Jaina Ulterior Motive of Mathematical Philosophy

Author(s): L C Jain, C K Jain
Publisher: Z_Deshbhushanji_Maharaj_Abhinandan_Granth_012045.pdf

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The use of the word "ARTHA SAMDRSTI" shows that it meant the introduction of symbolic norm and not the symbolic logic. The sombolic norm then paved the way to post-universal mathematics due to introduction of the relations in all perspectives. Logic brings forth contradictions, whereas the norms introduced by Syadvāda removes them, extending the symbolic logic to symbolic norms, or mathematics to extended post-universal (lokottara) mathematics of measures and norms. According to Godel, in any system broad enough to contain all the formulas of a formalized elementary number theory, there exist theorems (formulas) that can neither be proved nor disproved within the system. Syadvada system allows such a situation in the karma system where assertorial and non-assertorial phenomena occur in nature. For example, a free soul or a free particle could travel a distance of fourteen rājus within an indivisible instant, implying its existence in a stretch of fourteen räjus within the indivisible instant--a paradoxical situation.'
In addition to the above, Mahalanobis found in Syādvāda a close relevance to the concepts of probability, and the phrases used in Syādvāda to have a special significance in relation to the logic of statistical inference. Syāt' means relative, 'Vada' means assertion. The seven predicates may be described as follows : 1. Relatively, it is ; 2. Relatively, it is not ; 3. Relatively, it is and it is not ; 4. Relatively, it is non-assertorial ; 5. Relatively, it is and yet is non-assertorial; 6. Relatively, it is and it is not as well as it is non-assertorial. The above form the dialectic of seven-fold predications, save that the word 'is' above may be replaced by 'is existent'. The word 'non-assertorial' has been used by other authors as indeterminate, indescribable, inexpressible and indefinite. The situation is comparable also to the propositional and nonpropositional statements of Russell
The above seven universes are necessary and sufficient to exhaust the possibilities of all knowledge in forms of norms of measures (pramåna) and schema (naya) and many-ended-ness (anekānta) of a variable object. According to Mahalanobis, the fourth category, being a synthesis of three basic modes, the third denoting inexpressibility, indefiniteness or indeterminateness, supplies the logical foundations of the modern concept of probability. But the fact, that the positivity of the statement leads to statistics and not to probability, has urged many scholars to deny the inclusion of the probabilistic situation asserted by Mahalanobis.
The methodology of the Syä dväda system seems to have motivated the trend of symbolization of the relational semantic material of Karma theory, and after Virasena, imperfect attempts may be traced in the later commentaries.
The system theoretic approach demands causality in practical schema, whereas the determiniastic schema in Jainology may be put up in words of Satkari Mookerjee, and may be said to have an important hearing on modern scientific attitude, "..... ... neither synchronism nor succession is believed by the Jaina to be essential characteristic of causal relation. Causality is a relation of determination. The effect is that whose coming into being is necessarily determined by the being of another. The determinant is called the cause and the determinatum is called the effect. The determinant may be synchronous with the determined or may be separated by an interval ..." He further states, "What is the organ of the knowledge of
1. (a) Nyāyāvatāra of Siddhasena Divākara (C. 480-550 A. D.).
(b) Apta Mimänasā of Samantabhadra (c. 600 A. D.). (c) Syädväda Mañjari of Mallisena (1292 A. D.). (d) For a comprehensive bibliography, cf. Jaina, H. L., Bharatiya Samskrti men Jaina Dharma Kā
Yogadana, Bhopal, 1962. 2. Cf. 12 (c), and 27. op cit. 3. Mookerjee, S., The Jaina Philosophy of Non-Absolutism, Calcutta, 1944, p. 190.
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आचार्यरत्न श्री देशभूषण जी महाराज अभिनन्दन ग्रन्थ