  Propositions, on Kaplan’s theory, have truth-values with respect to circumstances of evaluation, which Kaplan identifies with pairs of times and possible worlds,  \(\langle t, w \rangle\). A single proposition may be true with respect to one circumstance of evaluation and false with respect another. For example, the proposition \(\langle \text{Mary}, \text{being a philosopher} \rangle\) may be true at \(\langle t_1, w_1 \rangle\) and yet false at \(\langle t_1, w_2 \rangle\) because, in \(w_1\), Mary is a philosopher at time \(t_1\), whereas in world \(w_2\) she is not a philosopher at time \(t_1\). Similarly, if time \(t_0\) is a time before Mary became a philosopher in \(w_1\), and \(t_1\) is a time after which she became a philosopher in \(w_1\), then \(\langle \text{Mary},\) \(\text{being a philosopher} \rangle\) is false at \(\langle t_0, w_1 \rangle\) but true at \(\langle t_1, w_1 \rangle\). In the remainder of this section, we will usually, for the sake of simplicity, pretend that Kaplan’s circumstances of evaluation are just possible worlds, and ignore variation in truth-value over time.