<p>The paper reflects an interdisciplinary dialogue between legal science, terminology science and computer science aimed at analyzing one specific aspect within the process of digitization of legal operations, in particular via AI: what is the role of labelling and categorization in language and law, and how might legal interpretation be influenced by AI?. We show how a potential challenge in legal AI lies in the obliteration of a certain indeterminacy in legal terms (both concrete and abstract), by arguing that terminology could help controlling the use AI systems make of legal language (via the distinction and systematization of simple terms, concepts, etc.). Terminology-aware generative models would allow more controlled reasoning across languages and jurisdictions and could facilitate explainability by linking each generated statement to a definitional network, thereby exposing the underlying semantic structure of the legal domain. This might help build a trustworthy, explainable AI for law. In this view, terminology could provide an epistemic infrastructure for legal language within an AI operated world, by anchoring generative systems to the conceptual order of law, and by preserving the necessary interplay between determination and indeterminacy that characterises legal language, preventing the risk of current hallucination, over determinacy or the complete loss of penumbra and indeterminacy.</p>