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 saying yes without qualification but nothing 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 is legitimate.

For example, consider the question

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 question 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 following declarative sentences above, which correspond to affirmative and negative answers to the question, respectively:

That is, we can take each of these to presuppose John owns a car.

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 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, and something that is a presupposition in this 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: they would be in the same position as regards truth and falsity since neither would have a truth value at all.

Semantic presupposition is unlike the phenomena of speech acts and implicatures in that it requires fundamental changes to the simple model of language that are not simply additions to it. The simply 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 owns.

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. But we will not go quite so far as to consider no logical relations at all between 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. 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 guard against the failures of truth value that result when semantic presuppositions are false. We will assume that every sentence has a truth value under all possibilities; but, since we will eventually analyze sentences into component terms, an assumption about the meanings of sentences is not enough.

We will assume that any term which ought to refer does have a reference value but allow this value to be either an actual object or an empty or nil reference value to cover the case of undefined terms like the building between Center Hall and Sparks Center that do not refer to actual objects. 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 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; the name and this sort of way of handling failure of presuppositions are due to Bas van Fraassen. Our use of it 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.