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 con ...
'' 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
(Devanaga ...
(c. 5th century BCE); the
Vaisheshika
Vaisheshika or Vaiśeṣika ( sa, वैशेषिक) is one of the six schools of Indian philosophy (Vedic systems) from ancient India. In its early stages, the Vaiśeṣika was an independent philosophy with its own metaphysics, epistemolog ...
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 atoms ...
(c. 6th century BCE to 2nd century BCE); the analysis of
inference by
Gotama (c. 6th century BC to 2nd century CE), founder of the
Nyaya school of
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
The tetralemma is a figure that features prominently in the logic of India. Definition
It states that with reference to any a logical proposition X, there are four possibilities:
: X (affirmation)
: \neg X (negation)
: X \land\neg X (both)
: \n ...
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 premise ...
, 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
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 of Nabadwi ...
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 one ...
'' (
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 literature, Sanskrit Indian epic poetry, epics of ancient India in Hinduism, the other being the ''Ramayana, Rāmāyaṇa''. It narrates the s ...
'' (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 has some similarities) for his formulation of
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 ...
. 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 Kauṭil ...
(c. 350-283 BCE) in his ''
Arthashastra'' 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
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 ...
refined the ''Catuskoti'' form of logic. The Catuskoti is also often glossed ''
Tetralemma
The tetralemma is a figure that features prominently in the logic of India. Definition
It states that with reference to any a logical proposition X, there are four possibilities:
: X (affirmation)
: \neg X (negation)
: X \land\neg X (both)
: \n ...
'' (Greek) which is the name for a largely comparable, but not equatable, 'four corner argument' within the tradition of
Classical logic.
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 philosophy
Western philosophy encompasses the 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-Socratics. The word ' ...
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
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, 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
( 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 conditioned predication and;
*
Nayavāda – The theory of partial standpoints.
These
Jain philosophical concepts made most important contributions to the ancient
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 ...
, especially in the areas of skepticism and relativity.
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
Pravachanasāra (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
''Tattvārthasūtra'', meaning "On the Nature '' ''artha">nowiki/>''artha''.html" ;"title="artha.html" ;"title="nowiki/>''artha">nowiki/>''artha''">artha.html" ;"title="nowiki/>''artha">nowiki/>''artha''of Reality 'tattva'' (also known as ...
, 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)
*
Haribhadra
Aacharya Haribhadra Suri was a Svetambara mendicant Jain leader, philosopher , doxographer, and author. There are multiple contradictory dates assigned to his birth. According to tradition, he lived c. 459–529 CE. However, in 1919, a Jain m ...
suri (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 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 Stanfor ...
(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 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 Mithila may refer to:
Places
* Mithilā, a synonym for the ancient Videha state
** Mithilā (ancient city), the ancient capital city of Videha
* Mithila (region), a cultural region (historical and contemporary), now divided between India and Nepal
...
. 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
Udayana, ( Devanagari: उदयन) also known as Udayanācārya (Udyanacharya, or Master Udayana), (circa 975 - 1050 CE) was an Indian philosopher and logician of the tenth century of the Nyaya school who attempted to devise a rational theo ...
(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
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 conce ...
, 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.
Epis ...
, 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 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 ph ...
'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
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 conce ...
. Udayana in particular developed theories on "restrictive conditions for universals" and "
infinite
Infinite may refer to:
Mathematics
* Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
*Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
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
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
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 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
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 ...
, 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.
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 branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...
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 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]
See also
*
*
*
Tarka-Sangraha
*
Debates in ancient India
There was, for a considerable period of time, a very lively and extensively practiced tradition of formal debates in ancient India. These debates were conducted, sometimes with royal patronage, to examine various religious, philosophical, moral an ...
*
Seven valued logic
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 OntologyAn 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, 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