1.3.5. Presupposition

When the yes answer to a yes-no question would be tantamount to making a true but misleading assertion, we would avoid answering yes without adding a qualification, but no sort of qualification would make the answer no appropriate. Another of the complications of the simple picture of language appears in connection with yes-no questions for which neither answer seems legitimate.

For example, consider the question

asked about someone who does not have a car at all. In such a case, we would be at a loss to answer the question directly. This is usually explained by saying that the question presupposes that John has a car and has no appropriate direct answer when this presupposition does not hold. And we can say something similar about the following declarative sentences, which correspond to affirmative and negative answers to the question, respectively:

That is, just like the question, we can take each of these assertions to presuppose John has a car.

We could capture these limits on appropriateness by regarding presupposition as a sort of implicature. That is, we might say that John having a car constitutes a necessary condition for the appropriateness of either of the assertions above. But many have held that in contexts where John has no car, it is not only the case that neither sentence is appropriate but the case that neither is true. Since one would be true if the other was false, this means that neither claim would have a truth value. If this point of view is correct, what is missing in these assertions when John has no car 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 is a presupposition in this strong sense is said to be 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: both would have no truth value so they would be in the same position as regards truth and falsity.

Semantic presupposition is unlike the phenomena of speech acts and implicatures in that it requires fundamental changes to the simple model of language and not merely additions to it. The simple model is built around the assumption that a sentence has a truth value in every possible world, and dropping that assumption would force radical changes. And 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 then 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 use of possessives that we saw in the example of John’s car are also common, and they represent a closely related sort of case because John’s car might be paraphrased by the definite description the car John has.

The approach we will take to these sorts of semantic presupposition has two features that it shares with our approaches to other complicating phenomena. 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 as such. However, 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. In 8.4.2 we will consider an account of definite descriptions according to which the first of these sentences implies the second.

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 do not recognize the failures of truth value that result when semantic presuppositions are false. so we will assume that every sentence has a truth value under all possibilities. But, since we will eventually analyze sentences into units smaller than sentences, an assumption about the meanings of sentences is not enough.

We will assume in addition that any term which ought to refer does have a reference value. We allow this to be either an actual object or an empty or nil reference value. The latter option is designed for the case of undefined terms like the building between Center Hall and Sparks Center that do not refer to actual objects. We will need to distinguish these two sorts of reference value 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 value and every sentence a truth value. The references and truth values we assume for this reason can be regarded as stipulations added to the conventional meanings of these expressions, and we will consider only logical properties and relations that hold no matter how such stipulations are made. Such assignments of supplementary semantic values are usually called super-valuations; both the name and this way of handling failure of presuppositions are due to Bas van Fraassen. Our use of the approach will generally stay in the background, but we will look at the assumptions we are making a little more closely in 6.1.3 when we have begun to analyze sentences into expressions that are not sentences.