Judaism

Pythagoras of Samos, and Xenophanes of Colophon

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An essay on the origins of Greek philosophy
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Pythagoras of Samos (c 582-504 BC)

Pythagoras, who, from his habit of saying he was a lover of wisdom, coined the word “philosophy” which in Greek is “love of wisdom”, lived from around 582 to 504 BC and was another remarkable thinker from Asia Minor. Pythagoras, the son of Mnesarchus, seems to have been born at Samos and certainly spent his early manhood there, where he studied under Thales. He is said to have gone from Greece to Egypt as a young man, and spent ten years as a priest in training, before he was captured by raiding Persians, who sold him in Babylon as a slave. After ten years there, he gained his freedom, but stayed in Babylon for ten more years, studying mathematics in the mystery schools. Much of this might be legendary.

Heraclitus speaks of him in the past tense, and Aristoxenus said Pythagoras left Samos to escape from Polycrates’ tyranny (532 BC). Timaeus seems to have said he came to Italy in 529 BC where he settled at Croton and remained there for twenty years. Croton was a Greek colony on the southern coast that had long been in friendly relations with Samos and was famed for its athletes and its doctors. There Pythagoras founded his society and his doctrine was adopted and developed by a large following of Pythagoreans, including Damon. He died at Metapontum, whither he had retired when the Crotoniates rose in revolt against his authority.

The life of Pythagoras is surrounded in mythology and it is hard to discern what is historical. Yet, the earliest reference to him is almost a contemporary one. Some verses are quoted from Xenophanes, in which he says that Pythagoras once heard a dog howling and appealed to its master not to beat it, as he recognized the voice of a departed friend. From this we know that he taught the doctrine of transmigration—reincarnation.

Heraclitus, in the next generation, speaks of his having carried scientific investigation (historie) further than any one, though he made use of it for purposes of imposture. Later, though still within the century, Herodotus speaks of him as “not the weakest scientific man (sophistes) among the Hellenes”, and he says he had been told by the Greeks of the Hellespont that the legendary Scythian Salmoxis had been a slave of Pythagoras at Samos. He does not believe that for he knew Salmoxis lived many years before Pythagoras. The story is evidence that Pythagoras was well known in the fifth century, both as a scientific man and as a preacher of immortality.

Regarding the world as perfect harmony, dependent on the reality of number, he aimed at inducing humankind likewise to lead a harmonious life. Principles of mathematics and number formed the basis of all things. The Pythagoreans discovered irrational numbers, but cult members were sworn to secrecy concerning the discovery, as this was regarded as a threat to their system.

He believed in the magic of the gods, was influenced by the cult that worshipped the god Dionysos, and he believed in Zeus, Apollo and other Greek gods and in the old and common notion of the transmigration of souls. He believed that the dust one can see aimlessly floating about in sunlight was pulled about by a spirit. But he also believed in self-examination, and he was interested in astronomy and mathematics and wished to apply observation and reason toward understanding the universe and its gods. He wished to combine his ideas on religion, astronomy and mathematics into a coherent view that would create a way of life beneficial to others.

Pythagoras and his followers advanced astronomy by examining the movements of celestial bodies. They observed the shadow of the earth on the moon, and they made some calculations and concluded that the earth was a sphere. They also concluded that the earth was one of a group of planets. They blended these observations with Greek religion, concluding that the sun reflected light from a great fire at the center of the universe, which they called the throne of Zeus, around which, they believed, all else revolved.

Pythagoras advanced geometry from practical measurements to new geometric theorems. He found harmony in geometry and arithmetic, and in the harmonics of sound he found mathematics—that the tone of a vibrating string depends upon its length. He concluded that mathematical harmony was a part of the perfection of the heavens. Like the Sumerians and others, he believed that the heavens moved but were essentially unchanging, as permanent as the realities of mathematics. He believed that the universe and mathematics were in essence created by the gods. He believed that mathematics held the universe together and that its harmony created a kinship between the gods and humankind. Seeing reality as idea and unchanging, Pythagoras described the changes one saw on earth as an illusion. He described knowledge through sense perception as faulty compared to the reason that allowed one to grasp unchanging mathematical principles.

Having given mathematics a divine significance, Pythagoras searched for signs of divinity within numbers. With much theorizing he found what he was looking for. For example, the first number greater than 1 that could be the square of two other numbers is the number 4, and mixing this with his belief about justice as a work of the gods he concluded that the number 4 contained the divinity of justice.

