Philosophers · 哲學家 · The Early Modern Age
G. W. Leibniz 萊布尼茲 · Gottfried Wilhelm Leibniz
A court librarian who invented the calculus, built a calculating machine, read the Book of Changes as binary arithmetic, and argued that no machine could perceive.
一位宮廷圖書館員：他發明了微積分，造了一台計算機，把《易經》讀成二進位算術，並且論證沒有任何機器能夠知覺。
- Born 出生
- July 1, 1646, Leipzig, Saxony
- Died 去世
- November 14, 1716, Hanover
- Employment 職業
- Counselor, librarian, and historian to the dukes of Hanover, from 1676
- Invented 發明
- The calculus (independently of Newton); a machine that multiplies; binary arithmetic
- Main works 主要著作
- Discourse on Metaphysics (1686); Theodicy (1710); Monadology (1714)
- Wrote in 寫作語言
- Latin, French, and German; most of it left unpublished
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
The boy in his father’s library 父親書房裡的男孩
Leibniz was born in Leipzig in 1646, two years before the end of the Thirty Years’ War, which had killed perhaps a third of the population of the German lands. His father, a professor of moral philosophy, died when he was six and left a library. The boy was given the run of it at eight, taught himself Latin from an illustrated history, and by his teens had read the ancient authors and the medieval logicians. He took a doctorate in law at twenty and was offered a professorship, which he refused. He wanted, he said, a larger sphere of action, and he entered the service of a prince.
萊布尼茲 1646 年生於萊比錫，兩年後三十年戰爭才結束；那場戰爭也許奪走了德意志地區三分之一的人口。他的父親是道德哲學教授，在他六歲時去世，留下了一間藏書室。這個男孩八歲時獲准在裡面自由出入，靠著一本有插圖的史書自學了拉丁文；到十幾歲，他已經讀過古代作家與中世紀的邏輯學家。他二十歲取得法學博士學位，並且得到一個教授職位，他回絕了。他說，他想要一個更大的活動範圍；於是他進入一位君主的幕下服務。
A diplomatic errand took him to Paris in 1672, and the four years he spent there made him a mathematician. He arrived knowing little of the subject. Under the guidance of the Dutch physicist Christiaan Huygens he mastered it, and in the autumn of 1675 he worked out the differential and integral calculus, with the notation, dx and the long S of the integral sign, that is still used. Newton had reached the same results a decade earlier by another route and had published nothing. On a visit to London in 1673 Leibniz showed the Royal Society a wooden model of a machine that could multiply and divide by means of a stepped drum, and was elected a fellow.
1672 年，一趟外交差事把他帶到了巴黎；他在那裡度過的四年，使他成為數學家。他到的時候對這門學問所知甚少。在荷蘭物理學家惠更斯的指引下，他掌握了它；1675 年秋天，他推演出了微分與積分，連同那套沿用至今的記號：dx，以及積分號那個拉長的 S。牛頓早十年就用另一條路得到了同樣的結果，卻什麼也沒發表。1673 年造訪倫敦時，萊布尼茲向皇家學會展示了一台機器的木製模型，它靠一個階梯狀的滾筒就能做乘法與除法；他因此當選為會員。
Forty years in Hanover 漢諾威的四十年
No post could be found for him in Paris, and in 1676 he accepted one at the small court of Hanover, where he remained for the rest of his life. His duties were to keep the library and to write the history of the ruling family. Around them he pursued a range of projects that has never been matched. He designed windmills to drain the silver mines of the Harz mountains. He worked for the reunion of the Catholic and Protestant churches. He founded the academy of sciences in Berlin, and he studied fossils, Chinese philosophy, and the origins of languages. He corresponded with more than a thousand people. Very little of his philosophy was printed. It lay in letters and in drafts, and scholars are still editing them.
