Admissibility Boundary Science: Predicate Exhaustion, Irreversibility, and the Typing of Meaning

This publication introduces Admissibility Boundary Science (ABS), a foundational classification framework that addresses the semantic viability of predicates applied to persistent, irreversible systems. Distinct from incompleteness (Gödel), undecidability (Turing), or information capacity (Shannon), ABS identifies a novel limit—predicate exhaustion—where predicates transition from being meaningful to becoming structurally undefined due to irreversible accumulation in systems. Central to ABS is the Admissibility Typing Principle (ATP-Ω), which asserts that predicates must be semantically well-typed with respect to the system’s irreversible structure before they can yield truth values. When irreversibility disrupts this semantic mapping, predicates do not become false—they cease to exist as meaningful propositions. ABS demonstrates that undefinedness is a lawful scientific endpoint, not an epistemic failure. It separates system stability from repairability, showing that systems may remain operational even as the conceptual language to describe their recoverability exhausts. The paper formalizes criteria for predicate exhaustion and applies this to domains such as medicine, governance, and infrastructure, where repair or curability predicates may become ill-typed under irreversible change. ABS extends the philosophy of boundary theorems into a structural science of inquiry limits, reframing scientific rigor not as completeness, but as discernment regarding the admissibility of questions themselves.