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56: Śramana, Vol 62, No. 1 January-March 2011
must choose between a fixed form of the liberated jiva or the fixed size of the cosmic realm that they inhabit. It seems that the Jaina philosopher must make this choice of doctrinal interaction with the belief in beginningless past.
According to Jaina cosmology, the universe was never created and has existed for an infinite past. The Jains also maintain that that there are repeating periods of incline and decline that repeat their cycle for infinite time in the past and the future. Each period produces 48 Tirthankaras, 24 in the upward part of the cycle and 24 on the downward. Now if 48 Tīrthankaras are produced every time cycle and there are infinite time cycles, then there are infinite multiples of 48 Tirthankaras. Infinite multiples of 48 Tirthankaras yeilds an infinite number of Tirthankaras, each retaining the form of its last bodily incarnation. If there is an infinite number of Tirthankaras and each has a form then one would think that they would take up an infinite amount of space. No matter how small the form of each Tirthankara, so long as they are infinite in number, it would seem that they cannot be restricted to a determinate space regardless of how large the space may be. Thus it appears that jīvas either retain a form after liberation or the space that they occupy is not fixed.
There is, however, a problem with the above position. Ana Bajzelj has pointed out that the form of the liberated jīvas may overlap.28 This is a very keen insight to the problem, but requires some explanation. One might object that an infinite number of center points would produce an infinite special volume, but this is not the case. If the forms of the liberated jīvas overlap then they are, according to contemporary mathematics, able to occupy a fixed volume so long as their center points remained distinct from one another and the form of the largest jīva was the same size or smaller than the special volume in which it resides. In mathematical theories of infinity, there can be a fixed space with infinite points. Let us take a moment to properly understand this solution.
