Construct · 3 fields · 3 citations
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In logic an argument is a set of statements, one of which, the conclusion, is claimed to follow from the others, the premises. Copi, Cohen, and Rodych open Introduction to Logic with exactly this: an argument is not a quarrel but a structured offering of reasons, and the questions asked of it are whether it is valid, whether the premises are true, and so whether it is sound. The referent is a piece of reasoning set out in language, and the unit is the premise-and-conclusion pair. What makes this meaning distinct is that an argument here is judged by whether the conclusion is supported, a property no angle, input, or grammatical participant can have.[1]
In mathematics the argument of a complex number is its angle: for a number written in polar form, the argument is the angle its vector makes with the positive real axis, so that a number is fixed by a modulus and an argument together. Needham sets this out geometrically in Visual Complex Analysis, where arg(z) is the phase and multiplication is rotation. The word carries a second, older mathematical use as well, in which the argument of a function is simply its input. The referent is a number's position on the plane, and the unit is an angle in radians. This meaning shares nothing with the logical one but the spelling: there is no conclusion and nothing to be valid, only a direction.[2]
In linguistics an argument is a participant that a predicate requires in order to be complete: the verb give, for instance, calls for a giver, a thing given, and a recipient, and each of those is one of its arguments. Carnie describes this in Syntax: A Generative Introduction through argument structure and theta roles, the analysis descending from Tesniere's notion of valency, the number of arguments a predicate can take. The referent is a slot in a predicate's frame and the phrase that fills it, and the unit is one such participant. It differs from the logical meaning in that nothing here is offered in support of anything: an argument is demanded by a word's meaning, not marshalled toward a conclusion.[3]
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