^{page 52 note 1} Met.,  4, 1006 a 3–4. Other statements of this law have been formalized by BocheńSki, I.M., Ancient Formal Logic, Amsterdam, 1951, 38–40Google Scholar; cf. also J. L. Ackrill, Mind, Lxii,1953, 110–12.

^{page 52 note 2} Ibid., 14–15; cf. translation of W. D. Ross, Oxford, 1908.

^{page 52 note 3} Burtt, E.A.,‘What can Western philosophy learn from India ?’, Philosophy East and West, v, 1955–6, 202Google Scholar.

^{page 52 note 4} The principle called catuṣkoṭi. See P. T. Raju, ‘The principle of four-cornered negation in Indian philosophy’, Review of Metaphysics, vii, 1954, 694–713; Murti, T. R. V., The central philosophy of Buddhism, London, 1955, 129–31, 146–8Google Scholar. The earliest occurrence perhaps in the Pali canon is Majjhima-nikāya, sutta 63 (transl. H. C. Warren, Buddhism in translations, Cambridge, Mass., 1946, 117–22). For a formalization see: H. Nakamura, ‘Buddhist logic expounded by means of symbolic logic’, Journal of Indian and Buddhist Studies, vii, 1958, 384–5. The same formalization in an earlier Japanese version (in Indogaku Bukkyŀgaku kenkyŪ, iii, 1954,223–31) was criticized by R. H. Robinson,‘Some logical aspects of Nāgārjuna's system’, Philosophy East and West, vi, 1957, 302. The validity of this criticism may be questioned.

^{page 53 note 1} Āpastamha-śrauta-sūtra, 24.1.16–20.

^{page 53 note 2} W. Caland in his translation ad loc. specifies this by the following example: ‘Z. B. muss ein anderer als der Adhvaryu, da dieser beschaftigt ist, das Opfertier losbinden’.

^{page 54 note 1} See especially Thieme, P., Pāṇxini and the Veda, Allahabad, 1935, 67Google Scholar sq.; Renou, L., La Durghaṇxavṭtti de Śaraṇadeva, i, 1 (introduction), Paris, 1940, 7Google Scholar

^{page 54 note 2} Renou, cf. L., Études vēdiques et pāĥinēennes, vi (Le destin du Veda dans l'lnde), Paris, i 1960, 66Google Scholar.

^{page 54 note 3} Mīmāṃsā is closest to the paribhāsā sections of the sūtras. SeeGarge, D. V., Citations in Śabara-bhāṢya,1952, 50Google Scholar sq.

^{page 54 note 4} Staal, J. F., ‘The theory of definition in Indian logic’, JA08, LXXXI, 2, 1961, 124Google Scholar.

^{page 55 note 1} See Renou, L., ‘Connexions entre le rituel et la grammaire en Sanskrit’, JA, CCXXXIII, 1941–2, 116–17Google Scholar, also for what follows.

^{page 55 note 2} Pāṇini, 1.4.2: vipratiṢedhe param, kāryam. This principle is not valid for the Tripādī(Pāḥini, 8.2–4): cf.Buiskool, H. E., PŪrvatrāsiddham, Amsterdam, 1934Google Scholar.

^{page 55 note 3} It is irrelevant in the present context that the term paramin the sŪtra may mean desirable(iṢṭtam), as it is interpreted by Patañjali (see Buiskool, op. cit., 66–7, 71–6).

^{page 55 note 4} adloc.; ed. Kielhorn, I, 304.

^{page 55 note 5} See Renou, L., Terminologie grammaticale du Sanskrit, Paris, 1957, 280Google Scholar (s.v. vipratiṢedha).

^{page 55 note 6} This rule is discussed in another context by the present author in ‘A method of linguistic description: the order of consonants according toPāḥini’, Language [to be published, 1962].

^{page 55 note 7} cf. paribhāṢā 38 of Nāgoj012B Bhatta's ParibhāṢenduśekhara ed. and transl. F. Kielhorn, Bombay, 1868, 34, 320; cf. also Renou, L., Études védiques et pāḥqinéennes, ii, Paris, 1956,143Google Scholar.

^{page 55 note 8} If param means ‘desirable’, i j can be interpreted to mean that j is more desirable than i.

^{page 56 note 1} ad Pāḥini, 1.4.2.

^{page 56 note 2} Renou, Termirnologie, 49

^{page 56 note 3} See Renou, , in ‘Connexions’, JA, CCXXXIII, 1941–2, p. 117, n. 2.Google Scholar

^{page 56 note 4} Although here param hag a different meaning: see above, p. 55, n. 1.

^{page 56 note 5} cf. the article quoted above, p. 54, n. 4.

