Nyaya Philosophy Of Language Essay

Nyāya (Sanskrit: न्याय, ny-āyá), literally means "rules", "method" or "judgment".[1][2] It is also the name of one of the six orthodox (astika) schools of Hinduism.[2] This school's most significant contributions to Indian philosophy was systematic development of the theory of logic, methodology, and its treatises on epistemology.[3][4]

Nyaya school's epistemology accepts four out of six Pramanas as reliable means of gaining knowledge – Pratyakṣa (perception), Anumāṇa (inference), Upamāṇa (comparison and analogy) and Śabda (word, testimony of past or present reliable experts).[5][6][7] In its metaphysics, Nyaya school is closer to Vaisheshika school of Hinduism than others.[2] It holds that human suffering results from mistakes/defects produced by activity under wrong knowledge (notions and ignorance).[8] Moksha (liberation), it states, is gained through right knowledge. This premise led Nyaya to concern itself with epistemology, that is the reliable means to gain correct knowledge and to remove wrong notions. False knowledge is not merely ignorance to Naiyyayikas, it includes delusion. Correct knowledge is discovering and overcoming one's delusions, and understanding true nature of soul, self and reality.[9]

Naiyyayika scholars approached philosophy as a form of direct realism, stating that anything that really exists is in principle humanly knowable. To them, correct knowledge and understanding is different than simple, reflexive cognition; it requires Anuvyavasaya (अनुव्यवसाय, cross-examination of cognition, reflective cognition of what one thinks one knows).[10] An influential collection of texts on logic and reason is the Nyayasutras, attributed to Aksapada Gautama, variously estimated to have been composed between 6th-century BCE and 2nd-century CE.[11][12]

Nyaya school shares some of its methodology and human suffering foundations with Buddhism; however, a key difference between the two is that Buddhism believes that there is neither a soul nor self;[13] Nyaya school like other schools of Hinduism believes that there is a soul and self, with liberation (moksha) as a state of removal of ignorance, wrong knowledge, the gain of correct knowledge and unimpeded continuation of self.[14][15]


Nyaya (न्याय) is a Sanskrit word which means method, rule, specially a collection of general or universal rules.[1] In some contexts, it means model, axiom, plan, legal proceeding, judicial sentence, or judgment. In the theory of logic, and Indian texts discussing it, the term also refers to an argument consisting of an enthymeme or sometimes for any syllogism.[1] In philosophical context, Nyaya encompasses propriety, logic and method.[16]

Nyaya is related to several other concepts and words used in Indian philosophies: Hetu-vidya (science of causes), Anviksiki (science of inquiry, systematic philosophy), Pramana-sastra (epistemology, science of correct knowledge), Tattva-sastra (science of categories), Tarka-vidya (science of reasoning, innovation, synthesis), Vadartha (science of discussion) and Phakkika-sastra (science of uncovering sophism, fraud, error, finding fakes).[17] Some of these subsume or deploy the tools of Nyaya.


Nasadiya Sukta

Rig Veda, Creation....10:129-1, 10:129-6[18][19]
Then was not non-existent nor existent:

there was no realm of air, no sky beyond it.
What covered in, and where? and what gave shelter?
Was water there, unfathomed depth of water?
Who really knows? Who will here proclaim it?
Whence was it produced? Whence is this creation?

The gods came after this world's production,
Who knows then whence it first came into being?"

The historical development of Nyaya school is unclear, although Nasadiya hymns of Book 10 Chapter 129 of Rigveda recite its spiritual questions in logical propositions.[18] In early centuries BCE, states Clooney, the early Nyaya scholars began compiling the science of rational, coherent inquiry and pursuit of knowledge.[20] By 2nd century CE, Aksapada Gautama had composed Nyayasutras, a foundational text for Nyaya school, that primarily discusses logic, methodology and epistemology.[12] The Nyaya scholars that followed refined it, expanded it, and applied it to spiritual questions. While the early Nyaya scholars published little to no analysis on whether supernatural power or God exists, they did apply their insights into reason and reliable means to knowledge to the questions of nature of existence, spirituality, happiness and moksha. Later Nyaya scholars, such as Udayana, examined various arguments on theism and attempted to prove existence of God.[21] Other Nyaya scholars offered arguments to disprove the existence of God.[20][22][23]

The most important contribution made by the Nyaya school to Hindu thought has been its treatises on epistemology and system of logic that, subsequently, has been adopted by the majority of the other Indian schools.[10]

Sixteen Padārthas or Categories[edit]

The Nyaya metaphysics recognizes sixteen padarthas or categories and includes all six (or seven) categories of the Vaisheshika in the second one of them, called prameya.[24] These sixteen categories are pramāṇa (valid means of knowledge), prameya (objects of valid knowledge), saṁśaya (doubt), prayojana (aim), dṛṣṭānta (example), siddhānta (conclusion), avayava (members of syllogism), tarka (hypothetical reasoning), nirṇaya (settlement), vāda (discussion), jalpa (wrangling), vitaṇḍā (cavilling), hetvābhāsa (fallacy), chala (quibbling), jāti (sophisticated refutation) and nigrahasthāna (point of defeat).[25][26]


The Nyaya school of Hinduism developed and refined many treatises on epistemology that widely influenced other schools of Hinduism. Nyaya treated it as theory of knowledge, and its scholars developed it as Pramana-sastras. Pramana, a Sanskrit word, literally is "means of knowledge". It encompasses one or more reliable and valid means by which human beings gain accurate, true knowledge.[27] The focus of Pramana is how correct knowledge can be acquired, how one knows, how one doesn't, and to what extent knowledge pertinent about someone or something can be acquired.[6][28]

The Naiyayikas (the Nyaya scholars) accepted four valid means (pramaṇa) of obtaining valid knowledge (pramana) - perception (pratyakṣa), inference (anumāna), comparison (upamāna) and word/testimony of reliable sources (śabda). The Nyaya scholars, along with those from other schools of Hinduism, also developed a theory of error, to methodically establish means to identify errors and the process by which errors are made in human pursuit of knowledge. These include Saṁśaya (समस्या, problems, inconsistencies, doubts) and Viparyaya (विपर्यय, contrariness, errors)[29] which can be corrected or resolved by a systematic process of Tarka ( तर्क, reasoning, technique).[30][31]

Pratyaksha aka Perception[edit]

Pratyakṣa (perception) occupies the foremost position in the Nyaya epistemology. Perception can be of two types, laukika (ordinary) and alaukika (extraordinary).[32] Ordinary perception is defined by Akṣapāda Gautama in his Nyaya Sutra (I,i.4) as a 'non-erroneous cognition which is produced by the intercourse of sense-organs with the objects'.

Indian texts identify four requirements for correct perception:[33]Indriyarthasannikarsa (direct experience by one's sensory organ(s) with the object, whatever is being studied), Avyapadesya (non-verbal; correct perception is not through hearsay, according to ancient Indian scholars, where one's sensory organ relies on accepting or rejecting someone else's perception), Avyabhicara (does not wander; correct perception does not change, nor is it the result of deception because one's sensory organ or means of observation is drifting, defective, suspect) and Vyavasayatmaka (definite; correct perception excludes judgments of doubt, either because of one's failure to observe all the details, or because one is mixing inference with observation and observing what one wants to observe, or not observing what one does not want to observe).[33]

Ordinary perception to Nyaya scholars was based on direct experience of reality by eyes, ears, nose, touch and taste.[32] Extraordinary perception included yogaja or pratibha (intuition), samanyalaksanapratyaksa (a form of induction from perceived specifics to a universal), and jnanalaksanapratyaksa (a form of perception of prior processes and previous states of a 'topic of study' by observing its current state).[32][34]

Determinate and indeterminate perception[edit]

The Naiyyayika maintains two modes or stages in perception. The first is called nirvikalpa (indeterminate), when one just perceives an object without being able to know its features, and the second savikalpa (determinate), when one is able to clearly know an object.[35] All laukika and alaukika pratyakshas are savikalpa, but it is necessarily preceded by an earlier stage when it is indeterminate. Vātsāyana says that if an object is perceived with its name we have determinate perception but if it is perceived without a name, we have indeterminate perception. Jayanta Bhatta says that indeterminate perception apprehends substance, qualities and actions and universals as separate and indistinct something and also it does not have any association with name, while determinate perception aprrehends all these together with a name. There is yet another stage called Pratyabhijñā, when one is able to re-recognise something on the basis of memory.[36]

Anumāna aka Inference[edit]

Anumāna (inference) is one of the most important contributions of the Nyaya. It can be of two types: inference for oneself (Svarthanumana, where one does not need any formal procedure, and at the most the last three of their 5 steps), and inference for others (Parathanumana, which requires a systematic methodology of 5 steps). Inference can also be classified into 3 types: Purvavat (inferring an unperceived effect from a perceived cause), Sheshavat (inferring an unperceived cause from a perceived effect) and Samanyatodrishta (when inference is not based on causation but on uniformity of co-existence). A detailed analysis of error is also given, explaining when anumana could be false.[36]

Theory of inference[edit]

The methodology of inference involves a combination of induction and deduction by moving from particular to particular via generality. It has five steps, as in the example shown:[citation needed]

  • There is fire on the hill (called Pratijñā, required to be proved)
  • Because there is smoke there (called Hetu, reason)
  • Wherever there is smoke, there is fire, e.g. in a kitchen (called Udāhārana, example of vyāpti)
  • The hill has smoke that is pervaded by fire (called Upanaya, reaffirmation or application)
  • Therefore, there is fire on the hill (called Nigamana, conclusion)

