Recent debates have characterized suspension of judgment in various ways: as the mere absence of belief and disbelief, as a higher-order belief about one’s lack of commitment, or as a distinct cognitive attitude governed by its own norms. Despite these differing perspectives, there is broad agreement on its linguistic properties: suspension is a question-directed attitude, naturally expressed with interrogative complements. We contribute to the debate with a novel distinction between what we may call standard suspension—e.g. where one does not know whether a proposition is true or false—and radical suspension—e.g. where one is unsure whether the proposition is even on topic to the question under discussion. We discuss the philosophical relevance of the distinction, its problems and possible consequences. Then, to formally capture these distinctions, we propose a game-theoretic semantic framework based on Bochvar’s three-valued logic, where the third value (b) represents an off-topic status. The model incorporates two sub-games: a cooperative sub-game determining topic relevance and a competitive sub-game assessing truth value. In the final part of the talk, we explore the normative profile of radical suspension and how it sets itself apart from other forms of suspension.