Nyāya, (Sanskrit: Rule, or Method), one of the six orthodox systems (darsana) of Indian philosophy, important for its analysis of logic and epistemology. The major contribution of the Nyāya system is its working out in profound detail the reasoning method of inference. The Nyāya philosophical system admits the existence of a supreme soul and in recognising analogy as akind of evidence in addition to the three kinds - perception, inference, and testimony. The speciality of the Nyāya is the development of dialectical method. It discusses methods of reasoning with the greatest subtlety. It starts with sixteen topics for discussion which leave nothing to be desired to the most contentious dialectician : First of all, there is the proof and the thing to be proved. The Nyāya syllogism consists of five parts - 1) the proposition, 2) the reason, 3) the instance, 4) the application of the reason, and 5) the conclusion. The following is a generally quoted instance of Nyaya syllogism :

1. The hill is fiery (Proposition)
2. For it smokes (Reason)
3. Whatever smokes is fiery, as a kitchen (Instance)
4. The hill is smoking (Application of the reason)
5. Therefore it is fiery (Conclusion)

References :

• A History of Hindu Civilisation During British Rule (1896) Vol 2 - By Pramatha Nath Bose