Indian logic
Encyclopedia
The development of Indian logic dates 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), 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
. The Indian tradition continued to develop through to early modern times, in the form of the Navya-Nyāya
school of logic.
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".
Medhatithi Gautama (c. 6th century BCE) founded the anviksiki school of logic. The Mahabharata
(12.173.45), around the 5th century BCE, 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
. Logic is described by Chanakya
(c. 350-283 BCE) in his Arthashastra
as an independent field of inquiry anviksiki.
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.
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
.
, 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
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.
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. In the process, the Jains came out with their doctrines of relativity
used for logic and reasoning:
These Jain philosophical
concepts made most important contributions to the ancient Indian philosophy
, especially in the areas of skepticism and relativity.
Following is the list of Jain philosophers who contributed to Jain Logic:
) 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 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.
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).
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
. 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:
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 Thomson's Laws of Thought (1853), 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
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.
Indian logic attracted the attention of many Western scholars, and has had an influence on pioneering 19th-century logicians such as Charles Babbage
, Augustus De Morgan
, and particularly George Boole
, as confirmed by his 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 Sanscrit and Greek languages, have been the two which have independently formed systems of logic."
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)
In his Histoire de la logique, Robert Blanché, the author of Structures intellectuelles, published in 1966, mentions that Bochenski speaks about a sort of Indian logical triangle to be compared with the logical square,invented by Aristotle and Apuleius. It seems that with this logical triangle, Indian logic proposes a useful approach to the problem of particular propositions.
Vyakarana
The Sanskrit grammatical tradition of ' is one of the six Vedanga disciplines. It has its roots in late Vedic India, and includes the famous work, The Sanskrit grammatical tradition of ' is one of the six Vedanga disciplines. It has its roots in late Vedic India, and includes the famous work, ...
rules of Pāṇini (c. 5th century BCE); the Vaisheshika
Vaisheshika
Vaisheshika or ' is one of the six Hindu schools of philosophy of India. Historically, it has been closely associated with the Hindu school of logic, Nyaya....
school's analysis of atomism
Atomism
Atomism is a natural philosophy that developed in several ancient traditions. The atomists theorized that the natural world consists of two fundamental parts: indivisible atoms and empty void.According to Aristotle, atoms are indestructible and immutable and there are an infinite variety of shapes...
(c. 2nd century BCE); the analysis of inference
Inference
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...
by Gotama
Nyaya Sutras
The Nyāya Sūtras are an ancient Indian text on of philosophy composed by ' . The sutras contain five chapters, each with two sections...
(c. 2nd century), founder of the Nyaya
Nyaya
' is the name given to one of the six orthodox or astika schools of Hindu philosophy—specifically the school of logic...
school of Hindu philosophy
Hindu philosophy
Hindu philosophy is divided into six schools of thought, or , which accept the Vedas as supreme revealed scriptures. Three other schools do not accept the Vedas as authoritative...
; and the tetralemma
Tetralemma
The tetralemma is a figure that features prominently in the classical logic of the Greeks. It states that with reference to any a logical proposition X, there are four possibilities:-External links:* Wiktionary definition of tetralemma*...
of Nagarjuna
Nagarjuna
Nāgārjuna was an important Buddhist teacher and philosopher. Along with his disciple Āryadeva, he is credited with founding the Mādhyamaka school of Mahāyāna Buddhism...
(c. 2nd century CE). Indian
Indian philosophy
India has a rich and diverse philosophical tradition dating back to ancient times. According to Radhakrishnan, the earlier Upanisads constitute "...the earliest philosophical compositions of the world."...
logic stands as one of the three original traditions of logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, alongside the Greek
Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
and Chinese traditions
Logic in China
In the history of logic, logic in China plays a particularly interesting role due to its length and relative isolation from the strong current of development of the study of logic in Europe and the Islamic world, though it may have some influence from Indian logic due to the spread of...
