Do the Greeks have an inner self?

Though many people would argue that the Greeks had no since of “inner self” I would argue that it is because of the difference between Greek society and our society make it seem that they have no since of the inner self.  The reason is that in Greek society what your community thinks of you are more important because the Greeks have a shame culture while we now have a guilt culture.  This is clear through Achilles withdrawing from the war.  To many people his withdraw seemed to be cowardice but the reason for his withdraw was that he had kleos (honor) taken from him, which is a reasonable thing to do in Greek society, but it is because of the difference between a shame and guilt culture that you could possibly think that the Greeks had no since of inner self.   That is why Achilles withdrawing shows that he valued his life more than the kleos that he could have gained.  Though some may argue that this is untrue I believe that every human has had self-awareness and because of this I think it is absurd to think that there is a group of humans who didn’t, they may have cared more about the group then themselves but this is still present in today’s society.