In Nyāya terminology for this example, the hill would be called as paksha (minor term), the fire is called as sādhya (major term), the smoke is called as hetu, and the relationship between the smoke and the fire is called as vyapti (middle term). Hetu further has five characteristics: (1) It must be present in the Paksha, (2) It must be present in all positive instances, (3) It must be absent in all negative instances, (4) It must not incompatible with the minor term or Paksha and (5) All other contradictions by other means of knowledge should be absent. The fallacies in Anumana (hetvābhasa) may occur due to the following:[citation needed]

  1. Asiddha: It is the unproved hetu that results in this fallacy. [Paksadharmata]
    • Ashrayasiddha: If Paksha [minor term] itself is unreal, then there cannot be locus of the hetu. e.g. The sky-lotus is fragrant, because it is a lotus like any other lotus.
    • Svarupasiddha: Hetu cannot exist in paksa at all. E.g. Sound is a quality, because it is visible.
    • Vyapyatvasiddha: Conditional hetu. `Wherever there is fire, there is smoke'. The presence of smoke is due to wet fuel.
  2. Savyabhichara: This is the fallacy of irregular hetu.
    • Sadharana: The hetu is too wide. It is present in both sapaksa and vipaksa. `The hill has fire because it is knowable'.
    • Asadharana: The hetu is too narrow. It is only present in the Paksha, it is not present in the Sapaksa and in the Vipaksha. `Sound is eternal because it is audible'.
    • Anupasamhari: Here the hetu is non-exclusive. The hetu is all-inclusive and leaves nothing by way of sapaksha or vipaksha. e.g. 'All things are non-ternal, because they are knowable'.
  3. Satpratipaksa: Here the hetu is contradicted by another hetu. If both have equal force, then nothing follows. 'Sound is eternal, because it is audible', and 'Sound is non-eternal, because it is produced'. Here 'audible' is counterbalanced by 'produced' and both are of equal force.
  4. Badhita: When another proof (as by perception) definitely contradicts and disproves the middle term (hetu). 'Fire is cold because it is a substance'.
  5. Viruddha: Instead of proving something it is proving the opposite. 'Sound is eternal because it is produced'.

Upamāna aka Comparison, Analogy[edit]

Upamāna (उपमान) means comparison and analogy.[6][7]Upamana, states Lochtefeld,[37] may be explained with the example of a traveller who has never visited lands or islands with endemic population of wildlife. He or she is told, by someone who has been there, that in those lands you see an animal that sort of looks like a cow, grazes like cow but is different from a cow in such and such way. Such use of analogy and comparison is, state the Indian epistemologists, a valid means of conditional knowledge, as it helps the traveller identify the new animal later.[37] The subject of comparison is formally called upameyam, the object of comparison is called upamānam, while the attribute(s) are identified as sāmānya.[38] Thus, explains Monier Williams, if a boy says "her face is like the moon in charmingness", "her face" is upameyam, the moon is upamānam, and charmingness is sāmānya. The 7th century text Bhaṭṭikāvya in verses 10.28 through 10.63 discusses many types of comparisons and analogies, identifying when this epistemic method is more useful and reliable, and when it is not.[38] In various ancient and medieval texts of Hinduism, 32 types of Upamāna and their value in epistemology are debated.

Śabda aka Word, Testimony[edit]

Śabda (शब्द) means relying on word, testimony of past or present reliable experts.[6][39] Hiriyanna explains Sabda-pramana as a concept which means testimony of a reliable and trustworthy person (āptavākya). The schools of Hinduism which consider it epistemically valid suggest that a human being needs to know numerous facts, and with the limited time and energy available, he can learn only a fraction of those facts and truths directly.[40] He must rely on others, his parent, family, friends, teachers, ancestors and kindred members of society to rapidly acquire and share knowledge and thereby enrich each other's lives. This means of gaining proper knowledge is either spoken or written, but through Sabda (words).[40] The reliability of the source is important, and legitimate knowledge can only come from the Sabda of reliable sources.[39][40] The disagreement between the schools of Hinduism has been on how to establish reliability. Some schools, such as Carvaka, state that this is never possible, and therefore Sabda is not a proper pramana. Other schools debate means to establish reliability.[41]

Testimony can be of two types, Vaidika (Vedic), which are the words of the four sacred Vedas, and Laukika, or words and writings of trustworthy human beings. Vaidika testimony is preferred over Laukika testimony. Laukika-sourced knowledge must be questioned and revised as more trustworthy knowledge becomes available.[citation needed]

Comparison with other schools of Hinduism[edit]

Each school of Hinduism has its own treatises on epistemology, with different number of Pramanas. For example, compared to Nyaya school's four pramanas, Carvaka school has just one (perception), while Advaita Vedanta school recognizes six means to reliable knowledge.[5][39]

The Nyaya theory of causation[edit]

Nyaya-Vaisheshika offers one of the most vigorous efforts at the construction of a substantialist, realist ontology that the world has ever seen. It provides an extended critique of event-ontologies and idealist metaphysics. (...) This ontology is Platonistic, realistic, but neither exclusively physicalistic nor phenomenalistic.

— Karl Potter, The Encyclopedia of Indian Philosophies[42]

A cause is defined as an unconditional and invariable antecedent of an effect and an effect as an unconditional and invariable consequent of a cause. The same cause produces the same effect; and the same effect is produced by the same cause. The cause is not present in any hidden form whatsoever in its effect.

The following conditions should be met:

  1. The cause must be antecedent [Purvavrtti]
  2. Invariability [Niyatapurvavrtti]
  3. Unconditionality [Ananyathasiddha]

Nyaya recognizes five kinds of accidental antecedents [Anyathasiddha]

  1. Mere accidental antecedent. E.g., The colour of the potter's cloth.
  2. Remote cause is not a cause because it is not unconditional. E.g., The father of the potter.
  3. The co-effects of a cause are not causally related.
  4. Eternal substances, or eternal conditions are not unconditional antecedents, e.g. space.
  5. Unnecessary things, e.g. the donkey of the potter.

Nyaya recognizes three kinds of cause:

  1. Samavayi, material cause, e.g. thread of a cloth.
  2. Asamavayi, colour of the thread which gives the colour of the cloth.
  3. Nimitta, efficient cause, e.g. the weaver of the cloth.

Anyathakyativada of Nyaya[edit]

The Nyaya theory of error is similar to that of Kumarila's Viparita-khyati (see Mimamsa). The Naiyyayikas also believe like Kumarila that error is due to a wrong synthesis of the presented and the represented objects. The represented object is confused with the presented one. The word 'anyatha' means 'elsewise' and 'elsewhere' and both these meanings are brought out in error. The presented object is perceived elsewise and the represented object exists elsewhere. They further maintain that knowledge is not intrinsically valid but becomes so on account of extraneous conditions (paratah pramana during both validity and invalidity).

Nyaya on God and salvation[edit]

Early Naiyyayikas wrote very little about Ishvara (literally, the Supreme Soul). Evidence available so far suggests that early Nyaya scholars were non-theistic or atheists.[43][44] Later, and over time, Nyaya scholars tried to apply some of their epistemological insights and methodology to the question: does God exist? Some offered arguments against and some in favor.[20]

Arguments that God does not exist[edit]

In Nyayasutra's Book 4, Chapter 1, verses 19-21, postulates God exists, states a consequence, then presents contrary evidence, and from contradiction concludes that the postulate must be invalid.[45]

The Lord is the cause, since we see that human action lacks results.
This is not so since, as a matter of fact, no result is accomplished without human action.
Since this is efficacious, the reason lacks force.

— Nyaya Sutra, IV.1.19 - IV.1.21 [45]

A literal interpretation of the three verses suggests that Nyaya school rejected the need for a God for the efficacy of human activity. Since human action and results do not require assumption or need of the existence of God, sutra IV.1.21 is seen as a criticism of the "existence of God and theism postulate".[45] The context of the above verses includes various efficient causes. Nyayasutra verses IV.1.22 to IV.1.24, for example, examine the hypothesis that "random chance" explains the world, after these Indian scholars had rejected God as the efficient cause.[20]

Arguments that God exists[edit]

Udayana's Nyayakusumanjali gave the following nine arguments to prove the existence of creative God:[21]

  • Kāryāt (lit. "from effect"): The world is an effect, all effects have efficient cause, hence the world must have an efficient cause. That efficient cause is God.[21]
  • Āyojanāt (lit., from combination): Atoms are inactive. To form a substance, they must combine. To combine, they must move. Nothing moves without intelligence and source of motion. Since we perceive substance, some intelligent source must have moved the inactive atoms. That intelligent source is God.[21]
  • Dhŗtyādéḥ (lit., from support): Something sustains this world. Something destroys this world. Unintelligent Adrsta (unseen principles of nature) cannot do this. We must infer that something intelligent is behind. That is God.[21]
  • Padāt (lit., from word): Each word has meaning and represents an object. This representational power of words has a cause. That cause is God.
  • Pratyayataḥ (lit, from faith): Vedas are infallible. Human beings are fallible. Infallible Vedas cannot have been authored by fallible human beings. Someone authored the infallible Vedas. That author is God.[21]
  • Shrutéḥ (lit., from scriptures): The infallible Vedas testify to the existence of God. Thus God exists.[21]
  • Vākyāt (lit., from precepts): Vedas deal with moral laws, the rights and the wrongs. These are divine. Divine injunctions and prohibitions can only come from a divine creator of laws. That divine creator is God.[21]
  • Samkhyāviśeşāt (lit., from the specialty of numbers): By rules of perception, only number "one" can ever be directly perceived. All other numbers other than one, are inferences and concepts created by consciousness. When man is born, his mind is incapable of inferences and concepts. He develops consciousness as he develops. The consciousness development is self-evident and proven because of man's ability with perfect numerical conception. This ability to conceive numerically perfect concepts must depend on something. That something is divine consciousness. So God must exist.[21]
  • Adŗşţāt (lit., from the unforeseen): Everybody reaps the fruits of his own actions. Merits and demerits accrue from his own actions. An Unseen Power keeps a balance sheet of the merit and demerit. But since this Unseen Power is Unintelligent, it needs intelligent guidance to work. That intelligent guide is God.[21]


