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Parmenides of Elea ( / p ɑːr ˈ m ɛ n ɪ d iː z . ˈ ɛ l i ə / Greek: Παρμενίδης ὁ Ἐλεάτης fl. late sixth or early fifth century BC ) was a pre-Socratic Greek philosopher from Elea in Magna Graecia (meaning "Great Greece," the term which Romans gave to Greek-populated coastal areas in Southern Italy). He is thought to have been in his prime (or "floruit") around 475 BC. [a]
Parmenides has been considered the founder of metaphysics or ontology and has influenced the whole history of Western philosophy.  [b] He was the founder of the Eleatic school of philosophy, which also included Zeno of Elea and Melissus of Samos. Zeno's paradoxes of motion were to defend Parmenides' view.
The single known work by Parmenides is a poem whose original title is unknown but which is often referred to as On Nature. Only fragments of it survive, but its importance lies in the fact that it contains the first sustained argument in the history of Western philosophy. In his poem, Parmenides prescribes two views of reality. In "the way of truth" (a part of the poem), he explains how all reality is one, change is impossible, and existence is timeless, uniform, and necessary. In "the way of opinion", Parmenides explains the world of appearances, in which one's sensory faculties lead to conceptions which are false and deceitful, yet he does offer a cosmology.
Parmenides' philosophy has been explained with the slogan "whatever is is, and what is not cannot be". He is also credited with the phrase out of nothing nothing comes. He argues that "A is not" can never be thought or said truthfully, and thus despite appearances everything exists as one, giant, unchanging thing. This is generally considered one of the first digressions into the philosophical concept of being, and has been contrasted with Heraclitus's statement that "No man ever steps into the same river twice" as one of the first digressions into the philosophical concept of becoming. Scholars have generally believed that either Parmenides was responding to Heraclitus, or Heraclitus to Parmenides.
Parmenides' views have remained relevant in philosophy, even thousands of years after his death. Alexius Meinong, much like Parmenides, defended the view that even the "golden mountain" is real since it can be talked about. The rivalry between Heraclitus and Parmenides has also been re-introduced in debates in the philosophy of time between A theory and B theory.
Democritus was said to be born in the city of Abdera in Thrace, an Ionian colony of Teos,  although some called him a Milesian.  He was born in the 80th Olympiad (460–457 BC) according to Apollodorus of Athens,  and although Thrasyllus placed his birth in 470 BC,  the later date is probably more likely.  John Burnet has argued that the date of 460 is "too early" since, according to Diogenes Laërtius ix.41, Democritus said that he was a "young man (neos)" during Anaxagoras's old age (c. 440–428 ).  It was said that Democritus's father was from a noble family and so wealthy that he received Xerxes on his march through Abdera. Democritus spent the inheritance which his father left him on travels into distant countries, to satisfy his thirst for knowledge. He traveled to Asia, and was even said to have reached India and Ethiopia. 
It is known that he wrote on Babylon and Meroe he visited Egypt, and Diodorus Siculus states that he lived there for five years.  He himself declared  that among his contemporaries none had made greater journeys, seen more countries, and met more scholars than himself. He particularly mentions the Egyptian mathematicians, whose knowledge he praises. Theophrastus, too, spoke of him as a man who had seen many countries.  During his travels, according to Diogenes Laërtius, he became acquainted with the Chaldean magi. "Ostanes", one of the magi accompanying Xerxes, was said to have taught him.  It was also said he learned with the gymnosophists in his journey to India. 
After returning to his native land he occupied himself with natural philosophy. He traveled throughout Greece to acquire a better knowledge of its cultures. He mentions many Greek philosophers in his writings, and his wealth enabled him to purchase their writings. Leucippus, the founder of atomism, was the greatest influence upon him. He also praises Anaxagoras.  Diogenes Laertius says that he was friends with Hippocrates,  and he quotes Demetrius saying: "It would seem that he also went to Athens and was not anxious to be recognized, because he despised fame, and that while he knew of Socrates, he was not known to Socrates, his words being, 'I came to Athens and no one knew me.'"  Aristotle placed him among the pre-Socratic natural philosophers. 
The many anecdotes about Democritus, especially in Diogenes Laërtius, attest to his disinterest, modesty, and simplicity, and show that he lived exclusively for his studies. One story has him deliberately blinding himself in order to be less disturbed in his pursuits  it may well be true that he lost his sight in old age. He was cheerful, and was always ready to see the comical side of life, which later writers took to mean that he always laughed at the foolishness of people. 
He was highly esteemed by his fellow citizens, because as Diogenes Laërtius says, "he had foretold them some things which events proved to be true," which may refer to his knowledge of natural phenomena. According to Diodorus Siculus,  Democritus died at the age of 90, which would put his death around 370 BC, but other writers have him living to 104,  or even 109. 
Popularly known as the Laughing Philosopher (for laughing at human follies), the terms Abderitan laughter, which means scoffing, incessant laughter, and Abderite, which means a scoffer, are derived from Democritus.  To his fellow citizens he was also known as "The Mocker". Hence the reference in Horace's Epistles, "Si foret in terris, rideret Democritus" ("If he were on earth, Democritus would laugh [at the vanity of human ambitions and amusements]"  ).
Most sources say that Democritus followed in the tradition of Leucippus and that they carried on the scientific rationalist philosophy associated with Miletus. Both were thoroughly materialist, believing everything to be the result of natural laws. Unlike Aristotle or Plato, the atomists attempted to explain the world without reasoning as to purpose, prime mover, or final cause. For the atomists questions of physics should be answered with a mechanistic explanation ("What earlier circumstances caused this event?"), while their opponents search for explanations which, in addition to the material and mechanistic, also included the formal and teleological ("What purpose did this event serve?"). Eusebius quoting Aristocles of Messene places Democritus in a line of philosophy that began with Xenophanes and culminated in Pyrrhonism. 
Quote by Democritus: "If you seek tranquility, do less." From Meditations by Marcus Aurelius according to Gregory Hayes, IV:24 (ref. G. Hayes' Notes) 
Later Greek historians consider Democritus to have established aesthetics as a subject of investigation and study,  as he wrote theoretically on poetry and fine art long before authors such as Aristotle. Specifically, Thrasyllus identified six works in the philosopher's oeuvre which had belonged to aesthetics as a discipline, but only fragments of the relevant works are extant hence of all Democritus's writings on these matters, only a small percentage of his thoughts and ideas can be known.
The theory of Democritus held that everything is composed of "atoms," which are physically, but not geometrically, indivisible that between atoms, there lies empty space that atoms are indestructible, and have always been and always will be in motion that there is an infinite number of atoms and of kinds of atoms, which differ in shape and size. Of the mass of atoms, Democritus said, "The more any indivisible exceeds, the heavier it is." However, his exact position on atomic weight is disputed. 
Leucippus is widely credited with having been the first to develop the theory of atomism, although Isaac Newton preferred to credit the obscure Mochus the Phoenician (whom he believed to be the biblical Moses) as the inventor of the idea on the authority of Posidonius and Strabo.  The Stanford Encyclopedia of Philosophy notes, "This theologically motivated view does not seem to claim much historical evidence, however". 
Democritus, along with Leucippus and Epicurus, proposed the earliest views on the shapes and connectivity of atoms. They reasoned that the solidness of the material corresponded to the shape of the atoms involved. Thus, iron atoms are solid and strong with hooks that lock them into a solid water atoms are smooth and slippery salt atoms, because of their taste, are sharp and pointed and air atoms are light and whirling, pervading all other materials.  Using analogies from humans' sense experiences, he gave a picture or an image of an atom that distinguished them from each other by their shape, their size, and the arrangement of their parts. Moreover, connections were explained by material links in which single atoms were supplied with attachments: some with hooks and eyes, others with balls and sockets.  The Democritean atom is an inert solid (merely excluding other bodies from its volume) that interacts with other atoms mechanically. In contrast, modern, quantum-mechanical atoms interact via electric and magnetic force fields and are far from inert.
The theory of the atomists appears to be more nearly aligned with that of modern science than any other theory of antiquity. However, the similarity with modern concepts of science can be confusing when trying to understand where the hypothesis came from. Classical atomists could not have had an empirical basis for modern concepts of atoms and molecules.
However, Lucretius, describing atomism in his De rerum natura, gives very clear and compelling empirical arguments for the original atomist theory. He observes that any material is subject to irreversible decay. Through time, even hard rocks are slowly worn down by drops of water. Things have the tendency to get mixed up: Mix water with soil and mud will result, seldom disintegrating by itself. Wood decays. However, there are mechanisms in nature and technology to recreate "pure" materials like water, air, and metals. [ citation needed ] The seed of an oak will grow out into an oak tree, made of similar wood as historical oak trees, the wood of which has already decayed. The conclusion is that many properties of materials must derive from something inside, that will itself never decay, something that stores for eternity the same inherent, indivisible properties. The basic question is: Why has everything in the world not yet decayed, and how can exactly some of the same materials, plants, and animals be recreated again and again? One obvious solution to explain how indivisible properties can be conveyed in a way not easily visible to human senses, is to hypothesize the existence of "atoms". These classical "atoms" are nearer to humans' modern concept of "molecule" than to the atoms of modern science. The other central point of classical atomism is that there must be considerable open space between these "atoms": the void. Lucretius gives reasonable arguments [ citation needed ] that the void is absolutely necessary to explain how gases and liquids can flow and change shape, while metals can be molded without their basic material properties changing.
The atomistic void hypothesis was a response to the paradoxes of Parmenides and Zeno, the founders of metaphysical logic, who put forth difficult-to-answer arguments in favor of the idea that there can be no movement. They held that any movement would require a void—which is nothing—but a nothing cannot exist. The Parmenidean position was "You say there is a void therefore the void is not nothing therefore there is not the void."   The position of Parmenides appeared validated by the observation that where there seems to be nothing there is air, and indeed even where there is not matter there is something, for instance light waves.
The atomists agreed that motion required a void, but simply ignored the argument of Parmenides on the grounds that motion was an observable fact. Therefore, they asserted, there must be a void. This idea survived in a refined version as Newton's theory of absolute space, which met the logical requirements of attributing reality to not-being. Einstein's theory of relativity provided a new answer to Parmenides and Zeno, with the insight that space by itself is relative and cannot be separated from time as part of a generally curved space-time manifold. Consequently, Newton's refinement is now considered superfluous. 
The knowledge of truth, according to Democritus, is difficult, since the perception through the senses is subjective. As from the same senses derive different impressions for each individual, then through the sensual impressions we cannot judge the truth. We can interpret the senses' data and grasp the truth only through the intellect, because the truth is in an abyss:
And again, many of the other animals receive impressions contrary to ours and even to the senses of each individual, things do not always seem the same. Which then, of these impressions are true and which are false is not obvious for the one set is no more true than the other, but both are alike. And this is why Democritus, at any rate, says that either there is no truth or to us at least it is not evident. 
Furthermore, they find Xenophanes, Zeno of Elea, and Democritus to be sceptics: … Democritus because he rejects qualities, saying,"Opinion says hot or cold, but the reality is atoms and empty space," and again, "Of a truth we know nothing, for truth is in a well." 
