The notion 'subject' is an ancient one in the Western linguistic tradition, going back to at least Aristotle. In modern Western linguistics, the notion of 'subject' remains an important descriptive notion; in some theoretical approaches, grammatical relations like subject and object are derivative notions, definable in terms of e.g. phrase structural configuration; in others, subject and object remain basic categories of grammar. Going beyond theoretical distinctions, a wide array of crosslinguistic evidence shows that among the arguments of different types of predicates in most languages there is a privileged type of argument, a privileged argument position, which displays a set of distinctive, even unique, morphosyntactic properties in that language (e.g. Keenan 1976). Such properties include e.g. obligatoriness, particular case marking (e.g. nominative), particular syntactic position (e.g. Spec,TP), potential for deletion under coordination, ability to bind reflexive anaphors, etc., but differ somewhat between languages. However it is understood theoretically, recognizing this privileged argument role, the 'subject', is crucial in understanding and analyzing the many linguistic phenomena which depend on it.
The Indian tradition, beginning with Pāṇini, is widely claimed to entirely lack the notion of 'subject' (e.g. Cardona 1974: 244–245). Kiparsky (2009) claims not only that the concepts of subject and object play no role in Pāṇini's grammar, but that in fact his grammar deals with some phenomena, e.g. agreement, the better for it. However, it has been argued by Keidan (2017) that the lack of the notion of subject in Pāṇinian grammar has been overstated, and that the later tradition, at least, does move towards a notion similar to the Western notion 'subject'.
2 The kartṛ
The relevant notion in the Indian tradition is the kāraka relation kartṛ. For a more general introduction to the kārakas, kartṛ, and argument structure in the Indian tradition, see entry 'Argument structure'. The term kartṛ is often translated as 'agent'. As shown in 'Argument structure', the kāraka relations such as kartṛ are similar, but not identical, to the semantic roles of the Western tradition. The kārakas are not semantic, but grammatical categories, which mediate between semantics and the morphosyntactic realization of argument relations. Nevertheless, in textbook examples the kartṛ is equivalent to the notion of agent:
In the derivation of both (1) and (2), Devadatta is assigned the role of kartṛ. In active sentences like (1), the kartṛ gets nominative case. In passive sentences like (2), the kartṛ appears in the instrumental case, while the karman (≈ logical object) appears in the nominative.
Pāṇini's own semantic definition of kartṛ is usually interpreted as referring to an independent agent or actor:
However, this implication of agency appears not always to work. For example, if one is talking about cutting with an axe, one might ordinarily say:
An axe is an instrument of cutting, in Pāṇinian terms the 'most effective means', designated karaṇa, while the kartṛ, understood as the independent agent, is the human, Devadatta. But it is also possible to say:
Here, since it receives nominative case and the verb is active, the axe must be the kartṛ. Yet for an axe to cut there must be a human agent wielding it, and in any act of cutting the axe remains the instrument, the karaṇa. The tradition explains this partly by recourse to the perspective or scope of the expression, and partly to speaker intention: it is possible to restrict one's perspective, or the scope of an expression, to a sub-part of an event; in this case, if we exclude the human agent from consideration, a speaker may wish to speak of the axe as the independent argument, that is as the argument whose participation in the event is not dependent on another expressed argument. (The axe in any case retains the semantic properties associated with the label karaṇa, but since only one label can apply and since kartṛ is defined later in the grammar, only the label kartṛ will apply. See 'Argument structure'.)
The notion of sub-parts of events leads to the notion of primary and subsidiary kartṛs. For example, the verb cook denotes the full sequence of situations involved in an act of cooking, from the mental effort of the agent, the putting the pot on the stove, putting water and grain in it, setting the fire, heating, etc. Besides referring to the composite as a whole, the verb can also refer to constituent parts. These constituent parts can be considered as having their own sets of arguments and hence kāraka relations. The composite/principal situation is the pradhāna-kriyā, and its kartṛ is the pradhāna-kartṛ, while each subsidiary situation, guṇa-kriyā, has a subsidiary agent, guṇa-kartṛ. So while in (5) there is still a human agent who is the pradhāna-kartṛ of the overall event of cutting, the agent of the subsidiary event of, say, the axe-blade moving through a piece of wood at speed, is the axe.
In any case, we must reckon with uses of kartṛ which do not correspond to the notion of 'agent'. In fact, in active sentences there must be a kartṛ, and that kartṛ must appear in the nominative case, when expressed. In this sense, then, the kartṛ is more like the subject of an active verb, or 'logical subject', than specifically an agent.
