 Double-indexing explains how we can regard the reference of “the second-largest city in the United States” in  (11)  to be Chicago, without taking “the second-largest city in the United States” to be an indexical like “I”. On this view, “the second-largest city in the United States” does not vary in content depending on the context of utterance; rather, the content of this phrase is such that it determines a different reference with respect to different circumstances of evaluation. In particular, it has Los Angeles as its reference with respect to the present state of the actual world, and has Chicago as its reference with respect to the state of actual world 100 years  ago.[2]  Because “the second-largest city in the United States” refers to different things with respect to different circumstances, it is not a  rigid designator (see entry)—these  being expressions which (relative to a context of utterance) refer to the same object with respect to every circumstance of evaluation at which that object exists, and never refer to anything else with respect to another circumstance of evaluation. (The term “rigid designator” is due to Kripke [1972].)