>Goszei at 08:43, 15 February 2021

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The development of '''Indian logic''' dates back to the ''[[anviksiki]]'' of Medhatithi Gautama (c. 6th century BCE); the [[Vyakarana|Sanskrit grammar]] rules of [[Pāṇini]] (c. 5th century BCE); the [[Vaisheshika]] school's analysis of [[atomism]] (c. 6th century BCE to 2nd century BCE); the analysis of [[inference]] by [[Nyāya Sūtras|Gotama]] (c. 6th century BC to 2nd century CE), founder of the [[Nyaya]] school of [[Hindu philosophy]]; and the [[tetralemma]] of [[Nagarjuna]] (c. 2nd century CE).

[[Indian philosophy|Indian]] logic stands as one of the three original traditions of [[logic]], alongside the [[Organon|Greek]] and the [[Chinese logic]]. The Indian tradition continued to develop through early to modern times, in the form of the [[Navya-Nyāya]] school of logic.

==Origins==
{{Rquote|right|"Who really knows? <br/>Who will here proclaim it? <br/>Whence was it produced? Whence is this creation? <br/>The gods came afterwards, with the creation of this universe. <br/>Who then knows whence it has arisen?"|[[Nasadiya Sukta]], concerns the [[origin of the universe]], [[Rig Veda]], ''10:129-6'' <ref name="Kramer1986">{{cite book|author=Kenneth Kramer|title=World Scriptures: An Introduction to Comparative Religions|url=https://books.google.com/books?id=RzUAu-43W5oC&pg=PA34|date=January 1986|publisher=Paulist Press|isbn=978-0-8091-2781-8|pages=34–}}</ref><ref name="Christian2011">{{cite book|author=David Christian|title=Maps of Time: An Introduction to Big History|url=https://books.google.com/books?id=7RdVmDjwTtQC&pg=PA18|date=1 September 2011|publisher=University of California Press|isbn=978-0-520-95067-2|pages=18–}}</ref><ref name="Singh2008">{{cite book|author=Upinder Singh|title=A History of Ancient and Early Medieval India: From the Stone Age to the 12th Century|url=https://books.google.com/books?id=H3lUIIYxWkEC&pg=PA206|year=2008|publisher=Pearson Education India|isbn=978-81-317-1120-0|pages=206–}}</ref>}}
The [[Nasadiya Sukta]] of the ''[[Rigveda]]'' ([[Mandala 10|RV 10]].129) contains [[ontological]] speculation in terms of various logical divisions that were later recast formally as the four circles of ''[[Tetralemma|catuskoti]]'': "A", "not A", "A and 'not A'", and "not A and not not A".<ref>[[Subhash Kak|S. Kak]] (2004). ''The Architecture of Knowledge''. CSC, Delhi.</ref>

Medhatithi Gautama (c. 6th century BCE) founded the ''anviksiki'' school of logic.<ref>S. C. Vidyabhusana (1971). ''A History of Indian Logic: Ancient, Mediaeval, and Modern Schools''.</ref> The ''[[Mahabharata]]'' (12.173.45), around the 4th century BCE to 4th century CE, refers to the ''anviksiki'' and ''tarka'' schools of logic. {{IAST|[[Pāṇini]]}} (c. 5th century BCE) developed a form of logic (to which [[Boolean logic]] has some similarities) for his formulation of [[Vyakarana|Sanskrit grammar]]. Logic is described by [[Chanakya]] (c. 350-283 BCE) in his ''[[Arthashastra]]'' as an independent field of inquiry ''anviksiki''.<ref>R. P. Kangle (1986). ''The Kautiliya Arthashastra'' (1.2.11). Motilal Banarsidass.</ref>

==The schools==
===Vaisheshika===
{{Main|Vaisheshika}}
Vaisheshika, also Vaisesika, (Sanskrit: वैशेषिक) is one of the six [[Hindu philosophy|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 [[Kanada (philosopher)|Kanāda]] (or Kana-bhuk, literally, atom-eater) from around the 2nd century BCE.

===Catuskoti===
{{Main|Catuskoti}}
In the 2nd century, the [[Buddhist philosophy|Buddhist]] philosopher [[Nagarjuna]] refined the ''Catuskoti'' form of logic. 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]].