There are two kinds of knowing, the one he calls "legitimate" (γνησίη, gnēsiē, "genuine") and the other "bastard" (σκοτίη, skotiē, "secret"). The "bastard" knowledge is concerned with the perception through the senses therefore it is insufficient and subjective. The reason is that the sensual perception is due to the effluences of the atoms from the objects to the senses. When these different shapes of atoms come to us, they stimulate our senses according to their shape, and our sensual impressions arise from those stimulations. 
The second sort of knowledge, the "legitimate" one, can be achieved through the intellect, in other words, all the sense data from the "bastard" must be elaborated through reasoning. In this way one can get away from the false perception of the "bastard" knowledge and grasp the truth through inductive reasoning. After taking into account the sense impressions, one can examine the causes of the appearances, draw conclusions about the laws that govern the appearances, and discover the causality (αἰτιολογία, aetiologia) by which they are related. This is the procedure of thought from the parts to the whole or else from the apparent to nonapparent (inductive reasoning). This is one example of why Democritus is considered to be an early scientific thinker. The process is reminiscent of that by which science gathers its conclusions:
But in the Canons Democritus says there are two kinds of knowing, one through the senses and the other through the intellect. Of these he calls the one through the intellect 'legitimate' attesting its trustworthiness for the judgment of truth, and through the senses he names 'bastard' denying its inerrancy in the discrimination of what is true. To quote his actual words: Of knowledge there are two forms, one legitimate, one bastard. To the bastard belong all this group: sight, hearing, smell, taste, touch. The other is legitimate and separate from that. Then, preferring the legitimate to the bastard, he continues: When the bastard can no longer see any smaller, or hear, or smell, or taste, or perceive by touch, but finer matters have to be examined, then comes the legitimate, since it has a finer organ of perception. 
In the Confirmations . he says: But we in actuality grasp nothing for certain, but what shifts in accordance with the condition of the body and of the things (atoms) which enter it and press upon it. 
Democritus used to say that 'he prefers to discover a causality rather than become a king of Persia.' 
Ethics and politics
The ethics and politics of Democritus come to us mostly in the form of maxims. As such, the Stanford Encyclopedia of Philosophy has gone as far as to say that: "despite the large number of ethical sayings, it is difficult to construct a coherent account of Democritus's ethical views," noting that there is a "difficulty of deciding which fragments are genuinely Democritean." 
He says that "Equality is everywhere noble," but he is not encompassing enough to include women or slaves in this sentiment. Poverty in a democracy is better than prosperity under tyrants, for the same reason one is to prefer liberty over slavery. In his History of Western Philosophy, Bertrand Russell writes that Democritus was in love with "what the Greeks called democracy." Democritus said that "the wise man belongs to all countries, for the home of a great soul is the whole world."  Democritus wrote that those in power should "take it upon themselves to lend to the poor and to aid them and to favor them, then is there pity and no isolation but companionship and mutual defense and concord among the citizens and other good things too many to catalogue." Money when used with sense leads to generosity and charity, while money used in folly leads to a common expense for the whole society—excessive hoarding of money for one's children is avarice. While making money is not useless, he says, doing so as a result of wrongdoing is the "worst of all things." He is on the whole ambivalent towards wealth, and values it much less than self-sufficiency. He disliked violence but was not a pacifist: he urged cities to be prepared for war, and believed that a society had the right to execute a criminal or enemy so long as this did not violate some law, treaty, or oath. 
Goodness, he believed, came more from practice and discipline than from innate human nature. He believed that one should distance oneself from the wicked, stating that such association increases disposition to vice. Anger, while difficult to control, must be mastered in order for one to be rational. Those who take pleasure from the disasters of their neighbors fail to understand that their fortunes are tied to the society in which they live, and they rob themselves of any joy of their own. Democritus believed that happiness (euthymia) was a property of the soul. He advocated a life of contentment with as little grief as possible, which he said could not be achieved through either idleness or preoccupation with worldly pleasures. Contentment would be gained, he said, through moderation and a measured life to be content one must set one's judgment on the possible and be satisfied with what one has—giving little thought to envy or admiration. Democritus approved of extravagance on occasion, as he held that feasts and celebrations were necessary for joy and relaxation. He considers education to be the noblest of pursuits, but cautioned that learning without sense leads to error. 
Democritus was also a pioneer of mathematics and geometry in particular. We only know this through citations of his works (titled On Numbers, On Geometrics, On Tangencies, On Mapping, and On Irrationals) in other writings, since all of Democritus's body of work did not survive the Middle Ages.
According to Archimedes,  Democritus was among the first to observe that a cone and pyramid with the same base area and height has one-third the volume of a cylinder or prism respectively. Archimedes pointed out that Democritus didn't provide any proof of this statement, which was instead provided by Eudoxus of Cnidus.  
Moreover Plutarch (Plut. De Comm. 39) stated that Democritus had raised the following question: if a plane parallel to the base cuts a cone, are the surfaces of the section and of the base od the cone equal or unequal? If they are equal, the cone becomes a cylinder, while if they are unequal, the cone becomes an "irregular cone" with indentations or steps.  This question could be easily solved through calculus and it's been suggested, therefore, that Democritus may be considered a forerunner of infinitesimals and of integral calculus.  
Anthropology, biology, and cosmology
His work on nature is known through citations of his books on the subjects, On the Nature of Man, On Flesh (two books), On Mind, On the Senses, On Flavors, On Colors, Causes concerned with Seeds and Plants and Fruits, and Causes concerned with Animals (three books).  He spent much of his life experimenting with and examining plants and minerals, and wrote at length on many scientific topics.  Democritus thought that the first humans lived an anarchic and animal sort of life, going out to forage individually and living off the most palatable herbs and the fruit which grew wild on the trees. They were driven together into societies for fear of wild animals, he said. He believed that these early people had no language, but that they gradually began to articulate their expressions, establishing symbols for every sort of object, and in this manner came to understand each other. He says that the earliest men lived laboriously, having none of the utilities of life clothing, houses, fire, domestication, and farming were unknown to them. Democritus presents the early period of mankind as one of learning by trial and error, and says that each step slowly led to more discoveries they took refuge in the caves in winter, stored fruits that could be preserved, and through reason and keenness of mind came to build upon each new idea.  
Democritus held that originally the universe was composed of nothing but tiny atoms churning in chaos, until they collided together to form larger units—including the earth and everything on it.  He surmised that there are many worlds, some growing, some decaying some with no sun or moon, some with several. He held that every world has a beginning and an end and that a world could be destroyed by collision with another world. 
Like the other atomists, Democritus believed in a flat Earth and challenged arguments for its sphericity. 
According to Bertrand Russell, the point of view of Leucippus and Democritus "was remarkably like that of modern science, and avoided most of the faults to which Greek speculation was prone." 
Karl R. Popper  admired Democritus's rationalism, humanism, and love of freedom and writes that Democritus, along with fellow countryman Protagoras, "formulated the doctrine that human institutions of language, custom, and law are not taboos but man-made, not natural but conventional, insisting, at the same time, that we are responsible for them."
None of Democritus's writings have survived to the present day complete only fragments are known from his vast body of work. 
Empedocles (Empedokles) was a native citizen of Akragas in Sicily.   He came from a rich and noble family.    Very little is known about his life. His grandfather, also called Empedokles, had won a victory in the horse-race at Olympia in [the 71st Olympiad] OL. LXXI (496–95 BC).    His father's name, according to the best accounts, was Meton.   
All that can be said to be known about the dates of Empedocles is, that his grandfather was still alive in 496 BC that he himself was active at Akragas after 472 BC, the date of Theron’s death and that he died later than 444 BC. 
Empedocles "broke up the assembly of the Thousand. perhaps some oligarchical association or club."  He is said to have been magnanimous in his support of the poor  severe in persecuting the overbearing conduct of the oligarchs  and he even declined the sovereignty of the city when it was offered to him. 
According to John Burnet: "there is another side to his public character . He claimed to be a god, and to receive the homage of his fellow-citizens in that capacity. The truth is, Empedokles was not a mere statesman he had a good deal of the 'medicine-man' about him. . We can see what this means from the fragments of the Purifications. Empedokles was a preacher of the new religion which sought to secure release from the 'wheel of birth' by purity and abstinence. Orphicism seems to have been strong at Akragas in the days of Theron, and there are even some verbal coincidences between the poems of Empedokles and the Orphicsing Odes which Pindar addressed to that prince." 
His brilliant oratory,  his penetrating knowledge of nature, and the reputation of his marvelous powers, including the curing of diseases, and averting epidemics,  produced many myths and stories surrounding his name. In his poem "Purifications" he claimed miraculous powers, including the destruction of evil, the curing of old age, and the controlling of wind and rain.
Empedocles was acquainted or connected by friendship with the physicians Pausanias, and with various Pythagoreans and even, it is said, with Parmenides and Anaxagoras.  The only pupil of Empedocles who is mentioned is the sophist and rhetorician Gorgias. 
Timaeus and Dicaearchus spoke of the journey of Empedocles to the Peloponnese, and of the admiration, which was paid to him there  others mentioned his stay at Athens, and in the newly founded colony of Thurii, 446 BC  there are also fanciful reports of him travelling far to the east to the lands of the Magi. 
The contemporary Life of Empedocles by Xanthus has been lost.
According to Aristotle, he died at the age of sixty ( c. 430 BC ), even though other writers have him living up to the age of one hundred and nine.  Likewise, there are myths concerning his death: a tradition, which is traced to Heraclides Ponticus, represented him as having been removed from the Earth whereas others had him perishing in the flames of Mount Etna. 
According to Burnet: "We are told that Empedokles leapt into the crater of Etna that he might be deemed a god. This appears to be a malicious version of a tale set on foot by his adherents that he had been snatched up to heaven in the night. Both stories would easily get accepted for there was no local tradition. Empedokles did not die in Sicily, but in the Peloponnese, or, perhaps, at Thourioi. It is not at all unlikely that he visited Athens. . Timaios refuted the common stories [about Empedokles] at some length. (Diog. viii. 71 sqq. Ritter and. Preller .). He was quite positive that Empedokles never returned to Sicily after he went to Olympia to have his poem recited to the Hellenes. The plan for the colonisation of Thourioi would, of course, be discussed at Olympia, and we know that Greeks from the Peloponnese and elsewhere joined it. He may very well have gone to Athens in connexion with this." 
Empedocles is considered the last Greek philosopher to write in verse. There is a debate  about whether the surviving fragments of his teaching should be attributed to two separate poems, "Purifications" and "On Nature", with different subject matter, or whether they may all derive from one poem with two titles,  or whether one title refers to part of the whole poem. Some scholars argue that the title "Purifications" refers to the first part of a larger work called (as a whole) "On Nature".  There is also a debate about which fragments should be attributed to each of the poems, if there are two poems, or if part of it is called "Purifications" because ancient writers rarely mentioned which poem they were quoting.
Empedocles was undoubtedly acquainted with the didactic poems of Xenophanes and Parmenides  —allusions to the latter can be found in the fragments—but he seems to have surpassed them in the animation and richness of his style, and in the clearness of his descriptions and diction. Aristotle called him the father of rhetoric,  and, although he acknowledged only the meter as a point of comparison between the poems of Empedocles and the epics of Homer, he described Empedocles as Homeric and powerful in his diction.  Lucretius speaks of him with enthusiasm, and evidently viewed him as his model.  The two poems together comprised 5000 lines.  About 550 lines of his poetry survive.
