<p>A major issue for the trustworthiness of modern AI-models is their lack of robustness. A notorious example is that putting a small sticker on a stop sign can cause AI-models to classify it as a speed limit sign. This is not just an engineering challenge, but also a philosophical one: we need to better understand the concepts of robustness and trustworthiness. Here, we contribute to this using methods from (formal) epistemology and prove a no-go result: No matter how these concepts are understood exactly, they cannot have four prima facie desirable properties without trivializing. To do so, we describe a modal logic to reason about the robustness of an AI-model, and then we prove that the four properties imply triviality via a novel interpretation of Fitch’s lemma. We then discuss the consequences for explicating a viable notion of robustness for AI. A broader theme of the paper is to build bridges between AI and epistemology: Not only does epistemology provide novel methods for AI, but modern AI also provides many new questions and perspectives for epistemology.</p>