The beginning of the formation of this school is the end of the 6th century. BC.

| The Pythagorean school arose as a kind of religious order, with its own etiquette and strict rules of conduct. Among these rules was the strictest prohibition to preach the doctrine to other people who were not members of the Pythagorean Union. The teachings of the Pythagoreans were perceived as a secret, which only adherents of this union could comprehend. The Pythagoreans did not set forth their teaching in writing, it existed with them on the basis of oral tradition, they kept it in their memory and preached only to a trusted circle of people. They severely punished those who divulged their teachings to those who were not initiated into Pythagoreanism.

Therefore, the paucity of information about early Pythagorean philosophy is quite understandable. It increases only after the Pythagorean Union ceased to exist and the ban on disclosing the doctrine was lifted.

The revival of Pythagoreanism falls on the 1st century. AD and associated with activities Apollonius of Tyana, who wrote the essay "Life of Pythagoras". The further development of the Pythagorean tradition was carried out on the basis of Neoplatonism.

A.O. Makovelsky proposed the following periodization of the formation of Pythagoreanism: (a) from the founding of the Pythagorean Union in 531 BC. until the destruction of the school around 500 BC. At this time lived the Pythagoreans Pythagoras, Hippas, Demoked, and others; (b) from 500 to the formation of the main system of scientific Pythagoreanism, which took shape in the middle of the 5th century. BC.; (c) completion of the main system of scientific Pythagoreanism in Philolaus; (d) the last third of the 5th c. BC. - Pythagoreans in exile; (e) Pythagoreanism of the 4th century. BC. - Archytas of Tarentum and other "last Pythagoreans". |

The founder of the Pythagorean Union is traditionally considered Pythagoras. The representatives of early Pythagoreanism were Hippasus, Parmeniscus, Kerkops, Brontin; middle - Philolaus of Croton (Terentsky), Hebrew, botanist menestor, mathematician Theodore and cosmologists Ekfant, Giket (Letius) And Xuthus (Simplice); late - Lrhit of Terent, Okkel, Xenophilus and many others.

Bust of Pythagoras

I Pythagoras(c. 570-496 BC) - the creator of Pythagorean philosophy, which combined Eastern science with Hellenic mythology. His fortieth birthday (akme) fell on the 30s of the 6th century. BC. He was originally from the island of Samos. Pupil of Anaximander and Pherecydes. Studied in Egypt and Babylonia; returned home at the age of 56. In 532-531. he leaves Samos and arrives in Italy, in the policy of Croton, where he founded his school - the Pythagorean Union. Pythagoras died at the age of 75. According to some sources, Pythagoras himself did not write anything, according to others, “On nature","ABOUT state,"ABOUT education", "ABOUT soul","ABOUT the world","ABOUT piety", "Sacred Word" Pythagoras was the first thinker who, according to legend, called himself a philosopher, that is, "lover of wisdom."

The change in the direction of scientific research of the Pythagoreans was due number, understood as Start instead of water, air or fire. The most famous and meaningful characteristic of Pythagorean thought belongs to Aristotle:

The Pythagoreans, having taken up mathematics, were the first to develop it and ... began to consider its beginnings to be the beginnings of everything that exists. And since among these beginnings numbers by nature are [the first beginnings in mathematics, then in them they saw the beginnings of all things], - more than in fire, earth and water ... they saw that the properties and relationships inherent in harmony are expressible in numbers; therefore, it seemed to them that everything else in its nature is clearly comparable to numbers and that numbers are the first in all nature, they assumed that the elements of numbers are the elements of everything that exists [things] and that the whole sky is harmony and number 1.

Elsewhere in his Metaphysics, Aristotle writes that for the Pythagoreans, "numbers are things themselves"; "things are made of numbers"; "Number is the essence of all things." In other words, the logic of the Pythagoreans is presented in development from the first position to the third: from the identification of numbers and things to the understanding that numbers are not things and things are not numbers, but numbers are the essence of things.

Such an understanding by the Pythagoreans of the beginning of being is not clear to common sense. However, upon careful consideration of the surrounding world, it is quite obvious that everything is based not only on qualitative characteristics, but also on quantitative characteristics of being. So, molecular motion in a substrate (for example, in water) when changing temperature regime can be reflected on the numerical scale of the thermometer. Sound and music are also translated into numerical ratios: the difference in the sound of strings in musical instrument correlated with the length of the strings; the harmonic ratios of the octave, fifth, and fourth are governed by numerical laws (1:2, 2:3, 3:4).

In this world, everything can be expressed by means of numbers and the mathematical regularity underlying being: the cyclical development of inorganic and organic systems, the chronology of epochs, centuries, the sequence of months and days, etc.

