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Glory of Jain Culture
points of view, a single proposition about its state marred the prospects of its description in various aspects in the old philosophies. But the Jaina philosophy was free from this mono-ended pursuit and it followed the poly-endedness. This led it 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, through the word "syat" in the course of the parikarmastaka not only among the finitie sets but also for the innumerate and infinite sets of various comparabilities. Today the problem of the compara bills still unsolved in the modern set theory infinities of various types. In the Jaina set theory there are not only the constant sets but also the variable sets scaling the infinites of the Karma theory through constructions and other analytical methods. The various types of units, measures and calculations between them were needed of their Karma system and cybernetics which was an aggregate of various subsystems and groups of operations to annihilate the Karma state matrix. Thus the School had its own formalism of symbolism and its symbolic logic applied in the Karma theory became mathematics as in terms of Russell. 2. THE INNUMERATE IN THE JAINA SET THEORY: A PHILOSOPHICAL SUBSYSTEM
The Cantor's theory of sets, faced the contradictions, antinomies, and the
inconsistencies as any theory has to face for its survival. His sets included the infinite sets, not of the philosophies, but of proper characteristics that could prove that a set though infinite could be greater than another set and also could be constructed through the principle of generalized induction. Comparability between infinite sets arose a new arena of research, beyond the old philosophical domain in which there was no place to compare infinities as in old mathematical improper infinities for their smallness of greatness. With such a new prospect of the infinities, the Jaina Karma philosophy took a start. Through the various sequences ranging from the unity to the supermum set of omniscience (Kevala Jnana), the Jainas located the terms of various types of sets involved in the calculations of annihilation of the Karma perpetual cycle of births and deaths. They filled up the gaps between such types of sets which had the number of members as numerate, the innumerate and the infinite.
Thus the Jaina School took a positivistic approach in introducing the innumerate and the infinite. They were meant to explain the endless processes from ab aeterno to ad infinitum, the relations between various sets involved in the realities of life of various types. They had to find, mathematically, a path to perpetual immortality in which there was neither births, rebirths and the agonies of the old age, perpetual and endless bliss, infinite power and knowledge. They
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Mathematical Philosophy in the Jaina School of Thought
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