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JAIN JOURNAL
infinite moments as was entire space constituted of infinite space points. Large part of Jain cosmology deals with finite determinations of these various infinites, innumerables, infinitesimal and innumerableth quantities and their relations. Fascinating aspects of Jain thought is the theory of number evolved for the purpose. Notion of transfinite number, detailed consistent hierarchy of transfinities and valid operations on them were developed. 4 However there exists confusion on genesis and content of various facets of this theory of number. What exactly necessitated three-fold classification of numbers into samkhyāta (numerable), asamkhyāta (innumerable), and ananta (infinite) and their further classification into 3-fold, 6-fold, 9-fold, sub-classes respectively ? Were āsamkhyāta-ś and ananta-s really understood as transfinite numbers or as large finite numbers ? How exactly hierarchy of these numbers and valid operations on them were evolved ? Whether this theory had internal consistency ? What were major turning points and issues of debates within this theory ?
These are some of the questions being dealt in this paper. Particular issues of confusion are identified and resolved and logical genesis of Jain theory of number is recreated. It is our contention that proper understanding of content of Jain transfinite number theory is possible only in the wider context of Jain thought, in particular Jain ontology and what we have called elsewhere Jain theory of measurement. Jain theory of measurement dealt with physical actual infinity' and mathematical determination of hierarchy of these actual infinities was sought though there remained a discord between notion of physical actual infinity and transfinite numbers. A confusion in Jain texts regarding infinitude of term asamkhyata is due to this discord. In the first section of the paper an attempt has been made to demonstrate that asamkhyāta and ananta were transfinite numbers. Good deal of Jain transfinite number theory is also outlined in this section. In section two attempt is made to understand theory of hierarchy of actual infinites and theory of transfinite number on the foundation of theory of measurement with a view to understand exact content and gensis of Jain theory of transfinite numbers.
• Such an attempt stands out as unique in Indian tradition and perhaps in the whole
world before late 19th century. Nothing more than that 'all infinities are equal' could be said even by numerous approaches which regarded Universe as infinite or God as infinite. Jain theory of transfinites is outlined in pioneering work of A.N. Singh (1942) "Mathematics of Dhavala" in ppi-xxi in Satkhandagama and its commentary Dhavala, vol IV, Ksetra-sparsana-kalanugame.
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