The development of Indian logic dates back to the ''

anviksiki Ānvīkṣikī is a term in Sanskrit denoting roughly the "science of inquiry" and it should have been recognized in India as a distinct branch of learning as early as 650 BCE. However, over the centuries its meaning and import have undergone co ...

'' of Medhatithi Gautama (c. 6th century BCE); the

Sanskrit grammar The grammar of the Sanskrit language has a complex verbal system, rich nominal declension, and extensive use of compound nouns. It was studied and codified by Sanskrit grammarians from the later Vedic period (roughly 8th century BCE), culminati ...

rules of

Pāṇini , era = ;;6th–5th century BCE , region = Indian philosophy , main_interests = Grammar, linguistics , notable_works = ' ( Classical Sanskrit) , influenced= , notable_ideas= Descriptive linguistics (Devana ...

(c. 5th century BCE); the Vaisheshika school's analysis of

atomism Atomism (from Greek , ''atomon'', i.e. "uncuttable, indivisible") is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms. References to the concept of atomism and its atom ...

(c. 6th century BCE to 2nd century BCE); the analysis of

inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''wikt:infer, infer'' means to "carry forward". Inference is theoretically traditionally divided into deductive reasoning, deduction and in ...

by Gotama (c. 6th century BC to 2nd century CE), founder of the

Nyaya (Sanskrit: न्याय, ''nyā-yá''), literally meaning "justice", "rules", "method" or "judgment",Hindu philosophy Hindu philosophy encompasses the philosophies, world views and teachings of Hinduism that emerged in Ancient India which include six systems ('' shad-darśana'') – Samkhya, Yoga, Nyaya, Vaisheshika, Mimamsa and Vedanta.Andrew Nicholson ( ...

; and the tetralemma of

Nagarjuna Nāgārjuna . 150 – c. 250 CE (disputed)was an Indian Mahāyāna Buddhist thinker, scholar-saint and philosopher. He is widely considered one of the most important Buddhist philosophers.Garfield, Jay L. (1995), ''The Fundamental Wisdom of ...

(c. 2nd century CE).

Indian Indian or Indians may refer to: Peoples South Asia * Indian people, people of Indian nationality, or people who have an Indian ancestor ** Non-resident Indian, a citizen of India who has temporarily emigrated to another country * South Asia ...

logic stands as one of the three original traditions of

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...

, alongside the

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

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

The

Nasadiya Sukta The Nāsadīya Sūkta (after the incipit ', or "not the non-existent"), also known as the Hymn of Creation, is the 129th hymn of the 10th mandala of the Rigveda (10:129). It is concerned with cosmology and the origin of the universe. Nasadiya Su ...

of the ''

Rigveda The ''Rigveda'' or ''Rig Veda'' ( ', from ' "praise" and ' "knowledge") is an ancient Indian collection of Vedic Sanskrit hymns (''sūktas''). It is one of the four sacred canonical Hindu texts ('' śruti'') known as the Vedas. Only on ...

'' ( RV 10.129) contains

ontological In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exi ...

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". Medhatithi Gautama (c. 6th century BCE) founded the ''anviksiki'' school of logic. The ''

Mahabharata The ''Mahābhārata'' ( ; sa, महाभारतम्, ', ) is one of the two major Sanskrit epics of ancient India in Hinduism, the other being the '' Rāmāyaṇa''. It narrates the struggle between two groups of cousins in the K ...

'' (12.173.45), around the 4th century BCE to 4th century CE, refers to the ''anviksiki'' and ''tarka'' schools of logic. (c. 5th century BCE) developed a form of logic (to which

Boolean logic In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas ...

has some similarities) for his formulation of

. Logic is described by

Chanakya Chanakya ( Sanskrit: चाणक्य; IAST: ', ; 375–283 BCE) was an ancient Indian polymath who was active as a teacher, author, strategist, philosopher, economist, jurist, and royal advisor. He is traditionally identified as Kauṭi ...

(c. 350-283 BCE) in his ''

Arthashastra The ''Arthashastra'' ( sa, अर्थशास्त्रम्, ) is an Ancient Indian Sanskrit treatise on statecraft, political science, economic policy and military strategy. Kautilya, also identified as Vishnugupta and Chanakya, is ...

'' as an independent field of inquiry ''anviksiki''.

The schools

Vaisheshika

Vaisheshika, also Vaisesika, (Sanskrit: वैशेषिक) is one of the six Hindu schools of

Indian philosophy Indian philosophy refers to philosophical traditions of the Indian subcontinent. A traditional Hindu classification divides āstika and nāstika schools of philosophy, depending on one of three alternate criteria: whether it believes the Veda ...

. 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.

