Argument

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In philosophy: Argument (philosophy) [r]: A set of statements, one of which is the conclusion, the others premises (or premisses). ^[e]

In mathematics, the word "argument" is used

(with a similar meaning as in philosophy) as an alternative to: Proof [r]: A sequence of arguments which establishes that some mathematical statement is implied by a certain set of assumptions. ^[e]

and

as an alternative word for the (independent or input) "variable" of a function.