Pythagoras created a religious sect organized around strict religious rules. Believing that souls migrated after death into the bodies of other beings, he saw the possibility of an animal containing a human-like soul, and therefore he saw eating animals as cannibalism and as an abomination. He and his followers became vegetarians. But they forbade the eating of beans, which they thought harmful to the soul.

In his later years, according to his followers, Pythagoras searched for the significance of his own brilliance and concluded that he was semi-divine. After his death, some of his followers described him as having been capable of miracles. Some claimed that he was the son of Apollo. But whatever he was, he had created a school of philosophy that would influence other Greek philosophers and rival the views of those who believed in the validity of sense perception.

Plato was deeply interested in Pythagoreanism, but he only mentions Pythagoras once by name in all his writings, and all he says then is that he won the affections of his followers to an unusual degree by teaching them the Pythagorean “way of life”. Even the Pythagoreans are only once mentioned by name, where Socrates says they regard music and astronomy as sister sciences. Yet, Plato tells us a good deal about men whom we know from other sources to have been Pythagoreans. He does not say that Echecrates and Philolaus belonged to the school, and he gives Pythagorean views anonymously, as those of “ingenious persons”. Timaeus the Locrian, into whose mouth Plato has placed a Pythagorean cosmology, is not revealed as being in the Pythagorean society, even though he comes from Italy.

Aristotle

Aristotle imitates his master’s reserve in this matter. The name of Pythagoras occurs only twice in the genuine works that have come down to us. Alcmaeon was said to have been a young man in the old age of Pythagoras, and a quotation from Alcidamas says that “the men of Italy honored Pythagoras”. Aristotle is not so shy of the word “Pythagorean” as Plato, but he writes “the men of Italy who are called Pythagoreans”, and refers to particular doctrines as those of “some of the Pythagoreans”. It seems there was doubt in the fourth century about who the Pythagoreans really were.

Aristotle also wrote a treatise on the Pythagoreans which no longer exists, but which later writers quote. These are valuable because they concern the religious side of Pythagoreanism.

Other ancient authorities on Pythagoras were Aristoxenus of Taras, Dicaearchus of Messene and Timaeus of Tauromenium. The account of the Pythagorean Order in the Life of Pythagoras by Iamblichus is based mainly on Timaeus, who was no doubt an uncritical historian, but who had access to information about Italy and Sicily which makes his testimony valuable when it can be recovered. Aristoxenus had been personally acquainted with the last generation of the Pythagorean society at Phlius. But he wanted to show Pythagoras simply as a man of science, and was anxious to refute the idea that he was a religious teacher. Dicaearchus tried to make out that Pythagoras was simply a statesman and reformer.

The Lives of Pythagoras, by Porphyry, Iamblichus, and Diogenes Laertius, are a mass of incredible fiction. The oldest accounts show Pythagoras as a wonder-worker, but fourth century writers tried to deny it. This helps to account for the cautious references of Plato and Aristotle.

The extensive travels to Egypt, Babylon and India attributed to Pythagoras by late writers are probably apocryphal. The close relations between Polycrates of Samos and Amasis could support a visit to Egypt. Herodotus notes that the Egyptians had practices akin to Orphic, Bacchic and Pythagoreans ones, and adds that the belief in transmigration came from Egypt, a mistake because the Egyptians did not believe in transmigration.

The Pythagorean Order was simply a religious fraternity, and not originally a political league. Nor is there any evidence that the Pythagoreans favored the aristocratic party. The main purpose of the order was the cultivation of holiness. It resembled an Orphic society, though Apollo, and not Dionysos, was the chief Pythagorean god. That is doubtless due to the connexion of Pythagoras with Delos, and explains why the Crotonites identified him with Apollo Hyperboreus.

For a time the new order succeeded in securing supreme power in the Achaean cities, but reaction soon came. Accounts of these events are confused by failure to distinguish between the revolt of Cylon in the lifetime of Pythagoras himself, and the later risings which led to the expulsion of the Pythagoreans from Italy. Cylon, who is expressly stated by Aristoxenus to have been one of the first men of Croton in wealth and birth, was able to bring about the retirement of Pythagoras to Metapontum, another Achaean city, and it was there that he passed his remaining years.

