 The distinction between the two concepts of truth in a world can be explained within a theoretical framework known as two-dimensional semantics, which assigns to a sentence like (5) an intension that is a function, not from worlds to truth-values, but from pairs of worlds to truth-values. The intension of (5) is the function that assigns the true to a pair of worlds \(\langle u; w \rangle\) just in case the object that is the last celestial body visible in the morning in \(u\) is the second planet in  \(w\).[6]  This account makes it easy to define the two notions of truth in a world. A sentence \(P\) is true in \(w\) considered as actual just in case the two-dimensional function assigns the true to \(\langle w; w\rangle\). \(P\) is true in \(w\) considered as counterfactual just in case, where \(u\) is the actual world, the two-dimensional function assigns the true to \(\langle u; w\rangle\). Note that the two-dimensional intension of (5) determines whether (5) is true at a world \(w\) considered as actual. But it does not in general determine whether (5) is true at \(w\) considered as counterfactual. That also depends on which world is actual. Knowledge of a sentence’s two-dimensional intension is therefore not in general sufficient to know whether the sentence is true at \(w\) considered as counterfactual. Further empirical evidence may be required.