We propose a stratified theory of negation in a weak 2-categorical framework, distinguishing three levels of logical behavior: classical elimination, paraconsistent containment, and dialectical generation. The key idea is that dialectical negation is not truth-functional but arises from non-confluent colimit structures in a weak 2-category. We formalize this via differentiation spans and pushout constructions, defining a generative negation operator N induced by failure of structural identification. We introduce a paraconsistent comparison model based on De Morgan algebraic categories, and show that any structure-preserving pseudo 2-functor from the dialectical system into classical or paraconsistent logical categories cannot exist. This yields a strong non-embedding theorem: dialectical negation cannot be reduced to classical logic or paraconsistent logic under any structure-preserving mapping. We further interpret the construction computationally via non-confluent rewriting systems, where contradiction corresponds to branching and generation arises from failure of confluence. The result suggests that negation should be understood not as a truth-operation, but as a stratified family of structural transformations across categorical levels. This work aims to provide a categorical foundation for dialectical structures beyond classical logical frameworks.
Yugo Hidaka (Sat,) studied this question.