For the Pythagoreans, a number is something real, moreover, it is more real than things. In this sense, it is the beginning that forms all things. For the modern understanding, the number is an abstraction, a product of thinking, and for the Pythagorean world outlook - reality, the nature of things.

In direct connection with the concept of number is also doctrine of opposites. Considering the numbers, the Pythagoreans single out in them such an opposite as even and odd numbers. The main ten opposites are: limit - infinite, odd - even, one - many, right - left, male - female, resting - moving, straight - crooked, light - shadow, good - bad, square - rectangle.

The main philosophical meaning is the opposition of the limiting and the limitless. This antithesis, apparently, was interpreted as a premise of the cosmos. The infinite (apeiron) in the doctrine of the cosmos appears as a physically infinite void containing the cosmos. The world is born through the inhalation of this emptiness by the “One” (its genesis is unknown) with the subsequent formation of numbers and things. If number is the harmony of the limiting (abstract number) with the infinite (abstract substance), then everything is order. And since the order in Greek is "kosmos",

then Pythagoras was "the first to designate space with all the things that are there, as the order that is in it.

The doctrine of space the Pythagoreans laid the foundations of Plato's objective-idealistic system. Indeed, the foundations of the classical objective idealism of ancient philosophy are formed not on the opposition of number and thing as primary to secondary, but on absolute identification general and individual, quantitative and qualitative characteristics of being. The Pythagoreans identified number and things, and their single Universe as a harmony of the limit (abstract number) and the infinite (abstract matter), i.e. the cosmos, consisting of “number-things”, breaks up into the material, real, physical, visible world and the invisible, ideal world. It is here that Plato's objective idealism originates.

Nevertheless, the Pythagoreans themselves are not idealists, although there is an idealistic tendency in their philosophical outlook. In the early period of the development of ancient philosophy, the opposite of the material principle and the ideal principle is not realized. Such an understanding is inherent in the later philosophical teachings of ancient philosophy (Plato and others).

The Pythagoreans made a great contribution to the development mathematics. Rational thinking helped Pythagoras formulate a number of important provisions in number theory, arithmetic, and geometry. However, his characteristic combination of mathematical research with mythology led to esoteric calculations about the transmigration of souls and other mystical ideas. The Pythagoreans connected the number seven with a deity. Understanding man as a disciple of God, they believed that each of the people should prepare for union with God.

The true understanding of the world, according to Pythagoras, rests on three foundations: morality, religion And knowledge. The morality of Pythagoras is the morality of an aristocrat. Tasks scientific knowledge subordinated to the interests of religion.

For the social views of the Pythagoreans, like all the ancient Greeks of the VI century. BC, characteristically misunderstanding qualitative differences between nature and society. Awareness of this difference will find a place in the teachings of the sophists, who will draw a definition between the laws of nature and the laws of society, between social man and natural man. Therefore, when Pythagoras set social laws, a system state structure, justice and justice in dependence on the gods, this reflected the general lag of ancient social thought from the teachings of metaphysics.

Subsequently, in the later teachings of the Pythagoreans, the gods are transformed into numbers and geometric figures, and the first principle will be cosmic harmony - the true root cause of the world order, which among the Pythagoreans corresponded to the logos of Heraclitus.

• According to Aristotle, Pythagorean philosophy includes four large sections: the doctrine of numbers, the doctrine of opposites, cosmology and cosmogony, and the idea of ​​the soul.
• Aristotle. T. 1. S. 77-78.

Pythagoreanism- another of the currents of ancient Greek philosophy, named after its founder, philosopher, scientist and outstanding thinker. (VI-IV centuries BC)

The teachings of the Pythagoreans, like many other currents in philosophy ancient greece(and in particular their founders), probably not having, and maybe having claims to political, social and socio-cultural power, were often strongly disliked by those who stood at the levers of power at that time. In this regard, many prominent philosophers and sages, followed by the people, had to flee from their own land and hide from judgment, or from death. (Socrates suffered a similar fate, but did not flee.)

Philosophy of Pythagoras

Pythagoras was the first to call himself a philosopher. The very word "philosophy" is an innovation of Pythagoras. He also defined the universe as a beautiful order. The subject of the teachings of Pythagoras was built mainly on numbers, the philosopher believed that everything consists of the harmony of numbers. Pythagoras supplemented Anaximander's apeiron and geometrized the physical world, thereby laying the foundation for analytical geometry. Origin Pythagorean school associated with the arrival of Pythagoras in Croton (about 532 BC), where he founded a political community (geteria), which later became the core of the philosophical and scientific school.

Philosophy of Pythagoreanism

The history of Pythagorean philosophy is divided into two stages:

• Early - from the foundation of the community to Philolaus (c. 530-430)
• Late - from Philolaus to the disappearance of the school (c. 430-330)

Representatives, according to the list compiled by Aristoxenus, are only 218 people. Mostly they were members of the geteria and adherents of a special way of life, some were engaged in science and philosophy.