In the old editions of Empedocles, only about 100 lines were typically ascribed to his "Purifications", which was taken to be a poem about ritual purification, or the poem that contained all his religious and ethical thought. Early editors supposed that it was a poem that offered a mythical account of the world which may, nevertheless, have been part of Empedocles' philosophical system. According to Diogenes Laërtius it began with the following verses:
Friends who inhabit the mighty town by tawny Acragas
which crowns the citadel, caring for good deeds,
greetings I, an immortal God, no longer mortal,
wander among you, honoured by all,
adorned with holy diadems and blooming garlands.
To whatever illustrious towns I go,
I am praised by men and women, and accompanied
by thousands, who thirst for deliverance,
some ask for prophecies, and some entreat,
for remedies against all kinds of disease. 
In the older editions, it is to this work that editors attributed the story about souls,  where we are told that there were once spirits who lived in a state of bliss, but having committed a crime (the nature of which is unknown) they were punished by being forced to become mortal beings, reincarnated from body to body. Humans, animals, and even plants are such spirits. The moral conduct recommended in the poem may allow us to become like gods again. If, as is now widely held, this title "Purifications" refers to the poem "On Nature", or to a part of that poem, this story will have been at the beginning of the main work on nature and the cosmic cycle. The relevant verses are also sometimes attributed to the poem of "On Nature", even by those who think that there was a separate poem called "Purifications".
On Nature Edit
There are about 450 lines of his poem "On Nature" extant,  including 70 lines which have been reconstructed from some papyrus scraps known as the Strasbourg papyrus. The poem originally consisted of 2000 lines of hexameter verse,  and was addressed to Pausanias.  It was this poem which outlined his philosophical system. In it, Empedocles explains not only the nature and history of the universe, including his theory of the four classical elements, but he describes theories on causation, perception, and thought, as well as explanations of terrestrial phenomena and biological processes.
Although acquainted with the theories of the Eleatics and the Pythagoreans, Empedocles did not belong to any one definite school.  An eclectic in his thinking, he combined much that had been suggested by Parmenides, Pythagoras and the Ionian schools.  He was a firm believer in Orphic mysteries, as well as a scientific thinker and a precursor of physics. Aristotle mentions Empedocles among the Ionic philosophers, and he places him in very close relation to the atomist philosophers and to Anaxagoras. 
Another of the fragments of the dialogue On the Poets (Aristotle) treats more fully what is said in Poetics ch. i about Empedocles, for though clearly implying that he was not a poet, Aristotle there says he is Homeric, and an artist in language, skilled in metaphor and in the other devices of poetry.
Empedocles, like the Ionian philosophers and the atomists, continued the tradition of tragic thought which tried to find the basis of the relationship of the One and the Many. Each of the various philosophers, following Parmenides, derived from the Eleatics, the conviction that an existence could not pass into non-existence, and vice versa. Yet, each one had his peculiar way of describing this relation of Divine and mortal thought and thus of the relation of the One and the Many. In order to account for change in the world, in accordance with the ontological requirements of the Eleatics, they viewed changes as the result of mixture and separation of unalterable fundamental realities. Empedocles held that the four elements (Water, Air, Earth, and Fire) were those unchangeable fundamental realities, which were themselves transfigured into successive worlds by the powers of Love and Strife (Heraclitus had explicated the Logos or the "unity of opposites"). 
The four elements Edit
Empedocles established four ultimate elements which make all the structures in the world—fire, air, water, earth.   Empedocles called these four elements "roots", which he also identified with the mythical names of Zeus, Hera, Nestis, and Aidoneus  (e.g., "Now hear the fourfold roots of everything: enlivening Hera, Hades, shining Zeus. And Nestis, moistening mortal springs with tears").  Empedocles never used the term "element" ( στοιχεῖον , stoicheion), which seems to have been first used by Plato.  According to the different proportions in which these four indestructible and unchangeable elements are combined with each other the difference of the structure is produced.  It is in the aggregation and segregation of elements thus arising, that Empedocles, like the atomists, found the real process which corresponds to what is popularly termed growth, increase or decrease. Nothing new comes or can come into being the only change that can occur is a change in the juxtaposition of element with element.  This theory of the four elements became the standard dogma for the next two thousand years.
Love and Strife Edit
The four elements, however, are simple, eternal, and unalterable, and as change is the consequence of their mixture and separation, it was also necessary to suppose the existence of moving powers that bring about mixture and separation. The four elements are both eternally brought into union and parted from one another by two divine powers, Love and Strife (Philotes and Neikos).   Love ( φιλότης ) is responsible for the attraction of different forms of what we now call matter, and Strife ( νεῖκος ) is the cause of their separation.  If the four elements make up the universe, then Love and Strife explain their variation and harmony. Love and Strife are attractive and repulsive forces, respectively, which are plainly observable in human behavior, but also pervade the universe. The two forces wax and wane in their dominance, but neither force ever wholly escapes the imposition of the other.
According to Burnet: "Empedokles sometimes gave an efficient power to Love and Strife, and sometimes put them on a level with the other four. The fragments leave no room for doubt that they were thought of as spatial and corporeal. . Love is said to be "equal in length and breadth" to the others, and Strife is described as equal to each of them in weight (fr. 17). These physical speculations were part of a history of the universe which also dealt with the origin and development of life." 
The sphere of Empedocles Edit
As the best and original state, there was a time when the pure elements and the two powers co-existed in a condition of rest and inertness in the form of a sphere.  The elements existed together in their purity, without mixture and separation, and the uniting power of Love predominated in the sphere: the separating power of Strife guarded the extreme edges of the sphere.  Since that time, strife gained more sway  and the bond which kept the pure elementary substances together in the sphere was dissolved. The elements became the world of phenomena we see today, full of contrasts and oppositions, operated on by both Love and Strife.  The sphere of Empedocles being the embodiment of pure existence is the embodiment or representative of God. Empedocles assumed a cyclical universe whereby the elements return and prepare the formation of the sphere for the next period of the universe.
Empedocles attempted to explain the separation of elements, the formation of earth and sea, of Sun and Moon, of atmosphere.  He also dealt with the first origin of plants and animals, and with the physiology of humans.  As the elements entered into combinations, there appeared strange results—heads without necks, arms without shoulders.   Then as these fragmentary structures met, there were seen horned heads on human bodies, bodies of oxen with human heads, and figures of double sex.   But most of these products of natural forces disappeared as suddenly as they arose only in those rare cases where the parts were found to be adapted to each other did the complex structures last.  Thus the organic universe sprang from spontaneous aggregations that suited each other as if this had been intended.  Soon various influences reduced creatures of double sex to a male and a female, and the world was replenished with organic life.  It is possible to see this theory as an anticipation of Charles Darwin's theory of natural selection, although Empedocles was not trying to explain evolution. 
Perception and knowledge Edit
Empedocles is credited with the first comprehensive theory of light and vision. Historian Will Durant noted that "Empedocles suggested that light takes time to pass from one point to another."  . He put forward the idea that we see objects because light streams out of our eyes and touches them. While flawed, this became the fundamental basis on which later Greek philosophers and mathematicians like Euclid would construct some of the most important theories of light, vision, and optics. 
Knowledge is explained by the principle that elements in the things outside us are perceived by the corresponding elements in ourselves.  Like is known by like. The whole body is full of pores and hence respiration takes place over the whole frame. In the organs of sense these pores are specially adapted to receive the effluences which are continually rising from bodies around us thus perception occurs.  In vision, certain particles go forth from the eye to meet similar particles given forth from the object, and the resultant contact constitutes vision.  Perception is not merely a passive reflection of external objects. 
Empedocles noted the limitation and narrowness of human perceptions. We see only a part but fancy that we have grasped the whole. But the senses cannot lead to truth thought and reflection must look at the thing from every side. It is the business of a philosopher, while laying bare the fundamental difference of elements, to show the identity that exists between what seem unconnected parts of the universe. 
In a famous fragment,  Empedocles attempted to explain the phenomenon of respiration by means of an elaborate analogy with the clepsydra, an ancient device for conveying liquids from one vessel to another.   This fragment has sometimes been connected to a passage in Aristotle's Physics where Aristotle refers to people who twisted wineskins and captured air in clepsydras to demonstrate that void does not exist.  There is however, no evidence that Empedocles performed any experiment with clepsydras.  The fragment certainly implies that Empedocles knew about the corporeality of air, but he says nothing whatever about the void.  The clepsydra was a common utensil and everyone who used it must have known, in some sense, that the invisible air could resist liquid. 
Like Pythagoras, Empedocles believed in the transmigration of the soul/metempsychosis, that souls can be reincarnated between humans, animals and even plants.  For Empedocles, all living things were on the same spiritual plane plants and animals are links in a chain where humans are a link too.  Empedocles was a vegetarian   and advocated vegetarianism, since the bodies of animals are the dwelling places of punished souls.  Wise people, who have learned the secret of life, are next to the divine,   and their souls, free from the cycle of reincarnations, are able to rest in happiness for eternity. 
Diogenes Laërtius records the legend that Empedocles died by throwing himself into Mount Etna in Sicily, so that the people would believe his body had vanished and he had turned into an immortal god  the volcano, however, threw back one of his bronze sandals, revealing the deceit. Another legend maintains that he threw himself into the volcano to prove to his disciples that he was immortal he believed he would come back as a god after being consumed by the fire. Horace also refers to the death of Empedocles in his work Ars Poetica and admits poets the right to destroy themselves. 
In Icaro-Menippus, a comedic dialogue written by the second century satirist Lucian of Samosata, Empedocles' final fate is re-evaluated. Rather than being incinerated in the fires of Mount Etna, he was carried up into the heavens by a volcanic eruption. Although a bit singed by the ordeal, Empedocles survives and continues his life on the Moon, surviving by feeding on dew.
Empedocles' death has inspired two major modern literary treatments. Empedocles' death is the subject of Friedrich Hölderlin's play Tod des Empedokles (The Death of Empedocles), two versions of which were written between the years 1798 and 1800. A third version was made public in 1826. In Matthew Arnold's poem Empedocles on Etna, a narrative of the philosopher's last hours before he jumps to his death in the crater first published in 1852, Empedocles predicts:
To the elements it came from
Everything will return.
Our bodies to earth,
Our blood to water,
Heat to fire,
Breath to air.
In his History of Western Philosophy, Bertrand Russell humorously quotes an unnamed poet on the subject – "Great Empedocles, that ardent soul, Leapt into Etna, and was roasted whole." 
In J R by William Gaddis, Karl Marx's famous dictum ("From each according to his abilities, to each according to his needs") is misattributed to Empedocles. 
In 2006, a massive underwater volcano off the coast of Sicily was named Empedocles. 
In 2016, Scottish musician Momus wrote and sang the song "The Death of Empedokles" for his album Scobberlotchers. 
