Nagarjuna and Shunyavada.
Though the beginnings of Mahayana are to be found in the Mahasangikas and many of their early sects, Nagarjuna gave it a philosophical basis. Not only is the individual person empty and lacking an eternal self, according to Nagarjuna, but the dharmas also are empty. He extended the concept of shunyata to cover all concepts and all entities. "Emptiness" thus means subjection to the law of causality or "dependent origination" and lack of an immutable essence and an invariant mark (nihsvabhavata). It also entails a repudiation of dualities between the conditioned and the unconditioned, between subject and object, relative and absolute, and between samsara and Nirvana. Thus, Nagarjuna arrived at an ontological monism; but he carried through an epistemological dualism (i.e., a theory of knowledge based on two sets of criteria) between two orders of truth: the conventional (samvrtti) and the transcendental (paramartha). The one reality is ineffable. Nagarjuna undertook a critical examination of all the major categories with which philosophers had sought to understand reality and showed them all to involve self-contradictions. The world is viewed as a network of relations, but relations are unintelligible. If two terms, A and B, are related by the relation R, then either A and B are different or they are identical. If they are identical, they cannot be related; if they are altogether different then they cannot also be related, for they would have no common ground. The notion of "partial identity and partial difference" is also rejected as unintelligible. The notion of causality is rejected on the basis of similar reasonings. The concepts of change, substance, self, knowledge, and universals do not fare any better. Nagarjuna also directed criticism against the concept of pramana, or the means of valid knowledge.

 Nagarjuna's philosophy is also called Madhyamika, because it claims to tread the middle path, which consists not in synthesizing opposed views such as "The real is permanent" and "The real is changing" but in showing the hollowness of both the claims. To say that reality is both permanent and changing is to make another metaphysical assertion, another viewpoint, whose opposite is "Reality is neither permanent nor changing." In relation to the former, the latter is a higher truth, but the latter is still a point of view, a drsti, expressed in a metaphysical statement, though Nagarjuna condemned all metaphysical statements as false.

 Nagarjuna used reason to condemn reason. Those of his disciples who continued to limit the use of logic to this negative and indirect method, known as prasanga, are called the prasangikas: of these, Aryadeva, Buddhapalita, and Candrakirti are the most important. Bhavaviveka, however, followed the method of direct reasoning and thus founded what is called the svatantra (independent) school of Madhyamika philosophy. With him Buddhist logic comes to its own, and during his time the Yogacaras split away from the Shunyavadins.

Contributions of Vasubandhu and Asanga.
Converted by his brother Asanga to the Yogacara, Vasubandhu wrote the Vijnapti-matrata-siddhi ("Establishment of the Thesis of Cognitions--Only"), in which he defended the thesis that the supposedly external objects are merely mental conceptions. Yogacara idealism is a logical development of Sautrantika representationism: the conception of a merely inferred external world is not satisfying. If consciousness is self-intimating (svaprakasha) and if consciousness can assume forms (sakaravijnana), it seems more logical to hold that the forms ascribed to alleged external objects are really forms of consciousness. One only needs another conception: a beginningless power that would account for this tendency of consciousness to take up forms and to externalize them. This is the power of kalpana, or imagination. Yogacara added two other modes of consciousness to the traditional six: ego consciousness (manovijnana) and storehouse consciousness  (alaya-vijnana). The alaya-vijnana contains stored traces of past experiences, both pure and defiled seeds. Early anticipations of the notions of the subconscious or the unconscious, they are theoretical constructs to account for the order of individual experience. It still remained, however, to account for a common world--which in fact remains the main difficulty of Yogacara. The state of Nirvana becomes a state in which the alaya with its stored "seeds" would wither away (alayaparavrtti). Though the individual ideas are in the last resort mere imaginations, in its essential nature consciousness is without distinctions of subject and object. This ineffable consciousness is the "suchness" (tathata) underlying all things. Neither the alaya nor the tathata, however, is to be construed as being substantial.

 Vasubandhu and Asanga are also responsible for the growth of Buddhist logic. Vasubandhu defined "perception" as the knowledge that is caused by the object, but this was rejected by Dignaga, a 5th-century logician, as a definition belonging to his earlier realistic phase. Vasubandhu defined "inference" as a knowledge of an object through its mark, but Dharmottara, an 8th-century commentator pointed out that this is not a definition of the essence of inference but only of its origin.