. The Indian tradition continued to develop through to early modern times, in the form of the Navya-Nyāya
Navya-Nyaya
The Navya-Nyāya or Neo-Logical darśana of Indian logic and 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...
school of logic.
Origins
The Nasadiya SuktaNasadiya Sukta
The Nasadiya Sukta is the 129th hymn of the 10th Mandala of the Rigveda. It is concerned with cosmology and the origin of the universe. It is known for its skepticism...
of the Rigveda
Rigveda
The Rigveda is an ancient Indian sacred collection of Vedic Sanskrit hymns...
(RV 10
Mandala 10
The tenth Mandala of the Rigveda has 191 hymns. Together with Mandala 1, it forms the latest part of the Rigveda, containing much mythological material, including the Purusha sukta and the dialogue of Sarama with the Panis , and notably containing several dialogue hymns...
.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti
Tetralemma
The tetralemma is a figure that features prominently in the classical logic of the Greeks. It states that with reference to any a logical proposition X, there are four possibilities:-External links:* Wiktionary definition of tetralemma*...
: "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
Mahabharata
The Mahabharata is one of the two major Sanskrit epics of ancient India and Nepal, the other being the Ramayana. The epic is part of itihasa....
(12.173.45), around the 5th century BCE, refers to the anviksiki and tarka schools of logic. (c. 5th century BCE) developed a form of logic (to which Boolean logic
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...
has some similarities) for his formulation of Sanskrit grammar
Vyakarana
The Sanskrit grammatical tradition of ' is one of the six Vedanga disciplines. It has its roots in late Vedic India, and includes the famous work, The Sanskrit grammatical tradition of ' is one of the six Vedanga disciplines. It has its roots in late Vedic India, and includes the famous work, ...
. Logic is described by Chanakya
Chanakya
Chānakya was a teacher to the first Maurya Emperor Chandragupta , and the first Indian emperor generally considered to be the architect of his rise to power. Traditionally, Chanakya is also identified by the names Kautilya and VishnuGupta, who authored the ancient Indian political treatise...
(c. 350-283 BCE) in his Arthashastra
Arthashastra
The Arthashastra is an ancient Indian treatise on statecraft, economic policy and military strategy which identifies its author by the names Kautilya and , who are traditionally identified with The Arthashastra (IAST: Arthaśāstra) is an ancient Indian treatise on statecraft, economic policy and...
as an independent field of inquiry anviksiki.
Vaisheshika
Vaisheshika, also Vaisesika, (Sanskrit: वैशॆषिक) is one of the six Hindu schoolsHindu philosophy
Hindu philosophy is divided into six schools of thought, or , which accept the Vedas as supreme revealed scriptures. Three other schools do not accept the Vedas as authoritative...
of Indian philosophy
Indian philosophy
India has a rich and diverse philosophical tradition dating back to ancient times. According to Radhakrishnan, the earlier Upanisads constitute "...the earliest philosophical compositions of the world."...
. 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
Kanada
It has been claimed that Kashyapa, later known as Kanada was a Hindu sage and philosopher who founded the philosophical school of Vaisheshika. He talked of Dvyanuka and tryanuka...
(or Kana-bhuk, literally, atom-eater) from around the 2nd century BCE.
Catuskoti
In the 2nd century, the BuddhistBuddhist philosophy
Buddhist philosophy deals extensively with problems in metaphysics, phenomenology, ethics, and epistemology.Some scholars assert that early Buddhist philosophy did not engage in ontological or metaphysical speculation, but was based instead on empirical evidence gained by the sense organs...
philosopher Nagarjuna
Nagarjuna
Nāgārjuna was an important Buddhist teacher and philosopher. Along with his disciple Āryadeva, he is credited with founding the Mādhyamaka school of Mahāyāna Buddhism...
refined the Catuskoti form of logic. The Catuskoti is also often glossed Tetralemma
Tetralemma
The tetralemma is a figure that features prominently in the classical logic of the Greeks. It states that with reference to any a logical proposition X, there are four possibilities:-External links:* Wiktionary definition of tetralemma*...