^{page 57 note 1} Mīmāmsā-nyāya-prakāቛa, ed. and transl. F. Edgerton, New Haven, 1921, sections 320–8

^{page 57 note 2} De int. 12, 21 b 1–8.

^{page 57 note 3} See Staal, J. F., ‘The construction of formal definitions of subject and predicate’, TPS,1960, 89–103Google Scholar.

^{page 57 note 4} See, e.g., Boeheński, Ancient formal logic, 3.

^{page 57 note 5} See, e.g., Bocheński, op. cit., 59

^{page 58 note 1} See, e.g., Mīmāmsā-nyāya-prakāśa, section 10.

^{page 58 note 2} The term uttarapada literally denotes the second member of a compound. According to the Sanskrit grammarians the negative particle combines with a following noun into a nominal compound (generally either tatpuruṢa or bahuvrīhi), so that the following noun is appropriately designated by the term uttarapada. Since paryuāsa applies also to verbs, uttarapada has been here translated by ‘next word’.

^{page 58 note 3} Mīmārrisā-nyāya-prakāśa, section 330.

^{page 58 note 4} Mīmārrisā-nyāya-prakāśa, sections 332–40.

^{page 59 note 1} Edgerton, op. cit., p. 170, n. 222.

^{page 59 note 2} Mīmāṃsā-nyāya-prakāśa, sections 341–50. These sentencesreflect Vedic sentences where the second object follows the verb but is preceded by na, e.g. Aitareya-Brāhmaḥa, 1.17.13, prayājān evātra yajanti nānuyājān ‘in this case they offer the fore-sacrifices, not the aftersacrifices’. See Gonda, J., Four studies in the language of the Veda, 's-Gravenhage, 1959, 7–70Google Scholar(‘Amplified sentences and similar structures’, 60).

^{page 59 note 3} The Mīmāṃsā distinction was alsoadopted in dharmaśāstra. It occurs ina medieval work on gotra and pravara: see Brough, J., The early Brahmanical system of Gotra and Pravara: atranslation of the Gotra-pravara-mañjarī of Purusottama-pandita, Cambridge, 1953, p. 70Google Scholar, n. 3.

^{page 59 note 4} cf. Edgerton, op. cit., p. 167, n. 219.

^{page 59 note 5} Renou, Durghatavṛtti, 114; also Renou, , JA, CCXLV, 2, 1957, p. 131Google Scholar, n. 9, and Terminologie,

^{page 60 note 1} c f. the article quoted above, p. 55, n. 6.

^{page 62 note 1} BrahmasūtrabhāṢya, 1.1.3. Ed. Ninjaya Sāgara, Bombay, 1934, 52–3. always assumes that no two Vedic utterances are contradictories. See e.g. de Smet, R., ‘The theological method of Samkara’, Revue Philosophique de Louvain, iii, 1954, 31–74CrossRefGoogle Scholar, and n. 47.

^{page 62 note 2} In Mīmāmsā this is called soḍaśi-nyaya ‘principle of the ṣoḍaśin cup’: see, e.g., Garge, op. cit., 265.

^{page 62 note 3} na tu vastv evaṃ naivam asti nāstīti vā vikalpyate / vikalpanās tu puruṣabuddhyapeksāḥ / navastuyāthātmyajñdnaṃ puruṣabuddhyapekṣam / kiṃ tarhi vastutantram eva tat / nahi sthānāvekasmin sthānur vā sthānur'nyo veti tattvajáānaṃ bhavati / tatra puruso 'nyo veti mithyājñānam /sthānur eveti tattvajñānaṃ vastutantratvāt / evam bhŪtavastuviṣayāftām prāmāḥāṃ vastutantram//

^{page 63 note 1} See, for instance, Oldenberg, H., Die Weltanschauung der Brahmana-Texte, Göttingen, 1919,110–23Google Scholar.

^{page 63 note 2} BrahmasŪtrabhāsya, 1.1.4. Ed. Sāgara, Nirḥaya, 83; discussed by the present author in Advaita and neo-PlaUmism: a critical study in comparative philosophy, Madras, 1961, 101–2Google Scholar, and cf. 80–1.

^{page 63 note 3} dhyānaṃ cintanaṃ yady ap'i; mānasarṃ tathāpi puruṣeဥa kartumakartumanyathā vā hartuṃialcyam purusatantratvāt / jñānaṃ tu pramānajanyam / pramānam ca yathābhŪtavastuvisayam /ato jñanaṃ kartumakartumanyathā vā kartumasakyaṃ kevalaṃ vastutaniram eva tat / na codanātantram / nāpi puruṣatantram //

^{page 63 note 4} cf. Benou, JA, ccxxxnr, 1941–2, 115: ‘le style nominal, repreśentē de facon rigoreuse par les sŪtra grammaticaux et quereprendront les sŪtra philosophiques, cede la place, dans le rituel, a un style verbal characterise par l'indicatif descriptif, l'optatif prescriptif, l'absolutif d'enchainement temporel...’.

