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the attempt to formulate definitions with the strictest formal rigour and to offer criticisms with that over- emphasis of formalism and scholasticism which attained their cul- mination in the writings of later Nyaya writers such as Raghunatha Siromani, Jagadiga Bhattacarya, Mathuranatha Bhattacarya and Gadadhara Bhattacarya. It is generally believed that such methods of overstrained logical formalism were first started by Gangeéga Upadhyaya of Mithila early in the thirteenth century. But the truth seems to be that this method of logical formalism was steadily growing among certain writers from as early as the tenth and eleventh centuries. One notable instance of it is the formu- lation of the maha-vidya modes of syllogism by Kularka Pandita in the eleventh century. There is practically no reference to this maha-vidya syllogism earlier than Sriharsa(a.D. 1187). References to this syllogism are found in the writings of Citsukha Acarya (A.D. 1220), Amalananda, called also Vyasasrama (A.D. 1247), Anandajiiana (A.D. 1260), Venkata (a.D. 1369), Sesa Sarngadhara (A.D. 1450) and others?. The maha-vidya syllogisms were started probably some time in the eleventh century, and they continued to be referred to or refuted by writers till the fifteenth century, though it is curious to notice that they were not mentioned by Gangega or any of his followers, such as Raghunatha, Jagadisa and others, in their discussions on the nature of kevalanvayi types of inference. 1 gandhe gandhantara-prasanjika na ca yuktir asti; tadastitve vd ka no hanih; tasya apy asmabhih khandaniyatvat. Sriharsa’s Khandana-khanda-khadya, p. 1181, Chowkhamba edition. 2 athava ayam ghatah etadghatanyatve sati vedyatvanadhikarananya-padar- hatvat patavad ity-adimahdavidya-prayogair api vedyatva-siddhir apy iihaniya.— Citsukha Acarya’s Tattva-pradipikd, p. 13, also p. 304. The commentator Pratyag- rupa-bhagavan mentions Kularka Pandita by name. evam sarvad mahavidyds tac- chaya vanye prayogah khandaniyda iti—Amalananda’s Vedanta-kalpa-taru, p. 304 (Benares, 1895). sarvasv eva mahavidyasu, etc.—-Anandajfiana’s Tarka-samgraha, p. 22. Also Venkata’s Nydya-parisuddhi, pp. 125, 126, 273-276, etc., and Tattva-mukta-kalapa with Sarvartha-siddhi, pp. 478, 485, 486-491. Mr M. R. “Telang has collected all the above references to maha-vidyd in his introduction to the Maha-vidya-vidambana, Gaekwad’s Oriental Series, Baroda, 1920. 120 The Sankara School of Vedanta [cH. In all probability maha-vidya syllogisms were first started by Kularka Pandita in his Dasa-slokt-maha-vidya-sitra containing sixteen different types of definitions for sixteen different types of maha-vidya syllogisms. Assuming that Kularka Pandita, the founder of mahd-vidyad syllogisms, flourished in the eleventh century, it may well be suggested that many other writers had written on this subject before Vadindra refuted them in the first quarter of the thirteenth century. Not only does Vadindra refer to the arguments of previous writers in support of maha-vidya and in refutation of it in his Mahd-vidya-vidambana, but Bhuvana- sundara Siri also in his commentary on the Maha-vidya-vidambana refers to other critics of maha-vidya. Recently two different com- mentaries have been discovered on mahd-vidya, by Purusottama- vana and Piirnaprajfia. Venkata in his Nya@ya-parisuddhi refers to the Mahda-vidya, the Mana-manohara and the Pramana-manjari, and Srinivasa in his commentary Nyd@ya-sara on the Nydaya-pari- §uddhi describes them as works which deal with roundabout syllogisms (vakranumana)!. This shows that for four or five centuries maha-vidya syllogisms were in certain quarters supported and refuted from the eleventh century to the sixteenth century. It is well known that the great Mimamsa writers, such as Kumiarila Bhatta and his followers, believed in the doctrine of the eternity of sounds, while the followers of the Nyaya and Vaisesika, called also Yaugicaryas, regarded sound as non-eternal (anitya). Maha-vidya modes were special modes of syllogism, invented prob- ably by Kularka Pandita for refuting the Mimamsa arguments of the eternity of sounds and proving the non-eternity of sounds. If these modes of syllogism could be regarded as valid, they would also have other kinds of application for the proving or disproving of other theories and doctrines. The special feature of the maha- vidya syllogisms consisted in their attempt to prove a thesis by the kevalanvayi method. Ordinarily concomitance (vyapti) con- sists in the existence of the reason (hetu) in association with the probandum and its non-existence in all places where the pro- bandum is absent (sadhyabhavavad-avrttitvam). But the kevalan- vayt form of inference which is admitted by the Naiyayikas applies to those cases where the probandum is so universal that there is no case where