Jain Journal 1990 07

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

Page 16

JULY, 1990
From Table I and Table III values of Band 2 and hence all other values can be derived out of a and some asamkhyāta dravya-s and ananta räsi-s. Value of a is not evident from these Tables and it is on this value that issue of finitude or infinitude hinges.27 Is a a transfinite number? If it is transfinite then all asamkhyāta and ananta numbers are transfinites and Jains have a theory of transfinite members. If, on the other hand, a is finite than from jpA till jAA are certainly finite. If innumerable space points of 6 dravyas and innumerable quantity of 4 aggregates is consi
nite than even B would be finite. Hence jpa to jaa would be finite. This had been noticed by a veteran scholar A. N. Singh.28 As Dhavala categorically states that ananta is a transfinite number it would mean that maa and uaa are the only transfinites as 6 physical ananta quantities are added to obtain them.
We notice here that for obtaining various classes and subclasses of numbers two kinds of quantities are used by Jains, (1) Mathematical quantities as jAA=Q2x, where «=jpA etc., and (2) physical quantities, such as 6 dravya-s, 6 rāśi-s etc. From cosmological arguments outlined earlier we know for certain that physical quantities are actual inifinites and hence there number has to be a transfinite number. We do not see any reason to accept A. N. Singh's argument that ananta pradeśa of pudgala or ananta pradeśa of alokākāśa are transfinite numbers but asamkhyāta pradeśa of lokākāśa or asamkhyāta pradeśa of a soul are not transfinites. This has been argued purely from a cosmological viewpoint. By accepting this cosmological viewpoint of physical actual infinities in MAA, JPA (=B) and higher up in the hierarchy of numbers become transfinite. From cosmology argument again, it can be said that even jaghanyayuktasamkhyāta (juA) is also a transfinite number as it is equated by Jain theoreticians with avali (minimum numerable unit of time).29 One āvali is a physical actual infinity constituted out of asamkhyāta infinitesimal instants of time or kālanu30 and in this sense number of avali has to be a transfinite number. Hence juA=« Oc is a transfinite
37 A complicated determination procedure for value of a is given in Anuyogadvara
sutra (sutra 508 or pp 650-664). A different procedure can be found in Trilokasara of Nemicandra. Value of a in Anuyogadvara sutra is given by using method of simili and it leaves indeterminates whether a is finite or infinite. Nemicandra is clear on finitude of a.
A. N. Singh (1942). 29 Anuyogadvara sutra (sutra 511 or p 662]/avaliyavi tattiya ceva/'avali (unit of
time) is that (jaghanyayuktasamkhyata). Anuyogadvara sutra (sutra 367 or p 247]/asamkhiijanam samayanam samudayasa mitisamagamenam sa ega avali attivuccai/'one avali is formed out of collection of innumerable time instants'.