Philosophers · 哲學家 · Greece and Rome
Pythagoras 畢達哥拉斯 · Πυθαγόρας
The founder of a brotherhood that kept silence, shared its goods, refused beans, and taught that the soul is reborn and that the world is made of number.
一個兄弟會的創立者;這個團體守靜默、財物共有、不吃豆子,並且教導靈魂會轉生、世界是由數構成的。
- Born 出生
- c. 570 BCE, on the island of Samos
- Died 去世
- c. 495 BCE, at Croton or Metapontum in southern Italy
- Founded 創立
- A religious and philosophical community at Croton, c. 530 BCE
- Writings 著作
- None survive, and he may have written nothing
- Known for 特點
- Rebirth of the soul, the ratios of musical harmony, a theorem he did not discover
- Said to have coined 據說創造了
- The word philosopher, “lover of wisdom”
中文翻譯Every paragraph has a Chinese translation. Tap 中譯▾ under a paragraph to open that one, or use Show Chinese · 顯示中譯 at the top to open them all. 每一段都有中譯:點段落下方的「中譯」只開那一段,或按上方的「顯示中譯」一次全部打開。
Life · 生平
A life in three scenes 三幕人生
From Samos to Croton 從薩摩斯到克羅頓
Nothing written by Pythagoras survives, and the first full accounts of his life date from seven or eight centuries after his death. What follows is tradition, some of it early. He was born about 570 BCE on Samos, an island off the coast of what is now Turkey, the son of a man named Mnesarchus. Later writers send him to Egypt and Babylon to learn from the priests. When he came home he found Samos under the tyrant Polycrates, and about 530 he sailed west to Croton, a Greek city on the toe of Italy.
畢達哥拉斯寫的東西,沒有任何一樣流傳下來;而關於他生平最早的完整記述,寫於他死後七、八百年。以下所說的是傳統,其中有一些很早。他大約在公元前 570 年生於薩摩斯;那是今天土耳其外海的一座島。他的父親名叫姆涅薩爾科斯。後來的作者說他去過埃及與巴比倫,向祭司們學習。他回家的時候,發現薩摩斯落在僭主波利克拉特斯手裡;大約在 530 年,他向西航行到克羅頓,義大利「腳尖」上的一座希臘城市。
There he founded a community that was at once a school, a religious order, and for a time a governing party. Diogenes Laertius reports that its members, about three hundred in number, ran the city so well that its constitution was “in effect a true aristocracy.” Asked by a ruler what he was, Pythagoras is said to have answered, “A philosopher,” and to have compared life to the great games. Some come to compete and some come to sell, “but the best as spectators.” If the story is true, this is the first use of the word.
他在那裡創立了一個團體;它同時是一所學校、一個宗教修會,並且有一段時間是執政的黨派。第歐根尼・拉爾修記載:它的成員大約三百人,把這座城市治理得很好,使它的政體「實際上成了真正的貴族政治」。有一位統治者問畢達哥拉斯他是什麼人;據說他回答:「一個愛智者(philosopher)。」並且把人生比作盛大的競技會:有些人來比賽,有些人來做買賣,「而最好的人是來觀看的」。如果這個故事是真的,這就是這個詞第一次被使用。
The rule of the brotherhood 兄弟會的規矩
The community lived by rule. Members held their property in common, and the saying “Friends have all things in common” was attributed to the founder. A newcomer kept silence for five years, listening to the master’s teaching without seeing him, and was admitted to his presence only after an examination. Women were admitted as well as men, which was unusual in Greece. There were rules about food, the most famous being the ban on beans, for which ancient writers gave a dozen conflicting reasons. Teachings were handed down by word of mouth and introduced with the phrase that became a proverb in Latin: ipse dixit, “he himself said it.”
這個團體依規矩生活。成員的財產共有;「朋友之間一切共有」這句話被歸給創立者。新來的人要守五年的靜默,只聽老師的教導而見不到他;通過考核之後,才獲准見他的面。女性與男性一樣可以加入,這在希臘很不尋常。飲食上有種種規定;最出名的是不准吃豆子,而古代的作者為此給出了十幾個互相衝突的理由。教導是口耳相傳的,並且用一個後來在拉丁文裡成了諺語的說法來起頭:ipse dixit,「他親口說的」。
The doctrine for which he was best known in his own time was the rebirth of the soul. He claimed, the story goes, to remember his former lives, among them that of a Trojan warrior named Euphorbus. His contemporary Xenophanes made fun of this in verses that are the earliest surviving reference to him. Passing a man who was beating a puppy, Pythagoras cried: “Stay, smite not! ’Tis a friend, a human soul; I knew him straight whenas I heard him yelp!” The joke is evidence. Within his lifetime he was known for teaching that souls pass between humans and animals, and for acting on it.
