The Navya-Nyāya or Neo-Logical "darśana (view, system, or school) of "Indian logic and "Indian philosophy was founded in the 13th century "CE by the philosopher "Gangeśa Upādhyāya of "Mithila and continued by "Raghunatha Siromani. It was a development of the classical "Nyāya darśana. Other influences on Navya-Nyāya were the work of earlier philosophers "Vācaspati Miśra (900–980 CE) and "Udayana (late 10th century). It remained active in India through to the 18th 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. In his book, Gangeśa both addressed some of those criticisms and – more important – critically examined the Nyāya darśana himself. He held that, while Śrīharśa had failed to successfully challenge the Nyāya realist "ontology, his and Gangeśa's own criticisms brought out a need to improve and refine the logical and linguistic tools of Nyāya thought, to make them more rigorous and precise.
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. The results, especially his analysis of "cognition, were taken up and used by other darśanas.
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-)perception (pratyakşa), inference (anumāna), comparison or similarity (upamāna), and testimony (sound or word; "śabda).
This later school began around "eastern India and "Bengal, and developed theories resembling modern logic by the 16th century, such as "Gottlob Frege's "distinction between sense and reference of proper names" and his "definition of number," as well as the Navya-Nyaya theory of "restrictive conditions for universals" anticipating some of the developments in modern "set theory. "Udayana in particular developed theories on "restrictive conditions for universals" and ""infinite regress" that anticipated aspects of modern set theory. According to Kisor Kumar Chakrabarti:
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. [...] In this section the discussion will center around some of the 'restrictive conditions for universals (jatibadhaka) proposed by Udayana. [...] Another restrictive condition is "anavastha or vicious infinite regress. According to this restrictive condition, no universal (jati) can be admitted to exist, the admission of which would lead to a vicious infinite regress. As an example Udayana says that there can be no universal of which every universal is a member; for if we had any such universal, then, by hypothesis, we have a given totality of all universals that exist and all of them belong to this big universal. But this universal is itself a universal and hence (since it cannot be a member of itself, because in Udayana's view no universal can be a member of itself) this universal too along with other universals must belong to a bigger universal and so on ad infinitum. What Udayana says here has interesting analogues in modern set theory in which it is held that a set of all sets (i.e., a set to which every set belongs) does not exist.
This paper consists of three parts. The first part deals with Frege's distinction between sense and reference of proper names and a similar distinction in Navya-Nyaya logic. In the second part we have compared Frege's definition of number to the Navya-Nyaya definition of number. 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.
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