===Nyaya===
{{Main|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 [[Akṣapāda Gotama|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 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===
{{Further|Anekantavada|Syadvada|Jain philosophy}}
[[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 [[:Category:Jain texts|Jain texts]], deliberative exhortations on any subject in all its facts, may they be constructive or obstructive, inferential or analytical, enlightening or destructive.<ref>{{cite book | last =Hughes | first =Marilynn | title =The voice of Prophets | publisher =Lulu.com | year =2005 | location =Morrisville, North Carolina | series =Volume 2 of 12 | isbn =1-4116-5121-9 }} P. 590{{self-published source|date=February 2021}}</ref>{{self-published inline|date=February 2020}} The Jains have doctrines of [[Relativism|relativity]] used for logic and reasoning:
*[[Anekantavada|Anekāntavāda]] – the theory of relative pluralism or manifoldness;
*[[Syadvada|Syādvāda]] – the theory of conditioned predication and;
*[[Nayavada|Nayavāda]] – The theory of partial standpoints.

These [[Jain philosophy|Jain philosophical]] concepts made most important contributions to the ancient [[Indian philosophy]], especially in the areas of skepticism and relativity.<ref>*{{cite book | last =McEvilley | first =Thomas | title =The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies | publisher =Allworth Communications , Inc. | year =2002 | location =New York | isbn =1-58115-203-5 }} p335"</ref>

Following is the list of Jain philosophers who contributed to Jain Logic:
*[[Kundakunda]] (2nd century CE), exponent of Jain mysticism and [[Anekantavada#Nayav.C4.81da|Jain nayas]] dealing with the nature of the soul and its contamination by matter, author of [[Pancastikayasara|Pañcāstikāyasāra]] (Essence of the Five Existents), the [[Pravachanasara|Pravachanasāra]] (Essence of the Scripture) and the [[Samayasara|Samayasāra]] (Essence of the Doctrine).
*[[Umasvati|Umāsvāti]] or Umasvami (2nd century CE), author of first Jain work in Sanskrit, [[Tattvartha Sutra|Tattvārthasūtra]], expounding the [[Jain philosophy]] in a most systematized form acceptable to all sects of Jainism.
*[[Siddhasen Diwakar|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]]suri (8th century CE), a Jaina thinker, author and great proponent of [[Anekantavada|anekāntavāda]] and classical yoga, as a soteriological system of meditation in Jaina context. His works include {{IAST|Ṣaḍdarśanasamuccaya}} and Yogabindu.
*[[Hemacandra|Aacharya Hemacandra]] (1089–1172 CE) - a Jaina thinker, author, historian, grammarian and logician. His works include [[Yogaśāstra]] and [[Hemachandra#Trishashthi-Shalaka-Purusha|Trishashthi Shalaka Purusha charitra]].
*[[Yasovijaya|Mahopadhya Yaśovijayaji]] (1624–88 CE) – Jain logician and considered as intellectual giant to contribute to Jaina philosophy.
*[[Acharya Mahapragya]] (1920–2010 CE);– Jain logician and considered as intellectual giant and encyclopedia to contribute to Jaina philosophy. The Eminent Scholar of Philosophy, Dr. 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 the one of the best work on the subject in modern era. Acharya Mahapragya is known for his enlightening discourses. 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 mainly include ‘Jain Darshan-Mannan aur Mimansa’, ‘Jain Dharma Aur Sanskriti’, ‘Jain Darshan and Anekantvad’, ‘Jain Dharma aur Darshan’, and many more.

===Buddhist logic===
{{Main|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 highly formal scheme of the [[Hetucakra]] (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===
{{Main|Navya-Nyāya}}
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 (India)|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 [[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 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).

This later school began around [[East India|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]].<ref>{{citation|title=Some Comparisons Between Frege's Logic and Navya-Nyaya Logic|author=Kisor Kumar Chakrabarti|journal=Philosophy and Phenomenological Research|volume=36|issue=4|date=June 1976|pages=554–563|publisher=International Phenomenological Society|jstor=2106873|quote=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.}}</ref> Udayana in particular developed theories on "restrictive conditions for universals" and "[[Infinity|infinite]] regress" that anticipated aspects of modern set theory. According to Kisor Kumar Chakrabarti:<ref>{{citation|title=Some Comparisons Between Frege's Logic and Navya-Nyaya Logic|author=Kisor Kumar Chakrabarti|journal=Philosophy and Phenomenological Research|volume=36|issue=4|date=June 1976|pages=554–563|publisher=International Phenomenological Society|jstor=2106873}}</ref>

{{quote|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 [[Henry Thomas Colebrooke|Henry T. Colebrooke's]] ''The Philosophy of the Hindus: On the Nyaya and Vaisesika Systems'' in 1824,<ref>Colebrooke, Henry Thomas "Essays on the Religion and Philosophy of the Hindus" London: Williams and Norgate, 1858 available online at https://archive.org/details/essaysonreligio00colegoog</ref> 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. [[Max Mueller]] contributed an appendix to the 1853 edition of [[William Thomson (bishop)|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 only, by Hindus and Greeks."<ref>Mueller, Max "Of Indian Logic" Appendix To Thomson's Laws of Thought, London: Longmans Green and Co 1853 online at https://archive.org/details/anoutlinenecess03thomgoog</ref>

Jonardon Ganeri has observed that this period{{which|date=August 2016}} saw [[George Boole]] (1815-1864) and [[Augustus De Morgan]] (1806-1871) make their pioneering applications of algebraic ideas to the formulation of logic (such as [[algebraic logic]] and [[Boolean logic]]), and has 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 propositional logic are likely to have stimulated their willingness to look outside the system.

