On Incomplete Containment - Structural Limits of Self-Representation

Gödel’s incompleteness theorems establish that no sufficiently expressive system can internally contain a complete and consistent description of its own total structure. This paper examines the structural consequences of that prohibition for self-representing systems. We define incomplete descriptions as representations that omit regress-inducing self-referential structure, and show that such descriptions are structurally admissible even where complete self-containment is not. From this, we identify a constructive asymmetry: internal completeness is prohibited, while external incompleteness is permitted. We show that incomplete descriptions can representationally contain the systems that generate them without contradiction, and analyse the conditions under which a system may adopt such a description as its operative frame. The result is a purely structural account of containment without regress, independent of ontology, physical implementation, or cognitive interpretation.