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How did Gautama’s five-membered Nyaya syllogism differ from Aristotle’s three-part syllogism?

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Ancient logic Zeno's paradox, illustrated by Achilles' racing a tortoise.

Gautama’s five-membered Nyaya syllogism differs from Aristotle’s three-part syllogism primarily in its structure and its emphasis on material truth alongside formal validity.12

Aristotle’s syllogism, central to his logic, consists of three propositions: two premises and a conclusion. It focuses on the formal relationship between terms (major, minor, and middle) to ensure that if the premises are true, the conclusion must necessarily follow.2

In contrast, Gautama’s five-membered syllogism (avayava) includes:1
1. Pratijna: A statement of what is to be proved.
2. Hetu: A statement of the reason.
3. Udaharana: A general rule supported by an example (e.g., a kitchen).
4. Upanaya: The application of the rule to the specific case.
5. Nigamana: The final conclusion.1

The inclusion of an example in the Nyaya system highlights a desire to ensure not only formal validity but also material truth. While Aristotle’s approach is often viewed as a logic of abstract propositions, Indian logic is characterized as a logic of cognitions, deeply integrated with epistemology and the human striving to understand reality.13