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.