巴黎找不到給他的職位；1676 年，他接受了漢諾威那個小宮廷的一個職位，此後終身留在那裡。他的職責是管理圖書館，以及為統治家族撰寫家史。圍繞著這些職責，他推動了範圍之廣至今無人能及的種種計畫。他設計風車，要為哈茨山的銀礦排水。他為天主教會與新教教會的重新合一而奔走。他創立了柏林的科學院；他研究化石、中國哲學與語言的起源。他跟一千多人通信。他的哲學付印的非常少。它躺在信件與草稿裡，學者至今還在整理。
His curiosity about China was unusual for his time and was free of condescension. In 1697 he published a collection of reports from the Jesuit mission, in the preface of which he proposes that China should send missionaries to Europe to teach the practice of ethics. In 1701 the Jesuit Joachim Bouvet sent him from Beijing a diagram of the sixty-four hexagrams of the Book of Changes. Leibniz had recently devised a way of writing every number with only the signs 0 and 1, and he saw at once that if a broken line is read as 0 and an unbroken line as 1, the hexagrams in that arrangement count from 0 to 63. He concluded that the ancient Chinese had possessed his binary arithmetic and later forgotten it. He was wrong about the history. The notation is the one on which every computer now runs.
他對中國的好奇，在他的時代是不尋常的，而且沒有居高臨下的態度。1697 年，他出版了一部耶穌會傳教團報告的彙編；在序言裡，他提議中國應該派傳教士到歐洲來，教導倫理的實踐。1701 年，耶穌會士白晉從北京寄給他一張《易經》六十四卦的圖。萊布尼茲不久前才設計出一種只用 0 與 1 兩個記號就能寫出每一個數的方法；他立刻看出，如果把陰爻讀作 0、陽爻讀作 1，那個排列裡的卦就是從 0 數到 63。他的結論是：古代的中國人曾經擁有他的二進位算術，後來忘了。就歷史而言他錯了。而那套記號，就是今天每一台電腦賴以運作的那一套。
The quarrel and the empty funeral 爭端與冷清的葬禮
His last years were poisoned by the dispute over the calculus. Newton’s followers accused him of having stolen the idea during his London visits, and in 1712 a committee of the Royal Society, whose report Newton himself secretly drafted, found against him. Historians now agree that the two discoveries were independent. In 1714 his employer became King George I of Great Britain and moved the court to London. Leibniz asked to follow and was told to stay in Hanover and finish the family history, which had reached the year 1005. He died there in November 1716. A friend recorded that he was buried more like a robber than like what he was, the ornament of his country. Of the whole court, only his secretary attended the funeral.
他的晚年被微積分的爭端毒害了。牛頓的追隨者指控他在造訪倫敦期間偷了這個想法；1712 年，皇家學會的一個委員會作出了對他不利的裁定，而那份報告是牛頓本人暗中起草的。歷史學家現在一致認為，這兩項發現是各自獨立的。1714 年，他的雇主成了大不列顛國王喬治一世，把宮廷遷到了倫敦。萊布尼茲請求隨行，得到的答覆是留在漢諾威，把那部家史寫完；當時它才寫到西元 1005 年。1716 年 11 月，他在那裡去世。一位朋友記載：他下葬的樣子，比較像個盜賊，而不像他實際上的身分，也就是他的國家的光彩。整個宮廷，只有他的秘書出席了葬禮。
- 1646Born in Leipzig生於萊比錫
- 1673Shows his calculating machine in London在倫敦展示計算機
- 1675Works out the calculus in Paris在巴黎推演出微積分
- 1676Enters the service of Hanover進入漢諾威宮廷
- 1703Paper on binary arithmetic and the hexagrams發表二進位算術與卦象的論文
- 1710Theodicy《神義論》
- 1714Monadology《單子論》
- 1716Dies in Hanover卒於漢諾威
The central idea · 核心觀念
Nothing is without a reason 沒有任何事是沒有理由的
Leibniz said that all our reasoning rests on two principles. The first is that a contradiction cannot be true. The second, which he made his own, is the principle of sufficient reason: “there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us.” Nothing simply happens to be the case. From this one demand he drew a whole account of the world. If there must be a reason why this universe exists and no other, the reason can only be that it is the best of those that were possible, and that a perfect being chose it for that reason. If two things were exactly alike in every respect, there could be no reason for one to be here and the other there, so no two things are exactly alike.