(Greek) which is the name for a largely comparable, but not equatable, 'four corner argument' within the tradition of Classical logic
Classical logic
Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...
.
Nyaya
Nyāya (ni-āyá, literally "recursion", used in the sense of "syllogismSyllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
, 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
Nyaya Sutras
The Nyāya Sūtras are an ancient Indian text on of philosophy composed by ' . The sutras contain five chapters, each with two sections...
, 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
Western philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....
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
JainismJainism
Jainism is an Indian religion that prescribes a path of non-violence towards all living beings. Its philosophy and practice emphasize the necessity of self-effort to move the soul towards divine consciousness and liberation. Any soul that has conquered its own inner enemies and achieved the state...
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. In the process, the Jains came out with their doctrines of relativity
Relativism
Relativism is the concept that points of view have no absolute truth or validity, having only relative, subjective value according to differences in perception and consideration....
used for logic and reasoning:
- AnekāntavādaAnekantavada' is one of the most important and fundamental doctrines of Jainism. It refers to the principles of pluralism and multiplicity of viewpoints, the notion that truth and reality are perceived differently from diverse points of view, and that no single point of view is the complete truth.Jains...
– the theory of relative pluralism or manifoldness; - SyādvādaSyadvadaSyādvāda is the Doctrine of Postulation of Jainism. In other words, Syādvāda provides the body of teachings or instruction which one uses to derive a postulate or axiom. The starting assumption or postulate is given as saptabhanginaya, from which other statements are logically derived...
– the theory of conditioned predication and; - Nayavāda – The theory of partial standpoints.
These Jain philosophical
Jain philosophy
Jain philosophy deals extensively with the problems of metaphysics, reality, cosmology, ontology, epistemology and divinity. Jainism is essentially a transtheistic religion of ancient India. It is a continuation of the ancient tradition which co-existed with the Vedic tradition since ancient...
concepts made most important contributions to the ancient Indian philosophy
Indian philosophy
India has a rich and diverse philosophical tradition dating back to ancient times. According to Radhakrishnan, the earlier Upanisads constitute "...the earliest philosophical compositions of the world."...
, especially in the areas of skepticism and relativity.
Following is the list of Jain philosophers who contributed to Jain Logic:
- KundakundaKundakundaKundakunda is a celebrated Jain Acharya, Jain scholar monk, 2nd century CE, composer of spiritual classics such as: Samayasara, Niyamasara, Pancastikayasara, Pravacanasara, Atthapahuda and Barasanuvekkha. He occupies the highest place in the tradition of the Jain acharyas.He belonged to the Mula...
(2nd century CE), exponent of Jain mysticism and Jain nayas dealing with the nature of the soul and its contamination by matter, author of PañcāstikāyasāraPancastikayasaraPañcastikayasara, or the essence of reality, is a Digambara text by Kundakunda is part of his trilogy, known as the prahbrta-traya or the nataka-traya. Kundakunda explains the Jaina concepts of Ontology and Ethics...
(Essence of the Five Existents), the Pravacanasāra (Essence of the Scripture) and the SamayasāraSamayasara' is a famous Jain text by Acharya Kundakunda.Its ten chapters discuss the nature of jiva , its attachment to karmas and moksha....
(Essence of the Doctrine). - Umāsvāti or Umasvami (2nd century CE), author of first Jain work in Sanskrit, TattvārthasūtraTattvartha SutraTattvartha Sutra is a Jain text written by Acharya Umaswati. It was an attempt to bring together the different elements of the Jain path, epistemological, metaphysical, cosmological, ethical and practical, otherwise unorganized around the scriptures in an unsystematic format...
