Possibility Without Viability

This paper demonstrates that logical or mathematical possibility does not entail viability under admissibility and standing constraints. It shows that many formally consistent structures, models, or extensions remain non-viable because they cannot preserve standing when evaluated at the admissibility boundary. The distinction between possibility and viability is shown to be structural and binary, not a matter of degree, plausibility, or empirical likelihood. The argument is strictly eliminative and non-constructive, introducing no selection principles, heuristics, or construction methods. By enforcing viability as a necessary condition beyond mere possibility, the paper closes a broad class of speculative, anthropic, and modal arguments that conflate formal consistency with legitimate existence.