Keywords: Sense and Denotation; Frege-Church Argument (Slingshot); Truth-Makers; Forcing; Possible Worlds.
We discuss the notion of denotation of a sentence in the context of Frege's division between sense and denotation. We first analyse Frege's arguments in favour of such a notion and stress some of its inadequacies, that we try to overcome by supplementing Frege's theory with a theory of truth-makers. Our first proposal relies upon the notion of thought and, because that fails, we move on to consider a theory of facts analogous to that of logical atomism. We try to develop it initially by giving criteria in order to bypass the Frege-Chuch argument against facts. Then we consider a relation of truth-making based on the relation of forcing, as it is used in the classical interpretation of intuitionistic logic. Our truth-makers are understood as mereological parts of possible worlds. Some analogies and differences between the present notion of fact (as truth-maker) and the classical one of logical atomism are discussed.