Early School: doctor Demoked, Ayakmeon, Brontin (addressee of Alkmaeon's book), Hippasus, Parmenides' teacher Aminius, natural philosopher and botanist Menestor from Sybaris, Hyptt., mathematician Theodore from Cyrene.

Late School: Philolaus and Lysis (the teacher of the commander Epaminondas) lived in Thebes; Philolaus' followers were Simmias

The Pythagoreans believed in the transmigration of souls. They also believed that the soul is dualistic and has male and female principles.

The Pythagoreans have already spoken about the duality of their doctrine, which is divided into two opposites: the limit and the boundless. They denied the possibility of the infinite as a common and unified beginning of all things, in accordance with their thinking, which would not give room for the limit. The limit and the infinite are closely connected and interdependent on each other. “…Nature is well-coordinated from boundless and defining beginnings…” — says Philolaus, a prominent representative of the Pythagorean school.

Pythagoras and the Pythagoreans set the science of mathematics on its feet, pushing and defining it to the fore. A significant foundation was laid in science, later developed by other thinkers. The Pythagoreans defined everything through numbers: music, the cosmos, and even the human soul.

The harmony of the world, present in all living and existing things, is represented by the law of the entire universe, and is plurality in unity and unity in plurality. To the question of how truth is thought, and whether it is thought at all, the number answers. Number is the measure of everything.

For people today, this measure is only a quantitative value, but for the teachings of the Pythagoreans, this value plays the role of the force that moves the unit of the whole and imparts certain properties to it. For example, one is the cause of unity, two is the cause of division, etc.

The world is like an oscillating sphere in infinity. Unity, arising from nothing, attracts the nearby sides of infinity, bringing them into the category of limit. When the sides of the infinite appear in the fullness of unity, a void is formed in unity, crushing the original category of unity into various kinds of parts.

But there are also other teachings, taken from a certain angle and voiced by Parmenides and Zeno, regarding the cosmology of the Pythagoreans. and Zeno raised the unity to a higher degree, with mediocre functionality, defining and most prominent in terms of functionality being. That is, representatives on this score have a more centralized point of view on this most unified principle.

But almost simultaneously with the materialistic view of the world, idealistic ideas arise, which are closely connected with religion and are a refined form of religious ideas. This idealistic view of the world was developed by Pythagoras and his followers. The reactionary nature of Pythagoreanism was also manifested in the secret nature of the activities of the school, whose political views reflected the ideology of aristocratic reaction. There are legends about Pythagoras that he was in Egypt, was initiated by the priests into the secrets of their sacred science.

A characteristic feature of the Pythagorean school is the deification of numbers: "Numbers rule the world." The Pythagoreans searched in numerical terms mystical secrets and revelations. The omnipotence of numbers is manifested in the fact that everything in the world can be subordinated to numerical relations. There is a legend that Pythagoras perceived the discovery of the incommensurability of the diagonal of a square with its side as the beginning of chaos, and ordered his students to keep this discovery a secret. The Pythagoreans believed in the transmigration of souls, demanded the veneration of gods, ancestors, authorities. Justice is mathematically expressed by the square, for it renders equal to equal.

But, after the Ionians it was impossible to return to the religious concept of the universe. In their physics, the Pythagoreans were forced to develop an idea of ​​the structure of the universe, in which, despite the presence of mystical elements, the views of Anaximander and Anaximenes received further development. This circumstance, which we reveal throughout the history of science, reveals the fact that the struggle between materialism and idealism leads to the victory of materialism.

This is precisely what the cosmogony of the Pythagoreans, set forth later by the Pythagorean Philolaus (470-399), speaks of. Considering the sphere as the most perfect form, the Pythagoreans taught about the sphericity of the Earth and about its movement along the sphere around the “central fire”. Nine more spheres revolve around the same central fire: the sphere of Mercury, Venus, Mars, Jupiter, Saturn, the Sun, the Moon, the stars and, finally, the “counter-earth” (the body introduced by the Pythagoreans in order to obtain a harmonic number of celestial spheres - ten). The Pythagoreans taught that the movement of these spheres is accompanied by harmonic musical sounds, inaudible to us, coordinated among themselves (“the harmony of the world”). Lenin rightly saw in this cosmogony of the Pythagoreans "a hint at the structure of matter." It should be noted that Copernicus referred to the teaching of the Pythagoreans about the movement of the earth, and the church in its rulings called the Copernican System "false Pythagorean teaching."

