# What is the sense of using word “argument”, for inputs of a function?

In computer jargon, we refer to "inputs of a function" as "arguments". I was wondering what the sense is in doing so.

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The computing use comes directly from mathematics, where, according to the OED, it is:

Math. and Computing. An independent variable of a function (e.g. x and y in z = f(x, y)).

Their first use in maths:

1865 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art I. 768 Any trigonometrical function of ϕ is termed an elliptic function, having the argument u and modulus k.

This meaning can be traced back to an earlier sense:

2. Astron. and Math. The angle, arc, or other mathematical quantity, from which another required quantity may be deduced, or on which its calculation depends.

It's first recorded in Chaucer around 1400. The third sense (also first recorded in the same Chaucer) is:

3. A statement or fact advanced for the purpose of influencing the mind; a reason urged in support of a proposition; spec. in Logic, the middle term in a syllogism. Also fig.

And for good measure, the first sense is:

1. Proof, evidence, manifestation, token. (Passing from clear proof in early, to proof presumptive in later usage; cf. argue v. 3) arch.

There are some eight various senses altogether.

So, an argument is a fact or something that drives forward reasoning, or the output of a calculation, a mathematical function or computing function.

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I feel this answer is in some way partial. –  Edwin Ashworth Jan 1 at 16:36
First cite of a use in math, maybe, but it can hardly be the first use: it doesn't define it in any way, so if this really was a new meaning at the time, it would have made no sense to anyone. –  Marthaª Jan 1 at 16:37
@EdwinAshworth: THWACK!!! –  Marthaª Jan 1 at 16:38
@Martha: I'm tempted to ask “Is that American for hello?” but you might be one of the apparently few people over there who don't watch Downton. (It was nice to see Shirley MacLaine managing to trump Maggie Smith later.) –  Edwin Ashworth Jan 1 at 16:44
Well, the answer pretty much answers the QUESTION (about sense, not about origin as such). The jump between "Argument" in Logic and in Astronomy still seems a bit large but I can accept the argument "token of knowledge, that gives desired result after processing". –  SF. Jan 1 at 17:29
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From the Wiktionary entry for argument...

Etymology:
From Middle English, from Anglo-Norman, from Old French,
from Latin argumentum (“proof, evidence, token, subject, contents”)

In which context it's worth noting Wiktionary definition #7

(programming) A parameter in a function definition; an actual parameter, as opposed to a formal parameter.

Effectively, the argument is the contents/value of a specific actual parameter as passed, rather than the name of the variable carrying the passed value into the function.

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It's a nominalization from the Latin verb argūere, 'show, prove, assert, declare, make clear, reprove, accuse, charge with, blame, censure, denounce as false'. It's not what we mean in English as "arguing"; in Latin it had more to do with persuasion and rhetoric than logic -- logic was just a special variety of rhetoric, and mathematics didn't exist as such outside of Euclid and abacus techniques. –  John Lawler Jan 1 at 19:14
@John: I'm supposing that in the actual meaning under consideration here, the sense is extrapolated from a specific value (or case) that "bolsters" an argument. –  FumbleFingers Jan 1 at 19:20
+1 The distinction between parameter and argument is important. A parameter is a thing over which something is parameterised; an argument is a value by which you instantiate the parameterised thing. In a typed setting, the type of a function is a theorem, and the function is a proof; when evaluating the proof, an argument is evidence for a specific type. –  Jon Purdy Jan 1 at 19:31
@Jon: I'll take that as further evidence that this particular usage can reasonably be linked to the more familiar argument = reason given in support of a theory (which also spreads in another direction to give an exchange of diverging or opposite views, typically a heated or angry one). –  FumbleFingers Jan 1 at 22:38

BTW, I feel this question would be more aptly asked in the Programmer's/Software engineering forum.

Who used it first - Mathematics or Linguistics?

Regardless of precedence, the use of the term argument certainly was inherited directly from computer science linguistics, which was both a significant benefactor and beneficiary to the field of linguistics.

An argument is a token that forms part of the syntax tree.

When computational linguists (mathematician Admiral Grace Hopper being a well-known one) design or analyse a computational language, they would construct a syntax tree. And guess what ... the term argument would be part of their consideration, wouldn't it?

Grace Hopper being a pioneer in the field of computational linguistics must have contributed significantly to the prevalent use of the term argument in computer programming, as we are well aware she had also given us the term debugging.

Since she was a mathematician, she would have leaned heavily on the meaning of arguments in Mathematics.

Avram Noam Chomsky introduced Phrase-Structural Analysis into linguistics. According to the Wikipedia article on him, he made major contributions to analytic philosophy, and "His work has influenced fields such as artificial intelligence, cognitive science, computer science, logic, mathematics, music theory and analysis, political science, programming language theory and psychology."

I would liken an argument in a syntax tree to a child node to a predicate node.

As example of arguments, while outmoded "Sauserrean" structured grammarians use the term transitive verbs, phrase-structural linguists use the more flexible term valency of a verb. Where, the valency of a verb is the number of arguments a verb would take, as explained in my (less than precise) argument at The subject is after the verb in this sentence?, where I confuse the use of arguments vs adjuncts.

I am sure the precision of my historical account of linguistics is left to desire, as it merely points to the areas of historical research. However, I believe it is accurate in pointing out that the use of the term argument has direct genealogy from computational linguistics which descended from structural analysis in Linguistics, which in turn cross contributed with Mathematics and Philosophy,

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