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A definition may be a statement of the essential properties of a certain thing, or a statement of equivalence between a term and that term's meaning. The two are not mutually exclusive, nor are they equivalent.
| Nothing is more usual than for philosophers to encroach on the province of grammarians, and to engage in disputes of words, while they imagine they are handling controversies of the deepest importance and concern. - David Hume |
One can distinguish a number of different kinds and techniques of definition, including:
Just as arguments can be good or bad, definitions can be good or bad. A definition gives us the meaning of a word. To understand this more deeply requires an elucidation of a few features of meaning, the principal ones being extension, intension, ambiguity, and vagueness.
The distinction between the extensionThe extension of an idea or (linguistic) expression consists of the things that it applies to; it contrasts with intension. This general notion is from semantics, and has been applied to some other fields. In mathematics In mathematics, the extension of a and the intensionThe intension of a word or phrase (not to be confused with intention or intentionality may be regarded as a description, or set of properties (if one can indulge talk of properties at all), which applies to each member of the word's extension, and which d of a word is very similar to the distinction between a word's denotation and connotation. For example, the extension of the word "bachelor" would be all and only the bachelors in the world. The extension of this word would include several hundreds of millions of men. The intension of the word is more brief because it includes just two properties: the property of being a man, and the property of being unmarried. Basically, all bachelors are unmarried men, and only bachelors are unmarried men.
The sort of definition that philosophers are interested in, insofar as they are interested in definitions at all, is one that identifies a word's intension, rather than its extension. A definition of the word 'bachelor' is 'unmarried man'. Aside from being practically impossible, such a list is not what is generally desired. What is desired is a description of what all those things we call 'bachelors' have in common that distinguishes them from all non-bachelors. A list of all bachelors would be static, and could not expand to determine whether any new human is a bachelor or not.
There are two different ways in which the meanings of words can be unclear. Words can be unclear in the sense of being ambiguousA word, phrase, sentence, or other communication is called ambiguous if it can be reasonably interpreted in more than one way. The simplest case is a single word with more than one sense: The word "bank", for example, can mean "financial institution", "ed, of being vagueAmbiguity 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, or a combination of the two. Most words are, in fact, both ambiguous and vague. This is not a skeptical or even a controversial claim; to say that many, or perhaps even most, words are both ambiguous and vague is not to say that they have no meaning. It is to say, first, that many individual words have many distinct senses; and, second, that those senses are often, in ordinary language, not meant to be exhaustively precise. A word that is both ambiguous and vague, whose extreme limits are fuzzy and undefined, can still contain a rich fund of meaning.