The Naiyyayikas believe that the bondage of the world is due to false knowledge, which can be removed by constantly thinking of its opposite (pratipakshabhavana), namely, the true knowledge.[46] So the opening aphorism of the Nyāya Sūtra states that only the true knowledge lead to niḥśreyasa (liberation).[26] But the Nyaya school also maintains that the God's grace is essential for obtaining true knowledge.[47]Jayanta, in his Nyayamanjari describes salvation as a passive stage of self in its natural purity, unassociated with pleasure, pain, knowledge and willingness.[48]

Literature of Nyaya[edit]

The earliest text of the Nyāya School is the Nyāya Sūtra of Akṣapāda Gautama. The text is divided into five books, each having two sections. Vātsāyana's Nyāya Bhāṣya is a classic commentary on the Nyāya Sūtra. Udyotakara's Nyāya Vārttika (6th century CE) is written to defend Vātsāyana against the attacks made by Dignāga. Vācaspati Miśra's Nyāyavārttikatātparyaṭīkā (9th century CE) is the next major exposition of this school. Two other texts, Nyāyaṣūcinibandha and Nyāyasūtraddhāra are also attributed to him. Udayana's (984 CE) Nyāyatātparyapariśuddhi is an important commentary on Vācaspati's treatise. His Nyāyakusumāñjali is the first systematic account of theistic Nyāya. His other works include Ātmatattvaviveka, Kiraṇāvali and Nyāyapariśiṣṭa. Jayanta Bhatta's Nyāyamañjari (10th century CE) is basically an independent work. Bhāsavarajña's Nyāyasāra (10th century CE) is a survey of Nyāya philosophy.[49]

The later works on Nyāya accepted the Vaiśeṣika categories and Varadarāja's Tārkikarakṣā (12th century CE) is a notable treatise of this syncretist school. Keśava Miśra's Tārkabhaṣā (13th century CE) is another important work of this school.[50]

Gangeśa Upādhyāya's Tattvacintāmaṇi (12th century CE) is the first major treatise of the new school of Navya-Nyāya. His son, Vardhamāna Upādhyāya's Nyāyanibandhaprakāśa (1225 CE), though a commentary on Udayana's Nyāyatātparyapariśuddhi, incorporated his father's views. Jayadeva wrote a commentary on Tattvacintāmaṇi known as Āloka (13th century CE). Vāsudeva Sārvabhauma's Tattvacintāmaṇivyākhyā (16th century CE) is first great work of Navadvipa school of Navya-Nyāya. Raghunātha Śiromaṇi's Tattvacintāmaṇidīdhiti and Padārthakhaṇḍana are the next important works of this school. Viśvanatha's Nyāyasūtravṛtti (17th century CE) is also a notable work.[51] The Commentaries on Tattvacintāmaṇidīdhiti by Jagadish Tarkalankar (17th century CE) and Gadadhar Bhattacharya (17th century CE) are the last two notable works of this school.

Annaṁbhatta (17th century CE) tried to develop a consistent system by combining the ancient and the new schools, Prācina nyāya and Navya-Nyāya and Vaiśeṣika to develop the nyāya-vaiśeṣika school. His Tarkasaṁgraha and Dīpikā are the popular manuals of this school.[51]

See also[edit]


  1. ^ abcnyAya Monier-Williams' Sanskrit-English Dictionary, Cologne Digital Sanskrit Lexicon, Germany
  2. ^ abcNyaya: Indian Philosophy Encyclopædia Britannica (2014)
  3. ^B Gupta (2012), An Introduction to Indian Philosophy: Perspectives on Reality, Knowledge and Freedom, Routledge, ISBN 978-0415800037, pages 171-189
  4. ^PT Raju (1985), Structural Depths of Indian Thought: Toward a Constructive Postmodern Ethics, State University of New York Press, ISBN 978-0887061394, page 223
  5. ^ abcJohn A. Grimes, A Concise Dictionary of Indian Philosophy: Sanskrit Terms Defined in English, State University of New York Press, ISBN 978-0791430675, page 238
  6. ^ abcdDPS Bhawuk (2011), Spirituality and Indian Psychology (Editor: Anthony Marsella), Springer, ISBN 978-1-4419-8109-7, page 172
  7. ^ abcGavin Flood, An Introduction to Hinduism, Cambridge University Press, ISBN 978-0521438780, page 225
  8. ^Vassilis Vitsaxis (2009), Thought and Faith, Somerset Hall Press, ISBN 978-1935244042, page 131
  9. ^BK Matilal (1997), Logic, Language and Reality: Indian Philosophy and Contemporary Issues, Motilal Banarsidass, ISBN 978-8120807174, pages 353-357
  10. ^ abOliver Leaman (2006), Nyaya, in Encyclopaedia of Asian Philosophy, Routledge, ISBN 978-0415862530, pages 405-407
  11. ^Jeaneane Fowler (2002), Perspectives of Reality: An Introduction to the Philosophy of Hinduism, Sussex Academic Press, ISBN 978-1898723943, page 129
  12. ^ abB. K. Matilal "Perception. An Essay on Classical Indian Theories of Knowledge" (Oxford University Press, 1986), p. xiv.
  13. ^KN Jayatilleke (2010), Early Buddhist Theory of Knowledge, ISBN 978-8120806191, pages 246-249, from note 385 onwards;
    Steven Collins (1994), Religion and Practical Reason (Editors: Frank Reynolds, David Tracy), State Univ of New York Press, ISBN 978-0791422175, page 64; Quote: "Central to Buddhist soteriology is the doctrine of not-self (Pali: anattā, Sanskrit: anātman, the opposed doctrine of ātman is central to Brahmanical thought). Put very briefly, this is the [Buddhist] doctrine that human beings have no soul, no self, no unchanging essence.";
    Edward Roer (Translator), Shankara's Introduction, p. 2, at Google Books, pages 2-4
    Katie Javanaud (2013), Is The Buddhist 'No-Self' Doctrine Compatible With Pursuing Nirvana?, Philosophy Now;
    John C. Plott et al (2000), Global History of Philosophy: The Axial Age, Volume 1, Motilal Banarsidass, ISBN 978-8120801585, page 63, Quote: "The Buddhist schools reject any Ātman concept. As we have already observed, this is the basic and ineradicable distinction between Hinduism and Buddhism".
  14. ^BK Matilal (1997), Logic, Language and Reality: Indian Philosophy and Contemporary Issues, Motilal Banarsidass, ISBN 978-8120807174, pages 354-355
  15. ^David Ambeul (1998), Ontology in Indian Philosophy, in Routledge Encyclopedia of Philosophy (Editor: Edward Craig), Routledge, ISBN 978-0415073103, pages 118-127
  16. ^The Spectator at Google Books, Hindu Philosophy, Volume 32, page 1260
  17. ^N Sinha (1990), The Nyaya Sutras of Gotama, Motilal Banarsidass, ISBN 978-8120807488, see Introduction, pages i-ii
  18. ^ abDavid Christian (1 September 2011). Maps of Time: An Introduction to Big History. University of California Press. pp. 18–. ISBN 978-0-520-95067-2. 
  19. ^Kenneth Kramer (January 1986). World Scriptures: An Introduction to Comparative Religions. Paulist Press. pp. 34–. ISBN 978-0-8091-2781-8. 
  20. ^ abcdFrancis X. Clooney (2010), Hindu God, Christian God: How Reason Helps Break Down the Boundaries, Oxford University Press, ISBN 978-0199738724, pages 18-19, 35-39
  21. ^ abcdefghijSharma, C. (1997). A Critical Survey of Indian Philosophy, Delhi: Motilal Banarsidass, ISBN 81-208-0365-5, pp.209-10
  22. ^G Jha (1919), Original atheism of the Nyaya, in Indian Thought - Proceedings and Transactions of the First Oriental Congress, Vol ii, pages 281-285
  23. ^Dale Riepe (1979), Indian Philosophy Since Independence, Volume 1, BR Grüner Netherlands, ISBN 978-9060321133, page 38
  24. ^Sharma, C. (1997). A Critical Survey of Indian Philosophy, Delhi: Motilal Banarsidass, ISBN 81-208-0365-5, p.192
  25. ^Hiriyanna, M. (1993, reprint 2000). Outlines of Indian Philosophy, Delhi: Motilal Banarsidass, ISBN 81-208-1099-6, pp.245,245n
  26. ^ abChattopadhyaya, D. (1986), Indian Philosophy: A Popular Introduction, People's Publishing House, New Delhi, ISBN 81-7007-023-6, p.163
  27. ^James Lochtefeld, "Pramana" in The Illustrated Encyclopedia of Hinduism, Vol. 2: N-Z, Rosen Publishing. ISBN 0-8239-2287-1, pages 520-521
  28. ^Karl Potter (2002), Presuppositions of India's Philosophies, Motilal Banarsidass, ISBN 81-208-0779-0, pages 25-26
The Nyaya school considers perception, inference, comparison/analogy, and testimony from reliable sources as four means to correct knowledge, holding that perception is the ultimate source of such knowledge.[5][7]


Nyāya (literally “rule or method of reasoning”) is a leading school of philosophy within the “Hindu umbrella”—those communities which saw themselves as the inheritors of the ancient Vedic civilization and allied cultural traditions. Epistemologically, Nyāya develops of a sophisticated precursor to contemporary reliabilism (particularly process reliabilism), centered on the notion of “knowledge-sources” (pramāṇa), and a conception of epistemic responsibility which allows for default, unreflective justification accorded to putatively veridical cognition. It also extensively studies the nature of reasoning in the attempt to map pathways which lead to veridical inferential cognition. Nyāya's methods of analysis and argument resolution influenced much of classical Indian literary criticism, philosophical debate, and jurisprudence. Metaphysically, Nyāya defends a robust realism, including universals, selves, and substances, largely in debate with Buddhist anti-realists and flux-theorists. Nyāya thinkers were also India’s most sophisticated natural theologians. For at least a millennium, Nyāya honed a variety of arguments in support of a baseline theism in constant engagement with sophisticated philosophical atheists, most notably Buddhists and Mīmāṁsakas (Hindu Ritualists).

