  Perry (1977, 1979) and Kaplan (1989a), claim that belief is a binary relation that agents can bear to propositions. But they say that this relation is mediated by a third entity. (Compare with assertion: assertion is a binary relation between agents and propositions, but it is mediated by sentences, or their characters.) Thus Perry and Kaplan claim that agents can believe a singular proposition in different ways. (Compare again with assertion: John can assert the singular proposition that he is shopping in at least two ways, by uttering either ‘John is shopping’ or ‘I am shopping’.) Moreover, a rational agent can rationally believe both a proposition and its negation, as long as he does so in suitably different ways.