India's Founding Book of Logic Lists 22 Ways to Lose an Argument — Walking Out Is One, and So Is Saying "You Too"

Calcutta, 1864: a pink paper wrapper at the Baptist Mission Press

The Baptist Mission Press, Calcutta. A printer named C. B. Lewis is putting out an instalment for the Asiatic Society of Bengal. It is number 56 in the New Series of the Bibliotheca Indica, a collection of oriental texts published under the Society's supervision. The paper wrapper is pink. Under an engraving of a pillared building, the title runs in Devanagari and then in English: The Nyaya Darsana of Gotama, with the Commentary of Vatsyayana, edited by Pandita Jayanarayana Tarkapanchanana, Fasciculus I. The date at the foot is 1864. (Bibliotheca Indica, New Series No. 56, wrapper; Bayerische Staatsbibliothek copy)

Half a century later, in Allahabad, Ganganatha Jha put Vatsyayana's commentary into English. His first volume came off the Belvedere Steam Printing Works in 1915, priced at six rupees. (Jha 1915, vol. I, title page) Inside it is a sentence that sets the tone. The science of reasoning, he says, "is the lamp of all Sciences." (Vatsyayana, Bhasya on Nyaya Sutra 1.1.1, trans. Jha 1915)

A few pages on, he shows what he means with a small walk. A man is told by someone he trusts that there is fire at a certain place. Drawing nearer, "if we happen to see smoke issuing, we infer, from this, the existence of fire." Then, "actually getting at the place, we directly see the fire." (Vatsyayana, Bhasya on 1.1.3, trans. Jha 1915) Word, then inference, then sight: three kinds of evidence, one fire.

That walk is the seed of the most famous argument in Indian logic. This Investigation follows it to the debate hall, and then to your phone.

At a glance

• Five steps make a proper argument in Nyaya: proposition, reason, example, application, conclusion. (Nyaya Sutra 1.1.32, trans. Vidyabhusana 1913, p. 10)
• Five fallacies of the reason are named: the erratic, the contradictory, the equal to the question, the unproved and the mistimed. (Nyaya Sutra 1.2.4, Vidyabhusana p. 15)
• Twenty-two "occasions for rebuke" close the book, from "hurting the proposition" to "the semblance of a reason"; the translator adds that there are "infinite" more. (Nyaya Sutra 5.2.1 and gloss on 5.2.25, Vidyabhusana pp. 167, 175)
• Twenty-four "futilities", trick rejoinders that only look like answers, fill the first chapter of Book V. (Nyaya Sutra 5.1.1, Vidyabhusana p. 140)
• About 450 CE is the translator's date for Vatsyayana's commentary; the Stanford Encyclopedia puts it in the fifth century and the sutra itself around the second century CE. (Vidyabhusana 1913, Introduction, p. x; SEP, "Logic in Classical Indian Philosophy," §§3.1–3.2)
• Ten steps, or three: rivals wanted more and fewer, and the Nyaya commentators argued for exactly five. (Bhasya and Vartika on 1.1.32, trans. Jha 1915)
• Twenty-one definitions of "wherever there is smoke there is fire" were rejected by the fourteenth-century logician Gangesha before he accepted his own. (SEP, "Analytic Philosophy in Early Modern India," §8.2; SEP, "Epistemology in Classical Indian Philosophy," §8)

First, the words a beginner needs

Nyaya. Nyāya. "Method" or "rule"; the name of the Indian school of logic and debate, and of its founding text, the Nyāya Sūtra. The text is ascribed to Gautama, also called Akshapada.

Sutra, bhashya. Sūtra, bhāṣya. A sutra is a very short rule meant to be memorised; a bhashya is the commentary that explains it. Vatsyayana's is the oldest surviving commentary on the Nyaya Sutra.

Pramana. Pramāṇa. A means of knowing. Nyaya accepts four: perception, inference, comparison and the word of a reliable person. (Nyaya Sutra 1.1.3)

Inference. Anumāna. Knowing something you cannot see from a sign you can see.

Member. Avayava. One of the five steps of a spoken argument: proposition (pratijñā), reason (hetu), example (udāharaṇa), application (upanaya) and conclusion (nigamana).