Nyāya’s prehistory is tied to ancient traditions of debate and rules of reasoning (vāda-śāstra). The oldest extant Nyāya text is the Nyāya-sūtra attributed to Gautama (c. 200 C.E.). Throughout much of Nyāya’s formative period the philosophical development of the school took place through commentaries on the sūtras (with important exceptions including works of Jayanta, c. 875, Udayana, c. 975, and the somewhat heterodox Bhāsarvajña, c. 875). Leading commentators include Vātsyāyana (c. 450), Uddyotakara (c. 600) Vācaspati Miśra (c. 900) and Udayana. The school would enter its “new” phase (navya-nyāya) in the work of the eminent epistemologist Gaṅgeśa Upādhyāya (c. 1325). This article focuses on the older tradition of Nyāya, beginning with the sūtras, with occasional gestures toward developments within the new school.  Given the breadth of Nyāya thought, this discussion has to exclude some important topics for the sake of economy, such as aesthetics, philosophy of language, and theory of value. The article's primary focus is on epistemology and metaphysics. There is a brief consideration of Nyāya’s philosophy of religion.

Table of Contents

  1. Epistemology
    1. Perception
      1. The Characteristics of Perception
      2. Extraordinary Perceptual States
      3. Introspection
    2. Inference
      1. The Characteristics of Inference
      2. The Structure of Inference
      3. Inferential Defeaters or Fallacies
      4. Suppositional Reasoning
    3. Analogical Reasoning
    4. Testimony
    5. Non-pramāṇa Epistemic Capacities
    6. General Theory of Knowledge
      1. A Causal Theory of Knowledge
      2. Internalist Constraints
      3. A Relational Theory of Cognition
      4. Response to Skepticism
  2. Metaphysics
    1. Substance
    2. Quality
    3. Action
    4. Universal
    5. Inherence
    6. Individuator
    7. Absence
    8. Causation
  3. Philosophy of Religion
  4. References and Further Reading
    1. Sanskrit Source Materials
    2. Primary Texts in English Translation
    3. Studies of Nyāya Epistemology, Metaphysics, and Philosophy of Religion in English
    4. General Studies

1. Epistemology

The Nyāya-sūtra opens with a list of its primary topics, sixteen items which may be grouped into the following four categories: epistemology, metaphysics, procedures and elements of inquiry, and debate theory. That Nyāya’s initial topic is epistemology (pramāṇas, “knowledge-sources”) is noteworthy. Both the sūtras and the commentarial tradition argue that epistemic success is central in the search for happiness, since we must understand the world properly should we desire to achieve the goods it offers.Vātsyāyana claims that while Nyāya’s metaphysical concerns overlap with other, more scripturally-based Hindu schools, what distinguishes Nyāya is a reflective concern with evidence, doubt and the objects of knowledge. He further defines Nyāya’s philosophical method as the “investigation of a subject by means of knowledge-sources” (NB 1.1.1). Importantly, the pramāṇas are not simply the means by which individuals attain veridical cognition. They are also the final court of appeals in philosophical dispute. Uddyotakara thus claims the best kind of demonstrative reasoning occurs when the pramāṇas are deployed in concert in order to establish a fact.

The four pramāṇas are perception, inference, analogical reasoning, and testimony. We will discuss them in order. Then, we will consider Nyāya’s theory of knowledge in general.

a. Perception (pratyakṣa)

i. The Characteristics of Perception

Nyāya-sūtra 1.1.4 defines perceptual cognition as follows.

A perceptual cognition arises by means of the connection between sense faculty and object, is not dependent on words, is non-deviating, and is determinate.

This sūtra provides four conditions which must be met for cognition to be perceptual. The first, that cognition arises from the connection between sense faculty and object, evinces Nyāya’s direct realism. It is such connection, the central feature of the causal chain which terminates in perceptual cognition, which fixes the intentionality of a token percept. Uddyotakara enumerates six kinds of connection (sannikarṣa) to account for the fact that that we perceive not only substances, but properties, absences, and so on: (i) conjunction (samyoga), the connection between a sense faculty and an object; (ii) inherence in what is conjoined (saṁyukta-samavāya), the connection between a sense faculty and a property-trope which inheres in an object; (iii) inherence in what inheres in what is conjoined (saṁyukta-samaveta-samavāya), the connection between a sense faculty and the universal which is instantiated in a property-trope; (iv) inherence (samavāya), the kind of connection which makes auditory perception possible; (v) inherence in what inheres (samaveta-samavāya), the connection between the auditory faculty and universals which inhere within sounds; (vi) qualifier-qualified relation (viśeṣya-viśeṣaṇa-bhāva), the connection which allows for the perception of inherence and absence in objects. In all cases, the perceptual cognition is born of connection between a sense faculty and an occurrent fact or object.

The second condition, that the cognition produced is not dependent on words, has a somewhat complicated interpretive history. Generally, Nyāya holds that ordinary perception involves concept deployment. Therefore, this restriction does not endorse a view held by the Buddhist Dignāga and his followers, that genuine perception is non-conceptual (kalpanā-apodha). Still, the meaning of avyapadeśya is disputed amongst Naiyāyikas. On one reading, this qualification serves the purpose of distinguishing between perceptually and testimonially generated cognitions. The latter also require information provided by the senses but further require the deployment of semantic and syntactic knowledge. An allied reading suggests that while involving the application of concepts, perception of an object is often causally prior to speech acts involving it.

The third, “non-deviating” condition blocks false cognitions, like the misperception that an oyster shell is a piece of silver, from the ranks of pramāṇa-born. This is tied to the Nyāya notion that pramāṇas are by definition inerrant, and that false cognitive presentations are not truly pramāṇas but pseudo-pramāṇas (pramāṇa-ābhāsa). Though we may mistakenly take a pseudo-pramāṇa, like the illusion of a person in the distance, to be the real thing, it is not. “Perception” and similar pramāṇa-terms have success grammar for Nyāya.

The fourth, “determinate” condition blocks cognitions which are merely doubtful from the ranks of the pramāṇa-born. Dubious cognitions, like that of a distant person at dusk, do not convey misleadingly false information, but being unclear, they do not properly apprehend the object in question. It could be a person or a post. As such, one neither correctly grasps its character nor falsely takes it to represent accurately a certain object. Later Naiyāyikas, most notably Vācaspati Miśra, read the qualifiers “notdependent on words” and “determinate” disjunctively, in order to say that perception may be non-propositional or propositional. However anachronistic this may be as an interpretation of the Nyāya-sūtra, this division is accepted by later Nyāya.

ii. Extraordinary Perceptual States

Nyāya admits of certain kinds of extraordinary perception in order to account for cognitive states that are perceptual in character, but distinct from those commonly experienced. They involve modes of sense-object connection other than the six kinds noted above. Later Nyāya (beginning at least with Jayanta) recognizes three kinds of extraordinary perception: (i) yogic perception, (ii) perception of a universal through an individual which instantiates it, and (iii) perception of an object’s properties as mediated by memory.

Yogic perception includes experiential states reported by contemplatives in deep mediation. Their cognitive objects (usually the deep self or God) are taken to be experienced in a direct and unmediated way, but generally without the operation of the external senses. Given their experiential character and their putative agreement with other sources of knowledge like scripture and inference, yogic experiences are prima facie taken to be veridical, produced by non-normal perception.

Perception of a universal through an individual which instantiates it is Nyāya’s response to the problem of induction. Nyāya holds that universals are perceptually experienced as instantiated in individuals (see the third of Uddyotakara’s six kinds of connection above). But the notion that we may have apprehension of all of the individuals which instantiate a universal, qua their being instantiations of the universal, is further accepted by Nyāya in order to explain how we attain to knowledge of vyāpti, or invariable relation between universals, which undergirds causal regularities of various sorts. Unless one’s experience of some particular smoke instance as conjoined with a fire instance allows him to experience all instances of smoke qua smoke as being conjoined with all instances of fire qua fire, through the natural tie between the universals smokiness and fieriness, inductive extrapolation would be impossible. Nyāya thus solves the problem of induction by appeal to extraordinary perception. This does not imply that we are always able to recognize such relations. It may take repeated experience for us to notice the ever-present connection. But when such recognition arises, it is due to perceptual experience, not an extrapolative projection of past experience.

