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infinities were defined and the mathematical infinity was elaborated in detail. The important observation is that all types of mathematical and non-mathematical sets were to be treated only through the set of integers or natural numbers alone.
An important treatment of the infinities in the Trilokasara2, deserving special attention of the historians of mathematics, is about the fourteen divergent sequences which help to locate (topologically) finite and transfinite sets of various types of objects needed for the exposition of the Karma (action) theory. This records a means of the topological studies comparable to that adopted by Georg Cantor, and those which are indispensable in mathematical sciences. Apart from this, one also gets introduced to the several types of postulated fluents, their properties, and enumeration of their events and interactions through various types of units coglomerated as the fluent sets, the space-point sets, the time-instant sets, and the phase sets. The abstract three mathematical universes accomodate many types of universes of the bios and matter. Thus a philosophical unified universe is introduced mathematically to include all natural phenomena of the astral, human, and the sub-human universes3.
3. THE SET THEORETIC DEVELOPMENT
For the treatment of any unified system theory, one needs a set-theoretic approach which has gained an unparalleled support of the modern methodology in the development of technology and theoretical as well as practical sciences. About two and a half thousand years ago, this necessity was realized in India in the Jaina School and sufficient material is now available in the Satkhaṇḍāgama, Dhavala, Jayadhavala Gommatasara, Labdhisara, and their detailed commentaries wherein only the set-theoretic material could be traced with mathematical and logical treatment. They give out the secrets of their approaches which may be precisely exposed here as follows:
(A) The basic word for set is 'RASI', akin to Latin, 'RATIO' meaning reason; the Greek equivalent being, 'horos' (LOGOS), meaning a 'word' and also the 'mind' behind a word. Satkhaṇḍāgama exposes its synonym in samûha, ogha, puñja, vṛnda, sampāta, samudaya, pinda, avaśeşa, abhinna and sāmānya. Virasena has made use of the rasi practically in every mathematical sentence. Cosmological sets are related in the Tiloyapanpatti and the Trilokasära, whereas philosophical sets are found based in the Satkhandagama texts. In the book three of the Dhavala, the sets of souls in various control and rummage stations are exposed through their measures in fluent, quarter, time and phase. They find symbolic expressions in the commentaries of the Gommatasära Jivakända. All types of sets of ultimate particles and their relations among themselves and those with the soul in Karmic bonds are depicted in various details in the Mahabandha and Gommaṭasara Karmakaṇḍa texts and the symbolic treatment in the commentaries." These also include statistical details, forming the steel framework of the bios-machine systems described in system-theoretic details in other texts.
1.
Cf. ibid.
2.
Cf. 1 (r).
3. (a) Vid. Tiloyapanpatti of Yativṛṣabha, Pt. I (1943), Pt. II (1951), Sholapur. (b) Trilokasära of Nemicandra, Sri Mahaviraji (1976). (c) Vid. also other texts on Karanänuyoga Group.
4. (a) Satkhaṇḍāgama of Puspadanta and Bhutabali, ed. Shaha Sumati Bai, Phaltan (1965). (b) Vid.
also Satkhaṇḍagama, alongwith Dhavala commentaries by Virasena, books 1-16, Amaraoti and Vidisha, 1939-1959. (c) Vid. also Gommaṭasara, alongwith Jivatattva Pradipika and Samyakjñānacandrikā commentaries ed. by G. L. Jain and S. L. Jain, Calcutta, (c. 1919); (i) Jivakäṇḍa, pp. 329, (ii) Karmakaṇḍa, pp. 1200 (d) Mahabandha by Bhútabali, books 1-7, Kashi, 1947-1958. Vid. Arthasamdrsti chapter on Gommaṭasära Jivakāṇḍa and Karmakaṇḍa in 308 pages, (12c). op. cit.
आचार्य रत्न श्री देशभूषण जी महाराज अभिनन्दन पन्न
5.
५२
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