos were held prisoners until puberty; only then, after these animals burst open, could men and women come out, now able to feed themselves.[28]
„

Anaximander put forward the idea that humans had to spend part of this transition inside the mouths of big fish to protect themselves from the Earth's climate until they could come out in open air and lose their scales.[29] He thought that, considering humans' extended infancy, we could not have survived in the primeval world in the same manner we do presently.
Even though he had no theory of natural selection, some people consider him as evolution's most ancient proponent. The theory of an aquatic descent of man was re-conceived centuries later as the aquatic ape hypothesis. These pre-Darwinian concepts may seem strange, considering modern knowledge and scientific methods, because they present complete explanations of the universe while using bold and hard-to-demonstrate hypotheses. However, they illustrate the beginning of a phenomenon sometimes called the "Greek miracle": men try to explain the nature of the world, not with the aid of myths or religion, but with material principles. This is the very principle of scientific thought, which was later advanced further by improved research methods.

PYTHAGORAS OF SAMOS
(Greek: Ὁ Πυθαγόρας ὁ Σάμιος, Pythagoras the Samian, or simply Ὁ Πυθαγόρας; born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy. Herodotus referred to him as "the most able philosopher among the Greeks". His name led him to be associated with Pythian Apollo; Aristippus explained his name by saying, "He spoke (agor-) the truth no less than did the Pythian (Pyth-)," and Iamblichus tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and beneficial to humankind.[1]
He is best known for the Pythagorean theorem, which bears his name. Known as "the father of numbers", Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings. We do know that Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. According to Iamblichus, Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons."
He was the first man to call himself a philosopher, or lover of wisdom,[2] and Pythagorean ideas exercised a marked influence on Plato. Unfortunately, very little is known about Pythagoras because none of his writings have survived. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.
Pythagoreans: The organization was in some ways a school, in some ways a brotherhood, and in some ways a monastery. It was based upon the religious teachings of Pythagoras and was very secretive. At first, the school was highly concerned with the morality of society. Members were required to live ethically, love one another, share political beliefs, practice pacifism, and devote themselves to the mathematics of nature.
Pythagoras's followers were commonly called "Pythagoreans". They are generally accepted as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.
The Pythagoreans observed a rule of silence called echemythia, the breaking of which was punishable by death. This was because the Pythagoreans believed that a man's words were usually careless and misrepresented him and that when someone was "in doubt as to what he should say, he should always remain silent". Another rule that they had was to help a man "in raising a burden, but do not assist him in laying it down, for it is a great sin to encourage indolence", and they said "departing from your house, turn not back, for the furies will be your attendants"; this axiom reminded them that it was better to learn none of the truth about mathematics, God, and the universe at all than to learn a little without learning all. (The Secret Teachings of All Ages by Manly P. Hall).
In his biography of Pythagoras (written seven centuries after Pythagoras's time), Porphyry stated that this silence was "of no ordinary kind." The Pythagoreans were divided into an inner circle called the mathematikoi ("mathematicians") and an outer circle called the akousmatikoi ("listeners"). Porphyry wrote "the mathematikoi learned the more detailed and exactly elaborated version of this knowledge, the akousmatikoi (were) those who had heard only the summary headings of his (Pythagoras's) writings, without the more exact exposition." According to Iamblichus, the akousmatikoi were the exoteric disciples who listened to lectures that Pythagoras gave out loud from behind a veil.
The akousmatikoi were not allowed to see Pythagoras and they were not taught the inner secrets of the cult. Instead they were taught laws of behavior and morality in the form of cryptic, brief sayings that had hidden meanings. The akousmatikoi recognized the mathematikoi as real Pythagoreans, but not vice versa. After the murder of a number of the mathematikoi by the cohorts of Cylon, a resentful disciple, the two groups split from each other entirely, with Pythagoras's wife Theano and their two daughters leading the mathematikoi.
Theano, daughter of the Orphic initiate Brontinus, was a mathematician in her own right. She is credited with having written treatises on mathematics, physics, medicine, and child psychology, although nothing of her writing survives. Her most important work is said to have been a treatise on the principle of the golden mean. In a time when women were usually considered property and relegated to the role of housekeeper or spouse, Pythagoras allowed women to function on equal terms in his society.
The Pythagorean society is associated with prohibitions such as not to step over a crossbar, and not to eat beans. These rules seem like primitive superstition, similar to "walking under a ladder brings bad luck". The abusive epithet mystikos logos ("mystical speech") was hurled at Pythagoras even in ancient times to discredit him. The prohibition on beans could be linked to favism, which is relatively widespread around the Mediterranean.
The key here is that akousmata means "rules", so that the superstitious taboos primarily applied to the akousmatikoi, and many of the rules were probably invented after Pythagoras's death and independent from the mathematikoi (arguably the real preservers of the Pythagorean tradition). The mathematikoi placed greater emphasis on inner understanding than did the akousmatikoi, even to the extent of dispensing with certain rules and ritual practices. For the mathematikoi, being a Pythagorean was a question of innate quality and inner understanding.
There was also another way of dealing with the akousmata — by allegorizing them. We have a few examples of this, one being Aristotle's explanations of them: "'step not over a balance', i.e. be not covetous; 'poke not the fire with a sword', i.e. do not vex with sharp words a man swollen with anger, 'eat not heart', i.e. do not vex yourself with grief," etc. We have evidence for Pythagoreans allegorizing in this way at least as far back as the early fifth century BC. This suggests that the strange sayings were riddles for the initiated.
The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods.
Much of their mysticism concerning the soul seem inseparable from the Orphic tradition. The Orphics advocated various purificatory rites and practices as well as incubatory rites of descent into the underworld. Pythagoras is also closely linked with Pherecydes of Syros, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherekydes was Pythagoras's most intimate teacher. Pherekydes expounded his teaching on the soul in terms of a pentemychos ("five-nooks", or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a symbol of recognition among members and as a symbol of inner health (ugieia).

