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mathematical pursuits, before the development of symbolic expressions, at the time when sentenial and syncopated expressions found their place in texts as well as in lectures1. The works of Yativṛṣabha and Virasena are testimony to this. According to Yativṛṣabha, the suborder of third prabhṛta of the tenth vastu, in the fifth purva, called Jñana Pravada, is of five types: anupūrvi, nāma, pramāņa, vaktavyatā, and arthadhikara. Vaktavyata (assertoriality)-sub-order is of three types: svasamaya, parasamaya, and tadubhaya2. A quotation by Virasena asserts, 'Relative to controls and events, that fluent is one without leaving its various-own-forms and positively it is many, relative to its own controls and events, without leaving its one-ness. Thus, O, Jaina, the object in infinite forms is stated in sentences, in order, through part acceptance phases. He further exlains, 'Relative to dravyarthika naya, there is one-ness in one and many. Relative to paryāyārthika naya, from an arbitrary 'one' number, the remaining 'one' numbers are different, therefore there is many-ness in them. Relative to naigama naya, the dvitva (duality) etc., phase comes into being, which leads to acceptance of number-division." In this style Virasena puts up the doubt, "The past time is ab-aeterno, how can its measure be established ?" The explanation is, No, because, if its measure is not recognized, its non-existence will be infered. But the knowledge of its being ab-aeterno happens to be, hence it will be having beginning, and as this is also not so, because there is contradiction in such a recognition."
Further the mathematical import of the following logic for fineness decision is worthy of attention. Virasena mentions, "Many preceptors state that it is fine, that which is accumulation of many points. It has also been stated-Time measure is fine, and quarter measure is finer, because in an innumerable part of a finger, there are innumerable kalpas. But this assertion is not eventuated, because on such a recognition, fluent description will follow the quarter description. Doubt: How is this? Explanation: Because, in a fluent finger, composed of infinite point-like ultimate particles, relative to embedding, there is only one quarter finger, but relative to counting, there are infinite quarter fingers. Hence quarter is fine and fluent is finer, because there are infinite quarter-fingers in a fluent finger."
Thus Syādvada appears to show relational universes and not the probable universes. Due to relation, an object may be small or great, or both, or a combinatorial situation of all these. As a theory of relations Syādvada is also a theory of dynamic and static functional structures with constructibility, consistency, and completeness. It was beyond Boole's logic and Russell's symbolic logic. It formed a complete system of universes of assertions negations and unassertoriality. This formed a landmark in the logical foundations of the 'post-universal' mathematics, providing mathematical properties of one-ness and manyness as well as intermediary-ness to the object. For example: logarithm of two to the base two was given as one, that of four as two, and that of three was regarded as unassertorial for it had a value in between one and two, although it was not needed to be calculated in approximation the school dealt with.
(c) Mehta, M. L., Psychological Analysis of Jaina Karma Philosophy, Thesis, B. H. U., Amritsara (1954).
(d) Kothari, D. S., Reality and Physics: Some Aspects, Jour. of Phys. Edn., 8.2, Jan. 1978, pp. 1-6. (e) Barlingay, S. S., A Modern Introduction to Indian Logic, New Delhi, (1976), pp. 4, 5, 6-7, 9, 62, 72, 73, 88.
(f) Muni Nathmal, Jaina Nyaya Ka Vikäsa, Raj. Univ., Jaipur, 1977. For bibliography, vid. pp. 175-179.
1.
Cf. 1 (s), op. cit.
2.
Cf. 26 (b) op. cit.
3.
Cf. 12 (b), Book 3, p. 6, v. 5.
4.
Cf. ibid, p. 30.
6. Cf. ibid, pp. 27-28.
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