We had a hint:

"And then," spat Harry, the fury coming fully into his voice, the cold rage at the universe for being like that and at himself for being so stupid, "I asked Hermione and she said that they were just afterimages, burned into the stone of the castle by the death of a wizard, like the silhouettes left on the walls of Hiroshima. And I should have known! I should have known without even having to ask! I shouldn't have believed it even for all of thirty seconds! Because if people had souls there wouldn't be any such thing as brain damage, if your soul could go on speaking after your whole brain was gone, how could damage to the left cerebral hemisphere take away your ability to talk?"