That great apes are the only primates to recognise their reflections is often taken to show that they are self‐aware—however, there has been much recent debate about whether the self‐awareness in question is psychological or bodily self‐awareness. This paper argues that whilst self‐recognition does not require psychological self‐awareness, to claim that it requires only bodily self‐awareness would leave something out. That is that self‐recognition requires ‘objective self‐awareness’—the capacity for first person thoughts like ‘that's me’, which involve self‐identification and so are vulnerable to error through misidentification. This objective self‐awareness is distinct from bodily or psychological self‐awareness, requires cognitive sophistication and provides the beginnings of a more conceptual self‐representation which might play a role in planning, mental time travel and theory of mind.