What is required is only that the mode associated with 'Hesperus' differs from that associated with 'Phosphorus', not that the mode be a property the referent uniquely instantiates.
If propositions are unstructured and distinct from sets, there are several possibilities for explaining their identity conditions. First, identity conditions might be specified in terms of possible attitudes. One possibility is this: P=Q if, necessarily whoever believes (asserts, denies, etc.) P believes (asserts, denies, etc.) Q, and vice versa. Second, proposition identity might be reduced to property identity in the manner of Myhill (1963) and Zalta (1983). Thus, Zalta (1983, 72) offers the