1.3.7. Presupposition

When the yes answer to a yes-no question would be tantamount to making a true but misleading assertion, it is appropriate to answer yes only if we add a qualification. But it is still possible to give an affirmative answer in such a case, and no 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.

Take, for example, consider the question

asked about someone who does not have a car. 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: each would have no truth value so the two would be in the same position as regards truth and falsity.

In this example, the presupposition is something that is required for the term John’s car to have anything to refer to. That is a common source of semantic presuppositions but not the only one. Another is category mistakes, where what fails is not the reference of terms but the proper meshing of different terms. There is no problem of reference in the sentences The square root of 2 is blue and The square root of 2 is not blue, but it is natural to suppose that neither has a truth value because the adjective blue simply does not apply to numbers: it does not serve to distinguish between those that are and those that are not blue. Here the failed presupposition is that the square root of 2 falls in the category to which blue does apply, that the square root of 2 is colored.

Semantic presupposition is unlike the phenomena we have considered so far 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 this assumption can be retained in the face of indexicality and vagueness by adding the context of use and delineations of terms as further factors on which the truth value depends. Even when delineations are seen as an idealization, they are an ideal limit of features whose reality is not in doubt. But only more radical additions will preserve truth values in the case of semantic presupposition, and accepting the absence of truth values would force equally radical changes to the simple model of language. There is little consensus, even among logicians who accept the idea of semantic presuppositions, about the sort changes that are best, but here we will follow the first path and assume that the missing truth values have been somehow specified. As in the cases of indexicality and vagueness, we will be interested only in logical properties and relations that hold no matter which truth values are specified, but at a couple of points in the course, we will need to pay a little more attention to the devices used to specify these values.

The classic examples of semantic presupposition arising from the requirements of reference 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. Definite descriptions that refer contingently are so common that we must take some account of 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 does share one feature with our approaches to other complicating phenomena: 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, and comparing this approach to one that does not recognize this implication will force us to consider what is to be said when the second sentence is false. We will lay some groundwork for this later discussion in ch. 6, when we first analyze sentences into expressions that are not sentences and begin to consider expressions whose function is to refer rather than to have truth values. Until then, we will simply assume that all sentences, even those containing definite descriptions or possessives, have truth values in all possible worlds without considering what devices might be employed to achieve this.