 What does O’Leary learn when he comes to accept Daniels’ assertion of ‘Lloyd is I.L. Humberstone’? Since the actual world is like i, the literal semantic content of the asserted sentence is a necessary truth. But necessary truths rule out no empirical possibilities whatsoever, so this cannot be the informative proposition that is conveyed by Daniels’ assertion. Moreover, O’Leary is not in a position to recognize that this is the literal semantic content of the sentence, since he doesn’t know whether the actual world is like i or j. The natural suggestion is that the information conveyed by Daniels’ assertion is that the real world is like i and not j. When O’Leary accepts ‘Lloyd is I.L. Humberstone’, he will no longer treat the possibility that the man in front of him is not the author of the famous article as a live option: this empirical possibility will be eliminated from his context set. Thus, the proposition that seems to be conveyed by Daniels’ assertion corresponds to the diagonal intension determined by our 2D matrix for that assertion. Moreover, this observation generalizes: when subjects are partially ignorant of the semantic values of their words, the diagonal proposition determined by the propositional concept can capture the empirical information conveyed by the assertion.