Skip to main content
Log in

The Search for Definitions in Early Nyāya-Vaiśeṣika

  • Published:
Journal of Indian Philosophy Aims and scope Submit manuscript


The search for definitions is ubiquitous in Sanskrit philosophy. In many texts across traditions, we find philosophers presenting their theories by laying down definitions of key theoretical categories, by testing those definitions, and by refuting competing definitions of the same theoretical categories. Call this the method of definitions. The aim of this essay is to explore a challenge that arises for this method: the paradox of definitions. It arises from the claim that the method of definitions is either (i) redundant because it does not provide us any knowledge that we did not already possess, or (ii) impossible to successfully pursue because it leads to an infinite regress. Neither of these alternatives should be acceptable to the defender of this method. To focus our discussion, I will show how this challenge arose for—and was arguably resolved by—early Nyāya-Vaiśeṣika thinkers active in the first millennium CE and at the very beginning of the second millennium. In response to the paradox of definitions, these Nyāya-Vaiśeṣika thinkers claimed that the purpose of a definition is to remove either metaphysical ignorance about the distinction between theoretically significant kinds or kind-membership, or metalinguistic ignorance about the meaning or the application-conditions of theoretically significant terms. I will show how this discussion helps us to ward off certain misconceptions about the method of definitions in Nyāya-Vaiśeṣika.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. This method is discussed by Ganeri (2017) and Das (2018) in the context of characterising Śrīharṣa’s (12th century CE) own method of attacking definitions. Several text-traditions—besides Nyāya and Vaiśeṣika—exemplify this method: the tradition of Buddhist epistemology initiated by Dignāga (5th–6th century CE) and Dharmakīrti (7th century CE) and the tradition of Jaina epistemology beginning with Akalaṅka (8th century CE) and carried forward by his commentators such as Prabhācandra (11th century CE) and Vādirājasūri (11th century CE). It is also perhaps interesting to study the parallels between the conceptions of definitions found in Sanskritic traditions and other ancient traditions. As Charles (2006) and Fine (2010) suggest, a version of the distinction between what I later call the co-extensive property strategy and the metalinguistic strategy are already present in the Meno. For other discussions of definitions in Greek philosophy, see the essays in Charles (2010).

  2. When I use the term “Nyāya-Vaiśeṣika,” I do not mean to imply that the Nyāya and the Vaiśeṣika text-traditions ought to be conceived as parts of a single overarching text-tradition. That would be historically incorrect, even though earlier Nyāya authors like Vātsyāyana (4th–5th centuries CE) and Uddyotakara (6th century CE) often consciously sought to bridge the gap between the two traditions and later figures like Udayana (10th/11th century CE) synthesized the commitments of the two text-traditions. For a history of the Vaiśeṣika tradition and its subsequent convergence with Nyāya, see Thakur (2003). When I say “Nyāya-Vaiśeṣika,” what I have in mind is a disjunctive category: it covers thinkers who are active solely within the Nyāya text-tradition, thinkers who are active solely within the Vaiśeṣika text-tradition, and thinkers like Udayana who are active in both.

  3. For other discussions of definitions in Nyāya-Vaiśeṣika, see Matilal (1981, 1990), Bhattacharya (1990, ch. 5) and Chakrabarti (1995, ch. 4). Some but not all these authors overlook the earlier Nyāya-Vaiśeṣika thinkers whom I discuss. But some of them also discuss figures in later Nyāya, such as Gadādhara Bhaṭṭācārya (17th century CE) and Viśvanātha Nyāyapañcānana (17th century CE), whom I ignore.

  4. Here, I am relying on an interpretation of Carnap due to Flocke (2021). For other work on conceptual engineering, see Haslanger (2000), Cappelen (2018), Chalmers (2020), and the essays in Burgess et al. (2020).

  5. The Sanskrit term “lakṣaṇa” is derived from the verbal root “√lakṣ” by adding the suffix “lyuṭ” to it. The verbal root “√lakṣ” means to observe or to recognise. So, etymologically, the term refers to something by means of which an object is observed or recognized (lakṣyate ’neneti): in other words, a mark, a sign, an indication, or a characteristic.

  6. Bhattacharya (1990, ch. 5) claims that this aspect of lakṣaṇas constitutes a key difference between the Nyāya conception of lakṣaṇa and what he calls the “Western” conception of definitions. For Bhattacharya, according to this “Western” conception, a definition is the explication of the meaning of a linguistic expression, so the target of a definition is a linguistic expression. I disagree: real definitions, as we shall see later, do not explicate the meaning of any linguistic expression. So, I will retain the English word “definition” instead of switching to Bhattacharya’s unwieldy convention of using “definition*” to talk about the Nyāya conception of lakṣaṇa.

  7. NBh 3.11–13 ad NS 1.1.1: “Still, what is this nyāya? Nyāya is the examination of some object by means of the methods of knowing. And it is an inference that is based on perception and authoritative testimony (āgama); it is rational inquiry (anvīkṣā). Rational inquiry is the subsequent investigation of what has been observed (īkṣitasya) on the basis of perception and inference. That which proceeds by means of it is said to be the science of rational inquiry (ānvikṣikī), i.e., the science of Nyāya or the treatise of Nyāya.” (kaḥ punar ayaṃ nyāyaḥ? pramāṇair arthaparīkṣaṇaṃ nyāyaḥ | pratyakṣāgamāśritam anumānam, sā ’nvīkṣā | pratyakṣāgamābhyām īkṣitasyānvīkṣaṇam anvīkṣā | tayā pravartata ity ānvīkṣikī nyāyavidyā nyāyaśāstram |)

  8. NBh 4.13–17 ad NS 1.1.1: “The five parts of the entire collection of linguistic expressions, in which the proof of an object to be proved is completed, are the thesis (pratijñā) and so on; they are called “the parts of an argument” [in NS 1.1.1] with reference to the collection. In those parts, there is a confluence of the methods of knowing. The thesis is [based on] authoritative testimony. The statement of the reason (hetu) is [based on] inference. The illustration (udāharaṇa) is [based on] perception. The application (upanayana) is [based on] analogy. The conclusion (nigamana) is a demonstration of the capacity that all these methods have for a confluence with respect to a single object. This precisely is called the ‘highest nyāya.’ Truth-directed, victory-directed, and destructive debates proceed by means of this [nyāya], and not in any way other than this.” (sādhanīyārthasya yāvati śabdasamūhe siddhiḥ parisamāpyate tasya pañcāvayavāḥ pratijñādayaḥ, samūham apekṣyāvayavā ucyante | teṣu pramāṇasamavāyaḥ, āgamaḥ pratijñā | hetur anumānam | udāharaṇaṃ pratyakṣam | upanayanam upamānam |sarveṣām ekārthasamavāye sāmarthyapradarśanaṃ nigamanam iti | so 'yaṃ paramo nyāya iti | etena vādajalpavitaṇḍāḥ pravartante nāto 'nyatheti |)

  9. Here, I translate the Sanskrit word “jñāna” as “awareness.” Typically, this Sanksrit word picks out contentful, occurrent mental states, like experiences and thoughts. But, often, it is translated as “cognition” rather than “awareness.” This is slightly misleading. Typically, in contemporary philosophy and cognitive science, the term “cognition” is reserved for mental states, like beliefs and judgements, whose contents can be verbally reported and directly used for reasoning and the control of action. But, for at least some Sanskrit philosophers, a jñāna needn’t be like this: for example, for Buddhist philosophers working within the tradition of Dignāga and Dharmakīrti and Nyāya philosophers beginning with Gaṅgeśa Upādhyāya (14th century CE), non-conceptual perceptual experiences count as jñānas, but do not have contents that can be verbally reported or directly used for reasoning and the control of action. So, I choose the more neutral term “awareness” to refer to all jñānas.

  10. NS1.1.1:

    pramāṇaprameyasaṃśayaprayojanadṛṣṭāntasiddhāntāvayavatarkanirṇayavādajalpavitaṇḍāhetvābhāsac-chalajātinigrahasthānānāṃ tattvajñānān niḥśreyasādhigamaḥ || My translation of “tattva” as “nature” fits its etymology: the word is derived by adding a “tva” suffix to “tat” (which is the equivalent of the demonstrative “that”). It roughly means an object’s state of being what it is. But this is different from the way Vātsyāyana explains the term in his preamble to the Nyāyasūtra (NBh 1.16–18): “Still, what is tattva? It is the existence of something that exists, and the non-existence of something that doesn’t exist. That which is existent—when it is being apprehended as it is and without any error in the form, ‘This is existent’—is tattva. And that which is non-existent—when it is being apprehended as it is and without error in the form, ‘This is non-existent,’—is tattva.” (kiṃ punas tattvam? sataś ca sadbhāvo 'sata cāsadbhāvaḥ | sat sad iti gṛhyamāṇaṃ yathābhūtam aviparītaṃ tattvaṃ bhavati | asac cāsad iti gṛhyamāṇaṃ yathābhūtam aviparītaṃ tattvaṃ bhavati |) This implies that tattva is the ontological status of any object; while this ontological status may be one aspect of the nature of an object, it does not exhaust it. However, as we shall soon see, Vātsyāyana uses the word “tattva” a bit differently in another context to refer to the true nature of an object; see the passage in fn. 15. Uddyotakara’s explanation of the term “tattva” also supports my translation (NV 10.17–19): “Tattva is the entities’ being the cause of the arising of an awareness regarding themselves in the way they are distinguished (yathavyavasthita) [from other entities]. A certain entity, which is distinguished [from other entities] in a certain way, serves as the cause of the arising of an awareness regarding something of that kind. So, this is its tattva.” (tattvam padārthānāṃ yathāvasthitātmapratyayotpattinimittatvam | yaḥ yathāvyavasthitaḥ padārthaḥ saḥ tathābhūtasya pratyayasyotpattinimittaṃ bhavatīty etat tattvam |) For Uddyotakara, the tattva of an entity is its causal capacity to give rise to a state of awareness regarding itself as distinct from other entities. Arguably, this capacity is nothing but the nature of that entity, which helps us distinguish it from other objects of similar and dissimilar kinds.

  11. See Olivelle’s (2013, pp. 66–68) translation of the relevant section of the Arthaśāstra.

  12. NBh 5.18–6.3: “This very science of rational inquiry, which is divided into kinds of entities (padārthaiḥ) such as the methods of knowing and so forth, ‘is the lamp of all the sciences, the means of all actions, the basis of all dharmas, and has been described in the enumeration of the sciences.’ So, this awareness of the nature [of things] [mentioned in the Nyāyasūtra 1.1.1], which is for the sake of attaining the highest good, is to be understood in accordance with each science. However, in this science of the inner self, the awareness of the nature [of things] is the awareness of the self and so on. The attainment of the highest good is the attainment of liberation” (seyam ānvīkṣikī pramāṇādibhiḥ padārthair vibhajyamānā – pradīpaḥ sarvavidyānām upāyaḥ sarvakarmaṇām | āśrayaḥ sarvadharmāṇāṃ vidyoddeśe prakīrtitā || tad idaṃ tattvajñānaṃ niḥśreyasādhigamārthaṃ yathāvidyaṃ veditavyam | iha tv adhyātmavidyāyām ātmādijñānaṃ tattvajñānam | niḥśreyasādhigamo ’pavargaprāptiḥ |) The verse quoted by Vātsyāyana is from the second chapter of Kauṭilya’s Arthaśāstra, called “The Enumeration of the Sciences” (vidyoddeśa) in where the science of rational inquiry is mentioned alongside the three other sciences; for an alternative translation, see Olivelle (2013, p. 67).