Elephants in t… 13 September 2011
An interesting take on zeno's paradox
Luke Cash 28 September 2011
Zeno's Dichotomy Paradox
Zeno's Dichotomy Paradox is refuted by modern day philosophy, because a distinction is now made between a potential infinity and an "actual infinity". Al-Ghazali first established this when he, amongst his criticism of Islamic philosophers who believed in a universal understanding of Platonic Forms, used similar logic to refute the idea of an actual infinity.
In the other discussion, it was hinted at that in modern set theory the use of actually infinite sets is commonplace. The set of the natural numbers <0,1,2. >has an actually infinite number of members in it. The number of members in this set is not merely potentially infinite, rather the number of members is actually infinite according to set theory.
But this merely shows that if you adopt certain axioms and rules, then you can talk about actually infinite collections in a consistent way without contradicting yourself. All it does is shows how to set up a certain universe of discourse for talking consistently about actual infinities. But it does nothing to show that such mathematical entities really exist or that an actually infinite number of things can really exist.
This isn't a claim an actually infinite number of things involves a logical contradiction but that it is really impossible. For example, the claim that something came into existence from nothing isn't logically contradictory, but nonetheless it is really impossible.
The absurdities of an actual infinity
First, let's define what absurd means here:
absurd - utterly or obviously senseless, illogical, or untrue contrary to all reason or common sense
So when we say it results in an absurdity, we don't mean to imply that it's merely "baffling", or that it is "misunderstood" or that it is contrary to our knowledge. But rather, it is because we do understand the concept of actual infinity and the implications of it existing in actuality, that such examples cannot be true (thus, absurd).
German mathematician David Hilbert used the following illustration to show why an actual infinity is impossible. It's called "Hilbert's Hotel".
Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied – that is to say every room contains a guest. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms.
Suppose a new guest arrives and wishes to be accommodated in the hotel. Because the hotel hasinfinitely many rooms, we can move the guest occupying room 1 to room 2, the guest occupying room 2 to room 3 and so on, and fit the newcomer into room 1. By repeating this procedure, it is possible to make room for any finite number of new guests.
It is also possible to accommodate a countably infinite number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and in general room n to room 2n, and all the odd-numbered rooms will be free for the new guests.
This of course, results in the hotel being always able to accommodate guests, even though all the rooms were full when the guests arrived. The sign outside the hotel could read: "No Vacancy (Guests Welcome)".
It gets even more absurd. What happens if some of the guests start to check out? Suppose all the guests in the odd numbered rooms check out. In this case, an infinite number of people has left. and there are just as many guests who have remained behind. And yet. there are no fewer people in the hotel! The number is just infinite. The manager decides that having a hotel 1/2 full is bad for business. This isn't a problem with an actual infinity. By moving the guests as before, only in reverse order, he converts the half-empty hotel into one that is full! Seems like a simple way to keep doing business (in this absurd reality). but not necessarily.
What happens if guests 4, 5, 6, etc. check out? In a single moment the hotel is reduced to a mere 3 guests (1, 2 and 3). The infinite just converted to finitude. Yet, it is the case that the same # of guests checked out this time as when all the guests in the odd-numbered rooms checked out. Hilbert's Hotel is absurd. It is impossible in actuality."
Peter Adamson 1 October 2011
Without getting into Hilbert's Hotel which is above my pay grade, I just wanted to note that Aristotle is actually the originator of the actual/potential infinity distinction. He basically allows potential infinities in various contexts, but doesn't allow actual infinity in any context. (And this is indeed the core of his response to Zeno.) He's followed in that by most ancient and medieval thinkers.
Al-Ghazali was joining an ongoing debate about the eternity of the world, part of which was the question of whether a world that has already existed for an eternity would somehow involve actual infinity. For instance al-Ghazali's predecessor in the Islamic tradition, al-Kindi, argued that the world is not eternal precisely on the basis that an actually infinite number of moments would already have had to elapse. In general I'd say that the pro-eternity camp felt obligated to insist that an already eternal world would involve only potential infinity. We'll get to this in due course!
Not sure what you mean about al-Ghazali objecting to Platonic Forms, though?
In reply to Infinities by Peter Adamson
Right, that comment about al-Ghazali originating that idea was definitely from left field, and I didn't mean that. I was thinking of al-Ghazali in that he had some interesting things to say about the subject, and he (IMO) did the best job of defining "potential" and "actual" infinities when it comes to medieval philosophers, using those ideas to refute a static, eternal backwards and forwards, creation.
He also wrote about Greek philosophy and his issues with it, if I remember correctly. I'll try to get back to you soon with those works.
Peter Adamson 8 March 2012
Ghazali and infinity
Interesting -- well, I think Averroes would be very unhappy with your praise of Ghazali because he complains that Ghazali fails precisely to make this distinction between actual and potential infinity (which is Aristotelian). Philoponus is the most acute eternity opponent here, I think, because he argues explicitly that past infinite time would be an _actual_ infinity. Ghazali thinks that too I suppose but he is less clear, the point emerges best when he draws an analogy between infinite time and infinite spatial extent.
Needless to say this will all be covered with care in future episodes.
In reply to Ghazali and infinity by Peter Adamson
I'll have to look into that. I'd certainly trust your opinion better than mine at this rate. Thanks for your time.
Luke Cash 28 September 2011
Also on Zeno's work
The arrow at rest actually seems reminiscient of Newtonian physics. Do you think there would be any substance to that comparison? I think it would have substance if Zeno was thinking of the arrow in the sense that it was being propelled, or a Greek might have termed it compelled, to go in the velocity it went.
Peter Adamson 1 October 2011
In reply to Also on Zeno's work by Luke Cash
This has indeed occasioned a good deal of comment about the arrow. One way of thinking about it might be that Zeno is precisely not anticipating Newton, because he is thinking of an arrow in mid-flight "at a moment" as being simply at rest, which leaves out the idea of impetus. There is an interesting anticipation of theories of momentum or impetus in the late ancient thinker John Philoponus. stay tuned for episode 93 or so.
Here is an interesting resource on paradoxes from University of Notre Dame.
The link goes to the page about Zeno:
Do we truly understand the Eleatics position on the infinite?
When I imagine Zeno and Parmenidies giving discourse on "Oneness" and the paradox of movement, it strikes me that these men held onto these doctrines, and found them to hold keen to truth. It brings the thought to mind: Did the Eleatics imagine things in being were possessive of the infinite?
It seems as though they did, for by stating that "All is one", and that there is no such thing as non-being, everything that we seem to know and surrounds us must be eternal (infinite) in nature and made up of things that have no beginning or end. A constant state of being.
Upholding the paradox of movement, Zeno undoubtedly moved around each day. So what was at the core of his belief, to allow him to hold true to the paradox, though he defied it at every moment?
Enter the Eleatic perception of oneness, of infinity: if all is one, nothing is short of oneness, making us, and everything else, infinite and eternal. Thus, by being, we are eternal and infinite.
Lets go from there, and look at the dichotomy paradox. If we must be in contact with an infinite number of things on our path from the baseline to the service line on a tennis court, we'd struggle as a finite being, with not enough "Time" to reach all those points. However, does this not change once we perceive ourselves possessed of oneness, being infinite ourselves? It is but a trivial matter to reach all the points, because they are not separate from us: we are in contact and a part of everything else. We can traverse the distance because it is a part of us, a part of the oneness that pervades all things. The reduction (1/2, 1/4, 1/8, etc) always leads back to the whole, and this must have been at the core of their philosophy. I may be 1 out of 7 billion people, but we're all people, and people may be one of a certain species, etc etc until we reach the most elementary piece from which all things have their origin - the oneness that Parmenides and Zeno advocated for.
I close with a question: how close can we really get to these minds, thousands of years later, pervaded with centuries of philosophy and thought, influenced by modern science and mathematics? Can we experience as they did the intoxication of their knowledge and profound reasoning? And what steps were there beyond the writings we have? Ah, so much dashing about the shadows of history, with only morsels to sate ourselves with! But the quest through darkness, unearthing light, never loses its appeal through millennia - let us continue to add to the store of treasures to be found!
Peter Adamson 4 April 2012
Well I certainly share your eloquently phrased worry in the last paragraph. Particularly worrying for me given that I do this for a living. But I think the goal has to be to read them as sympathetically as possible and try to come up with an interpretation that makes sense given their own philosophical concerns, insofar as we can understand them - it's crucial to figure out what sorts of pressure (philosophical or otherwise) these long-dead people were responding to with their theories.
Along these lines I would also like to agree with your point about Zeno: surely he knew he was moving around all the time? So there is a deep problem here about the Eleatics and what they would say about the deliverances of everyday experience. Are these just an illusion? Or perhaps a less-than-fully-adequate understanding of reality? Remember that Parmenides also wrote his Way of Opinion which accepts multiplicity, motion, etc. So a good answer to this question is basically a plausible interpretation of the Poem and, in particular, why it includes a Way of Opinion, not just a Way of Truth.
In reply to The Eleatics by Peter Adamson
Way of knowledge
Great work Peter! I am listening eagerly, with no background in philosophy, (and english is a second language). I experience the same pull as the person writing the previous post, which is to listen to these thinkers whith as much empathy as I can. The presocratics' schools, make me wonder if their search for an explanation of reality, was supposed to lead them to a fundamental experience. You say at one point, (paraphrasing), that ". their approach is a conceptual analysis rather than a search for empirical evidence". But is it possible that they were looking for an empirical "universal experience of beingness" through their reflexions? I studied the Bön/buddhist tradition, and a lot of what they are doing, ressemble what Bön practionners call "exhausion of the mind" exercises. The Koan version in Zen has that same function I believe. It is meant to bring you to the edge of conceptual analysis, (similar to Zeno paradoxes), to liberate you into pure beingness. This state comes from relasing the tension after creating an extreme investigation of the paradoxical nature of life, to get to its outer limits, to the "Unbounded Wholeness" that Bön mystics talk about (very similar to Anaximander). Is it possible that the writings of these philosophers had an adjoined "meditative" praxis in reality, that were maybe the real secret of the schools, and were transmitted directly form teacher to disciple? It might be that limiting the analysis and critic of these thinkers to the logical aspect of their arguments, makes us "literalists/reductionists", and that we are missing the real function of their work, which would be to teach us to get to an actual experience, (although it does not contradict more thought processes if required to reach the state). In the same line of reasoning (which is far fetched and probably difficult to prove), the real function of their thought processes, might have been to do away with them all together. I know it is probably a very biased and historically unsubstantiated approach, but there was so much (and still is), of that clear delineation between theory and practice in ancient cultures, and the importance of direct, but very often secret transmission of knowledge. I am tempted to contend, that through time and within the constraint of our era, we are all searching for a way to end the divisive nature of our mind, to reach an experience of lasting peace, and what best way to achieve this than do it than through the mental temporary breakdown we experience when confronted with
unsolvable paradoxes? Best to you and thank you for your great work.
Peter Adamson 28 December 2018
Thanks for your comment! That's an interesting idea and I would go with it to a certain extent: especially the Eleatics (Parmenides, Zeno, and Melissus) were in some sense trying to show the boundaries of what can be thought, or at least the falsehood of thinking as we normally do it. Of course we can't know what went on in terms of practices or teacher-student training in this tradition, as we have only the texts, or rather not even those but only fragments and reports. However I have to say that if your reading is anywhere near the truth, then Plato and Aristotle were staggeringly far off the mark in their reports of what the Presocratics were up to, since they present the Presocratics basically as cosmologists. In that sense I think what you're suggesting is not only unsupported by the evidence we have, but contradicted by that evidence.