Disturbances still went on, however, at Croton after the departure of Pythagoras for Metapontum and after his death. The Cyloneans set fire to the house of the athlete Milo, where the Pythagoreans were assembled. Only two, who were young and strong, Archippus and Lysis, escaped. The coup d’Etat of Croton can hardly have occurred before 450 BC. Polybius implies that the burning of the Pythagorean “lodges” (sunedria) in the Achaean cities went on for a long time, till at last peace and order were restored by the Achaeans of Peloponnesus. At a later date some of the Pythagoreans were able to return to Italy, and once more acquired great influence there.

Pythagoras’s opinions are even less well known than his life. Plato and Aristotle knew nothing for certain of ethical or physical doctrines going back to the founder. Aristoxenus gave a string of moral precepts. Dicaearchus said hardly anything of what Pythagoras taught his disciples was known except the doctrine of transmigration, the periodic cycle, and the kinship of all living creatures. Pythagoras apparently preferred oral instruction to the dissemination of his opinions by writing, and only in Alexandrian times did anyone venture to forge books in his name. The writings ascribed to the first Pythagoreans were also forgeries of the same period. The early history of Pythagoreanism is conjectural.

He taught the doctrine of transmigration. Now this is most easily to be explained as a development of the primitive belief in the kinship of men and beasts, a view which Dicaearchus said Pythagoras held. Further, this belief is commonly associated with a system of taboos on certain kinds of food, and the Pythagorean rule is best known for its prescription of similar forms of abstinence. It seems certain that Pythagoras brought this with him from Ionia. Timaeus told how at Delos he refused to sacrifice on any but the oldest altar, that of Apollo the Father, where only bloodless sacrifices were allowed.

Regarding the vegetarianism of the Pythagoreans, Aristoxenus denigrates Pythagoras as a flesh and bean eater, but in his day strict observance had been relaxed, except by some whom the heads of the Society refused to acknowledge. The “Pythagorists” or “Akousmatics”, who clung to the old practices, were classed as heretics, and accused of being followers of one Hippasus, excommunicated for revealing secret doctrines.

The mainstream followers of Pythagoras were the “Mathematicians”—even though the friends of Aristoxenus did not practice abstinence, plenty of people in the fourth century calling themselves followers of Pythagoras did. Isocrates confirms they still observed the rule of silence. The “Akousmatics”, never quite died out. Diodorus of Aspendus and Nigidius Figulus bridge the gap between them and Apollonius of Tyana.

Pythagoras taught the kinship of beasts and men, and his rule of abstinence from flesh was based on taboo, not on humanitarian or ascetic grounds. Porphyry, in Defence of Abstinence, says Pythagoreans as a rule abstained from flesh, but ate it when they sacrificed to the gods. Primitive peoples often slay the sacred animal and eat it on solemn occasions, though in ordinary circumstances this would be the greatest of all impieties. Here is a primitive belief. The Orphics ate raw flesh at their initiation and then were lifetime vegetarians, and this is probably Pythagorean practice.

Of the Pythagorean rules and precepts that have come down to us, some of them, derived from Aristoxenus and preserved by Iamblichus, are precepts of morality that do not go back to Pythagoras himself. Others consist of rules called Akousmata, which points to their being the property of the sect which had faithfully preserved the old customs. Later writers interpret them as “symbols” of moral truth but it does not require a practiced eye to see that they are genuine taboos. The Pythagorean rule was:

If this were all, we should delete the name of Pythagoras from the history of philosophy, and relegate him to the class of quack gurus. That would be wrong. The Pythagorean Society became the chief scientific school of Greece, and it is certain that Pythagorean science goes back to the early years of the fifth century, and therefore to the founder. Heraclitus, who is not partial to him, says that Pythagoras had pursued scientific investigation further than other men. Herodotus called Pythagoras “by no means the weakest sophist of the Hellenes”, a compliment that does not imply the slightest disparagement.

The Orphic and other Orgia were to obtain release from the “wheel of birth” by means of “purifications”. The central novelty of Pythagoras apparently was that it suggested what “purification” really was. Aristoxenus said that the Pythagoreans employed music to purge the soul as they used medicine to purge the body. Such methods of purifying the soul were familiar in the Orgia of the Korybantes, and explain the Pythagorean interest in Harmonics. But, if we can trust Heraclides, Pythagoras first distinguished the “three lives”, the Theoretic, the Practical and the Apolaustic that Aristotle made use of in the Ethics.

