श्री वीरसेनाचार्य (आधुनिक न्यायशास्त्र के संदर्भ में )
By प्रोफेसर एल.सी. जैन, कु. प्रभा जैन
Summary
The text discusses the contributions of Śrī Vīrasenācārya, a 9th-century Jain scholar who authored the Dhavalā and Jayadhavalā commentaries on the Digambara Jain āgamic texts, Ṣaṭkhaṇḍāgama and Kaṣāya Prābhṛta. His work involved presenting the original material in an unprecedented manner, incorporating mathematical perspectives and numerical logic. The mathematical and logical aspects are further elaborated in later commentaries by Nemicandra Siddhāntacakravartī, such as the Gommaṭasāra. The text highlights that these Jain works use mathematics to explain karmic theory, employing analysis, synthesis, set theory, and atomic theory. It compares this to modern scientific theories like relativity and quantum theory, and specifically to Georg Cantor's set theory, which faced criticism from Bertrand Russell due to paradoxes like the barber paradox. The text explains Russell's paradox using symbolic logic, showing how Cantor's axiom of abstraction leads to contradictions. It then poses questions about infinite sets, cardinality, and the validity of Jain mathematical methods. The text returns to Vīrasenācārya's logical style, emphasizing his use of āgamic authority and rigorous reasoning to define concepts like śāśvatānanta (eternal infinite) and apradeśānanta (partless infinite). It provides examples of his logical arguments, such as the discussion of mithyādṛṣṭi (false-believer) souls and their relation to infinite time cycles, and the use of mathematical operations like multiplication and division in the context of infinite quantities. The text concludes by noting that many of these mathematical and logical insights remain embedded in later commentaries and require further study.
Conclusion
The document reveals that Śrī Vīrasenācārya’s 9th-century mathematical logic, embedded in the Dhavalā and Jayadhavalā commentaries, anticipated modern set theory by defining infinite, numerable, and non-numerable quantities with rigorous axioms. His work, using Kannada script and Prakrit, systematically applied operations like multiplication and division to infinite sets, avoiding the self-referential paradoxes that later plagued Cantor’s set theory, as exposed by Russell. This suggests that Jain logic offers a pre-emptive resolution to foundational crises in modern mathematics, particularly through its concept of “ananta” (infinite) with bounded, non-contradictory definitions. The implications are profound: Vīrasenācārya’s framework provides a viable alternative for axiomatic set theory, potentially resolving issues like the well-ordering theorem and cardinality comparisons. However, much of this knowledge remains embedded in unpublished commentaries, requiring urgent