The Three-Part Inference and the Syllogism 因明三支與三段論
“Sound is impermanent, because it is produced, like a pot; and whatever is permanent, like space, is not produced.” Buddhist logicians built their arguments around an example and a counterexample, where Aristotle built his around a universal rule. What each form guarantees, why John Stuart Mill took seriously the charge that every syllogism begs the question, and what the Indian form was for. 「聲是無常；所作性故；若是所作，見彼無常，如瓶等；若是其常，見非所作，如虛空等。」佛教的邏輯學家，把論證建立在一個例子與一個反例上；亞里斯多德則把論證建立在一條全稱的規則上。兩種形式各自保證了什麼？為什麼約翰・史都華・彌爾認真看待「每一個三段論都在乞題」這項指控？而印度的這種形式是為了什麼？
D14 Dharma and the West · 佛法與西方哲學Knowledge and Logic · 知識與邏輯Advanced · 高級about 30 min
因明三支
— Pāli hetu-vidyā, trairūpya Sanskritthe science of reasons; the three-membered argument
The verdict · 判定
Closest: John Stuart Mill, who held that all inference really runs from observed cases to new ones, and that the general premise of a syllogism is a record of such cases. The Indian argument puts the cases in plain view, a positive example and a negative one. The likeness to Aristotle is real at the level of form, and it ends at what makes the argument good. For Aristotle validity is a matter of form alone. For Dignāga a reason is good only if it is present in the subject, found with what is to be proved, and never found without it, and the last two are matters of experience.
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。
1 · What the Dharma says · 佛法怎麼說
Thesis, reason, example 宗、因、喻
Indian philosophy was argued in public. Teachers of rival schools debated before kings and assemblies, and losing could cost a school its patrons. The Nyāya school set out a standard form for a proof in five parts. The hill has fire. Because it has smoke. Wherever there is smoke there is fire, as in a kitchen. The hill has smoke. So the hill has fire. Buddhist logicians shortened it. The manual of Dignāga’s school that Xuanzang translated into Chinese names three members, “the thesis, the reason, and the example,” and gives a model built on a Buddhist doctrine. “Sound is impermanent” is the thesis. “Because it is produced” is the reason. Then comes the example in two forms: “Whatever is produced is seen to be impermanent, like a pot,” and “whatever is permanent is seen not to be produced, like space.”
The heart of the system is a test for a good reason, which the manual calls its three marks. “The reason has three marks. What are the three? It is present throughout the subject, it is definitely present in similar cases, and it is absent from all dissimilar cases.” Applied to the model: sound is produced, so the reason is present in the subject. Pots and other produced things are impermanent, so it is found in similar cases. Nothing permanent, such as space, is produced, so it is absent from the dissimilar cases. The two examples are there to show the second and third marks at work. The positive example shows the reason together with what is to be proved. The negative example shows that wherever the property to be proved is absent, the reason is absent too.
The manual spends most of its length on the ways arguments go wrong, and some of its examples are memorable. A thesis can contradict perception, as in “sound is not heard,” or contradict itself, as in “my mother is a barren woman.” A reason can fail to be established, as when one argues that sound is impermanent “because it is seen by the eye.” It can be inconclusive, as when one argues that sound is permanent “because it is knowable,” since permanent and impermanent things are both knowable. It can even prove the opposite of what was intended. The list was meant for use. A debater who knew it could find the fault in an opponent’s proof, and a student who knew it could find the fault in his own.
Aristotle invented formal logic in the Prior Analytics, and his definition is still standard. “A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so.” Its basic pattern is the first figure: “If A is predicated of all B, and B of all C, A must be predicated of all C.” The Buddhist model fits it exactly, with produced things as the middle term. The important difference is that Aristotle studied validity in abstraction from content. Letters stand for the terms, and the conclusion follows whatever they are. Examples play no part in the proof. The Indian logicians never separated form from content in this way. An argument was always about something, addressed to someone, and judged by whether its reason really had the three marks in the world. The Greeks produced a theory of validity, and the Indians produced a theory of good reasons.
