The term lak.san, a in Sanskrit has been used in many senses, 1 but in logical treatises it mainly stands for "definition". The general problem of "definition" as it is found in Sanskrit philosophical texts has been studied by many scholars. 2 Mlle. Biardeau has skillfully handled the question emphasizing the Nygya and the Vedfintic traditionsa; and quite recently J. F. Staal has attempted a "formalisation of the theory of definition" in Navya-Nyfiya 4 with the help of the notations of Boolean algebra. 5 In his concluding remark, Prof. Staal notes that unlike a large number of cases in Indian logic the doctrines of lak.satza and sarhkara "show a marked extensional character". 6 The purpose of the present paper is to examine the problems of lak.san, a and sathkara in some detail in order to * I wish to express my gratitude to Professor Daniel H. H. Ingalls for the many remarks and suggestions which have been instrumental in shaping this paper. I also thank my friend J. Masson for his helpful remarks on points of style. 1 In the grammatical tradition, for instance, lak.sa.na stands for sf~tra or grammatical rules, and lak~ya stands for words. (Cf. Mahabha.sya, Paspag~ttmika, Varttika 14).
J. F. Staal has discussed this in his paper "The Theory of Definition in Indian Logic," JAOS, 33 (1961), pp. 122-6. One remark may be added to his discussion. The scheme for a samj~a satra of Pa.nini roughly corresponds to the notion of "nominal or syntactical definition" of the modern formal logicians. Such definitions are explained as "conventions which provide that certain symbols or expressions shah stand (as substitutes or abbreviations) for particular formulas of the system". They "may be theoretically dispensed with and all formulas written in full." See Alonzo Church, Dictionary of Philosophy, (D. D. Runes) (New York), p. 74-5.
See A. B. Keith, lndian Logic and Atomism, pp. 153-4, S. Radhakrishnan, Indian Philosophy, II, p. 47, A. Foucher, La Compendium des topiques, pp. 7-14, & D. H. H. Ingalls, Materials for the study of Navya-Nyftya Logic (to be abbreviated as MN), t951, pp. 80-1.
8 See her "La d6finition dans la pens6e indienne", JA, 1957, pp. 371-84. 4 Navya-Nyfiya is usually considered to have begun with Gafige~a, whose date is now usually placed in the 14th century A.D. See D. C. Bhattacharyya, Bange Navya-Nyaya Carca (Calcutta, 1952). 5 J.F. Staal, op. cit., p. 126. 6 He also refers to I. M. Bochefiski, who holds that Indian logic is intensional and thus differs from Western logic which is more or less extensional in character.