Discovering the Philosophical Ideas of Pythagoras

 In this post, explore the philosophical ideas and ideas of Pythagoras, one of the most influential figures in ancient Greece! 

Discovering the Philosophical Ideas of Pythagoras 

Pythagoras is one of the most famous Greek philosophers, whose ideas and theories had an immense influence on ancient Greece. His philosophy to life was centered around mathematics, stressing the importance of numbers in order to understand the world. He also advocated a vegetarian lifestyle, with a strong emphasis on community and collective well-being. In this post, we'll explore Pythagoras's philosophical ideas and how they shaped his view of the world and our lives today.

Pythagoras a Mathematician (570- 495) BCE

Who is Pythagoras and what did he do ?

PYTHAGORAS, whose influence in ancient and modern times is my subject in this article. intellectually one of the most important men that ever lived, both when he was wise and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him, and in him is intimately connected with a peculiar form of mysticism. The influence of mathematics on philosophy, partly owing to him, has, ever since his time, been both profound and unfortunate.

biography about Pythagoras

Let us begin with what little is known of his life. He was a native of the island of Samos, and flourished about 532 B.C. Some say he was the son of a substantial citizen named Mnesarchos, others that he was the son of the god Apollo; I leave the reader to take his choice between these alternatives. More myth about Pythagoras, some people say his thigh made of gold, He had ability to fly. he Can write on moon, He could also do time travel and he was able to talk animals. Pythagoras claimed could remember his last four lives.

Pythagoras was fond of traveling. Some people say that he had traveled to India. We know Pythagoras, Thales, Anaximander, Anaximenes, natural philosopher through Aristotle.

According to legend, before he arrived in South Italy he had travelled extensively in Egypt and other countries of the East. There is, however, no historical evidence of this. There is nothing in itself improbable in the belief that Pythagoras made these travels, but it cannot be accepted as proved for lack of evidence. The legend is really founded simply upon the oriental flavour of his doctrines. 

Pythagoras was the first to call himself a philosopher. Greek scholar people was called sage. but Pythagoras want different name that's way he called himself a philosopher (lover of wisdom). 

Polycrates was a patron of the arts, and beautified Samos with remarkable public works. Anacreon was his court poet. Pythagoras, however, disliked his government, and therefore left Samos. It is said, and is not improbable, that Pythagoras visited Egypt, and learnt much of his wisdom there; however that may be, it is certain that he ultimately established himself at Croton, in southern Italy.  

Pythagoras arrived in Croton, it had just been defeated by Locri. At Croton Pythagoras first one who open his own first school (academy). Pythagoras founded a society of disciples, which for a time was influential in that city. But in the end the citizens turned against him, and he moved to Metapontion (also in southern Italy), where he died. He soon became a mythical figure, credited with miracles and magic powers.  

he was also the founder of a school of  an aristocratic communist school in Croton in 530 BCE, also called Mathematicians school. The Pythagorean secret society consisted of learners and listeners. The Pythagorean school of symbol was Tetractys. Good thing was in school, Women can participate in the Pythagorean school. Pythagoras said ''women can become philosopher''.

Pythagoras's followers were commonly called "Pythagoreans." For the most part we remember them as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.

Beyond the lasting mathematical contributions of Pythagoras, he is also remembered for ushering in a new era of philosophy and religion. His core philosophical ideas were intertwined with a powerful religious mysticism and he attempted to bridge science and spirituality as one entity. He believed that matter was composed of numbers and a ‘harmony of the spheres’ could be uncovered through music. The Pythagorean School lasted for around four centuries after his death until it was eventually replaced by Plato’s academy.

Discovering the Philosophical Ideas of Pythagoras 

Pythagoras was an influential philosopher and mathematician who brought a unique perspective to understanding the world through numbers and equations. He believed that at the center of many patterns which exist in nature, there is mathematical harmony and order. His teachings focus on the fundamental principles of mathematics, astronomy, music, and ethics, and have been studied for centuries. His ideas have contributed greatly to modern philosophy and are highly relevant today.

Pythagoras is one of the most interesting and puzzling men in history. Not only are the traditions concerning him an almost inextricable mixture of truth and falsehood, but even in their barest and least disputable form they present us with a very curious psychology. 

In addition to mathematical contributions, Pythagoras had a great impact on philosophy and religion. 

What did Pythagoras say about beans 

He founded a religion, of which the main tenets were the transmigration of souls †and the sinfulness of eating beans. His religion was embodied in a religious order, which, here and there, acquired control of the State and established a rule of the saints. But the unregenerate hankered after beans, and sooner or later rebelled. Some of the rules of the Pythagorean order were:

Pythagorean beans order were.