亞里斯多德在《前分析篇》裡發明了形式邏輯；他的定義至今仍是標準。「三段論是這樣一種言說：其中陳述了某些東西之後，由於它們是如此，便有某種不同於所陳述之物的東西，必然地隨之而來。」它的基本模式是第一格：「如果 A 述說所有的 B，而 B 述說所有的 C，那麼 A 必然述說所有的 C。」佛教的範例恰好合乎這個模式；「所作」是中詞。重要的差別在於：亞里斯多德是把有效性從內容裡抽離出來研究的。用字母代表詞項；不管它們是什麼，結論都推得出來。例子在證明裡不扮演任何角色。印度的邏輯學家從來沒有用這種方式把形式與內容分開。一個論證總是關於某樣東西、說給某個人聽的；而它的好壞，取決於它的因在世界上是不是真的具備三相。希臘人產生了一套關於「有效性」的理論；印度人產生了一套關於「好理由」的理論。
Mill raised the oldest objection to the syllogism in its sharpest form. Take “All men are mortal; the Duke of Wellington is a man; therefore the Duke of Wellington is mortal.” If the first premise is known to be true, the duke’s mortality must already have been known, so the argument seems to beg the question. Mill’s answer was that the general premise is not really the ground of the conclusion. The ground is the many observed deaths of other people, and the general statement is a memorandum of them. “Not only may we reason from particulars to particulars without passing through generals, but we perpetually do so reason.” The child who has burned his fingers avoids the candle without ever having formed the maxim that fire burns. This is very close to the Indian picture, in which the example, the kitchen or the pot, is part of the evidence and is stated in the argument itself. Mill’s rules for finding causes, by checking agreement and difference among cases, also match the second and third marks: the reason found with the property, and absent where the property is absent.
The British philosopher Stephen Toulmin complained that formal logic had little to say about how arguments work in courts, laboratories, and committees. He proposed a layout with more parts than the syllogism: a claim, the data offered for it, a warrant that licenses the step from data to claim, the backing that supports the warrant, a qualifier saying how strong the claim is, and the rebuttals under which it would fail. The Indian three-membered argument maps onto this closely. The thesis is the claim, the reason is the data, the general statement is the warrant, the example is its backing, and the dissimilar example and the catalog of fallacies anticipate the rebuttals. Toulmin was trying to recover what the Indian logicians had never lost, logic as the practice of giving reasons to someone who may disagree. He drew his models from law. Theirs came from the debating hall.
Who is closest, and where the likeness ends 誰最接近，相似到哪裡為止
On form the closest parallel is Aristotle. The Buddhist model argument, once its example is removed, is a valid syllogism in the first figure, and scholars have long noted the match. On what makes an argument good, Mill is closer. He and the Indian logicians agree that a general rule earns its place only through observed cases, and that a careful reasoner must look for cases where the reason appears without the property. On the practice of argument Toulmin is closest. He and they treat an argument as a move in an exchange, made to persuade someone who may push back.
The likeness ends at the purpose. Aristotle wanted a science of demonstration, Mill a logic for the natural sciences, and Toulmin a logic for practical fields. The Buddhist logicians wanted these things too, and their model argument shows what else they wanted. Its conclusion is that sound is impermanent, one of the three marks of existence, and the argument is a step toward the insight that frees. Dharmakīrti said that the purpose of the whole inquiry into means of knowledge is to know what to take up and what to avoid. The manual distinguishes inference for oneself, which is the private act of understanding, from inference for others, which is the spoken proof. A teacher who argues well for others is offering another person the chance to see what he has seen.
Thesis, reason, example (similar and dissimilar)宗、因、喻（同喻與異喻）
Thesis, reason, example, application, conclusion宗、因、喻、合、結
Two premises and a conclusion兩個前提與一個結論
Observed cases, then the new case觀察過的案例；然後是新案例
Premises and conclusion in a formal language形式語言裡的前提與結論
Role of examples例子的角色
Part of the proof證明的一部分
Part of the proof證明的一部分
None in the proof itself在證明本身裡沒有角色
The real evidence真正的證據
None沒有
What makes it good什麼使它成為好論證
The three marks, checked in the world因三相；在世界上查核
A pervasion known from experience一個由經驗得知的遍充關係
Valid form有效的形式
Sound induction健全的歸納
Valid form, true premises有效的形式；真的前提
Treatment of error對錯誤的處理
A detailed catalog of fallacies一份詳細的過失清單
A catalog of pseudo-reasons一份似因的清單
Sophistical refutations辯謬篇
Fallacies of induction歸納的謬誤
Invalid forms無效的形式
Purpose目的
Understanding for oneself and for others, toward release自悟與悟他；朝向解脫
Right knowledge in debate, toward release辯論中的正確知識；朝向解脫
A science of demonstration一門證明的科學
The logic of the sciences科學的邏輯
The study of valid inference as such研究有效推論本身
5 · The step the Dharma takes further · 佛法多走的一步
The counterexample, and the listener 反例，與聽者
The first further step is the dissimilar example. Aristotle’s form does not ask for it, and modern logic counts it as redundant, since it follows from the general premise. The Indian logicians required it to be stated, and the reason is practical. A person who asserts that everything produced is impermanent is easily convinced by the cases that agree with him. The third mark forces him to turn and look at the other side: is there anything permanent that is produced? Western philosophy reached the same lesson later and stated it as a principle of science. A general claim is tested by the search for a counterexample, and Popper built a philosophy of science on it. The Buddhist logicians had written the search into the form of every argument. It is a discipline against confirmation bias, the habit of looking only for cases that agree.