HERACLITUS
of Ephesus (Ancient Greek: Ἡράκλειτος ὁ Ἐφέσιος — Hērákleitos ho Ephésios, English Heraclitus the Ephesian) (ca. 535–475 BC) was a pre-Socratic Greek philosopher, a native of Ephesus, Ionia, on the coast of Asia Minor.
Heraclitus is known for his doctrine of change being central to the universe, and that the Logos is the fundamental order of all.
The obscure: At some time in antiquity he acquired an epithet denoting that his major sayings were difficult to understand. Timon of Phlius calls him "the riddler" (ainiktēs) according to Diogenes Laertius, [1] who had just explained that Heraclitus wrote his book "rather unclearly" (asaphesteron) so that only the "capable" should attempt it. By the time of Cicero he had become "the dark" (Ancient Greek ὁ Σκοτεινός — ho Skoteinós[2]) because he had spoken nimis obscurē, "too obscurely", concerning nature and had done so deliberately in order to be misunderstood. The customary English translation of ὁ Σκοτεινός follows the Latin, "the obscure."

The weeping philosopher: Diogenes Laertius ascribes to Theophrastus the theory that Heraclitus did not complete some of his works because of melancholia.[1] Later he was referred to as the "weeping philosopher", as opposed to Democritus, who is known as the "laughing philosopher".[3] If Stobaeus[4] writes correctly, Sotion in the early 1st century AD was already combining the two in the imaginative duo of weeping and laughing philosophers: "Among the wise, instead of anger, Heraclitus was overtaken by tears, Democritus by laughter." The view is expressed by the satirist Juvenal:[5]
The first of prayers, best known at all the temples, is mostly for riches .... Seeing this then do you not commend the one sage Democritus for laughing ... and the master of the other school Heraclitus for his tears?
The motif was also adopted by Lucian of Samosata in his "Sale of Creeds", in which the duo is sold together as a complementary product in the satyrical auction of philosophers. Subsequently they were considered an indispensable feature of philosophic landscapes. Montaigne proposed two archetypical views of human affairs based on them, selecting Democritus' for himself.[6] The weeping philosopher makes an appearance in William Shakespeare's The Merchant of Venice.[7] Donato Bramante painted a fresco, "Democritus and Heraclitus", in Casa Panigarola in Milan.[8] And so on.
The naturalist: Diogenes says that the book attributed to Heraclitus was On Nature (peri physeōs).[1] Heraclitus' statement that "nature likes to hide"[9] places him among those seeking the hidden nature of things, including those who were finding an explanation in substance.
Heraclitus had a rather different idea of the hidden nature than substance, but he was being called physicus at least as early as Cicero:[10]
nemo physicus obscurus? ... valde Heraclitus obscurus ....
no physicus was obscure? ... Heraclitus the obscure certainly was.
If physis is nature, then physikos must translate to naturalist, but the term in English can have a great many meanings not necessarily implied by the ancient Greek.
Panta rhei, "everything is in a state of flux": Πάντα ῥεῖ (panta rhei) "everything is in a state of flux" either was not spoken by Heraclitus or did not survive as a quotation of his. This famous aphorism used to characterize Heraclitus' thought comes from Simplicius.[21] The word rhei, adopted by rhe-o-logy, is simply the Greek word for "to stream."[22]

