The Collapse of Semiosis: The Non-Usurpation Rule as a Unified Solution to Self-Referential Paradoxes

Charles Sanders Peirce’s triadic model of the sign presupposes a continuous community of interpretation. This paper interrogates the ontological status of the sign in the "Last Human" scenario. We argue that the extinction of the community results in a categorical collapse of the Object and Interpretant, reducing the sign to a mere biological index. Central to our argument is the introduction of the Non-Usurpation Rule: a set-theoretic constraint which postulates that a subset (the individual) cannot legitimately employ global properties bestowed by the mother set (the community) to define reality. We distinguish strictly between Definition (global/normative) and Description (local/phenomenological). We provide a step-by-step formal derivation proving that without a community, the "Last Human" loses the capacity for truth-functional definition. Furthermore, we extend this framework to analyze the limits of Artificial Intelligence and digital isolation, suggesting that meaning is an emergent property of shared vulnerability.