  13. NV 20.12–21: “So, this awareness of the nature [of things], which is for the sake of attaining the highest good, is to be understood in accordance with each science. In all the sciences, there is an awareness of the nature [of things] as well as the attainment of a highest good. [Question:] First of all, what is the awareness of the nature [of things] in the triple? And what is the attainment of the highest good? [Reply:] First of all, the awareness of the nature [of things] consists in the comprehensive awareness of [components such as] welcome, etc. (svāgatādiparijñānam) of the means such as the agnihotra sacrifice and so on, as well as the comprehensive awareness of [the means] being unobstructed, etc. (anupahatādiparijñānam). Moreover, the attainment of the highest good is the attainment of heavenly bliss. That is to say: in this [triple], heavenly bliss is stated to be the result. [Question:] What is the awareness of the nature [of things] in economics? And what is the attainment of the highest good? [Reply:] The comprehensive awareness of the land, etc. is the awareness of the true nature [of things]. The awareness of the nature [of things] is this [awareness] which takes the form, “The land is not damaged by thorns and so on.” The highest good is the attainment of a crop of grain, which is the result of that awareness. [Question:] What is the awareness of the nature [of things] in government? And what is the attainment of the highest good? [Reply:] The application of conciliation, generosity, punishment, and sowing dissension—according to the time, the place, and one’s power—is the awareness of the nature [of things]. The attainment of the highest good is the conquest of the world. However, in this science of the inner self, the awareness of the nature [of things] is the awareness of the self and so on. The attainment of the highest good is the attainment of liberation.” (tad idam tattvajñānam niḥśreyasādhigamaś ca yathā-vidyam veditavyam | sarvāsu vidyāsu tattvajñānam asti niḥśreyasādhigamaś ca iti | trayyāṃ tāvat kiṃ tattvajñānaṃ kaś ca niḥśreyasādhigama iti? tattvajñānaṃ tāvat agnihotrādisādhanānāṃ svāgatādiparijñānam anupahatādiparijñānaṃ ca | niḥśreyasādhigamo ’pi svargaprāptiḥ | tathā hy atra svargaḥ phalaṃ śrūyata iti | atha vārtāyāṃ kiṃ tattvajñānaṃ kaś ca niḥśreyasādhigama iti | bhūmyādiparijñānaṃ tattvajñānam | bhūmiḥ kaṇṭakādyanupahatety etad tattvajñānam | niḥśreyasaṃ sasyādhigamas tatphalaṃ | daṇḍanītyām kiṃ tattvajñānam kaś ca niḥśreyasādhigama iti ? sāmadānadaṇḍabhedānāṃ yathākālaṃ yathādeśaṃ yathāśakti viniyogaḥ tattvajñānam | niḥśreyasam api pṛthivīvijaya iti | iha tu adhyātmavidyāyām ātmādijñānaṃ tattvajñānaṃ niḥśreyasādhigamo ’pavargaprāptir iti |)

    Elsewhere, Uddyotakara makes two relevant remarks. First, he distinguishes goods (śreyas) into two kinds—observed and unobserved—and claims that the only observed good is pleasure (sukha) while the unobserved good consists in the cessation of what is harmful, i.e., pain (NV 2.2–5): “Moreover, a good is either pleasure or the cessation of what is harmful. That good—when divided—is distinguished into two kinds, depending on whether it is observed or unobserved. The observed [good] is pleasure. The unobserved [good] is the cessation of what is harmful. The cessation of what is harmful, too, can be of two kinds: absolute and non-absolute. The non-absolute [cessation of what is harmful] takes place through the avoidance of causes of pain, such as thorns and so on. But the absolute [cessation of what is harmful] takes place through the abandonment of pain that is divided into twenty-one varieties.” (śreyaḥ punaḥ sukham ahitanivṛttiś ca | tac chreyo bhidyamānaṃ dvedhā vyavatiṣṭhate dṛṣṭādṛṣtabhedena | dṛṣṭaṃ sukham | adṛṣṭam ahitanivṛttiḥ | ahitanivṛttir apy ātyantikī cānātyantikī ca | anātyantikī kaṇṭakāder duḥkhasādhanasya parihāreṇa | ātyantikī punar ekaviṃśatiprabhedabhinnaduḥkhahānyā |) Second, he applies this distinction between goods to the highest goods (NV 10.19–22): “Moreover, the highest good is of two kinds depending on the distinction between what is observed and what is unobserved. Of those two, the observed highest good is due to the awareness of the nature of entities such as the methods of knowing and so on…But the other [or higher] highest good arises from the awareness of the nature of a knowable object like the self, etc.” (niḥśreyasaṃ punar dṛṣṭādṛṣṭabhedāt dvedhā bhavati | tatra pramāṇādipadārthatattvajñānān dṛṣṭaniḥśreyasam |…paraṃ tu niḥśreyasaṃ ātmādeḥ prameyasya tattvajñānād bhavatīti |) As it is clear from the context (NV 10.22–11.9), the highest good of the unobserved kind is liberation, which consists in the complete cessation of all pain. So, Uddyotakara’s view is that Nyāya promotes the observed highest goods, pursued by the other sciences, by providing knowledge about the methods of knowing and so on, but—insofar as it functions as a science of the inner self—it promotes the unobserved highest good of liberation by providing knowledge about knowable objects like the self and so on. For further discussion of the early Nyāya theory of liberation, see Das (2020c).

  14. NS 1.1.3: pratyakṣānumānopamānaśabdāḥ pramāṇāni |

  15. NBh 8.7–9 ad NS 1.1.3: trividhā cāsya śāstrasya pravṛttir uddeśo lakṣaṇaṃ parīkṣā ceti | tatra nāmadheyena padārthamātrasyābhidhānam uddeśaḥ | tatroddiṣṭasya tattvavyavacchedako dharmo lakṣaṇam | lakṣitasya yathālakṣaṇam upapadyate na veti pramāṇair avadhāraṇaṃ parīkṣā | Here, at least, the translation “tattva” as “nature” seems uncontroversial, since a definition doesn’t straightforwardly give us any clue about the ontological status of any object, but only tells us what it is.

  16. NV 26.7–16 ad NS 1.1.3: lakṣaṇataś catuṣṭvādhigatiḥ iti cet—na, lakṣaṇasya itaravyavacchedahetutvāt | syād eṣā buddhir lakṣaṇataḥ pramāṇacatuṣṭvaṃ gamyata iti, yasmāt caturṇām lakṣaṇam uktam iti | na, lakṣaṇasyetaravyavacchedahetutvāt | lakṣaṇaṃ khalu lakṣyaṃ padārthaṃ samānāsamānajātīyebhyaḥ vyavacchinatti, niyamaṃ tu na śaknoti kartum anyārthatvāt iti | anyāsaṃbhavasya tato ’nadhigateḥ | na hi lakṣaṇato ’nyāsaṃbhavo ’dhigamyate | tataś caturṇām anabhidhāne caturṇāṃ lakṣaṇopadeśe syāt saṃśayaḥ:--kiṃ vidyamānāni na lakṣitāni, utāho avidyamānānīti | tasmāt saṃśayanivṛttyarthaṃ yukto vibhāgoddeśa iti |

  17. Uddyotakara makes a similar point while justifying the five-fold classification of the pseudo-reasons (hetvābhāsa) (NV 162.7–10 ad NS 1.2.4): “[The opponent:] The five-foldness of the pseudo-reasons is known on the basis of their defining characteristics. The five-foldness is known by means of just these [sūtras], which are the definitional sūtras for the five pseudo-reasons. So, a sūtra that is given for the sake of a restriction [like NS 1.2.4] is futile. [Reply:] It is not the case that it is futile, because a defining characteristic distinguishes one thing from another. A defining characteristic distinguishes one thing from another. However, it does not serve the purpose of laying down a restriction, because a restriction is not known by means of a defining characteristic.” (lakṣaṇata eva pañcatvaṃ gamyata iti cet? yany etāni pañcahetvābhāsānāṃ lakṣaṇasūtrāṇi tair eva pañcatvaṃ gamyata iti niyamārthaṃ sūtram anarthakam | nānarthakam, lakṣaṇasya itaretaravyavacchedakatvāt | itaretaravyavacchedakaṃ lakṣaṇam, na punar niyamārtham | na hi niyamo lakṣaṇena gamyata iti |)

  18. NS 1.1.4: indriyārthasannikarṣottpannaṃ jñānam avyapadeśyam avyabhicāri vyavasāyātmakaṃ pratyakṣam |

  19. A full list given at NV 29.20–23 ad NS 1.1.4.

  20. NV 30.3–5 ad NS 1.1.4: “This sūtra is not for the sake of determining a cause, but rather for distinguishing [perception] from objects of similar and dissimilar kinds, on account of which a unique cause of perception is being stated, but the non-unique causes are not being denied.” (nedaṃ kāraṇāvadhāraṇārthaṃ sūtram, api tu samānāsamānajātīyaviśeṣaṇārtham | yat pratyakṣasyāsādhāraṇaṃ kāraṇam abhidhīyate, na punar sādhāraṇam kāraṇaṃ nivartyata iti |) Similarly, compare NV 194.4–6 ad NS 2.1.21: “Even on the position that [the property of arising from sense-object contact] is a defining characteristic [of perception], there is no problem; for the contact between the sense and the object is unique [to perception]. The contact between the sense and the object is a cause in virtue of being the producer of perception, and it is a defining characteristic in virtue of distinguishing it from objects of similar and dissimilar kinds” (lakṣaṇapakṣe ’pi na doṣaḥ | asādhāraṇatvāt indriyārthasannikarṣasyeti | indriyārthasannikarṣaḥ pratyakṣotpādakatvāt kāraṇaṃ ca, samānāsamānajātīyebhyo viśeṣakatvāt lakṣaṇaṃ ceti |)

  21. NBh 64.6–11 ad NS 2.1.17: saṃvedyāni ca pratyakṣādīni pramāṇāni, pratyakṣeṇopalabhe anumānenopalabhe upamānenopalabhe āgamenopalabhe | pratyakṣaṃ me jñānam ānumānikaṃ me jñānam aupamānikaṃ me jñānam āgamikaṃ me jñānam iti viśeṣā gṛhyante | lakṣaṇataś ca jñāpyamānāni jñāyante viśeṣeṇendriyārthasannikarṣotpannaṃ jñānam ity evamādinā |

  22. VS 1.1.1: athāto dharmaṃ vyākhyāsyāmaḥ |

  23. VS 1.1.2: yato 'bhyudayaniḥśreyasasiddhiḥ sa dharmaḥ |

  24. VSV 2–4 ad VS 1.1.1: “The following was revealed to a certain Brahmin whose impurities had been removed by Vedic practice: ‘Joy and sorrow, however, do not affect one who has no body” (Chāndoya Upaniṣad 8.12.1). Then, having reflected on this sentence, that Brahmin went to Kaṇabhakṣa. Then, he said: ‘Blessed One! By this sentence, becoming disembodied is described as the means to repose (kṣema). So, tell me: what is the means [to disembodiment]?’ Then, the sage said: “Dharma.'” (kasyacid brāhmaṇasya vedābhyāsavaśena vyapagatakalmaṣasyedaṃ pratibabhau: ‘aśarīraṃ vāva santaṃ priyāpriye na spṛśata’ iti | tata idaṃ vākyam ālocya kaṇabhakṣaṇam ājagāma | tato ’bhyuvāca: “bhagavann! anena vākyena vyapahataśarīra[tva]sya kṣemasādhanatā kathyate | tad ucyatāṃ: ka upāya?” iti | tato munir abhyuvāca: “dharma” iti |) My translation of the Upaṇisadic passage is borrowed from Olivelle (1998, p. 285).

