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Five Steps of Proof

Tarka Sangraha, Anumana 9

प्रतिज्ञा-हेतु-उदाहरण-उपनय-निगमनानि पञ्चावयवाः । पर्वतो वह्निमानिति प्रतिज्ञा । धूमवत्वात् इति हेतुः । यो यो धूमवान् स वह्निमान् यथा महानस इत्युदाहरणम् । तथा च अयमिति उपनयः । तस्मात्तथेति निगमनम् ॥

Meaning · English

Claim, reason, example, application and conclusion are the five parts. 'The hill has fire' is the claim. 'Because it has smoke' is the reason. 'Whatever has smoke has fire, as a kitchen does' is the example. 'And this hill is like that' is the application. 'Therefore it is so' is the conclusion.

How do you lay out an inference so that someone else can check it? For the Nyaya school, a complete proof has five parts. Pratijna, the claim: the hill has fire. Hetu, the reason: because it has smoke. Udaharana, the example: wherever there is smoke there is fire, as in a kitchen. Upanaya, the application: this hill has that kind of smoke. Nigamana, the conclusion: so the hill has fire. In his own commentary, Annambhatta explains what each part does. The claim names a place and what is to be shown about it. The reason names the sign, phrased as 'because of'. The example states vyapti, the fixed rule that this sign never occurs without the thing it signals. The application says the sign, carrying that rule, is present right here. The conclusion restates the claim, now backed by the reason. He adds that it holds only if nothing already known contradicts it. Each step answers a question a listener could fairly ask.

1. Today, whenever you make a claim in conversation, say your reason aloud with the word 'because'. 2. Take five minutes with paper and write one belief you hold as five short lines, following the hill-and-smoke pattern. 3. Look at your third line, the general rule, and name one familiar case where it plainly holds, the way the kitchen does for smoke. 4. Spend one more minute looking for a case where the sign appears without the thing. If you find one, the proof fails, so cross it out.

Modern formal logic would compress this to two premises: a general rule and a particular case, giving the conclusion by straightforward deduction. On that view the opening claim and the closing conclusion repeat each other. The Nyaya form, though, is built for public argument, where stating the aim first and closing the loop helps a listener follow. Argumentation theory today also values grounding a rule in a shared example. The hard part is the rule itself. Hume argued that no number of smoky kitchens guarantees the next smoke has fire. Science generalises from cases too, and treats its rules as revisable when a counter-example turns up. Stage fog, for instance, looks like smoke without fire, which is why Nyaya insists the sign be the real thing. How a general rule is ever justified remains an open question.

अर्थ · हिन्दी

In this book

• Before: For Yourself, For Another · Tarka Sangraha, Anumana 6
• Next: Agreement and Absence · Tarka Sangraha, Anumana 11
• All of Tattva · Ask Krishna about it

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