Jain Journal 1990 10

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

Page 42

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The Jains considered dravya-s to be of two kinds from the point of view of infinitesimals: (a) Those whose elements are rigidly bound to make just one bounded whole. Their oneness can not be broken physically though conceptually they contain infinite elements. These are dharmastikāya and adharmastikāya coextensive with and having this property in common with lokākāśa. And (b) those whose elements are not rigidly bound and admit of unending multitude compared to (a) kind of dravya-s. These are rest of the four dravya-s. This is an important distinction as it is very significant for the distinction of asamkhyāta and ananta kind of mathematical actual infinities or transfinite numbers. The infinite elements of each dravya-s are of two kinds from a mathematical view point because of abovementioned distinction. Infinite elements of rigidly bounded dravya-s were called by Jains asamkhyāta bhāga (innumerableth elements) and infinite elements of loosely bounded dravya-s were called ananta bhāga. Both kind of elements were indivisible, only difference being that elements of first constitute actual infinity of lower cardinality than the elements of second. Asamkhyāta class of numbers have lower cardinality than ananta class of numbers. The elements of dharmästikäya, adharmāstikāya and lokākāśa were space points (pradeśa), that of jivāstikāya were souls, that of pudgalāstikāya were material monads (paramāņu), that of kāla dravya were moments (samaya), and that of ākāśa were space points (pradeśa). Actual infinity of dharma, adharma and lokākāśa have asamkhyāta space-points,61 that of jivāstikāya have ananta souls that of pudgala have ananta material monads, that of kala have ananta moments, that of ākāśa have ananta space points. According to Jains one soul has an spatial extension because of its astikāya nature and it is a rigidly bounded entity unbreakable into parts. Thus each soul had spatial extension of asamkhyāta space-points. 62 In Table IV we have outlined elements and hierarchy of actual infinities of ontologically important entities.
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60 Dhavala [III, p. 29, gatha 9]/dhammadhammagasa tinni vi tullani honli thovani; vaddhidu jivapoggalakalagasa anantagana/"dharma dravya, adharma dravya and cosmic space, these three are same and rigid; and jiva dravya, pudgala dravya, moments of time, space points at akasa, these due to more and more increase are infinite times".
61 Tatvarthasutra [5.7 and 5.13].
Pravacanasara [2.48] says that one space point, space occupied by a material monad, is capable of giving room to monads of all entities.
62 Tatvarthasutra [5.8].