Ambiguity is one way in which the meanings of words and phrases can be unclear, but there is another way, which is different from ambiguity: vagueness. For example, some men are definitely bald, and there is no debating the matter, for instance, Patrick Stewart (Captain Picard of Star Trek). Other men are definitely not bald, for example, Bill Clinton. Then there are quite a few men who carefully comb a scanty amount of hair over their scalps, about whom we are not sure whether to say they are bald or not. There is no clear line.

Another example of a vague concept is the concept of a heap. Two or three grains of sand is not a heap, but a thousand is. How many grains of sand does it take to make a heap? There is no clear line. (See the paradox of the heap.)

When we look at a man with thinning hair or a small pile of sand, and we do not know whether to call the man "bald", or the sand a "heap", we have found a borderline case; it is not clear if the concept applies. We can make a general principle, which might work as a definition of the word "vague":

Vagueness describes a concept where there is no clear fact of the matter whether the concept applies or not.

Consider those animals in Alaska that are the result of breeding Huskies and wolves: are they dogs? It is not clear: they are borderline cases of dogs. This means our ordinary concept of doghood is not clear enough to let us rule conclusively in this case.

Vagueness is important philosophically. Suppose we want to come up with a definition of "right" in the moral sense. We want a definition to cover actions that are clearly right and exclude actions that are clearly wrong, but what do we do with the borderline cases? Surely there are such cases. Some philosophers say we should try to come up with a definition that is itself unclear on just those cases. Others say that we have an interest in making our definitions more precise than ordinary language, or our ordinary concepts, themselves allow; they recommend we advance precising definitions. So, some philosophers want their definitions to be unclear in precisely those areas in which the ordinary concept to be defined is unclear, while other philosophers want their definitions to be more precise than the ordinary concepts.

Many scientific concepts are of necessity vague, for instance species in biology cannot be precisely defined, owing to unclear cases such as ring species. Nonetheless, the concept of species can be clearly applied in the vast majority of cases. As this example illustrates, to say that a definition is "vague" is not necessarily a criticism.

Fuzzy logic is a form of logic created to allow reasoning with vagueness.

References

• Vagueness: A Reader, ed. by Rosanna Keefe and Peter Smith (MIT Press: pbk 1999)
  The editors' long introduction gives a clear and very useful overview of theories of vagueness, and they collect many classic papers on the subject.