 According to counterpart theory, I might have had three hands only in the derived sense by having counter-parts that have three hands (see Kripke 1980: 45). This does not sit well with the intuition that I strictly and literally speaking might have had three hands. The identification of possible worlds with constructions out of compossible states of affairs is faithful to this intuition. I have different properties in different possible worlds, if the possible worlds contain different states of affairs that involve me. One possible world contains the state of affairs MT’s having three hands; the possible world that is actual contains the state of affairs MT’s having two hands. The different possible worlds under discussion don’t overlap, yet the possibilities involve me (see Forbes 1987: 141).