Mathematical Philosophy in Jaina Thought

Summary

This article explores the deep integration of mathematical thinking within Jain philosophy, particularly through the framework of Karma theory and the Jaina set theory (rāśi siddhānta). It draws a parallel between Western mathematical philosophy—developed by figures like Russell and Cantor—and the logical, symbolic, and metaphysical treatment of numbers and infinities in Jainism. Key points include: i) Jaina thinkers addressed infinity, the innumerate, and logical paradoxes long before modern set theory. ii) They developed their own symbolic and logical systems using the principle of syādvāda (relativity of truth), enabling the treatment of finite, innumerate, and infinite sets in Karma metaphysics. iii) Texts such as the Dhavalā, Trilokasāra, and Tiloyapaṇṇatti provided precise mathematical frameworks for modeling cosmic structures and karmic particles. iv) The concept of indivisible units of space (pradeśa) and time (samaya) allowed Jain philosophy to tackle paradoxes similar to Zeno’s and Russell’s, resolving them through a logic rooted in experience and symbolic abstraction. v) Jain mathematics avoids contradictions like Russell’s paradox by defining sets (e.g., omniscient beings) with real existential limits.