  25. VSV 12–15 ad VS 1.1.2: “Since actions such as sacrifices, the worship of deities, and so on—which are brought about by means of ghee, flowers, and the like—are incapable of yielding any result at a later time because they are destroyed at that very [earlier] time, the cause from which prosperity and the highest good arise should be understood as dharma. Prosperity consists in the attainment of a desired body in the realms of Brahmā and so on, and the cessation of what is undesirable. The highest good is liberation which takes the form of the absence of specific [or Vaiśeṣika] qualities of the inner self” (yāgadevatāpūjādikriyāṇām ājyapuṣpādinirvartyānāṃ tadaiva vinaṣṭatvād uttarakālaṃ phaladānāśakter yasmād dhetor abhyudayaniḥśreyase bhavataḥ, sa dharma iti boddhavyaḥ | abhyudayo brahmādilokeṣu ceṣṭaśarīraprāptiḥ, anarthoparamaś ca | niḥśreyasam adhyātmano vaiśeṣikaguṇābhāvarūpo mokṣaḥ |)

  26. PDS 4.4–5: dravyaguṇakarmasāmānyaviśeṣasamavāyānāṃ ṣaṇṇāṃ padārthānāṃ sādharmyavaidharmyatattvajñānaṃ nihśreyasahetuḥ |

  27. VSV 4.4–9 ad VS 1.1.6: evaṃ ṣaṇṇāṃ padārthānāṃ sādharmyavaidharmyaparijñānaṃ viṣayadoṣadarśanadvāreṇa vairāgyotpattau satyāṃ niḥśreyase sādhye dharmahetuḥ | abhyudaye sādhye dharmahetutvaṃ punar amīṣāṃ: ‘same yajet’eti pṛthivyāḥ; ‘adho ’ṃbūni nayatī’tyādi yathāsvam anyeṣāṃ dravyāṇāṃ; guṇānāṃ tu ‘kṛṣṇam ālabhet’etyādi; karmaṇāṃ tu ‘vrīhīn avahantī’tyādi | vijñātasādharmyavaidharmyāṇāṃ ca dravyādīnām abhyudayaniḥśreyasahetutvāt, sādharmyaṃ tāvat kathayati |

  28. VS 1.1.14: kriyāvad guṇavat samavāyikāraṇam iti dravyalakṣaṇam |

  29. VS 1.1.15: dravyāśrayy aguṇavān saṃyogavibhāgeṣv akāraṇam anapekṣa iti guṇalakṣaṇam |

  30. VS 1.1.16: ekadravyam aguṇaṃ saṃyogavibhāgeṣv anapekṣaṃ kāraṇam iti karmalakṣaṇam |

  31. See Thakur (2003, p. 30) for an explanation of these sūtras along these lines.

  32. PDS 28.9: pṛthivītvābhisambandhāt pṛthivī |

  33. PDS 272.10: lakṣaṇabhedād eṣāṃ dravyaguṇakarmebhyaḥ padārthāntaratvaṃ siddham |

  34. To be fair, these Nyāya-Vaiśeṣika thinkers themselves do not put the matter in terms of extensional adequacy. The later Naiyāyikas put the idea in terms of bidirectional invariable concomitance (samaniyatatva). Two properties X and Y are bidirectionally invariably concomitant if and only if X does not occur at a place where the absence of Y occurs, and Y does not occur at a place where the absence of X occurs. Suppose K is the kind to be defined, and C is the defining characteristic of instances of K. The later Naiyāyikas claim that the delimitor of the property of being the target of definition (lakṣyatāvacchedaka)—i.e., the property of being an instance of K—and the defining characteristic C must be bidirectionally invariably concominant. This implies that these two properties must have the same extension. For discussion of this notion, see Matilal (1990, pp. 164ff.) and Bhattacharya (1990, ch. 5).

  35. For recent defences of the method of conceptual analysis, see Chalmers (1996) and Jackson (1998). For dissent from it, see Devitt (1996), Kornblith (2002), and Papineau (2013).

  36. The basic idea underlying the paradox is implicit in Moore (1903), but was formulated clearly by Langford (1942). Wiggins (2007) traces the paradox back to an exchange between Husserl and Frege.

  37. Later, in this paper, I consider other formulations of this problem given by Śrīdhara, Vyomaśiva, and Udayana.

  38. NBhū 6.10–11: prasiddhāni pramāṇāni vyavahāraś ca tatkṛtaḥ | pramāṇalakṣaṇasyoktau jñāyate na prayojanam || This is verse I.2 in Nyāyavatāra (NA 353.7–8).

  39. NBhū 6.12–15: anenaitad ucyate—na hi tāval lakṣaṇena lakṣyaṃ kriyate, gavādeḥ sāsnādilakṣaṇenaikakālatvadarśanād, ātmādilakṣyasya ca nityatvāt | nāpi jñāpyate, lakṣaṇāprasiddhāv api loke lakṣyapratītidarśanāt, anavasthāprasaṅgaś ca durnivāraḥ syāt |

  40. NBhū 6.16–20: atha pravṛttinivṛttirūpaḥ śābdo bādhyabādhakavyavahāraś ca pramāṇādiṣu lakṣaṇam antareṇa na sidhyatīti, na; tasyāpi siddhatvāt | loke bādhyabādhakalakṣaṇo ’pi siddha eveti | saṃjñā niyamenāprasiddheti cet, na; prasiddhatvāt | tathā hi strīśūdrādayo ’pi bruvanto dṛśyante—tvadīyaṃ vacaḥ pratyakṣeṇaiva bādhyata ity evamādi | tasmāt pramāṇādilakṣaṇaṃ niṣprayojanam iti |

  41. Similar solutions to paradoxes of inquiry were discussed by both Kumārila Bhaṭṭa (7th century CE) and Śaṃkara (8th century CE). For discussion, see Carpenter and Ganeri (2010).

  42. NVTṬ 86.8–10 ad NS 1.1.4: yaḥ khalu kutaścid vyāmohāt samānāsamānajātīyavyāvṛttaṃ tadrūpaṃ na śaknoti grahītum, so ’nena lakṣaṇena bodhyate | evaṃlakṣaṇakaṃ pratyakṣam iti |

  43. NK 84.8, 84.13–15, 85.6: uddeśakramenạ pṛthivyāḥ prathamaṃ vaidharmyam āhapṛthivītvābhisambandhāt pṛthivīti | yo vā pṛthivīti loke śṛṇoti na jānāti tasyāḥ svarūpaṃ kīdṛg iti, taṃ prati tasyāḥ svaparajātīyavyāvṛttasvarūpapratipādanārtham asādhāraṇo dharmaḥ kathyate, yā loke pṛthivīti vyapadiśyate sā pṛthivī, pṛthivītvābhisambandhāt | yathā ’’hoddyatakaraḥ'samānāsamānajātīyavyavacchedaḥ lakṣaṇārthaḥ’ iti |

  44. VV 56.1–4: “Earth is the property-bearer. The target property is [conveyed by] ‘…is distinct from other entities,’ since it is connected to earthhood. But that which isn’t distinct from other entities isn’t connected to earthhood, e.g., water and so on. And it is not the case that earth is not connected in that manner to earthhood. Therefore, it is distinct from other entities” (pṛthivī dharmiṇī itarebhyo bhidyata iti sādhyo dharmaḥ, pṛthivītvābhisambandhāt, yas tv itarasmān na bhidyate na cāsau pṛthivitvena sambaddho yathodakādi, na ca tathā pṛthivītvena nābhisambaddhā pṛthivī, tasmād itarebhyo bhidhyata iti). See also Udayana’s presentation of the same inference in the passage quoted in fn. 50.

  45. NVTP 124.1–5 ad NS 1.1.4: kaḥ punar anena lakṣaṇena pratipādayiṣyata ityata āha—yaḥ khalv iti | na ca sarve vyāmūḍhāḥ, yena pratipādyapratipādakavyavasthā na syāt | na ca sarvatra vyāmoho yenānavasthā syāt, na ca sarve vyāmohahetavo yenāpratipattiḥ syāt | na ca sarvāpratipattiḥ, yenāśrayāsiddhiḥ syād iti bhāvaḥ ||

  46. This anti-sceptical assumption may be motivated by the Nyāya theory of content itself. If we were confused about everything, then we could not be aware of anything. Our capacity to be aware of objects itself depends on our having knowledge of those objects. For the Naiyāyikas, a state of awareness cannot be directed at an object—a particular or a property—that does not exist. Even in a case where an agent misascribes a property to a particular to which it does not belong, the agent’s erroneous awareness is directly at an existent particular and an existent property (as well as an existent relation that could connect the relevant property to certain particulars). If I misperceive a mother-of-pearl as a piece of silver, I may misascribe the property of silverhood to the mother-of-pearl. But both the mother-of-pearl and the silverhood exist. For the Naiyāyikas, it is possible for an agent to be in such states of error only because they have undergone other knowledge-events, where they have encountered instances of the relevant property at other times or places and have acquired knowledge of that property. So, unless I had veridically perceived silverhood elsewhere, e.g., in a shop that sells silver cutlery, I could not now take the mother-of-pearl before me as a piece of silver.

  47. VV 57.1–4: nanu kim itarasmād vyāvṛttā pramāṇasiddhā pṛthivī pakṣīkriyate, atha aprasiddhaiveti? yadi aprasiddhā, pakṣīkaraṇam ayuktam | atha pramāṇasiddhā vyāvṛttatayā, tarhi vyartham | athāvyavṛttatayopalabdhā, tad asat | vyāvṛttaṃ hi padārthānāṃ svarūpam, tena ca vapuṣā gṛhyamāṇā dharmiṇo na rūpāntareṇeti dṛṣṭam |

  48. KirA 29.1–2: nanu pṛthivīsvarūpasiddhu kiṃ lakṣaṇena? siddhe [siddhau] sādhanasya vaiyarthyāt, tadasiddhau āsrayāsiddheḥ |

  49. VV 57.4–6: naitad evam | lokaprasiddhivaśena pṛthivyāḥ pakṣīkaraṇāt | tathā hi, yatra janānāṃ pṛthivīti vyavahāraḥ sā pakṣīkṛtety abādhaḥ |

  50. KirA 29.2–3: na; svarūpasiddhāv apītaravyavacchedasya sādhyamānatvat | tathā hi ‘pṛthivī abādibhyo bhidyate pṛthivītvāt | yat punar itarebhyaḥ na bhidyate nāsau pṛthivī, yathā ’bādi | na ceyaṃ na pṛthivī, tasmād itarebhyo bhidyate | Note that, in the Ahmedabad edition of the text (to which I am referring), there is an extra “na” after “itarebhyo” in the last line. This is surely a mistake, since the conclusion of the argument is supposed to be that earth is distinct from other entities. The mistake is absent from the Calcutta edition of the text: see KirC 190.3.

  51. See the passage quoted in fn. 52.

  52. KirA 29.8–9: kevalavyatirekihetuviśeṣa eva lakṣaṇam | tathā cācāryāḥ ‘samānāsamānajātīyavyavacchedo lakṣaṇārthaḥ’ iti | Udayana doesn’t tell us who “ācāryāḥ” (translated above as “teachers”) refers to. But my assumption is that, following Śrīdhara, he is simply referring to Uddyotakara.

