 If we modify the conception of content by letting indices contain, in addition to a possible world parameter, parameters for an agent and a time, we get a conception of content on which a content is a function from triples of a world, an agent, and a time to truth values. This conception is one way of capturing the kind of content represented by the diagonal proposition in  section 4.4.  The diagonal proposition was a function from centered worlds to truth values, and a centered world can be thought of as a triple of a world, an agent, and a time (with the agent and time fixing the “center” of the centered world). On this conception, Oscar’s and Twin Oscar’s thoughts can have different truth values even though they have the same content, since, although the world and time parameters of the index in which their thoughts occur are the same, the agent parameter is different.