Contributions of Dignaga and Dharmakirti.
Dignaga's Pramanasamuccaya ("Compendium of the Means of True Knowledge") is one of the greatest works on Buddhist logic. Dignaga gave a new definition of "perception": a knowledge that is free from all conceptual constructions, including name and class concepts. In effect, he regarded only the pure sensation as perception. In his theory of inference, he distinguished between inference for oneself and inference for the other and laid down three criteria of a valid middle term (hetu), viz., that it should "cover" the minor premise (paksa), be present in the similar instances (sapaksa), and be absent in dissimilar instances (vipaksa). In his Hetucakra ("The Wheel of 'Reason"'), Dignaga set up a matrix of nine types of middle terms, of which two yield valid conclusions, two contradictory, and the rest uncertain conclusions. Dignaga's tradition is further developed in the 7th century by Dharmakirti, who modified his definition of perception to include the condition "unerring" and distinguished, in his Nyayabindu, between four kinds of perception: that by the five senses, that by the mind, self-consciousness, and perception of the yogins. He also introduced a threefold distinction of valid middle terms: the middle must be related to the major either by identity ("This is a tree, because this is an oak") or as cause and effect ("This is fiery, because it is smoky"), or the hetu is a nonperception from which the absence of the major could be inferred. Dharmakirti consolidated the central epistemological thesis of the Buddhists that perception and inference have their own exclusive objects. The object of the former is the pure particular (svalaksana), and the object of the latter (he regarded judgments as containing elements of inference) is the universal (samanyalaksana). In their metaphysical positions, Dignaga and Dharmakirti represent a moderate form of idealism.
 
 

Principal texts and relation to Shabara.
Kumarila commented on Jaimini's sutra as well as on Shabara's bhasya. The Varttika (critical gloss) that he wrote was commented upon by Sucarita Mishra in his Kashika ("The Shining"), by Someshvara Bhatta in his Nyayasudha ("The Nectar of Logic"), and Parthasarathi Mishra in Nyayaratnakara ("The Abode of Jewels of Logic"). Parthasarathi's Shastradipika ("Light on the Scripture") is a famous independent Mimamsa treatise belonging to Kumarila's school.

 Prabhakara, who most likely lived after Kumarila, was the author of the commentary Brhati ("The Large Commentary"), on Shabara's bhasya. On many essential matters, Prabhakara differs radically from the views of Kumarila. Prabhakara's Brhati has been commented upon by Shalikanatha in his Rjuvimala ("The Straight and Free from Blemishes"), whereas the same author's Prakaranapañcika ("Commentary of Five Topics") is a very useful exposition of the Prabhakara system. Other works belonging to this school are Madhava's Jaiminiya-nyayamala-vistara ("Expansion of the String of Reasonings by Jaimini"). Appaya Diksita's Vidhirasayana ("The Elixir of Duty"), Apadeva's Mimamsa-nyaya-prakasha (Illumination of the Reasonings of Mimamsa) and Laugaksi Bhaskara's Artha-samgraha ("Collection of Treasures").

 Where Kumarila and Prabhakara differed, Kumarila remained closer to both Jaimini and Shabara. Kumarila, like Jaimini and Shabara, restricted Mimamsa to an investigation into dharma, whereas Prabhakara assigned to it the wider task of enquiring into the meaning of the Vedic texts. Kumarila understood the Vedic injunction to include a statement of the results to be attained; Prabhakara--following Badari--excluded all consideration of the result from the injunction itself and suggested that the sense of duty alone should instigate a person to act.

Metaphysics and epistemology.
Both the Bhatta (the name for Kumarila's school) and the Prabhakara schools, in their metaphysics, were realists; both undertook to refute Buddhist idealism and nihilism. The Bhatta ontology recognized five types of entities: substance (dravya), quality (guna), action (karma), universals (samanya), and negation (abhava). Of these, substance was held to be of ten kinds: the nine substances recognized by the Vaishesikas and the additional substance "darkness." The Prabhakara ontology recognized eight types of entities; from the Bhatta list, negation was rejected, and four more were added: power (shakti), resemblance (sadrsa), inherence-relation (samavaya), and number (samkhya). Under the type "substance," the claim of "darkness" was rejected on the ground that it is nothing but absence of perception of colour; the resulting list of nine substances is the same as that of the Vaishesikas. Though both the schools admitted the reality of the universals, their views on this point differed considerably. The Prabhakaras admitted only such universals as inhere in perceptible instances and insisted that true universals themselves must be perceivable. Thus, they rejected abstract universals, such as "existence," and merely postulated universals, such as "Brahminhood" (which cannot be perceptually recognized in a person).