Catuskoti

In the 2nd century, the

Buddhist Buddhism ( , ), also known as Buddha Dharma and Dharmavinaya (), is an Indian religion or philosophical tradition based on teachings attributed to the Buddha. It originated in northern India as a -movement in the 5th century BCE, and ...

philosopher

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 Classical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this class ...

Nyaya

''Nyāya'' (''ni-āyá'', literally "recursion", used in the sense of "

syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be tru ...

, 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 (Sanskrit: न्याय, ''nyā-yá''), literally meaning "justice", "rules", "method" or "judgment",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 A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

that has subsequently been adopted by most of the other Indian schools (orthodox or not), much in the same way that

Western philosophy Western philosophy encompasses the philosophy, philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre-Socratic p ...

can be said to be largely based on

Aristotelian logic In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...

. 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 Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United ...

Jain logic

Jainism Jainism ( ), also known as Jain Dharma, is an Indian religion. Jainism traces its spiritual ideas and history through the succession of twenty-four tirthankaras (supreme preachers of ''Dharma''), with the first in the current time cycle bein ...

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 Jain literature (Sanskrit: जैन साहित्य) refers to the literature of the Jain religion. It is a vast and ancient literary tradition, which was initially transmitted orally. The oldest surviving material is contained in the c ...

, deliberative exhortations on any subject in all its facts, may they be constructive or obstructive, inferential or analytical, enlightening or destructive. The Jains have doctrines of relativity used for logic and reasoning: *

Anekāntavāda ( hi, अनेकान्तवाद, "many-sidedness") is the Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects. According to Jainism ...

– 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

, especially in the areas of skepticism and relativity. Following is the list of Jain philosophers who contributed to Jain Logic: *

Kundakunda Kundakunda was a Digambara Jain monk and philosopher, who likely lived in the 2nd CE century CE or later. His date of birth is māgha māsa, śukla pakṣa, pañcamī tithi, on the day of Vasant Panchami. He authored many Jain texts such ...

(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 Pravachanasāra (Essence of the Scripture) and the

Samayasāra ''Samayasāra'' (''The Nature of the Self'') is a famous Jain text composed by '' Acharya Kundakunda'' in 439 verses. Its ten chapters discuss the nature of '' Jīva'' (pure self/soul), its attachment to Karma and Moksha (liberation). ''Samay ...

(Essence of the Doctrine). * Umāsvāti or Umasvami (2nd century CE), author of first Jain work in Sanskrit, Tattvārthasūtra, expounding the

Jain philosophy Jain philosophy refers to the ancient Indian philosophical system found in Jainism. One of the main features of Jain philosophy is its dualistic metaphysics, which holds that there are two distinct categories of existence, the living, consciou ...

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) * Haribhadrasuri (8th century CE), a Jaina thinker, author and great proponent of

anekāntavāda ( hi, अनेकान्तवाद, "many-sidedness") is the Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects. According to Jainism ...

and classical yoga, as a soteriological system of meditation in Jaina context. His works include and Yogabindu. * Aacharya Hemacandra (1089–1172 CE) - a Jaina thinker, author, historian, grammarian and logician. His works include

Yogaśāstra ''Yogaśāstra'' (''lit.'' "Yoga treatise") is a 12th-century Sanskrit text by Hemachandra on Svetambara Jainism. It is a treatise on the "rules of conduct for laymen and ascetics", wherein "yoga" means "ratna-traya" (three jewels), i.e. right be ...

and Trishashthi Shalaka Purusha charitra. * 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 University of Rajasthan is a public and state university in Jaipur, Rajasthan, India and is one of the oldest universities in the state. It was set up on 8 January 1947 as the University of Rajputana Rājputana, meaning "Land of the ...

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

Indian Buddhist logic (called

Pramana ''Pramana'' (Sanskrit: प्रमाण, ) literally means "proof" and "means of knowledge".Vasubandhu Vasubandhu (; Tibetan: དབྱིག་གཉེན་ ; fl. 4th to 5th century CE) was an influential Buddhist monk and scholar from ''Puruṣapura'' in ancient India, modern day Peshawar, Pakistan. He was a philosopher who wrote commentary ...

(400–800 CE), Dignāga (480–540 CE), and

Dharmakīrti Dharmakīrti (fl. c. 6th or 7th century; Tibetan: ཆོས་ཀྱི་གྲགས་པ་; Wylie: ''chos kyi grags pa''), was an influential Indian Buddhist philosopher who worked at Nālandā.Tom Tillemans (2011)Dharmakirti Stanford ...

(600–660 CE). The most important theoretical achievements are the doctrine of

Trairūpya ''Trairūpya (''Sanskrit; English: "the triple-character of inferential sign") is a conceptual tool of Buddhist logic. The Trairūpya, ‘three conditions’, is oft accredited to Dignaga (c. 480-540 CE) though is now understood to have originated ...