The closest quote from Heraclitus is provided by Plato:[23]
πάντα χωρεῖ καὶ οὐδὲν μένει
Panta chōrei kai ouden menei
Instead of "flow" Plato uses chōrei, to change chōros, or ground, and not to "remain", with which menei is cognate. Just previously Plato explained:[24]
τὰ ὄντα ἰέναι τε πάντα καὶ μένειν οὐδέν
ta onta ienai te panta kai menein ouden
"All beings going and remaining not at all"
At first thought Heraclitus might be supposed to be asserting nothing more profound or obscure than that we exist in a field or continuum in which everything is constantly in flux or process: a non-remarkable observation for such a famous philosophy. However the assertions of flow are coupled in many fragments with the enigmatic river image:[25]
"Ποταμοῖς τοῖς αὐτοῖς ἐμβαίνομέν τε καὶ οὐκ ἐμβαίνομεν, εἶμέν τε καὶ οὐκ εἶμεν."
"We both step and do not step in the same rivers. We are and are not."
As a fellow Ionian, Heraclitus was certainly familiar with the preceding substance solution of the Milesian school to the problem of change. The problem only exists under the law of identity, one formulation of which is the law of excluded middle. The classical formulation of that law had to wait for Aristotle but it was nevertheless known and operant in pre-socratic philosophy.
In the fragment above Heraclitus is proposing that another law also is in effect. The law of identity states that an identity, say A, is identical to itself, is not non-A, and is not both A and non-A. Heraclitus affirms the middle in the passage above, that the A is both A and not-A. As far as the assertion is true, the change problem disappears and does not need a solution.
According to fragment DK B91: "nor is it possible to touch a mortal substance twice" and DK B6: "The sun is ... not only new each day but forms continually new ...." the Heraclitean law only applies in cases where the identity is sampled diachronically. The sampling rate can be adjusted to as rapidly as an object can be touched, or to the rate of flow of the stream, or daily, or by extrapolation to the frequency at which a photon can be perceived. Heraclitus just said "continually" and theorized: "simultaneously it forms and dissolves."[26]
It seems clear that the stream of the metaphor is time and that the stepping in it is the instant of the present. Heraclitus is therefore asserting that an object is and is not identical with itself of x instants ago.
Kalliste Harmonia, "the fairest harmony": Milesian philosophy was based on a binary law, which postulates a binary existence: objects either fully exist as completely identical to themselves or do not exist at all. There are two states, off or on. In Heraclitus the existence can be both off and on: a middle state of existing that is to some degree off and to some degree on.
The middle characteristic results from Heraclitus' existence being a derived quantity rather than a given one. It is the resultant of "simultaneous formation and dissolution" (see previous section) in the current instant, which explains such fragments as:
The way up and the way down are one and the same.[27]
... what is drawn together and what is drawn asunder ... The one is made up of all things and all things issue from the one.[28]
In the circumference of the circle the beginning and the end are common.[29]
... it (substance) approaches and departs.[26]
As for the resultant, it is a "harmony":[30]
ἐκ τῶν διαφερόντων καλλίστην ἁρμονίαν
ek tōn diapherontōn kallistēn harmonian
"out of discord comes the fairest harmony."[31]
Hodos ano kato, "the way up and the way down": In ὁδὸς ἄνω κάτω[32] the structure anō katō is more accurately translated as a hyphenated word: "the upward-downward path." They go on simultaneously and instantaneously (see previous section) and result in "hidden harmony".[33] A way is a series of transformations which imply a chronological sequence no matter how closely spaced: the πυρὸς τροπαὶ, "turnings of fire,"[34] first into sea, then half of sea to earth and half to rarified air.
The transformation is a replacement of one element by another: "The death of fire is the birth of air, and the death of air is the birth of water;"[35] moreover, the replacement is quantitatively determined, in which there appears to be a foreshadowing of conservation of mass:
"Sea ... is measured by the same amount (logos) as before it became earth"[36]
or again:
This world, which is the same for all,[37] no one of gods or men has made. But it always was and will be: an ever-living fire, with measures of it kindling, and measures going out.[38]
This latter phraseology is further elucidated:
All things are an interchange for fire, and fire for all things, just like goods for gold and gold for goods.[39]
This is certainly a foreshadowing of Conservation of energy.[40]
Dike eris, "strife is justice": If objects are new from moment to moment so that one can never touch the same object twice, then each object must dissolve and be generated continually momentarily and an object is a harmony between a building up and a tearing down. This is a foreshadowing of the scientific concept of equilibrium in many contexts. Heraclitus calls the oppositional processes eris, "strife", and hypothesizes that the apparently stable state, dikē, or "justice," is a harmony of it:[41]
We must know that war (polemos) is common to all and strife is justice, and that all things come into being through strife necessarily.
As Diogenes explains:[42]
All things come into being by conflict of opposites, and the sum of things (ta hola, "the whole") flows like a stream.
In the bow metaphor Heraclitus compares the resultant to a strung bow held in shape by an equilibrium of the string tension and spring action of the bow:[43]
There is a harmony in the bending back (palintropos) as in the case of the bow and the lyre.
Heraclitus here references the Scythian bow, the horns of which pointed forward unstrung but back strung, or the deformation of the cross-bar of the lyre under string tension. The palintropos of an object would therefore be its stinting from the growth of the current instant by the decay of the object of the previous. This identity-not-identity accounts for such statements as:[44]
It is one and the same thing to be living and dead, awake or asleep, young or old.
A change is the result of a change in balance:[45]
Cold things become warm, and what is warm cools; what is wet dries, and the parched is moistened.
Hepesthai to ksuno, "follow the common": The idea that the universe changes according to a plan or logos, with which the truly aware soul should cooperate, is expressed in the notable but obscure DK B1 and DK B2. The first phrase of the first fragment can be interpreted as "of the logos which is as I describe it" or "though this word is true evermore" depending on how the words are to be regarded as clustered and what is or is not implied by them. The meaning of logos also is subject to interpretation: "word", "plan", "formula", "measure", "proportion", "reckoning."
However translated it refers to Heraclitus' vision of the operation of the universe and therefore is not the progenitor of the logos of any other creed, doctrine or religion. The ancient Greek word, which is frequent and also appears in a large number of English words, such as logic, was certainly not a neologism of Heraclitus: he was not "the first" to use it. There is no univocal word, logos, and if there ever was one, its meaning is lost in prehistory.[46]
The problem with the Heraclitean logos is that his explanation of it did not survive. Whatever it was, "all things come to pass in accordance with this word"[47] and "the word is common."[48] It is "the account which governs the universe (ta hola, the whole)."[49]
Logos appears to be some sort of natural law and yet men must "follow the common (hepesthai tō ksunō)"[50] and not live having "their own judgement (phonēsis)" implying a voluntary assent, which natural law does not offer. He distinguishes between human laws and divine law (tou theiou "of God").[51]
He removes the human sense of justice from his concept of God; i.e., man is not the image of God: "To God all things are fair and good and just, but men hold some things wrong and some right."[52] God's custom has wisdom but man's does not[53] and yet both man and God are childish: "human opinions are children's toys"[54] and "Time is a child moving counters in a game; the kingly power is a child's."[55]
Wisdom is "to know the thought by which all things are steered through all things",[56] which must not imply that men are or can be wise. Only Zeus is wise.[57] To some degree then Heraclitus seems to be in the mystic's position of urging men to follow God's plan without much of an idea what that may be. In fact there is a note of despair: "The fairest universe (kallistos kosmos) is but a heap of rubbish (sarma, sweepings) piled up (kechumenon, poured out) at random (eikē)."[58] This may be a foreshadowing of scientific randomness rather than an internal struggle, but the evidence is too scant to make either presumption.
Influence: Many philosophers have expressed the belief that they were influenced by Heraclitus, whether accurately or not. Some of the more notable ones are mentioned in this section; others will be found in linked articles where they exist. Coincidental resemblances are too numerous for consideration in one article.