 The epistemologies of the two schools differ as much as their ontologies. As ways of valid knowing, the Bhattas recognized perception, inference, verbal testimony (shabda), comparison (upamana), postulation (arthapatti), and nonperception (anupalabdhi). The last is regarded as the way men validly, and directly, apprehend an absence: this was in conformity with Shabara's statement that abhava (nonexistence) itself is a pramana (way of true knowledge). Postulation is viewed as the sort of process by which one may come to know for certain the truth of a certain proposition, and yet the Bhattas refused to include such cases under inference on the grounds that in such cases one does not say to himself "I am inferring" but rather says "I am postulating." "Comparison" is the name given to the perception of resemblance with a perceived thing of another thing that is not present at that moment. It is supposed that because the latter thing is not itself being perceived, the resemblance belonging to it could not have been perceived; thus, it is not a case of perception when one says "My cow at home is similar to this animal."

 The Prabhakaras rejected nonperception as a way of knowing and were left with a list of five concerning definitions of perception. The Bhattas, following the sutra, define perception in terms of sensory contact with the object, whereas the Prabhakaras define it in terms of immediacy of the apprehension.

Ethics.
As pointed out earlier, Kumarila supported the thesis that all moral injunctions are meant to bring about a desired benefit and that knowledge of such benefit and of the efficacy of the recommended course of action to bring it about is necessary for instigating a person to act. Prabhakara defended the ethical theory of duty for its own sake, the sense of duty alone being the proper incentive. The Bhattas recognize apurva (supersensible efficacy of actions to produce remote effects) as a supersensible link connecting the moral action performed in this life and the supersensible effect (such as going to heaven) to be realized afterward. Prabhakara understood by apurva only the action that ought to be done.

Hermeneutics and semantics.
In their principles of interpretation of the scriptures, and consequently in their theories of meaning (of words and of sentences), the two schools differ radically. Prabhakara defended the thesis that words primarily mean either some course of action (karya) or things connected with action. Connected with this is the further Prabhakara thesis that the sentence forms the unit of meaningful discourse, that a word is never used by itself to express a single unrelated idea, and that a sentence signifies a relational complex that is not a mere juxtaposition of word meanings. Prabhakara's theory of language learning follows these contentions: the child learns the meanings of sentences by observing the elders issuing orders like "Bring the cow" and the juniors obeying them, and he learns the meaning of words subsequently by a close observation of the insertion (avapa) and extraction (uddhara) of words in sentences and the resulting variations in the meaning of those sentences. From this semantic approach follows Prabhakara's principle of Vedic interpretation: all Vedic texts are to be interpreted as bearing on courses of action prescribed, and there are no merely descriptive statements in the scriptures. 
Furthermore, only the Vedic injunctions yield the authoritative verbal testimony that may be regarded as a unique way of knowing, whereas all other verbal knowledge is really inferential in character. In matters concerning what ought to be done, Prabhakara therefore regarded only the Vedas as authoritative.

 Kumarila's theory is very different. In his view, words convey their own meanings, not relatedness to something else. He therefore was more willing to accommodate purely descriptive sentences as significant. Furthermore, he regarded sentence meaning as composed of separate word meanings held together in a relational structure; the word meaning formed,for him, the simplest unit of sense. Persons thus learn the meaning of words by seeing others talking as well as from advice of the elders.

Religious consequences.
The Mimamsa views the universe as being eternal and does not admit the need of tracing it back to a creator. It also does not admit the need of admitting a being who is to distribute moral rewards and inflict punishments--this function being taken over by the notion of apurva, or supersensible power generated by each action. Theoretically not requiring a God, the system, however, posits a number of deities as entailed by various ritualistic procedures, with no ontological status assigned to the gods.
 
 

The linguistic philosophers considered here are the grammarians led by Bhartrhari (7th century AD) and Mandana-Mishra (8th century AD); the latter, reputed to be a disciple of Kumarila, held views widely different from the Mimamsakas. The grammarians share with the Mimamsakas their interest in the problems of language and meaning. But their own theories are so different that they cut at the roots of the Mimamsa realism. The chief text of this school is Bhartrhari's Vakyapadiya. Mandana's chief works are Brahma-siddhi ("Establishment of Brahman"), Sphota-siddhi ("Establishment of Word Essence"), and Vidhiviveka ("Inquiry into the Nature of Injunctions").

