1  Vagueness arises from the use of terms that are inherently vague. 2  The cabinet minister who says, My officials are monitoring this situation very closely, and I can promise that we shall take all appropriate measures to ensure that the situation is resolved in a way that is fair to all the parties involved. Vagueness in Sentences and Words.  2 The primary application of 'vague' is to sentences, not to words. 3  But the vagueness of a sentence does not imply that vagueness of every constituent word.