By the way the point about using conceptual analysis and not empirical inquiry was only supposed to be about the Eleatics, I don't think it necessarily applies to, say, Heraclitus or Anaxagoras, though it would fit for the Atomists quite well.
Infinity in modern mathematics
Your presentation of modern mathematics' treatment of Zeno's paradoxes, which was basically that mathematics just asserts finite answers, is really inaccurate and misleading. As far back as Ancient Greek mathematicians like Eudoxus and Archimedes, and certainly after modern developments which started in the 1800s, mathematicians have done a lot of work analysing these matters, culminating in a substantive and rigorous body of work called "Analysis". This provides real answers to questions about the nature of infinite series in mathematics and physics, definitely not just a set of assertions.
Peter Adamson 12 July 2014
I'm not sure what exact phrase you're picking up on here (this episode was a long time ago!) but I don't recall accusing mathematicians, ancient or modern, of merely asserting anything. I think I just said that with modern mathematics one can easily model infinite series that look like Zeno's paradox e.g. 1/2 +1/4 + 1/8. and there is no problem with seeing such a series as adding up to 1. Then I think I might have added that there is still a question as to whether that mathematical model in fact corresponds to what is happening in physical reality, like in space and time - and obviously that is not a question that mathematics by itself can (or needs to) answer.
In reply to infinity by Peter Adamson
It's around 8.20 where you're talking about a mathematical approach, and you say,
"we now have no problem that 1/2 + 1/4 + . just adds up to one in fact, we might say that the number represented by this series just IS 1".
Well, anybody who did say this would be wrong to do so. This excerpt sounded like you were essentially presenting the aforementioned fact as an axiomatic or close-to-axiomatic fact of mathematics, which nowadays is very far from the case - it can be given a substantive deduction from some very conservative axioms of logic and sets. And I don't think the wider context provided any further clarification.
And with respects to that wider context of models, I think this becomes a kind of important point. because the fact that the deduction IS substantive means there's really no reason to think of it as a tautological question of justifying an abstract model rather, it reduces to justifying the much more fundamental and evident axioms. Once these are granted, the resolution to Zeno's problems just becomes a matter of logical consequence.
I suppose the wider point I'm making is that I felt like that section presented the mathematical work as unequivocally independent of the arguments, when the mathematics is actually substantive and of real consequence to the philosophical and physical questions. in fact I'd go so far as to say that mathematical and philosophical arguments are essentially the same thing in this case. Zeno was, after all, in the mere act of talking about these matters, adopting a whole bunch of tacit axioms about space and time, and using standard logical inferences. All mathematics does is state what these are in a formal language. which has the advantage of throwing the wobblier aspects of his discourse into sharp relief.
But of course, you have a finite time in which to distil an infinite number of arguments and counterarguments, so I suppose truncations are, regrettably, inevitable.
Peter Adamson 13 July 2014
Right, I was definitely sketching the mathematical solution there rather than really getting into it. In fact (though again I don't really remember, since I wrote the script years ago now) I was probably trying to evade any commitment by saying "we might say that. " The point you make is an interesting one. Zeno himself was almost certainly adopting a strategy like the one you suggest here: consider various assumptions about space and time, and show that on any of the assumptions motion is impossible. Here it is important that the dichotomy is only one of an array of paradoxes, and was probably meant to be complemented by others.
Anyway I would certainly agree with your basic point, which is that modern mathematicians would trace these points about infinite series to more fundamental axioms. I do still think that there is a question about whether the mathematical modeling of a motion (however we justify the model) is going to correspond to what is really happening in physical reality. There is a basic question there about philosophy of mathematics and science, and philosophers have taken various views on it, e.g. that mathematics is only instrumentally useful for doing physics. But I wasn't, of course, trying to get very far into those issues in this podcast, just to explain that Zeno's paradox is more challenging than one might think, even in light of subsequent developments in mathematics.
In reply to Math again by Peter Adamson
Indeed, I don't think there is any way he could avoid such a strategy. In simply using the word "space", he is communicating to us a concept with a bunch of properties if this weren't the case and he weren't asserting any properties at all for the object at hand, then the word wouldn't refer to anything - and then we might as well conceptualise "space" as referring to giraffes - and then find the rest of the argument nonsensical. So, whilst the issue of whether various axioms behind a "mathematical" argument veritably describe motion is definitely something that needs to be considered, that's not a problem about mathematics per se the same exact issue is the case with the tacit properties behind Zeno's argument. And so when (speaking rhetorically of course) you said, "to a mathematical resolution, Zeno would ask you why your model is correct", my first response to Zeno would be, "but you haven't even tried to specify what you take the properties of space to be - so what is YOUR model, and then why is THAT correct?".
P.S. thanks for all the food for thought Peter. It's hard to make critical objections without sounding negative so let me say this podcast is truly fantastic. I tried a couple of other philosophy podcasts recently but they absolutely pale in comparison. in fact this applies to a bunch of books I've tried too, including Russell's famous one. Masterful from the very beginning.
Peter Adamson 17 July 2014
Thanks very much! Regarding Zeno, remember that he doesn't (at least in theory) even believe there is such a thing as motion or "space". Rather the dialectical situation is that he is implicitly assuming what is, for him, a false premise which is that space is extended and is infinitely divisible. If someone rejected that and said that space had other properties, e.g. is not infinitely divisible, he could and in fact did offer different paradoxes aiming at this rival assumption. In other words Zeno doesn't want to make any particular claim about the nature of motion or space, rather he wants to show that any non-Eleatic theory (any theory that makes motion possible) will have to make some such assumptions, which will lead to a contradiction/paradox. Does that make sense?
Can time really pass?
I'm thinking about a paradox, which may be parallel to Dichotomy paradox.
We can divide a time period (say one hour) infinitely many times. So if one hour is going to pass, first half an hour should pass and so on.
I'm wondering why Eleatics did not conclude that time does not pass at all. Maybe because it was not among Parmenides' teachings?
Or maybe they did but I have not heard of it?
Peter Adamson 19 July 2014
Eleatics on time
There is no Zeno argument quite like the one you are describing, though the Arrow in particular looks like it is raising questions about time. However Parmenides' Poem itself does say "it was not and will not be, but is," which has often been taken to be a denial of time's applying to Being - sometimes people credit him with the notion of timeless eternity though others find that a bit much to read into the passage. It could for instance just mean that Being does not change (in other words, it is what it is now and was never different, and will never be different - this is bound up with the infamous problem about whether the verb "to be" is being used by Parmenides existentially or as implying a predicate, like "to be/exist" vs. "to be blue").
Paradox of travelling a distance (infinite series): Zeno
If there are infinte mid distances in between a finite distance then is also infinite half-time avialable within the finite time.Does that solve that paradox, doc ?
Peter Adamson 31 May 2015
Maybe I don't follow what you're suggesting, but I think that just IS the paradox: that a finite distance contains an infinity of parts, which can't all be traversed.
In reply to Zeno by Peter Adamson
Paradox of travelling a distance (infinite series): Zeno
I got that. What I was exphasizing that just like there is an infinite series of half-distance within the given distance (that has to be traversed), there is smilarly an infinite series of "half-time" within the estimated time to cover that distance. For example if that particular distance (lets say 20 m) is covered in 2 min, then half of that is covered in 1 min, 5 m with will be covered in 30 sec, 2.5 m will be covered in 15 sec and so forth. Which means as the distance can be broken into intifinte halves similarly time can be broken into infinite halves. So infinite steps were taken in simlar infinte moments of time and those infinite moments of time made it possible to traverse those infinite series of half distances. I hope I was able to explain this. English is not my mother tongue actually.
Peter Adamson 1 June 2015
Oh, I see. Your solution is in fact exactly what Aristotle thinks, and how he responds to Zeno. I probably discuss that in episode 40.
Griffin Werner 21 February 2018
Motion is impossible
I don't see it as rediculous for Parmenides and his followers to think that motion is impossible. They obviously are not referring to the idea of motion that modern people would think based on Newton's Laws and modern physics. I can understand how the Eleatics would see me walking down the street for example as not moving. Obviously, I am moving, but that is only with respect to some other observer: the street, the sun, someone watching. If two people are moving at the same speed relative to each other, then they seem to not be moving at all to each other. I think the Eleatic notion that moving/motion is impossible is given credence due to this notion of relativity.
Though Melissus wouldn't like it, if we were to think of the sphere of reality as a clear, solid, glass ball, it would look to us that not only is the ball not moving, but nothing inside of it is moving either. However, that is not the case. From the perspective of an atom inside the ball, there is a lot of motion happening, with electrons flying around and everything shaking like crazy. If we go even smaller to the perspective of a proton on an atom in the ball, its vibrating along with all the protons and neutrons around it and can see streaks of electron flying by every so often. If we tell the proton that moving is impossible, it would just laugh because obviously it is impossible (no, laughing protons are not impossible). However, looking at the ball in its totality (oneness), we see it as not moving at all. By analogy, I think this is the perspective that Parmenides and the Eleatics had of reality. It is pretty convincing, and I can see why it lasted as long as it did in the history of philosophy. I like Aristotle's view that as one thing moves, it allows another to take its place, similar to what goes on at the quantum level in the glass ball.
There is still the whole problem of the "outside" which would imply non-being, but despite that, I think it problematic to apply the modern conception of motion (which is packed with unique meaning given the last 4 hundred years of physics) with the presocratic. I would be interested to see the original work of Parmenides and other Eleadics in the Greek to see if that would shed light on what seems obviously wrong in Eleadic thought from the modern perspective.
Peter Adamson 22 February 2018
In reply to Motion is impossible by Griffin Werner
Relativity and Eleaticism
That's a nice thought but it doesn't, I would say, capture what the Eleatics were claiming. They are apparently saying not just that existence as a whole doesn't move, as with your glass ball example, but that it contains no internal motion either. In fact there is no multiplicity at all in their metaphysics. So we can't ascribe to them the view that, for instance, two things are unmoving relative to one another, or that two things are moving within an unmoving larger whole: rather, there are never two things at all, only one thing, namely Being. Still I like your instinct to try to find a way to make it make sense!
Griffin Werner 22 February 2018
In reply to Relativity and Eleaticism by Peter Adamson
If what you say is true, then
If what you say is true, then I find it very difficult to see the world from the perspective of an Eleatic given my experience of reality. If I am going to criticize their metaphysic, I want to do it on their terms. Obviously there is a multiplicity I am me and my computer is not me. However, the idea of a computer cannot exist independently from anything else in existence. One could argue that my computer and I being different is just a useful categorical tool used by humans in order to make sense of the world. Meaning, there is no real separation/difference/multiplicity. Everything simply is. In Eleatic terms, there is only one thing, Being.
I find it hard to believe that if I were to ask an Eleatic if he and I were different or if he and I together made two people that he would say no. Sure, ultimately there is no separation and all is one. I can get behind that. It may be the case that everything simply is and that multiplicity is an illusion, but in order to live a human life, I would argue that one (including the Eleatics) must give into the illusion at least a little bit. My experience tells me that there is separation, even if it's an illusion.
