Protocol Boundaries and the Unprovable Identity: Formal Limits of Self-Knowledge from IEM to the Tarski's Undefinability Limit
Zenodo (CERN European Organization for Nuclear Research) February 28, 2026 Daniel Osipenkov
A formal-philosophical framework analyzes the constitutive limitations of self-referential cognition using modal logic, type theory, proof theory, and phenomenology. Protocols are systems of constraints that constitute experience rather than distort reality. The identity axiom linking a code to its intended expression is unprovable in any consistent, recursively axiomatizable theory extending Robinson's arithmetic Q. First-person authority in judgments like 'I have a headache' corresponds formally to this unprovability. A hierarchy of theories reaches a limit called Silence, where the self dissolves as a temporary effect of protocol operation. The framework implies limits on machine self-awareness: no consistent formal AI can prove a sentence expressing its own identity.