Of the other Daturphilosophical views of the Pythagoreans, let us mention their theory of "visual rays", which was very widespread in ancient optics. According to this theory, vision is due to special rays emanating from the eyes. But at the same time, the Pythagoreans taught that the rays from the Sun penetrate "through thick and cold ether." In this regard, Lenin noted: “So, for thousands of years, the conjecture about the ether has existed, remaining to this day, a guess. But already now 1000 times more digs are ready, leading to the solution of the issue, the scientific definition of the ether.”

The merit of the Pythagoreans is the introduction of mathematics into natural science, a guess about the structure of the universe. But from the Pythagoreans, in accordance with their idealistic views, comes the bare symbolism and mysticism of numbers, which leads to reactionary, anti-scientific statements in our time.

The heyday of Greek civilization falls on the period between the VI century BC. and the middle of the 2nd century BC. e.

The development of knowledge among the Greeks has no analogues in the history of that time.

The scale of comprehension of sciences can be imagined at least by the fact that in less than three centuries Greek mathematics has gone its way - from Pythagoras to Euclid, Greek astronomy - from Thales to Euclid, Greek natural science - from Anaximander to Aristotle and Theophrastus, Greek geography - from Hekcatea of ​​Miletus to Eratosthenes and Hipparchus, etc.

The discovery of new lands, land or sea voyages, military campaigns, overpopulation in fertile areas - all this was often mythologized. In the poems, with the artistic skill inherent in the Greeks, the mythical side by side with the real. They set out scientific knowledge, information about the nature of things, as well as geographical data. However, the latter are sometimes difficult to identify with today's ideas.

The Greeks paid great attention specifically to the geographical knowledge of the Earth. Even during military campaigns, they did not leave the desire to write down everything that they saw in the conquered countries. In the troops of Alexander the Great, even special pedometers were allocated, which counted the distances traveled, made a description of the routes of movement and put them on the map.

Based on the data they received, Dikearchus, a student of the famous Aristotle, compiled a detailed map of the ecumene of that time, according to him.

The simplest cartographic drawings were known even in primitive society, long before the advent of writing. This can be judged by rock paintings.

Architecture, sculpture, painting

The leading architectural structures in Greece of the classical period were temples and theaters. In the 5th century BC. urban planning emerges. The main architectural structure was the temple.

Painting was widespread in ancient Greece, but, unfortunately, almost did not survive to our time. Certain ideas about Greek painting give us red-figure and black-figure vases that have come down to us.

Pythagorean school

Pythagoras, the founder of the school, like Thales, traveled a lot and also studied with the Egyptian and Babylonian sages. Returning around 530 BC. e. to Magna Graecia (a region of southern Italy), he founded something like a secret spiritual order in the city of Croton. It was he who put forward the thesis “Numbers rule the world”, and with exceptional energy he was engaged in its justification. At the beginning of the 5th century BC e., after an unsuccessful political speech, the Pythagoreans were expelled from southern Italy, and the union ceased to exist, but the popularity of the doctrine from dispersion only increased. Pythagorean schools appeared in Athens, on the islands and in the Greek colonies, and their mathematical knowledge, strictly guarded from outsiders, became common property.

Many of the achievements attributed to Pythagoras are probably in fact the merit of his students. The Pythagoreans were engaged in astronomy, geometry, arithmetic (number theory), created the theory of music. Pythagoras was the first European to understand the significance of the axiomatic method, clearly highlighting the basic assumptions (axioms, postulates) and the theorems deduced from them deductively.

The geometry of the Pythagoreans was mainly limited to planimetry (judging by the later works that have come down to us, very fully expounded) and ended with the proof of the “Pythagorean theorem”. Although regular polyhedra were also studied.

A mathematical theory of music was built. The dependence of musical harmony on the ratios of integers (string lengths) was a strong argument of the Pythagoreans in favor of the primordial mathematical harmony of the world, sung by Kepler 2000 years later. They were sure that "the elements of numbers are the elements of all things ... and that the whole world as a whole is harmony and number." The basis of all the laws of nature, the Pythagoreans believed, is arithmetic, and with its help one can penetrate into all the secrets of the world. Unlike geometry, their arithmetic was not built on an axiomatic basis, the properties of natural numbers were considered self-evident, but the proofs of theorems were steadily carried out here too.

The Pythagoreans advanced a lot in the theory of divisibility, but they became overly fond of games with "triangular", "square", "perfect", etc. numbers, which, apparently, were given a mystical meaning. Apparently, the rules for constructing "Pythagorean triples" were already open then; exhaustive formulas for them are given by Diophantus. The theory of greatest common divisors and least common multiples is also apparently of Pythagorean origin. Probably, they also built a general theory of fractions (understood as ratios (proportions), since the unit was considered indivisible), learned to perform comparison (reduction to a common denominator) and all 4 arithmetic operations with fractions.

