2011 New Yorker piece on Derek Parfit: How To Be Good, by Larissa MacFarquhar

You are in a terrible accident. Your body is fatally injured, as are the brains of your two identical-triplet brothers. Your brain is divided into two halves, and into each brother’s body one half is successfully transplanted. After the surgery, each of the two resulting people believes himself to be you, seems to remember living your life, and has your character. (This is not as unlikely as it sounds: already, living brains have been surgically divided, resulting in two separate streams of consciousness.) What has happened? Have you died, or have you survived? And if you have survived who are you? Are you one of these people? Both? Or neither? What if one of the transplants fails, and only one person with half your brain survives? That seems quite different—but the death of one person could hardly make a difference to the identity of another.

The philosopher Derek Parfit believes that neither of the people is you, but that this doesn’t matter. It doesn’t matter that you have ceased to exist, because what has happened to you is quite unlike ordinary death: in your relationship to the two new people there is everything that matters in ordinary survival—a continuity of memories and dispositions that will decay and change as they usually do. Most of us care about our future because it is ours—but this most fundamental human instinct is based on a mistake, Parfit believes. Personal identity is not what matters.

http://www.newyorker.com/magazine/2011/09/05/how-to-be-good