1. To abstain from beans.

2. Not to pick up what has fallen.

3. Not to touch a white cock.

4. Not to break bread

5. Not to step over a crossbar.

6. Not to stir the fire with iron.

7. Not to eat from a whole loaf.

8. Not to pluck a garland.

9. Not to sit on a quart measure.

10. Not to eat the heart.

11. Not to walk on highways.

12. Not to let swallows share one's roof.  so on and so further.

13. When the pot is taken off the fire, not to leave the mark of it in the ashes, but to stir       them together. 

14. Do not look in a mirror beside a light.

  Pythagoras Greek god

"The School of Pythagoras represents the main current of that mystical tradition which we have set in contrast with the scientific tendency." He regards Parmenides, whom he calls "the discoverer of logic," as "an offshoot of Pythagoreanism,  Pythagoreanism, he says, was a movement of reform in Orphism, and Orphism was a movement of reform in the worship of Dionysus. 

Pythagorean mysticism

The opposition of the rational and the mystical, which runs all through history, first appears, among the Greeks, as an opposition between the Olympic gods and those other less civilized gods who had more affinity with the primitive beliefs dealt with by anthropologists. In this division, Pythagoras was on the side of mysticism, though his mysticism was of a peculiarly intellectual sort. He attributed to himself a semi-divine character, and appears to have said: "There are men and gods, and beings like Pythagoras." All the systems that he inspired, Cornford says, "tend to be otherworldly, putting all value in the unseen unity of God, and condemning the visible world as false and illusive, a turbid medium in which the rays of heavenly light are broken and obscured in mist and darkness."

Pythagoras reincarnation 

He believed that the soul is immortal and capable of eternal progression through successive lives, making him one of the first to develop the idea of reincarnation. He also taught that as humans progressed through various cycles of existence, their ultimate goal was spiritual enlightenment. Furthermore, he believed that all life had an intrinsic value, inspiring a sense of reverence for all living things throughout history.

Pythagoras taught "first, that the soul is an immortal thing, and that it is transformed into other kinds of living things; further, that whatever comes into existence is born again in the revolutions of a certain cycle, nothing being absolutely new; and that all things that are born with life in them ought to be treated as kindred."  It is said that Pythagoras, like the Hindus believe in reincarnation or transmigration of the soul. 

In the society that he founded, men and women were admitted on equal terms; property was held in common, and there was a common way of life. Even scientific and mathematical discoveries were deemed collective, and in a mystical sense due to Pythagoras even after his death. Hippasos of Metapontion, who violated this rule, was shipwrecked as a result of divine wrath at his impiety.

What are Pythagoras philosophy of ethic

But what has all this to do with mathematics? It is connected by means of an ethic which praised the contemplative life. sums up this ethic as follows:

"We are strangers in this world, and the body is the tomb of the soul, and yet we must not seek to escape by self-murder; for we are the chattels of God who is our herdsman, and without his command we have no right to make our escape. In this life, there are three kinds of men, just as there are three sorts of people who come to the Olympic Games. The lowest class is made up of those who come to buy and sell, the next above them are those who compete. Best of all, however, are those who come simply to look on. The greatest purification of all is, therefore, disinterested science, and it is the man who devotes himself to that, the true philosopher, who has most effectually released himself from the 'wheel of birth.''

It is interesting to observe, Pythagorean ethic, the opposition to modern values. In connection with a football match, modern-minded men think the players grander than the mere spectators. Similarly as regards the State: they admire more the politicians who are the contestants in the game than those who are only onlookers. This change of values is connected with a change in the social system the warrior, the gentleman, the plutocrat, and the dictator, each has his own standard of the good and the true. 

The gentleman has had a long innings in philosophical theory, because he is associated with the Greek genius, because the virtue of contemplation acquired theological endorsement, and because the ideal of disinterested truth dignified the academic life. The gentleman is to be defined as one of a society of equals who live on slave labour, or at any rate upon the labour of men whose inferiority is unquestioned. It should be observed that this definition includes the saint and the sage, insofar as these men's lives are contemplative rather than active.

Whatever may be thought of a social system which tolerates slavery, it is to gentlemen in the above sense that we owe pure mathematics. The contemplative ideal, since it led to the creation of pure mathematics, was the source of a useful activity; this increased its prestige, and gave it a success in theology, in ethics, and in philosophy, which it might not otherwise have enjoyed.

