Starts off by saying some people have said identity statements, specifically scientific discoveries, have been described as contingent. Kripke thinks all of these statements are necessary if they are true, w/ notion of rigid and non-rigid designators. Rigid designator: same object designated by term in all possible worlds. Ex. the square root of 25, in all possible worlds, =5; referent will always be the same. Non-rigid designator: different possible objects could be designated by term in all possible worlds. The inventor of bifocals could be a different person in a different world. Philosophers want to keep these contingency claims for our theoretical understanding of mind-body problem. Problem for identity theorists: claims are now necessary so they cannot reply to the objection (that we can imagine pain existing w/out a state of body, even no mind) #3 explain the role of after-images for philosophers like place and smart.