萊布尼茲說，我們一切的推理都建立在兩條原理上。第一條是：矛盾不可能為真。第二條是他使之成為自己的招牌的，就是充足理由律：「若沒有一個充足的理由說明它為什麼是這樣而不是別樣，就不可能有任何事實是真實的或存在的，也不可能有任何陳述是真的，儘管這些理由通常不能為我們所知。」沒有任何事情只是「剛好如此」。從這一個要求，他引出了一整套對世界的說明。如果必須有一個理由說明為什麼存在的是這個宇宙、而不是別的宇宙，那個理由只能是：它是所有可能的宇宙當中最好的，而一位完美的存在者正是為此選擇了它。如果兩個東西在每一方面都完全相同，就不可能有理由說明為什麼一個在這裡、另一個在那裡；所以沒有兩個東西是完全相同的。
The strangest consequence concerns what the world is made of. Anything extended in space can be divided, and what can be divided is a collection and depends on its parts. The ultimate constituents must therefore be simple, without parts, and so without extension. Leibniz called them monads. Since a thing without parts cannot be pushed or altered from outside, “the Monads have no windows, through which anything could come in or go out.” Each unfolds its own states from within, as a mind does, and what a monad has is perception, in degrees that run from the dim stirrings of what we call matter to the clear awareness of a rational soul. Each perceives the whole universe from its own position and is “a perpetual living mirror of the universe.” No monad acts on any other. They agree with one another because they were set in order together at the creation, like clocks made so well that they keep the same time forever. He called this the pre-established harmony.
最奇特的後果，關乎世界是由什麼構成的。任何在空間中有廣延的東西都可以分割；而可以分割的東西是一個集合，依賴於它的部分。所以，最終的構成者必須是單純的，沒有部分，因而也沒有廣延。萊布尼茲稱它們為「單子」。由於沒有部分的東西無法從外面被推動或改變，「單子沒有窗戶，沒有任何東西可以經由窗戶進出」。每一個單子都從內部展開它自己的狀態，就像一個心那樣；單子所擁有的是知覺，程度不等，從我們稱為物質的那種昏暗的擾動，一直到理性靈魂清楚的覺察。每一個單子都從自己的位置知覺整個宇宙，是「宇宙的一面永恆的活鏡子」。沒有任何單子作用於別的單子。它們彼此一致，是因為它們在創世時就被一起安排妥當了，像是造得精良到永遠走得一樣準的鐘。他稱之為「預定和諧」。
…there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us.……若沒有一個充足的理由說明它為什麼是這樣而不是別樣，就不可能有任何事實是真實的或存在的，也不可能有任何陳述是真的，儘管這些理由通常不能為我們所知。
The principle of sufficient reason, in the form he gave it two years before his death. 充足理由律；這是他去世前兩年給它的表述。
The strongest objection · 最強的反駁
The best of all possible worlds 所有可能世界中最好的一個
On November 1, 1755, an earthquake destroyed Lisbon while the churches were full for All Saints’ Day, and tens of thousands died. Four years later Voltaire published Candide, in which the tutor Pangloss, a disciple of Leibniz, passes through war, shipwreck, the earthquake, and the Inquisition explaining at each disaster that all is for the best. The satire is unfair in one respect. Leibniz did not say that everything in the world is good. He said that a world with free creatures and regular laws could not have had less evil in total without being worse in some other way, and that we, who see a fragment, are in no position to judge the whole. But the unfairness does not remove the difficulty. A claim that would be equally consistent with any amount of suffering explains none of it, and it is hard to say to the parents of a drowned child that the alternative worlds were worse.