在他自己的時代,他最出名的教義是靈魂的轉生。傳說他宣稱記得自己的前世,其中一世是一位名叫歐福耳玻斯的特洛伊戰士。與他同時代的色諾芬尼用詩句取笑這件事;那是現存最早提到他的文字。畢達哥拉斯經過一個正在打小狗的人身邊,喊道:「住手,別打了!那是一位朋友,一個人的靈魂;我一聽到牠叫,就認出他來了!」這個笑話是一項證據。在他有生之年,人們就知道他教導「靈魂在人與動物之間往來」,並且知道他照著這個教導行事。
The bean field 豆田
The brotherhood’s power made enemies. About 500 BCE a man who had been refused admission, or in another version the citizens of Croton fearing a tyranny, set fire to the house where the Pythagoreans were meeting. The accounts of the founder’s death disagree. In the best-known one he escaped the flames and ran until he came to a field of beans. He stopped, saying that he would be captured sooner than cross it, and his pursuers cut his throat. In another he reached the temple of the Muses at Metapontum and starved there after forty days.
這個兄弟會的權勢樹立了敵人。大約公元前 500 年,一個被拒絕入會的人(另一個版本說是害怕出現僭主政治的克羅頓公民)放火燒了畢達哥拉斯派聚會的房子。關於創立者之死的記述並不一致。在最出名的那個版本裡,他逃出了火場,一路跑到一片豆田前面。他停了下來,說他寧可被抓,也不穿過去;追他的人割斷了他的喉嚨。在另一個版本裡,他逃到了梅塔龐托的繆斯神廟,在那裡絕食四十天而死。
The communities were broken up, and the survivors scattered across the Greek world. They split into those who kept the rules and sayings and those who pursued mathematics and the study of nature. It was the second group, a century later, that impressed Plato, and through Plato the Pythagorean conviction that reality is mathematical entered the main line of European thought.
那些團體被打散了,倖存者流散到希臘世界各地。他們分成了兩派:一派保守著規矩與格言;另一派從事數學與自然的研究。一個世紀之後,打動柏拉圖的是第二派;而經由柏拉圖,畢達哥拉斯派的那個信念——實在是數學的——進入了歐洲思想的主流。
- c. 570 BCEBorn on Samos生於薩摩斯
- c. 530 BCELeaves Samos under Polycrates and settles at Croton在波利克拉特斯統治下離開薩摩斯,定居克羅頓
- c. 530–500 BCEThe brotherhood grows and governs Croton兄弟會壯大,並治理克羅頓
- c. 500 BCEThe meeting house is burned聚會所被焚
- c. 495 BCEDies at Croton or Metapontum死於克羅頓或梅塔龐托
- c. 450 BCEPythagoreans driven from the cities of southern Italy畢達哥拉斯派被逐出南義大利各城
- c. 388 BCEPlato visits the Pythagorean Archytas at Tarentum柏拉圖到塔蘭托拜訪畢達哥拉斯派的阿爾庫塔斯
- 3rd c. CEDiogenes Laertius, Porphyry, and Iamblichus write the surviving Lives第歐根尼・拉爾修、波菲利與楊布里科斯寫下現存的幾部傳記
The central idea · 核心觀念
All is number 萬物皆數
The discovery that tradition credits to Pythagoras concerns sound. Stop a stretched string at half its length and it sounds an octave higher. Stop it at two-thirds and it sounds a fifth higher, and at three-quarters a fourth. The intervals that the ear hears as concordant correspond to the ratios 2:1, 3:2, and 4:3, which use only the first four whole numbers. A quality that everyone had taken to be a matter of feeling turned out to have an exact numerical structure. It was the first law of nature to be stated in mathematical form.
傳統歸功於畢達哥拉斯的那個發現,與聲音有關。把一根拉緊的弦在一半長度的地方按住,它發出的音高了八度。按在三分之二的地方,高了五度;按在四分之三的地方,高了四度。耳朵聽來和諧的音程,對應的比例是 2:1、3:2、4:3;它們只用到了最前面的四個整數。一種人人都以為只是感覺的性質,結果有著精確的數字結構。這是第一條以數學形式陳述的自然定律。
His followers generalized without restraint. Aristotle reports that since numbers seemed to be the first things in the whole of nature, “they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.” The planets, moving at distances that stand in harmonic ratios, were thought to produce a music that we do not notice because we have heard it since birth. Aristotle also records the weakness of the method. Ten being the perfect number, there had to be ten heavenly bodies. Only nine could be seen, so they invented a tenth, the “counter-earth.” The same school thus produced the idea behind mathematical physics and an early example of fitting the facts to the theory.