  53. NVTṬ 77.12–17: tathā hi lakṣaṇaṃ nāma vyatirekihetuvacanam | tad dhi samānāsamānajātīyebhyo vyavacchidya lakṣyaṃ vyavasthāpayati | na cāsya dharmidarśanam antareṇa pakṣadharmatā sidhyatīti tadupadarśanāya nāmadheyamātreṇa dharmiṇām uddeśaḥ | yady api ca pratilakṣaṇam uddiṣṭā eva dharmiṇaḥ, tathā'pi śāstrābhisaṃbandhaparād api vākyāt samadhigamyanta ity uddeśo ’py uktaḥ | na cāparīkṣito hetur vyatirekī catūrūpo bhavatīti parīkṣā ’py avaśyaṃ kartavyā |

  54. NBhū 7.1–4: atra tāvad utpattipakṣe 'nabhyupagama eva parihāraḥ | pratipattis tu lakṣaṇadvāreṇa dṛṣṭaiva gavādau | tathā hi—bahuṣv api goṣv asādhāraṇalakṣaṇadarśanenātmīyāṃ gāṃ niścinoti, lakṣaṇānabhijñas tu sandihyata iti | evaṃ sarvatra sthāvarajaṅgamaratnādiviśeṣeṣv apy udāharaṇaṃ draṣṭavyam |

  55. NBhū 7.4–8: “[The opponent:] If a defining characteristic too were ascertained on the basis of another defining characteristic, there would be a regress. [Reply:] For the rule [that a defining characteristic is required for generating certainty about kind-membership] is accepted only with respect to matters that are subject to uncertainty. The following rule is accepted: ‘Only with respect to a thing about which there is uncertainty, there is certainty on the basis of the apprehension of a defining characteristic.’ And it is not the case that there is uncertainty with respect to everything. For no uncertainty arises regarding specific characteristics such as the crookedness [of a tree-trunk] in the same way as there is uncertainty with respect to an object such as that tree-trunk.” (lakṣaṇasyāpi lakṣaṇāntareṇa niścaye saty anavastheti cet, na; sandehaviṣaya eva niyamābhyupagamāt | yatraiva vastuni sandehas tatraiva lakṣaṇopalambhapūrvako niścaya ity ayaṃ niyamo ’bhyupagamyate | na ca sarvatra sandeho ’sti, na hi sthāṇvādiṣv iva vakrādiviśeṣeṣv api sandeha utpadyate |)

  56. NBhū 7.8–13: tadabhyupagame ca pratyakṣādivirodhaḥ syāt | atha kasmāt sthāṇvādiṣv eva sandeho bhavati, na vakrādiviśeṣaparamparāsv apīti ? sthāṇvādiṣu sandehakāraṇasadbhāvād itaratrāsadbhāvād iti | na, atrāpi paryanuyogānivṛtteḥ, kasmāt tadviśeṣaparamparāsv api sandehakāraṇaṃ na bhavatīti ? vastusvabhāvair atrottaraṃ vācyam | ye evaṃ bhavanti | vayaṃ tu yathādṛṣṭam arthaṃ bruvāṇā nopālambham arhāmaḥ |

  57. NBhū 10.1–2: śāstram antareṇāpi pramāṇādilakṣaṇaṃ prasiddham eva | anyathā laukikāḥ kathaṃ pramāṇādivyavahāraṃ kurvantīty ato ’narthakaṃ tadarthaṃ śāstram iti cet…

  58. NBhū 10.2–5: na, bhrāntinivṛttaye 'nuvādakaraṇāt | darśanāntarābhiniviṣṭaiḥ khalu bhrāntair anyathā ’nyathā lakṣaṇābhidhānena loke ’pi pramāṇādiṣu visaṃvādyate, ataḥ prasiddahm eva lakṣaṇam anūdya tadbhramo nivarttyate bhrāntapitṛdarśanasya taccihnānuvādena bhramanivṛttivat…

  59. NBhū 10.6–11: “To explain: the defining characteristic of a method of knowing, etc. is asserted by repetition in cases where error-ridden people think that correct methods of knowing directed at the self and the like are fake methods of knowing (pramāṇābhāsa), and that methods of knowing like postulation (arthāpatti) and so on, which are not distinct entities, are distinct entities. By contrast, the defining characteristic of a method of knowing, etc. is denied in cases where [those error-ridden people] think that even fake methods of knowing bearing on matters such as non-duality [of awareness], momentariness, the non-eternality of the Veda, the non-existence of entities such as the self, and so on, are [genuine] methods of knowing just like perception, and that even methods of knowing that are distinct entities are not distinct entities. So, in this manner, the need for repetition is to be noted with respect to the defining characteristics of the self and so on, and with respect to the defining characterisics of uncertainty and so on” (tathā hi—pratyakṣādilakṣaṇam anūdya yatra bhrāntāḥ samyak pramāṇeṣv apy ātmādiviṣayeṣu pramāṇābhāsatām anarthāntareṣv apy arthāpattyādiṣv arthāntaratāṃ ca pratipadyante, tatra vidhīyate | yatra punaḥ pramāṇābhāseṣv apy advaitakṣaṇikatvavedānityatvātmādyasattvādiviṣayeṣu pratyakṣādipramāṇatām arthāntareṣv apy anarthāntaratāṃ ca pratipadyante, tatra pratiṣidhyate – ity evam ātmādilakṣaṇeṣu saṃśayādilakṣaṇeṣu cānuvādaprayojanaṃ draṣṭavyam iti |)

  60. NBhū 7.13: sandehaviṣaye ’pi niścayo viśeṣadarśanāt, na lakṣaṇadarśanād iti cet |

  61. NBhū 7.15–8.6: na; viśeṣāṅkacihnalakṣaṇaśabdānāṃ paryāyatvāt | avyāpakātivyāpakayor api lakṣaṇatvaprasaṅga iti cet, na; ativyāpakasyāpi viśeṣakatvāt | viṣāṇādy api kenacid vailakṣaṇyenāvagamyate yadā, tadā golakṣaṇatveneṣṭam | avyāpako ’pi viśeṣo lakṣaṇatvenābhyupagamyate, yathā dravyasya kriyāvattvam ; na hi kriyāvattvam upalabhyamānaṃ dravyaniścayaṃ na karoti | yad eva kriyāvat tad eva dravyam ity abhiprāyavataḥ khalv avyāptidoṣa udbhāvyate niṣkriyasyākāśāder adravyatvaprasaṅga iti | yat kriyāvat tad dravyam evety abhiprāyavatas tu niravadyaṃ lakṣaṇam iti |

  62. NBhū 8.6–13: “By this reasoning, the following are explained: (a) that desire, etc. is the defining characteristic of the self, (b) that being the substratum of effort is [the defining characteristic] of the body, (c) the absence of simultaneous production of awareness is [the defining characteristic] of the inner sense; (d) that the defining characteristic of ascertainment (nirṇaya) is “the determination of an object which arises, after uncertainty, by means of taking up a position and a counter-position.” However, even though the aforementioned defining characteristics are absent from other targets such as a liberated self and so on, the treatment of objects as self and so on (ātmādivyavahāra) is established on the basis of some other defining characteristic. Just as ether and the like are treated as substances on the basis of their possession of qualities despite the absence of the possession of motion, so also (a) liberated selves are treated as selves on the basis of their selfhood; (b) crippled inner senses are treated as inner senses on the basis of their property of being inner senses; (c) bodies caught under rocks are treated as bodies on the basis of their bodyhood; (d) instances of ascertainment that take place with respect to [something placed in] the palm of one’s hand are treated as ascertainment on the basis of their being states of non-erroneous and certain firsthand awareness. So, one should reason in this manner about other cases as well.” (etenecchādy ātmalakṣaṇaṃ, ceṣṭāśrayatvaṃ śarīrasya, yugapajjñānānutpattir manasaḥ, vimṛśyetyādi nirṇayasya lakṣaṇaṃ ca vyākhyātam | lakṣyāntare tu muktātmādāv uktalakṣaṇābhāve ’pi lakṣaṇāntarād ātmādivyavahāraḥ sidhyati | yathā kriyāvattvābhāve 'py ākāśādiṣu guṇavattvādilakṣaṇād dravyavyavahāraḥ, evam ātmatvān muktātmasv ātmavyavahāraḥ, raṇḍāntaḥkaraṇeṣu manastvān manovyavahāraḥ, śilāntargataśarīreṣu śarīratvād indriyāśrayatvāc ca śarīravyavahāraḥ, karatalādinirṇayeṣv avyabhicāriniścayānubhavatvān nirṇayavyavahāraḥ – ity evam anyatrāpy ūhyam iti |)

  63. NBhū 8.13–16: lakṣaṇāntaram evāstu vyāpakatvād, anarthakam avyāpakalakṣaṇābhidhānam iti cet, na; asyāpi svalakṣyaniścaye samarthatvāt, ātmatvādipratipattāv icchādilakṣaṇasyaiva samarthatvāc ca |

  64. Nbhū 8.17–22: “[The opponent:] Given that there is disagreement even with respect to a defining characteristic, if one were to state a further defining characteristic, then there would be a regress. [Reply:] No, because it is impossible for there to be disagreement with respect to everything. Why? First of all, if this disagreeing person apprehends the nature of conscious and unconscious things, of means and ends, and so forth, then in a manner analogous to those cases (tannyāyena) something can be properly established for this particular person. But if this disagreeing person does not apprehend anything, then the utterance of any specific linguistic expression will not take place in response to this particular person. Why? If someone were to say whatever [he likes] even after having seen a tree, etc. then he should be ignored just like an insane person.” (lakṣaṇe ’pi vipratipattau lakṣaṇāntarābhidhāne saty anavastheti cet, na ; sarvatra vipratipattyasaṃbhavāt | katham ? yadi tāvad ayaṃ vipratipadyamānaḥ cetanācetanopāyopeyādisvarūpaṃ pratipadyate, tadā puruṣaviśeṣaṃ prati tannyāyenānyo ’py arthaḥ prasādhayitavyaḥ | atha kiñcid api na pratipadyate, tadā puruṣaviśeṣaṃ prati śabdaviśeṣoccāranaṃ na prāpnoti | kutaḥ ? vṛkṣādikaṃ dṛṣṭvā ’pi yat kiṃcid brūyāt, tataś conmattavad upekṣaṇīyaḥ syāt |)

  65. NBhū 9.1–5: “Moreover, this [endless] sequence of defining characteristics isn’t accepted. Why? For, since the defining characteristic of defining characteristics distinguishes the class of all defining characteristics, it distinguishes itself too. This is just as in the following cases. The utterance (vākya), ‘All sound is impermanent,’ conveys its own impermanence as well. This [Vedic] injunction, ‘One should study the Veda,’ enjoins its own status as something to be studied.” (na ceyaṃ lakṣaṇaparamparā ’bhyupagamyate, kasmāt? lakṣaṇalakṣaṇasya sakalalakṣaṇavargavyavacchedakatvena svātmano ’pi vyavacchedakatvāt | yathā anityaḥ sarvaḥ śabda ity etad vākyaṃ svātmano ’py anityatām abhidhatte | svādhyāyo ’dhyetavyaḥ ity ayaṃ vidhiḥ svātmano ’py adhyeyatvaṃ vidhatta iti |)

  66. NBhū 9.5–7: “[The opponent:] The identity of the object and the instrument, in relation to the same action, is untenable. [Reply:] No, because it is observed in some cases, just as in the case of the knower and the knowable object. [The opponent:] In virtue of just that example, there should be a lack of distinction in all cases. [Reply:] No, because the distinction amongst the cloth, the shuttle, and the loom [of the weaver] is established by means of perception and so on.” (karmakaraṇayor ekakriyāyām ekatvam ayuktam iti cet, na, pramātṛprameyavat kvacid dṛṣṭatvāt | taddṛṣṭāntenaiva sarvadā ’py abhedaprasaṅga iti cet, na, paṭaturīvemādīnāṃ bhedasya pratyakṣādisiddhatvāt |)

