¹ See Hailperin, T., ‘A theory of restricted quantification’, Journal of Symbolic Logic, xxii, 1957, 19–35; 113–29.CrossRefGoogle Scholar For another symbolism cf. Bosser, J. B., Logic for mathematicians, New-York, 1953, 140–50.Google Scholar

¹ It is possibly connected herewith that Alexander of Aphrodisias, the Greek commentator on Aristotle, seems to have been the first to state explicitly what a variable is. See Bocheński, I. M., Formale Logik, Freiburg/München, 1956, 157.Google Scholar

² Less often and in a more complicated way these languages do express what the article expresses. It might be asked whether restricted-variables might be useful in the study of medieval logic too. B. Boehner (Medieval logic, Manchester, 1952) uses individual and predicate variables only.

³ 2.2.29.

⁴ Mahābhāṣya, 2.1.6. This and some of the following references have been traced back with the help of Renou, L., Terminologie, grammaticale du Sanskrit, Paris, 1957.Google Scholar

¹ Pāṇini, 1.2.43. The chief member is called pradhāna. It is possible that the tatpuruṣa originated from a combination of words where the upasarjana word kept its case-ending (see, however, Burrow, T., The Sanskrit language, London, 1955, 208).Google Scholar In the Ṛgveda it sometimes preserves (part of) its case-ending (see Renou, L., Études védiques et pāṇinéennes, I, Paris, 1955, 51)Google Scholar; in the Atharvaveda especially the locative termination (see Renou, L., ‘Linguistic remarks on the Paippalāda version of the Atharvaveda’, Felicitation volume presented to S. K. Belvalkar, Banaras, 1957, 70).Google Scholar The logicians argue that the lakṣaṇā is not understood because of the recollection of such an elided case-ending (lupta-vibhakteḥ smaraṇam), for the meaning is grasped also by somebody who does not remember this case-ending: Siddhānta-muktāvalī, ed. Śukla, Hari Rāma, Banaras, 1951Google Scholar (to be abbreviated as SM), 294.Google Scholar Cf. also the translation of Svāmī Mādhavānanda, Calcutta, 1954, 162.

² tatpuruṣe tu pūrvapade lakṣaṇā: SM, 293Google Scholar, ad Bhāṣā-pariccheda (to be abbreviated as BP), 82.Google Scholar

³ śaktiḥ padena saha padārthasya saṃbandhaḥ (SM, 265).

⁴ By Mm. Bhīmācārya Jhalakīkar, Poona, 1928, 311, s.v. tatpurusa.

⁵ cf. Pāṇini, 1.1.68, and Brough, J., ‘Theories of general linguistics in the Sanskrit grammarians’, Transactions of the Philological Society, 1951, 28–31.Google Scholar

¹ Pāṇini, 1.4.14, 103. An example, also from the Śabdaśaktiprakāśikā, quoted by Chakravarti, P. B. (The philosophy of Sanskrit grammar, Calcutta, 1930, 300, n. 1)Google Scholar states how the ṣaṣṭhī ‘genitive’ is implied by lakṣaṇā: rājapuruṣa ityādau pūrvapade ṣaṣṭhyartha-saṃbandhe lakṣaṇeti maṇikṛduktam api saṃgacchate’ in cases such as rājapuruṣa, etc., the meaning of the genitive is implied in the first word, as also laid down by the author of the Tattva-cintāmaṇi’.

² 1.2.42.

¹ It is interesting to observe in B. Faddegon's discussion of the subdivisions of the compounds (Studies on Pāṇini's Grammar, Amsterdam, 1936, 61–2)Google Scholar how Wackernagel differed mainly from Pāṇini by utilizing the categories of noun and adjective.

² Böhtlingk's index mentions three Sūtras, and six sūtras using guṇavacana ‘Eigenschaftswort’.

³ 2.2.24.

⁴ As the Kāśikā says (Renou, , Terminologie, 108).Google Scholar

⁵ gopadasya gomati lakṣaṇā (SM, 292).