他的追隨者毫無節制地加以推廣。亞里斯多德記載:既然數看起來是整個自然裡最先的東西,「他們就假定數的元素是萬物的元素,而整個天是一個音階、一個數」。行星在彼此成和諧比例的距離上運行;人們認為它們會產生一種音樂,而我們之所以沒注意到,是因為從出生起就一直聽著。亞里斯多德也記下了這個方法的弱點。十是完美的數,所以天體必須有十個。看得見的只有九個;於是他們發明了第十個:「對地」。就這樣,同一個學派產生了數學物理背後的那個觀念,也產生了一個「讓事實遷就理論」的早期實例。
They supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.他們假定數的元素是萬物的元素,而整個天是一個音階、一個數。
Aristotle writes “the so-called Pythagoreans” and never attributes a doctrine to Pythagoras by name. It is the best evidence we have, and it is about the school. 亞里斯多德寫的是「所謂的畢達哥拉斯派」,而且從來沒有指名把任何一條學說歸給畢達哥拉斯本人。這是我們手上最好的證據;而它談的是那個學派。
The strongest objection · 最強的反駁
The number that is not a number 不是數的數
The doctrine was refuted from within. If all things are number, and number means whole numbers and their ratios, then every length should be expressible as a ratio of whole numbers. Take a square whose side is one unit. By the theorem that carries Pythagoras’s name, the square on its diagonal is two. Some member of the school proved that no ratio of whole numbers, when multiplied by itself, gives exactly two. The diagonal and the side have no common measure. Later legend says that the man who made this public, Hippasus, was drowned at sea for it. Whatever happened to him, the discovery stood, and Greek mathematics was rebuilt on geometry as a result.
這個學說是從內部被駁倒的。如果萬物皆數,而「數」指的是整數與整數之比;那麼每一個長度都應該能表示成整數之比。取一個邊長為一個單位的正方形。依照那條冠著畢達哥拉斯之名的定理,它的對角線上的正方形是二。這個學派裡有人證明了:沒有任何一個整數之比,自乘之後恰好等於二。對角線與邊沒有共同的度量單位。後來的傳說說,把這件事公開的那個人——希帕索斯——因此被淹死在海裡。不管他遭遇了什麼,這個發現站住了;而希臘數學因此在幾何的基礎上重新建立。
A second objection is Aristotle’s. A number is not a cause. To say that justice is the number four or marriage the number five explains nothing about justice or marriage, and the heavens were given a tenth body for the sake of tidiness. Aristotle’s point is fair against the school’s excesses. The core of the idea has outlasted it: modern physics says that the behavior of things is captured by equations, which is close to what the octave first suggested.
第二個反駁是亞里斯多德的。數並不是原因。說正義是四這個數、婚姻是五這個數,對正義或婚姻什麼也沒有解釋;而天空為了整齊,被多加了第十個天體。對於這個學派的過頭之處,亞里斯多德的批評是公道的。這個觀念的核心卻比他的批評活得更久:現代物理學說,事物的行為是由方程式掌握的;這跟八度音當初所提示的很接近。
How we know · 史料
A man behind a curtain 帷幕後面的那個人
Pythagoras is the hardest of the early philosophers to see. He wrote nothing, or nothing that lasted. His followers were sworn to secrecy and credited every discovery of the school to the master. Within a few generations he was the subject of miracle stories: he had a golden thigh, he was seen in two cities at the same hour, a river greeted him by name. The detailed Lives were written in the third century CE by authors who wanted a pagan holy man to set beside Christ.
在早期的哲學家當中,畢達哥拉斯是最難看清的一位。他什麼也沒寫,或者說,沒寫下任何流傳下來的東西。他的追隨者發誓保密,並且把這個學派的每一項發現都歸功給老師。不出幾代,他就成了神蹟故事的主角:他有一條黃金的大腿;有人在同一個時刻看到他出現在兩座城市;有一條河叫著他的名字向他問好。詳細的傳記,是公元三世紀的作者寫的;他們想要一位異教的聖人,好跟基督並列。
The earliest witnesses are few and not friendly. Xenophanes mocks him over the puppy. Heraclitus says that he practiced inquiry more than any other man and made a wisdom of his own out of “much learning” and “poor workmanship.” These lines confirm that there was such a man, that he was famous, that he taught rebirth, and that he was learned. They say nothing about mathematics. Scholars today divide over whether the historical Pythagoras was a mathematician at all, or a religious teacher whose followers later became mathematicians and gave him the credit.
最早的見證人很少,而且並不友善。色諾芬尼拿小狗的事嘲笑他。赫拉克利特說,他比任何人都更致力於探究,而用「博學」與「拙劣的手藝」為自己拼湊出一套智慧。這幾行字證實了:確實有這麼一個人;他很出名;他教導轉生;他很有學問。它們完全沒有提到數學。今天的學者意見分歧:歷史上的畢達哥拉斯到底是不是一位數學家?還是一位宗教導師,他的追隨者後來成了數學家,並把功勞歸給了他?