  67. NBhū 9.7–15: “Thus, in the same way, since a statement of a defining characteristic is the cause of certainty with respect every intentional object of uncertainty, such a statement isn’t useless. [The opponent:] If a defining characteristic itself is the cause of certainty, then does a method of knowing have no purpose? [Reply:] No, since a defining characteristic also has certainty as its end, it is a method of knowing. [The opponent:] Is a defining characteristic is method by which a method of knowing proceeds (pramāṇaparyāya), or is it one of the methods of knowing such as perception, but something that is distinct from them? [Reply:] Some say, “It is a negative-only reason.” However, we have already said that the terms “specific characteristic,” “mark,” and “defining characteristic” are synonyms. Therefore, it is not a method (paryāya) by which a method of knowing proceeds, because anything that serves as a means for a method of knowing is a method of knowing. Rather, a defining characteristic is something that distinguishes a knowable object. And, in virtue of assisting the senses and so on, it comes to possess designations like “perception,” and so on. [This is why], just like the parts of an argument, a defining characteristic is mentioned separately [in Nyāyasūtra 1.1.1 by means of the word “nature” (tattva)] for the sake of a certain purpose.” (tad evaṃ sarvatra sandehaviṣaye niścayahetutvāt na lakṣaṇavacanaṃ niṣprayojanam iti | lakṣaṇasyaiva niścayahetutve nirarthakaṃ pramāṇam iti cet, na, lakṣaṇasyāpi niścayasādhanatvena pramāṇatvāt | atha lakṣaṇaṃ kiṃ pramāṇaparyāyaḥ, uta pratyakṣādīnām anyatamat tadarthāntaraṃ veti ? kevalavyatirekīty eke | asmābhis tv abhihitam eva viśeṣāṅkādiśabdāḥ paryāyā iti | ata eva na pramāṇaparyāyaḥ pramāṇasādhanasya sarvasyāpi pramāṇatvāt, lakṣaṇaṃ tu prameyaviśeṣakam eva | tac cendriyādisahakāritvena pratyakṣādivyapadeśam api labhate | tasyāvayavādivat prayojanavaśāt pṛthag abhidhānam |)

  68. VV 57.25–26: tathaikaṃ vākyam āvartyamānaṃ bhūyāṃsam artham āheti śabdārthanirūpaṇ-atvenābhisambaddhyate pṛthivītvābhisambandhād iti |

  69. NK 84.7–10: uddeśakrameṇa pṛthivyaḥ prathamaṃ vaidharmyam āhapṛthivītvābhisambandhāt pṛthivīti | yo hi pṛthivīṃ svarūpato jānan napi kutaścid vyāmohāt pṛthivīti na vyavaharati taṃ prati viparyayasambandhāvyabhicāreṇa vyavahārasādhanārtham asādhāraṇo dharmaḥ kathyatepṛthivītvābhisambandhāt pṛthivīti |

  70. NK 84.11–13: iyaṃ pṛthivīti vyavahartavyā pṛthivītvābhisambandhāt yat punaḥ pṛthivīti na vyavahriyate, na tat pṛthivītvenābhisambaddham, yathā ’bādikam, na ceyaṃ pṛthivītvena nābhisambaddhā, tasmāt pṛthivīti vyavahartavyeti |

  71. KirA 29.16–19: vyavahārasiddhir vā lakṣaṇaprayojanam | tathā hi—vivādādhyāsitaṃ dravyaṃ pṛthivīti vyavahriyate, pṛthivītvāt | yat punar pṛthivīti na vyavahriyate na sā pṛthivī, yathā abādi | na ceyaṃ na pṛthivī, tasmāt na tathā [na] vyavahriyate | Here, both the Ahmedabad and Calcutta editions of the text are missing the extra negation that I have added in square brackets. This is necessary to make sense of the text, since the conclusion of the inference is that the substance under dispute is indeed spoken of as “earth.” So, two negations are necessary to cancel each other out.

  72. NK 85.7–9: etenaitad api pratyuktam, yad uktam aparaiḥ prasiddhāś cet, padārthā na lakṣaṇīyāḥ, aprasiddhā natarām aśakyatvāt, svarūpeṇāvagatasyāpi vyavahāraviśeṣapratipādanārthaṃ sāmānyena prasiddhasya viśeṣāvagamārthañ ca lakṣaṇasya pravṛtteḥ |

  73. NK 85.10–13: nanv evaṃ saty anavasthā, lakṣyaval lakṣaṇasyāpy anyato lakṣaṇīyatvād iti cen na, apratītau lakṣaṇasyāpekṣitvāt, sarvatra cāpratītyabhāvāt, tathā hi---śirasā pādena gavām anubadhnanti vidvāṃsaḥ, na punar etāv apy anyataḥ samīkṣante | yas tu sarvathaivāpratipanno na taṃ praty upadeśaḥ, tasya bālamūkādivad anadhikārāt |

  74. For the locus classicus of this view, see Grice (1989). Grice says that a conceptual analysis of an expression E is a general characterisation of the conditions under which one would correctly apply E. To arrive at such an analysis, the proponent makes use of her own linguistic competence, what Grice calls the agent’s “ability to apply or withhold E in particular cases” (p. 174).

  75. NS 1.1.15: buddhir upalabdhir jñānam iti anarthāntaram |

  76. NV 75.5–7: etaiḥ paryāśabdair yo ’bhidhīyate padārthaḥ, sā buddhir iti | paryāyaśabdāḥ kathaṃ lakṣaṇam? vyavacchedahetutvāt | sarvaṃ hi lakṣaṇaṃ itaretarapadārthavyavacchedakam | etaiś ca paryāyaśabdair nānyaḥ padārtho ’bhidhīyata ity asādhāraṇatvāt lakṣaṇam |

  77. NVTṬ 195.13–19: pṛcchatikatham iti | samānāsamānajātīyavyavacchedakaṃ hi lakṣaṇam avyabhicāritayā | paryāyaśabdāś ca saṃketamātrādhīnapravṛttayaḥ kva nāma na saṃbhavanti? tasmāt naite lakṣaṇam iti bhāvaḥ | uttaramvyavacchedeti | nanu vyabhicārasaṃbhavena vyavacchedakatvam ayuktam ity ata āhaetaiś ceti | saṃketo hi dvedhā, sarvajanīno yathā gauriti gojātīyasya vācakaḥ, prādeśikaś ca yathā caitra iti puruṣabhedasya | tatra sarvajanīnaḥ śaknoti vyavacchedabuddhiṃ bhāvayitum, tadvivakṣayaivoktametaiś ceti |

  78. NVTP 256.6–7: tenāyam arthaḥ | eteṣāṃ śabdānāṃ vyavahriyamāṇānāṃ yad ekaṃ pravṛttinimittaṃ tadyogād itarebhyo buddhir bhidyata iti |

  79. See, for different notions of real definition, Robinson (1954, ch. 6).

  80. KirA 30.7–9: yat punar āha bhūṣaṇo ‘lakṣaṇaṃ cihnaṃ liṅgam iti paryāyā’ iti, tad asat; vyāvṛttau sādhye anvayino ’navakāśāt | vyutpannasya svayam eva vyavahārāt | avyutpannasya sapakṣaparicayābhāvāt |

  81. KirP 197.12–15: “Even though there is a contradiction because, in virtue of [Udayana’s own statement] beginning with ‘Then, let this be….,” a positive correlation [between the defining characteristic and the target property] has been admitted on the basis of the example of a pot in the case where something other than a pot is made the site, nevertheless there is no room for a positive reason when all things delimited by earthhood have been made the site. This is the import.” (yady apy āstāṃ tāvad ityādinā ghaṭānyapakṣīkaraṇe ghaṭadṛṣṭāntenānvayo svīkṛta eveti virodhas tathā ’pi pṛthivītvāvacchinnayāvatpakṣīkaraṇe nānvayino ’vakāśa iti bhāvaḥ |) The reference is to an earlier passage which I haven’t discussed so far. But I address this passage (quoted in fn. 92), and the problem that Vardhamāna is referring to, in the appendix to this essay.

  82. KirA 30.9–15: kathaṃ tarhi śāstre ‘kriyāvad dravyam’ iti dravyalakṣaṇeṣu paṭhyate? dravyasyaivāyam asādhāraṇo dharmaḥ samavāyikāraṇatvavad guṇavattvavac ceti pratipādanārtham, na tu lakṣaṇatvena dravyamātraṃ pakṣīkṛtya, vyāvṛttisādhane bhāgāsiddhatvāt | mūrtadravyamātrapakṣīkaraṇe ’py asādhāraṇatvāt | tasmād vāyumanasor apratyakṣatvena dravyatvavipratipattau ca kriyāvattvena tat prasādhya bhāgāsiddhiḥ pariharaṇiyeti tasya tātparyam |

  83. In his commentary Rahasya, Mathurānātha Tarkavāgīśa (16th century CE) explains this principle by quoting the larger verse that it is part of (KirR 123.16–18): “My father has been killed by a trifling amount (kiñcitkayā) [of wine]; nevertheless, I blame this [wine] that has killed my kin and drink it” (hataḥ kiñcitkayā pitā | tathāpy enāṃ svagotraghnīṃ nindāmi ca pibāmi ca ||)

  84. KirA 30.14–16: ye tu pramāṇam eva sarvasya vyavasthāpakaṃ na tu lakṣaṇam, tadapekṣāyām anavasthām āhuḥ; teṣāṃ nindāmi ca pibāmi ceti nyāyaḥ | yato ’vyāptyativyāptiparihāreṇa tattadarthavyavasthāpakaṃ tattadvyavahāravyāvasthāpakaṃ ca pramāṇam upādadate tad eva lakṣaṇam |

  85. KirA 30.16–19: anuvādaḥ sa iti cet, asmākam apy anuvāda eva | na hy alaukikam iha kiñcid ucyate | na cānavasthā, vaidyakādau rogādilakṣaṇavad vyākaraṇādau śabdādilakṣaṇavac ca vyavasthopapatteḥ | tatrāpi hi saṃbandhavyavahāram āśritya lakṣaṇair api vyutpaṭṭiḥ | According to a variant reported by the Ahmedabad edition of the text, “saṃbandhavyavahāram” should be read as “saṃmugdhavyavahāram” (KirA 30, fn. 8). In his commentary, Mathurānātha makes two helpful comments (KirP 123.30–124.4). First, he notes that the definitions in grammar that Udayana mentions are the definitions of grammatical categories like nominal bases (prātipadika). Second, he glosses “saṃbandhavyavahāram āśritya” as “with the help of awareness of the usage of the expression ‘fever’ and so on, pertaining to a qualificand of the relevant properties” (prakṛtadharmaviśeṣyakajvarādivyavahārajñānasahakāreṇa).

  86. PS 1.2.45: arthavad adhātur apratyayaḥ prātipadikam |

  87. KirA 29.4–5: tathā ’py aprasiddhaviśeṣaṇaḥ pakṣaḥ, itaravyavacchedasya kvacid apy aprasiddheḥ, siddhau vā sādhanavaiyarthyāt |

  88. KirA 29.5–7: na; itaravyāvṛtter ghaṭādāv eva pratyakṣasiddhatvāt | kintv āparamāṇor ā ca bhūgolakāt pṛthivītvanimittākrānte vyāptyā vyavacchedabhedavyāvṛttyā vyāvṛttir na siddheti sādhyata iti na doṣaḥ | In the Calcutta edition of the text, “vyavacchedabhedavyāvṛttyā” is printed as “avacchedabhedavyāvṛttyā”; see KirC 191.4. This fits the later occurrence of the same phrase in the opponent’s objection: see KirA 29.9–11 which is translated in fn. 53. Accordingly, I translate “vyavaccheda” as “delimitation” in my translation, rather than as “exclusion” or “distinction.”

