On Incomplete Containment - Representational Shells and the Structural Limits of Self-Description
Abstract
A sufficiently expressive system cannot construct an inwardly closed, self-validating representation of itself: the semantic and validation conditions required for such closure generate regress or inconsistency. This paper shows that the same systems may nevertheless construct outward \emph{representational shells}---incomplete descriptions that encode the generating system's externally specifiable structure while omitting the conditions of their own generation and validation. Because a shell does not attempt semantic self-closure, it can representationally contain the system that produced it without contradiction. We identify a constructive asymmetry: outward shell construction is structurally admissible, while inward self-validating closure is not. We show that a shell's representational capacity exceeds what is available under nesting, admitting parallel encodings of a generating system that are mutually inaccessible from within any single encoded instance. We then analyse the conditions under which a system may adopt a shell as its operative representational frame (migration), and show that embedding within a shell eliminates operational access to a global descriptive vantage (perspective collapse). The argument draws on G\"{o}del's incompleteness theorems, Tarski's undefinability result, and the non-internalisability of global soundness, but the contribution is a structural synthesis rather than a new result in formal logic: it unifies these established constraints into a directional account of how self-representing systems may construct descriptions that contain them.
Fields of Study & Subjects
Philosophy and Theoretical Science
Embodied and Extended Cognition
Logic
Reasoning
and Knowledge
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 1 March 2026
- Language
- EN
- Document type
- Preprint