- 2a : not clearly defined, grasped, or understood : indistinct <only a vague notion of what's needed>; also : slight <a vague hint of a thickening waistline> <hasn't the vaguest idea>
- b : not clearly felt or sensed : somewhat subconscious <a vague longing>
- 3: not thinking or expressing one's thoughts clearly or precisely <vague about dates and places>
- 4: lacking expression : vacant <vague eyes> <a vague stare>
- 5: not sharply outlined : hazy <met by vague figures with shaded torchlights — Earle Birney>
- if the concept's extension is unclear;
- if there are objects which one cannot say with certainty whether belong to a group of objects which are identified with this concept or which exhibit characteristics that have this predicate (so-called "border-line cases");
- if the Sorites paradox applies to the concept or predicate.
In everyday speech, vagueness is an inevitable, often even desired effect of language usage. However, in most specialized texts (e.g., legal documents), vagueness is distracting and should be avoided whenever possible.
Vagueness is philosophically important. Suppose one wants to come up with a definition of "right" in the moral sense. One wants a definition to cover actions that are clearly right and exclude actions that are clearly wrong, but what does one do with the borderline cases? Surely, there are such cases. Some philosophers say that one should try to come up with a definition that is itself unclear on just those cases. Others say that one has an interest in making his or her definitions more precise than ordinary language, or his or her ordinary concepts, themselves allow; they recommend one advances precising definitions.
Vagueness is also a problem which arises in law, and in some cases judges have to arbitrate regarding whether a borderline case does, or does not, satisfy a given vague concept. Examples include disability (how much loss of vision is required before one is legally blind?), human life (at what point from conception to birth is one a legal human being, protected for instance by laws against murder?), adulthood (most familiarly reflected in legal ages for driving, drinking, voting, consensual sex, etc.), race (how to classify someone of mixed racial heritage), etc. Even such apparently unambiguous concepts such as gender can be subject to vagueness problems, not just from transsexuals' gender transitions but also from certain genetic conditions which can give an individual both male and female biological traits (see intersexual).
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. 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 one's ordinary concept of doghood is not clear enough to let us rule conclusively in this case.
One theoretical approach is that of fuzzy logic, developed by American mathematician Lotfi Zadeh. Fuzzy logic proposes a gradual transition between "perfect falsity", for example, the statement "Bill Clinton is bald", to "perfect truth", for, say, "Patrick Stewart is bald". In ordinary logics, there are only two truth-values: "true" and "false". The fuzzy perspective differs by introducing an infinite number of truth-values along a spectrum between perfect truth and perfect falsity. Perfect truth may be represented by "1", and perfect falsity by "0". Borderline cases are thought of as having a "truth-value" anywhere between 0 and 1 (for example, 0.6). Advocates of the fuzzy logic approach have included K. F. Machina (1976) and Dorothy Edgington (1993).