  89. In his commentary Prakāśa, Vardhamāna Upādhyāya (14th century CE) explains the phrase precisely in this way (KirA 29.20–21): “ ‘Exclusion of specific delimitations’ is an explanation of just the expression ‘by means of a relation of pervasion.’ A specific delimitation is [a property such as] pothood, clothhood and so on. The meaning of ‘exclusion’ is something that is characterised by the exclusion, i.e., the absence, of that [specific delimitation].” (vyaptyety asya vyākhyānam avacchedeti | avacchedabhedaḥ ghaṭatvapaṭatvādiḥ| tasya vyāvṛttyā virahitattvena lakṣitā vyāvṛttir ity arthaḥ |) The parallel text in the Calcutta edition (KirP 193.9–11) seems wrong to me.

  90. Before the opponent raises this worry, he makes a different point that is not dialectically effective. Even if we perceive pots and cloths as distinct from water and so on, the property of being distinct from water and so on is not well-established for us as a property of all instances of earth. So, would that also not raise the problem of the site’s having an unestablished qualifier? Udayana expresses the worry as follows (KirA 29.9–11): “If this is so, then the distinctness [from water and so on] is not established for any object that bears the mark of earthhood by means of a relation of pervasion which involves the exclusion of [other more] specific delimitations. So, once again, the problem of the site’s having a qualifier that is not well-established will follow.” (evaṃ tarhi pṛthivītvanimittākrānte vyāptyā ’vacchedabhedavyāvṛttyā vyāvṛttiḥ kvacin na siddhā, iti punar apy aprasiddhaviśeṣaṇatvaṃ samāyātam |) As Udayana notes, this is a bad objection: in order to make an inference, the target property does not have to be well-established for us as a property of the site, since that would make the very act of proving the target property futile. He says (KirA 29.11–13): “No; for only a novel qualifier that is connected to the site should be established even when [the site] is characterised by the presence [of the target property] everywhere. This is because a property that is well-established is present in the property-bearer, but it is not the case that a property is established only insofar as it is well-established to be present in the relevant property-bearer; for, if that were the case, due to the establishment [of the property in the property-bearer], establishing it would be futile.” (na; pakṣasambandhino viśeṣaṇasya sarvatrānvayiny api apūrvasya sādhyatvāt | prasiddho hi dharmo dharmiṇam anveti na tu dharmyanvitatayaiva prasiddhaḥ sādhyata iti | tathā sati siddheḥ sādhanavaiyarthyād iti |)

  91. KirA 29.13–15: “Even then, if the distinctness from other entities is established by perception in the case of a pot, etc., then it should be established in the case of atoms and the like merely on the basis of a positive correlation on the strength of those examples [i.e., the pot, the cloth, and so on]. Why is the negative correlation [alone] given a place of honour by way of including the pot, etc. also in the site?” (tathāpi ghaṭādau ced itaravyāvṛttiḥ pratyakṣasiddhā tatas taddṛṣṭāntabalenānvayād eva paramāṇvādau sādhyatāṃ kiṃ ghaṭādikam api pakṣe nikṣipya vyatireka ādriyata iti cet…)

  92. KirA 29.15–16: āstāṃ tāvad ayaṃ suhṛdupadeśaḥ, kevalavyatirekilakṣaṇaṃ tāvan nirvyuḍham |

  93. KirA 29.19–30.1: “Even in this case, since the intentional object of linguistic usage is established by its own nature, there is no problem of the site’s being unestablished. For a confused person, since linguistic usage of the expression “earth” is established, there is no problem of [the site’s] having an unestablished qualifier.” (atrāpi vyavahāraviṣayasya svarūpataḥ siddher nāśrayāsiddhiḥ | pṛthivīvyavahārasya saṃmugdhasya siddher nāprasiddhaviśeṣaṇatvam |)

  94. KirA 30.1–3: “As for the site, since anything that possesses a particular mark (nimittaviśeṣavataḥ) is being established [to be something that is correctly spoken of as “earth”], establishing this is not futile. And if all earth is made into the site, then the reason cannot be a positive one.” (pakṣe nimittaviśeṣavataḥ sādhyatvān na sādhanavaiyarthyam, sarvapṛthivīpakṣīkaraṇena ca nānvayitvam |)

  95. KirA 30.3–5: yad yasyānvayavyatirekāv anuvidhatte tat taddhetukam, yathā ghaṭādi mṛdādihetukam, anuvidhatte ca pṛthivīvyavahāraḥ pṛthivītvasyānvayavyatirekau iti cet |

  96. KirA 30.4–5: na, pṛthivītvanimittakatve pṛthivīvyavahārasya sādhye anvayābhāvāt | kevalaṃ sarvanāmnā vyavahāramātreṇa vakro ’yam anvayaḥ, sa ca vyatirekān na bhidhyate, vivakṣābhedāt |

  97. Compare Vardhamāna’s explanation of this point (KirC 197.9–10): “The reason is that whatness (yattva) or thatness (tattva) is not uniform, so the statement of a positive correlation by means of variables depending on the apprehension of a negative pervasion is what is meant by ‘disingenuity.’” (na hi yattvaṃ tattvaṃ vā ’nugatam iti vyatirekavyāptigraham upajīvya sarvanāmnā ’nvayābhidhānam eva vakratvārthaḥ|)

  98. See, for example, Udayana’s remarks on postulation (arthāpatti) as a kind of negative-only inference (i.e., inference based on negative-only reasons) in Nyāyakusumāñjali (NKu 425.3–6 and 426.1–2): “[The Bhāṭṭa opponent:] A negative-only inference that is accepted by others [i.e., the Naiyāyikas] is an instance of postulation, because there is no positive correlation. [Reply:] We do not forbid the use of the term ‘posulation’ in such a specific manner with regard to an inference. [The opponent:] Why is the word ‘inference’ used in that case? [Reply:] Because it arises from an inferential mark that is invariably related [to the target property]. For the property of not occurring without the target property is common to a negative-only reason just as it is to a positive reason. And the ascertainment of that property takes place either through positive and negative correlations, or by one of the two [i.e., by either solely positive or solely negative correlations]. Therefore, it is reasonable that the word ‘postulation’ is a synonym of ‘inference’, or a term that describes a species of that inference, just like ‘pūrvavat’ and so on.” (kevalavyatireky anumānaṃ parābhimatam arthāpattiḥ; anvayābhāvād iti cet—evam etāvatā viśeṣeṇānumāne ’rthāpattivyavahāraṃ na vārayāmaḥ | tatrānumānavyavahāraḥ kuta iti cet—avinābhūtaliṅgasamutpannatvāt | sādhyadharmeṇa vinā hy abhavanam anvayina iva vyatirekiṇo ’py aviśiṣṭam, tanniścayaś cānvayavyatirekābhyām anyatareṇa veti | tasmād arthāpattir ity anumānasya paryāyo ’yam, tadviśeṣavacanaṃ vā pūrvavadādivad iti yuktam |) For a translation and some discussion of this passage, see Das (2020b).

  99. In his commentary Prakāśa, Vardhamāna mentions both these responses, by partially quoting Gaṅgeśa’s Tattvacintāmaṇi (KirP 194.7–16): “However, our father [Gaṅgeśa] has said, ‘The mutual absences of the thirteen [other kinds of entities] such as water and so on—which are well-established—are established in earth. For this very reason, even though there is an awareness of the mutual absence of water and so on taken together, the mutual absences of the thirteen [other kinds of entities] are to be established by means of a negative-only [reason]. So, [the reason does not have] the status of being positive, or of being uncommon (nānvayitvāsādhāraṇye). However, in fact, in the case of a negative-only [reason] that has an absence as its target property, a target property that is not itself well-established is established. The absence of the absence that is pervaded by the absence of the reason is established in the site by means of a reason that takes the form of the absence of the absence of the pervader. For, when the site is apprehended as possessing the absence of the pervader, the absence of the pervaded entity must necessarily be present [in it]. That is to say: the absence of earthhood is apprehended as the pervader of water and so on. So, by means of earthhood that has the nature of the absence of that absence, the mutual absence [of water and so on]—which is not well-established [in earth]—is established, since the awareness of the counterpositive has already taken place.” (asmatpitṛcaraṇās tu jalādīnāṃ trayodaśānyonyābhāvās trayodaśasu prasiddhāḥ pṛthivyāṃ sādhyate | ata evākāśe militajalādipratiyogikānyonyābhāvapratītāv api vyatirekiṇā trayodaśānyonyābhāvāḥ sādhyā iti [nānvayitvāsādhāraṇye |] vastutas tv abhāvasādhyake vyatirekiṇy aprasiddham eva sādhyaṃ siddhyati | yasyābhāvasya hetvabhāvo vyāpako gṛhītas tasyābhāvaḥ pakṣe vyāpakābhāvābhāvarūpeṇa sādhanena sidhyati | vyāpakābhāvavattayā jñāte vyāpyābhāvaśyambhāvāt | tathā hi jalādivyāpakaḥ pṛthivītvābhāvo jñāta iti tadabhāvābhāvātmakatvena pṛthivītvena pṛthivyām anyonyābhāvo ’prasiddha eva siddhyati | pratiyogijñānasya vṛttatvād ity āhuḥ |) What Vardhamāna quotes here is in fact of an amalgam of two passages in the section on negative-only inference in Tattvacintāmaṇi, see TCMC 618.4–8 and 641.8–10 and 641.1–2. Following Gaṅgeśa’s text, I have corrected the edition of Vardhamāna’s Prakāśa from “nānvayitvāt sādhāraṇye” to “nānvayitvāsādhāraṇye”, since the point is that the relevant relation of pervasion in this case is not known on the basis of positive correlations, and the reason does not suffer from the fault of uncommonness (asādhāraṇya), i.e., the fault of being present only in the site (without the target property) and not elsewhere.

  100. Gaṅgeśa’s argument here depends on the principle that, for any positive entity X (i.e., an entity belonging to any Vaiśeṣika ontological category other than absence), the absence of the absence of X is X. This principle became controversial amongst later Nyāya thinkers such as Raghunātha Śiromaṇi (15th century CE). For discussion of this principle in relation to negative-only reasons, see Das (2020a).


Primary Texts and Abbreviations

  • KirA Udayana’s Kiraṇāvalī in Praśastapādabhāṣyam: With the Commentary Kiraṇāvalī of Udayanācārya. Edited by Jitendra S. Jetly. Baroda: Oriental Institute, 1971.

  • KirC Udayana’s Kiraṇāvalī in Kiraṇāvalī. Edited by Sivachandra Sarvabhauma. Calcutta: Asiatic Society, 1911.

  • KirP Vardhamāna’s Prakāśa in Kiraṇāvalī. Edited by Sivachandra Sarvabhauma. Calcutta: Asiatic Society, 1911.

  • NA Siddhasena Divākara’s Nyāyāvatāra in Jaina Epistemology in Historical and Comparative Perspective: Critical Edition and English Translation of Logical-epistemological Treatises: Nyāyāvatāra, Nyāyāvatāravivṛti and Nyāyāvatāraṭippana with Introduction and Notes. Edited by Piotr Balcerowicz. Stuttgart: Steiner, 2001.

