There are two dominant approaches to semantics. One sees the task of semantics as to provide a systematic account of the truth conditions of (actual and potential) sentence uses. The other assumes that a use of a sentence expresses a statement (proposition, thought—terminology varies here), a statement being the sort of thing that can be asserted and believed, and also the sort of thing that, as a representation of how the world is, can be assessed as true or false. The task of semantics, on this view, is systematically to spell out how sentence uses are associated with statements.

While the aims of the two types of theories are different, they are related. A use of a sentence to make a statement is, after all, presumably true (or false) in virtue of the truth (or falsity) of the statement made. Hence, to assign statements to...