⁶ 1.1.14.

⁷ Mahābhāṣya, 1.1.5, ed. Kielhorn, i, 70.Google Scholar

¹ Ingalls, D. H. H., Materials for the study of Navya-nyāya logic, Cambridge, Mass., 1951, 36.Google Scholar

² See above, p. 109.

³ That is, the abhāvīya-pratiyogī (cf. Ingalls, 55).

⁴ cf. Ingalls, 54–8. See also the present author's review of Ingalls' work, to be published in the Indo-Iranian Journal.

¹ ‘Means of formalisation in Indian and Western logic’, in Proceedings of the XIIth International Congress of PhilosophyGoogle Scholar (Venice, 1958).Google Scholar

² A one-to-one(-to-one) correspondence where it is possible to pair off the elements in such a manner that the structure is not affected.

¹ SM, 220Google Scholar; cf. Ingalls, 62.

¹ This expression occurs in every predicate calculus. It may be incorporated in the formal system either as an axiom or a definition (e.g. Quine, W. V. O., Mathematical logic, Cambridge, Mass., 1951, 102)Google Scholar or as a theorem (e.g. Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, New York, 1946, 62Google Scholar; Kleene, S. C., Introduction to metamathematics, Amsterdam, 1952, 162).Google Scholar

² See e.g. Quine, , op. cit., 57Google Scholar (17); Hilbert, and Ackermann, , op. cit., 8 (26)Google Scholar; Kleene, , op. cit., 116(30).Google Scholar

³ See above, p. 109.

⁴ op. cit., 74–7.

¹ Ingalls, 53–4, referring to BP, 8.Google Scholar

² Professor Brough suggested the possibility of the convertibility of A into B and vice versa in connexion with the formalizations of definitions I and II.

³ Ingalls, 75.

¹ Here we follow the commentary of Svāmī Mādhavānanda, 112, note.

¹ Pramāṇa-candrikā, ed. and trans. Maitra, S. K., Calcutta, 1936, 57, 144.Google Scholar

² Vedānta-paribhāṣā, 2.10.

³ cf. also Renou, L. JA, ccxxxiii, 1941–21942, 165.Google Scholar

⁴ See e.g. Dasgupta, S. N., A history of Indian philosophy, II, 222.Google Scholar

⁵ Nyāyakośa s.v. dravya. Substance is also guṇavat ‘possessing qualities’ (Vaiśeṣilea-sūtra, 1.1.15) and guṇa is dravyāśrayī ‘having substance as its locus’ (ibid., 16). But in Advaita brahmaṇo dravyatvāśiddhiḥ, ‘it has not been established that Brahman is a substance’ (Vedāntaparibhāṣā, 2.25).

⁶ cf. Renou, , TerminologieGoogle Scholar, avant-propos: ‘… il n'y a pas toujours interêt à dissocier (la valeur technique d'un mot) de la valeur “mondaine” (laukika)’.

¹ Adhikaraṇa (cf. German ‘Grund’), the kāraka-relation of the locative, may sometimes be used to elucidate what constitutes a reason. Cf. Hartmann, P.'s comment (Nominale Ausdrucks-formen im wissenschaftlichen Sanskrit, Heidelberg, 1955, 60Google Scholar, n. 79a), ‘dass unter der lokativischen Zuschreibung auch ein Verursachtsein mitgedacht werden kann’, based upon a remark by H. Oldenberg. This is already recognized in Patañjali's subdivision of adhikaraṇa into three kinds, the first of which is called vyāpaka (Renou, Terminologie, 301Google Scholar, and cf. Chakravarti, , op. cit., 251).Google Scholar

² Taittirīyopaniṣad, 2.4. I should like to express here my gratitude to Professor E. W. Beth (Amsterdam) for the interest he has taken in these investigations and for the valuable suggestions he has given.

³ op. cit. (p. 110, n. 1), 512.

¹ cf. the article quoted above, p. 115, n. 1.