 Counterpart theory was first introduced by Lewis in “Counterpart Theory and Quantified Modal Logic” (1968) as a way of making modal discourse extensional. Instead of worrying just what a name inside the scope of a modal operator might mean, we translate the language of quantified modal logic into a language without operators, but with quantifiers over worlds and other non-actual individuals. So instead of saying □Fa, we say ∀w∀x ((Ww ∧ Ixw ∧ Cxa) ⊃ Fx). That is, for all w and x, if w is a world, and x is in w, and x is a counterpart of a, then Fx. Or, more intuitively, all of a’s counterparts are F. The paper shows how we can extend this intuitive idea into a complete translation from the language of quantfied modal logic to the language of counterpart theory. In “Tensions” (1974a) Lewis retracts the claim that it is an advantage of counterpart theory over quantified modal logic that it is extensional rather than intensional, largely because he finds the distinction between these two notions much more elusive than he had thought. But he still thought counterpart theory had a lot of advantages, and these were pressed in chapter 4.