The founder of the school of Navya-(New) Nyaya, with an exclusive emphasis on the pramanas, was Gangesha Upadhyaya (13th century), whose Tattvacintamani ("The Jewel of Thought on the Nature of Things") is the basic text for all later developments. The logicians of this school were primarily interested in defining their terms and concepts and for this purpose developed an elaborate technical vocabulary and logical apparatus that came to be used by, other than philosophers, writers on law, poetics, aesthetics, and ritualistic liturgy. The school may broadly be divided into two subschools: the Mithila school represented by Vardhamana (Gangesha's son), Paksadhara or Jayadeva (author of Aloka gloss), and Shankara Mishra (author of Upaskara); and the Navadvipa school, whose chief representatives were Vasudeva Sarvabhauma (1450-1525), Raghunatha Shiromani (c. 1475-c. 1550), Mathuranatha Tarkavagisha (fl. c. 1570), Jagadisha Tarkalankara (fl. c. 1625), and Gadadhara Bhattacarya (fl. c. 1650).

 By means of a new technique of analyzing knowledge, judgmental knowledge can be analyzed into three kinds of epistemological entities in their interrelations: "qualifiers" (prakara); "qualificandum," or that which must be qualified (vishesya); and "relatedness" (samsarga). There also are corresponding abstract entities: qualifierness, qualificandumness, and relatedness. The knowledge expressed by the judgment "This is a blue pot" may then be analyzed into the following form: "The knowledge that has a qualificandumness in what is denoted by 'this' is conditioned by a qualifierness in blue and also conditioned by another qualifierness in potness."

 A central concept in the Navya-Nyaya logical apparatus is that of "limiterness" (avacchedakata), which has many different uses. If a mountain possesses fire in one region and not in another, it can be said, in the Navya-Nyaya language, "The mountain, as limited by the region r, possesses fire, but as limited by the region r' possesses the absence of fire." The same mode of speech may be extended to limitations of time, property, and relation, particularly when one is in need of constructing a description that is intended to suit exactly some specific situation and none other.

 Inference is defined by Vatsayana as the "posterior" knowledge of an object (e.g., fire) with the help of knowledge of its mark (e.g., smoke). For Navya-Nyaya, inference is definable as the knowledge caused by the knowledge that the minor term (paksa, "the hill") "possesses" the middle term (hetu, "smoke"), which is recognized as "pervaded by" the major (sadhya, "fire"). The relation of invariable connection, or "pervasion," between the middle (smoke) and the major (fire)--"Wherever there is smoke, there is fire"--is called vyapti.

 The logicians developed the notion of negation to a great degree of sophistication. Apart from the efforts to specify a negation with references to its limiting counterpositive (pratiyogi), limiting relation, and limiting locus, they were constrained to discuss and debate such typical issues as the following: Is one to recognize, as a significant negation, the absence of a thing x so that the limiter of the counterpositive x is not x-ness but y-ness? 
In other words, can one say that a jar is absent as a cloth even in a locus in which it is present as a jar? Also, is the absence of an absence itself a new absence or something positive? Furthermore, is the absence of colour in general nothing but the sum total of the absences of the particular colours, or is it a new kind of absence, a generic absence? Gangesha argued for the latter alternative, though he answers the first of the above three questions in the negative.

 Though the philosophers of this school did not directly write on metaphysics, they nevertheless did tend to introduce many new kinds of abstract entities into their discourse. These entities are generally epistemological, though sometimes they are relational. Chief of these are entities called "qualifierness," "qualificandumness," and "limiterness." Various relations were introduced, such as direct and indirect temporal relations, paryapti relation (in which a number reside, in sets rather than in individual members of those sets), svarupa relation (which holds, for example, between an absence and its locus), and relation between a knowledge and its object.

