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In grammar and linguistics, the term complement is used with different meanings, so it is difficult to give a single precise definition and explanation. In a broad general sense however, a complement can be understood as a word, phrase or clause that is necessary to complete the meaning of a given expression. The terms complement and argument overlap in meaning and use. A given complement is therefore often also an argument. Complements are not adjuncts, however.
In many traditional grammars, the terms subject complement and object complement are employed to denote the predicative expressions (e.g. predicative adjectives and nominals) that serve to assign a property to a subject or object, e.g.
Although widespread in school grammar, this use of terminology is not employed by many modern theories of syntax, which typically view the expressions in bold as part of the clause predicate, which means they are not complements of the subject or object, but rather they are properties that are predicated of the subject or object.
In many modern grammars (for instance in those that build on the X-bar schema), the object argument of a verbal predicate is called a complement. In fact, this use of the term is the one that currently dominates in linguistics. A main aspect of this understanding of complements is that the subject is usually NOT a complement of the predicate, e.g.
The noun phrases (NPs) the counter and the tub are necessary to complete the meaning of the verbs wiped and scoured, respectively, hence they are complements.
While it is less common to do so, one sometimes extends this reasoning to subject arguments:
In these examples, the subject and object arguments are taken to be complements. In this area then, the terms complement and argument overlap in meaning and use. Note that this practice takes a subject complement to be something much different from the subject complements of traditional grammar, which are predicative expressions, as just mentioned above.
Construed in the broadest sense, any time a given expression is somehow necessary in order to render another expression "complete", it can be characterized as a complement of that expression, e.g.
Construed in this broad sense, many complements cannot be understood as arguments. The argument concept is tied to the predicate concept in a way that the complement concept is not.
In linguistics, an adjunct is an optional, or structurally dispensable, part of a sentence, clause, or phrase that, when removed, will not affect the remainder of the sentence except to discard from it some auxiliary information. A more detailed definition of the adjunct emphasizes its attribute as a modifying form, word, or phrase that depends on another form, word, or phrase, being an element of clause structure with adverbial function. An adjunct is not an argument (nor is it a predicative expression), and an argument is not an adjunct. The argument-adjunct distinction is central in most theories of syntax and semantics. The terminology used to denote arguments and adjuncts can vary depending on the theory at hand. Some dependency grammars, for instance, employ the term circonstant (instead of adjunct), following Tesnière (1959).