But now, in inner awareness there is a more complex form of self-awareness. Not only am I aware of myself by virtue of the egocentric structure 'I...'. But in inner awareness I am aware of my passing experience by virtue of the reflexive structure 'in this very experience [I see this frog]', and part of what I am so aware of is myself, subject of the experience. Part of my inner awareness of my experience, then, is an inner awareness of myself by virtue of the structure 'in this very experience I ...'. Hence, I apperceive myself not only through the egocentric content 'I ...'. but also through the reflexive-egocentric content 'in this very experience I...'. Inner awareness of self rides piggyback, then, on egocentric awareness of self. Importantly, both the structure ' I . . . ' and the structure 'in this very experience I ...' are parts of the modality, not the mode, of presentation in an experience. When Hume et al. had difficulty finding the self, or self-awareness, they were looking in the wrong place, and in the wrong way. They were seeking selfawareness, and hence the self, in some special mode of presentation - in something like visual perception perhaps, though an 'inner' perception of the self. But self-awareness - the most common and primordial form of self-awareness - is not a mode of presentation of oneself; it is rather a part of the modality of presentation in any intentional experience, residing in the structure 'I...', or 'in this very experience I...'. To vary Sartre's metaphor: I am aware of myself not when I look for myself, but when I look for anything at all…
Smith, David W. 1986. “The structure of (self-) consciousness.” Topoi 5 (2): 149–56. doi:10.1007/BF00139228.