^{page 63 note 5} This holds on the vyāvahārika level. Śaiikara's explicit statements are somewhat obscured in Lacombe, o., L'Absoluselon le Vedānta, Paris, 1937, 124Google Scholar

^{page 63 note 6} Brough, who rightly stressed this Mīmāmsā preoccupation with injunctions, has also drawn attention to the fact that the termsvidhi and pratiṣedha came to refer to indicative sentences as well: ‘although later Indian logic deals largely in indicative sentences, the linguistic thought of philosophers in India was not so strictly confined to indicative propositions as that of logicians in the west. This influence can be traced in the terms vidhiand pratiṣedha, originally meaning injunction and prohibition, but in later texts occasionally used to apply simply to positive and negative statements’ (Brough, J., ‘Some Indian theoriesof meaning’, TPS, 1953, 162Google Scholar).

^{page 64 note 1} Ed. F. Kielhom, i, 5; cf. ed. and transl. Chatterji, K. C., Calcutta, 1957, 34–5Google Scholar.

^{page 64 note 2} Śabdānuśāsanam idānīṃ kartavyam, / tat kathaṃ kartavyam / kiṃ śabdopadeśaḥ kartavyaḥ āhosvid apaśubdopadeśaḥ āhosvid ubhayopadeśah iti / anyataropadeśena kṛtaṃ syāt / tad yathā bhakṣyaniyamenābhakṣyapratiṣedho gamyate / paṇca pañcanakhā bhakṣyāḥ ity ukte gamyata etad ato‘nye’bhakṣyā iti / abhakṣyapratiṣedhena vābhakṣyaniyamaḥ / taḍ yathā abhakṣyo grāmyaknkkuṭaḥ abhakṣyo grāmyasūkaraḥ ity ukte gamyata etad āraṇyo bhakṣya iti / evam ihāpi / yadi tāvacchabdopadeśaḥ kriyate gaur ity etasminn upadiṣte gamyata etad gāvyMāyo'paśabda iti / yathāpy apaśabdopadeśaḥ kriyate gāvyādiṣūpadiṣṭeṣu gamyata etad gaur ity eṣa śabda iti //

^{page 65 note 1} Mahābhāṣya ad Pāṇini, 1.1.44, ed. Kielhorn, I, 103; cf. Paranjpe, V. G., Le vārtika de Kātyāyana, Paris, 1922, 30–1Google Scholar.

^{page 65 note 2} Renou, Terminologie, 219.

^{page 65 note 3} A similar quotation (dvau nañau prakṛtyartharṃgamayataḥ;) is found in Chakravarti, P. C., The linguistic speculations of the Hindus, Calcutta, 1933, p. 436, n. 3Google Scholar.

^{page 65 note 4} Ingalls, D. H. H., Materials for the study of Navya-nyāya logic, Cambridge, Mass., 1951, 68–72Google Scholar; cf. Staal, J. F., Indo-Iranian Journal, iv, 1, 1960, 70–1Google Scholar.

^{page 66 note 1} Delbriick, B., Vergleichende Syntax der indogermanischen Sprachen, Strassburg, i–III, 1893–1900, II, 535–6Google Scholar.

^{page 66 note 2} See, e.g., Jespersen, O., The philosophy of grammar, London, 1948, 331–4Google Scholar.

^{page 66 note 3} See Ingalls, loc. cit.

^{page 66 note 4} Delbrück, n, 533.

^{page 66 note 5} See Graham, A. C.,BSOAS, xxn, 3, 1959, 567Google Scholar, and Asia Major, NS, vn, 1–2,1959, 88Google Scholar.

^{page 66 note 6} Asia Major, NS, vn, 1–2, 1959, 91Google Scholar, ‘One saying that it is an ox, the other that it is not, is “contesting the other's case‐. Their claims will not both fit’. The first negative particle translates the term negation fei, the second the sentence negation pu. Cf. also Staal, J. F., TPS,1960,93Google Scholar.

^{page 66 note 7} nañɹnuyājaśabdena saṃbandham āśritya paryudāsa āśrīyate, nañanuyājaśabdābhyām anuydjāvyatirildalaksandt: Mñānisā-nyāya-prakāsa, section 34.

^{page 67 note 1} Delbrück, II, 524

^{page 67 note 2} Delbrück, II, 534.

^{page 67 note 3} Kāśikā; to Panini, 2.2.6, and 6.3.73.

^{page 67 note 4} Pānini, 6.3.73.

^{page 67 note 5} Delbrück, n, 529–33.

^{page 67 note 6} Delbrück, n, 533.

