Jain Journal 1990 07

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

Page 20

JULY, 1990
(d) Derived out of subtraction :
Only two singular quantities us and uAA are derived by subtracting--one from jpA and jpa respectively. This case has been dealt above.
First two classes of operations seem to be justified from the viewpoint of transfinite number theory. But the last two classes of operations are quite different as they deal purely with operation on physical actual infinities whose quantity are not indicated in terms of any ordinals (a, B etc.). A unified picture of Jain concern with transfinite numbers and physical actual infinities can only be constructed if unified view of Jain physical and mathematical concern is taken. This unified view is possible on the basis of principal concern of the Jains ordering actual infinities. Motivation behind drive for ordering actual infinities stems for a unique Jain theory of measurement which forms a subject-matter of the next section.
It has been demonstrated in this section that asamkhyāta and ananta were used in the sense of transfinite numbers in Jain literature though there existed an apparent confusion regarding transfinitude of asamkhyāta. But why did Jains expound two categories of transfinite numbers, viz., asamkhyāta and ananta ? Why was not one category with different internal orders adopted by Jain theoreticians ? The reason for this lies in the Jain theory of measurement which in fact provided a basic thrust for Jain concern about transfinite numbers and actual infinities and their mutual ordering. Besides reason for confusion regarding asamkhyāta can also be illuminated from the investigation of theory of measurement.
[To be concluded]