Plato: In Heraclitus a perceived object is a harmony between two fundamental units of change, a waxing and a waning. He typically uses the ordinary word "to become" (gignesthai or ginesthai, root sense of being born), which led to his being characterized as the philosopher of becoming rather than of being. He recognizes the changing of objects with the flow of time; in fact, this is the view of modern science, which recognizes nothing static and sees a balance between processes everywhere, though not those of Heraclitus.
Plato argues against Heraclitus as follows:[59]
How can that be a real thing which is never in the same state? ... for at the moment that the observer approaches, then they become other ... so that you cannot get any further in knowing their nature or state .... but if that which knows and that which is known exist ever ... then I do not think they can resemble a process or flux ....
In Plato one experienced unit is a state, or object existing, which can be observed. The time parameter is set at "ever"; that is, the state is to be presumed present between observations. Change is to be deduced by comparing observations, but no matter how many of those you are able to make, you cannot get through the mysterious gap between them to account for the change that must be occurring there.
Bearden's presentation of a relativistic solution to the change problem (under External links below) distinguishes between space and spacetime, the latter being an aspect of reality mathematically defined by Albert Einstein. An object in spacetime has four dimensions in directions x, y, z, and t, where t is time, containing within its boundaries change, so that it is not deduced but is delivered in experience. To take an observation is to reduce the object to nearly three dimensions; that is, to eliminate the time depth, which is equivalent to saying that Plato's states of existence only appear when you look for them, but even as you ponder the observation, time and change do not stop; reality continues to be delivered in units of spacetime.[60]
Aristotle: Aristotle brings his logic to bear against Heraclitus in Metaphysics invoking the identity laws:[61]
... there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate.
Bearden describes "one subject" as a snapshot in spacetime. The identity laws apply to simultaneous snapshots of A and B but as soon as they are not simultaneous the change problem occurs. Says Bearden, the laws:
... are monocular, unchanging, 3-dimensional, spatial, non-temporal relational statements. Any statement that is temporal, changing or 4-dimensional will thus appear as a logical paradox to this logical shorthand.
If the "one subject" becomes 4-dimensional, any delimited chunk includes starting and ending snapshots as well as everything in between. If over that time A becomes not-A then both are in the "one subject". As the identity law is only applied subsequent to the experience of A and not-A the two are superimposed in the final snapshot: the object is both A and not-A.
Bearden therefore postulates a conditional identity law: the first three apply if time is not considered but if it is then the dual, or Heraclitean law, applies. Aristotle might have had access to this result if he had applied his theory of act and potency, which asserts that an object is actually what it is sampled to be and is potentially whatever it has been or will be. An object might be therefore actually A and potentially not-A simultaneously.
Stoics: Stoicism is a school of thought comprising many philosophers between the 3rd century BC and about the 6th century AD.
See also: Category:Stoic philosophers
It began among the Greeks and became the major philosophy of the Roman Empire before declining with the rise of Christianity in the 3rd century.
Throughout their long tenure the Stoics believed that the major tenets of their philosophy derived from the thought of Heraclitus.[62] According to Long, "the importance of Heraclitus to later Stoics is evident most plainly in Marcus Aurelius."[63] Explicit connections of the earliest Stoics to Heraclitus showing how they arrived at their interpretation are missing but they can be inferred from the Stoic fragments. Long concludes to "modifications of Heraclitus."[64]
The Stoics were interested in Heraclitus' treatment of fire. In addition to seeing it as the most fundamental of the four elements and the one that is quantified and determines the quantity (logos) of the other three, he presents fire as the cosmos, which was not made by any of the gods or men, but "was and is and ever shall be ever-living fire."[27] This is the closest he comes to a substance, but it is an active one altering other things quantitatively and performing an activity Heraclitus describes as "the judging and convicting of all things."[65] It is "the thunderbolt that steers the course of all things."[66] There is no reason to interpret the judgement, which is actually "to separate" (krinein), as outside of the context of "strife is justice" (see subsection above).
The earliest surviving Stoic work, the Hymn to Zeus of Cleanthes,[67] though not explicitly referencing Heraclitus, adopts what appears to be the Heraclitean logos modified. Zeus rules the universe with law (nomos) wielding on its behalf the "forked servant", the "fire" of the "ever-living lightening." So far nothing has been said that differs from the Zeus of Homer. But then, says Cleanthes, Zeus uses the fire to "straighten out the common logos" that travels about (phoitan, "to frequent") mixing with the greater and lesser lights (heavenly bodies). This is Heraclitus' logos, but now it is confused with the "common nomos", which Zeus uses to "make the wrong (perissa, left or odd) right (artia, right or even)" and "order (kosmein) the disordered (akosma)."[68]
In short, the logos has developed from being an impersonal and even random eternal quantitative plan of change associated with the upward-downward way and especially fire taking precedence even over the will of Zeus, who did not create it, to being the instrument and design of God, who is personal, whose children humans and only humans are,[69] which he uses to bring about order and correct wrong. It remained logically only to affirm unequivocally the identity of God with his logos, which was done in the Gospel of John.
For more details on this topic, see Christ the Logos.
The Stoic modification of Heraclitus' idea of the Logos was also influential on Jewish philosophers such as Philo of Alexandria, who connected it to "Wisdom personified" as God's creative principle. Philo uses the term Logos throughout his treatises on Hebrew Scripture in a manner clearly influenced by the Stoics.

PARMENIDES OF ELEA
(Greek: Παρμενίδης ο Ἐλεάτης, early 5th century BC) was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy, his only known work is a poem which has survived only in fragmentary form. In it, Parmenides describes two views of reality. In the Way of Truth, he explained how reality is one; change is impossible; and existence is timeless, uniform, and unchanging. In the Way of Opinion, he explained the world of appearances, which is false and deceitful. These thoughts strongly influenced Plato, and through him, the whole of western philosophy..
Overview: Parmenides is one of the most significant of the pre-Socratic philosophers.[10] His only known work, conventionally titled On Nature, is a poem, which has only survived in fragmentary form. Approximately 150 lines of the poem remain today; reportedly the original text had 3,000 lines. It is known, however, that the work originally divided into three parts:
A proem, which introduced the entire work,
A section known as "The Way of Truth" (aletheia), and
A section known as "The Way of Appearance/Opinion" (doxa).
The poem is a narrative sequence in which the narrator travels "beyond the beaten paths of mortal men" to receive a revelation from an unnamed goddess (generally thought to be Persephone) on the nature of reality. Aletheia, an estimated 90% of which has survived, and doxa, most of which no longer exists, are then presented as the spoken revelation of the goddess without any accompanying narrative.
Parmenides attempted to distinguish between the unity of nature and its variety, insisting in the Way of Truth upon the reality of its unity, which is therefore the object of knowledge, and upon the unreality of its variety, which is therefore the object, not of knowledge, but of opinion. In the Way of Opinion he propounded a theory of the world of seeming and its development, pointing out however that, in accordance with the principles already laid down, these cosmological speculations do not pretend to anything more than mere appearance.
Proem: In the Proem Parmenides describes his journey from darkness to light. Carried in a whirling chariot, and attended by the daughters of the Sun, he reaches a temple sacred to an unnamed goddess (variously identified by the commentators with Nature, Wisdom, or Themis), by whom the rest of the poem is spoken. He must learn all things, she tells him, both truth, which is certain, and human opinions; for, though one cannot rely on human opinions, they represent an aspect of the whole truth.