Familiar instance. Dṛṣṭānta. A case that "an ordinary man and an expert" agree about. (1.1.25, p. 8)

Pervasion. Vyāpti. The rule that links sign and conclusion: "wherever there is smoke there is fire."

Fallacy of the reason. Hetvābhāsa, literally "a reason that only looks like a reason."

Discussion, wrangling, cavil. Vāda, jalpa, vitaṇḍā. Three kinds of debate: one to find the truth, one to win, one only to attack.

Occasion for rebuke. Nigrahasthāna. A move that loses you the debate on the spot.

Syllogism. Aristotle's word, borrowed by translators for the five-step argument. Not an exact fit.

The claim we are testing

The usual story: the hill-and-smoke argument comes straight from Gautama's sutra, it is older than Aristotle, and it is Aristotle's syllogism with two extra steps.

1. The Nyaya Sutra lays down a five-step argument and a rulebook for fair debate. True. Sutra 1.1.32 names the five members, 1.1.33–39 define them, 1.2.1–3 define three kinds of debate, and Book V lists 24 trick rejoinders and 22 ways to lose. (Vidyabhusana 1913, pp. 10–15, 140, 167)
2. The hill-smoke-kitchen argument is in Gautama's sutra. Myth. The Stanford survey notes that, unlike the medical Caraka-samhita, the Nyaya Sutra gives no illustration of its five-part argument, and that it names fallacies with "neither examples nor explanations." (SEP, "Logic in Classical Indian Philosophy," §§3.2–3.3) Vatsyayana's own worked example is about sound and a cup. The hill comes from the commentary tradition and the translators' notes.
3. It is older than Aristotle. Unsupported. Aristotle lived 384–322 BCE. (SEP, "Aristotle") The 1913 translator's date of about 550 BCE for Gautama is his own reckoning from the Vayu Purana and teacher-lists, and he doubts the whole text is Gautama's. (Vidyabhusana, Introduction) Modern scholarship places the text around the second century CE.
4. It is Aristotle's syllogism with extra steps. Myth. Nyaya requires an agreed example; Aristotle's syllogism does not. (Prior Analytics II.24; Matilal 1998, pp. 15–16)

The sutra never mentions a hill

Open the sutra at 1.1.32 and you find one line of Sanskrit: pratijñāhetūdāharaṇopanayanigamanāni avayavāḥ. (GRETIL text) Vidyabhusana translates: "The members (of a syllogism) are proposition, reason, example, application, and conclusion." (1.1.32, p. 10)

The hill is not there. It sits underneath, in the translator's bracketed note: "This hill is fiery, Because it is smoky, Whatever is smoky is fiery, as a kitchen, So is this hill (smoky), Therefore this hill is fiery." (gloss on 1.1.32, p. 10)

"A proposition is the declaration of what is to be established." (1.1.33, p. 11) State the claim first, plainly, so everyone knows what is on trial.

"The reason is the means for establishing what is to be established through the homogeneous or affirmative character of the example." (1.1.34, p. 11) The reason does not float free. It counts only because something everyone knows has the same feature.

The example is "a familiar instance which is known to possess the property to be established." (1.1.36, p. 11) There is also a negative example, a known case that lacks both the property and the reason. (1.1.37, p. 12)

"Application is a winding up, with reference to the example, of what is to be established as being so or not so." (1.1.38, p. 12) This is the step that says: our case is like the example.

"Conclusion is the re-stating of the proposition after the reason has been mentioned." (1.1.39, p. 13)

When Vatsyayana illustrates these sutras, he does not use a hill. He uses sound. His proposition is "Sound is non-eternal," and his example is "such things as the dish, the cup." (Bhasya on 1.1.33 and 1.1.36, trans. Jha 1915) Vidyabhusana's notes follow him with a pot: "Sound is non-eternal, Because it is produced, Whatever is produced is non-eternal, as a pot." (1.1.34–39, pp. 11–13)

So where did the hill come from? In Jha's 1915 translation the "mountain" and the "culinary hearth" turn up in his footnotes, one of them explaining Vachaspati Mishra's later sub-commentary. (Jha 1915, notes on the commentaries to 1.1.1 and 1.1.25) By the time of the later Nyaya manuals it was, in the words of the Stanford survey, "the standard inference." (SEP, "Analytic Philosophy in Early Modern India," §8.3) The hill is real Nyaya. It is just not Gautama's own sentence.

