Perspective of System‑Theoretic Technique in Jaina School of Mathematics between 1400–1800 A.D.
Summary
The article reviews the evolution of a distinctive system-theoretic methodology within the Jaina school of mathematics between the fifteenth and eighteenth centuries. Drawing on commentarial literature such as the Dhavala, Kaṣāya‑pāhuḍa and Labdhisāra, L.C. Jain explains how medieval scholars such as Nemicandra and the eighteenth‑century polymath Todaramal formulated a symbolic language to describe complex karmic processes. Their models were based on set‑theoretic principles: entities like jīva (living souls) and pudgala (material aggregates) are treated as elements in a universe of discourse, and operations like subsistence, rise, decay and annihilation are mapped as transitions between states. The paper shows how these early analysts decomposed dynamic processes into input, state and output variables; defined observables and non‑observables; and used diagrams to express reachability and feedback. Jain situates the material against the broader Sauraseni Jaina scriptural corpus, noting, for example, that the Kaṣāya‑pāhuḍa Sutta influenced later system‑theoretic commentaries. He also surveys contributions of Dhundhari and Sanskrit commentators who translated and extended these ideas. Throughout, the article emphasises that the Jaina concept of karma provided a philosophical foundation for modelling interaction between bios and matter: the bondage of the soul by karma is treated as a system whose behaviour can be controlled through spiritual practices. By reformulating ancient doctrinal concepts in terms of modern systems theory, the paper highlights the sophistication of medieval Indian intellectual traditions and argues that they anticipated many features of contemporary control theory, including notions of automation and simultaneous processes. The extensive footnotes cite a wide range of primary sources, underscoring the depth of the tradition.
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Conclusion
L.C. Jain’s study demonstrates that long before the advent of modern systems theory, Jaina scholars were using set‑theoretic models to explain the karma process. By formalising the behaviour of souls and matter through symbolic operations, they built a conceptual bridge between metaphysics and mathematical analysis.