... today is August the 17th? I just saw the moon (4:30 CEST) and I have the strong impression that the unlit (by the Sun) part of the Moon is anyway "visible" as a very very dark grey portion.
It will be impossible to find it against the dark sky if not for the companion bright slice. What I see basically fills the round, just is smaller as compared to the bright part.
This latter effect it is explainable by the fact that bright lights appear to us bigger as compared to less luminous objects when put in direct comparison. This is matter of perception. As such my question is: I am also just perceiving the rest of the moon because I know is there or indeed I see something real?
To me, it is reasonable that Earth can illuminate the Moon, however I am not sure. Moreover, the "Earth phase" as seen by the Moon should be crucial here. If I am right, this might explain why sometimes I see the above phenomenon but more often I don't.