Jain Journal 1990 10

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

Page 43

OCTOBER, 1990
Hierarchy of Global Actual Infinities in Increasing Order of Cardinality
Dharmastikāya Adharmästikäya Lokākāśa
Eka Jiva
Jivāstikāya Pudgalāstikaya
Kāla dravya Alokākāśa
Akāsāstikāya
TABLE IV
(asamkhyāta space-points) (asamkhyāta space-points) (asamkhyāta space-points) (asamkhyāta space-points) (ananta souls)
(ananta material monads) (ananta time instant) (ananta space-point) (ananta space-point)
Cardinality of Asamkhyāta
number
Cardinality of Ananta number
In essence all these dravya-s are representable in three kinds of infinitesimals. These are pradeśa (space-point), samaya (time instant), and paramāņu (material monad). 63 On the basis of these three infinitesimals infinite paryaya-s in each dravya-s is measurable. In fact all actual infinites are evaluated on the basis of these three infinitesimals by the Jain theoreticians. These three infinitesimals provided analytical link between dravya and paryaya aspect of reality. They provided foundations of novel Jain theory of measurement. Unlike modern transfinite number theory due to Cantor the Jaina continum had three kinds of infinitesimals and not one.
83
Pradeśa, paramāņu and samaya are uniquely related to each other according to Jains. Pradeśa was size of space occupied by one paramāņu and samaya was time taken for a paramāņu to transverse from one pradeśa to another.65 Based of these three infinitesimals and the unique relation between them Jains developed standard of measurement of paryaya-s, of all entities in the world.
According to Jaina thought only paryaya aspect of reality was subject to measurement and no dravya aspect of reality. That is, only
63 Sthanangasutra [3.328] / tao acchejja pannatta, sam jahasamae, padese, paramanu/ 'three unpiercables are said to be samaya (moment), pradesa (space point) and paramanu (material monad)'. These three are also called, according to Sthanangasutra [3.329-335], adhijja (divisionless), adajjha (indestructible), agijjha (unconsumable), anaddha (unhalfable), amajjha (middleless) and apaesa (spatial extensionless). 64 Pravacanasara [2.45 and 4.8].
65 Pravacanasara [2.47].