The changes in the meanings of words are often very instructive. I spoke above about the word "orgy"; now I want to speak about the word "theory." This was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation." In this state, he says, "The spectator is identified with the suffering God, dies in his death, and rises again in his new birth." For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, "theory" gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation. To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural even if untrue. It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.

So much by way of explanation of the two aspects of Pythagoras: as religious prophet and as pure mathematician.

contribution of Pythagoras to mathematics

Pythagoras say '' Everything is Number, The world is number.

Contributions of Pythagoras in mathematics , as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logically nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music, and the connection which he established between music and arithmetic survives in the mathematical terms "harmonic mean" and "harmonic progression."

 He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares and cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or, as we should more naturally say, shot) required to make the shapes in question. He presumably thought of the world as atomic, and of bodies as built up of molecules composed of atoms arranged in various shapes. In this way he hoped to make arithmetic the fundamental study in physics as in aesthetics. 

Pythagoras theorem numerology

One of the most famous results of Pythagoras' theories was his theorem that the square of the hypotenuse (the longest side of a right-angled triangle) is equal to the sum of the squares of the other two sides. This theorem forms one of the foundations for modern geometry and has become known as The Pythagorean Theorem. Additionally, it played an important role in establishing mathematics as an essential tool for understanding and describing nature, rather than just abstract knowledge.

The greatest discovery of Pythagoras, or of his immediate disciples, was the proposition about right-angled triangles, that the sum of the squares on the sides adjoining the right angle is equal to the square on the remaining side, the hypotenuse.

Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables, which appeared to disprove his whole philosophy. In a right-angled isosceles triangle, the square on the hypotenuse is double of the square on either side. Let us suppose each side an inch long; then how long is the hypotenuse? Let us suppose its length is m/n inches. Then m2/n2 = 2. If m and n have a common factor, divide it out; then either m or n must be odd. Now M2 = 2n2,    therefore M2 is even, therefore m is even; therefore n is odd. Suppose m = 2p. Then 4p2 = 2n2, therefore n2 = 2p2 and therefore n is even, contra hyp. Therefore no fraction m/n will measure the hypotenuse.  This argument proved that, whatever unit of length we may adopt, there are lengths which bear no exact numerical relation to the unit, in the sense that there are no two integers m, n, such that m times the length in question is n times the unit. This convinced the Greek mathematicians that geometry must be established independently of arithmetic. 

Personal religion is derived from ecstasy, theology from mathematics; and both are to be found in Pythagoras

Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as in a super-sensible intelligible world. Geometry deals with exact circles, but no sensible object is exactly circular; however carefully we may use our compasses, there will be some imperfections and irregularities. This suggests the view that all exact reasoning applies to ideal as opposed to sensible objects; it is natural to go further, and to argue that thought is nobler than sense, and the objects of thought more real than those of sense-perception. 

how did Pythagoras influence Plato -  Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer.  Pythagoras, and notably ever since Plato, very completely dominated by mathematics and mathematical method.

Pythagoras math and music

Pythagoras is best known for his contributions to mathematics, but he was also an important figure in philosophy and music theory. He discovered the mathematical ratios behind musical harmony and consonance, developing the foundational theory of acoustics. His belief that whole numbers represented the harmonious structure of the universe also inspired Greek philosophers to explore the connections between mathematics and divinity.

music theory were particularly influential and included the idea that various ratios between frequencies create pleasing harmonies. He even believed that planets’ orbits emitted melodies, or a celestial harmony, as they moved through space. He is also credited as coming up with the first known theory of natural selection and argued that a species adapts to its environment in order to survive. This set him apart from other pre-Socratic philosophers who accepted natural phenomena as divine or random occurrences.

The combination of mathematics and theology, which began with Pythagoras It is only in quite recent times that it has been possible to say clearly where Pythagoras was wrong. I do not know of any other man who has been as influential as he was in the sphere of thought. I say this because what appears as Platonism is, when analysed, found to be in essence Pythagoreanism. The whole conception of an eternal world, revealed to the intellect but not to the senses, is derived from him.

External link 

Xenophanes philosophy

Anaximenes philosophy

Bibliography

A History of Western Philosophy Book by Bertrand Russell

The-history-of-philosophy-by-a.-c.-grayling

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Barnes, J., The Presocratic Philosophers, 2nd edn, London: Routledge & Kegan Paul, 1982

Hussey, E., The Presocratics, London: Duckworth, 1995 Kirk, G. S., J. E. Raven and M. Schofield, The Presocratic Philosophers,

2nd edn, Cambridge: Cambridge University Press, 1984 Osborne, C., Presocratic Philosophy: A Very Short Introduction, Oxford: Oxford University Press, 2004