In this world, the body is the tomb of the soul, yet escape by suicide is impossible because we are the chattels of God, our herdsman (an expression popular with Zoroaster), and without his consent we have no right to leave the flock. Three kinds of men appear in life, just as three sorts of men visit the Olympic Games. The lowest class comes to buy and sell, the next comes to compete, the best men come to look on. The greatest purification of all is observation or science, and the man who devotes himself to it is the true philosopher, who most effectively releases himself from the “wheel of birth”. Most of his followers, the sect of the Akousmatics, would be content with the humbler kinds of purification. A few would rise to the higher doctrine.

In his treatise on Arithmetic, Aristoxenus said that Pythagoras was the first to carry its study beyond the needs of commerce. By the end of the fifth century BC we find that there is a widespread interest in such subjects and they are studied for their own sake. This new interest cannot have been wholly the work of a school, it must have originated with some great man—Pythagoras it must be. The more primitive any Pythagorean doctrine appears, the more likely it is to be that of Pythagoras himself, especially if it has points of contact with contemporary ideas. When later Pythagoreans teach things that were anachronisms in their own day, we are dealing with doctrine bearing the authority of the master. Only by separating the earliest form from the later one can the place of Pythagoreanism in Greek thought be made clear, though no one can draw the line between successive stages with certainty.

Eurytus was the disciple of Philolaus, and Aristoxenus mentioned him along with Philolaus as having taught the last of the Pythagoreans, the men with whom he himself was acquainted. He therefore belongs to the beginning of the fourth century BC, by which time the Pythagorean system was fully developed, and he was no eccentric enthusiast, but one of the foremost men in the school. He used to give the number of all sorts of things, such as horses and men, and demonstrated these by arranging pebbles. Aristotle compares his procedure to that of those who bring numbers into figures (schemata) like the triangle and the square.

These statements imply the existence of a numerical symbolism quite distinct from the alphabetical notation and from the Euclidean representation of numbers by lines. The former was inconvenient for arithmetical purposes, because the zero was not yet invented. The representation of numbers by lines was adopted to avoid the difficulties raised by the discovery of irrational quantities, and is of much later date. Numbers were originally represented by dots arranged in symmetrical and easily recognized patterns, like the marks on dice or dominoes.

Pythagoras knew the use of the triangle 3, 4, 5 in constructing right angles. It was familiar in the East from a early date, and Thales introduced it to the Hellenes, if they did not know it already. Later writers call it the “Pythagorean triangle”. The Pythagorean theorem is that, in a right-angled triangle, the square on the hypoteneuse is equal to the sum of squares on the other two sides. This proposition was quite probably discovered by Pythagoras.

From the Pythagorean theorem, the square on the diagonal of a square is double the square on its side, and this ought to be capable of arithmetical expression. But no square number can be divided into two equal square numbers, and so the problem cannot be solved. Thus, Pythagoras stumbled on the fact that the square root of two is a surd.

The early Pythagoreans, and probably Pythagoras himself, studied proportion and the “harmonic”, stands in close relation to his discovery of the octave. In the harmonic proportion 12:8:6, 12:6 is the octave, 12:8 the fifth, and 8:6 the fourth.. Pythagoras discovered these intervals.

Pythagoras concluded all things were numbers. According to the Pythagoreans the “right time” was seven, justice was four, and marriage three. These identifications, with a few others like them, belong to Pythagoras or his immediate successors.

In Pythagorean cosmology, like that of the Babylonians, the earth was a sphere. Pythagoras knew the evening and morning star were the same planet. He taught the earth is suspended in the midst of the universe, which rotates around it. There were three parts to the universe: the zone of air and clouds above the earth, in which exists all that is subject to change and corruptible, was called Ouranos; the region above the moon, with the sun and planets was called Cosmos, and the sphere of the fixed stars was called Olympus. There were spheres for the sun and moon, one for each of the five known planets, one for the stars, the earth itself, and a “counter-earth” was postulated to bring the number of heavenly spheres up to ten, since ten was considered a perfect number.