The Way of Truth: Parmenides. Detail from The School of Athens by Raphael.
The Way of Truth discusses that which is real, which contrasts in some way with the argument of the Way of Opinion, which discusses that which is illusory. Under the Way of Truth, Parmenides stated that there are two ways of inquiry: that it is, that it is not.[11] He said that the latter argument is never feasible because nothing can not be:
For never shall this prevail, that things that are not are. (B 7.1)
There are extremely delicate issues here. In the original Greek the two ways are simply named "that Is" (hopos estin) and "that Not-Is" (hos ouk estin) (B 2.3 and 2.5) without the "it" inserted in our English translation. In ancient Greek, which, like many languages in the world, does not always require the presence of a subject for a verb, "is" functions as a grammatically complete sentence. A lot of debate has been focused on where and what the subject is. The simplest explanation as to why there is no subject here is that Parmenides wishes to express the simple, bare fact of existence in his mystical experience without the ordinary distinctions, just as the Latin "pluit" and the Greek uei ("rains") mean "it rains"; there is no subject for these impersonal verbs because they express the simple fact of raining without specifying what is doing the raining. This is, for instance, Hermann Fraenkel's thesis (Dichtung und Philosophie des fruehen Griechentums, 1962) [2] Many scholars still reject this explanation and have produced more complex metaphysical explanations. Since existence is an immediately intuited fact, non-existence is the wrong path because a thing cannot disappear, just as something cannot originate from nothing. In such mystical experience (unio mystica), however, the distinction between subject and object disappears along with the distinctions between objects, in addition to the fact that if nothing cannot be, it cannot be the object of thought either:
Thinking and the thought that it is are the same; for you will not find thought apart from what is, in relation to which it is uttered. (B 8.34-36)
For thought and being are the same. (B 3)
It is necessary to speak and to think what is; for being is, but nothing is not. (B 6.1-2)
Helplessness guides the wandering thought in their breasts; they are carried along deaf and blind alike, dazed, beasts without judgment, convinced that to be and not to be are the same and not the same, and that the road of all things is a backward-turning one. (B 6.5-9)
Thus, he concluded that "Is" could not have "come into being" because "nothing comes from nothing". Existence is necessarily eternal. Parmenides was not struggling to formulate the conservation of mass-energy; he was struggling with the metaphysics of change, which is still a relevant philosophical topic today.
Moreover he argued that movement was impossible because it requires moving into "the void", and Parmenides identified "the void" with nothing, and therefore (by definition) it does not exist. That which does exist is The Parmenidean One, which is timeless, uniform, and unchanging:
How could what is perish? How could it have come to be? For if it came into being, it is not; nor is it if ever it is going to be. Thus coming into being is extinguished, and destruction unknown. (B 8.20-22)
Nor was [it] once, nor will [it] be, since [it] is, now, all together, / One, continuous; for what coming-to-be of it will you seek? / In what way, whence, did [it] grow? Neither from what-is-not shall I allow / You to say or think; for it is not to be said or thought / That [it] is not. And what need could have impelled it to grow / Later or sooner, if it began from nothing? Thus [it] must either be completely or not at all. (B 8.5-11)
[What exists] is now, all at once, one and continuous... Nor is it divisible, since it is all alike; nor is there any more or less of it in one place which might prevent it from holding together, but all is full of what is. (B 8.5-6, 8.22-24)
And it is all one to me / Where I am to begin; for I shall return there again. (B 5)

Perception vs. Logos: Parmenides claimed that the truth cannot be known through sensory perception. Only pure reason (Logos) will result in the understanding of the truth of the world. This is because the perception of things or appearances (the doxa) is deceptive. We may see, for example, tables being made from wood and destroyed, and speak of birth and demise; this belongs to the superficial world of movement and change. But this genesis-and-destruction, as Parmenides emphasizes, is illusory, because the underlying material of which the table is made will still exist after its destruction. What exists must always exist. And we arrive at the knowledge of this underlying, static, and eternal reality (aletheia) through reasoning, not through sense-perception.
For this view, that That Which Is Not exists, can never predominate. You must debar your thought from this way of search, nor let ordinary experience in its variety force you along this way, (namely, that of allowing) the eye, sightless as it is, and the ear, full of sound, and the tongue, to rule; but (you must) judge by means of the Reason (Logos) the much-contested proof which is expounded by me. (B 7.1-8.2)