If the Eleatics were seriously telling people that they weren't moving when they were clearly walking or that there was no difference or separation between themselves and a tree, it seems to me that they were simply crazy, or they were caught up in an abstract argument that seemed to defy their immediate experience, and instead of trying to figure out the flaws in the abstract argument, they just decided that all experience is an illusion.
I think what I am trying to say is that based on my understanding of the Eleatic worldview, one cannot prove that it is correct or not in the same way that I cannot prove that I actually exist or not.
It could be that I'm misunderstanding their worldview, but I feel as if understanding their worldview from their perspective can't lead to the conclusion that they were simply dumb because they thought motion was impossible when it clearly is. It had to have made sense from their perspective.
Peter Adamson 22 February 2018
In reply to If what you say is true, then by Griffin Werner
Well, basically what you are implying there is that there cannot have been any monists (people who deny the reality of multiplicity) in the history of philosophy, because monism is obviously false. But in fact monism appears recurrently, and apparently independently, in the history of philosophy: for instance in Advaita Vedanta, and also in a different way in Spinoza. The Eleatics do seem to have been monists, and in fact to have said exactly what you are saying is so unbelievable: remember that Parmenides also wrote a "way of opinion" in addition to the monist "way of truth", in which he basically makes the concession of giving a theory of reality that coheres with how it _seems_ to be. An interesting question is why we have the way of truth and the way of opinion but it seems pretty clear that the way of truth is privileged and that it does involve denying multiplicity.
More generally, lots of philosophers in history have had radically revisionary theories of reality: everything is an illusion, only immaterial things exist, moral judgments do not have any basis in reality, we cannot know anything for sure, etc. etc. I think one should approach these theories "charitably" in the sense of trying to understand what reasoning drove them to such radical conclusions but not in the sense of deciding they can't possibly be serious in putting forward their revisionary theories, because we find them so counterintuitive.
Griffin Werner 23 February 2018
In reply to Silly Eleatics by Peter Adamson
Okay, I think I get it now. If I was in a room with an Eleatic, and he was explaining to me his monist theory, my critique of him would be that: the very fact that he is explaining his theory to me implies a contradiction because he would have to accept that he and I were different to even have the conversation. His responce to me would be something like, "No it is not a contradiction. Everything is simply one. These ideas of 'you,' 'I,' and 'conversation' are illusions. Therefore, there is no multiplicity, no motion, no duality." Is that more or less accurate?
Thank you, by the way, for your work on this podcast. I am really enjoying it so far. Hopefully I will be able to catch up soon, as I am only on episode 15. I'm especially excited to listen to the Islamic World talks, as I have almost no background in the History of Islamic thought. I wish you the best as you continue with this massive project.
Peter Adamson 23 February 2018
In reply to Thanks! by Griffin Werner
Talking to Eleatics
Yes, that is exactly the idea. In fact the response you suggest, that merely the possibility of putting forward the Eleatic to another person shows that it is wrong, is reminiscent of some ancient critiques of radical philosophical positions. For instance Aristotle argues that no one can assert that the law of non contradiction is false and Plato in several places points out that there are theories whose assertion is self-undermining. I guess though that, as you say, the Eleatic would happily admit that the appearance of having a conversation with him is just another illusion.
Hope you enjoy the rest of the series!
Alexander Johnson 15 July 2018
I have an issue with the contemporary view of Zeno's paradox as not giving the people of the era the credit they deserve in terms of intellectual capacity, and just is not very satisfying. However, when i read it, instead of a paradox of motion, but a paradox of discreet space, it makes more sense. I understand that discrete vs continuous was a debate at this time in mathimatics as well, which would further that viewpoint. That instead of proving motion to be impossible, it proves that motion through a set of discreet points requires an infinite number of them, so discreet motion is impossible. Thus motion must be expressed as continous. This would then draw into question, if the path from A to B is continous, not a sum of discreet points, then how can we even say the fixed points of A and B exist? This would also feed into Parmenides's theories then, because A and B would be part of a continous whole. The arrow in motion, but at a fixed point, would also then line up with this view instead of just motion. So I ask, do we know for sure that Zeno's paradox is about the impossibility of motion? Or do we just know the paradox, and infered it to be about motion?
Peter Adamson 16 July 2018
In reply to Paradoxes by Alexander Johnson
Is the paradox about motion?
Well, perhaps we don't know anything about it "for sure" since we rely on later testimonies but Aristotle's presentation of the Dichotomy is certainly in terms of moving across an extended space. Remember too that motion is involved in some of the other paradoxes like the Arrow and Moving Rows. But you may be right in the sense that Zeno could be using motion to critique the idea of discrete space the ultimate target is a matter for debate. However the Eleatic background, to my mind, makes motion a more likely target than space. After all Parmenides' Being is spatial (it is a sphere), but unchanging/unmoving.
Alejandro 7 February 2019
If things are many, then things are infinite
Many philosophers and mathematicians claim that, when Zeno says that if a distance is infinitely divisible, then it's infinitely large, his mistake lies in thinking that the sum of of infinite series is infinite, which is not the case. I think it was Vlastos who said that the only way for the sum of an infinite series to be infinite is if it has a smallest member. Why do you think he says that?
Alejandro 14 February 2019
I just found the text
I just found the text containing the Vlastos argument I was talking about: "There must have been some tacit assumption which would have made it seem obviously true that any collection of an infinite number of sizeable parts would have to be infinitely large: so very obviously. that even someone who knew all about Aristotle's theorem (as Simplicius certainly did, and some of Epicurus' associates almost as certainly) would not think of applying it to the present case, but infer forthwith inflnity of size for the container from infinity of number of the parts contained. I cannot imagine what this could be except that the collection had a smallest member. This would be quite sufficient to make the conclusion seem a matter of course: given an infinity of nonoverlapping parts the least of which has some finite magnitude, it would be obvious that the aggregate magnitude would be infinite." Try as I might, I fail to see how having a smallest member could make the sum infinite. If ½ + ¼ + 1/8 + 1/16 + 1/32 + 1/64…. (no smallest term) converges on 1, why would the sum of the members of this geometric series be infinite if, say, 1/64 were the smallest member?
Peter Adamson 14 February 2019
In reply to I just found the text by Alejandro
Vlastos on Zeno
Well, that probably seems obvious to you because you learned math in high school after, and not before, the invention of calculus. The notion that an infinite series could add up to a finite result is in fact staggeringly counterintutive, even though it is true: somehow, you add an infinite number of lengths of positive quantity and the result is only, say, one meter long in total. Aristotle is actually the first person to make the point, as far as I know - that this is possible because the amounts being taken diminish in size as you go. However even he doesn't think this is possible with an actual series, only that you can take arbitrarily small portions by dividing smaller and smaller, but always with a finite and not infinite number of parts. He would have agreed with Zeno and think that your "obvious truth" (namely that an infinite series of actual parts of positive size would yield a finite result) is obviously false.
One relevant point here may be that for the Greeks such quantities would not be represented with the kind of notation you used, but with the quantities as line segments, because they tended to think of numbers geometrically. So you're asking them to accept that you put an infinite number of line segments next to one another, each of which has a positive length, but the whole thing is finite. Again that may be true but it is far from intuitive.
Alternatively could it be that you and Vlastos are thinking about different paradoxes by Zeno? Maybe he is not talking about the dichotomy (travel half of the path, half of the half, etc) but another argument given by Zeno which is about adjacent bodies.
Alejandro 14 February 2019
In reply to Vlastos on Zeno by Peter Adamson
Thank you, Peter. I now see
Thank you, Peter. I now see where I made the mistake: Vlastos is indeed talking of another paradox—the one where he says that, if things are many, then they are both infinitely small and infinitely large. I realize now that how you make the divisions matters. In the Dichotomy and the Achilles, you first divide the distance in half, then either the first or second resulting halves in half, then the quarters, ad infinitum. The result is that you never get from A to B, or that you can never leave A at all. In this paradox, the dichotomizing is done in such a way that the result is equal parts, instead of the parts represented by the notation I used (geometric series), and now I understand why Vlastos says what he says: if there is a smallest part, and it has magnitude, the sum of all members will be infinite! Thank you very, very much for helping me see this. Studying philosophy on your own is a, as they say, fraught with peril. Having the help of a scholar like you makes all the difference.
Peter Adamson 15 February 2019
In reply to Thank you, Peter. I now see by Alejandro
Ah, good. Glad this cleared it up!
This site/project/enterprise is magnificent. I cannot praise it highly enough. It makes the rubbish strewn underground car park of the internet worthwhile. Please carry it on and bring it up to the present day.
Peter Adamson 8 February 2019
Rubbish strewn car park
Ha! Thanks, that is one of the nicer compliments I have ever gotten on the podcast. I should put that in big letters at the top of the website.
Anyway glad you're enjoying it - as for bringing it up to the present day, as I always say I have no plans to stop anytime soon, so let's see how far I can get.
Giovani Dalla … 26 August 2019
Emptiness in our modern conception of the world m
Great work of yours. I am listening to it so voraciously. Thank you for this great encyclopedia of philosophy you made.
I would just like to precise about modern concepts of vacuum. Today, we have no vacuum at all. I mean, there is energy in vacuum and a principle of uncertainty developped by Heizenberg states that particules can appear and disappear at anytime in the vacuum. Plus, the particules are not corpuscles, they are kind of waves as well and therefore they do “occupy” the full spaces of atoms and molecules. Complex to explain it, but I would just point out then that emptiness is not very acceptable in today’s physics.
Peter Adamson 26 August 2019
Yes, I guess that must be right - my knowledge of modern physics is not what it should be! But I guess perhaps the real question, philosophically, is whether empty space is conceptually permitted in our physics or not, and I guess that in modern physics, it is?
Carroll Boswell 10 November 2019
Math and reality
I thought that was a very good point that modern math, specifically calculus, does not answer Zeno's paradox. It is a model for reality only and not necessarily reality itself. But doesn't a mathematical model for what Zeno claims is impossible at least show that it is non-contradictory? In fact, the question of the connection between math and reality is still an open question. As I understand it, general relative implies that space is quantized, that is, that there is a shortest possible distance between two points. Space is not a continuum, in other words. I am not a good physicist so I may be misunderstanding them.
Peter Adamson 10 November 2019
In reply to math and reality by Carroll Boswell
Well, I think if you agree that there is an open question as to whether a mathematical model captures the physical reality, it is also an open question whether the consistency of the mathematical model shows that motion is non-contradictory (to put it another way, if the claimed inconsistency turns on our concept of physical motion or space, then math has nothing to say about it. arguably). Not sure what modern physicists would say but at least, if this line of defense for Zeno is a good one, the physicist would be the right person to show why he was wrong and not the mathematician.
Carroll Boswell 12 November 2019
In reply to Math by Peter Adamson
Models vs reality
This seems a lot more complicated to me and not so clear. If Zeno is trying to prove that motion is inherently self-contradictory, then the existence of a mathematical model for motion refutes him. The question of the relation of a mathematical model to reality is one thing, but is it really tenable that something self-contradictory could be modeled by something logically consistent? Put another way, can self-contradiction ever be "approximately" consistent? This is really a question about the nature of logic and its relation to reality. It seems to me that if something self-contradictory can be disguised as logical consistency then we are losing our grip on the validity of logic as a whole. Or am I missing something?
