Current debates on generative AI focus predominantly on performance, scalability, and explainability. It is often implicitly assumed that systems capable of producing impressive outputs can also be operated responsibly in critical technical, economic, or legal contexts. This paper challenges that assumption. It starts from a simple axiom: A technical system that is structurally required to generate an answer to every input cannot be operated in a trustworthy manner. Trustworthiness presupposes a formalized capacity for refusal. On this basis, the paper analyzes the operationality of probabilistic AI systems, in particular large language models. It shows that probabilistic inference does not constitute an operational decision, but merely generates plausible possibilities. When inference and output are structurally coupled, uncertainty is suppressed rather than represented and is translated into plausibility by default. The paper further argues that explainability cannot resolve this limitation. Explanations operate retrospectively and can illuminate how an output was generated, but they cannot determine whether generating and releasing that output was permissible in the first place. As a result, explainability functions as an interpretative overlay rather than a mechanism of operational control. The absence of formalized decision boundaries and non-decision states constitutes a fundamental operational limit of always-answer AI systems. This limit is independent of model architecture, training data, or computational scale. Without the technical possibility of non-decision, such systems may remain powerful tools, but they cannot be deployed as trustworthy decision systems in responsibility-critical domains. This paper is part of a series examining accountability, auditability, and operational viability in probabilistic and agentic AI systems. A German-language version is available on Zenodo (DOI: 10.5281/zenodo.18659699)
Thomas Gessler (2026) studied this question.