The Pythagoreans held, Aristotle tells us, that there was “boundless breath” outside the heavens, and that it was inhaled by the world. That is the doctrine of Anaximenes. The further development of the idea must be due to Pythagoras. After the first unit had been formed—however that was—the nearest part of the Boundless was first drawn in and limited, and that it is the Boundless thus inhaled that keeps the units separate from each other. It shows the interval between them. This is a primitive way of describing discrete quantity.

In these passages of Aristotle, the “breath” is also spoken of as the void or empty. This is a confusion already held by Anaximenes, and air and vapor are also confused. Pythagoras seemed to identify the Limit with fire, and the Boundless with darkness. Aristotle says that Hippasus made Fire the first principle, and Parmenides, in discussing the opinions of his contemporaries, attributes to them the view that there were two primary “forms”, Fire and Night.

The Pythagoreans taught that there was not one principle underlying the sensible universe, but ten, and that these were organized in contrasting pairs, the Table of Opposites:

Light and Darkness appear in the Pythagorean table of opposites under the heads of the Limit and the Unlimited respectively. The identification of breath with darkness here implied is a strong proof of the primitive character of the doctrine, for in the sixth century darkness was supposed to be a sort of vapor, while in the fifth its true nature was known. Plato, with his usual historical tact, makes the Pythagorean Timaeus describe mist and darkness as condensed air. A “field” of darkness or breath marked out by luminous units is an image the starry heavens would suggest.

Also attributable to Pythagoras might be the Milesian view of a plurality of worlds, though not an infinite number. Petron, one of the early Pythagoreans, said there were just a hundred and eighty-three worlds arranged in a triangle.

Anaximander had regarded the heavenly bodies as wheels of “air” filled with fire which escapes through certain orifices, and Pythagoras will have had the same view. Anaximander only assumed three such wheels, and Pythagoras will have identified the intervals between these with the three musical intervals he had discovered, the fourth, the fifth, and the octave. That would be the beginning for the doctrine of the “harmony of the spheres”. The word harmonia means octave.

The distinction between the diurnal revolution of the heavens from east to west, and the slower revolutions of the sun, moon, and planets from west to east, may also be referred to the early days of the school, and probably to Pythagoras himself. It is a complete break with the theory of a vortex, and suggests that the heavens are spherical. That was the only way to get out of the difficulties of Anaximander’s system. If it is to be taken seriously, the motions of the sun, moon, and planets are composite. On the one hand, they have their own revolutions with varying angular velocities from west to east, but they are also carried along by the diurnal revolution from east to west. Apparently this was expressed by saying that the motions of the planetary orbits, which are oblique to the celestial equator, are mastered by the diurnal revolution.

The Ionians, down to the time of Democritus, never accepted this view. They clung to the theory of the vortex, whereby all the heavenly bodies revolved in the same direction, so that those, which on the Pythagorean system have the greatest angular velocity, have the least on theirs. On the Pythagorean view, Saturn, for instance, takes about thirty years to complete its revolution; on the Ionian view it is “left behind” far less than any other planet, that is, it more nearly keeps pace with the signs of the Zodiac.

Pythagoras also discovered the sphericity of the earth, which the Ionians, even Anaxagoras and Democritus, refused to accept, though he still probably retained the geocentric system, and that the discovery that the earth was a planet belongs to a later generation.

This account of the views of Pythagoras is partly conjectural and incomplete. Those portions of the Pythagorean system that seem be the oldest are attributed to him. Some confirmation is found in the second part of the poem of Parmenides and the system of the later Pythagoreans. The great contribution of Pythagoras to science was his discovery that the concordant intervals could be expressed by simple numerical ratios. In principle, at least, that suggests an entirely new view of the relation between the traditional “opposites”. If a perfect attunement (harmonia) of the high and the low can be attained by observing these ratios, it is clear that other opposites may be similarly harmonized. The hot and the cold, the wet and the dry, may be united in a just blend. The word temperature and the medical doctrine of the “temperaments” reflect this idea. The famous doctrine of the Mean is only an application of the same idea to the problem of conduct. Greek philosophy was henceforward dominated by the notion of the perfectly tuned string.

Xenophanes of Colophon (570-475 BC)

Italy was also the home of Eleatic doctrine of the One, called after the town of Elea, the headquarters of the school. Xenophanes of Colophon was the founder of the Eleatic school of philosophy, the father of pantheism, who declared an impersonal God to be the eternal unity, permeating the universe, and governing it by his thought.