Perception of the properties of an object mediated by memory involves the visual experience of unpresented properties of an object which is currently seen. Standard examples include seeing a piece of sandalwood as fragrant or seeing a piece of ice as cold. Here, there is a standard kind of sense object connection, but some of the phenomenal features of the experience, while veridical, are not generated by the ordinary connection. They are rather mediated by a special connection grounded in memory. What distinguishes this kind of perception from straightforward inference is that the property in question is experienced with a phenomenal character lacking in inference. This suggests that what may be considered inference for some may take the form of perception for others, depending on their familiarity with the conceptual connection between the properties in question.

iii. Introspection

Nyāya holds that while cognitions reveal or present their intentional objects, they rarely present themselves directly. When they are directly cognized, cognitions are grasped by other, apperceptive cognitions. As apperceptive awareness reveals a cognition along with its predication content or “objecthood” (that is, my cognition of a red truck is apperceptively cognized as having the predication content “red” and “truck-hood”), it is practically indefeasible. But, as Gaṅgeśa notes, this indefeasibility does transfer to the content of the original cognition (which is itself object of the apperceptive awareness). I may have mistaken a purple truck for a red truck, forgetting that my eyewear distorts certain colors. Apperception is subsumed by Nyāya into the category of perception. In this case, the operative sense faculty is the “inner organ” (manas) and the object is a cognition conceived of as a property of a self. Gaṅgeśa argues at length with a Prābhākara Mīmāṁsaka (a representative of another leading Hindu school), defending Nyāya’s version of apperception against the Mīmāṁsā view that each cognition itself has a component of reflectively self-awareness.

A few words on manas (the inner organ): NS 1.1.16 argues that the absence of simultaneous cognition from all of the senses indicates the presence of a faculty which governs selective attention. The manas is identified as this faculty, an insentient psychological apparatus which processes the information of the senses. A formulation of perception by the Vaiśeṣika school (Vaiśeṣika-sūtra 3.1.18), accepted by Nyāya, is that it normally consists in a chain of connection between four things: a self and its manas, the manas and a sense organ, and the sense organ and an object. Manas also is the faculty which governs mnemonic retrieval and, as noted above, apperceptive awareness of mental states. Selves, in the Nyāya view, are fundamentally loci of awareness, cognition, and mnemonic dispositions (saṁskāra). But just as they rely on the five senses to experience the world, they rely on manas for the functioning of memory and apperception.

To conclude, we may note that perception is commonly called the jyeṣṭapramāṇa (the “eldest” knowledge source) by Nyāya, since other pramāṇas depend on perceptual input, while perception operates directly on the objects of knowledge. Indeed, Gaṅgeśa suggests the following definition of a perceptual cognition: “a cognition that does not have another cognition as its proximate instrumental cause.” Inference, analogy, and testimony, on the other hand, depend on immediately prior cognitions to trigger their functioning. The normative status accorded to veridical perceptual cognition is primarily a matter of causation and intentionality (viṣayatā). If a cognition is caused by the appropriate causal chain, starting with the contact of a sense faculty and an external object (or, in the case of apperception, the internal organ and an immediately prior cognition), and the cognition produced has an “objecthood” or intentionality which accurately targets the object in question, the cognition is veridical and has the status prāmāṇya (pramāṇā-derived).

b. Inference (anumāna)

i. The Characteristics of Inference

Nyāya-sūtra 1.1.5 defines inference as follows.

[An inferential cognition] is preceded by that [perception], and is threefold: from cause to effect, from effect to cause or from that which is commonly seen.

This definition is somewhat elliptical. But it focuses on the fundamental character of inference: it is a cognition which follows from another cognition owing to their being conceptually connected in some way. Etymologically, anumāna means “after-cognizing”. Inference follows from an earlier cognition, “that” in the sūtra above. Vātsyāyana interprets “that” (tat) to refer to a perceptual cognition, and suggests that perceptual cognition precedes inference in two ways: (i) to engage in inference requires having perceptually established a fixed relationship between an inferential sign and the property to be inferred, and (ii) perceptual input triggers inference in that one must cognize the inferential sign as qualifying the locus of an inference. He provides a more explicit definition of inference as “a ‘later cognition’ of an object by means of cognition of its inferential sign” (NB 1.1.3).

Uddyotakara reasonably broadens the scope of “that” in NS 1.1.5 to refer to pramāṇa-produced cognitions of any kind which may trigger inference (NV 1.1.5). The meaning of reasoning from cause to effect and from effect to cause should be clear. Uddyotakara interprets reasoning from what is “commonly seen” as that which is grounded in non-causal correlations that have proven invariable. Vātsyāyana offers another reading: when the relationship between an inferential sign and the inferential target is not perceptible, the target may be inferred owing to the similarity of the unseen prover with something known. The classic example of this kind of inference is as follows: Desire, aversion, and knowledge are properties. Properties require substances which instantiate them. Therefore there is anunseen substance which instantiates desire, aversion, and knowledge: the inner self (NB 1.1.5). Though the connection between mental states like desire and the self which supports them is unseen, the similarity between mental states and other, commonly seen properties (like the color green) is enough to allow for the inference to a property-bearer.

The history of Nyāya’s logical theory is extensive. Here, we will note a few salient points and focus on inference as understood in the period most important to this study (the final great creative period of what is normally known as “Old Nyāya”). First, in Nyāya, logic is subsumed within epistemology, and therefore tends to have a strong informal and cognitive flavor, mapping paths of reasoning that generate veridical cognitions and noting the common ways that reasoning goes wrong. Fundamentally, one makes inferences for oneself. Formal proofs are meant to mirror the kind of reasoning that takes place internally, for didactic or polemical purposes. The first explicit recognition of this dual nature of inference is commonly attributed to the Buddhist Dignāga, who coined the terms svārthānumāna (inference for oneself) and parārthānumāna (inference for another). Such a division is implicit, however, in the Nyāya-sūtra’s distinction between inference as an individual’s source of knowledge (NS 1.1.5) and as a systematic method of proof meant to convince another (NS 1.1.32-39).

Second, inference is triggered by the recognition of a sign or mark, whose relationship with some other object (property or fact) has been firmly established. The primary cause of an inferential cognition is an immediately prior “subsumptive judgment” (parāmarśa) which grasps an inferential sign as qualifying an inferential subject (the locus of the inference), while recollecting the sign’s invariable concomitance with some other fact or object. The two fundamental requirements for inference are, therefore, awareness of pakṣadharmatā, the inferential mark’s qualifying the locus of the inference, and vyāpti, the sign’s invariable concomitance with the target property or probandum. A paradigmatic act of inference to oneself is: “There is fire on that mountain, since there is smoke on it,” which is supported by the awareness that fire is invariably concomitant with smoke. Naiyāyikas examine and standardize the conditions under which invariable concomitance (vyāpti) between a probans and a target fact is established.

Third, as logic’s function is to generate veridical cognition, Nyāya does not stress the distinction between soundness and validity in respect to the quality of an argument. Both formal fallacies and the inclusion of false premises lead to hetv-ābhāsa (“pseudo provers” or logical defeaters), since they engender false cognition.

ii. The Structure of Inference

Concerning inference for polemical or didactic purposes, Nyāya employs a formal five-step argument illustrated by the following stock example.

  1. There is fire on the hill (the pratijñā, thesis).
  2. Because there is smoke on the hill (the hetu, reason or probans).
  3. Wherever there is smoke, there is fire; like a kitchen hearth and unlike a lake (the udāharaṇa, illustration of concomitance).
  4. This hill is likewise smoky (the upanaya, application of the rule).
  5. Thus, there is fire on the hill (the nigamana, conclusion).

In practice, the five-membered “syllogism” is often truncated into three steps as follows.

A is qualified by S,
because it is qualified by T
(whatever is qualified by T is qualified by S) like (Tb&Sb).

Again, the stock example:

The hill is qualified by fieriness
because it is qualified by smokiness
(whatever is qualified by smokiness is qualified by fieriness) like a kitchen hearth and unlike a lake.

The basic components of the argument are:

  • the inferential subject (pakṣa), the locus of the inferential sign; the hill in our example. The general conditions for something to be taken up as a subject for inference, are that it be under dispute or currently unknown, with no reports from other knowledge sources available to definitively settle the issue.
  • the “prover” or inferential sign (hetu); smoke (more precisely, smokiness)
  • the probandum (sādhya), the property to be proved by the inference; fire (more precisely, fieriness)
  • the “pervasion” or concomitance (vyāpti) that grounds the inference, which is implicit in the step: “wherever there is smoke, there is fire
  • a corroborative instance (sapakṣa); a locus known to be qualified by both the prover (hetu) and the probandum (sādhya); this is a token of inductive support for the vyāpti; a kitchen hearth. There are also known negative examples, (vipakṣa) of something that lacks both the prover property and the probandum; where there is no fire, there is no smoke, like a lake. Obviously, an instantiation of the prover property in the vipakṣa class vitiates the argument.

This stock inference asserts that there is fire on the mountain (the mountain is qualified by the property of fieriness, Fm). Why?  Because the mountain is qualified by the property of smokiness, Sm. There is an implied concomitance which grounds the inference: “Whatever is qualified by smokiness is qualified by fieriness,” ∀x(Sx-->Fx). In the language of Nyāya, fire “pervades” smoke. This is an epistemic pervasion: we never find smoke instances without fire instances. As such, smoke is a prover property that allows us to infer the presence of fire. Finally, an example must be included in the syllogism to illustrate the inductive grounding which undergirds the invariable concomitance. In kitchen hearth k, fire is known to be concomitant with smoke, (Sk&Fk). In some instances, negative examples are used to indicate the vyāpti through contraposition. Wherever there is no fire there is no smoke, as illustrated in a lake, (~Fl& ~Sl).