, expounding the Jain philosophyJain philosophyJain philosophy deals extensively with the problems of metaphysics, reality, cosmology, ontology, epistemology and divinity. Jainism is essentially a transtheistic religion of ancient India. It is a continuation of the ancient tradition which co-existed with the Vedic tradition since ancient...
in a most systematized form acceptable to all sects of Jainism. - Siddhasena DivākaraSiddhasen DiwakarSiddhasen Diwakar was a highly intelligent Jain acharya of his time. Siddhasen could study the scriptures and realize their truth in a short time. In due course he became the best known Jain scholar of the time. He was like the illuminating lamp of the Jain order and therefore came to be known...
(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) - HaribhadraHaribhadraHaribhadra Suri was a Svetambara mendicant Jain leader and author.-History:There are multiple contradictory dates assigned to his birth. These include 459, 478, and 529. However, given his familiarity with Dharmakirti, a more likely choice would be sometime after 650...
(8th century CE) , a Jaina thinker, author and great proponent of anekāntavādaAnekantavada' is one of the most important and fundamental doctrines of Jainism. It refers to the principles of pluralism and multiplicity of viewpoints, the notion that truth and reality are perceived differently from diverse points of view, and that no single point of view is the complete truth.Jains...
and classical yoga, as a soteriological system of meditation in Jaina context. His works include and Yogabindu. - Hemacandra (1089–1172 CE) - a Jaina thinker, author, historian, grammarian and logician. His works include Yogaśāstra and Trishashthishalakapurushacharitra.
- Yaśovijaya GaṇiYasovijayaYaśovijaya , a seventeenth century Jain philosopher-monk was one of India’s greatest philosopher and logician. He was a thinker, prolific writer and commentator who had a strong and lasting influence on Jainism...
(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 a 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. His books have a unique combination of simplicity in expression and originality.
Buddhist logic
Indian Buddhist logic (called PramanaPramana
Pramana is an epistemological term in Hindu and Buddhist dialectic, debate and discourse.Pramāṇavāda and Hetuvidya can be glossed in English as Indian and Buddhist Epistemology and Logic, respectively.-In Hinduism:...
) flourished from about 500 CE up to 1300 CE. The three main authors of Buddhist logic are Vasubandhu
Vasubandhu
Vasubandhu was an Indian Buddhist monk, and along with his half-brother Asanga, one of the main founders of the Indian Yogācāra school. However, some scholars consider Vasubandhu to be two distinct people. Vasubandhu is one of the most influential figures in the entire history of Buddhism...
(400–800 CE), Dignāga
Dignaga
Dignāga was an Indian scholar and one of the Buddhist founders of Indian logic.He was born into a Brahmin family in Simhavakta near Kanchi Kanchipuram), and very little is known of his early years, except that he took as his spiritual preceptor Nagadatta of the Vatsiputriya school, before being...
(480–540 CE), and Dharmakīrti
Dharmakirti
Dharmakīrti , was an Indian scholar and one of the Buddhist founders of Indian philosophical logic. He was one of the primary theorists of Buddhist atomism, according to which the only items considered to exist are momentary states of consciousness.-History:Born around the turn of the 7th century,...
(600–660 CE). The most important theoretical achievements are the doctrine of Trairūpya
Trairūpya
Trairūpya is a conceptual tool of Buddhist logic. The Trairūpya, ‘three conditions’, is oft accredited to Dignaga though is now understood to have originated with his teacher Vasubandhu Trairūpya (Sanskrit; English: "the triple-character of inferential sign") is a conceptual tool of Buddhist...
(Skrt. त्रैरूप्य) and the hiqhly formal scheme of the Hetucakra
Hetucakra
Hetucakra is a Sanskrit text on logic written by Dignaga . It concerns the application of his 'three modes’ in a valid inference within the Indian logico-epistemic tradition, sometimes referred to as Buddhist logic....
(Skrt. हेतुचक्र) ("Wheel of Reasons") given by Dignāga
Dignaga
Dignāga was an Indian scholar and one of the Buddhist founders of Indian logic.He was born into a Brahmin family in Simhavakta near Kanchi Kanchipuram), and very little is known of his early years, except that he took as his spiritual preceptor Nagadatta of the Vatsiputriya school, before being...
