What or where is our real sense of self?

[Lievo]

Would a person with absolutely no memory have self?

You may wish to read http://en.wikipedia.org/wiki/The_Man_Who_Mistook_His_Wife_for_a_Hat" . Likely the best pop book on neuropsychologia ever. It mentions among other things the case of anterograde amnesia that Pythagorean and Apeiron mentionned, and discuss your question specifically (argue for a yes).

 

[Pythagorean]

And of course, amnesiacs can still learn implicit memories, since their basal ganglia are still in tact, though implicit memory are not conscious.

Parkinsons and Huntingtons patients, on the other hand, are associated with basal ganglia problems.

The two different kinds of damage are associated with different kinds of learning deficiencies, though amnesiacs are clearly the case for the more popular autobiographical memory.