Nyāya-sūtra 1.1.25 defines an example (dṛṣṭānta) as “something about which experts and laypersons have the same opinion (buddhi-sāmyam).” Vātsyāyana (NB Intro.; translation in Gangopadhyaya 1982: 5) elaborates:

Corroborative instance is an object of perception—an object about which the notions (buddhi) of the layman as well as the expert are not in conflict. . . It is also the basis of the application of nyāya (reasoning). By (showing) the contradiction of the dṛṣṭānta the position of the opponent can be declared as refuted. By the substantiation of the dṛṣṭānta, one’s own position is well-established. If the skeptic (nāstika) admits a corroborative instance, he has to surrender his skepticism. If he does not admit any, how can he silence his opponent?

Regarding agreement between laypersons and experts, the basic idea, of course, is that supporting examples should be non-controversial. A good illustration of this is found in Uddyotakara’s Nyāya-vārttika (2.1.16). Debating with a Buddhist interlocutor over the existence of property-bearing substances, he claims “there is no example whatever (na hi kaściddṛṣṭāntaḥ) . . . about which both parties agree (ubhaya-pakṣa-sampratipannaḥ).”

In another interpretation of the three kinds of inference in the sūtra, Uddyotakara introduces three kinds of argument: wholly-positive, wholly-negative, and positive-negative. Wholly-positive inference occurs when there are attested cases of sapakṣa but no vipakṣaknown. From a Buddhist perspective, the inference “whatever exists is momentary, like a cloud” would require this kind of inference, since there would be no available vipakṣato illustrate the non-presence of the prover. In cases where the property to be proven is entirely subsumed within the pakṣa, a wholly-negative form is employed. The vyāpti is contraposed, as in the following inference: “A living body has a self because it breathes. Whatever does not have a self does not breathe, like a pot.” Most inferences are in principle amenable to the positive-negative form, like “There is fire on that hill, since there is billowing smoke over it. Wherever there is smoke, there is fire, like a kitchen hearth, and unlike a lake.”

iii. Inferential Defeaters or Fallacies

Naiyāyikas provide various typologies of inferential fallacies and defeaters (hetv-ābāsa, “pseudo provers”). We may note five common kinds: (i) fallacies of deviation occur when the prover or inferential sign is not reliably correlated with the inferential target. To argue that “my mother must be visiting, since there is a Mazda parked outside” would involve the fallacy of deviation, since “Owning a Mazda” is a property that tracks not only my mother but many other drivers. It cannot, therefore, reliably indicate her presence. (ii) fallacies of contradiction occur when the prover in fact establishes a conclusion opposed to the thesis that someone defends. This would occur should someone argue that “Jones was not a kind man, since he gave his life for others,” as giving one’s life for others is an indicator of kindness or compassion. (iii) fallacies of unestablishment occur when a supposed prover is not actually the property of the inferential subject. Should someone argue “I know that your mother is in town, since I saw a Prius parked outside your home,” the prover is unestablished, since my mother does not in fact own a Prius. (iv) argumentsare rebutted, when their conclusions are undermined by information gleaned by more secure knowledge sources. Someone may argue that my friend must be out of town, since he hasn’t answered his phone all week. But if I just saw the friend in question at the local coffee shop, my perceptual knowledge rebuts his prover, invalidating it. Similarly, (v) arguments are counterbalanced when counterarguments of equal or greater force are put forth in support of an opposing conclusion. Disputant a argues that the inherent teleology of biological processes proves the existence of God. Disputant b argues that the existence of gratuitous evil proves that there is no God. Pending further philosophical work, argument b neutralizes the conclusion of argument a.

iv. Suppositional Reasoning

Tarka, suppositional or dialectical reasoning, is crucial to Nyāya’s philosophical program. Still, according to Vātsyāyana, it is not a full-fledged independent pramāṇa. Rather it is an “assistant to the pramāṇas” (pramāṇa-anugrahaka) (NB Introduction). Tarka is commonly employed as a form of reductio argument for the sake of judging competing claims or arguments, a reductio which depends not only on logical inconsistency, but on incoherence with deeply-held beliefs or norms. In the face of competing claims x and y about subject s, tarkais employed to show that x violates such norms, thereby shifting the presumptive weight to alternative y. Vātsyāyana (NB1.1.40) offers the example of competing claims about the nature of the self. Some say that the self is a product which comes to exist within time while others claim that it is unproduced and eternal. The Naiyāyika deploys tarkaby arguing that a consequence of the former view is that one’s initial life circumstances would not be determined by his karmic inheritance from previous lives, a severe violation of fundamental metaphysical positions held by almost every Indian school. As such, strong presumptive weight should be given to the latter view. This example illustrates the way in which considerations of negative coherence govern tarka’s deployment.

Vātsyāyana notes that the reason tarkais not an independent pramāṇa is that it does not independently establish the nature of the thing in question (anavadhāranāt). It provides consent (anujānāti) for one of two alternatives independently supported by apparent pramāṇas, by illustrating problems with the competing view. Uddyotakara (NV 1.1.1) adds that it is excluded from the ranks of pramāṇa because it does not provide definitive cognition (pramāṇamparicchedakaṁnatarkaḥ).

Later Naiyāyikas extol tarka as a means to test dubious inferential concomitances (vyāpti) by testing them against more fundamental holdings of various sorts. Tarka also has a crucial role in the management of philosophical doubt. Against the skeptic, Nyāya argues that doubt is not always reasonable. Tarka helps to distinguish legitimate doubt from mere contentiousness by illustrating which claims are better motivated and hence deserving of presumptive weight.

c. Analogical Reasoning (upamāna)

Nyāya-sūtra1.1.6 defines analogyas follows.

Analogy makes an object known by similarity with something already known.

Naiyāyikas commonly frame analogy as a means of vocabulary acquisition, and it has a severely restricted scope compared with the other pramāṇas. The standard example involves a person who is told that a water buffalo looks something like a cow and that such buffalo are present in a certain place in the countryside. Later, when out in the countryside, he recognizes that the thing he is seeing is similar to a cow, and therefore is a water buffalo. The cognition “That thing is a water buffalo,” born of the recollection of testimony regarding its similarity with a cow and the perception of such common features, is paradigmatically analogical. Though most of the other schools either reduce analogy to a more fundamental pramāṇaor conceive of it in very different terms (Mīmāṁsā conceives of it as the capacity by which we apprehend similarity itself), Nyāya contends that the cognition in question is sui generis analogical, though it incorporates information from other pramāṇas.

d. Testimony (śabda)

NS1.1.5 defines testimony as follows.

Testimony is the assertion of a qualified speaker.

The semantic range of āpta (“authority,” “credible person”) includes expertise, trustworthiness, and reliability. Vātsyāyana claims that an āpta possesses direct knowledge of something, and a willingness to convey such knowledge without distortion (NB 1.1.7). It is clear, though, that Nyāya does not require any kind of special expertise from such a speaker in normal situations. Nor does a hearer need positive evidence of trustworthiness. Mere absence of doubt in the asserter’s ability to speak authoritatively about the issue at hand is enough. Testimony is thus thought of as a transmission of information or content. A person attains an accurate cognition through some pramāṇatoken. In a properly functioning testimonial exchange, she bestows the information apprehended by the initial cognition to an epistemically responsible hearer. On such grounds, Uddyotakara notes that testimonial utterances may be divided into those whose contents are originally generated by perception or by inference. Jayanta likewise claims that the veridicality or non-veridicality of a testimonial cognition is dependent on the speaker’s knowledge of the content of her statement and her honesty in relating it.Vātsyāyana (NB 2.1.69) illustrates a levelheaded frankness about testimony’s importance, noting that “in accord with knowledge gained by testimony, people undertake their common affairs.” Uddyotakarasimilarlyrecognizes that testimony has the widest range of any source of knowledge, far outstripping what one may know from personal perception, inference or analogy.

e. Non-pramāṇa Epistemic Capacities

From the sūtra period, Nyāya recognizes a number of epistemic capacities which are nevertheless considered non-pramāṇa (NS 2.2.1-12). They are not considered independent pramāṇas for one of two reasons: (i) they are reducible to subspecies of other pramāṇas, or (ii) they do not produce the specific kind of cognitions which a pramāṇa must deliver. A core locus of debate amongst classical Indian thinkers is the nature and number of pramāṇas. Nyāya contends that the above four are the only irreducible sources of knowledge, which subsume all other kinds.

f. General Theory of Knowledge

i. A Causal Theory of Knowledge

Naiyāyikas speak of cognitive success in causal terms. “Pramāṇa” normally refers to a means or process by which veridical awareness-episodes (pramā) are generated, as seen above. Vātsyāyana glosses the meaning of pramāṇaas “that by which something is properly cognized (pramītyateanena)” (NB1.1.3).  Uddyotakara concurs: “what is spoken of as a pramāṇa? A pramāṇais the cause of a [veridical] cognition” (upalabdhi-hetupramāṇam) (NV1.1.1). Moreover, despite its focus on reflective consideration of belief and valid cognition, Nyāya argues that the simple,unreflective functioning of a pramāṇa like perception or testimony is enough to generate knowledge in the absence of countervailing evidence.

ii. Internalist Constraints

Nyāya does maintain an internalist constraint: Once doubt arises—by adversarial challenge, peer disagreement, inconsistency between differentcognitions, and so forth —a cognition must be validated in order to maintain the status of being “pramāṇa-produced.” Doubt triggers a second-order concern with reflective inquiry and certification. The sūtras state that “Where there is doubt, there must be ongoing examination” (NS 2.1.7). Uddyotakara therefore claims that doubt is an essential component of investigation (vicāra-aṅga) (NV 1.1.23). Validation involves consciously reflecting on the etiology of a cognition to ensure that it is the product of a properly-functioning pramāṇa. It may also involve the deployment of other pramāṇasin the hopes for a convergence of knowledge-sources (pramāṇa-saṁplava) in support of the doubted cognition. In his opening comments on the Nyāya-sūtra, Vātsyāyana famously provides a pragmatic test (but not definition) of truth: cognitions which guide us to successful action are likely veridical.

iii. A Relational Theory of Cognition

Nyāya epistemologists speak of cognition (jñāna, buddhi, upalabdhi, pratyaya): generally immediate awareness states of what Nyāya understands to be a mind-independent external reality. In the case of apperception, one cognizesher own mental states. Ontologically, cognitions are considered properties (guṇas) of individual selves (ātmans). Memory dispositions, when triggered, generate cognition about the past. With a few exceptions, cognitions target things other than themselves.