 As his first principle, Bhartrhari rejects a doctrine on which the realism of Mimamsa and Nyaya had been built--the view that there is a kind of perception that is nonconceptualized and that places persons in direct contract with things as they are. For Bhartrhari this is not possible, for all knowledge is "penetrated" by words and "illuminated" by words. Thus, all knowledge is linguistic, and the distinctions of objects are traceable to distinctions among words. The metaphysical monism of word (shabdadvaita) is not far from this--i.e., the view that the one word essence appears as this world of "names and forms" because of man's imaginative construction (kalpana). Metaphysically, Bhartrhari comes close both to Shankara's Advaita and the Buddhist philosophers, such as Dharmakirti. This metaphysical theory also uses the doctrine of sphota ("that from which the meaning bursts forth"). 
Most Indian philosophical schools were concerned with the problem of what precisely is the bearer of the meaning of a word or a sentence. If the letters are evanescent and if, as one hears the sounds produced by the letters of a word, each sound is replaced by another, one never comes to perceive the word as a whole, and the question is how one grasps the meaning of the word. The same problem could be stated with regard to a sentence. The Mimamsakas postulated an eternity of sounds and distinguished between the eternal sounds and sound complexes (words, sentences) from their manifestations. The grammarians, instead, distinguished between the word and sound and made the word itself the bearer of meaning. As bearer of meaning, the word is the sphota.

 Sounds have spatial and temporal relations; they are produced differently by different speakers. But the word as meaning bearer has to be regarded as having no size or temporal dimension. It is indivisible and eternal. Distinguished from the sphota are the abstract sound pattern (prakrtadhvani) and the utterances (vikrtadhvani). Furthermore, Bhartrhari held that the sentence is not a collection of words or an ordered series of them. A word is rather an abstraction from a sentence; thus, the sentence-sphota is the primary unit of meaning. A word is also grasped as a unity by an instantaneous flash of insight (pratibha). This theory of sphota, which is itself a linguistic theory required by the problems arising from the theory of meaning, was employed by the grammarians to support their theory of word monism.

 Mandana-Mishra, in his Vidhiviveka, referred to three varieties of this monism: shabdapratyasavada (the doctrine of superimposition on the word; also called shabdadhyasavada), shabda-parinamavada (the doctrine of transformation of the word), and shabdavivartavada (the doctrine of unreal appearance of the word). According to the first two, the phenomenal world is still real, though either falsely superimposed on words or a genuine transformation of the word essence. The last, and perhaps most consistent, doctrine holds that the phenomenal distinctions are unreal appearances of an immutable word essence.

Mandana attempted to integrate this linguistic philosophy into his own form of advaitavada, though later followers of Sankara did not accept the doctrine of sphota. Even Vacaspati, who accepted many of Mandana's theories, rejected the theory of sphota and in general conformed to the Shankarite's acceptance of the Bhatta epistemology.
 
 

The old school.
Although as early as the commentators Prashastapada (5th century AD) and Uddyotakara (7th century AD) the authors of the Nyaya-Vaisesika schools used each other's doctrines and the fusion of the two schools was well on its way, the two schools continued to have different authors and lines of commentators. About the 10th century AD, however, there arose a number of texts that sought to combine the two philosophies more successfully. Well known among these syncretist texts are the following: 
Bhasarvajna's Nyayasara ("The Essence of Nyaya"; written c. 950), 
Varadaraja's Tarkikaraksa ("In Defense of the Logician"; c. 1150), 
Vallabha's Nyayalilavati ("The Charm of Nyaya"; 12th century), 
Keshava Mishra's Tarkabhasa ("The Language of Reasoning"; c. 1275), 
Annam Bhatta's Tarkasamgraha ("Compendium of Logic"; c. 1623), and 
Vishvanatha's Bhasapariccheda ("Determination of the Meaning of the Verses"; 1634). 

 Both the Nyaya-Vaishesika schools are realistic with regard to things, properties, relations, and universals. Both schools are pluralistic (also with regard to individual selves) and theistic. Both schools admit external relations (the relation of inherence being only partly internal), atomistic cosmology, new production, and the concept of existence (satta) as the most comprehensive universal. Both schools regard knowledge as a quality of the self, and they subscribe to a correspondence theory regarding the nature of truth and a theory of pragmatism-cum-coherence regarding the test of truth. The points that divide the schools are rather unimportant: they concern, for example, their theories of number, and some doctrines in their physical and chemical theories.

