 The second moral is that—given certain assumptions about meaning in chess notation—we can have productive and systematic understanding of representations even if the system itself is not compositional. The assumptions in question are that (i) the description I gave in the first paragraph of this section fully determines what the simple expressions of chess notation mean and also how they can be combined to form complex expressions, and that (ii) the meaning of a line within a chess notation determines a move. One can reject (i) and argue, for example, that the meaning of \(\bB\) in \(\b{Bb5}\) contains an indexical component and within the context of a description, it picks out a particular bishop moving from a particular square. One can also reject (ii) and argue, for example, that the meaning of \(\b{Bb5}\) is nothing more than the meaning of ‘some bishop moves from somewhere to square \(\b{b5}\)’—utterances of \(\b{Bb5}\) might carry extra information but that is of no concern for the semantics of the notation. Both moves would save compositionality at a price. The first complicates considerably what we have to say about lexical meanings; the second widens the gap between meanings of expressions and the information conveyed by their utterances. Whether saving compositionality is worth either of these costs (or whether there is some other story to be told about our understanding of the Algebraic notation) is by no means clear. For all we know, Algebraic notation might be non-compositional.