 Among the Navya-Nyaya philosophers, Raghunatha Shiromani in Padarthatattvanirupana undertook a bold revision of the traditional categorial scheme by (1) identifying "time," "space," and "ether" with God; (2) eliminating the category of mind by reducing it to matter; (3) denying atoms (paramanu) and dyadic (paired) combinations of them (dvyanuka), (4) eliminating "number," "separateness," "remoteness," and "proximity" from the list of qualities; and (5) rejecting ultimate particularities (vishesa) on the grounds that it is more rational to suppose that the eternal substances are by nature distinct. He added some new categories, however, such as causal power (shakti) and the moment (ksana), and recognized that there are as many instances of the relation of inherence as there are cases of it (as contrasted with the older view that there is only one inherence that is itself present in all cases of inherence).
 
 

Texts and commentaries until Vacaspati and the "Samkhya-sutras."
There are three commentaries on the Samkhya-karika: that by Raja, much referred to but not extant; that by Gaudapada (7th century), on which there is a subcommentary Candrika by Narayanatirtha; and the Tattva-kaumudi by Vacaspati (9th century). The Samkhya-sutras are a much later work (c. 14th century) on which Aniruddha (15th century) wrote a vrtti and Vijnanabhiksu (16th century) wrote the Samkhya-pravacana-bhasya ("Commentary on the Samkhya Doctrine"). Among independent works, mention may be made of Tattvasamasa ("Collection of Truths"; c. 11th century).

 The Yoga-sutras were commented upon by Vyasa in his Vyasa-bhasya (5th century), which again has two excellent subcommentaries: Vacaspati's Tattvavaisharadi and Vijnanabhiksu's Yogavarttika, besides the vrtti by Bhoja (c. 1000).
 
 

For Vacaspati, creation was viewed in terms of the mere presence of the selves and the mere presentation to them of Matter (the undifferentiated primeval stuff). Such a view has obvious difficulties, for it would make creation eternal, because the selves and Matter are eternally copresent. Vijnanabhiksu considered the relation between the selves and Matter to be a real relation that affects Matter but leaves the selves unaffected. Creation, in accordance with Bhiksu's theism, is due to the influence of the chief self--i.e., God. Furthermore, whereas the earlier Samkhya authors, including Vacaspati, did not consider the question about the ontological status of the gunas, Bhiksu regards them as real, as extremely subtle substances--so that each guna is held to be infinite in number. In general, the Samkhya-sutras show a greater Brahmanical influence, and there is a clear tendency to explain away the points of difference between the Samkhya and the Vedanta. The author of the sutras tried to show that the Samkhya doctrines are consistent with theism or even with the Upanisadic conception of Brahman. Vijnanabhiksu made use of such contexts to emphasize that the atheism of Samkhya is taught only to discourage men to try to be God, that originally the Samkhya was theistic, and that the original Vedanta also was theistic. The Upanisadic doctrine of the unity of selves is interpreted by him to mean an absence of difference of kind among selves, which is consistent with the Samkhya. Maya (illusion) for Bhiksu means nothing but the prakrti (Matter) of the Samkhya. 
The sutras also give cosmic significance to mahat, the first aspect to evolve from Matter, which then means cosmic Intelligence; a sense not found in the karikas.

 In epistemology the idea of reflection of the spirit in the organs of knowing, particularly in the buddhi, or intelligence, comes to the forefront. Every cognition ( jnana) is a modification of the buddhi, with consciousness reflected in it. Though this is Vacaspati's account, it does not suffice according to Bhiksu. If there is the mere reflection of the self in the state of the buddhi, this can only account for the fact that the state of cognition seems to be a conscious state; it cannot account for the fact that the self considers itself to be the owner and experiencer of that state. Accounting for this latter fact, Bhiksu postulated a real contact between the self and buddhi as a reflection of the buddhi state back in the self.

 Vacaspati, taking over a notion emphasized in Indian epistemology for the first time by Kumarila, introduced into the Samkhya theory of knowledge a distinction between two stages of perceptual knowledge. In the first, a stage of nonconceptualized (nirvikalpaka) perception, the object of perception is apprehended vaguely and in a most general manner. In the second stage, this vague knowledge (alocanamatram) is then interpreted and conceptualized by the mind. The interpretation is not so much synthesis as analysis of the vaguely presented totality into its parts. Bhiksu, however, ascribed to the senses the ability to apprehend determinate properties, even independently of the aid of manas. For Samkhya, in general, error is partial truth; there is no negation of error, only supplementation, though later Samkhya authors tended to ascribe error to wrong interpretation.

