Our study of deductive logic will be guided by a picture according to which language serves to convey information and the information conveyed by a sentence is to be found in the proposition it expresses. This picture is oversimplified and something must be said about three respects in which the actual operation of language is more complex: the existence of speech acts whose function is not to convey information, the phenomenon of deixis or indexicality which causes the proposition expressed by a sentence to depend on the context in which the sentence is used, and the possibility of conveying information beyond the proposition expressed by a sentence through implicature and presupposition. These three features of language provide the heart of the study of pragmatics as distinct from semantics. The attitudes we will take to these complexities differ. Regarding the first, we will limit our consideration to the speech act of assertion and to its function of conveying information.
We handle indexicality by treating sentences only within a single context of use and consider only properties and relations of sentences that hold no matter what that context is. Analogous ideas can be used to approach the problem of vagueness.
We will consider only what is implied by a sentence as part of its truth conditions and not further information that may be implicated as conditions for appropriate assertion beyond the requirements for truth (and we will use responses to yes-no questions as one test for the difference).
Since a semantic presupposition is something that must hold in order for a sentence to have a truth value at all, sentences with non-tautologous presuppositions can fail to have truth values. Ideally, we would avoid sentences where such presuppositions appear, but the pervasiveness of definite descriptions. Instead, we will treat all terms as if they refer and thus will not attempt to capture semantic presuppositions of sentences containing them.