Vagueness

1. Vagueness in language and the world

Many linguistic terms are vague. But of what exactly does their vagueness consist? Consider, for example, the term ‘bald’. This term has borderline cases of application. There are people to whom the term, as it is ordinarily used, neither clearly applies nor clearly fails to apply. In this respect, the term ‘bald’ is different from the term ‘square root’, say. There are no borderline square roots, nor could there be. Let us say that a general term (a word or phrase which potentially applies to many things) is intensionally vague (that is, vague with respect to its meaning) only if its meaning permits possible borderline cases of application. Then ‘bald’ is intensionally vague.

Vagueness can also be found in singular terms (words or phrases that potentially apply to single things). Consider, for example, ‘the friend of Amy’. Suppose Amy has a love–hate relationship with Jane, without Amy clearly having any other friends. Then, it is indeterminate whether the singular term, ‘the friend of Amy’, designates Jane. So, ‘the friend of Amy’ has a possible borderline case of designation. And this indicates that it is intensionally vague.

It is plausible to suppose that intensional vagueness in general terms is more basic than intensional vagueness in singular terms, since uncontroversial examples of vague singular terms either contain vague general terms (non-relational or relational) or are the abstract singular counterparts to those terms. In the case of ‘the friend of Amy’, the term ‘friend of’ is intensionally vague.

The vagueness so far discussed does not require vagueness in the world. But worldly vagueness can be treated in a similar way. Suppose, as we normally do, that there really is a nonlinguistic property of being red, a property expressed by the predicate ‘is red’. This predicate is vague and so is the property. Just as the former has borderline cases of application, so too the latter has borderline instances (objects which are neither clearly red nor clearly not red). Moreover, even if the actual world had not contained borderline red objects, still, intuitively, that would not have shown that the property, redness, is not vague. What the vagueness of properties seems to require is that there be possible borderline instances. Consider next concrete objects, for example, Mount Everest. Some molecules are definitely inside Everest and some are definitely outside. But intuitively, some have a borderline status: there is no determinate fact of the matter about whether they are inside or outside. Everest, then, has borderline spatiotemporal parts. In this way, it is like a cloud. So Everest is a vague concrete object.

There is another way in which, according to some philosophers, objects in the world can be vague. If, for a given object, o, there is an object, o′, such that it is indefinite whether o is identical with o′, then o, by virtue of its entering into an indefinite identity relation, is a vague object. Here is one possible example (due to D. Parfit, cited in Broome 1984). There is a club which has a clubhouse, a membership list and a set of rules. This club is never formally disbanded, but through time its members meet less and less frequently and the clubhouse becomes run down. There are no meetings for several years. Twelve years later, however, a few of the original members get together with some new people and start to meet once more in the same building (now redecorated). The club they belong to at this later date has the same name as the earlier one.

It has been held that the claim that the first club is identical with the second one is indefinite. Moreover, this indefiniteness, it has been suggested, is not an epistemic matter, since there is no further information which would settle the issue. On this view, each club has a vague identity and is thereby a vague object.

There is at least one respect in which the proposed characterizations of vagueness are incomplete. Consider the following sequence of conditionals, each of which includes the vague term ‘tall’:

Intuitively, there is no sharp dividing line between the true conditionals in this sequence and those that have some other value. This fact is not captured in the earlier account of intensional vagueness. But it seems to be part and parcel of our ordinary conception of the vagueness of terms such as ‘tall’ or ‘bald’. Their vagueness is robust or resilient. And a corresponding point can be made about vague concrete objects. For example, it does not seem to be true that there is a sharp dividing line between the molecules that are inside Everest and those that have a borderline status.