  • NS Gautama’s Nyāyasūtra in Gautamīyanyāyadarśana with Bhāṣya of Vātsyāyana. Edited by Anan-talal Thakur. New Delhi: Indian Council of Philosophical Research, 1997

  • NBh    Vātsyāyana’s Nyāyabhāṣya in Gautamīyanyāyadarśana with Bhāṣya of Vātsyāyana. Edited by Anantalal Thakur. New Delhi: Indian Council of Philosophical Research, 1997.

  • NBhū  Bhāsarvajña’s Nyāyabhūṣaṇa Śrīmadācāryabhāsarvajñapraṇītasya Nyāyasārasya Svopajñaṃ Vyākhyānaṃ Nyāyabhūṣaṇam. Edited by Svāmī Yogīndrānanda. Varanasi: Ṣaḍdarśana Prakāśana Pratiṣṭhāna.

  • NK     Śrīdhara’s Nyāyakandalī in Nyāyakandalī Being a Commentary On Praśastapādabhāṣya, With Three Sub-commentaries. Edited by Jitendra S. Jetly and Vasant G. Parikh. Baroda: Oriental Institute, 1991.

  • NKA  Udayana’s Nyāyakusumāñjali in The Nyāyakusumāñjali of Śrī Udayanācārya with Four Commentaries: The Bodhinī, Prakāśa, Prakāśikā (Jalada) and Makaranda by Varadarāja, Varddhamānopādhyāya, Mecha Thakkura and Rucidattopādhyāya and with Notes by Śrī Dharmadatta (Bachchā Jhā). Edited by Padmaprasāda Updhyāya and Dhuṇḍirāja Śāstrī. Varanasi: Chowkhamba Sanskrit Series, 1957.

  • NM I  Jayanta Bhaṭṭa’s Nyāyamañjarī in Nyāyamañjarī: Sampādakagrathitanyāyasaurabhākhyaṭippaṇīsamanvitā. Vol. I. Edited by K. S. Varadacharya. Mysore: Oriental Research Institute, 1969.

  • NV    Uddyotakara’s Nyāyavārttika in Nyāyabhāṣyavārttika of Bhāravdāja Uddyotakara. Edited by Anantalal Thakur. New Delhi: Indian Council of Philosophical Research, 1997.

  • NVTṬ  Vācaspati Miśra’s Nyāyavārttikatātparyaṭīkā in Nyāyavārttikatātparyaṭīkā of Vācaspatimiśra. Edited by Anantalal Thakur. New Delhi: Indian Council of Philosophical Research, 1996.

  • NVTP  Udayana’s Nyāyavārttikatātparyapariśuddhi in Nyāyavārttikatātparyapariśuddhi of Udayanācārya. Edited by Anantalal Thakur. New Delhi: Indian Council of Philosophical Research, 1996.

  • PS        Pāṇini’s Aṣṭādhyāyī in Kāṣikā: A Commentary on Pāṇini's Grammar by Vāmana and Jayāditya. Edited by Aryendra Sharma. Hyderabad : Osmania University, Sanskrit Academy, 1969–1985. URL = < >

  • PDS  Praśastapāda’s Padārthadharmasaṅgraha in Praśastapādabhāṣyam: With the Commentary Kiraṇāvalī of Udayanācārya. Edited by Jitendra S. Jetly. Baroda: Oriental Institute, 1971.

  • TCMC Gaṅgeśa Upādhyāya’s Tattvacintāmaṇi in The Tattvacintāmaṇi of Gaṅgeśa Upādhyāya; Anumityādibādhānta Anumānakhaṇḍā with the Commentary ‘Rahasya’ by Mathurānātha Tarkavāgīśa, Volume II Part I. Edited by Kāmākhyānātha Tarkavāgīśa. Calcutta: Asiatic Society, 1897. Reprinted in Delhi: Chaukhamba Sanskrit Pratishthan, 1990.

  • VSB   Kaṇāda’s Vaiśeṣikasūtra Vaiśeṣikasūtra of Kaṇāda with the Commentary of Candrānanda. Crit-ically edited by Muṇi Śrī Jambuvijayaji. Baroda: Oriental Institute, 1961.

  • VSV    Candrānanda’s Vṛtti on the Vaiśesikasūtra in Candrānanda’s commentary on the Vaiśeṣika-Sūtra. Edited by Ferenc Ruzsa. Critical edition of all MSS [available at: (17 April 2019)].

  • VV    Vyomaśiva’s Vyomavatī in Vyomavatī. Edited by Gaurīnātha Śāstrī. Varanasi: Sampurnanand Sanskrit Vishvavidyalaya, 1983.

Translations and Other Literature

  • Bhattacharyya, S. (1990). Gadādhara's theory of objectivity: Containing the text of Gadādhara's Viṣayatāvāda with an English translation, explanatory notes, and a general introduction (Vol. 1). Indian Council of Philosophical Research.

  • Boghossian, P. (1996). Analyticity reconsidered. Noûs, 30(3), 360–391.

    Article  Google Scholar 

  • Burgess, A., Cappelen, H., & Plunkett, D. (Eds.). (2020). Conceptual engineering and conceptual ethics. Oxford University Press.

    Google Scholar 

  • Carpenter, A., & Ganeri, J. (2010). Can you seek the answer to this question? (Meno in India). Australasian Journal of Philosophy, 88(4), 571–594.

    Article  Google Scholar 

  • Cappelen, H. (2018). Fixing language: An essay on conceptual engineering. Oxford University Press.

    Book  Google Scholar 

  • Chakrabarti, K. K. (1995). Definition and induction a historical and comparative study. University of Hawaii Press.

    Book  Google Scholar 

  • Chalmers, D. (1996). The conscious mind: In search of a fundamental theory. Oxford University Press.

    Google Scholar 

  • Chalmers, D. (2020). What is conceptual engineering and what should it be? Inquiry: An Interdisciplinary Journal of Philosophy.

    Article  Google Scholar 

  • Charles, D. (2006). Types of definition in the Meno. In L. Judson & V. Karasmanis (Eds.), Remembering Socrates: Philosophical essays. Oxford University Press.

  • Charles, D. (Ed.) (2010). Definition in Greek philosophy. Oxford University Press.

  • Devitt, M. (1996). Coming to our senses: A naturalistic program for semantic localism. Cambridge University Press.

    Google Scholar 

  • Das, N. (2018). Śrīharṣa. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2021 ed.).

  • Das, N. (2020). Raghunātha on Arthāpatti. In M. Keating (Ed.), Controversial reasoning in Indian philosophy: Major texts and arguments on Arthāpatti. Bloomsbury Academic.

    Google Scholar 

  • Das, N. (2020). Udayana’s Flower-offering of reason. In M. Keating (Ed.), Controversial reasoning in Indian philosophy: Major texts and arguments on Arthāpatti . Bloomsbury Academic.

    Google Scholar 

  • Das, N. (2020). Vātsyāyana’s guide to liberation. Journal of Indian Philosophy, 48(5), 791–825.

    Article  Google Scholar 

  • Fine, G. (2010). Signification, essence, and Meno’s paradox: A reply to David Charles’s ‘Types of Definition in the Meno’. Phronesis, 55(2), 125–152.

    Article  Google Scholar 

  • Fine, K. (1994). Essence and modality. Philosophical Perspectives 8(Logic and Language), 1–16.

  • Flocke, V. (2021). How to engineer a concept. Philosophical Studies, 178, 3069–3083.

    Article  Google Scholar 

  • Ganeri, J. (2017). Śrīharṣa’s dissident epistemology. In J. Ganeri (Ed.), The Oxford handbook of Indian philosophy. Oxford University Press.

    Google Scholar 

  • Grice, H. P. (1989). Post-war Oxford philosophy. In Studies in the way of words (pp. 171–180). Harvard University Press.

  • Haslanger, S. (2000). Gender and race: (What) Are they? (What) do we want them to be? Noûs, 34, 31–55.

    Article  Google Scholar 

  • Jackson, F. (1998). From metaphysics to ethics: A defence of conceptual analysis. Oxford University Press.

    Google Scholar 

  • Kornblith, H. (2002). Knowledge and its place in nature. Oxford University Press.

    Book  Google Scholar 

  • Langford, C. H. (1942). The notion of analysis in Moore’s philosophy. In P. A. Schilpp (Ed.), The philosophy of G. E. Moore. Northwestern University Press.

    Google Scholar 

  • Matilal, B. K. (1981). Introduction. In M. Tachikawa (Ed.), The structure of the world in Udayana’s realism: A study of the Laksaṇāvalī and the Kiraṇāvalī. D. Reidel.

    Google Scholar 

  • Matilal, B. K. (1990). Logic, language and reality: Indian philosophy and contemporary issues. Motilal Banarasidass.

    Google Scholar 

  • Moore, G. E. (1903). Principia Ethica. Dover.

    Google Scholar 

  • Olivelle, P. (1998). The early Upanishads: Annotated text and translation. Oxford University Press.

    Google Scholar 

  • Olivelle, P. (2013). King, governance, and law in Ancient India: Kauṭilya’s Arthaśāstra. Oxford University Press.

    Book  Google Scholar 

  • Papineau, D. (2013). The poverty of conceptual analysis. In M. Haug (Ed.), The Armchair or the Laboratory? (pp. 166–194). Routledge.

    Google Scholar 

  • Quine, W. V. O. (1951). Two dogmas of empiricism. Philosophical Review, 60(1), 20–43.

    Article  Google Scholar 

  • Robinson, R. (1954). Definition. Oxford University Press.

    Google Scholar 

  • Rosen, G. (2015). Real definition. Analytic Philosophy, 56(3), 189–209.

    Article  Google Scholar 

  • Tachikawa, M. (1981). The structure of the world in Udayana’s realism: A study of the Laksaṇāvalī and the Kiraṇāvalī. D. Reidel.

    Google Scholar 

  • Thakur, A. (2003). Origin and development of the Vaiśeṣika system. Centre for Studies in Civilizations.

    Google Scholar 

  • Wiggins, D. (2007). Three moments in the theory of definition or analysis: Its possibility, its aim or aims, and its limit or terminus. Proceedings of the Aristotelian Society, 107(1 Pt 1), 73–109.

    Article  Google Scholar 

  • Williamson, T. (2007). The philosophy of philosophy. Wiley-Blackwell.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Nilanjan Das.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Appendix: On Treating Defining Characteristics as Negative-Only Reasons

Appendix: On Treating Defining Characteristics as Negative-Only Reasons

The aim of this appendix is to survey some of the technical problems that Udayana raises for the view that defining characteristics are negative-only reasons. We have considered two kinds of inferences where defining characteristics play this role.


The Thesis. Earth is distinct from water and so on.

The Statement of the Reason. For it possesses earthhood.

The Illustration. Whatever is not distinct from water and so on lacks earthhood, e.g., water.

The Application. Earth does not lack earthhood.

The Conclusion. Therefore, it is distinct from other entities.


The Thesis. This substance under dispute is spoken of as “earth.”

The Statement of the Reason. For it possesses earthhood.

The Illustration. Whatever is not spoken of as “earth” lacks earthhood, just like water and so on.

The Application. This does not lack earthhood.

The Conclusion. Therefore, this is spoken of as “earth.”

Udayana considers several objections against (A).

The first is that the site of the inference suffers from the problem of having a qualifer that is not well-established (aprasiddhaviśeṣaṇatā).

