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Abstract

Nāgārjuna’s arguments in the Mūlamadhyamakakārikā rely extensively on modus tollens, yet this inference is invalid in the paraconsistent frameworks typically used to formalize the catuṣkoṭi. We develop a modal extension of Belnap-Dunn semantics to address this, expressed as: ¬□(v(P) = t) ∧ ¬□(v(P) = f) ∧ ¬□(v(P) = b) ∧ ¬□(v(P) = n). This formula applies self-reflexively, resolves longstanding interpretive debates regarding verses within Nāgārjuna’s Mūlamadhyamakakārikā and Vigrahavyāvartanī such as his “no thesis” defense, and bridges interpretive gaps between traditionally designated Eastern and Western logical traditions, providing a Western analytical translation of Indian dialectic into symbolic modal logic that is system-agnostic across K, T, S4, S5, non-normal logics, and neighborhood semantics. The modal operators function classically while the four-valued structure is modalized, preserving modus tollens at the level of modal reasoning while accommodating paraconsistent valuation at the object level. Self-application produces a non-terminating regress that is virtuous rather than vicious: each application is self-contained, demonstrating the unavailability of stable ground rather than constituting a failure to find it.

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