1755 年 11 月 1 日，一場地震摧毀了里斯本，當時各教堂正因為諸聖節而坐滿了人；數以萬計的人喪生。四年後，伏爾泰出版了《憨第德》：書裡的家庭教師潘格羅斯是萊布尼茲的信徒，他一路經歷戰爭、船難、那場地震與宗教裁判所，每逢一場災難就解釋說，一切都是為了最好的結果。這部諷刺作品在一點上是不公平的。萊布尼茲並沒有說世界上的每一件事都是好的。他說的是：一個有自由的受造者、有規律的法則的世界，如果總體上的惡要再少一些，就不可能不在別的某方面變得更糟；而我們只看到一個片段，沒有資格評判整體。然而，這份不公平並沒有消除困難。一個不論苦難有多少都同樣說得通的主張，並沒有解釋任何苦難；而且，很難對一個孩子溺死了的父母說：別的可能世界更糟。
A second objection is aimed at the principle itself. If everything has a sufficient reason, then everything that happens could not have been otherwise, including each human choice and God’s choice of this world, and freedom disappears. Leibniz replied that reasons “incline without necessitating.” His contemporaries were not persuaded, and the charge that his system is Spinoza’s necessity in more pious language has followed it ever since.
第二個反駁針對的是那條原理本身。如果每一件事都有充足的理由，那麼發生的每一件事都不可能是別的樣子，包括人的每一個選擇，以及上帝對這個世界的選擇；自由就消失了。萊布尼茲回答：理由「使人傾向，而不使人必然」。他同時代的人並沒有被說服；而「他的體系不過是用更虔誠的語言說出來的史賓諾莎式必然」這項指控，此後一直跟著它。
How we know · 史料
A philosophy left in the drawer 留在抽屜裡的哲學
Leibniz published one philosophical book in his lifetime, the Theodicy, a long and courtly defense of the goodness of God. The works on which his reputation now rests were not written for print. The Discourse on Metaphysics of 1686 was a private summary. The Monadology was composed in 1714 for a few correspondents and appeared only after his death, and its title was supplied by an editor. His reply to Locke, the New Essays, he withheld because Locke had died, and it was printed in 1765. The rest is in some fifteen thousand letters and a mass of notes. As a result there were for two centuries several Leibnizes. The eighteenth century knew the optimist of the Theodicy. Bertrand Russell, reading the logical papers around 1900, argued that the public system was a façade and that the real philosophy was a logic kept in the desk. The complete edition of his writings, begun in 1923, is expected to take many more decades.
萊布尼茲生前只出版過一本哲學書，《神義論》；那是一部冗長而帶著宮廷氣的著作，為上帝的善辯護。他今天的名聲所依靠的那些作品，都不是為了付印而寫的。1686 年的《形上學論》是一份私人的摘要。《單子論》是 1714 年為幾位通信者寫的，在他死後才面世，書名還是編者加的。他對洛克的回應《人類理解新論》，因為洛克已經去世而被他壓了下來，到 1765 年才印行。其餘的都在大約一萬五千封信與成堆的筆記裡。結果是，有兩個世紀之久，存在著好幾個萊布尼茲。十八世紀認識的是《神義論》裡的那位樂觀主義者。羅素在 1900 年前後讀了那些邏輯文稿，主張公開的體系只是門面，真正的哲學是鎖在書桌裡的一套邏輯。他的著作全集從 1923 年開始編纂，預計還要好幾十年才能完成。
Dharma and the West · 佛法與西方哲學
Leibniz and the Buddha 萊布尼茲與佛陀
One image in Leibniz has a famous Buddhist twin. Each monad, he says, is a living mirror that reflects the entire universe from its own point of view. The Huayan school of Chinese Buddhism describes the net of the god Indra, which stretches without limit in every direction and has a jewel at every knot. Each jewel reflects all the others, and in each reflection all the others are reflected again. The Huayan masters used the net to teach that every phenomenon contains and is contained by every other. The two images arose with no contact between them, and they are put to opposite uses. Leibniz’s mirrors are substances: each monad is a self-contained thing that could exist if no other did, and it only represents the rest. A jewel in Indra’s net is nothing apart from the others. It exists by interdependence, and that is what the Buddhist means by calling it empty.