When the Persians extended their empire to Greek areas in Asia Minor in the mid-500s, this young Greek chose to flee rather than live under Persian rule. He left his own country to go to Sicily, where he supported himself by reciting, at the court of Hiero, elegiac and iambic verses, which he had written in criticism of Homer and the Theogony of Hesiod. He rejected the revered poet Hesiod! From Sicily he passed over into Magna Graecia, where he took up the profession of philosophy, and a wanderer from city to city, attended by a slave. He introduced opinions of his own opposing the doctrines of Epimenides, Thales, and Pythagoras. He held the Pythagorean chair of philosophy for about seventy years, and lived to the extreme age of 95.

Xenophanes was an elegiac and satirical poet who approached the question of science from the standpoint of the reformer rather than of the scientific investigator. He favored what he thought was reason rather than being guided in outlook by emotions or mere tradition. The considerable remains of his poetry that survive are all in the satirist’s and social reformer’s vein, but the trouble is, it is difficult among it all to find a single point of view. One deals with the management of a feast, another denounces the exaggerated importance attached to athletic victories, and several attack the humanized gods of Homer.

Like the religious reformers of the day, Xenophanes turned his back on the anthropomorphic polytheism of Homer and Hesiod. He objected to mysticism and to divine revelations. He described the priests of the Dionysos movement as impostors. He was disgusted with the Greeks for their feeble resistance against the Persians, and his disgust spread to a rejection of religion. He was convinced that the tales of the poets were directly responsible for the moral corruption of the time.

Homer and Hesiod have ascribed to the gods all things that are a shame and a disgrace among mortals, stealing and adulteries and deceiving of another.

This was due to the representation of the gods in human form.

Mortals think that the gods are begotten, and wear clothes like their own, and have a voice and a form. If oxen and horses or lions had hands, and could paint with them, and produce works of art as men do, horses would paint the forms of the gods like horses, and oxen like oxen. Each kind would make their bodies in their own form. The Ethiopians say their gods are black and snub-nosed. The Thracians that theirs have blue eyes and red hair.

Xenophanes found the weapons he required for his attack on god-making in the science of the time. Traces of Anaximander’s cosmology in the fragments suggest Xenophanes may have been his disciple before he left Ionia. He seems to have taken the gods of mythology one by one and reduced them to meteorological phenomena, and especially to clouds. And he maintained there was only one god—namely, the world. God is one incorporeal eternal being, and, like the universe, spherical in form. He is of the same nature with the universe, comprehending all things within himself. He is intelligent, and pervades all things, but bears no resemblance to human nature either in body or mind.

So, his position seems pantheistic, although his use of the term “god” simply follows the use characteristic of the early cosmologists generally. Xenophanes did not regard this “god” with any religious feeling. It is quite unlike a man, and has no special organs of sense, but “sees all over, thinks all over, hears all over”. He does not go about from place to place, but does everything without toil. So, this god is a central force in the universe but not human-like in shape, thought or emotions. It was a god that was everywhere and everything, a god that was the whole universe. God was nature and nature was god.

Xenophanes himself tells us no more. If he had said anything more positive or more definitely religious, it would have been quoted by later writers. Yet, Xenophon’s god seems more advanced than Yehouah, and might have been His model if, as seems possible, it is based on Ahura Mazda. Through the sixth century the Greeks were developing a growing interest in other people. Learning about their customs and religions taught them that their own ideas were not sacred but merely conventional and could be challenged. The greatest external influence must have been the Medes and Persians at that time. Though he might have hated the Persians themselves, Xenophon might have challenged Homer’s loutish gods because he saw the Persian god as more noble and conducive to respectable and heroic behaviour. He sought to improve on it.

Xenophanes speculated that the earth stretched infinitely in all directions, that the earth was infinitely deep and that air extended infinitely upwards. If there had ever been a time when nothing existed, nothing could ever have existed. Whatever is, always has been from eternity, without deriving its existence from any prior principles. Nature, he believed, is one and without limit. What is one is similar in all its parts, else it would be many. The one infinite, eternal, and homogeneous universe is immutable and incapable of change.

All things come from the earth, and in earth all things end. All things are earth and water that come into being and grow. There never was nor will be a man who has certain knowledge about the gods and about all the things I speak of. Even if he should chance to say the complete truth, yet he himself knows not that it is so. But all may have their fancy.


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