For Nyāya, cognitions target their objects by means of a relation called “objecthood” (viṣayatā). Nyāya’s theory is thus not exactly representational, but relational. “Objecthood” minimally has a threefold structure (with the possibility of iteration) corresponding to three features of the external object in question: a portion of the cognition targets an object itself, a portion of the cognition targets a property of the object, and finally, a portion of the cognition targets the relationship between the object and its property. In cases of veridical cognition (pramā), the portion of cognition which targets a substantive and the portion which targets its property match up. Gaṅgeśa famously defines veridical cognition as “a cognitive state with predication content x about something in fact qualified by x” (Tattvacintāmaṇi, pramā-lakṣaṇa-vāda). Seeing a male human being as qualified by “man” would be a paradigm case of veridical cognition. Error is generally classified as a misfire of the property-scoping portion of cognition. In error, a substantive is indeed cognized, but the property which is targeted does not actually qualify the substantive in question. The cognition’s intentionality is bifurcated, so to speak, simultaneously scoping a substantive and a property which is in fact alien to it.

iv. Response to Skepticism

Nyāya is a staunchly anti-skeptical tradition of epistemology. While it does give an important role to doubt, which, as seen above, triggers reflection and philosophical review, it rejects the notion that doubt should be the starting place in philosophical reflection. Doubt itself should be motivated, as trust is a better default starting place in both ordinary life and philosophy. Pragmatically, Nyāya argues that the role of epistemology is to better hone our cognitive abilities in order to succeed in our life aims. But unrestricted doubt would undermine our ability to function on a basic level, and it therefore militates against the very point of epistemological inquiry. Theoretically, Nyāya argues that error and indeed doubt itself are conceptually parasitical on true cognition. Error and doubt only make sense against a background of true belief, and therefore reflection must start by taking putatively veridical cognition at face value. Allied to this is a strain of criticism that even the simple act of giving voice to skeptical arguments belays a philosopher’s dependence on knowledge sources, including the inductively-supported tie between words and their meanings, which a skeptic relies on to speak his case. Given that everyone, the skeptic included, relies on pramāṇas, they are to be given the lion’s share of default entitlement.

2. Metaphysics

Nyāya defends a realist and pluralist metaphysics of categories (padārthas, lit. “things denoted by words”), largely adapted, with some modifications, from its sister school Vaiśeṣika. The categories are substance, quality, action, universal, individuator, inherence and absence. They will be discussed individually below.

a. Substance (dravya), Including Self (ātman)

Substances are the bedrock of Nyāya/Vaiśeṣika metaphysics (hereafter, simply “Nyāya Metaphysics”), as other categories generally inhere within substances or are nested within properties that inhere within substances. Paradigmatic substances include the indestructible atoms of earth, water, air and fire; composite substances like pots and trees; inner “selves” (ātman) which are the eternal, reincarnating souls; and God, a unique ātman.

Naiyāyikas provide a number of arguments in support of a non-material self. A standard argument runs as follows: Things like desire, cognition, experiences of pleasure and pain and volition are qualities. All qualities inhere in substances. Therefore, there is a substance to which desire and the rest belong. This conclusion is then followed by an argument from elimination. None of the material elements like earth or water are the bearers of desire and the rest. Therefore, there must be a special, non-material substance, namely a self (see various commentaries on NS 1.1.10). This argument is bolstered by others meant to illustrate that the physical body, as a product of material elements cannot be the fundamental locus of conscious states.

Some of the richest debates in classical India take place between Nyāya and Buddhists over the reality of substances. The central concern of such debates is often the statusof individual selves—an important substance, to say the least. Famously, the Buddha declared that reality is “lacking a self” (anātman), and his followers develop a number of arguments which purport to illustrate this in two ways. (i) Diachronically: moment by moment, things are destroyed and new things arise, such that no substance (including selves) endures for longer than a moment. (ii) Synchronically: in a single moment, what we take to be wholes (including selves) are nothing more than heaps of micro-properties (illustrated by the famous chariot metaphor in The Questions of King Milinda.) The Buddhist position is that although there is no such thing as an enduring self, the need for moral continuity and other desiderata may be satisfied merely by the causal connections between events in a single causal stream which we refer to as a “person.”

Nyāya’s response is to defend the existence of substances generally and selves in particular. In defense of substances, it argues that composite substances have capacities beyond the mere collection of their parts (NS 2.1.35). Moreover, Nyāya argues that the Buddhist reduction, if carried out consistently, would lead to an absurdity. We can see composite substances, but we cannot seeentities like atoms, which exist below our perceptual threshold. But if substances are nothing but heaps of micro objects/properties, which themselves can be reduced, and so on, then we should not be able to perceive substances at all. Thus, there must be a unified identity for individual substances which undergirds their availability for perceptual experience (NS 2.1.36).

In defense of the diachronic existence of individual selves, Nyāya argues that our experience of recollection (“that is the very man I saw a week ago”) requires a locus of memory which spans the time between the initial experience and the re-experience of an object (NS 1.1.10 and allied commentaries). In this spirit, Uddyotakara, following Vātsyāyana, argues that if I am now a different self than the “me” of yesterday, I should not be able to recollect things which that “me” experienced, since one self is unable to recollect the content of another’s experience. In defense of the synchronic identity of selves, Nyāya argues that cross-modal recognition (“that thing I see is the same thing I am touching”) requires a single experiencer with the ability to synthesize data from various senses (NS 3.1.1-3). Early Nyāya’s arguments for the self find their apex in Udayana’s monograph Determining the Truth of the Self.

b. Quality

Qualities (guṇa), are property tropes which qualify substances. Unlike universals they are not repeatable. The red color of some particular fire hydrant is a quality. Like other instances of the color red it is inhered by the universal redness, but it is as particular as the hydrant which it qualifies. Qualities include color, number (which is thought to inhere in objects), spatial location, contact, disjunction, and so forth, along with qualities which are unique to selves, like desire, cognition, and karmic merit.

c. Action

Like qualities, actions (karma) inhere in substances and are non-repeatable tropes. But they have causal capacities which qualities lack, particularly the ability to engender conjunction and disjunction between substances.

d. Universal

Universals (sāmānya or jāti) inhere in substances (for examplepot-hood), qualities (redness) or motions (contraction-hood). Naiyāyikas argue that universals are required to account for common experiences of a recurring character, for the functioning of language, andto undergird causal regularities in nature (which are held to be relations between universals). As its theory of universals is developed, Nyāya recognizes entities which are like universals, but which are, for theoretical reasons, excluded from their ranks (upādhi). Udayana would famously chart the reasons for such exclusion. These are: (i) A true universal must be capable of more than one instance. Spacehood would not be a true universal, as it can only have one instance. (ii) Two universals which have the same exact instances are in fact the same universal, simply under two designations. (iii) Should two apparent universals share an instance, while one is not entirely subsumed within the other, both are mere upādhis. This criterion, which is the most controversial of the “universal-blockers,” suggests that the operative notion of universal here is something akin to natural kinds. (iv) Any supposed universal that would, if accepted, lead to an infinite regress (for example universal-hood), is not accepted. (v) There is no universal for individuators (see below), as their ontic function is to introduce primitive differentiation. (vi) There is no universal for inherence (see below), as this would engender a vicious infinite regress: inherence would require further inherence between it and its universal “inherencehood”, and so on.

e. Inherence

Inherence is a relation which is central to Nyāya’s ontology, by which qualities, actions, universals, and individuators relate to substances, by which universals relate to qualities and actions, and by which wholes relate to their parts. In the first instance, the brown color of a cow inheres in the cow. In the second, the universal brownness inheres in the quality trope brown. In the third, my car, a substance, is a single entity, which inheres in its various parts. Thus, your touching just one part of my car is enough to justify the claim “you touched my car” simpliciter. Nyāya contends that inherence is a self-linking property. It does not rely on other instances of inherence in order to “glue” it to the two elements which it relates. Thus it seeks to rebut regress arguments of the type advanced by recently by F. H. Bradley and by the classical Vedāntin Śaṅkarācārya (c. 9th century C.E.) in classical India.

f. Individuator

Individuators are the finest-grained causes of ontological distinction. They are the means by which individual atoms within the basic kinds “earth”, “water”, and so forth, and by which individual selves are ultimately particularized. Individuators for Nyāya’s ontology may be conceived as roughly analogous to haecceities within Western philosophical discourse.

