The Indian tradition continued to develop through early to modern times, in the form of the Navya-Nyāya school of logic.
Who then knows whence it has arisen?The Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti: "A", "not A", "A and 'not A'", and "not A and not not A".
The Catuskoti is also often glossed Tetralemma (Greek) which is the name for a largely comparable, but not equatable, 'four corner argument' within the tradition of Classical logic.
As a result, Nyaya scholars again went to great pains to identify, in each case, what it took to make knowledge valid, in the process creating a number of explanatory schemes.
Thus one finds in the Jain texts, deliberative exhortations on any subject in all its facts, may they be constructive or obstructive, inferential or analytical, enlightening or destructive.
The Navya-Nyāya or Neo-Logical darśana (school) of Indian philosophy was founded in the 13th century CE by the philosopher Gangesha Upadhyaya of Mithila.
Other influences on Navya-Nyāya were the work of earlier philosophers Vācaspati Miśra (900–980 CE) and Udayana (late 10th century).
Gangeśa's book Tattvacintāmaṇi ("Thought-Jewel of Reality") was written partly in response to Śrīharśa's Khandanakhandakhādya, a defence of Advaita Vedānta, which had offered a set of thorough criticisms of Nyāya theories of thought and language.
Tattvacintāmani dealt with all the important aspects of Indian philosophy, logic, set theory, and especially epistemology, which Gangeśa examined rigorously, developing and improving the Nyāya scheme, and offering examples.
Navya-Nyāya developed a sophisticated language and conceptual scheme that allowed it to raise, analyse, and solve problems in logic and epistemology.
It systematised all the Nyāya concepts into four main categories: sense or perception (pratyakşa), inference (anumāna), comparison or similarity (upamāna), and testimony (sound or word; śabda).
According to Kisor Kumar Chakrabarti:[10] In the third part we have shown how the study of the so-called 'restrictive conditions for universals' in Navya-Nyaya logic anticipated some of the developments of modern set theory.
According to this restrictive condition, no universal (jati) can be admitted to exist, the admission of which would lead to a vicious infinite regress.
Max Mueller contributed an appendix to the 1853 edition of Thomson's Outline of the Laws of Thought, in which he placed Greek and Indian logic on the same plane: "The sciences of Logic and Grammar were, as far as history allows us to judge, invented or originally conceived by two nations, Hindus and Greeks.