^{page 67 note 7} Bocheński, Ancient formal logic, 38.

^{page 67 note 8} Brhadāraṇyyakopaniṣat, 2.3.6, 3.9.26, 4.2.4, 4.23, 5.

^{page 67 note 9} See, e.g., Gonda, J., Four studies in the language of the Veda, 's-Gravenhage, 1959, 95–117Google Scholar(‘Why are ahiṃsā and similar conceps often expressed in a negative form ? ’ ); Nakamura, H., The ways of thinking of Eastern peoples, Tokyo, 1960, 23–32Google Scholar.

^{page 67 note 10} Nyāyabindu, Stcherbatskoy, T. I. (Bibliotheca Buddbica, VII), Petrograd,1918, 19Google Scholar; ed. Candraśekhara Sāstrī, Banaras, 1954, 23.

^{page 67 note 11} See J. F. Staal, ‘Contraposition in Indian logic’, to be published inProceedingsof the 1960 Internationa] Congress for Logic, Methodology and Philosophy of Science, Stanford, Calif.

^{page 68 note 1} Nyāya-sūtra, 1.2.6

^{page 68 note 2} See, e.g., Tarka-saṃgraha, 54, ed. Athalye, Y. V., Poona, 1930, 45–6, 302Google Scholar.

^{page 68 note 3} Datta, D. M.,‘Epistemological methods in Indian philosophy’, in Moore, C. A. (ed.), Essays in East-West philosophy, Honolulu, 1951, 73–88Google Scholar

^{page 68 note 4} Udayana,Nyāya-kusumāñjali, 3.8, Ibid., p. 88, n. 17.

^{page 68 note 5} See, e.g., Staal, J. F.,‘Correlations between language and logic in Indian thought’. BSOAS,xxin, 1, 1960, especially 116–17Google Scholar.

^{page 68 note 6} Since only the doctrines mentioned are dealt with in this paper, these conclusions do not Simply that there are not also other systems where the lawof contradiction is denied. Such systems exist in Buddhism (see, e.g., p. 52, n. 4, above, and Kunst, A., ‘The concept of the principle of excluded middle in Buddhism’, Rocznik Orientalistyczny, xxi, 1957, 141–7Google Scholar) and in Jainism (especially in the opportunist syaāvāda ‘let-it-be doctrine’). In Hinduism such thought appears in particular in the Advaita doctrine of the indeterminability (anirvacanīyatva) of the world-illusion, which is specified as sadasadbhyām anirvacanīya‘; indeterminable either as real or as unreal’ (similarly: sadasadbhyām vilakṢaṇa). If this ia interpreted as ~(aV ~ a), it violates the law of contradiction. In Advaita the world-illusion is therefore sarvanyāyavirodhinī; ‘opposed to all logic’ (Naiṣkarmyasiddhi, 3.66). These doctrines have been vehemently criticized in the name of logic and the law of contradiction both by Viśiṣṭādvaitins (see, e.g., Dasgupta, S. N., A history of Indian philosophy, III, Cambridge, 1952,177Google Scholar), and by Dvaitins (see, e.g., Dasgupta, rv, Cambridge, 1955, 204; Shastri, A. B., Studies in post-Śamkara dialectics, Calcutta,1936,180,195–6Google Scholar). The law of the excluded middle on the other hand seems to be accepted by the Advaitin Totaka who maintained that there exists no intermediary between sat‘being’ and asat‘non-being’ (see Hacker, P.,Untersuchungen über Texle desfrühen Advaitavāda,Mainz, 1950,163Google Scholar). Whereas we have seen that Śankara himself uses and accepts the law of contradiction, he can also be seen to argue in accordance with the law of double negation. An example occurs inBrahmasūtrabhāūya, 4.1.3, where the conclusion, that the worshipper is not different from the deity, is drawn from a scriptural statement which opposes the negation of this view, i.e.‘Now if someone worships a deity as other, saying “the deity is one and I am another’, he does not know’ (BḴhadāraṇ;yakopaniṣat, 1.4.10). Elsewhere Śankara appears to refer implicitly to the law of contradiction when saying that different Vedānta texts cannot teach different cognitions of Brahman, for it is certain that, if at all they differ, ‘only one of them is the right one, the others are erroneous’ (teṣam ekcam abhrāntaṃ bhrāntānītarāṇi: Brahmasūtrabhāṣya, 3.3.1; see Staal, J. F. in Atti del XII Congresso Irdernazionale di Filosofia,1958, x, Firenze, 1960,227Google Scholar).

^{page 69 note 1} cf. the article quoted above, p. 57, n. 3.

^{page 69 note 2} It has been pointed out, however, that purely nominal sentences of the type Pax vobiscum! have an optative character.