g. Absence

The ontological reality of absence, however attenuated, isaccepted by Nyāya in order to account for both linguistic practice involving negation and cognitive states which correctly ascertain non-existence of some kind.Vātsyāyana argues that the positive knowledge produced by a knowledge sourcegives immediate rise to knowledge of an absence insofar as one can reflect that if something was not made manifest at the time of the initial cognition (and provided that the thing in question is ordinarily cognizable), it was absent. Uddyotakara famously argues that negation is often perceptible: looking at my desk, I see the absence of a coffee mug, and such absence is “located” on the surface my desk. In this spirit, absence is generally thought of as a qualifier (viśeṣana) of some object or property, which is the qualificand (viśeṣya). The four basic kinds of absences accepted by Nyāya in its mature period are prior absence (of something before it is created), absence-by-destruction (of an object after it is destroyed), absolute absence (of something for some locus where it could never exist), and mutual absence (between two separately existing objects).

h. Causation

Naiyāyikas speak of a cause or causal condition as something which is necessarily antecedent to aspecific kind of effect without being “causally irrelevant”. Such causes are threefold. The (i) inherence cause, akin to a material cause, is the substratum out of which (or within which) an effect is made (the threads which together make up a cloth). The (ii) non-inherence cause includes properties of the inherence cause which influence the properties of the effect (the property of contact which inheres within the threads which make up a cloth). Finally, (iii), the instrumental/agential cause(s). This third category is a kind of catch-all which includes everything aside from the substratum and its properties. Central in this category are agents, their activities, and instruments used by then to produce effects. Out of the nexus of causal conditions which come together in the production of an effect, Naiyāyikas tend to speak of a most important factor as the trigger cause (for example the striking of a match against a rough surface which produces a lit match).

In order to weed out unnecessary or unimportant factors from the causal nexus which produces an effect, Nyāya includes the caveat that a proper cause must not be “causally irrelevant”. Causal irrelevance occurs in various ways. For example, something x which universally precedes a certain effect y, but whose relationship with the effect is mediated by some other factor z upon which it subsists is causally irrelevant. For example, a certain artist may create a unique kind of sculpture, and she is thus identified as a causal factor in its production. She may have certain properties (hair color, eye color, height) which also, by means of their subsisting in her, invariably precede the production of her sculptures. But since their participation in the causal event is derivative, they are deemed causally irrelevant and unworthy of being specified as causes.

3. Philosophy of Religion

Nyāya expressly conceives of itself as a rational defender of classical Hindu religious and theistic culture. Nyāya-sūtra begins by claiming that ascertainment of the ultimate good (niḥśreya) requires correct apprehension of reality, which gives rise to a sustained epistemological/metaphysical investigation of the kind the sūtras provide.Vātsyāyanaargues that as a discipline of inquiry, Nyāya is the support of all practices of legitimate dharma. Jayanta claims that amongst the various research programs in the umbrella of classical Vedic culture, Nyāya is of chief importance, since it aims to defend Vedic tradition and its manifold subdivisions of study from the attacks of rival, anti-Vedic philosophers. Though the Nyāya-sūtra overwhelmingly focuses on theoretical issues and not praxis, it nonetheless recommends that students of Nyāya engage in yogic practice (4.2.42) and defends the possibility of enlightenment (4.2.44-5).

From fairly early in its history, Nyāya specifically takes it upon itself to defend the existence of God (Īśvara). Nyāya primarily employs versions of the design inference. Paradigmatic arguments include:

Primordial matter, atoms and karma function when guided by a conscious agent because they are insentient (acetaṇatvāt) like an axe. As axes, due to insentience, operate only when directed by a sentient agent, so too do things like primordial nature, atoms and karma. Therefore, they too are directed by a cause possessed of intelligence. (Uddyotakara, NV 4.1.21)

Things like the earth have a maker as their cause, because they are products (kāryatvāt). (Udayana Nyāyakusumāñjali, Fifth Chapter)

With various formulations like the above, and extensive supporting arguments, Nyāya defends a version of the argument from design. Buddhist, Mīmāṁsā (and later, Jain) philosophers respond by charging Nyāya with violations of inferential boundaries: only by extrapolating far beyond the correlation between ordinary products and makers is Nyāya able to argue for a unique God-like maker of the world. A standard response, as seen in Vācaspati (NVT 4.1.21) is that even in straightforward general-to-particular inductive reasoning, we employ some degree of inference to the best explanation. This allows enough flexibility to infer new kinds of entities while appealing to correlations generated from ordinary experience.

4. References and Further Reading

a. Sanskrit Source Materials

  • JayantaBhaṭṭa. Nyāya-mañjarī. Critically Edited by Vidvan, K. S. Varadacarya.Vol 1. Mysore: Oriental Research Institute 1969.
  • JayantaBhaṭṭa. Nyāya-mañjarī. Critically Edited by Vidvan, K. S. Varadacarya.Vol 2. Mysore: Oriental Research Institute 1983.
  • Nyāya-Tarkatirtha, Taranatha and Amarendramohan Tarkatirtha, eds. Nyāyadarśanamwith Vātsyāyana’sBhāṣya [cited as NB above], Uddyotakara’s Vārttika[cited as NV], Vācaspati Miśra’s Tātparyaṭīkā [cited as NVT] & Viśvanātha’s Vṛtti. Calcutta: Munshiram Manoharlal 2003.
  • Udayana. Nyāyavārttikatātpāryaśuddhi of Udayanācārya. Edited by Anantalal Thakur. New Delhi: Indian Council of Philosophical Research.

b. Primary Texts in English Translation

  • Gangopadhyaya, Mrinalkanti, trans. Nyāya: Gautama’s Nyāya-sūtra with Vātsyāyana’s Commentary. Calcutta: Indian Studies 1982.
  • Iyer, S. R., Editor and Translator, Tarkabhāṣā of Keśava Miśra. Varanasi: Chaukhambha Orientalia, 1979.
  • JayantaBhaṭṭa. Nyāya-mañjarī. Translated by JanakiVallabhaBhattacaryya.Vol. 1. Delhi: Motilal Banarsidass 1978.
  • Jha, Sir Ganganatha, trans. The Nyāya-sūtras of Gautama.Vols 1-4. Delhi: Motilal Banarsidass 1999.
  • Phillips, Stephen and N. S. Ramanuja Tatacharya. Epistemology of Perception: Gaṅgeśa’s Tattvacintāmaṇi Jewel of Reflection on the Truth (About Epistemology), The Perception Chapter (pratyakṣa-khaṇḍa). New York: American Institute of Buddhist Studies 2004. [This also contains the Sanskrit text.]
  • Potter, Karl H., ed. Encyclopedia of Indian Philosophies.Vol. 2. Nyāya-Vaiśeṣika. Delhi: Motilal Banarsidass 1977. [This volume contains summary translations and helpful historical and conceptual introductions to early Nyāya and its individual philosophers.]
  • Udayana. Ātmatattvaviveka. Translation and commentary by N. S. Dravid.  Shimla: Indian Institute of Advanced Study 1995. [This also contains the Sanskrit text.]
  • Udayana. Nyāyakusumāñjali. Translation and commentary by N. S. Dravid. New Delhi: Indian Council of Philosophical Research 1996. [This also contains the Sanskrit text.]

c. Studies of Nyāya Epistemology, Metaphysics, and Philosophy of Religion in English

  • Bhattacaryya, Gopikamohan. Studies in Nyāya-vaiśeṣika Theism. Calcutta: Sanskrit College 1961.
  • Chakrabarti, Kisor Kumar. Classical Indian Philosophy of Mind: The Nyāya Dualist Tradition. Albany: State University of New York Press 1999.
  • Chemparathy, George. An Indian Rational Theology: Introduction to Udayana’s Nyāyakusumāñjali. Publications of the De Nobili Research Library, Vol. 1. Vienna: Gerold& Co.; Delhi: Motilal Banarsidass 1972.
  • Ghokale, Pradeep P. Inference and Fallacies Discussed in Ancient Indian Logic (with special reference to Nyāya and Buddhism). Bibliotheca Indo-Buddhica Series, Sunil Gupta, ed.Delhi: Sri Satguru Publications 1992.
  • Halbfass, Wilhelm. On Being and What There Is: Classical Vaiśeṣika and the History of Indian Ontology. Albany: State University of New York Press 1992. [Though this text focuses on Vaiśeṣika, it is relevant given the great overlap between Nyāya and Vaiśeṣika in metaphysical theory.]
  • Matilal, B. K. Perception. Oxford: Clarendon Press: Oxford 1986.
  • Matilal, B. K. The Character of Logic in India. Albany: SUNY Press 1998.

d. General Studies

  • Ganeri, Jonardon. Philosophy in Classical India: The Proper Work of Reason. London and New York: Routledge 2001.
  • Matilal, B. K. Nyāya-Vaiśeṣika. A History of Indian Literature, Vol. 6, Fasc. 2. Edited by Jan Gonda. Weisbaden: Otto Harrassowitz 1977.
  • Mohanty, J.N. Classical Indian Philosophy. Lanham: Rowman & Littlefield Publishers, Inc., 2000.
  • Phillips, Stephen. Classical Indian Metaphysics: Refutations of Realism and the Emergence of “New Logic.” Chicago: Open Court 1995.

Author Information

Matthew R. Dasti
Email: mdasti@bridgew.edu
Bridgewater State University
U. S. A.

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