 An important contribution to epistemology was made by the writers on the Yoga: this concerns the key notion of vikalpa, which stands for mental states referring to pseudo-objects posited only by words. Such mental states are neither "valid" nor "invalid" and are said to be unavoidable accompaniments of one's use of language.

Because the self is not truly an agent acting in the world, neither merit nor demerit, arising from one's actions, attaches to the self. Morality has empirical significance. In the long run, what really matters is knowledge. Nonattached performance of one's duties is an aid toward purifying intelligence so that it may be conducive to the attainment of knowledge: hence the importance of the restraints and observances laid down in the Yoga-sutras. The greatest good is freedom--i.e., aloofness (kaivalya) from matter.
 
 

Though Patanjali's yoga is known as Raja Yoga (that in which one attains to self-rule), Hatha Yoga (hatha = "violence," "violent effort": ha = "sun," tha = "moon," hatha = "sun and moon," breaths, or breaths travelling through the right and left nostrils) emphasizes bodily postures, regulation of breathing, and cleansing processes as means to spiritual perfection. A basic text on Hatha Yoga is the Hatha-yoga-pradipika ("Light on the Hatha Yoga"; c. 15th century). As to the relation between the two yogas, a well-known maxim lays down that "No raja without hatha, and no hatha without raja."
 
 

The one religious consequence of the Samkhya-Yoga is an emphasis on austere asceticism and a turning away from the ritualistic elements of Hinduism deriving from the Brahmanical sources. Though they continue to remain as an integral part of the Hindu faith, no major religious order thrived on the basis of these philosophies.
 
 

Fragments from the Mandukya-karika until Shankara.
No commentary on the Vedanta-sutras survives from the period before Shankara, though both Shankara and Ramanuja referred to the vrttis by Bodhayana and Upavarsa (the two may indeed be the same person). There are, however, pre-Shankara monistic interpreters of the scriptures, three of whom are important: Bhartrhari, Mandana (both mentioned earlier), and Gaudapada. Shankara referred to Gaudapada as the teacher of his own teacher Govinda, complimented him for having recovered the advaita (nondualism) doctrine from the Vedas, and also wrote a bhasya on Gaudapada's main work: the karikas on Mandukya Upanisad.

 Gaudapada's karikas are divided into four parts: the first part is an explanation of the Upanisad itself, the second part establishes the unreality of the world, the third part defends the oneness of reality, and the fourth part, called Alatasanti ("Extinction of the Burning Coal"), deals with the state of release from suffering. It is not accidental that Gaudapada used as the title of the fourth part of his work a phrase in common usage among Buddhist authors. His philosophical views show a considerable influence of Madhyamika Buddhism, particularly of the Yogacara school, and one of his main purposes probably was to demonstrate that the teachings of the Upanisads are compatible with the main doctrines of the Buddhist idealists. Among his principal philosophical theses were the following: All things are as unreal as those seen in a dream, for waking experience and dream are on a par in this regard. In reality, there is no production and no destruction. His criticisms of the categories of change and causality are reminiscent of Nagarjuna's.
Duality is imposed on this one reality by maya, or the power of illusion-producing ignorance. Because there is no real coming into being, Gaudapada's philosophy is often called ajativada ("discourse on the unborn"). Though thus far agreeing with the Buddhist Yogacarins, Gaudapada rejected their thesis that citta, or mind, is real and that there is a real flow of mental conception.
Shankara greatly moderated Gaudapada's extreme illusionistic theory. Though he regarded the phenomenal world as a false appearance, he never made use of the analogy of dream. Rather, he contrasted the objectivity of the world with the subjectivity of dreams and hallucinations. The distinction between the empirical and the illusory--both being opposed to the transcendental--is central to his way of thinking.
 
