<p><?tk 3?>This paper distinguishes between trustability and trustworthiness as two conceptually and normatively distinct conditions for legitimate trust, a distinction that has been largely absent from the philosophical literature. Trustworthiness concerns whether an agent merits trust, while trustability names a prior condition: whether the entity in question is even the kind of thing to which trust can coherently apply. Focusing on Faulkner’s grammar of trust and recent work by Massaguer Gómez on human–robot interaction, we argue that many artificial intelligence systems today elicit trust without being trustable—a category error with ethical consequences for the design, deployment, and governance of emerging technologies. We propose that trustability functions as a normative threshold for evaluating whether trust in AI is not only misplaced but also structurally incoherent, and we show how this concept allows us to differentiate between merely instrumental reliance and genuinely normatively structured trust. This clarifies when evaluations should shift from “trust” to reliance with accountability. We also examine relevant philosophical discussions that have anticipated parts of our argument, situating our approach within debates about trust in governments, institutions, and nonhuman agents, and clarifying how our framework builds upon and departs from existing positions. Finally, we explore the conceptual and institutional conditions under which future AI systems might become both trustable and trustworthy—outlining technical, moral, and political prerequisites for such a development. This distinction provides a framework for diagnosing inappropriate trust, clarifying when it is possible, when it is normatively justified, and when it is conceptually impossible.</p>