The first crack in the Pythagorean model of the world was their own proof of irrationality, formulated geometrically as the incommensurability of the diagonal of a square with its side. The impossibility of expressing the length of a segment by a number called into question the main thesis of Pythagoreanism. Even Aristotle, who did not share their views, expressed his amazement at the fact that there are things that "cannot be measured with the smallest measure."

The talented Pythagorean Theaetetus tried to save the situation. He (and later Eudoxus) proposed a new understanding of the number, which was now formulated in geometric language, and there were no problems of commensurability. However, it subsequently turned out that the construction of a numerical algebra on the basis of geometry was a strategic mistake of the Pythagoreans; for example, from the point of view of geometry, the expressions x2 + x and even x4 did not have a geometric interpretation, and therefore did not make sense. Later, Descartes did the opposite, building geometry on the basis of algebra, and made tremendous progress.

Theaetetus also developed a complete theory of divisibility and a classification of irrationalities. It can be assumed that the whole division with a remainder and the "Euclid's algorithm" for finding the greatest common divisor also first appeared among the Pythagoreans, long before Euclid's "Beginnings". Continued fractions as an independent object were singled out only in modern times, although their incomplete partials are naturally obtained in the Euclid algorithm.

Greek mathematics strikes, first of all, with the beauty and richness of its content. Many scientists of the New Age noted that they learned the motives for their discoveries from the ancients. The rudiments of analysis are noticeable in Archimedes, the roots of algebra in Diophantus, analytic geometry in Apollonius, etc. But the main thing is not even that. Two achievements of Greek mathematics far outlived their creators.

First, the Greeks built mathematics as an integral science with their own methodology based on clearly formulated laws of logic.

Secondly, they proclaimed that the laws of nature are comprehensible to the human mind, and mathematical models are the key to their knowledge.

In these two respects, ancient mathematics is quite modern.

Report: "Pythagorean school".

Ryazantsev Viktor Viktorovich

group P4-00-02

Pythagoreanism is an idealistic doctrine in ancient philosophy of the 6th-4th centuries. BC, which considered the number as the formative principle of all that exists and influenced the views of Plato and Neoplatonism. In the school founded by Pythagoras, secret rites were practiced, asceticism was preached, etc. The Pythagoreans developed the theory of music, problems of mathematics and astronomy and, on this basis, derived a system of knowledge about the world as a set of detailed numerical definitions (one - absolute, two - its unformed, potential division, three - abstract, four - concrete, bodily shape of the absolute, etc.). P.). Pythagoreanism contained a number of mystical ideas: about the transmigration of souls, about the "harmony of the heavenly spheres", i.e. about the subordination of the movement of the cosmos to musical relationships.

Introduction.

The history of Pythagoras and the Pythagoreans can be described tentatively. Probably at the end of the 6th c. under Pythagoras, the general theoretical content of Pythagoreanism, its religious, scientific and philosophy. Pythagoreanism reaches its peak at this time. In the second half of the 5th c. the philosophical teaching of the Pythagoreans, freed from religious prohibitions, comes to the fore. At the end of the 5th - the first half of the 6th century, Pythagoreanism develops into Platonism and merges with it in the activities of the ancient Academy.

1. Creation of the organization "Pythagorean Union".

Pythagoras, son of Mnesarchus, a Samian, was born in 576. BC. According to legend, he studied in Egypt and traveled a lot. Around 532. , hiding from the tyranny of Polycarp, he settled in Croton, where he quickly gained wide popularity and created a religious-philosophical and political organization - the Pythagorean Union. This alliance was aimed at the dominance of the best in the religious, scientific, philosophical - "moral" sense. Pythagoras tried to create an "aristocracy of the spirit" in the person of his disciples, who conducted state affairs so excellently that it was truly an aristocracy, which means "the rule of the best."

The ritual of initiation into the members of the Pythagorean brotherhood was surrounded by many mysteries, the disclosure of which was severely punished. “When the younger ones came to him and wished to live together,” says Iamblichus, “he did not immediately give consent, but waited until he checked them and made his judgment about them.” But also, having got into the order after a strict selection and trial period ", newcomers could only listen to the voice of the teacher from behind the curtain, but they were allowed to see him only after several years of purification by music and ascetic life. However, this was not a severe Christian asceticism that mortifies the flesh. Pythagorean asceticism for a beginner was reduced, first of all, to a vow "The first exercise of the sage," testifies Apuleius, "was for Pythagoras to humble his language and words to the end, those very words that poets call flying, to conclude, having plucked feathers, behind a white wall of teeth. In other words, here what the rudiments of wisdom boiled down to: to learn to think, to unlearn to talk.

Moral principles and commandments of Pythagoras.

The system of moral and ethical rules, bequeathed to his students by Pythagoras, was collected in the moral code of the Pythagoreans - "Golden Verses". They have been rewritten and supplemented throughout the thousand-year history. In 1808 rules were published in St. Petersburg, beginning with the words: Zoroaster was the legislator of the Persians.

