Introspection is the capacity by which we know our own conscious mental states. Several theories aim to explain it. According to acquaintance theory, we know our experiences by being acquainted with them. Acquaintance is non-causal, non-inferential, and non-observational. I present a dilemma for the acquaintance theory of introspection. Either subjects are always acquainted with all their experiences; or some attentional mechanism selects the relevant experiences (or aspects of experiences) for introspection. The first option is implausible: it implies that subjects are omniscient about their own experiences. The second option is also implausible: if acquaintance is a non-causal relation, introspection cannot target specific (aspects of) experiences without violating the principle of causal closure of the physical.