 Gregory Landini (1998) has proposed that there is indeed a coherent semantics for propositions and propositional functions in PM, which treats functions and propositions as linguistic entities. Landini proposes that this “nominalist semantics” is the intended interpretation of PM and is what remains of Russell’s earlier “substitutional theory.” He argues that Russell was led to this nominalism after first rejecting the reality of classes,then of propositional functions, and finally the reality of propositions. This rejection, according to Landini, leaves us with only a nominalist metaphysics of individuals and expressions as the interpretation of Russell’s logic. See also Cocchiarella (1980), who describes a “nominalist semantics” for ramified type theory, but rejects it as Russell’s intended interpretation. Sainsbury (1979) describes a “substitutional” interpretation of the quantifiers over propositional functions, but combines this with a truth-conditional semantics that does not require the ramification of the theory of types that is central to Russell’s interpretation in PM.