It's kind of like the half empty vs half full riddle. If your head and body split, do you have no head or no body?
No body. Otherwise put: if you have a full-body transplant (insanely, some doctor out there actually wants to try this), should you really be considered yourself or that person? Well, who was declared dead? In Mr. Williams' case, which part is frozen and which is now worm crap?