Why five steps, when two would do

Here is the obvious objection. "There is fire on the hill, because there is smoke" says it all. Why five?

Vatsyayana's answer is that each step carries a different kind of evidence. In Jha's translation: the proposition "is verbal"; the reason "is inferential"; the example "is perceptional"; the application "is analogical"; and the conclusion shows that all of them "bear upon the same object." (Bhasya on 1.1.1, trans. Jha 1915) It is the walk to the fire, written as one sentence.

He calls this five-fold statement "the highest form of reasoning," and Jha adds in brackets why: only then does reasoning succeed "in convincing the unbeliever." (Bhasya on 1.1.1, trans. Jha 1915) The audience is the point.

Not everyone agreed on five. Vatsyayana records a rival count: "Some logicians declare that there are ten Factors." Their extra five were desire to know, doubt, capacity to accomplish what is desired, purpose, and the dispelling of doubt. He rejects them. They help a discussion, he says, but are not parts of the proof. (Bhasya on 1.1.32, trans. Jha 1915) Vidyabhusana's samples of them are sharp. Doubting the reason: "That which you call smoke may be nothing but vapour." Testing the example: "in a red-hot iron-ball there is no smoke." (gloss on 1.1.32, p. 10)

The next commentator, Uddyotakara, says the exact number five was fixed against two rivals: some want ten factors and some want three. (Vartika on 1.1.32, trans. Jha 1915) The three-step camp was Buddhist (more on that below).

Nyaya then made the number a rule of debate. Sutra 5.2.12 says that an argument lacking "even one of its parts" is "saying too little." Sutra 5.2.13 says that more than one reason or example is "saying too much." (5.2.12–13, p. 172) Even the order is fixed: say the parts in a jumbled order and you lose for being "inopportune." (5.2.11, p. 171)

The kitchen is the whole argument

Most people treat the kitchen as decoration. It is the load-bearing wall. Sutra 1.1.25 defines the familiar instance as "the thing about which an ordinary man and an expert entertain the same opinion." Vidyabhusana's bracket names it: a kitchen "in which fire and smoke abide together, to the satisfaction of an ordinary man as well as an acute investigator." (1.1.25, p. 8)

The kitchen is not proof that smoke always means fire. It is a meeting point: before you argue about the hill, both sides must agree on one place where the rule visibly holds.

The philosopher Bimal Krishna Matilal made this point against a long habit of rewriting the Indian argument as: wherever there is smoke, there is fire; there is smoke on the hill; so there is fire there. That is the Western pattern logicians call Barbara. He argued that the cited kitchen changes things: it guarantees that the general rule is about something that actually exists, and it shows that the rule came from experience, which is also its weak spot. (Matilal 1998, pp. 15–16)

The 1913 notes point at a weak spot. Vidyabhusana's red-hot iron ball is a case of fire without smoke. That does not hurt the hill argument. Turn the argument round, though, and it collapses. Matilal's example: infer smoke in the kitchen from fire, and your reason is "deviating," because fire can be smokeless. (Matilal 1998, p. 5) The direction of the rule matters.

Five ways a reason can lie

Sutra 1.2.4 names five "fallacies of a reason." The Sanskrit is one long compound: savyabhicāra-viruddha-prakaraṇasama-sādhyasama-kālātītāḥ hetvābhāsāḥ. (GRETIL text) In Vidyabhusana's English, with his examples, here they are.

The erratic. "The reason which leads to more conclusions than one." (1.2.5, p. 15) His example: sound is eternal because it is intangible, like atoms. But intellect is intangible too, and not eternal. The same reason proves opposite things, so it proves nothing. (pp. 15–16)

The contradictory. "The reason which opposes what is to be established." (1.2.6, p. 16) "A pot is produced, because it is eternal."

The equal to the question. A reason that "provokes the very question for the solution of which it was employed." (1.2.7, p. 16) "Sound is non-eternal because it is not possessed of the attribute of eternality." Vidyabhusana's verdict: "the reason begs the question." (p. 16)

The unproved. "The reason which stands in need of proof in the same way as the proposition does." (1.2.8, pp. 16–17) "Shadow is a substance, because it possesses motion." Does a shadow move, or does the person casting it?

