  On Kaplan’s theory, we can speak not only of the truth-values of propositions at worlds, but also of the truth-values of sentences at pairs of worlds and contexts. The reason we can do this is that a context determines the content of a sentence, and the content of that sentence determines a truth-value at a world. For example, the content of the sentence ‘I am a philosopher’ in the context \(c_1\) described above is the singular proposition that Mary is a philosopher. This proposition is true with respect to world \(w_1\). So, the sentence ‘I am a philosopher’ is true with respect to \(c_1\) and \(w_1\). By contrast, the content of the sentence ‘I am a philosopher’ at the context \(c_2\) (in which John is the agent) is the singular proposition that John is a philosopher, and this proposition is false at \(w_1\) (let’s suppose). So, the sentence ‘I am a philosopher’ is false with respect to \(c_2\) and \(w_1\). So, the truth-value of the sentence ‘I am a philosopher’ is doubly relativized to both context and world. This sort of double-relativization is often called double-indexing. (See Vlach 1973 and Kamp 1973 for early examples of semantic theories that use double-indexing.)