 The matrix is defined only with respect to a specific set of relevant alternative possibilities, i and j, chosen in such a way as to reflect the subjects’ semantic understanding and our own explanatory interests. The vertical axis represents these possible worlds in their role as contexts of use, which determine the literal semantic content of the expressions used in them. The horizontal axis represents those same possible worlds as circumstances of evaluation, relative to which we evaluate the truth or falsity of the proposition expressed. Each row of the matrix thus represents a different proposition that might be literally expressed by the sentence. Stalnaker calls such matrices propositional concepts, since they reflect the subject’s current imperfect conception of the meaning of the  sentence.[22]  This particular matrix reflects the fact that O’Leary’s current epistemic state is compatible with the identity sentence expressing either a necessary truth or a necessary falsehood, depending on empirical facts about the actual context of use.