Peter Adamson 13 November 2019
In reply to models vs reality by Carroll Boswell
Physics vs math
I agree this is complicated and difficult. But my basic intuition here is that if we agree it is an open question whether the mathematical model represents the physical situation accurately and shows why motion is possible (if it in fact does: consider that the model involves approaching a limit getting infinitely closer as the time gets infinitely closer to the end moment of the motion. which sounds more like Zeno explaining why motion is impossible than an explanation of why it is possible) then the consistency of the mathematical model surely doesn't prove that a belief in motion is consistent. Zeno can say, "sure, the model is consistent, but it doesn't represent what is (supposedly) happening in the physical world: indeed it can't because motion, as I've shown, implies inconsistencies, so that alone proves that the model doesn't represent it because how can a consistent model represent an inconsistent physical scenario?" It would be worth thinking about whether this is a question begging response though.
Carroll Boswell 13 November 2019
In reply to Physics vs math by Peter Adamson
Let's turn it around
Perhaps I just need to digest this for a while to see what I am missing. But let's try one more time. Zeno attempts to prove that motion is self-contradictory by a thought experiment. Newton comes along and takes the same assumptions as Zeno and replies, "There is no inherent self-contradiction here." Newton hasn't proven that reality corresponds to the calculus model, with infinitesimals and what not, but it does seem that he has refuted Zeno's claim that motion is inconsistent. Zeno could still be correct that motion is illusory, but Zeno would be incorrect as to why it is known to be illusory, as to his proof. Zeno would need to start from different assumptions if he still wanted to make his case. I am sorry if I am getting tedious and just repeating myself. I am new to the philosophy business. I promise I will refrain from belaboring the point any further if if does strike you that I am just rehashing the same point here.
Peter Adamson 14 November 2019
In reply to let's turn it around by Carroll Boswell
I don't think that's quite right. Take any (supposed) phenomenon you like, call it P. Zeno says "I have an argument to show that P is contradictory" and Newton says, "I have a way of thinking about P that doesn't seem to involve a contradiction." Unless Newton shows exactly where Zeno's argument went wrong - that either the argument is invalid or has false premises - then he hasn't defused the argument, he's only given you a model for thinking about it that does not contradict itself.
To put it another way, positively offering a story about how something could work is not the same as refuting a negative argument that it can't work. To do that you have to address the argument directly, and the point we've been discussing is that you can't address Zeno's argument just with mathematics since his argument isn't purely mathematical.
Alexander Johnson 15 November 2019
In reply to Contradictions by Peter Adamson
Of course, both of this is assuming that Zeno whoever Zeno was trying to show was inconsistent (probably Pythagoreans) would have considered and accepted the notion that math and the real world don't correspond. Given that the models suggest a mathematical atomism (continuity is the sum of points), and that motion is a real-world phenomenon, I strongly doubt that Zeno's opponent would have granted such as suggestion. So, if the position Zeno is responding to will remain intact, it needs to respond to both.
However, that still leaves the possibility that Newton solved half the problem, though prior to calculus. However, this isn’t clear either. For one, Pythagorean atomism, which suggests that a continuum is a unity of points still has a couple of problems. After this, the doubt in mathematics wasn’t the possibility of continuum based mathematics (such as adding two line segments, or multiplying two line segments into a rectangle), but rather that a continuum was an infinite collection of points. Newton in “De Analysi Per Aequationes Numero Terminorum Infinitas” was able to show that math through infinite series of discrete numbers could be as soundly proven as algebra and geometry, but that doesn’t quite show that an infinite discrete sum is a value rather than approaches a value, prior to the operations that cancel out the infinite scale [likewise, the meaning of the sum of 1-2+4-8+16-32…..=1/3 is still debated]. We can see this debate continue in philosophy from the example given of the light switch (I don’t remember who), where we consider a light that is turned off and on each time Achilles reaches where the turtle was, will the light be on or off when Achilles finally reaches the turtle? Or will Achilles have to break the pattern of running only to where the turtle was?
Meanwhile, in the reality side, though my physics is worse, I believe at least in many circles, it is accepted that reality is discrete, not continuous. Zeno had his own response to this, which I can sum up as, let ABCD be a body that exists at point 0,1,2,3. Let EFGH be a body that exists at point 1,2,3,4. Now let both of them travel at the slowest speed possible towards one another. After one unit of time, A is now at 1, and E is now at 0. However, this means that A has travelled 2 spaces with respect to E, and essentially “jumped over it”, which implies a slower speed. This paradox, however, has been more adequately addressed. In the physical world, things can in fact move slower, because they exist in a probabilistic state. If you consider A as existing in a probabilistic cloud, it can still move slower than any theoretical slowest, by shifting its probability less than one plank length. This will result in the average expected location moving less than 1 plank length, even though it would be impossible for something to actually move less than 1 plank length. All you need mathematically to address that paradox is probability theory, and this actually addresses both reality and mathematics, rather than just solving it on the mathematical side.
I hope either of you found this helpful! (and that i hope i didn't make any mistakes!)
2. Atomist Doctrine
Leucippus is named by most sources as the originator of the theory that the universe consists of two different elements, which he called &lsquothe full&rsquo or &lsquosolid,&rsquo and &lsquothe empty&rsquo or &lsquovoid&rsquo. Both the void and the solid atoms within it are thought to be infinite, and between them to constitute the elements of everything. Because little is known of Leucippus' views and his specific contributions to atomist theory, a fuller discussion of the developed atomist doctrine is found in the entry for Democritus.
Early Greek atomism is generally taken to have been formulated in response to the Eleatic claim that &lsquowhat is&rsquo must be one and unchanging, because any assertion of differentiation or change within &lsquowhat is&rsquo involves the assertion of &lsquowhat is not,&rsquo an unintelligible concept. While Parmenides' argument is difficult to interpret, he was understood in antiquity to have forced philosophers after him to explain how change is possible without supposing that something comes from &lsquowhat is not,&rsquo i.e. nothing. Aristotle tells us that Leucippus tried to formulate a theory that is consistent with the evidence of the senses that change and motion and a multiplicity of things exists in the world (DK 67A7). In the atomist system, change only occurs at the level of appearances: the real constituents of being persist unchanged, merely rearranging themselves into new combinations that form the world of appearance. Like Parmenidean Being, the atoms cannot change or disintegrate into &lsquowhat is not&rsquo and each is a solid unit nonetheless, the combinations of atoms that form the world of appearance continually alter. Aristotle cites an analogy to the letters of the alphabet, which can produce a multitude of different words from a few elements in combinations the differences all stem from the shape (schêma) of the letters, as A differs from N by their arrangement (taxis), as AN differs from NA and by their positional orientation (thesis), as N differs from Z (DK 67A6).
Leucippus also reportedly accepted the Eleatic Melissus' argument that void is necessary for motion, but took this to be evidence that, since we experience motion, there must be void (DK 67A7). The reason for positing smallest indivisible magnitudes is also reported to be a response to Zeno's argument that, if every magnitude could be divided to infinity, motion would be impossible (DK 29A22). Leucippus is reported to hold that the atoms are always in motion (DK 67A18). Aristotle criticizes him for not offering an account that says not only why a particular atom is moving (because it collided with another) but why there is motion at all. Because the atoms are indestructible and unchangeable, their properties presumably stay the same through all time.
As Diogenes Laertius reports Leucippus' cosmology, worlds or kosmoi are formed when groups of atoms combine to form a cosmic whirl, which causes the atoms to separate out and sort by like kind. A sort of membrane of atoms forms out of the circling atoms, enclosing others within it, and creating pressure by whirling. The outer membrane continually acquires other atoms from outside when it contacts them, which take fire as they revolve and form the stars, with the sun in the outermost circle. Worlds are formed, grow and perish, according to a kind of necessity (DK 67A1).
One direct quotation preserved from Leucippus says that nothing happens in vain (matên) but everything from logos and by necessity (DK 67B2). This has been found puzzling, since the reference to logos might seem to suggest that things are ruled by reason, an idea that Democritus' system excludes. Either Leucippus' system is different in this respect from that of Democritus, or the reference to logos here cannot be to a controlling mind. Barnes takes there to be no grounds for preferring either interpretation (Barnes 1984), but Taylor argues that Leucippus' position is that an account (or logos) can be given of the causes of all occurrences (Taylor 1999, p. 189). There is nothing in other reports to suggest that Leucippus endorsed the idea of a universal intelligence governing events.
Pythagoras' most important belief was that the physical world was mathematical and that numbers were the real reality. ΐ]
- that at its deepest level, reality is mathematical in nature,
- that philosophy can be used for spiritual purification,
- that the soul can rise to union with the divine,
- that certain symbols have a mystical significance, and
- that all brothers of the order should observe strict loyalty and secrecy.
It is understandable. What is the life of a philosopher, especially one of such dignity as Aristotle, but his or her philosophy? A generalization hides here, not sufficiently questioned, and its workings can be seen in all lines of biographical material. The philosopher, the thinker, is presumed to have lived a life devoted to that, alone, or at least with no other significant emphasis. There are few exceptions to the rule, one being Nietzsche, whose life has been allowed to be portrayed as just as bizarre and dramatic as the thoughts in his writing.
In the biographies of dramatists and fiction writers, on the other hand, their lives are usually portrayed as being similar to the stories they made up in their works. Quite accurate in the case of Cervantes or Dostoevsky, but not necessarily so with all the rest of them.
This is a bias, a prejudice, very difficult for the biographer to avoid. When a significant person from history is contemplated, that which put him or her in the history books tends to overshadow all else, and what can be perceived through it is colored and shaped by that major accomplishment.
The renowned Swedish writer of fiction for children, Astrid Lindgren, was in her early nineties asked by a reporter what she regarded as her most important achievement. Her books about Pippi Longstocking, and other pleasantly memorable characters, have been printed in vast numbers and many languages. In Sweden she was praised like a kind of grandmother for several generations of Swedes. Astrid Lindgren paused a moment in confusion, before replying: "Why, my children, of course. What else could it be?"
People are children, lovers, parents, grandparents - and that part of their existence is normally regarded as dominant. Not so for the famous. With them we take for granted that the reason for their fame dominates their lives. That might be true for some, especially if their fame is unquestionable in their own lifetime. In most cases, though, few of them would dare to wager that their memory survives their death - in any other way than through their children.
So, a biographer would be wise to regard even the most formidable of historical figures as a commoner, a human acting as humans do, living, feeling and thinking pretty much like the rest of us, unless something else is evident. Not that we would care too much to write down the everyday drab reality of the greats, and settle with that, but it would aid to understanding their lives better. When they are raised to an elevated existence by biographers, their famous deeds may make sense, but little else. Even with their cherished accomplishments, I doubt that the extraordinary perspective leads to trustworthy explanations.