ANAXAGORAS
(Greek: Ἀναξαγόρας, c. 500 BC – 428 BC) was a Pre-Socratic Greek philosopher famous for introducing the cosmological concept of Nous (mind), the ordering force.
Biography
Anaxagoras appears to have had some amount of property and prospects of political influence in his native town of Clazomenae in Asia Minor. However, he supposedly surrendered both of these out of a fear that they would hinder his search for knowledge. Although a Greek, he may have been a soldier of the Persian army when Clazomenae was suppressed during the Ionian Revolt.
In early manhood (c. 464-461 BC) he went to Athens, which was rapidly becoming the centre of Greek culture. There he is said to have remained for thirty years. Pericles learned to love and admire him, and the poet Euripides derived from him an enthusiasm for science and humanity.
Anaxagoras brought philosophy and the spirit of scientific inquiry from Ionia to Athens. His observations of the celestial bodies and the fall of meteorites led him to form new theories of the universal order. He attempted to give a scientific account of eclipses, meteors, rainbows and the sun, which he described as a mass of blazing metal, larger than the Peloponnese. The heavenly bodies, he asserted, were masses of stone torn from the earth and ignited by rapid rotation. However, these theories brought him into collision with the popular faith; Anaxagoras' views on such things as heavenly bodies were considered "dangerous."
About 450[1] Anaxagoras was arrested by Pericles' political opponents on a charge of contravening the established religion (some say the charge was one of Medism). It took Pericles' power of persuasion to secure his release. Even so he was forced to retire from Athens to Lampsacus in Ionia (c. 434-433 BC). He died there in around the year 428 BC. Citizens of Lampsacus erected an altar to Mind and Truth in his memory, and observed the anniversary of his death for many years.
Anaxagoras wrote a book of philosophy, but only fragments of the first part of this have survived, through preservation in work of Simplicius of Cilicia in the sixth century AD.
Cosmological theory: All things have existed from the beginning. But originally they existed in infinitesimally small fragments of themselves, endless in number and inextricably combined. All things existed in this mass, but in a confused and indistinguishable form. There were the seeds (spermata) or miniatures of wheat and flesh and gold in the primitive mixture; but these parts, of like nature with their wholes (the homoiomereiai of Aristotle), had to be eliminated from the complex mass before they could receive a definite name and character. Mind arranged the segregation of like from unlike; panta chremata en omou eita nous elthon auta diekosmese. This peculiar thing, called Mind (Nous), was no less illimitable than the chaotic mass, but, unlike the logos of Heraclitus, it stood pure and independent (mounos ef eoutou), a thing of finer texture, alike in all its manifestations and everywhere the same. This subtle agent, possessed of all knowledge and power, is especially seen ruling in all the forms of life.[citation needed]
Mind causes motion. It rotated the primitive mixture, starting in one corner or point, and gradually extended until it gave distinctness and reality to the aggregates of like parts, working something like a centrifuge, and eventually creating the known cosmos. But even after it had done its best, the original intermixture of things was not wholly overcome. No one thing in the world is ever abruptly separated, as by the blow of an axe, from the rest of things.
It is noteworthy that Aristotle accuses Anaxagoras of failing to differentiate between nous and psyche, while Socrates (Plato, Phaedo, 98 B) objects that his nous is merely a deus ex machina to which he refuses to attribute design and knowledge.
Anaxagoras proceeded to give some account of the stages in the process from original chaos to present arrangements. The division into cold mist and warm ether first broke the spell of confusion. With increasing cold, the former gave rise to water, earth and stones. The seeds of life which continued floating in the air were carried down with the rains and produced vegetation. Animals, including man, sprang from the warm and moist clay. If these things be so, then the evidence of the senses must be held in slight esteem. We seem to see things coming into being and passing from it; but reflection tells us that decease and growth only mean a new aggregation (sugkrisis) and disruption (diakrisis). Thus Anaxagoras distrusted the senses, and gave the preference to the conclusions of reflection. Thus he maintained that there must be blackness as well as whiteness in snow; how otherwise could it be turned into dark water?
Anaxagoras marked a turning-point in the history of philosophy. With him speculation passes from the colonies of Greece to settle at Athens. By the theory of minute constituents of things, and his emphasis on mechanical processes in the formation of order, he paved the way for the atomic theory. However, his enunciation of the order that comes from an intelligent mind suggested the theory that nature is the work of design.


ERATOSTHENES OF CYRENE
(Greek Ἐρατοσθένης; 276 BC - 194 BC) was a Greek mathematician, poet, athlete, geographer and astronomer. He made several remarkable discoveries and inventions: he devised a system of latitude and longitude. He was the first person to calculate the circumference of the Earth (with remarkable accuracy), and the tilt of the earth's axis (again with remarkable accuracy); he may also have accurately calculated the distance from the earth to the sun and invented the leap day.[1] He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
His contemporaries nicknamed him "beta" (the Greek numeral "two") because he supposedly proved himself to be the second best in many fields.

Life: 19th century reconstruction of Eratosthenes's map of the known world, c.194 BC. Eratosthenes was born in Cyrene (in modern-day Libya). He was the chief librarian of the Great Library of Alexandria and died in the capital of Ptolemaic Egypt. He never married.
Eratosthenes studied in Alexandria and claimed to have also studied for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the first librarian, Apollonius of Rhodes, in that post[2]. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented[citation needed] the armillary sphere, which was widely used until the invention of the orrery in the 18th century.
In 194 BC Eratosthenes became blind and, according to legends, a year later, he starved himself to death.
He is credited by Cleomedes in On the Circular Motions of the Celestial Bodies with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).
Eratosthenes' measurement of the Earth's circumference: Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000 stadia (about 500 geographical miles or 950 km). He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion"[1] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.[2]
Although Eratosthenes' method was well founded, the accuracy of his calculation was inherently limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of the Tropic of Cancer, is not directly south of Alexandria, and the Sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. So the accuracy of Eratosthenes' size of the earth is surprising.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later.
The mysterious astronomical distances: Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the sun to be "σταδίων μυριάδας τετρακοσίας και οκτωκισμυρίας" (literally "of stadia myriads 400 and 80,000") and the distance to the moon to be 780,000 stadia. The expression for the distance to the sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974-1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad.
This testimony of Eusebius is dismissed by the scholarly Dictionary of Scientific Biography. It is true that the distance Eusebius quotes for the moon is much too low (about 144,000 km) and Eratosthenes should have been able to do much better than this since he knew the size of the Earth and Aristarchus of Samos had already found[citation needed] the ratio of the Moon's distance to the size of the Earth. But if what Eusebius wrote was pure fiction, then it is difficult to explain the fact that, using the Greek, or Olympic, stadium of 185 metres, the figure of 804 million stadia that he quotes for the distance to the Sun comes to 149 million kilometres. The difference between this and the modern accepted value is less than 1%


ARISTARCHUS
(Greek: Ἀρίσταρχος; 310 BC - ca. 230 BC) was a Greek astronomer and mathematician, born on the island of Samos, in Greece. He was the first person to present an explicit argument for a heliocentric model of the solar system, placing the Sun, not the Earth, at the center of the known universe (hence he is sometimes known as the "Greek Copernicus"). He was influenced by the Pythagorean Philolaus of Kroton, but in contrast to Philolaus he had both identified the central fire with the Sun, as well as putting other planets in correct order from the Sun. His astronomical ideas were rejected in favor of the geocentric theories of Aristotle and Ptolemy until they were successfully revived nearly 1800 years later by Copernicus and extensively developed and built upon by Johannes Kepler and Isaac Newton.
The Aristarchus crater on the Moon was named in his honour.

