The lakṣaṇa of a lakṣaṇa

The importance of definitions cannot be overstated in keeping concepts straight in our heads. In Indian philosophy, writers take great pains to define items and spend a lot of time testing their definitions for defects. Definitions are especially emphasized in nyāya, Indian logic. Importantly, there is even a definition of a definition in nyāya. Without such a definition, there would be no way to define something without defects.

In this article, I examine the definition of a definition by translating a passage from the Kiranavali commentary By Sri Krishna Vallabhacharya, to the Nyaya siddhanta muktavali of Vishvanatha Panchanana Bhattacharya. Babaji recently discussed this in his class on Nyāya-siddhānta-muktāvali. The commentary is available here for those interested: https://archive.org/details/kqPv_nyaya-siddhant-muktavali-of-vishvanath-panchanan-with-kiranavali-commentary-by-k/page/34/mode/2up

The three defects in a definition

A ‘lakṣaṇa’ is a defining characteristic which is used to successfully pick out the target and to exclude non-targets. A definition in nyāya consists of stating the lakṣaṇas, which helps us know the lakṣya. A lakṣya is the object which we seek to reach by means of the definition. As an example, in the definition: a cow is an animal with a dewlap, then the dewlap is the lakṣaṇa, and the cow is the lakṣya.

Śri Krishna Vallabhacarya defines a lakṣaṇa as follows:

अव्याप्त्यव्याप्त्यसंभवैतद्दोषत्रयरहितो धर्मो लक्षणम्

lakṣaṇa is that dharma, which is devoid of the three defects of avyāpti, ativyāpti, and asaṁbhava.

The word dharma refers to that ‘which is contained’, while the word dharmi refers to that ‘which contains’. So the lakṣana is a dharma that is contained in the lakṣya, which is the dharmi.

The definition above raises the question, of course, about the definitions of avyāpti and so on. Sri Krishna Vallabhacharya defines them also, which I examine below.

The definition of ativyāpti

Below, I present Sri Krishna Vallabhacharya’s definition and my translation. The definition will look complicated to those who are not familiar with the terminology of nyāya, so I provide notes for the reader to follow along after the translation.

अतिव्याप्तिः — लक्ष्यतावच्छेदकसामानाधिकरण्ये सति लक्ष्यतावच्छेदकावच्छिन्नप्रतियोगिताकभेदसामानाधिकरण्यम्,

ativyāpti —

[the defect of ativyāpti, or over-pervasion is the lakṣaṇa’s having] the property of being present in the same adhikaraṇa [substratum] as the difference [abhāva] which has counterpositiveness that is delimited by the lakṣyatā-delimiter, while the lakṣyatā-delimiter is present in the same adhikaraṇa as the lakṣaṇa.

[my notes-

this is a fancy way of saying a very simple thing. Suppose we define a cow as an animal with horns. In nyāya, it is customary to talk about cowness – a property common to all cows, and ‘hornness’, a property common to all horns. The idea is that cowness is perceived in a given cow, and hornness is perceived in a given horn. Now, the cow is the lakṣya, or target, while the horns are the lakṣaṇa, or the (proposed) defining characteristic. The problem of course is that horns are also present in a buffalo. So, there is the defect of ativyāpti, in the laksaṇa ‘horns’ or the corresponding property of ‘hornness’. That is, hornness is present in the substratum in which cowness is present (i.e. a cow), and also in the substratum in which cowness is absent (e.g. a buffalo).

In nyāya’s terminology, the target is cow, meaning there is targetness or lakṣyatā in the cow. Now there are many targets (say we define a buffalo or a tiger, then all these will have targetness). So we say that in the cow, the targetness (lakṣyatā) is delimited by cowness. That is, the larger set of targetness is conceptually set aside by the delimiter, cowness.

Now, a buffalo is different from the cow. In nyāya terminology, there is an absence, abhāva, of the cow in the buffalo. The pratiyogi or counterpositive of the abhāva, is the cow. The cow has pratiyogitā or counterpositiveness. This counterpositiveness is delimited by cowness (i.e. the cow’s absence is specifically being discussed). Hornness is present in the same substratum (buffalo) in which there is a difference from a cow, meaning the substratum has an absence delimited by cowness. This is the example the writer provides which I translate below:]

यथा गोर्लक्षणं ’शृंगित्व’मित्यत्र लक्ष्यतावच्छेदकगोत्वसमानाधिकरणत्वे सति लक्ष्यतावच्छेदकगोत्वावच्छिन्नप्रतियोगिताको ’गौरने’त्याकारकभेदो महिषादिवृत्तिस्तत्सामानाधिकरण्यं शृंगित्वे वर्तमानमिति ’श्रृंगित्व’मतिव्याप्तम्।

As in the case of the [proposed] lakṣaṇa of the cow as ‘hornness’ , while [hornness] has the property of being present in the same substratum [cow] as cowness, the delimiter of targetness, it also has the property of being present in the same substratum as a buffalo, in which there resides the difference of the type “not a cow”, which has counterpositiveness that is delimited by the lakṣyatā. Therefore, hornness is over-pervaded.