Maybe the lives of the philosophers were not that philosophical, the adventures of the poets not that adventurous, the days of the emperors not that glorious. We can see what they came to mean to mankind, but could they? Usually not. Picasso must have realized, around the time of his life that the Greeks called flourishing, the age of 40, that he would not be easily forgotten. So would Einstein, and the Beatles. Going further back, it is likely that Voltaire had the same trust, and Isaac Newton, Martin Luther, maybe Leonardo da Vinci, Charlemagne, and so on. Probably, there are also hundreds of names of giants in their times, now all but forgotten, who were convinced of making it to posterity.
Certainly, most of them had no idea. Shakespeare would never dream of it, Galileo Galilei would never count on it, van Gogh could not see it. Jesus would have no clue at all, if not indeed being informed by a heavenly father.
History may make sense in rear view, but is rarely predictable. There is even a natural conflict between the present and the future: what conforms to the presiding order is praised and elevated in the former, but what is singled out in the latter is change, the deviation from the standard. So, that which is cherished in the future is mostly neglected or even rejected in the present. Most innovators, of whatever kind, would in their lives only find support for a conviction of being erased by time. What are the odds of becoming a historical figure? Infinitesimal. Nothing to base one's life on.
Returning to Aristotle, if we consider the indications we have about his time and the modest role he played in it, Aristotle would have been very un-Aristotelian to assume a lasting influence. Not that he was unknown to the population of Athens and beyond, but modestly so. Most of Aristotle's writing was not even published during his lifetime. What was, had won him some respect, but far from devotion. It took centuries before Aristotle was regarded as anything but an eloquent student of Plato.
Since Plato already in those days had quite another reputation, and through his writing also Socrates, if Aristotle pondered the question at all, he would conclude that those names might remain, but his own be dust even quicker than his body would. It is even likely that Aristotle regarded himself as somewhat a failure, fleeing Athens at the end of his life, leaving little of proven perseverance.
Aristotle's will, quoted to us by Diogenes Laertius, implies a most modest care about his family, his slaves, and little else. In his life, Aristotle shunned political activity, and had little faith in seeing his philosophy contribute to society. His teacher's endeavor along those lines must have convinced Aristotle of its futility.
What of his own work could Aristotle see that would have any chance of lasting? Only his early works, predominantly defending and explaining the ideas of Plato - significantly different from his own, as they matured. Whatever Aristotle might have thought about it, as he progressed in years, he saw no other role for him in history, than that of yet another voice in the choir praising Plato's thoughts. And he could not even have been convinced of Plato's lasting impression.
Aristotle would have concentrated on living a decent life, and made no plans for eternity.
Genuine philosophical thought, depending upon original individual insights, arose in many cultures roughly contemporaneously. Karl Jaspers termed the intense period of philosophical development beginning around the 7th century and concluding around the 3rd century BCE an Axial Age in human thought.
In Western philosophy, the spread of Christianity in the Roman Empire marked the ending of Hellenistic philosophy and ushered in the beginnings of medieval philosophy, whereas in Eastern philosophy, the spread of Islam through the Arab Empire marked the end of Old Iranian philosophy and ushered in the beginnings of early Islamic philosophy.
Chinese philosophy is the dominant philosophical thought in China and other countries within the East Asian cultural sphere that share a common language, including Japan, Korea, and Vietnam.
Schools of thought Edit
Hundred Schools of Thought Edit
The Hundred Schools of Thought were philosophers and schools that flourished from the 6th century to 221 BCE,  an era of great cultural and intellectual expansion in China. Even though this period – known in its earlier part as the Spring and Autumn period and the Warring States period – in its latter part was fraught with chaos and bloody battles, it is also known as the Golden Age of Chinese philosophy because a broad range of thoughts and ideas were developed and discussed freely. The thoughts and ideas discussed and refined during this period have profoundly influenced lifestyles and social consciousness up to the present day in East Asian countries. The intellectual society of this era was characterized by itinerant scholars, who were often employed by various state rulers as advisers on the methods of government, war, and diplomacy. This period ended with the rise of the Qin Dynasty and the subsequent purge of dissent. The Book of Han lists ten major schools, they are:
- , which teaches that human beings are teachable, improvable and perfectible through personal and communal endeavour especially including self-cultivation and self-creation. A main idea of Confucianism is the cultivation of virtue and the development of moral perfection. Confucianism holds that one should give up one's life, if necessary, either passively or actively, for the sake of upholding the cardinal moral values of ren and yi.  . Often compared with Machiavelli, and foundational for the traditional Chinese bureaucratic empire, the Legalists examined administrative methods, emphasizing a realistic consolidation of the wealth and power of autocrat and state. (also called Daoism), a philosophy which emphasizes the Three Jewels of the Tao: compassion, moderation, and humility, while Taoist thought generally focuses on nature, the relationship between humanity and the cosmos health and longevity and wu wei (action through inaction). Harmony with the Universe, or the source thereof (Tao), is the intended result of many Taoist rules and practices. , which advocated the idea of universal love: Mozi believed that "everyone is equal before heaven", and that people should seek to imitate heaven by engaging in the practice of collective love. His epistemology can be regarded as primitive materialist empiricism he believed that human cognition ought to be based on one's perceptions – one's sensory experiences, such as sight and hearing – instead of imagination or internal logic, elements founded on the human capacity for abstraction. Mozi advocated frugality, condemning the Confucian emphasis on ritual and music, which he denounced as extravagant.
- Naturalism, the School of Naturalists or the Yin-yang school, which synthesized the concepts of yin and yang and the Five Elements Zou Yan is considered the founder of this school. 
- Agrarianism, or the School of Agrarianism, which advocated peasant utopiancommunalism and egalitarianism.  The Agrarians believed that Chinese society should be modeled around that of the early sage king Shen Nong, a folk hero which was portrayed in Chinese literature as "working in the fields, along with everyone else, and consulting with everyone else when any decision had to be reached." 
- The Logicians or the School of Names, which focused on definition and logic. It is said to have parallels with that of the Ancient Greek sophists or dialecticians. The most notable Logician was Gongsun Longzi.
- The School of Diplomacy or School of Vertical and Horizontal [Alliances], which focused on practical matters instead of any moral principle, so it stressed political and diplomatic tactics, and debate and lobbying skill. Scholars from this school were good orators, debaters and tacticians.
- The Miscellaneous School, which integrated teachings from different schools for instance, Lü Buwei found scholars from different schools to write a book called Lüshi Chunqiu cooperatively. This school tried to integrate the merits of various schools and avoid their perceived flaws.
- The School of "Minor-talks", which was not a unique school of thought, but a philosophy constructed of all the thoughts which were discussed by and originated from normal people on the street.
- Another group is the School of the Military that studied strategy and the philosophy of war Sunzi and Sun Bin were influential leaders. However, this school was not one of the "Ten Schools" defined by Hanshu.
Early Imperial China Edit
The founder of the Qin Dynasty, who implemented Legalism as the official philosophy, quashed Mohist and Confucianist schools. Legalism remained influential until the emperors of the Han Dynasty adopted Daoism and later Confucianism as official doctrine. These latter two became the determining forces of Chinese thought until the introduction of Buddhism.
Confucianism was particularly strong during the Han Dynasty, whose greatest thinker was Dong Zhongshu, who integrated Confucianism with the thoughts of the Zhongshu School and the theory of the Five Elements. He also was a promoter of the New Text school, which considered Confucius as a divine figure and a spiritual ruler of China, who foresaw and started the evolution of the world towards the Universal Peace. In contrast, there was an Old Text school that advocated the use of Confucian works written in ancient language (from this comes the denomination Old Text) that were so much more reliable. In particular, they refuted the assumption of Confucius as a godlike figure and considered him as the greatest sage, but simply a human and mortal.
The 3rd and 4th centuries saw the rise of the Xuanxue (mysterious learning), also called Neo-Taoism. The most important philosophers of this movement were Wang Bi, Xiang Xiu and Guo Xiang. The main question of this school was whether Being came before Not-Being (in Chinese, ming and wuming). A peculiar feature of these Taoist thinkers, like the Seven Sages of the Bamboo Grove, was the concept of feng liu (lit. wind and flow), a sort of romantic spirit which encouraged following the natural and instinctive impulse.
Buddhism arrived in China around the 1st century AD, but it was not until the Northern and Southern, Sui and Tang Dynasties that it gained considerable influence and acknowledgement. At the beginning, it was considered a sort of Taoist sect, and there was even a theory about Laozi, founder of Taoism, who went to India and taught his philosophy to Buddha. Mahayana Buddhism was far more successful in China than its rival Hinayana, and both Indian schools and local Chinese sects arose from the 5th century. Two chiefly important monk philosophers were Sengzhao and Daosheng. But probably the most influential and original of these schools was the Chan sect, which had an even stronger impact in Japan as the Zen sect.
Melissus Timeline - History
People - Ancient Greece : Meletus
Melētus in Harpers Dictionary of Classical Antiquities （Μέλητος) or Melītus (Μέλιτος). An obscure tragic poet, but notorious as one of the accusers of Socrates (q.v.). It was he who made the formal accusation before the archon but he was really the least important of the three accusers, and is said to have been bribed to take part in the proceedings. After the death of Socrates, Meletus was stoned to death by the people, in the revulsion of feeling which they experienced (Apol. Diod.xiv. 37 Diog. Laert. ii. 43).
Meletus in Wikipedia The Apology of Socrates by Plato names Meletus as the chief accuser of Socrates. He is also mentioned in the Euthyphro. Given his awkwardness as an orator, and his likely age at the time of Socrates' death, many hold that he was not the real leader of the movement against the early philosopher, but rather was simply the spokesman for a group led by Anytus. Meletus was probably a poet by trade and likely a religious fanatic who was more concerned with allegations of impiety than with the charges of corruption that were lodged against Socrates. Some believe Meletus was motivated primarily by the reports that Socrates had embarrassed the poets (in Plato's Gorgias, Socrates accuses poets and orators of flattery and says that they impress only women, children, and slaves). In the Euthyphro, Plato describes Meletus, the youngest of the three accusers, as having "a beak, and long straight hair, and a beard which is ill grown." Plato wrote that, prior to the prosecution of Socrates, Meletus was "unknown" to him. During the first three hours of trial, Meletus and the other two accusers each stood in the law court in the center of Athens to deliver previously crafted speeches to the jury against Socrates. No record of Meletus's speech survives. However, we do have Plato's record of Socrates' cross-examination of Meletus (in those days, the defendant always cross-examined the accuser). Using his characteristic Socratic method, Meletus is made to seem an inarticulate fool. He says that Socrates corrupts the young, and that Socrates is the only one to do so, but he can not provide a motive for why Socrates would do this. Socrates shows that if he were to do this it must surely be in ignorance, for no man would intentionally make bad those living around him. Concerning the accusation that Socrates believed in strange spirits and not the gods of the state, Socrates tricks Meletus into saying that spirits are the offspring of gods, and since no one believes in flutes playing without flute players, or in horses' offspring without horses, how could Socrates believe in the offspring of gods without believing in gods? For much of his cross examination Meletus remains silent, and we are led to believe that he does not have ready answers for Socrates. Greek historian Diogenes Laertius, writing in the first half of the 3rd century AD, dubiously reported that after the execution of Socrates "Athenians felt such remorse" that they banished Meletus from their city.