This paper develops a stratified theory of negation in order to clarify the structural differences between reductio ad absurdum in classical logic and dialectical negation in Hegelian philosophy. Although both reductio and dialectical reasoning involve contradiction, they operate at fundamentally different logical and ontological levels. This work proposes a three-level framework consisting of classical logic (L₀), paraconsistent logic (L₁), and a dialectical categorical system (L₂). Within this framework, contradiction functions respectively as elimination (L₀), containment (L₁), and generation (L₂). The paper introduces a formal reconstruction of these distinctions and provides a categorical semantics for dialectical negation. In L₂, contradiction is modeled as an internal structural component (ΔC) of conceptual objects, and negation is interpreted as a morphism generating conceptual transformation rather than as a truth-functional operator. A central result of the paper is a non-embedding theorem: there exists no structure-preserving mapping (functor) from the dialectical system into either classical or paraconsistent logic that preserves the generative role of contradiction. This establishes a formal sense in which dialectical negation is irreducible to both truth-functional and paraconsistent frameworks. By articulating negation as a stratified family of operations across different logical regimes, this work aims to bridge the gap between formal logic and dialectical philosophy. It contributes to ongoing discussions in philosophical logic, non-classical logic, and the formal interpretation of Hegelian dialectics.
Yugo Hidaka (Wed,) studied this question.