The second step is the listener. The manual opens by saying that proofs and refutations serve to bring understanding to others, and that perception and inference serve one’s own understanding. An argument for others must start from premises the other person already accepts. One of the listed faults is a reason accepted by only one party, and another is a thesis that both parties already grant, which proves nothing. Logic here is a form of courtesy. One meets the other person where he stands and walks with him, step by step, to where one wants him to see. The tradition of Buddhist debate in Tibetan monasteries still trains monks this way, with a challenger and a defender and a fixed form for each move. When the logic came to China with Xuanzang it was studied for a few generations and then largely set aside, and Chinese Buddhism turned to schools that distrusted argument. Something was lost. The Indian logicians had shown that rigorous reasoning and the path to release could be pursued by the same person, in the same act.
A reason, an example, and a counterexample 一個理由、一個例子，與一個反例
Westerners often assume that logic is a Greek invention and that Asian traditions relied on intuition or authority. The Buddhist logicians are the best correction available, and they are easy to present. Write the model argument on a board in plain English: sound is impermanent, because it is made; whatever is made is impermanent, like a pot; whatever is permanent is not made, like space. Ask the audience what the last line adds. Someone will say it checks for exceptions, and that is the point of the lesson. Then mention the list of fallacies, with the barren mother as the example everyone remembers. End with the purpose. These logicians argued carefully because the conclusions concerned how to live, and they thought that a careless argument on such matters does harm.
Buddhist logicians required every argument to give an example and a counterexample.
佛教的邏輯學家要求每一個論證，都要給一個例子與一個反例。
Their model was: sound is impermanent, because it is made, like a pot; and nothing permanent, like space, is made.
他們的範例是：聲是無常的，因為它是被造出來的，如瓶；而沒有任何常的東西（如虛空）是被造出來的。
The counterexample line is a built-in check against seeing only what agrees with you.
反例的那一行，是一個內建的檢查：防止你只看見與你相符的東西。
Aristotle studied valid form. The Indian logicians studied good reasons, which includes checking the world.
亞里斯多德研究的是有效的形式。印度的邏輯學家研究的是好的理由；而那包括去查核世界。
One of their textbook fallacies is “My mother is a barren woman.” The sentence refutes itself.
他們教科書裡的一個過失是：「我母是石女。」這句話自己駁倒了自己。
An argument for someone else has to start from what that person already accepts. They saw logic as a way of meeting another mind.
為別人而作的論證，必須從那個人已經接受的東西出發。他們把邏輯看成與另一顆心相遇的方式。
Phrases to avoid 要避開的說法
“Logic is a Western invention.” 「邏輯是西方的發明。」
India and China both had developed logics. Name Dignāga and Dharmakīrti.
印度與中國都有發展成熟的邏輯。說出陳那與法稱的名字。
“Indian logic is just the syllogism with extra steps.” 「印度邏輯不過是多了幾步的三段論。」
The extra steps carry the evidence and the check for exceptions. Say what each one does.
多出來的幾步，承載著證據，以及對例外的檢查。要說出每一步做了什麼。
“Buddhism goes beyond logic, so arguments don’t matter.” 「佛教超越了邏輯，所以論證不重要。」
A whole Buddhist school disagreed, and Tibetan monks still debate daily.
整整一個佛教學派不同意這一點；而藏傳的僧人至今仍天天辯經。
“The example is just an illustration.” 「例子只是一個說明。」
In this logic it is evidence. Removing it removes part of the support.
在這套邏輯裡，它是證據。拿掉它，就拿掉了一部分的支持。
Three languages · 三語對照
The vocabulary, in Chinese, Pāli, Sanskrit, and English 術語：中文、巴利文、梵文、英文
中文
Pāli
Sanskrit
English
因明
—
hetu-vidyā
the science of reasons; Buddhist logic
宗
—
pakṣa, pratijñā
the thesis
因
hetu
hetu, liṅga
the reason; the mark
喻
—
dṛṣṭānta
the example
因三相
—
trairūpya
the three marks of a good reason
遍是宗法性
—
pakṣadharmatva
the reason is present in the subject
同品定有性
—
sapakṣe sattvam
the reason is found in similar cases
異品遍無性
—
vipakṣe ’sattvam
the reason is absent from all dissimilar cases
為自比量・為他比量
—
svārthānumāna, parārthānumāna
inference for oneself; inference for others
似因
—
hetvābhāsa
a pseudo-reason; a fallacy of the reason
遍充
—
vyāpti
pervasion: the invariable connection of reason and property
三段論
—
—
the syllogism
Reading check · 理解測驗
Did it land? 讀懂了嗎
1. What are the three members of Dignāga’s argument?
2. What does the third mark of a good reason require?
3. Why is “my mother is a barren woman” listed as a fault?
4. What was Mill’s objection to the syllogism?
5. What does the lesson say the dissimilar example adds?
Write · 你怎麼講？
Write an argument for something you believe in the three-membered form: thesis, reason, a similar example, and a dissimilar example. Then check each of the three marks. About 150 words.