Even then, the site has a qualifier that is not well-established, because the distinctness [of earth] from other entities is not well-established anywhere; or, if it were established, it would be futile to establish it.”Footnote 87

For any inference, the target property—which qualifies or characterises the site—must be a property that is well-known to the inferring subject. Otherwise, the inferring subject would be inferring a property that she does not have clear understanding of. As a result, the site would suffer from the fault of having a qualifier that is not well-established (aprasiddhaviśeṣaṇatā). For (A), the worry is that, if the subject does not know that earth is distinct from other entities such as water and so on, she will not be sufficiently familiar with the target property. So, the site will have a qualifier that is not well-established in inferences like (A). But, if the property is well-established, then the agent already knows that earth is distinct from other entities. So, making an inference like (A) will be pointless.

Udayana responds to this worry as follows:

[Reply:] No, because the distinctness from other entities is established by perception indeed in case of objects like a pot. However, this distinctness is not established with respect to things that bear the mark of earthood (pṛthivītvanimittākrānte)—ranging from the atoms [of earth] up to the globe of the earth—by means of a relation of pervasion which involves the exclusion of [other more] specific delimitations (vyāptyā vyavacchedabhedavyāvṛttyā). So, that it is being established is not a problem.Footnote 88

Udayana’s point is this. The target property of this inference is not unestablished: when we look at familiar objects made of earth, e.g., a pot or a cloth, we are already perceptually aware of their distinctness from other entities such as water and so on. On the basis of these observations, we can learn certain kinds of generalizations: e.g., that all pots are distinct from entities other than earth, or that all cloths are distinct from entities other than earth. These generalizations capture relations of pervasion between (a) properties like pothood and clothhood (which are more specific than earthhood) and (b) the property of being distinct from water and so on. However, we cannot know on the basis of perception (or such generalizations alone) that all instances of earth—including imperceptible atoms or the entire planet earth—are distinct from other kinds of entities. Thus, to establish that these too are distinct from water and so on, we need a further inference. This inference will have to depend on our knowledge of a relation of pervasion between earthhood and the property of being distinct from water and so on. Unlike the other relations of pervasion that we may have already learnt about, this relation of pervasion involves the property of earthhood rather than the more specific properties like pothood and clothhood. That is why Udayana describes it as “a relation of pervasion which involves the exclusion of [other more] specific delimitations.”Footnote 89

The second problem is related but a bit more serious: it is the problem of available cases of positive correlation.Footnote 90 If Udayana is right, then we can indeed observe cases of positive correlation between earthhood and the property of being distinct from water and so on. In objects like the pot and the cloth, we encounter both the reason, i.e., earthhood, and the target property, i.e., distinctness from water and so on. Since such cases of positive correlation can be observed, what is the point of making an inference that involves a negative-only reason?Footnote 91 For example, one could make a different inference:


The Thesis. Imperceptible objects like atoms, the globe of earth, etc. are distinct from water, and so on.

The Statement of the Reason. For they possess earthhood.

The Illustration. Whatever possesses earthhood is distinct from water and so on, just like a pot.

The Application. Imperceptible objects like atoms, the globe of earth, etc. possess earthhood.

The Conclusion. Therefore, imperceptible objects like atoms or the globe of earth, etc. are distinct from water and so on.

The relevant reason, in this context, would function as a positive-and-negative reason. This is because the site—which is only restricted to imperceptible earthen objects—does not include the observed cases of positive correlation. As a result, the inferring subject could learn about the relation of pervasion on the basis of observed cases of positive correlation such as the pot or the cloth. Udayana’s response to this worry is brusque:

Then, let this be friendly advice. Still, the defining characterisic of a negative-only reason [or, the defining characteristic as a negative-only reason] is faultless.Footnote 92

Here, Udayana seems to concede that a defining characteristic could function as a positive-and-negative reason for making in an inference like (C), but he does not explain why we still need to construe defining characteristics as negative-only reasons anymore.

Later, Udayana argues that an inference like (B) not only avoids the problem of the site’s being unestablished, but also the two problems for (A) we have discussed in this appendix so far: the site’s having an unestablished qualifier and the availability of cases of positive correlation. First, the site of (B) is a substance that the inferring subject is already familiar with; it is an entity which—as Śrīdhara puts it—“is apprehended by its own nature” by the subject. So, the site of the inference is well-established. Thus, the inference does not suffer from the problem of having an unestablished site. Second, even a person who is confused about which objects the expression “earth” applies to is aware of the property of being called “earth.” So, the inference does not suffer from the problem of having an unestablished target property.Footnote 93 Third, even if that confused person is familiar with some earthen objects that are correctly spoken of as “earth”, e.g., a pot made of clay, it still makes sense for her to prove that any object of the relevant kind is correctly spoken of as “earth.” This is because she may not have antecedently observed linguistically competent members of her linguistic community applying the word “earth” correctly to imperceptible objects such as earth atoms or the entire planet earth. So, the inference is not futile. But this inference can only be based on a negative-only reason, because the site of the inference includes all the cases of positive correlation that the agent might have observed.Footnote 94

However, we might wonder whether we have to cast the relevant inference as an inference that involves a negative-only reason. Udayana is sensitive to this worry: he considers an objection from an opponent who wants to resist the idea that a defining characteristic should be treated as a negative-only reason. The opponent points out that there is a different way of reconstructing the inference.

Whatever conforms to the presence and the absence of whatever [else] has that [other thing] as its cause, just as the pot and so on have clay as their cause. And the use of the expression “earth” conforms to the presence and absence of earthhood.Footnote 95

The opponent wants to say that we can make a different inference in this case:


The Thesis. Any correct use of the expression “earth” has earthhood as its cause.

The Reason. For it conforms to the presence and the absence of earthhood (i.e., it takes place only when earthhood is present, but is absent when earthhood is absent).

The Illustration. Whatever conforms to the presence and absence of something else (in this way) has the latter as its cause, e.g., a clay pot that has clay as its cause.

The Application. Any correct use of the expression “earth” conforms to the presence and absence of earthhood.

The Conclusion. Therefore, it has earthhood as its cause.

This inference can remove any confusion that a linguistically incompetent agent might have about how to use the word “earth.” Yet, the inference, according to the opponent, is based on a positive-and-negative reason. The crucial premise of this argument is the following: if the presence of x is always preceded by the presence of y and that the absence of y is always followed by the absence of x, then y is a cause of x. For example, we observe that the arising of a pot is always preceded by the presence of clay; similarly, we also see that a clay pot never arises when there is no clay around. So, we can conclude that clay is the cause of a clay pot. Similarly, we observe that any correct application of the word “earth” only takes place when the object picked out by the word possesses earthhood, but if it does not possess earthhood, then the word cannot be correctly applied to it. So, we can learn on the basis of such positive and negative correlations that earthhood is the condition for correctly applying the word “earth.”

Udayana’s response to this objection involves two points.

No. For, if it is to be established that the application of the expression “earth” has earthhood as its condition (nimitta), then there is no positive correlation. This positive correlation—merely in virtue of being spoken of using variables (kevalaṃ sarvanāmnā vyavahāramātreṇa)—is disingenuous (vakraḥ). And, this is not distinct from a negative correlation because there is [only] a difference in the speaker’s intention.Footnote 96

The first claim is that, even while stating (D), the opponent is not relying on any case of positive correlation between the reason and the target property. This is presumably because the reason in this inference is the property of conforming to the presence and the absence of earthhood (pṛthivītvānvayavyatirekānuvidhāna) and the target property is having earthhood as a causal condition (pṛthivītvanimittakatva). So, a case of positive correlation would have to be some object that both (a) conforms to the prior presence and the prior absence of earthhood and (b) has earthhood as its causal condition. But the example that is used to motivate the relation of pervasion is the clay pot. This is something from which the reason and the target property are both absent. So, this is not a case of positive correlation.

Moreover, in (D), the relevant relation of pervasion is a bit too general: whatever conforms to the presence and the absence of something else has the latter as its cause. To check whether this relation of pervasion holds in the specific case of the reason and the target property of (D), we need to check if there are observed cases of positive correlation between the two. But Udayana’s (implicit) claim is that the only cases of positive correlation that we will find will be cases where an agent applies the word “earth” to an object o insofar as she undergoes an awareness of o as earth on the basis of its earthhood. But those are precisely the cases that are part of the site. Thus, there is no similar site (sapakṣa) (i.e., a place other than the site where the target property is present) that could confirm the relevant relation of pervasion. So, this relation of pervasion can only be confirmed by cases of negative correlation. This, in turn, will make the reason negative-only.

The second claim is that it is disingenuous of the opponent to state the relation of pervasion using variables like “whatever”, “that,” and so on.Footnote 97 Even though a relation of pervasion may look like a relation of positive pervasion when stated in this way, it need not actually be distinct from a relation of negative pervasion, i.e., a relation of pervasion that is apprehended on the basis of cases of negative correlation. This is because the variables could be interpreted in multiple ways depending on the speaker’s intention. For example, if the speaker’s intention were to pick out absences instead of positive entities by those variables, the relevant relation would end up being a relation of negative pervasion. In the final analysis, on Udayana’s view, there is no deep difference between relations of positive pervasion and relations of negative pervasion. For any two properties X and Y, X pervades Y just in case Y does not occur at a place where the absence of X occurs. This relation of pervasion can be expressed both positively and negatively: we can state it positively by saying, “Wherever Y occurs, X occurs,” or we can state it negatively by saying, “Wherever X does not occur, Y does not occur.”Footnote 98 What matters, however, is how we ascertain this relation of pervasion. We can either learn about this relation by observing cases of both positive and negative correlations, or by observing cases solely of positive correlations, or by observing cases solely of negative correlations. Udayana’s claim is that, in inferences like (B) and (D), the relation of pervasion can only be known on the basis of negative correlations between the reason and the target property.

Later Naiyāyikas like Gaṅgeśa Upādhyāya (14th century CE) clearly found Udayana’s response to the first problem for (A)— the site’s having qualifier that is not well-established—unsatisfactory. So, they sought to solve the problem in two different ways.Footnote 99 In his first solution, Gaṅgeśa grants that the target property in an inference like (A)—the distinctness from other entities such as water and so on—is in fact not well-established. But he notes that it can understood as a collection of thirteen distinctness-properties: namely, distinctness from water, the distinctness from fire, distinctness from wind, and so on. Each of these distinctness-properties can be known independently in other objects. For example, in samples of water, we can perceive the distinctness from fire, the distinctness from wind, and so on, but not the distinctness from water. Similarly, in samples of fire, we may observe the distinctness from water, the distinctness from wind, but not the distinctness from fire. By using “the method of a sieve” (cālanīnyāya), we can collect together all these different distinctness properties, and treat them jointly as the target property of our inference. This obviates the need to accept the claim that we can independently perceive the distinctness from entities other than earth in earthen objects like pots, etc.

The other solution that Gaṅgeśa proposes is a bit more conservative. This solution, too, begins with the concession that the target property in inference (A) may not be something that we are independently familiar with. But he reconstructs the inference differently. On this view, we can learn by observation that a certain relation of pervasion holds between the thirteen other kinds of entities, such as water, etc., and the absence of earthhood: “Whatever is either water, or fire, or wind, etc. lacks earthhood.” If we know that the absence of earthhood pervades water, etc. in this way, we can use earthhood—which, according to Gaṅgeśa, is in fact nothing but the absence of the absence of earthhood—to infer that earth is distinct from water, etc. because it possesses earthhood. If a property X pervades a property Y, then the absence of X must necessarily be accompanied by the absence of Y. Since anything that is identical to an entity other than earth (like water and so on) lacks earthhood, the absence of the absence of earthhood—i.e., earthhood—must be invariably accompanied by the property of being distinct from water and so on. Thus, we can still use earthhood to infer that earth is distinct from entities of other kinds.Footnote 100

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, N. The Search for Definitions in Early Nyāya-Vaiśeṣika. J Indian Philos 51, 133–196 (2023).

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: