Indian logic

The development of Indian logic can be said to date back to the "anviksiki" of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 2nd century BCE); the analysis of inference by Gotama (c. 2nd century BCE), founder of the Nyaya school of Hindu philosophy; and the tetralemma of Nagarjuna (c. 2nd century CE). Indian logic stands as one of the three original traditions of logic, alongside the Greek and Chinese traditions.

Origins

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". [S. Kak (2004). "The Architecture of Knowledge". CSC, Delhi.]

Medhatithi Gautama (c. 6th century BCE) founded the "anviksiki" school of logic. [S. C. Vidyabhusana (1971). "A History of Indian Logic: Ancient, Mediaeval, and Modern Schools".] The "Mahabharata" (12.173.45), around the 5th century BCE, refers to the "anviksiki" and "tarka" schools of logic. IAST|Pāṇini (c. 5th century BCE) developed a form of logic which had some similarities to Boolean logic for his formulation of Sanskrit grammar. Logic is described by Chanakya (c. 350-283 BCE) in his "Arthashastra" as an independent field of inquiry "anviksiki". [R. P. Kangle (1986). "The Kautiliya Arthashastra" (1.2.11). Motilal Banarsidass.]

Vaisheshika

Vaisheshika, also Vaisesika, (Sanskrit: वैशॆषिक) is one of the six Hindu schools of Indian philosophy. It came to be closely associated with the Hindu school of logic, Nyaya. Vaisheshika espouses a form of atomism and postulates that all objects in the physical universe are reducible to a finite number of atoms. Originally proposed by Kanāda (or Kana-bhuk, literally, atom-eater) from around the 2nd century BCE.

Tetralemma

In the 2nd century, the Buddhist philosopher Nagarjuna developed the "tetralemma" form of logic, also known as "catuskoti".

Nyaya

"Nyāya" ("ni-āyá", literally "recursion", used in the sense of "syllogism, inference") is the name given to one of the six orthodox or "astika" schools of Hindu philosophy — specifically the school of logic.

The Nyaya school of philosophical speculation is based on texts known as the "Nyaya Sutras", which were written by Gotama in around the 2nd century CE. The most important contribution made by the Nyaya school to modern Hindu thought is its methodology. This methodology is based on a system of logic that has subsequently been adopted by most of the other Indian schools (orthodox or not), much in the same way that Western science and philosophy can be said to be largely based on Aristotelian 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 , deliberative exhortations on any subject in all its facts, may they be constructive or obstructive, inferential or analytical, enlightening or destructive. [cite book | last =Hughes | first =Marilynn | title =The voice of Prophets | publisher =Lulu.com | date =2005 | location =Morrisville, North Carolina | series =Volume 2 of 12 | isbn =1411651219 P. 590] In the process, the Jains came out with their 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. [*cite book | last =McEvilley | first =Thomas | title =The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies | publisher =Allworth Communications , Inc | date =2002 | location =New York | isbn =1581152035 p335"]

Following is the list of Jain philosophers who contributed to Jain Logic:
*Kundakunda (2nd Century CE), exponent of Jain mysticism and Jain nayas dealing with the nature of the soul and its contamination by matter, author of Pañcāstikāyasāra (Essence of the Five Existents), the Pravacanasāra (Essence of the Scripture) and the 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)
*Haribhadra (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 IAST|Ṣaḍdarśanasamuccaya and Yogabindu.
*Hemacandra (1089–1172 CE) - a Jaina thinker, author, historian, grammarian and logician. His works include Yogaśāstra and Trishashthishalakapurushacharitra.
*Yaśovijaya (1624–88 CE) – Jain logician and considered last intellectual giant to contribute to Jaina philosophy.

Buddhist logic

Indian Buddhist logic (called Pramana) flourished from about 500 CE up to 1300 CE. The three main authors of Buddhist logic are Vasubandhu (400 - 800 CE), Dignāga (480 - 540 CE), and Dharmakīrti (600 - 660 CE). The most important theoretical achievements are the doctrine of Trairūpya (Skrt. त्रैरूप्य) and the hiqhly formal scheme of the Hetuchakra (Skrt. हेतुचक्र) ("Wheel of Reasons") given by Dignāga. There is a still living tradition of Buddhist logic in the Tibetan Buddhist traditions, where logic is an important part of the education of monks.

Navya-Nyaya

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

Gangeśa's book Tattvacintāmani ("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 importantly – critically examined the Nyāya darśana himself. He held that, while Śrīharśa had failed successfully to 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 or perception (pratyakşa), inference (anumāna), comparison or similarity (upamāna), and testimony (sound or word; śabda).

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, culminating in Henry T. Colebrooke's "The Philosophy of the Hindus: On the Nyaya and Vaisesika Systems" in 1824 (in Ganeri, 2001), which provided an analysis of inference and comparison to the received Aristotelian logic, resulting in the observation that the Aristotelian syllogism could not account for the Indian syllogism. Jonardon Ganeri observed that this period saw George Boole and Augustus De Morgan make their pioneering applications of algebraic ideas to the formulation of logic (such as Algebraic logic and Boolean logic), and suggested that these figures were likely to be aware of these studies in xeno-logic, and further that their acquired awareness of the shortcomings of traditional logic are likely to have stimulated their willingness to look outside the system.

Mathematicians are now aware of the influence of Indian mathematics on the European. For example, Hermann Weyl wrote: "Occidental mathematics has in past centuries broken away from the Greek view and followed a course which seems to have originated in India and which has been transmitted, with additions, to us by the Arabs; in it the concept of number appears as logically prior to the concepts of geometry." (Weyl, 1929)

Notes

References

* B. K. Matilal. "Logic, Language, and Reality: An Introduction to Indian Philosophical Studies". Delhi, 1985. ISBN 0-19-566658-5
* B. S. Gillon. " [http://www.rep.routledge.com/article/F045 Indian theories of inference (subscription)] ", in the Routledge Encyclopedia of Philosophy, 1998.
* J. Ganeri, editor. "Indian Logic: A Reader". Routledge Curzon, 2001
* V. Peckhaus. " [http://www-fakkw.upb.de/institute/philosophie/Personal/Peckhaus/Texte_zum_Download/dignaga.pdf Dignaga’s Logic of Invention] ". In Ivor Grattan-Guinness, editor, "History of the Mathematical Sciences", 2004.
* V. V. S. Sarma. [http://logic2005.hss.iitb.ac.in/pdfs/VVSSarma_Tutorial.pdf "Indian Systems of Logic (Nyaya): A Survey" (PDF)] ". "Proc. Bombay Logic Conference", 2005.

ee also

*Dharmakirti
*Dignāga

External links

* [http://nyaya.darsana.org Indian Logic Forum]
* [http://www.formalontology.it/indian-philosophy.htm Indian Logic and Ontology]
* [http://arxiv.org/abs/physics/0505172 Aristotle and Gautama on Logic and Physics]
* [http://pioneer.netserv.chula.ac.th/~hsoraj/web/APPEND.html Asian Philosophy and Critical Thinking: Divergence or Convergence?]