 

Though Vedanta is frequently referred to as one darshana (viewpoint), there are, in fact, radically different schools of Vedanta; what binds them together is common adherence to a common set of texts. These texts are the Upanisads, the Vedanta-sutras, and the Bhagavadgita--known as the three prasthanas (the basic scriptures, or texts) of the Vedanta. The founders of the various schools of Vedanta have all substantiated their positions by commenting on these three source books. The problems and issues around which their differences centre are the nature of Brahman; the status of the phenomenal world; the relation of finite individuals to the Brahman; and the nature and the means to moksa, or liberation. The main schools are: Shankara's unqualified nondualism (shuddhadvaita); Ramanuja's qualified nondualism (vishistadvaita), Madhva's dualism (dvaita); Bhaskara's doctrine of identity and difference (bhedabheda); and the schools of Nimbarka and Vallabha, which assert both identity and difference though with different emphasis on either of the two aspects. From the religious point of view, Shankara extolled metaphysical knowledge as the sole means to liberation and regarded even the concept of God as false; Ramanuja recommended the path of bhakti combined with knowledge and showed a more tolerant attitude toward the tradition of Vedic ritualism; and Madhva, Nimbarka, and Vallabha all propounded a personalistic theism in which love and devotion to a personal God are rated highest. Although Shankara's influence on Indian philosophy could not be matched by these other schools of Vedanta, in actual religious life the theistic Vedanta schools have exercised a much greater influence than the abstract metaphysics of Shankara.
 
 

Shankara's philosophy is one among a number of other nondualistic philosophies: Bhartrhari's shabdadvaita, the Buddhist's vijnanadvaita, and Gaudapada's ajativada. Shankara's system may then be called atmadvaita--the thesis that the one, universal, eternal, and self-illuminating self whose essence is pure consciousness without a subject (ashraya) and without an object (visaya) from a transcendental point of view alone is real. The phenomenal world and finite individuals, though empirically real, are--from the higher point of view--merely false appearances. In substantiating this thesis Shankara relied as much on the interpretation of scriptural texts as on reasoning. He set down a methodological principle that reason should be used only to justify truths revealed in the scriptures. His own use of reasoning was primarily negative; he showed great logical skill in refuting his opponents' theories. Shankara's followers, however, supplied what is missed in his works--i.e., a positive rational support for his thesis.

 Shankara's metaphysics is based on a criterion of reality, which may be briefly formulated as follows: the real is that whose negation is not possible. It is then argued that the only thing that satisfies this criterion is consciousness, because denial of consciousness presupposes the consciousness that denies. It is conceivable that any object is not existent, but the absence of consciousness is not conceivable. Negation may be either mutual negation (of difference) or absence. The latter is either absence of a thing prior to its origination or after its destruction or absence of a thing in a place other than where it is present. If the negation of consciousness is not conceivable, then none of these various kinds of negations can be predicated of consciousness. If difference cannot be predicated of it, then consciousness is the only reality and anything different from it would be unreal. If the other three kinds of absence are not predicable of it, then consciousness should be beginningless, without end, and ubiquitous. Consequently, it would be without change. Furthermore, consciousness is self-intimating; all objects depend upon consciousness for their manifestation. Difference may be either among members of the same class or of one individual from another of a different class or among parts of one entity. None of these is true of consciousness. In other words, there are not many consciousnesses; the plurality of many centres of consciousness should be viewed as an appearance. There is no reality other than consciousness--i.e., no real prakrti; such a thing would only be an unreal other. Also, consciousness does not have internal parts; there are not many conscious states. The distinction between consciousness of blue and consciousness of yellow is not a distinction within consciousness but one superimposed on it by a distinction among its objects, blue and yellow. With this, the Samkhya, Vijnanavadin Buddhist, and Nyaya-Vaishesika pluralism are refuted. Reality is one, infinite, eternal, and self-shining spirit; it is without any determination, for all determination is negation.