The term ati-vyāpti or over-pervasion derives from the concept of vyāpti which is used in the process of anumāna (discussed here).

The definition of avyāpti

He defines avyāpti next. With the above background, this terminology should now be easier to grasp–

लक्ष्यतावच्छेदक-समानाधिकरणात्यन्ताभावप्रतियोगित्वम्।

[avyāpti or under-pervasion is the lakṣaṇa’s having] the property of being the counterpositive of the atyanta-abhāva which is present in the same substratum as the lakṣyatā-delimiter.

[my notes: simply put, the above definition states that the lakṣaṇa is absent in a place where the lakṣya is present. However, it does not state that the lakṣaṇa is present in some substrata where the lakṣya is present. To address this, I propose that the first part of the definition in the ativyāpti case be carried forward – a procedure called anuvrtti in Sanskrit. That is, the proper definition is:

लक्ष्यतावच्छेदकसामानाधिकरण्ये सति लक्ष्यतावच्छेदक-समानाधिकरणात्यन्ताभावप्रतियोगित्वम्।

[avyāpti or under-pervasion is the lakṣaṇa’s having] the property of being the counterpositive of the atyanta-abhāva which is present in the same substratum as the lakṣyatā-delimiter, while the lakṣyatā-delimiter is present in the same adhikaraṇa as the lakṣaṇa.

He explains with an example:

यथा गोर्लक्षणं ’कपिलरूपवत्त्व’मित्यत्र लक्ष्यतावच्छेदकगोत्वसमानाधिकरणो यः ’कपिलरूपवत्त्वं नास्ती’त्यभावस्तत्प्रतियोगित्वं कपिलरूपवत्त्वे वर्तमानमिति ’कपिलरूपवत्त्व’मव्याप्तम्।

As in the case of the [proposed] lakṣaṇa of the cow as ‘brown’, [brown] has the property of having counterpositiveness of the abhāva of the form “brown is not present”, which is in the same substratum as cowness, that is the lakṣyatā delimiter. Therefore, brown is under-pervaded.

Of course, here, it is implied that the lakṣaṇa, ‘brown’ is present in some cows but absent in others.

The definition of asaṁbhava

He defines asaṁbhava next:

असंभवः — लक्ष्यतावच्छेदकव्यापकीभूताभावप्रतियोगित्वम्।

Asaṁbhava, or impossibility, is the [lakṣaṇa’s] property of being the counterpositive of the abhāva that pervades the lakṣyatā-avacchedaka.

[my notes- here, the lakṣaṇa is absent entirely from the lakṣyatā-avacchedaka. That means that the lakṣaṇa is never present in the same substratum as the specific lakṣya, such as a cow.]

यथा गोर्लक्षणम्- ’एकशफवत्त्व’मित्यत्र लक्ष्यतावच्छेदकगोत्वव्यापकीभूतो य ’एकशफवत्त्वाभाव’स्तत्प्रतियोगित्वमेकशफवत्त्वे-इत्येकशफवत्त्वम् असंभवदोषग्रस्तम्

As in the case of the [proposed] lakṣaṇa of the cow as ‘single-hoofed’, which has the property of having counterpositiveness of the abhāva of the form “single-hoofed is absent”, which pervades cowness, that is the lakṣyatā delimiter. Therefore, ‘single-hoofed’ is afflicted with the flaw of asaṁbhava, impossibility.

Returning back to the topic of establishing a proper lakṣaṇa, Sri Krishna Vallabhacharya writes:

एते दोषाः असाधारणत्वस्य विघटकाः।

These faults are the destroyers of asādhāraṇatva.

He will define asādharaṇatva later, but I include the essence of its definition here for convenience:

असाधारणत्वं च – लक्ष्यतावच्छेदकसमनियतत्वम्

asādhāraṇatva is the [lakṣaṇa’s] property of mutual pervasion with the lakṣyatā-delimiter

Here, he evokes the concept of sama-vyāpti or mutual pervasion. An example is: Wherever there is a triangle → the angle sum is 180°. Wherever the angle sum is 180° → it is a triangle. So the two are mutually co-existent – if one is present, the other is always present and vice versa. Likewise, a lakṣaṇa which lacks the above three faults, will be mutually co-existent with the lakṣya. That is, we can make the following statements:

if the lakṣaṇa lacks the above three defects:

where there is a lakṣaṇa, there is lakṣya – i.e. the lakṣaṇa is pervaded by the lakṣya
where there is lakṣya, there is lakṣaṇa – i.e. the lakṣya is pervaded by the lakṣaṇa

Along these lines then, each of the faults above interfere with sama-vyāpti in different ways. He writes:

अतिव्याप्तेः लक्ष्यतावच्छेदकव्याप्यत्वस्य, इतरयोश्च-लक्ष्यतावच्छेदकव्यापकत्वस्य विघटकत्वात्।

[these faults destroy asādhāraṇatva because] in the case of ativyāpti, the [lakṣaṇa-delimiter’s] being-pervaded-by the lakṣyatā-delimiter is destroyed, while in the other two cases, the [lakṣaṇa-delimiter’s] being-a-pervader of the lakṣyatā-avachhedaka is destroyed.