. 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 Gangesha UpadhyayaGangesha Upadhyaya
Gangesha Upadhyaya was an Indian mathematician and philosopher from the kingdom of Mithila. He established the Navya-Nyāya school. His Tattvacintāmaṇi also known as Pramāṇacintāmaṇi is the basic text for all later developments...
of Mithila
Mithila
Mithila was a city in Ancient India, the capital of the Videha Kingdom. The name Mithila is also commonly used to refer to the Videha Kingdom itself, as well as to the modern-day territories that fall within the ancient boundaries of Videha...
. It was a development of the classical Nyāya darśana. Other influences on Navya-Nyāya were the work of earlier philosophers Vācaspati Miśra
Vacaspati Misra
Vācaspati Miśra was an Indian philosopher who founded one of the main Advaita Vedanta schools, the Bhāmatī school , and whose work was an important forerunner of the Navya-Nyāya system of thought.Vācaspati was a Maithili Brahmin who lived near the frontier between India and Nepal Vācaspati Miśra...
(900–980 CE) and Udayana
Udayana
- Introduction :Udayana also known as Udayanācārya lived in the 10th century, in Kariyan village in Mithila, near present day Darbhanga, Bihar state, India. Udayana was a very important Hindu logician who attempted to reconcile the views held by the two major schools of logic...
(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
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, 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
Upamana
Upamana , in Hinduism, is a pramana, or means of having knowledge of something. Observance of similarities provides knowledge of the relationship between the two....
), and testimony (sound or word; śabda).
This later school began around eastern India
East India
East India is a region of India consisting of the states of West Bengal, Bihar, Jharkhand, and Orissa. The states of Orissa and West Bengal share some cultural and linguistic characteristics with Bangladesh and with the state of Assam. Together with Bangladesh, West Bengal formed the...
and Bengal
Bengal
Bengal is a historical and geographical region in the northeast region of the Indian Subcontinent at the apex of the Bay of Bengal. Today, it is mainly divided between the sovereign land of People's Republic of Bangladesh and the Indian state of West Bengal, although some regions of the previous...
, and developed theories resembling modern logic, such as Gottlob Frege
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
'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
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
. 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, culminating in Henry T. Colebrooke'sHenry Thomas Colebrooke
Henry Thomas Colebrooke was an English orientalist.-Biography:Henry Thomas Colebrooke, third son of Sir George Colebrooke, 2nd Baronet, was born in London. He was educated at home; and when only fifteen he had made considerable attainments in classics and mathematics...
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
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
could not account for the Indian syllogism. Max Mueller contributed an appendix to Thomson's Laws of Thought (1853), 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
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
and Augustus De Morgan
Augustus De Morgan
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him....
make their pioneering applications of algebraic ideas to the formulation of logic (such as Algebraic logic
Algebraic logic
In mathematical logic, algebraic logic is the study of logic presented in an algebraic style.What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics and connected problems...
and Boolean logic
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...
), 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.
Indian logic attracted the attention of many Western scholars, and has had an influence on pioneering 19th-century logicians such as Charles Babbage
Charles Babbage
Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...
, Augustus De Morgan
Augustus De Morgan
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him....
, and particularly George Boole
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
, as confirmed by his wife Mary Everest Boole
Mary Everest Boole
Mary Everest Boole was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as Philosophy and Fun of Algebra, and as the wife of fellow mathematician George 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 Sanscrit and Greek languages, have been the two which have independently formed systems of logic."
Mathematicians are now aware of the influence of Indian mathematics on the European. For example, Hermann Weyl
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
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)
In his Histoire de la logique, Robert Blanché, the author of Structures intellectuelles, published in 1966, mentions that Bochenski speaks about a sort of Indian logical triangle to be compared with the logical square,invented by Aristotle and Apuleius. It seems that with this logical triangle, Indian logic proposes a useful approach to the problem of particular propositions.