The Madhyamaka Inception: Reflexive Topos Logic and the Extension of Gödel's Incompleteness Theorems
Year: 2026
Type: preprint
Abstract: Gödel’s Incompleteness Theorems imposed an absolute epistemological limit on classical axiomatic formal systems, establishing that consistency and completeness are mutuallyexclusive within standard first-order logic. This paper introduces a novellogical framework—Reflexive Topos Logic (L∗)—formalizing the core ontological principles of Nagarjuna’s Madhyamaka philosophy (specifically Pratītyasamutpāda and Śūnyatā) into Grothendieck’s topostheory. We reformulate the classical propositional space by identifying it with the subobject classifier Ω∗ (the Reflexive Heyting Sheaf) within a dedicated reflexive topos RST. Withinthis category-theoretic framework, we formulate and prove two supplementary theorems toGödel’s foundations. We demonstrate that the classical Gödelian unprovable formula G∗ isa global section 1∗ → Ω∗ whose classical diagonal undecidability is a topological projectionof a static, single-axis evaluation. By utilizing the 4-fold cyclic automorphism group S actingon Ω∗, self-referential paradoxes are smoothly resolved as closed, holomorphic trajectorieson the valuation lattice. Finally, we prove that the system can self-consistently prove its ownglobal consistency, represented as the nilpotent boundary condition of the discrete exteriorderivative.
Author: Liu, Hongri
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165046521
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