Indian logic attracted the attention of many Western scholars, and had an influence on pioneering 19th-century logicians such as [[Charles Babbage]] (1791-1871), [[Augustus De Morgan]], and particularly [[George Boole]], as confirmed by Boole's wife [[Mary Everest Boole]] in an "open letter to Dr Bose" titled "Indian Thought and Western Science in the Nineteenth Century" written in 1901:<ref>Boole, Mary Everest "Collected Works" eds E M Cobham and E S Dummer London, Daniel 1931. Letter also published in the Ceylon National Review in 1909, and published as a separate pamphlet "The Psychologic Aspect of Imperialism" in 1911.</ref><ref>{{citation|title= Indian logic: a reader|author= Jonardon Ganeri|publisher= [[Routledge]] | location = Richmond, Surrey | orig-year= 2001 | year = 2013|isbn= 9781136119385 |page= vii | editor1-last = Ganeri | editor1-first = Jonardon | quote = The modern study of classical Indian systems of logic began with H. T. Colebrook's "discovery" of the Hindu syllogism - a schema for correct reasoning as described in the early Indian texts. The report of his discovery to the Royal Asiatic Society in 1824 led to a flurry of interest in Indian logic in the next thirty years, attracting the attention of even the best logicians of the time, people like Boole and De Morgan.
}}</ref>

De Morgan himself wrote in 1860 of the significance of Indian logic: "The two races which have founded the mathematics, those of the Sanscrit and Greek languages, have been the two which have independently formed systems of logic."<ref>
De Morgan, Augustus "Syllabus of a proposed system of logic", London : Walton and Maberly 1860; online at https://archive.org/details/syllabusofpropos00demoiala
</ref>

Mathematicians became 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. [...] But the present trend in mathematics is clearly in the direction of a return to the Greek standpoint; we now look upon each branch of mathematics as determining its own characteristic domain of quantities."<ref>Weyl, Hermann "The Theory of Groups and Quantum Mechanics", 1950, p.viii; online at https://books.google.com/books?id=jQbEcDDqGb8C</ref>

==See also==
*
*
*[[Tarka-Sangraha]]
*[[Debates in ancient India]]
*[[Jaina seven-valued logic|Seven valued logic]]

==Notes==
{{reflist}}

==References==
* Ganeri, Jonardon 2004. ''Indian Logic''. in: Gabbay, Dov & Woods, John (eds.),''Greek, Indian and Arabic Logic'', Volume I of the ''Handbook of the History of Logic'', Amsterdam: Elsevier, pp. 309–396.
* Ganeri, Jonardon (ed.) 2001. ''Indian Logic. A Reader''. New York: Routledge Curzon.
* Matilal, Bimal Krishnan 1985. ''Logic, Language, and Reality. An Introduction to Indian Philosophical Studies''. Delhi: Motilal Barnassidas, {{ISBN|0-19-566658-5}}
* Matilal, Bimal Krishnan 1998. ''The Character of Logic in India'', edited by Jonardon Ganeri and Heeraman Tiwari, Albany: State University of New York Press.
* Perrett, Roy (ed.) 2001. ''Logic and Language: Indian Philosophy'', New York: Routledge.

==External links==
*{{cite SEP |url-id=logic-india |title=Logic in Classical Indian Philosophy |last=Gillon |first=Brendan}}
* [https://www.ontology.co/indian-philosophy.htm Indian Logic and Ontology] An annotated bibliography
* [https://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?]
* Gillon, Brendan. "[http://www.rep.routledge.com/article/F045 Indian theories of inference (subscription)]", in the [[Routledge Encyclopedia of Philosophy]], 1998.
* Peckhaus, Volker. "[https://web.archive.org/web/20060209005339/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)]{{dead link|date=November 2017 |bot=InternetArchiveBot |fix-attempted=yes }}''. ''Proc. Bombay Logic Conference'', 2005.
*[https://archive.org/details/historyofthemedi031568mbp Vidhabhusana, Satis Chandra (1907). History of the Mediaeval School of Indian Logic. Calcutta University.]

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Indian logic - Revision history

>Goszei at 08:43, 15 February 2021