(Skrt. त्रैरूप्य) and the highly formal scheme of the

Hetucakra ''Hetucakra'' or ''Wheel of Reasons'' is a Sanskrit text on logic written by Dignaga (c 480–540 CE). It concerns the application of his 'three modes’ ( trairūpya), conditions or aspects of the middle term called ''hetu'' ("reason" for a conc ...

(Skrt. हेतुचक्र) ("Wheel of Reasons") given by Dignāga. There is still a vibrant 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 Gangesha Upadhyaya of Mithila. It was a development of the classical Nyāya darśana. Other influences on Navya-Nyāya were the work of earlier philosophers

Vācaspati Miśra Vachaspati (' "lord of Vāc (speech)") is a Rigvedic deity presiding over human life. The name is applied especially to Brhaspati, the lord of eloquence, but also to Soma, Vishvakarman and Prajapati Prajapati ( sa, प्रजापत� ...

(900–980 CE) and Udayana (late 10th century). Gangeśa's book

Tattvacintāmaṇi Tattvachintamani is a treatise in Sanskrit authored by 14th-century CE Indian logician and philosopher Gangesa (fl. c. 1325). The title may be translated into English as "A Thought-jewel of Truth." The treatise is also known as Pramāṇa-chintām ...

("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 Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...

, and especially

epistemology Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epi ...

, 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

eastern India East India is a List of regions of India, region of India consisting of the Indian states of Bihar, Jharkhand, Odisha and West Bengal and also the union territory of the Andaman and Nicobar Islands. The region roughly corresponds to the histo ...

and

Bengal Bengal ( ; bn, বাংলা/বঙ্গ, translit=Bānglā/Bôngô, ) is a geopolitical, cultural and historical region in South Asia, specifically in the eastern part of the Indian subcontinent at the apex of the Bay of Bengal, predom ...

, and developed theories resembling modern logic, such as

Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic p ...

'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

. 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:

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 T. Colebrooke's ''The Philosophy of the Hindus: On the Nyaya and Vaisesika Systems'' in 1824, which provided an analysis of inference and comparison to the received

, resulting in the observation that the Aristotelian

could not account for the Indian syllogism.

Max Mueller Max or MAX may refer to: Animals * Max (dog) (1983–2013), at one time purported to be the world's oldest living dog * Max (English Springer Spaniel), the first pet dog to win the PDSA Order of Merit (animal equivalent of OBE) * Max (gorilla) (1 ...

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 only, by Hindus and Greeks." Jonardon Ganeri has observed that this period saw

George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in ...

(1815-1864) and Augustus De Morgan (1806-1871) make their pioneering applications of algebraic ideas to the formulation of logic (such as

algebraic logic In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...

and

), 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 Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered ...

(1791-1871), Augustus De Morgan, and particularly

, as confirmed by Boole's wife

Mary Everest Boole Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as ''Philosophy and Fun of Algebra'', an ...

in an "open letter to Dr Bose" titled "Indian Thought and Western Science in the Nineteenth Century" written in 1901. De Morgan himself wrote in 1860 of the significance of Indian logic: "The two races which have founded the mathematics, those of the

Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had Trans-cultural diffusion ...

and Greek languages, have been the two which have independently formed systems of logic." Mathematicians became aware of the influence of Indian mathematics on the European. For example,

Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is asso ...

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."Weyl, Hermann "The Theory of Groups and Quantum Mechanics", 1950, p.viii; online at https://books.google.com/books?id=jQbEcDDqGb8C

Notes

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, * 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

*
Indian Logic and Ontology
An annotated bibliography
Aristotle and Gautama on Logic and Physics

* Gillon, Brendan.
Indian theories of inference (subscription)
, in the

Routledge Encyclopedia of Philosophy The ''Routledge Encyclopedia of Philosophy'' is an encyclopedia of philosophy edited by Edward Craig that was first published by Routledge in 1998 (). Originally published in both 10 volumes of print and as a CD-ROM, in 2002 it was made availabl ...

, 1998. * Peckhaus, Volker.
Dignaga’s Logic of Invention
. In

Ivor Grattan-Guinness Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his b ...

, editor, ''History of the Mathematical Sciences'', 2004. * V. V. S. Sarma
"Indian Systems of Logic (Nyaya): A Survey" (PDF)
'. ''Proc. Bombay Logic Conference'', 2005.
Vidhabhusana, Satis Chandra (1907). History of the Mediaeval School of Indian Logic. Calcutta University.
{{DEFAULTSORT:Indian Logic History of logic Indian philosophy