EMPIRICIST THEORIES OF PERSONAL IDENTITY STATE THAT THE IDENTITY OF A PERSON OVER TIME IS A MATTER OF BODILY CONTINUITY AND/OR SIMILARITY OF MEMORY AND CHARACTER. IN CONTRAST, THIS PAPER ARGUES THAT WHILE BODILY CONTINUITY AND SIMILARITY OF MEMORY AND CHARACTER ARE EVIDENCE OF PERSONAL IDENTITY, THEY DO NOT CONSTITUTE IT. IT IS SOMETHING UNDEFINABLE. THE DIFFICULTY OF KNOWING WHAT TO SAY IN PUZZLE CASES DOES NOT SHOW THAT PERSONAL IDENTITY EXISTS IN DIFFERENT DEGREES OR THAT WE HAVE TO MAKE (...) ARBITRARY JUDGMENTS ABOUT IT. IT SHOWS ONLY THAT SOMETIMES WE CANNOT KNOW WHO IS WHO. (shrink)