The mistimed. A reason "adduced when the time is past in which it might hold good." (1.2.9, p. 17) His example compares the sound of a drum with the colour of a jar: colour shows when a lamp touches the jar, but drum sound is heard after the stick has left the skin. (p. 17)

Then tricks with words. A quibble (chala) is defined as opposing a statement "by the assumption of an alternative meaning." (1.2.10, p. 17) A speaker says a boy is nava-kambala, "possessed of a new blanket." The quibbler replies that he is not "possessed of nine blankets," since he has only one; nava means both. (1.2.12, p. 18)

Three kinds of debate, and the thorn fence

Discussion (vāda) is the honest kind. "Discussion is the adoption of one of two opposing sides. What is adopted is analysed in the form of five members, and defended by the aid of any of the means of right knowledge, while its opposite is assailed by confutation, without deviation from the established tenets." (1.2.1, p. 14)

Wrangling (jalpa) "aims at gaining victory." It uses the same form "by quibbles, futilities, and other processes which deserve rebuke." (1.2.2, p. 15)

Cavil (vitaṇḍā) is wrangling with nothing to defend. "A caviller does not endeavour to establish anything, but confines himself to mere carping at the arguments of his opponent." (1.2.3 and gloss, p. 15)

Sutra 4.2.48 says one should enter discussions "with unenvious persons, such as disciples, preceptors, fellow-students and seekers of the summum bonum." (p. 138) The commentary adds that "unenvious" excludes those who "desire victory."

Then comes the surprise. Sutra 4.2.50 allows the dirty kinds, for one purpose: "Wranglings and cavils may be employed to keep up our zeal for truth just as fences of thorny boughs are used to safe-guard the growth of seeds." (p. 139) The gloss says these tactics may be used against people who argue "out of a bias for their own side," and that in themselves they "do not... deserve any profit or encomium." (p. 139) A fence, not a crop.

Twenty-two ways to lose, including leaving the room

Book V is a catalogue of defeat. Its first chapter lists 24 "futilities," rejoinders that only look like answers. (5.1.1, p. 140) Futility, says sutra 1.2.18, "consists in offering objections founded on mere similarity or dissimilarity." (p. 20)

The second chapter lists 22 "occasions for rebuke." (5.2.1, p. 167) Three read like a modern comment section.

Evasion. "'Evasion' arises if one stops an argument in the pretext of going away to attend another business." The gloss's man, finding he cannot win, says "he has to go away on a very urgent business." (5.2.20, p. 174)

Admission of an opinion. This is charging the other side with a fault "by admitting that the same defect exists in one's own side." One person says: "You are a thief." The other replies: "You too are a thief." Instead of answering the charge, he has thrown it back and so admitted it. (5.2.21, p. 174) The Sanskrit name is matānujñā.

Overlooking the censurable. Failing to rebuke someone who deserves it. The rulebook turns to the crowd: it is the audience's duty to censure the person who argues unfairly, and "if the audience failed to do their duty they would earn rebuke for themselves." (5.2.22 and gloss, pp. 174–175)

Others include shifting the topic, silence and "non-ingenuity," having no reply at all. (5.2.1, p. 167) The translator adds: "There are infinite occasions for rebuke of which only twenty-two have been enumerated here." (p. 175)

One caution: Vidyabhusana thought Book V "evidently not the production of Aksapada." (Introduction, p. x)

The Greek who argued without a kitchen

Aristotle (384–322 BCE) gave Europe its word "syllogism." (SEP, "Aristotle") His definition, in A.J. Jenkinson's translation: "A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so." (Prior Analytics 24b18–20, trans. Jenkinson)

His model form needs no example at all: "If A is predicated of all B, and B of all C, A must be predicated of all C." (Prior Analytics 25b37–39) All smoky things are fiery; this hill is smoky; so this hill is fiery. No kitchen required.

First, Aristotle did know arguments that lean on a similar case, and he kept them in a separate box. He calls it an "example." His illustration: to prove that fighting the Thebans would be an evil for Athens, you first show that fighting neighbours is an evil, using "similar cases" such as the Thebans' own war against the Phocians. Arguing by example, he says, is reasoning "from part to part." (Prior Analytics II.24, trans. Jenkinson) That is close in shape to Nyaya. But for Aristotle it sits outside the strict syllogism; for Nyaya the example is a required step.