萊布尼茲的一個意象，在佛教裡有一個著名的孿生兄弟。他說，每一個單子都是一面活的鏡子，從自己的觀點映照整個宇宙。中國佛教的華嚴宗描述了因陀羅網（帝釋天的網）：它往每一個方向無限延伸，每一個網結上都有一顆寶珠。每一顆寶珠都映照出所有其他的寶珠；而在每一個映像裡，所有其他的寶珠又再被映照出來。華嚴的祖師用這張網來教導：每一個現象都含攝其他一切現象，也被其他一切現象所含攝。這兩個意象是在彼此毫無接觸的情況下各自出現的，用途卻相反。萊布尼茲的鏡子是實體：每一個單子都是自足的東西，即使別的單子都不存在，它也能存在；它只是「表象」其餘的一切。因陀羅網上的一顆寶珠，離開了其他的寶珠就什麼也不是。它是靠相依而存在的；佛教徒說它是「空」的，指的就是這個。
The principle of sufficient reason has a nearer relative in dependent origination: “when this exists, that comes to be.” Both deny that anything arises without conditions. They differ on where the series ends. Leibniz argues that the chain of reasons must terminate in a being that contains the reason for its own existence, and that this is God. The Buddha declined to posit a first cause and described a web of conditions with no beginning that can be found. The problem that occupied Leibniz for forty years, how a good creator could permit evil, therefore does not arise in Buddhism in that form. Suffering is explained by craving and ignorance, with no one having chosen the arrangement (Dharma and the West, D4).
充足理由律在緣起裡有一個更近的親戚：「此有故彼有。」兩者都否認有任何東西是不依條件而生起的。它們的差別在於這個系列在哪裡結束。萊布尼茲論證：理由的鏈條必須終止於一個「自身就包含了自己存在的理由」的存在者，而那就是上帝。佛陀拒絕設定第一因；他描述的是一張因緣之網，找不到開端。因此，那個佔據了萊布尼茲四十年的問題（一位善的造物主怎麼會容許惡），在佛教裡並不以那種形式出現。苦是由渴愛與無明來說明的，並沒有誰選擇了這樣的安排（佛法與西方哲學 D4）。
Terms of art · 哲學術語
Words that come with him 跟著他一起來的詞
L. principium rationis sufficientis
Nothing is the case without a reason why it is so and not otherwise.
沒有任何事情是沒有「為什麼如此而不是別樣」的理由的。
Gk. monas ‘unit’
A simple substance without parts, whose only states are perceptions.
沒有部分的單純實體；它唯一的狀態是知覺。
The agreement of all substances with one another, arranged at the creation, without any acting on any other.
一切實體彼此之間的一致；它是在創世時安排好的，沒有任何實體作用於另一個。
If two things share every property, they are one thing.
如果兩個東西的一切性質都相同，它們就是同一個東西。
A complete way that things might have been. The actual world is one of them.
事物「本來可以是」的一種完整的樣子。現實世界是其中之一。
Gk. theos ‘god’ + dikē ‘justice’; coined by Leibniz
A defense of the justice of God in the face of evil.
面對惡的存在，為上帝的公義所作的辯護。
Reading check · 理解測驗
Did it land? 讀懂了嗎
1. What does the principle of sufficient reason assert?
2. Why do monads “have no windows”?
3. In what respect is Voltaire’s satire unfair to Leibniz?
Go further · 延伸
Where he appears 他出現在哪幾課
- G. W. Leibniz, The Monadology, translated by Robert Latta (1898) ↗Ninety numbered paragraphs; the whole system in an hour. 九十個編號段落；一小時讀完整個體系。
- Voltaire, Candide (1759) ↗The most effective reply ever made to a philosopher, and not an argument. 對一位哲學家所作過最有效的回應，而它並不是一個論證。
- Maria Rosa Antognazza, Leibniz: An Intellectual Biography (2009)The standard life. 標準的傳記。
- Stanford Encyclopedia of Philosophy, “Gottfried Wilhelm Leibniz” ↗