Discreteness, one of the design features of language, along with arbitrariness, etc., makes language much more flexible, productive and precise than other communicative systems. Although it mainly applies to the description of the secondary level of language structure, discreteness can also explain meaningful units, such as morphemes or words, at the primary level. Due to its discreteness, language is regarded, in semiotics, as "digital", in contrast with "analogical". Partially owing to the discreteness or discontinuity, language enables humankind to conceptualize and perceive the world and themselves with a kind of precision. However, this does not mean that language can mirror the world. Actually many things ( especially intangible things) in the world are not so discrete but rather gradable or continuous. Therefore, linguistic signs or words used to deal with them do not match them absolutely. There are gaps between words and what they refer to. To deal with this gap, sense and reference, two aspects of meaning, are employed in this paper, though with certain modification. While the sense of a word (or its dictionary meaning) is explicitly definable, its referential meaning may not. Some emotive and evaluative words may have certain variation of references continuously on a scale though their senses are discrete. Some common nouns' extensions or their referential meanings are also continuous. Words of this kind are found vague or fuzzy though they are clearly definable and in contrast in their senses. It is a worthwhile effort to probe into the nature of discreteness in both linguistic and semiotic contexts. To do this job presupposes reconsidering the classification of meaning, especially when taking into account the dichotomy between precision and vagueness of linguistic signs.