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The Jaina School of Mathematical Philosophy
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Prof. L.C. Jain
1. Introduction
It is due to the credit of Bertrand Russell that a new field of research in Mathematical Philosophy got originated with the publication of his work, "Introduction to Mathematical Philosophy" in 1969, after the dilemma of paradoxes and antinomies in the Contor's theory of sets. His remark is marvellous, opening, a vista in the, philosophical studies, "Early Greek geometers, passing from the empirical rules of Egyptian land-surveying to the general propositions by which those rules were found to be justifiable and thence to Euclid's axioms and postulates, were engaged in mathematical philosophy according to the above definitions but when once the axioms and postulates had been reached, their deductive employment, as we find it in Euclid, belonged to mathematic in the ordinary sense." In this way the studies in mathematical philosophy and those in philosophy of mathematics are distinguished, the former being somewhere in the middle, after a certain stage of development in the axiomatics, before deduction therefrom gain impetus.
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First of all we are attracted towards the mathematical methods pursued and adopted, both in Greece and India, round about the Christian era. Geometry is intuitionistic whereas algebras and arithmetic are logical, and both enrich the various fields of knowledge, extending them beyond the finite and the limited. The Pythagoreans held, "Then my noble friend, geometry will draw the soul towards the truth and create the spirit of philosophy, and raise up that which is now, unhappily, allowed to fall down"2, Plutorch remarked "Plato said that God geometrizes continurally." Plato forbade, "Let no one ignorant of geometry enter my door." Newton felt that geometry is founded in mechanical practise and is a
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