His most famous modern pythagorean theorem is a mathematical formula, which points out that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This formula has been applied to measure distance and space, for example, when planning and executing the construction of buildings. Although ancient writers attributed it to Pythagoras, modern scholars cited evidence from Babylonian literature written by Pythagoras some time ago, and they discussed the same formula, or at least very similar formula.
Although later writers (such as Diogenēs Laertius, A.D. 180-240) tried to arrange biographies according to the stories and fragments of early works, they knew almost nothing about Pythagoras' life. Larsho's biography of Pythagoras is the most complete, but unfortunately, the author has never quoted the sources he cited, so he can't prove many of his statements.
The difficulty of any discussion about Pythagoras lies in separating the real man and his teachings from the myths surrounding him.
Pythagoras had a great influence on later philosophers and the overall development of Greek philosophy. Plato (428/427-348/347 BC) quoted Pythagoras in some of his works. The Pythagorean thought understood and conveyed by other ancient writers is the basic form of Plato's philosophy. Aristotle (384-322 BC), a famous student of Plato, also integrated the teaching of Pythagoras into his own thoughts. Aristotle's works will influence philosophers, poets and theologians (and many others) from his time to the Middle Ages (about 476- 1500 CE) and modern times. Although Pythagoras was still a mysterious figure in ancient times, he was also one of the most important figures in the development of philosophy and religious thought.
Life and work
The understanding of Pythagoras came from later writers, who pieced together the life fragments of contemporaries and students. It is understood that Pythagoras was born in Samos Island in Asia Minor, and his ancestors left Frius. It was once settled, and the city was in the Peloponnesian Peninsula in the northwest, where the war in 380 BC was after the civil war. Because his father Mnesarchus is a rich businessman, he received a high-quality education. He may have studied in Babylon and Egypt, and he may have the best Greek tutor at that time. However, all this is speculative, because the information came from later writers who accepted others' articles about him uncritically. If there was an authoritative biography of Pythagoras, or his own original work, it would have been lost long ago. Comments by scholar forest e Baird:
Pythagoras is related to so many legends that few scholars dare to talk about his life, personality and even his teachings, adding that we are not sure whether our information is accurate or not. There is a man named Pythagoras who founded a Sect called Pythagoras. We don't have to doubt it. One of his historical witnesses is his contemporary youth Heraclitus, who thinks he is a bad man. However, as we all know, it is difficult to distinguish the teachings of Pythagoras himself from those of his followers. ( 14)
The history of Pythagoras has never been questioned. As Baird pointed out, Heraclitus (500 BC) thought Pythagoras was highly overestimated, while Xenophon (570- 478 BC), another contemporary visionary Clovon, laughed at Pythagoras' belief in reincarnation. The difficulty of any discussion about Pythagoras lies in trying to separate the real man and his teachings from the myths surrounding him, even in his life.
Pythagoras belief
As mentioned above, Pythagoras' works-if he wrote anything-have not been handed down, and the details of his teaching have been carefully preserved because he asked students to keep it secret. The philosopher Banrui (234-305 BC), who wrote the later Pythagoras biography, pointed out:
No one can be sure what he taught his disciples, because they remained unusually silent. Nevertheless, the following is well known. First, he said that the soul is immortal; The second is to migrate to other kinds of animals; Third, the same events happen repeatedly, and there is nothing new in the strict sense; Finally, everything with a soul should be regarded as the same kind. Pythagoras seems to be the first person to introduce these beliefs into Greece. (Robinson, 58 years old)
The Greek historian Herodotus (484 BC-425 BC/4 BC13 BC) mentioned Pythagoras in his history (although he was famous for refusing to reveal his name):
Besides, the Egyptians were the first to insist that the human soul is immortal. After the body dies, it will enter another animal born at the same time. When it completes a complete round of sea, land and air creatures, it will re-enter the human body at birth. Its cycle is three thousand years. Some Greeks adopted this theory, some in the past, some later, as if it were their own invention; I know their names, but I don't write them down (Book II. 123).
Like Pythagoras' theorem, Pythagoras' concept of soul reincarnation may also be borrowed. George ·GM· James, a scholar, pointed out in his book The Stolen Legacy: The Egyptian Origin of Western Philosophy that all the great philosophers before Socrates either studied in Egypt or in the Egyptian Mystery School in Asia Minor (James, 9). Thales (585 BC) is considered to be the first western philosopher to study in Babylon, and the other two most important pre-Socratic schools-anaximander (6 10- 546 BC) and Anaximenes (546 BC)-traveled widely and entered the mysterious school dominated by Egyptian religious thought.