Heliocentrism: The only work usually attributed to Aristarchus which has survived to the present time, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. It is peculiar and possibly informative that this work reckons the sun's diameter as 2 degrees, rather than the correct value, 1/2 degree. The latter diameter is known from Archimedes to have been Aristarchus's actual value.
Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner describes another work by Aristarchus in which he advanced an alternative hypothesis of the heliocentric model. Archimedes wrote: (translated into English)
You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.
Aristarchus thus believed the stars to be very far away, and saw this as the reason why there was no visible parallax, that is, an observed movement of the stars relative to each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with telescopes. The geocentric model, consistent with planetary parallax, was assumed to be an explanation for the unobservability of the parallel phenomenon, stellar parallax. The rejection of the heliocentric view was common, as the following passage from Plutarch suggests (On the Apparent Face in the Orb of the Moon):
Cleanthes [a contemporary of Aristarchus and head of the Stoics] thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the universe [i.e. the earth], . . . supposing the heaven to remain at rest and the earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis. [1]
The only other astronomer from antiquity who is known by name and who is known to have supported Aristarchus' heliocentric model was Seleucus of Seleucia, a Mesopotamian astronomer who lived a century after Aristarchus.


ASPASIA
(ca. 470 BC[1][2]–ca. 400 BC,[1][3] Greek: Ἀσπασία) was a Milesian woman who was famous for her involvement with the Athenian statesman Pericles.[4] Very little is known about the details of her life. She spent most of her adult life in Athens, and she may have influenced Pericles and Athenian politics. She is mentioned in the writings of Plato, Aristophanes, Xenophon, and other authors of the day.
Ancient writers also reported that Aspasia was a brothel keeper and a harlot, although these accounts are disputed by modern scholars, on the grounds that many of the writers were comic poets concerned with defaming Pericles.[5] Some researchers question even the historical tradition that she was a hetaera, or courtesan, and have suggested that she may actually have been married to Pericles.[α] Aspasia had a son by Pericles, Pericles the Younger, who later became a general in the Athenian military and was executed after the Battle of Arginusae. She is believed to have become the courtesan of Lysicles, another Athenian statesman and general, following the death of Pericles the Elder.

Ancient philosophical works: Aspasia appears in the philosophical writings of Plato, Xenophon, Aeschines Socraticus and Antisthenes. Some scholars argue that Plato was impressed by her intelligence and wit and based his character Diotima in the Symposium on her, while others suggest that Diotima was in fact a historical figure.[33][34] According to Charles Kahn, Professor of Philosophy at the University of Pennsylvania, Diotima is in many respects Plato's response to Aeschines' Aspasia.[35]
"Now, since it is thought that he proceeded thus against the Samians to gratify Aspasia, this may be a fitting place to raise the query what great art or power this woman had, that she managed as she pleased the foremost men of the state, and afforded the philosophers occasion to discuss her in exalted terms and at great length."
Plutarch, Pericles, XXIV
In Menexenus, Plato satirizes Aspasia's relationship with Pericles,[36] and quotes Socrates as claiming ironically that she was a trainer of many orators. Socrates' intention is to cast aspersions on Pericles' rhetorical fame, claiming, also ironically, that since the Athenian statesman was educated by Aspasia, he would be superior in rhetoric to someone educated by Antiphon.[37] He also attributes authorship of the Funeral Oration to Aspasia and attacks his contemporaries' veneration of Pericles.[38] Kahn maintains that Plato has taken from Aeschines the motif of Aspasia as teacher of rhetoric for Pericles and Socrates.[35] Plato's Aspasia and Aristophanes' Lysistrata are two apparent exceptions to the rule of women's incapacity as orators, though these fictional characters tell us nothing about the actual status of women in Athens.[39] As Martha L. Rose, Professor of History at Truman State University, explains, "only in comedy do dogs litigate, birds govern, or women declaim".[40]
Xenophon mentions Aspasia twice in his Socratic writings: in Memorabilia and in Oeconomicus. In both cases her advice is recommended to Critobulus by Socrates. In Memorabilia Socrates quotes Aspasia as saying that the matchmaker should report truthfully on the good characteristics of the man.[41] In Oeconomicus Socrates defers to Aspasia as more knowledgeable about household management and the economic partnership between husband and wife.[42]
Painting of Hector Leroux (1682–1740), which portrays Pericles and Aspasia admiring the gigantic statue of Athena in Phidias' studio
Aeschines Socraticus and Antisthenes each named a Socratic dialogue after Aspasia (though neither survives except in fragments). Our major sources for Aeschines Socraticus' Aspasia are Athenaeus, Plutarch, and Cicero. In the dialogue, Socrates recommends that Callias send his son Hipponicus to Aspasia for instructions. When Callias recoils at the notion of a female teacher, Socrates notes that Aspasia had favorably influenced Pericles and, after his death, Lysicles. In a section of the dialogue, preserved in Latin by Cicero, Aspasia figures as a "female Socrates", counseling first Xenophon's wife and then Xenophon himself (the Xenophon in question is not the famous historian) about acquiring virtue through self-knowledge.[43][35] Aeschines presents Aspasia as a teacher and inspirer of excellence, connecting these virtues with her status as hetaira.[44] According to Kahn, every single episode in Aeschines' Aspasia is not only fictitious but incredible.[45]
Of Antisthenes' Aspasia only two or three quotations are extant.[1] This dialogue contains much slander, but also anecdotes pertaining to Pericles' biography.[46] Antisthenes appears to have attacked not only Aspasia, but the entire family of Pericles, including his sons. The philosopher believes that the great statesman chose the life of pleasure over virtue.[47] Thus, Aspasia is presented as the personification of the life of sexual indulgence.[44]


