Jain Journal 1990 07

Author(s): Jain Bhawan Publication
Publisher: Jain Bhawan Publication

Page 11

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kālāņu would mean actual physical infinity and hence provide a consistent cosmological picture. It could be that the Jains from cosmological viewpoint had physical notion of actual infinity (concepts of infinitesimal and infinite) but from mathematical viewpoint they did not have such a notion of asamkhyāta, that is, notion of it as a transfinite number.
It appears that the above pointed confusion regarding finitude or infinitude of asamkhyāta is deep rooted even from consideration of Jain mathematics. In the Jain typology of numbers given in Table 120 asamkhyāta and ananta are treated similarly as distinct from the class of asamkhyāta suggesting similarity of their meaning as opposed to asamkhyāta. Even relations between various kinds of asamkhyāta numbers and ananta numbers are similar as shown in Table I. Values of a and B have not been indicated in the table as there is a confusion regarding these values in different texts but no confusion as far as relation between various classes of number goes. The similarity in relations of asamkhyāta and ananta is significant.
Moreover, even in Dhavala where finitude of asamkhyāta is categorically stated, similarity of various meanings of these two classes of numbers is projected. Identical eleven-fold classification of various meanings of terms ananta and asamkhyāta is made in Dhavala. In Table 1121 we have outlined this division in a way that parallel between ananta and asamkhyāta is apparent. Most interesting, in the context of our discussions, is that among the eleven kinds of meanings in Table II are apradeśikānanta and apradeśikāsamkhyāta. Apradesikānanta refers to one paramāņu of pudgala (material indivisible monad)22 and apradeśikāsamkhyāta refers to one pradeśa of a soul.23 Apradesi, an infinitesimal space less element, becomes extension of a material monad in the context of infinite (ananta) materiality and becomes one pradeśa of soul in the context of asamkhyāta pradesi soul. A conglomerate of infinite material monad (paramāņu)
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20 This Table is constructed from Anuyogadvara sutra [(a) sutra 497-518, and (b) p 644-684]. Classification of numbers in Dhavala [III 18, 126] has also been kept in mind while constructing this Table. For example Anuyogadvara sutra does not regard utkrsta anantananta as a number but Dhavala regards it as a number. 21 Table II is constructed out of Dhavala vol III. Numbers in square bracket indicate
22
23
page number of Vol III of Dhavala from where the information or quota is drawn. Dhavala [III, p 15]/jam tam apadesiyanantam tam paramanu/'one paramanu (material monad) is called apradesikananta (infinitiesimally spaceless)'. Dhavala [III, p 124]/jam tam apadesasamkhejjayam tam jogavibhaga paliccheda paducca ego jivapadeso/. 'in accordance with indivisible element by yoga, soul's one pradesa (region) is apradesasamkhyata (innumerably spaceless).