Whatever the reason, the secrecy of Pythagoras' theory greatly increased his mystery and prestige.
Then, it is quite possible that Pythagoras' thought is actually the Egyptian spirit transplanted to Greece. Pythagoras' famous secrecy measures may be to prevent this fact from spreading too widely, so as not to damage his reputation as an original thinker. It is said that he is charming and a powerful speaker. If his philosophy is exposed as simply repackaging Egyptian beliefs, his authority will be weakened.
For this reason or other reasons, he concealed his teachings. He may just think that the public will not understand or appreciate his ideas. Whatever the reason, secrecy greatly increased his mystery and reputation. His belief in the immortality and reincarnation of the soul naturally led to a vegetarian lifestyle, emphasizing not to harm any other creatures. This asceticism also made him ask his followers to further improve his reputation as a saint. Diogenēs Laertius described his diet and habits:
Some people say that he only eats honey or a little honeycomb or bread (he doesn't touch alcohol during the day); Or, as a treat, vegetables are cooked or raw. He eats seafood, but seldom. His robes are white and spotless, and his sheets are white and all wool. Because flax has not yet reached those places. No one has ever seen him sober, * * or drunk. He used to avoid laughter and pander to dirty jokes and vulgar stories. (8) 19)
Latius described Pythagoras as a Scata man who ate fish and seafood, but most other ancient writers insisted that he was a strict vegetarian and did not eat any meat that could be regarded as a living thing with a soul. He also gave up sex and remained single to keep his mental strength and clear head. By getting rid of worldly pleasures such as sex and food, he liberated himself from the interference of his body and focused on the improvement of his soul.
Some people think this asceticism is too much. As we all know, he and his followers especially don't eat or even touch beans (a statement of his death is actually that he won't enter the bean field to escape his pursuers, so he was killed). Latius also mentioned Xenophon's satirical criticism of Pythagoras' belief in reincarnation:
Once, they said that when a puppy was whipped, he (Pythagoras) passed by and he said piteously, "Stop! Don't hit it! Because when I heard my friend stick out his tongue, I recognized his soul. (8) 36)
For Xenophon, who refused to be reincarnated, Pythagoras' faith was as stupid as claiming to recognize the voice of a dead friend in a barking dog. However, for Pythagoras, vegetarianism, pacifism and humane treatment of other creatures are all part of the road to inner peace and even world peace, because as long as human beings kill, eat and be persecuted, they will never live in harmony. Cruel to animals. Cruelty to animals and eating animal meat belittle all life, insisting that some creatures (humans) are more valuable than others. Pythagoras believes that all creatures are born equal and should be respected.
Contemporary and later writers consider him a mystic-not a mathematician as sometimes defined today-and his school is related to spiritual salvation and miraculous enlightenment. A core belief that will have a great influence on Plato is that philosophical inquiry is very important for the salvation of the soul and the understanding of the ultimate truth. One aspect of this truth is that nothing will change significantly, and everything is an eternal and eternal cycle. According to Eudemus of Rhode Island (370 BC-300 BC), Pythagoras, an ancient writer and a student of Aristotle, believed that eternal samsara was a logical and mathematical necessity. Youdemos wrote:
If someone believes in the Pythagorean school, events will happen repeatedly in an arithmetic cycle, and I will talk to you again, just like you are now, holding this pointer in your hand, and everything else will be the same as now, so it can be assumed that time will be the same as now. (Baird, 16 years old)
In this belief, Pythagoras predicted the great German philosopher Frederic Nietzsche (1844- 1900 reigned) and his theory of eternal reincarnation. In this theory, Nietzsche claimed that if there was no "finish line" judged by God after death, a person's life would be automatically reset and repeated in exactly the same way. Nietzsche's theory is often interpreted as encouraging people to think carefully about how to spend their time, because people always look back on everything, big or small. The teachings of Pythagoras may also imply this.
Even if Pythagoras himself did not construct this concept in this way, he must have clarified this concept in some way so that later Pythagoras could repeat it. The idea of the cycle of life and the immortality of the soul is the core of Pythagoras' thought, which influenced many writers and thinkers in ancient Greece, but it was not as important as Plato.
Pythagoras and Plato
It is possible that Plato was a student of Socrates at first, insisting on dialectics to establish truth, and then gradually turned to accept Pythagoras' idealism-as some scholars claimed-but Socrates himself seems more likely to be consistent with Pythagoras' thought. There is really no way to establish any ideas along these lines, because most of our understanding of Socrates comes from Plato's dialogues, which were written after Socrates' death, when Plato had mature philosophical thoughts.