it is absent, and consequently it cannot have a reason (hetu) whose concomitance with it can be determined by * See M. R. Telang’s introduction to the Maha-vidya-vidambana. x1] Mahd-vidya and Development of Logical Formalism 121 its non-existence in all cases where the probandum is absent and its existence in all cases where the probandum is present. Thus in the proposition, “This is describable or nameable (idam abhi- dheyam) because it is knowable (prameyatvat),”’ both the pro- bandum and the reason are so universal that there is no case where their concomitance can be tested by negative instances. Maha-vidya syllogisms were forms of kevalanvayi inference of this type, and there were sixteen different varieties of it which had this advantage associated with them, that, they being kevalanvayi forms of syllogism, it was not easy to criticize them by pointing out defects or lapses of concomitance of the reason and the probandum, as no negative instances are available in their case. In order to make it possible that a kevalanvayi form of syllogism should be applicable for affirming the non-eternity of sound, Kularka tried to formulate propositions in sixteen different ways so that on kevalanvayi lines such an affirmation might be made about a subject that by virtue of it the non-eternity of sound should follow necessarily as the only consequence, other possible alternatives being ruled out. It is this indirect approach of inference that has been by the critics of mahd-vidya styled roundabout syllogism. Thus maha-vidya has been defined as that method of syllogism by which a specific probandum which it is desired to prove by the joint method of agreement and difference (3, anvaya-vyatireki-sadhya- visesam vady-abhimatam sadhayatt)is proved by the necessary impli- cation of the existence of a particular probandum in a particular subject (2, pakse vyapaka-pratitya-paryavasana-balat), affirmed by the existence of hetu in the subject on kevalanvayi lines (1, kevalan- vayini vyapake pravartamano hetuh). In other words, a reason which exists in a probandum inseparably abiding in a subject (paksa) without failure (proposition 1) proves (sddhayatz), by virtue of the fact, that such an unfailing existence of that probandum in that subject in that way is only possible under one supposition (pro- position 2), namely, the affirmation of another probandum in another subject (e.g. the affirmation of the probandum “‘non- eternity” to the subject ‘sound ”), which is generally sought to be proved by the direct method of agreement and difference (pro- position 3). This may be understood by following a typical maha- vidya syllogism. Thus it is said that by reason of knowability .(meyatva) as such the self, dissociated from the relations of all eternal and non-eternal qualities of all other objects excepting 122 The Sankara School of Vedanta [cH. sound, is related to a non-eternal entity (atma sabdetaranitya-nitya- yavrttitvanadhikarananitya-vrtti-dharmavan meyatvad ghatavat). Now by the qualifying’adjunct of “self” the self is dissociated from all qualities that it shares with all other eternal and non-eternal objects excepting sound, and the consequence is that it is left only with some kind of non-eternal quality in relation with sound, as this was left out of consideration in the qualifying adjunct, which did not take sound within its purview. Since many relations are also on the Nyaya view treated as qualities, such a non-eternal relation of the self to sound may be their mutual difference or their mutual negation (anyonyabhava). Now, if the self, which is incontestably admitted to be eternal, has such a non-eternal quality or relation to sound, then this can only be under one supposition, viz. that sound is non-eternal. But, since all other non-eternal relations that the self may have to other non-eternal objects, and all other eternal relations that it may have to other eternal objects,:and all other such relations that it may have to all eternal and non-eternal objects jointly, except sound, have already been taken out of consideration by the qualifying phrase, the in- separable and unfailing non-eternal quality that the self may have, in the absence of any negative instances, is in relation to sound; but, if it has a non-eternal quality in relation to sound, then this can be so only under one supposition, viz. that sound is itself non-eternal; for the self is incontestably known as eternal. This indirect and roundabout method of syllogism is known as maha- vidya. It is needless to multiply examples to illustrate all the sixteen types of propositions of mahd-vidya syllogism, as they are all formed on the same principle with slight variations. Vadindra in his Maha-vidya-vidambana refuted these types of syllogism as false, and it is not known that any one else tried to revive them by refuting Vadindra’s criticisms.