Mathematical Boundary Consciousness Theory: Exploring the Epistemic Limits and Structural Horizons of Formal Systems
Zenodo (CERN European Organization for Nuclear Research) August 6, 2026 DOI: 10.5281/zenodo.21816287 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that formal mathematical systems can be modeled as cognitive spaces with intrinsic awareness of their boundaries, and proves a Limit Theorem of Mathematical Consciousness holding that absolute systemic omniscience is structurally impossible. Proposes a taxonomy of mathematical limits and meta-systemic ascent based on incompleteness stratification and set-theoretic horizons. |
Abstract
This paper introduces the Mathematical Boundary Consciousness Theory (MBCT), a rigorous theoretical framework that investigates the epistemic limits, structural horizons, and self-referential boundaries of formal mathematical systems. Moving beyond traditional views of logical consistency and deduction, MBCT models formal systems as dynamic cognitive spaces equipped with intrinsic awareness of their own demarcation zones. We formalize the epistemic mapping of well-formed formulas into provable, refutable, and indeterminate domains, establishing a precise topological definition for the boundary set of unprovable propositions. Furthermore, we analyze the hierarchical stratification of incompleteness through Gödelian self-reference fixed-point equations and examine the outer horizons of set-theoretic universes governed by large cardinal consistency strengths. Finally, we formulate the Limit Theorem of Mathematical Consciousness, proving that absolute systemic omniscience is structurally impossible, thereby providing a unified taxonomy of mathematical limits and meta-systemic ascent.