In any case, Pythagoras' thought has a great influence on Plato's philosophy, including the concept of ultimate truth without opinions, the moral lifestyle that conforms to this truth, the immortality of the soul, the necessity of saving through philosophy, and learning is memory. The concept of Pythagoras is obvious in all Plato's works, but most notably in the dialogue between MINO and Fido.
In MINO, Socrates, Plato's hero, shows that what people call "learning" is actually just "remembering" the lessons of past lives. He proved his claim by letting an uneducated young slave solve geometry problems. Plato believes that if a person dies sane, then when a person is born, he will "remember" what he has learned in this life. I think what I "learned" in my life is actually just the "memory" of my previous life. What I knew in my previous life is the memory of my previous life.
Plato never solved the obvious problem of this theory: at a certain moment, the soul must really "learn" rather than just "remember". His claim that a person "remembers" what he learned in the ether between two lifetimes-not just in the form of mortals-does not solve this problem, because the soul still needs to "learn" at a certain point, whether in vivo or in vitro.
Pythagoras' assertion that "things are numbers" and people can understand the physical world through mathematics is also unique in Minogue's book, not only through Socrates' interaction with slaves, but also through his argument that virtue is the inherent unique quality of all people, regardless of their age, gender or social status, just like "numbers" inform and define the known world; People know reality by distinguishing between unity and duality.
This proposition will contribute to the development of Plato's famous formal theory, in which he describes an objective truth world that transcends the mortal realm, which is the basis and information of all human truths and gives them "real" value. Plato believed that there would be no real truth without this formal field. Only what you feel is true.
For Pythagoras, mathematics is the road to enlightenment and understanding. As he claimed, "Ten is the essence of numbers". This "number" not only means the unit of measurement, but also means to grasp and understand the world. He noticed how people count to ten with their fingers and then go back to another unit to start over. Similarly, the soul enters the body, lives for a period of time, dies for a period of time, returns to the origin, and then returns to the origin.
This concept has been fully explored in Plato's Phaedo, which describes Socrates' last day in prison before he was executed, focusing on the immortality and afterlife of the soul. From the beginning of the dialogue, Plato took advantage of the connection between Pythagoras and Filioud, and chose Cekla of Filioud as the interlocutor and audience of the narrator Fido. In addition, the role of West Mias and Siebers in Thebes-the central interlocutor of Socrates in Fido's narrative-is Pythagoras. Plato chose Eccletian to directly connect dialogue with Pythagoras' thought in the first line, but through West Mias and Cebes, Pythagoras' concept runs through.
At the end of the dialogue, Socrates gave all kinds of proofs about the immortality of the soul, and he ended up with this communication with Sabish:
Tell me, [Socrates said], what must be in the body to keep it alive?
A soul, [Sebes] replied.
Has it always been like this?
Of course, [Cebes] said.
So the soul always brings life to anything that contains her?
There is no doubt that [Cebes] answered.
Is there anything against life?
be
What is this?
Death.
We all agree that the soul can never accept the negative side she brings? "
"Yes, of course we know," said Sebes.
…
What is the name of something that denies death?
Immortality, [Cebes] said.
The soul denies death?
number
So the soul is immortal?
this is ...
Very good, [Socrates] said. Can we say that this has been proved? what do you think?
Socrates' previous mathematical proof of even and odd numbers finally led to the above proof, that is, "even number" cannot admit "odd number" to keep itself (even number), so life (soul) cannot admit death but still exists; Therefore, the soul must be immortal. This whole argument represents the Pythagorean thought understood by ancient writers and the Pythagorean thought practiced by Pythagoras in Plato's time.
conclusion
The Phaedo also determines the geographical position of the afterlife, and the church will use it to create the concepts of hell, purgatory and heaven in the future. The concept of purgatory first appeared in Fido 108b-d, the trial of the dead is 1 13d-e, the hell is113e-14a, and heaven is/4a. Plato's argument about the ultimate and undeniable realm of truth, from which all other truths are established, is also obvious in the gospel narrative of the Bible, especially the Gospel of John and the letters of St. Paul.
Although there is nothing definite about Pythagoras' life or original teachings, his thoughts were developed by later disciples and admirers, which was enough to influence the greatest Greek philosopher in ancient times. Plato's works established the discipline of philosophy, and in the past 2000 years, it has more or less penetrated into other disciplines. The details of Pythagoras' life may never be completely known, but his influence can still be felt all over the world today.