There are cases where both an affirmative sentence and the corresponding denial seem equally inappropriate assertions. For example, consider the sentences
in a context where we are speaking of someone who does not own a car at all. In such a case, we would be at a loss to answer the corresponding yes-no question Is John’s car green? directly. This is usually explained by saying that the question presupposes that John owns a car and has no appropriate direct answer when this presupposition does not hold. And we can say the same thing about the declarative sentences above, which correspond to affirmative and negative answers to the question, respectively.
This relation of presupposition might be regarded as a sort of implicature, with John owning a car constituting a necessary condition for the assertion of either sentence to be appropriate. But many logicians have held that the declarative sentences above have no truth value at all in contexts where John owns no car. This means that what is missing in such cases is not some quality like informativeness or relevance that we expect in addition to truth but instead something that is a precondition for either truth or falsity. Something that must be the case in order for a sentence to have any truth value is a semantic presupposition. If John having a car is a semantic presupposition of the two sentences above, it is easy to see why they seem equally inappropriate when John has no car: they would be in the same position as regards truth and falsity since neither would have a truth value.
Semantic presupposition represents another way that information could be derived from an assertion. A basic way of accommodating our beliefs to what others assert is to assume that their assertions have truth values, but a semantic presupposition is not an implication that must hold in order for a sentence to be true rather than false or an implicature that must hold in addition to conditions for truth in order for a sentence to be appropriate. It comes in at an earlier stage, as a precondition for the sentence having a truth value at all. Semantic presupposition is unlike the other complicating phenomena we have considered also in requiring changes to the simple model of language that are not simply additions to it. This model is built around the assumption that a sentence has a truth value in every possible world, and dropping this assumption would force radical changes. Because there is no consensus, even among logicians who accept the idea of semantic presuppositions, about the exact form such changes should take, we will not attempt to incorporate failures of truth value in our model of language.
In part, we will treat semantic presupposition as we do the variety of speech acts: by not considering the examples where it may be held to occur. But we cannot avoid all the difficult cases in this way. The classic examples of semantic presupposition are sentences containing phrases employing the definite article the to refer to something by way of a description of it. Such phrases, which logicians classify as definite descriptions, cause problems because their success in referring depends on the existence of objects satisfying the descriptions they offer. For example, both the sentence The building between Center Hall and Sparks Center is occupied and the sentence The building between Center Hall and Sparks Center is unoccupied seem inappropriate when no such building exists because the definite description the building between Center Hall and Sparks Center has nothing to refer to. And definite descriptions that refer contingently are so common that we cannot simply avoid all sentences containing them.
The approach we will take in such cases employs elements of the different ways we handle implicatures and vagueness. First, just as we do not attempt to capture relations of implicature in our study of logic, we will not attempt to capture relations of presupposition. So, for the most part, we will consider no special logical relation of presupposition between a sentence containing a definite description the X and sentences—such as Some X exists—which might be taken to express presuppositions of it. But we will not go quite so far as to consider no logical relations at all between such sentences. The line between implication and presupposition is controversial, and relations between sentences like The building between Center Hall and Sparks Center is occupied and There is a building between Center Hall and Sparks Center fall in the disputed area. These questions have been discussed for nearly a century (though not always in these terms) with strong arguments on both sides, and at one point in a later chapter we will consider an account of definite descriptions according to which sentences like these are related by implication.
Although we will not attempt to capture semantic relations of presupposition as such, we will need to apply our general account of logical properties and relations to sentences that may have such presuppositions. And we can do this only if we guard against the failures of truth value that are supposed to result when semantic presuppositions are false. First of all, we will continue to assume that every sentence has a truth value under all possibilities but, since we will eventually analyze sentences into component terms, we must do more. We will treat any term which ought to refer as having a reference but allow this reference to be either an actual object or an empty or nil reference value. We will make a distinction between the empty or nil reference value and actual objects only when we consider definite descriptions in the last chapter, so, for the most part, we will merely assume the every term has been somehow given a reference and every sentence a truth value. This is analogous to the way we handle vagueness, where we speak as if contexts of use were supplemented by precise delineations of vague terms. And, as in the case of vagueness, we will consider only logical properties and relations that hold no matter how such stipulations are made. (We will look more closely at the nature of the supplement required to insure reference and truth value in 6.1.2.)