 Gautama's sutras were commented upon about AD 400 by Vatsayana, who replied to the Buddhist doctrines, especially to some varieties of Shunyavada skepticism. Uddyotakara's Varttika (c. 635) was written after a period during which major Buddhist works, but no major Hindu work, on logic were written. Uddyotakara undertook to refute Nagarjuna and Dignaga. He criticized and refuted Dignaga's theory of perception, the Buddhist denial of soul, and the anyapoha (exclusion of the other) theory of meaning. Positively, he introduced, for the first time, the doctrine of six modes of contact (samnikarsa) of the senses with their objects, which has remained a part of Nyaya-Vaishesika epistemology. He divided inferences into those whose major premise (sadhya) is universally present, those in which one has to depend only upon the rule "Wherever there is absence of the major, there is absence of the middle (hetu)," and those in which both the positive and the negative rules are at one's disposal. He rejected the sphota theory and argued that the meaning of a word is apprehended by hearing the last letter of the word together with recollection of the preceding ones. 
Vacaspati Mishra in the 9th century wrote his Tatparyatika (c. 840) on Uddyotakara's Varttika and further strengthened the Nyaya viewpoint against the Buddhists. He divided perception into two kinds: the indeterminate, nonlinguistic, and nonjudgmental and the determinate and judgmental. In defining the invariable connection (vyapti) between the middle and the major premises, he introduced the concept of a vitiating condition (upadhi) and stressed that the required sort of connection, if an inference is to be valid, should be unconditional. He also proposed a modified version of the theory of the extrinsic validity of knowledge by holding that inferences as well as knowledges that are the last verifiers (phalajnana) are self-validating.

 Prashastapada's Vaishesika commentary (c. 5th century) does not closely follow the sutras but is rather an independent explanation. Prashastapada added seven more qualities to Kanada's list: heaviness (gurutva), fluidity (dravatva), viscidity (sneha), traces (samskara), virtue (dharma), vice (adharma), and sound. The last quality was regarded by Kanada merely as a mark of ether, whereas Prashastapada elevated it to a defining quality of the latter. He also made the Vaishesika fully theistic by introducing doctrines of creation and dissolution.

 The Nyaya-Vaishesika general metaphysical standpoint allows for both particulars and universals, both change and permanence. There are ultimate differences as well as a hierarchy of universals, the highest universal being existence. Substance is defined as the substrate of qualities and in terms of what alone can be an inherent cause. A quality may be defined as what is neither substance nor action and yet is the substratum of universals (for universals are supposed to inhere only in substances, qualities, and actions). Universal is defined as that which is eternal and inheres in many. Ultimate particularities belong to eternal substances, such as atoms and souls, and these account for all differences among particulars that cannot be accounted for otherwise. Inherence (samavaya) is the relation that is maintained between a universal and its instances, a substance and its qualities or actions, a whole and its parts, and an eternal substance and its particularity. This relation is such that one of the relations cannot exist without the other (e.g., a whole cannot exist without the parts). Negation (abhava), the seventh category, is initially classified into difference ("A is not B") and absence ("A is not in B"), absence being further divided into absence of a thing before its origin, its absence after its destruction, and its absence in places other than where it is present. For these schools, all that is is knowable and also nameable.

 Knowledge is regarded as a distinguishing but not essential property of a self. It arises when the appropriate conditions are present. Consciousness is defined as a manifestation of object but is not itself self-manifesting; it is known by an act of inner perception (anuvyavasaya). Knowledge either is memory or is not; knowledge other than memory is either true or false; and knowledge that is not true is either doubt or error. In its theory of error, these philosophers maintained an uncompromising realism by holding that the object of error is still real but is only not here and now. True knowledge (prama) apprehends its object as it is; false knowledge apprehends the object as what it is not. True knowledge is either perception, inference, or knowledge derived from verbal testimony or comparison. Perception is defined as knowledge that arises from the contact of the senses with their objects, and is viewed as either indeterminate and nonlinguistic or as determinate and judgmental. Both aspects of the definition of perception are viewed as valid--a point that is made against both the Buddhists and the grammarians. Furthermore, perception is either ordinary (laukika) or extraordinary (alaukika). The former takes place through any of the six modes of sense-object contact recognized in the system. The latter takes place when one perceives the proper object of one sense through another sense ("The cushion looks soft") or when, on recognizing universal in a particular, one perceives all instances of the universal as its instances. Also extraordinary are the perceptions of the yogins, who are supposed to be free from the ordinary spatiotemporal limitations.

 Four conditions must be satisfied in order that a combination of words may form a meaningful sentence: a word should generate an intention or expectancy for the words to follow ("Bring"--"What?"--"A jar"); there should be mutual fitness ("Sprinkle"--"With what?"--"Water, not fire"); there should be proximity in space and time; and the proper intention of the speaker must be ascertained, otherwise there would be equivocation.

 Among theistic proofs offered in the system, the most important are the causal argument ("The world is produced by an agent, since it is an effect, as is a jar"); the argument from a world order to a lawgiver; and the moral argument from the law of karma to a moral governor. Besides adducing these and other arguments, Udayana in his Nyaya-kusumanjali stressed the point that the nonexistence of God could not be proved by means of valid knowledge.