Lycurgus was the legislator of the Spartans.

Solon was the legislator of the Athenians.

Numa was the legislator of the Romans.

Pythagoras is the legislator of the whole human race.

Here are some extracts from a book containing 325 Pythagorean commandments:

Find yourself a true friend, having him, you can do without the gods.

Youth! If you wish yourself a long life, then refrain yourself from satiety and any excess.

Young girls! Remember that a face is beautiful only when it depicts a graceful soul.

Do not chase happiness: it is always in yourself.

Do not worry about gaining great knowledge: of all knowledge, moral science is perhaps the most necessary, but it is not taught.

Today it is absolutely impossible to say which of the hundreds of such commandments go back to Pythagoras himself. But it is quite obvious that they all express the eternal universal values ​​that remain relevant as long as a person is alive.

The lifestyle of the Pythagoreans.

The Pythagoreans led a special way of life, they had their own

special daily routine. The day of the Pythagoreans was to begin with verses:

Before you get up from the sweet dreams of the night

Think, spread out what things the day has prepared for you.

When they woke up, they did mnemonic exercises that helped memorize the necessary information, and then went to the seashore to meet the sunrise, pondered the affairs of the coming day, after which they did gymnastics and had breakfast. In the evening, they shared bathing, a walk, dinner, after which a libation to the gods and reading. Before going to bed, everyone gave himself an account of the past day, ending with his verses:

Do not allow lazy sleep on tired eyes,

Before you answer three questions about the day's business:

What I've done? What didn't he do? What is left for me to do?

The Pythagoreans paid much attention to medicine and psychotherapy. They developed techniques for improving mental abilities, the ability to listen and observe. They developed memory, both mechanical and semantic. The latter is possible only if the beginnings are found in the knowledge system.

As you can see, the Pythagoreans with equal zeal took care of both the physical and the spiritual development. It was they who gave birth to the term “kalokagathia”, denoting the Greek ideal of a person who combines the aesthetic (beautiful) and ethical (good) principles, the harmony of physical and spiritual qualities.

Throughout the history of Ancient Hellas (Greece), kalokagatiya remained a kind of cult for the ancient Greeks and passed from them to the ancient Romans.

The Pythagorean way of life was determined by the fact that there is no greater evil than anarchy (anarchy), that a person by nature cannot remain prosperous if no one is in charge. The supreme authority belongs to God. This is their principle and the whole way of life is arranged in such a way as to follow God. And the basis of this philosophy is that it is ridiculous to act like people who are looking for good somewhere else, and not with the Gods. After the Gods, rulers, parents and elders, as well as the law, should be respected.

The way of life of the Pythagoreans included the doctrine of various ways treatment of people depending on their status in society. The meaning of this way of life is the subordination of a person to authority. It is not difficult to see in the Pythagorean ideal a flexible socio-political concept adapted to the execution by the ruling groups of society. Built on the authority of society and the law, it requires adherence to paternal customs and laws, even if they are worse than others.

Religious and philosophical doctrine.

In the religious and philosophical teaching of early Pythagoreanism,

two parts are distinguished: “akusmata” (heard), i.e. positions, orally and without proof, presented by the teacher to the student, and “mathematics” (knowledge, teaching, science), i.e. actual knowledge.

The provisions of the first type included indications of the meaning of things, the preference for certain things and actions. They were usually taught in the form of questions and answers: What are the Isles of the Blessed? - Sun and moon. What is the most fair? - Offering Sacrifices. What is the most beautiful thing? - Harmony, etc.

The Pythagoreans had many symbolic sayings. The collection of these sayings, called akusmas, replaced the charter of the society. Here are some of the Pythagorean acusmas and their interpretations:

Do not eat the heart (i.e. do not undermine the soul with passions or grief)

Do not stir fire with a knife (i.e. do not hurt angry people)

When leaving, do not look back (i.e. before death, do not cling to life)

Do not sit down on a grain measure (i.e. do not live idly).

There is an opinion that initially the Pythagorean acusmas were understood in the literal sense, and their interpretations were contrived later. For example, the first akusma reflected the general Pythagorean ban on animal food, especially the heart is a symbol of all living things. But in its initial form, this is pure magic: defense against witchcraft, such as smoothing and rolling the bed, is necessary so that there are no body prints left on it that the sorcerer could influence and, thereby, damage the person. Or, for example, it was forbidden to touch beans, anyway, like human meat. According to one myth, the beans came from the drops of blood of the torn Dionysus Zagreus, which is why they were forbidden to eat. On the whole, all these stories only once again remind us that the Pythagoreans lived a very long time ago - two and a half millennia ago, that a clear mind and high morality were shrouded in the mind of an ancient person with a beautiful fairy-tale veil.

