Indian logic

Followers of Nyaya believed that obtaining valid knowledge was the only way to obtain release from suffering. They therefore took great pains to identify valid sources of knowledge and to distinguish these from mere false opinions. According to the Nyaya school, there are exactly four sources of knowledge (pramanas): perception, inference, comparison and testimony. Knowledge obtained through each of these can, of course, still be either valid or invalid. 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. In this sense, Nyaya is probably the closest Indian equivalent to contemporary analytic philosophy.

Jain logic

Jainism made its own unique contribution to this mainstream development of logic by also occupying itself with the basic epistemological issues, namely, with those concerning the nature of knowledge, how knowledge is derived, and in what way knowledge can be said to be reliable. Jain logic developed and flourished from 6th century BCE to 17th century CE. According to Jains, the ultimate principle should always be logical and no principle can be devoid of logic or reason. 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.^{[7][self-published source?]} The Jains have doctrines of relativity used for logic and reasoning:

• Anekāntavāda – the theory of relative pluralism or manifoldness;
• Syādvāda
   – the theory of conditioned predication and;
• Nayavāda – The theory of partial standpoints.

These Jain philosophical concepts made most important contributions to the ancient Indian philosophy, especially in the areas of skepticism and relativity.^[8]

Following is the list of Jain philosophers who contributed to Jain Logic:

• Samayasāra
  (Essence of the Doctrine).
• Umāsvāti or Umasvami (2nd century CE), author of first Jain work in Sanskrit, Tattvārthasūtra, expounding the Jain philosophy
  in a most systematized form acceptable to all sects of Jainism.
• Siddhasena Divākara
  (5th century CE), Jain logician and author of important works in Sanskrit and Prakrit, such as, Nyāyāvatāra (on Logic) and Sanmatisūtra (dealing with the seven Jaina standpoints, knowledge and the objects of knowledge).
• Akalanka (8th century CE), a Jain logician whose Sanskrit-language works are seen as landmarks in Indian logic; called the "Master of Jain logic".
• Haribhadrasuri (8th century CE), a Jaina thinker, author and great proponent of anekāntavāda and classical yoga, as a soteriological system of meditation in Jaina context. His works include Ṣaḍdarśanasamuccaya and Yogabindu.
• Aacharya Hemacandra (1089–1172 CE) - a Jaina thinker, author, historian, grammarian and logician. His works include Yogaśāstra and Trishashthi Shalaka Purusha charitra
  .
• Mahopadhya Yaśovijayaji
  (1624–88 CE) – Jain logician.
• Acharya Mahapragya (1920–2010 CE);– Jain logician. The scholar of Philosophy Daya Krishna has recognized Acharya Shri Mahapragya as the most knowledgeable person on the subject of Jain Logic. His book "New Dimensions in Jaina Logic" is one of the best works on the subject in modern era. In 1975, he was specially invited to deliver a series of nine lectures on Jain Logic at the University of Rajasthan
  at Jaipur. The University published these lectures in the form of a book entitled "Jain Nyay Ka Vikas". His books on the subjects include "Jain Darshan-Mannan aur Mimansa", "Jain Dharma Aur Sanskriti", "Jain Darshan and Anekantvad", "Jain Dharma aur Darshan".

The Navya-Nyāya or Neo-Logical darśana (school) of Indian philosophy was founded in the 13th century CE by the philosopher

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 or perception (pratyakşa), inference (anumāna), comparison or similarity (

This later school began around eastern India and Bengal, and developed theories resembling modern logic, 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.^[9] 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:^[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. [...] 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 got 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.

Influence of Indian logic on modern logic

In the late 18th-century British scholars began to take an interest in Indian philosophy and discovered the sophistication of the Indian study of inference. This process culminated in