HYPATIA OF ALEXANDRIA
(pronounced /haɪˈpeɪʃə/) (Greek: Ὑπατία; born between AD 350 and 370 – 415) was a Greek[1] scholar from Alexandria in Egypt,[2][3] considered the first notable woman in mathematics, who also taught philosophy and astronomy.[4] She lived in Roman Egypt, and was killed by a Coptic Christian mob who blamed her for religious turmoil. She has been hailed as a "valiant defender of science against religion",[5] and some suggest[who?] that her murder marked the end of the Hellenistic Age.[6][7]
A Neoplatonist philosopher, she followed the school characterized by the 3rd century thinker Plotinus, and discouraged mysticism while encouraging logical and mathematical studies.[8]

Life: Hypatia was the daughter of Theon, who was her teacher and the last known mathematician associated with the Musaeum of Alexandria.[9] She traveled to both Athens and Italy to study,[10] before becoming head of the Platonist school at Alexandria in approximately AD 400.[11] According to the Byzantine Suda, she worked as teacher of philosophy, teaching the works of Plato and Aristotle.[12] It is believed that there were both Christians[13] and foreigners[8] among her students.
Although Hypatia was herself a pagan, she was respected by a number of Christians, and later held up by Christian authors as a symbol of virtue.[8] The Suda controversially[14] declared her "the wife of Isidore the Philosopher"[12] but agreed she had remained a virgin.[15]
Hypatia rebuffed a suitor by showing him her menstrual rags, claiming they demonstrated that there was "nothing beautiful" about carnal desires.[12]
Hypatia maintained correspondence with her former pupil Bishop of Ptolomais Synesius of Cyrene.[16] Together with the references by Damascius, these are the only writings with descriptions or information from her pupils that survive.[17]
The contemporary Christian historiographer Socrates Scholasticus described her in his Ecclesiastical
History: There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner, which she had acquired in consequence of the cultivation of her mind, she not unfrequently appeared in public in presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more.[8]
Works: A 1885 painting by Charles William Mitchell.Many of the works commonly attributed to Hypatia are believed to have been collaborative works with her father, Theon Alexandricus.
A partial list of specific accomplishments:
A commentary on the 13-volume Arithmetica by Diophantus[18]
Edited the third book of her father's commentary on Ptolemy's Almagest[19]
Edited her father's commentary on Euclid's Elements[20]
Edited a commentary that simplified Apollonius's Conics[21]
She wrote the text The Astronomical Canon[22]
Her contributions to science are reputed to include the charting of celestial bodies[4] and the invention of the hydrometer,[23] used to determine the relative density and gravity of liquids.
Her pupil Synesius wrote a letter defending her as the inventor of the astrolabe, although earlier astrolabes predate Hypatia's model by at least a century - and her father had gained fame for his treatise on the subject.[21]
Death: Believed to have been the reason for the strained relationship between the Imperial Prefect Orestes and the Bishop Cyril, Hypatia attracted the ire of a Christian population eager to see the two reconciled.
One day in March 415,[24] during the season of Lent, her chariot was waylaid on her route home by a Christian mob, possibly Nitrian monks[24] led by a man identified only as "Peter".
She was stripped naked and dragged through the streets to the newly christianised Caesareum church and killed. Some reports suggest she was flayed with ostrakois (literally, "oyster shells", though also used to refer to roof tiles or broken pottery) and set ablaze while still alive, though other accounts suggest those actions happened after her death:
Legacy: Shortly after her death, a forged letter attacking Christianity was published under her name.[26] The pagan historian Damascius, "anxious to exploit the scandal of Hypatia's death",[22] laid the blame squarely on the Christians and Bishop Cyril.
In the 14th century, historian Nicephorus Gregoras described Eudokia Makrembolitissa as a "second Hypatia".[17]
In the early 18th century, the deist scholar John Toland used her death as the basis for an anti-Catholic tract entitled "Hypatia: Or the history of a most beautiful, most vertuous, most learned, and every way accomplish’d lady; who was torn to pieces by the clergy of Alexandria, to gratify the pride, emulation, and cruelty of their archbishop, commonly but undeservedly stil’d St. Cyril.[27] This led to a counter-claim being published by Thomas Lewis in 1721 entitled The History Of Hypatia, A most Impudent School-Mistress of Alexandria.[28]
Eventually, her story began to be infused with Christian details, as her story was first substituted for the missing history of Saint Catherine of Alexandria.[29][30]
In the nineteenth century, interest in the "literary legend of Hypatia" began to peak.[17]
Diodata Saluzzo Roero's 1827 Ipazia ovvero delle Filosofie suggested that Cyril had actually converted Hypatia to Christianity, and that she had been killed by a "treacherous" priest.
In his 1847 Hypatie and 1857 Hypatie et Cyrille, French poet Charles-Marie-René Leconte de Lisle portrayed Hypatia as the epitome of "vulnerable truth and beauty".[31]
Charles Kingsley's 1853 fictionalized novel Hypatia - or New Foes with an Old Face, which portrayed the scholar as a "helpless, pretentious, and erotic heroine",[32] recounted her conversion by a Jewish-Christian named Raphael Aben-Ezra after supposedly becoming disillusioned with Orestes.
In 1868, Julia Margaret Cameron produced a photographic depiction of the ancient scholar Hypatia.[33]
The lunar crater Hypatia was named after the philosopher, in addition to craters named for Cyril and her father Theon. Measuring 28x41 kilometres, the crater is located 4.3°S and 22.6°E of the meridian. The 180km Rimae Hypatia, is located north of the crater, one degree south of the equater, along the Mare Tranquillitatis.[34]