The phrase refers to Los Angeles with respect to the present state of the actual world, and to Chicago with respect to the state of the actual world 100 years ago.

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