He now explains all this in the context of anumāna, because the idea of vyāpti is central to anumāna or inference —

एतेषां दूषकताबीजं तु -’गौ:-इतरभिन्ना, श्रृंगित्वा’दितीतरभेदाSनुमापकेSतिव्याप्तिमति साधने ’साध्याभाववद्वृत्तित्वा’त्मकव्यभिचारः, अव्याप्तिमति असंभववति च तादृशे साधने भागाSसिद्धि-स्वरूपाSसिद्धी।

However, the root cause of their being defects is as follows. [In the anumāna,]
“a cow is different from non-cows” [sādhya is “different from non-cows”]
“because it has horns” [hetu],
the means [hetu] has the defect of ativyāpti in inferring the difference from non-cows. There is therefore the deviation called “sādhya-abhāva-vrttitva”, or “the hetu is present in the substratum where the sādhya is absent”. When the means [hetu] has the defects of avyāpti or asaṁbhava, there is bhāga-asiddhi, non-establishment [of the lakṣana] in some occurences of [lakṣya], or svarūpa-asiddhi, non-establishment in any occurence at all [of the lakṣya].

The lakṣaṇa of a lakṣaṇa

I now turn to the final part of this article.

लक्षणस्य लक्षणं – ’दूषणत्रयरहितधर्मत्वम्’, तदेवाSसाधरणधर्मत्वमिति।

The lakṣaṇa of a lakṣaṇa is: possessing the property of being free from the three defects, and that itself is the asādhārāna-dharma-ness.

He now defines asādhārānatva as follows. This definition demonstrates the genius of Sri Krishna Vallabhacharya — what I have included in this article is but one page of his commentary which runs into hundreds of pages on the subject of nyāya.

असाधारणत्वं च – लक्ष्यतावच्छेदकसमनियतत्वम्, समनियतत्वं च-स्व(लक्षण)समानाधिकरणभेदप्रतियोगितानवच्छेदको यो धर्मः (लक्ष्यतावच्छेदकरूपः) तत्समानाधिकरणभेदप्रतियोगितानवच्छेदकत्वम्

And asādhāraṇatva is the [lakṣaṇa’s] property of mutual pervasion with the lakṣyatā-delimiter. And mutual pervasion is: the [lakṣaṇa’s] property of not being the delimiter of the counterpositiveness of the difference [abhāva] which is present in the same adhikaraṇa (substratum) as the lakṣyatā-delimiter, i.e that dharma, which is not the delimiter of the counterpositiveness of the difference [abhāva] present in the same adhikaraṇa as the lakṣaṇa itself.

[my notes: Now this might look extremely cryptic, but it is actually quite beautiful and simple. The first part of the Sanskrit (स्व(लक्षण)समानाधिकरणभेदप्रतियोगितानवच्छेदको यो धर्मः) describes the following situation:

consider a particular substratum where the lakṣaṇa is present. Now consider a substratum which is different from this substratum. There, the lakṣya is not present. As an example, consider the lakṣaṇa of ‘dewlap’. It is present in an animal. Now consider all animals from a species that is different from this animal. The lakṣya-tā of cowness is never present in any of these other animals. Thus, cowness is present in the animals in which lakṣaṇa is present and not in animals that are non-cows (as cowness defines the cow). This expresses the following notion: where the substratum possessing the lakṣaṇa is absent, the lakṣya is absent there. Put differently,

wherever there is lakṣya-tā, there is lakṣaṇa-tā. Lakṣya is pervaded by the lakṣaṇa.

The second part of the Sanskrit (तत्समानाधिकरणभेदप्रतियोगितानवच्छेदकत्वम्) is to be understood as follows. Given the previous statement, the second part states that for any animal in which such a lakṣya is present, the lakṣaṇa is absent in animals different from it. That is,

wherever there is lakṣaṇa, there is lakṣya. Here, lakṣaṇa is pervaded by the lakṣya.

This completes the definition of sama-vyāpti].

He offers a rather curious example:

यथा ’सास्नावत्त्व’ समानाधिकरण-घटादिभेदप्रतियोगितानवच्छेदकगोत्वसमानाधिकरणकपिलगोभेदप्रतियोतिानवच्छेदकत्वं सास्नावत्वे वर्तते- इति तस्याSसाधारणधर्मत्वमुपपन्नम्।

[Example] the property of not delimiting the counterpositiveness of the difference [abhāva] of a brown cow, present in the same adhikaraṇa as cowness, which itself does not delimit the  counterpositiveness of the difference (abhāva) of pots and other items which is present in the same adhikaraṇa as dewlap, is present in the dewlap. Therefore, it is proven to have asādharaṇa dharma.

[my notes: Here, there is one subtlety that should be noticed. Consider that the dewlap is present in a non-brown cow. A non-brown cow is obviously different from a brown cow. Here, dewlap-possession cannot delimit the pratiyogitā associated with the difference from a brown cow, because dewlap-possession extends equally to non-brown cows!]