Second, the most famous "Aristotelian" syllogism is not in this book. "All men are mortal; Socrates is a man" is a textbook staple. We searched the Jenkinson translation of the Prior Analytics: the phrase "all men" does not occur once. (Prior Analytics, MIT Internet Classics Archive text)

Aristotle built a logic of forms valid whatever their content. Nyaya built a logic of public persuasion in which the content had to touch the ground. Matilal's view was that the example exposes the inductive side of the Indian argument, its dependence on experience, and that Indian logicians accepted this rather than hid it. (Matilal 1998, p. 16)

Gangesha and the smoke that would not stay defined

More than a thousand years after the sutra, Nyaya started again. The "new" school, Navya-Nyāya, grew from a single book: Gangesha's Tattvacintāmaṇi, the "Jewel of Reflection on the Truth." (SEP, "Analytic Philosophy in Early Modern India," introduction) A survey of Indian epistemology dates Gangesha to the fourteenth century. (SEP, "Epistemology in Classical Indian Philosophy," §8)

Later scholars kept returning to one small section of it: the definition of pervasion, the rule "wherever there is smoke there is fire." (SEP, "Analytic Philosophy in Early Modern India," §8.1) Gangesha lists twenty-one definitions and rejects all of them, then offers seven more he can accept. (same, §8.2)

Why so much trouble? One problem: the simple definition says: smoke proves fire if there is no place with smoke and no fire. But Navya-Nyaya treated some properties as present in one part of a thing and absent in another. The kitchen has fire in the hearth and no fire in the far corner. On the simple definition, the kitchen itself becomes a place with smoke "and" no fire, a fake counter-example. (same, §8.3) The familiar instance from 1.1.25 had become a test case for precision.

Gangesha also answered the oldest attack on inference: that no one can ever see that smoke means fire in every place and time. A person who truly doubted it would not, as he does, "resort to fire for smoke" when he wants to drive away mosquitoes. (Gangesha, inference chapter, trans. Phillips, quoted in SEP, "Epistemology in Classical Indian Philosophy," §8)

Read the actual document

"Discussion is the adoption of one of two opposing sides. What is adopted is analysed in the form of five members, and defended by the aid of any of the means of right knowledge, while its opposite is assailed by confutation, without deviation from the established tenets." — Nyaya Sutra 1.2.1, trans. S.C. Vidyabhusana (Allahabad, 1913), p. 14

In plain words: an honest debate has five rules. Pick a side and say it. Lay it out in the five steps. Back each step with evidence you could name: something seen, something inferred, a fair comparison, or a trustworthy word. Attack the other side by showing its consequences are absurd, not by mocking it. And do not quietly switch positions when you start losing. Book V makes that last rule bite: "deviating from a tenet" loses you the debate. (5.2.24, p. 175)

Using it on a forward

Here is a made-up forward of a familiar kind. "BREAKING: Board exams postponed! Circular attached. Same thing happened last year. Share before they delete it!"

Run it through the five steps.

1. Proposition. What exactly is claimed? "The board has postponed the exams." If it keeps changing as you ask questions, that is "shifting the proposition," item two of the 22. (5.2.1, p. 167)

2. Reason. "Because there is a circular." Now ask the unproved-reason question: does the reason itself need proof as much as the claim? (1.2.8) Is it really a board circular, or a picture of one? This is the 1913 note in modern dress: "That which you call smoke may be nothing but vapour." (gloss on 1.1.32, p. 10)

3. Example. What is the general rule, and what familiar case do both of us accept? "Notices on the board's own website are real" is a rule you can test, with a kitchen you can visit: the website. "It happened last year" is not a rule. It is one case, and one case can support opposite conclusions; that is the erratic reason. (1.2.5)

4. Application. Does the circular appear where real circulars appear? If not, the hill is not like the kitchen.

5. Conclusion. Only now may you say "the exams are postponed," or "this is not shown."

Then check the behaviour, Book V style. Does the sender answer "you also forwarded fake news last month"? That is matānujñā, "You too are a thief." (5.2.21) Does the argument end with "I'm busy, believe what you want"? Evasion. (5.2.20) And if you see it and say nothing, the old rulebook has a word for you too: overlooking the censurable. (5.2.22)

The strongest case for the other side

The Buddhist objection: five steps is padding. Dignaga's school cut the argument to three, and the Stanford survey shows his model keeps thesis, reason and examples and drops application and conclusion. (SEP, "Logic in Classical Indian Philosophy," §4.1) Matilal sums up the complaint: the Buddhists and others said the five-step form was too elaborate, and that the first two or three steps carry the whole logical load. (Matilal 1998, p. 4) Step five repeats step one. On logic alone, that is fair.

The Charvaka objection: you never saw "all smoke." The materialist Charvakas, known to us mainly through their opponents' summaries, attacked the rule itself. Madhava's fourteenth-century compendium Sarva-darsana-samgraha gives their case. Perception cannot show the rule, because the senses never touch "the past or the future," so "the universal proposition... becomes impossible to be known." Inference would need another inference, "ad infinitum." Testimony is no better: "there is no more reason for our believing on another's word that smoke and fire are invariably connected, than for our receiving the ipse dixit of Manu." (trans. Cowell & Gough 1882, pp. 5–7)

That is the problem of induction, stated in medieval India. The kitchen shows the rule held in one place, not on the hill. Gangesha's mosquito reply is about how people live, not a proof, and the Charvaka can fairly say so.

What we could not prove

• When Gautama lived. Vidyabhusana's 550 BCE rests on a Vayu Purana passage, Vedic teacher-lists and Pali references; he himself says only Book I can be ascribed to Gautama with any safety. Modern surveys say about the second century CE.
• Who first used the hill. The hill-and-kitchen argument is in Vidyabhusana's 1913 brackets, in Jha's footnotes from Vachaspati Mishra, and in the later manuals. We did not find it in the sutra or, as a five-step argument, in Vatsyayana's text as Jha translates it. Who wrote it first, we cannot say.
• Contact with Greek logic. Nothing we opened shows borrowing in either direction.
• The medical-text version. The Stanford survey says the Caraka-samhita, India's earliest medical text, also has a five-part argument with a worked example (Caraka-samhita 3.8.31) and a list of 14 ways to lose a debate. We did not open the Caraka-samhita itself.
• Vatsyayana's source verse. The "lamp of all Sciences" line in Vatsyayana matches, in translation, a verse in the Arthashastra about the science of inquiry, which Kautilya says "comprises the Philosophy of Sankhya, Yoga, and Lokayata." (Arthashastra, Book I, ch. 2, trans. Shamasastry) We did not compare the two Sanskrit texts ourselves, so we do not claim who quoted whom.
• The palm leaf. The BnF catalogue gives the script as Bengali; we could not identify which part of the Tattvacintamani is on the leaf.
• The Mahabharata line. Ganguli's translation praises the sage Narada as "competent to judge of the correctness or incorrectness of syllogistic statements consisting of five propositions." (Sabha Parva, section V) We cannot date the line.

Why it still matters today

Every Indian adult now carries a debate hall in their pocket. Most of what arrives skips steps: a claim and a reason, no example; one case passed off as a rule; "you too" in place of an answer.

The Nyaya rulebook does not tell you what to believe. It tells you what a claim owes you first: a clear statement, a true reason, a rule with an agreed case, a check that this case fits. And it gives the audience a job. And its honest debate is to be held with "unenvious persons," people who want the truth more than the win. (4.2.48) That is a standard for family groups too.

Verdict

The documents prove that India's founding book of logic set out a five-step public argument, defined each step, named five ways a reason fails, and listed 22 ways to lose a debate, including evasion and "You too are a thief." They prove that its oldest commentator defended exactly five steps against rivals who wanted ten or three, and tied each step to a different kind of evidence. They prove that the argument requires an agreed example, a real difference from Aristotle's syllogism.

They do not prove that the hill-and-kitchen argument is Gautama's own words, that the Nyaya Sutra is older than Aristotle, or that either tradition borrowed from the other. Nor does Nyaya answer the Charvaka's challenge that no one has seen all the smoke in the world.

My judgment: the five steps are less a proof machine than a courtesy. They make the arguer show his evidence in the order a listener can check it. That is still the best test for a forward.