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untruth. The parallel to this is the concept of syadvada in the Jaina philosophy. Thus the status of an object being relative to different points of view, a single proposition about its state marred the prospects of its description in various aspects in the old philosophies.
The Jaina philosophy, however, was free from this mono-ended pursuit and it followed a poly-endedness. This led to the existential and constructive spheres of the innumerate and the infinities in a proper and simple way through its set theory (rasi siddhanta). The secret of the mathematical philosophy in the Jaina School thus lay in their attempt to give a new shape to the expressions in logic and intuition. This was achieved with the word "syatin the course of the parikarmastaka, and not only among the finite sets, but, also for the innumerate and infinite sets of various comparabilities.
Today the problem of the comparability is still unsolved in the modern set theory of infinities of various types. In the Jaina set theory there are not only the constant sets but also the variable sets scaling the infinities of Jaina Karma theory through constructions and other analytical methods. The various types of units, measures and calculations between them were needed in their Karma system and cybernetics which was an aggregate of various sub-systems and groups of operations to annihilate the Karma state matrix. Therefore, the School had its own formalised symbolism and symbolic logic, that much like Russell later, became a Karma theory via mathematics.
The Innumerate in Jaina Set Theory: A Philosophical Sub-System
Cantor's theory of sets, had to face the contradictions, antinomies, and inconsistencies as any theory has to face for its survival. His sets included, not of the philosophies, but of proper characteristics that could prove that a set, though infinite, could be greater than another set, as well as that it could be constructed thorough the principle generalised induction. Comparability between infinite set began a new arena of research that went beyond the old philosophical domain in which there was no place to compare infinities (e.g., improper mathematical infinities for their smallness or greatness).
With such a new prospect of the infinities, the Jaina Karma philosophy took a new form. Through various sequences ranging from unity to the supreme sets of omniscience (kevala jnana), the Jainas located the terms of various types of sets involved in the calculations of annihilation of the perpetual karmic cycle of births and deaths. They filled the gaps between such sets as those which had the number of members as numerate, innumerate, and infinite.
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