the so-called core arguments of a verb, that is, the phrases that make up the sentence in combination with it
arguments to predicates and other sentential elements, such as the prepositional argument in "under the table" (which is the prepositional object "the table")
(in literature) a grand argument is a conceptually complete story with both an emotional and logical comprehensiveness.
(in oratory or law) the presentation of evidential reasoning in an attempt to persuade the listener of the correctness of the speaker's position (this usage not only covers logical arguments but also includes other forms of persuasion, such as purely emotional arguments)
(in common usage) a dispute, disagreement or antagonistic discussion