‘The School of Reasoning’ (also known as Ānvīkṣikī, and Tarkaśāstra), listed in modern works as one of the six darśanas or ‘schools of philosophy’, where it is paired with the Vaiśeṣika school. Drawing on Vedic concerns with formal debate, and valid means of proof, the foundational Nyāya text is Gautama's Nyāyasūtra (probably a composite text, redacted between 250–450 ce). As important for the subsequent tradition are two other texts: the first extant commentary on Gautama, Vātsyāyana's Nyāyabhāṣya (second half of 5th century ce), and Uddyotakara Bhāradvāja's Nyāyavārtikka (‘Elucidation of Nyāya’) (6th century), a defence of the system in response to Buddhist logic. Other major Nyāya works include Vācaspati Miśra's commentary on Uddyotakara, Nyāyavārtikka (‘Gloss on the True Intention of the Elucidation of Nyāya’) (c.960 ce), and Jayanta Bhaṭṭa's non- commentarial Nyāyamañjarī (‘Blooms of Nyāya’) (9th–10th century), dealing with Nyāya vis à vis Buddhism and the Mīmāṃsaka darśana.
A convergence of the Nyāya and Vaiśeṣika traditions is evident from the 12th century onwards, initially in the commentaries of Udayana (12th century), who continues the debate with the Buddhists in works such as Ātmatattvaviveka (‘The Discernment of the Reality of Self’), and Nyāyakusumāñjali (‘A Handful of Blooms of Nyāya’), defending the existence of both a permanent self and a God (īśvara). By the 14th century, a distinction was being drawn between Old Nyāya (prācīna-nyāya), and Navya-Nyāya (‘New Nyāya’), the analytical side of the reformulated and synthesized tradition. Navya-Nyāya, with its increased emphasis on the pramāṇas (valid means of knowledge), was firmly established in the Tattvacintāmaṇi (‘Thought-Jewel of Reality’) of Gaṅgeśa. Gaṅgeśa's son, Vardhamāna, was also a notable commentator, as was the former's disciple, Jayadeva Pakṣadhara, who established a Navya-Nyāya subschool based on his master's works. Further diversification followed with the creation of a Bengali sampradāya, carried forward by such authors as Raghunātha and his commentator, Gadādhara.
The principal concern of the classical Naiyāyikas was to develop and defend an epistemology and method of reasoning capable of providing certain knowledge about the nature of the world (including the reality of both a permanent self and God—often identified as Śiva), since it was precisely such knowledge which was thought to result in release (apavarga) from suffering. This approach was systematized into a list of sixteen topics, or categories of debate (padārthas), of which the first two, pramāṇa (the means of valid knowledge or cognition), and prameya (the objects of valid knowledge, i.e. what is known, a category subsuming the seven padārthas of the Vaiśeṣika system), were the most crucial. Nyāya recognized four pramāṇas: perception (pratyakṣa), inference (anumāna), analogy/comparison (upamāna), and verbal testimony (śabda). Much attention was paid to the manner in which the Naiyāyikas attempted a formal proof of inference through an elaborate five-part syllogism. The acquisition of knowledge through the pramāṇas, logic, and debate was supported and reinforced by various yogic practices and ethical restraints (yama). See also Vaiśeṣika.