Jain Journal 1990 07

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

Page 14

JULY, 1990
constitutes an object for the senses and infinite pradeśa of a soul constitates a "cognisable by senses' entity jiva or soul. In this sense both, a material object as well as soul are actual infinites as far as their spatial extension is concerned and hence both ananta and asamkhyāta denote idea of actual infinity. It needs to be noted from Table II that out of eleven fold classification only one, that is, gananā, is open to numeration and to possible meaning of mathematical actual infinity or transfinite numbers.
The similarity between asamkhyāta and ananta, as is evident from Dhavala, is much more detailed and intricate.24 Three more similarities, other than the one noted in Table I, are layed out in Table II. It is said in Dhavalā that out of elevenfold delineation of meanings of these two terms it is only gananānanta and garaṇasamkhyāta which are to be found layed out in structure of reality. Identical nine-fold division for gananananta (mathematical infinity) as well as gananasamkhyāta (mathematical innumerability) as given in Table I is to be found in Dhavala (III, p18) and Dhavala (III, p126) respectively. It is also said in Dhavala (III, pp18-19 and III, pp 126-127) that plural ananta refers to anantananta and plural asamkhyāta refers to asamkhyātasamkhyāta. Further it is said in Dhavalā (III, p19 and p127) that anantānanta refers to madhyamānantānanta (maa) and asamkhyātāsamkhyāta refers to madhyamāsamkhyātāsamkhyāta (mAA). maa is a measure of number of mithyādrsti jiya and mAA is a measure of number of mithyadrsti jiva in hell.25 Further similarity can be seen in the actual calculations of values of maa and mAA. These calculations as given in Dhavala are displayed in Table 11126 in such a way that parallelism is obvious.
The parallelism between ananta and asamkhyāta is all pervasive. It is involved in classification of various shades of meanings these two terms can have, in detailed typology of mathematical meaning of these two terms, and in actual mathematical relation of identical subdivisions of these two classes of numbers. Parallelism itself can not be a convincing argument for considering asamkhyāta and ananta as transfinite numbers or mathematical actual infinity and hence also calculation of values of various asamkhyāta and ananta as theory of transfinite numbers. A more detailed investigation of actual values of a, B & 2 can throw more light on the issue under consideration.
24 25 26
Dhavala (III, p 26] Ibid., p 129 This Table is constructed from Dhavala (III, pp 19-26] for ananta and from Dhavala (III, pp 127-129] for asamkhyata.