Dharma and the West · 佛法與西方哲學
Pythagoras and the Buddha 畢達哥拉斯與佛陀
The two men were near contemporaries and never heard of each other, and the resemblances have struck readers since antiquity. Each founded a community with a rule of life, shared property, a period of probation, and places for women. Each taught that beings are reborn across the line between human and animal, and drew from this a duty of kindness to animals. Each was said to remember his own former lives. Each valued silence and self-examination. Later Greeks guessed that Pythagoras had learned from India. There is no evidence that he did, and the likeness is better explained by two reforming teachers reaching similar conclusions from the same starting point, the belief in rebirth.
這兩個人幾乎是同時代的人,彼此從未聽說過對方;而兩者的相似之處,從古代起就讓讀者驚訝。兩人都創立了一個團體:有生活的規矩、共有的財物、一段考核期,並且有女性的位置。兩人都教導眾生的轉生跨越了人與動物的界線,並由此引出了善待動物的責任。兩人都被說成記得自己的前世。兩人都看重靜默與自我省察。後來的希臘人猜測,畢達哥拉斯是向印度學來的。沒有證據顯示他是;這種相似,更好的解釋是:兩位改革的導師,從同一個起點——對轉生的信仰——出發,得出了相似的結論。
The differences go deep. For Pythagoras what is reborn is a soul, a lasting thing that passes from body to body and remains itself. The Buddha taught rebirth and denied that there is any such thing. Pythagoras’s followers settled questions with “he himself said it.” The Buddha told his hearers not to accept a teaching out of respect for the teacher, and shortly before his death he said: “I’ve taught the Dhamma without making any distinction between secret and public teachings. The Realized One doesn’t have the closed fist of a tutor.” And where the Pythagoreans found release in contemplating the eternal order of number, the Buddha found it in seeing that nothing in experience is eternal (Dharma and Western Philosophy D2, D3).
差異卻很深。對畢達哥拉斯來說,轉生的是一個靈魂:一個持久的東西,從一個身體到另一個身體,始終是它自己。佛陀教導轉生,而否認有任何這樣的東西。畢達哥拉斯的追隨者用「他親口說的」來解決問題。佛陀告訴聽眾,不要因為尊敬老師就接受一個教導;而在去世前不久,他說:「我說法,不分祕密的與公開的教導。如來沒有『老師握緊的拳頭』。」此外,畢達哥拉斯派在觀想「數」的永恆秩序裡找到了解脫;佛陀則是在看清「經驗裡沒有任何東西是永恆的」當中找到了它(佛法與西方哲學 D2、D3)。
Terms of art · 哲學術語
Words that come with him 跟著他一起來的詞
Gk. philosophos ‘lover of wisdom’
A word tradition says Pythagoras was the first to apply to himself.
傳統上說,畢達哥拉斯是第一個用這個詞稱呼自己的人。
Gk. metempsychōsis
The passing of a soul at death into another body, human or animal.
靈魂在死亡時進入另一個身體;人或動物。
Gk. harmonia ‘fitting together’
The agreement of different notes, and by extension the ordered fitting together of any parts.
不同的音之間的協調;引申為任何部分之間有秩序的結合。
L. ratio; Gk. logos
The relation of one quantity to another, such as 3 to 2.
一個量與另一個量的關係,例如三比二。
Having no common unit of measure, as the side and diagonal of a square.
沒有共同的度量單位;例如正方形的邊與對角線。
The harmony that the planets were thought to make by their ordered motion.
人們認為行星有秩序的運行所產生的和聲。
Reading check · 理解測驗
Did it land? 讀懂了嗎
1. What did the Pythagoreans discover about musical intervals?
2. Why was the diagonal of a square a problem for the doctrine that all is number?
3. What does the earliest surviving reference to Pythagoras concern?
Go further · 延伸
Where he appears 他出現在哪幾課
- Diogenes Laertius, Lives of the Eminent Philosophers, Book VIII (tr. R. D. Hicks) ↗The fullest ancient Life, with the puppy, the beans, and three versions of his death. 最完整的古代傳記;有小狗、豆子,以及他的三種死法。
- Aristotle, Metaphysics, Book I, chapter 5 (tr. W. D. Ross) ↗The earliest sober account of what the Pythagoreans held. 對畢達哥拉斯派主張最早的持平記述。
- Stanford Encyclopedia of Philosophy, “Pythagoras” ↗A careful sorting of what can and cannot be known about him. 仔細分辨關於他哪些可知、哪些不可知。
- Stanford Encyclopedia of Philosophy, “Pythagoreanism” ↗The school after its founder, down to Plato’s time and beyond. 創立者之後的這個學派,直到柏拉圖的時代及其後。