The scientific worldview of the Pythagoreans. Cosmogony and

cosmology.

As for their own knowledge, Pythagoras is credited with geometric discoveries, such as the well-known Pythagorean theorem on the ratio of the hypotenuse and legs of a right triangle, the doctrine of five regular bodies, in arithmetic - the doctrine of even and odd numbers, the beginning of the geometric interpretation of numbers, etc. .

Pythagoras first used the word cosmos in its current sense to define the entire universe and its most important side - orderliness, symmetry, and hence beauty. The Pythagoreans proceeded from their main thesis that "order and symmetry are beautiful and useful, while disorder and asymmetry are ugly and harmful." But the beauty of the macrocosm - the Universe, the Pythagoreans believed, is revealed only to those who lead a correct, well-organized way of life, i.e. who maintains order and beauty in his microcosm. Consequently, the Pythagorean way of life had an excellent "cosmic goal - to transfer the harmony of the universe into the life of man himself."

The cosmogony of the Pythagoreans can be described as follows: the world, composed of the limit and the infinite, is a sphere that arises in the infinite emptiness and “breathes” it into itself, thereby expanding and dismembering. This is how the world space, celestial bodies, movement and time arise. In the middle of the world is fire, the home of Zeus, the connection and measure of nature. Next come the Counter-Earth, the Earth, the Moon, the Sun, the five planets and the world of the fixed stars. The counter-earth was introduced for a round count, as the tenth celestial body, with its help they explained lunar eclipses. The cosmic bodies originated from the central fire and revolve around it, attached to the crystal spheres. The planets, including the Earth, rotate from west to east, always facing the central fire on one side, so we do not see it. Our hemisphere is warmed by the rays of the central fire reflected by the Sun.

The cosmology of the Pythagoreans represents a significant step forward. Rejection of geocentrism, recognition of the spherical shape of the Earth, its daily circulation around the central fire, explanation solar eclipses the passage of the Moon between the Sun and the Earth, and the inclination of the earth's orbit with respect to the sun's seasons, represented a significant approximation to the truth.

But the matter is not limited to this physical picture. Pythagoreanism creates a certain logical scheme of the universe, correlated with a moral assessment. This side of the matter is presented in the doctrine of opposites, which is presented as follows: limit and infinity, odd and even, one and many, male and female, resting and moving, light and dark, good and bad, quadrangular and many-sided.

It's not just a matter of opposition - opposites unite. Speaking of Pythagoras as the founder of civic education, Iamblichus attributed to him the idea that none of the existing things is pure, everything is mixed, and fire with the earth, and fire with water, and air with them, and they with air, and even the beautiful with the ugly, and the just with the unjust.

The next idea of ​​the Pythagoreans is the idea of ​​harmony. Its origins can be sought, if not from Pythagoras himself, then from Alcmeon of Croton, a representative of Pythagorean medicine. This doctor considered everything that exists as a product of connection, mixing, harmonic fusion of opposites. He believed that the balance of the forces of moist, dry, cold, warm, bitter, sweet, etc., maintains health, and the dominance of one of them is the cause of the disease. Health is a proportionate mixture of such forces. This commensurate mixture was called “harmony” by the Pythagoreans, becoming one of the basic concepts of their teaching: everything in the world is necessarily harmonious. The gods are harmonious, the cosmos is harmonious, because all its constituent moments are absolutely coordinated into a single and inseparable whole. The state and the king are harmonious, because the strength of bonding all people into a single whole depends on it.

The physiological conjectures and discoveries of Alcmaeon are striking: he established that the organ of mental and mental processes is not the heart, as it was believed before, but the brain, established the difference between the ability to perceive and the ability to think, which belongs only to man, and also proved that sensations are communicated to the brain through special pathways connecting the sense organs with the brain.

The doctrine of the transmigration of souls.

It was in the teachings of Pythagoras and a lot of mystical, foggy

and simply ridiculous not only for our contemporaries, but also for the contemporaries of Pythagoras. Among such doctrines was the doctrine of the immortality of the soul, of the posthumous transmigration of the human soul into animals, that “everything that is born is born again at intervals of time, that there is nothing new in the world, and that all living things should be considered related to each other.”

The Pythagoreans had specific ideas about the nature and fate of the soul. The soul is a divine being, it is imprisoned in the body as a punishment for transgressions. The highest goal of life is to free the soul from bodily darkness and prevent it from moving into another body. To achieve this goal, it is necessary to fulfill the moral code of the “Pythagorean way of life”.

From the teaching on the transmigration of souls, prescriptions also followed, prohibiting the killing of animals and eating their meat, since the soul of a dead person could dwell in an animal.

This part of the Pythagorean doctrine was regarded by many with a very cool air, and was often ridiculed and attributed to foreign influence.