In terms of the possible scope of the term kartṛ, a complex but highly relevant construction is the so-called karmakartṛ construction, which corresponds to a type of fientive construction with theme subject. Consider the following sentences:
|'The rice is cooked by Devadatta.'|
|'The wood splits itself.'|
(6a) looks superficially like a passive of (1), equivalent to (2) but without the explicit oblique agent. Similarly, (6b) looks like a passive of an active sentence such as Devadattaḥ kāṣṭhaṃ bhinatti 'D. breaks the wood.' However, this similarity is only apparent. It is not that the animate agent of the action is unexpressed; rather, there is no animate agent in the scope of the expression. Importantly, despite the passive morphology on the verb, the nominative arguments in (6) do not have the kāraka label karman, but kartṛ. This is licensed by Pāṇini in the following rule:
This rule refers to a kartṛ which is karmaṇā tulyakriyaḥ 'whose relation to the event is equivalent/comparable (tulya) to that of a karman.' With reference to the examples in (6), the rice and the wood are kartṛs, even though their semantic relation to the events of cooking and breaking are that of a theme/patient, which would ordinarily be labelled as karman. By this rule, these kartṛs are treated like karmans, resulting in the passive morphology on the verbs. That these arguments are in fact kartṛs is clear from the fact that it is possible to say:
Here the instrumental marking on the noun can only be explained if the noun has the label kartṛ.
Initially, the karmakartṛ construction looks parallel to the case of the axe, discussed above: an argument with properties consistent with a 'lower' kāraka role gets the label kartṛ in the absence of an explicit human kartṛ in the scope of the expression. So just as the karaṇa 'axe' in (4) is labelled kartṛ in (5), so the karman of (1) becomes the kartṛ in (6a). However, this parallelism is only apparent. The construction illustrated in (6) and (8) is restricted by the tradition to a very specific semantic context: where the action of the verb comes about easily as a result of some particular property or properties of the argument in question. That is, (6a) means that the rice grains cook easily, more easily than normal, due to some quality of these particular grains; likewise with the splitting of the wood in (6b) and (8). This is close to the so-called 'middle construction' in English (Davidse & Heyvaert 2007).
Crucially, it is due to the particular property which facilitates the action of the verb that the argument in question is conceived of as a kartṛ. That is, we are not here dealing with a situation in which an argument with properties of one kāraka gets the label kartṛ merely because there is no other kartṛ in the scope of the expression. Rather, because of the specific semantics of the expression, an argument which in other contexts with the same verb would be treated as a karman, and which retains the same properties which justify that karman label, in this particular context is conceived as having the kartṛ-like, agent-like, property of independently causing (or at least, facilitating) the action of the verb.
The karmakartṛ construction does not therefore mean that karmans can freely be given the label kartṛ, in the absence of a more appropriate potential kartṛ. For Pāṇini, it may have been the case that only with verbs which could participate in the karmakartṛ construction could a karman be potentially treated as a kartṛ. But for the later tradition, this freedom is granted to potentially any transitive verb. The karmakartṛ construction itself is restricted to two classes of verb, karmasthakriyaka and karmasthabhāvaka, verb classes in which the action or state expressed by the verb is conceived primarily in relation to the karman. This includes the verbs pac 'cook' and bhid 'split', but does not include gam 'go', where the action of the verb resides primarily in the kartṛ, the goer. For the later tradition, verbs like gam 'go' can still be used as intransitives expressing the 'ease' of a particular activity (9b), only they do not adopt the passive morphology characteristic of the karmakartṛ construction (9c):
|'Devadatta goes to the village.'|
|'The village is easily gone to.'|
|(Intended: 'The village is easily gone to.'')|
What is important is that (b) cannot mean merely 'the village is gone to', without the further implication of ease due to some inherent property of the village. In fact, the apparent freedom for non-kartṛs to get the label kartṛ, exemplified by the sentences in (4)-(5) above, is even further restricted. The tradition focuses on cases where this is possible, such as verbs of cutting, which can be construed with the instrument as the highest semantic argument in the scope of the expression. But this is certainly not possible with all verbs, or with all kārakas. For example, if one does not express the agent (kartṛ) of a verb of giving, one cannot simply reclassify the beneficiary (saṃpradāna) as kartṛ. Likewise with a verb of fearing, it is not possible to express the source of fear (apādāna) as the kartṛ:
|'Devadatta gives to Yajñadatta.'|
|'Yajñadatta gives.' (Cannot mean 'Yajñadatta is given (something).')|
|'Devadatta fears Yajñadatta.'|
|'Yajñadatta fears.' (Cannot mean 'Yajñadatta is a source of fear.')|
These restrictions are first discussed in the Mahābhāṣya on Aṣṭ. 1.4.23, and later e.g. by Helārāja in his Prakīrṇaprakāśa on Vākyapadīya 3.7.21.
