How can sentences containing descriptive and singular terms come to represent the world, without any word-world semantic relation? "If reference is not a relation between a word and some object in the world, then it is completely mysterious how can the use of a name help us pick out anything in the world" says Peter Lupu.
Perhaps it is like chess, and the notation that we use to represent the pieces and the moves. Here is one well-known and simple game:
The major pieces get proper names (K for king, Q for queen). The minor pieces get descriptions ('Nc6' means that the only knight which is available to be moved to c6, is moved there). Play this game at your place, and leave the pieces where they are. I will then play the same game at my place. Then (if we have understood the language of chess correctly), the layout of pieces on my board will represent the layout on yours. So, if your board were the world, and mine was the mental representation, the one would match the other.