Philosophy of number.

The main philosophical orientation of Pythagoras was

philosophy of number. The numbers of the Pythagoreans at first did not differ at all from the things themselves and, therefore, were simply a numerical image. At the same time, not only physical things were understood numerically, but in general everything that exists, such as goodness or virtue. Then they began to be interpreted as essences, principles and causes of things.

The Pythagoreans, indulging in mathematical studies, considered the beginnings of everything to be numbers, since in numbers they found many similarities with what exists and happens, and in numbers the primary elements of all mathematical principles.

which is formed by the diagonals of a regular pentagon.

There is another striking fact. Exactly

the star pentagon is most common in wildlife (recall the flowers of forget-me-not, carnation, bluebell, cherry, apple tree, etc.) and is fundamentally impossible in crystal

personal grids of inanimate nature. Fifth-order symmetry is called the symmetry of life. This is a kind of protective mechanism of living nature against crystallization, against petrification, for the preservation of living individuality. And it is this geometric figure that the Pythagoreans choose as a symbol of health and life.

The Pythagorean star (pentagram) was a secret sign by which the Pythagoreans recognized each other.

Of the many numbers, the number "36" is sacred: 1 + 2 + 3.

It consists of a unit, and without a unit there is not a single number and it symbolizes “unity.” - the unity of being and the world.

It consists of two, which symbolizes the fundamental polarity in the Universe: light-darkness, good-evil, etc.

It consists of three, the most perfect of numbers, for it has a beginning, a middle, and an end.

In addition, amazing transformations are possible in the number “36”, for example: 36 = 1+2+3+4+5+6+7+8.

It can be concluded that the numbers of the Pythagoreans are the fundamental universal objects, to which it was supposed to reduce not only mathematical constructions but also the whole diversity of reality. Physical, ethical, social and religious concepts have received a mathematical coloring. The science of numbers is given a huge place in the system of worldview, i.e. in fact, mathematics is declared philosophy.

The Pythagoreans attributed special importance to numbers in the matter of knowledge. According to Philolaus, “number is the basis of the form and cognizability of everything that exists. Everything known has a number. For without it it is impossible to understand or know anything.”

CONCLUSION. Significance of religious, scientific and

philosophical doctrine of the Pythagoreans.

The long and complex history of Pythagorism raises many questions for researchers. However, we can formulate the following fairly well-founded assessments of the meaning and theoretical content of the Pythagorean teachings.

The ideology of Pythagorism includes three main components: religious-mythological-magical; scientific, connected with the development of mathematics; and philosophical. The last aspect demonstrates the desire to find the "beginning" of all things and with its help to explain the world, man and his place in space. However, the leading material tendency is replaced by an idealistic one, which was based on the most important discovery associated with the development of mathematical knowledge - the discovery of the possibility of identifying ordered and numerically expressible quantitative relations of everything that exists.

The numerical regularity of existence revealed by the Pythagoreans is an extended world of bodies, mathematical laws of motion celestial bodies, the laws of musical harmony, the law of beautiful arrangement human body and other discoveries - appeared as a triumph of the human mind, which a person owes to a deity.

Unfortunately, for a thousand years of ancient traditions, real information and causing deep respect for the personality of Pythagoras were mixed with many legends, fairy tales and fables. Many miracles could be told about Pythagoras. But the main miracle that glorified him was that he led mankind out of the labyrinths of myth-making and God-seeking to the shores of the ocean of exact knowledge. The morning bathing of the Pythagoreans in the waves of the Ionian Sea was also a daily prelude to sailing on the ocean of knowledge. Only the purpose of the voyage was not the search for treasure, but the search for truth.

Pythagoras was apparently the first to reveal to mankind the power of abstract knowledge. He showed that it is the mind, and not the senses, that bring true knowledge to a person. That is why he advised his students to move from the study of physical objects to the study of abstract mathematical objects. So mathematics becomes for Pythagoras an instrument of knowledge of the world. And mathematics is followed by philosophy, because philosophy is nothing but the extension of the accumulated special (in this case, mathematical) knowledge to the field of worldview. This is how the famous Pythagorean thesis is born: “Everything is a number”. Thus, in the depths of the Pythagorean union, mathematics and philosophy are born.

They considered it possible with the help of mathematics to achieve purification and union with the deity. Mathematics was one of constituent parts their religions. “God is unity, and the world is many and consists of opposites.

That which brings opposites to unity and unites

everything in space, there is harmony. Harmony is divine

and is in numerical terms. Who will study to the end

this divine numerical harmony, he himself will become divine

nym and immortal.”

Such was the Pythagorean union - the favorite brainchild of the great

th Hellenic sage. Truly it was a union of truth, goodness

and beauty.

IV. BIBLIOGRAPHY.

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