Is there anything in modern linguistic approaches to which the notion of kartṛ is equivalent? Undoubtedly, the use of the term kartṛ goes beyond an association with a notion of 'agent' specifically. The kartṛ is also not equivalent to the Western notion of subject; descriptively it is close to the logical subject or active subject, since the grammatical subject of every active verb is a kartṛ.
It has been recognized by some authors that the Western notion of subject is a composite, a conflation of more than one relation or function. For Bhat (1991), those notions are 'topic' and 'agent'; for Falk (2006) those notions are pivot, somewhat equivalent to 'topic' and GF, the highest available grammatical function. Keidan (2017) relates the non-agent uses of kartṛ to Bhat's notion of 'topic', and suggests that kartṛ, like subject, is at least partially a conflation of the notions of topic and agent. But this is not quite satisfactory for a number of reasons, in particular since the subject of a passive (necessarily a karman) can display 'topic' properties.
Rather, kartṛ is best understood as the grammatical instantiation of θ, the argument of a predicate which is highest on the semantic role hierarchy. (Within a 'proto-Role' approach like that of Dowty 1991, this would be the most proto-Agentive argument.) Thus it instantiates the agent, when an agent is present, but it may correspond to other semantic roles, in the absence of a higher role – and may override the instantiation of other semantic roles. By default, the highest semantic role is realised as the subject in active sentences, hence the association of kartṛ with both the active subject and the agent.
However, the association of the highest available semantic role with kartṛ is not free, but depends on the lexical properties of the verb. The tradition focuses on cases where this is possible, such as verbs of cutting, which can be construed with the instrument as the highest semantic argument in the scope of the expression. But the possibility is in fact highly restricted. Given what we have seen above, we can propose two constraints which may account for most or all of the restrictions seen:
b. An argument which qualifies for a 'lower' kāraka label cannot get the label kartṛ if it could be misinterpreted as having the properties of an agent.
(12b) explains why the axe can be a kartṛ in (5) but Yajñadatta cannot in (10b) or (11b). Because the axe is inanimate, its role in the action cannot be misinterpreted.
The Philosophical traditions
According to the tradition of Vyākaraṇa, as seen above, it is possible for non-animate entities to be kartṛs. For the grammarians, this is a practical solution to the reality of argument realization in Sanskrit, and has no necessary philosophical implications.
The traditions of Nyāya and Mīmāṃsā show more concern for identifying the true nature of kartṛ-hood, and of action in general. For the grammarians, the active finite verb endings designate the kartṛ, as discussed in 'Argument structure'. But for the Naiyāyikas (the philosophers of the Nyāya tradition), the active finite verbal endings denote kṛti, literally 'activity'. For the Naiyāyikas, every effect is ultimately the result of conscious activity on the part of an animate agent. Thus active finite verb endings denote conscious activity, and the kartṛ, which appears in the nominative in active sentences, is necessarily conscious and animate. This causes a problem for sentences like 'the axe cuts', or the common example ratho gacchati 'the chariot goes'. For the grammarians there is no problem in classifying an axe or a chariot as a kartṛ. But for the Naiyāyikas this is impossible; instead, they must have recourse to lakṣaṇā 'implication': since we cannot interpret an inanimate entity as kartṛ, we recognize that this cannot have been the intended meaning, and we infer the correct relation of the entity concerned to the verb concerned. Thus for the Naiyāyikas, inanimate entities are never classified as kartṛ, and the concept of kartṛ is correspondingly restricted to animate entities.
The Mīmāṃsā viewpoint is for the most part equivalent to that of the Naiyāyikas, except that some schools of Mīmāṃsā widen the conception of 'activity' (for them, bhāvanā 'bringing into being') to include non-conscious activity, thus allowing for kartṛ to apply to inanimate entities, as in Vyākaraṇa. For further discussion see Joshi (1960).
 Syntactically ergative and Philippine-type languages show two privileged positions with different properties corresponding to the types of properties typical of subjects in nominative-accusative languages. See Falk (2006) for discussion and analysis in relation to the notion 'subject'.
 The later tradition understands kartṛ in terms of their theory of verbal denotation: the kartṛ is the substratum (roughly, the locus) of the activity or action (vyāpāra/kriyā) which is part of the denotation of every verb.
 Ex. (9b) may seem fanciful to a reader with any decent knowledge of Sanskrit, but it is clearly licensed by the later grammarians, e.g. by Bhaṭṭojidīkṣita, Siddhāntakaumudī on Aṣṭ. 3.1.87.