Brain transplants and the dicephalus (an organism just like us except that it has two cerebrums) are thought to support the position that we are essentially thinking creatures, not living organisms. I try to offset the first of these intuitions by responding to thought experiments Peter Unger devised to show that identity is what matters. I then try to motivate an interpretation of the alleged conjoined twins as really just one person cut off from himself by relying upon what I take will be the reader's disagreement with Locke's conjecture that a dreaming Socrates and an awake Socrates are two distinct people.