What part of speech are mathematic operands?
November 17, 2017 1:46 PM   Subscribe

I just heard a colleague mumble a change order number in Spanish, his native language. He said, "Numbers are the one thing I still have to do in Spanish - I learned tres mas cuatro es siete, not three plus four." Which got me to thinking, what part of speech are math operands? They're telling you to do something (verb) but they don't conjugate. Are they a conjunction? Something weird?
posted by notsnot to Religion & Philosophy (16 answers total) 2 users marked this as a favorite
You're going to get a lot of contradictory answers here, and a lot of bickering over which is the right one.

The meta-level answer is that the traditional part-of-speech categories are just a rough and unscientific approximation of the truth — the linguistic equivalent of saying there are exactly four elements, or exactly seven colors.

In fact, it is really, really easy to find examples of words where reasonable people can disagree about which part-of-speech category they go in. Even tenured linguistics professors disagree about this stuff all the time. If you ask an honest linguist how many parts of speech there are, they'll probably say "Nobody has any idea, we don't all agree that the question is answerable, and some people even think it varies from one language to the next."
posted by nebulawindphone at 1:55 PM on November 17, 2017 [14 favorites]

The name of a function that combines number is addition. Adding things to a bucket is a verb. So at least two different?
posted by sammyo at 2:19 PM on November 17, 2017 [1 favorite]

Operands are numbers. Do you mean operators?
posted by caek at 2:30 PM on November 17, 2017 [3 favorites]

The first online dictionary I looked at says plus is a preposition when used like "two plus three is five".
posted by SemiSalt at 2:32 PM on November 17, 2017

I generally agree with the descriptivist perspective of nebulawindphone above.

But for what it's worth, the OED calls them prepositions. This makes a certain amount of sense, as prepositions are generally used to describe the relationship between two noun phrases. So we could decompose the sentence "two plus three equals five" as

(two (plus three)) equals (five)

We have the subject, which is a "two" with a "three" placed in a relationship to it by the preposition "plus". "equals" is then the verb of the sentence, and "five" is the object.
posted by Johnny Assay at 2:33 PM on November 17, 2017

FWIW, m-w.com calls plus (in the sense of "two plus two," scroll down), minus, and times prepositions (like the "by" in "divided by"), but ultimately I agree with nebulawindphone.
posted by DevilsAdvocate at 2:34 PM on November 17, 2017

It also depends on the binary operators. Sure, maybe plus is a preposition, but many mathematicians read A~B as "A twiddles B", or "A wiggle B". And "twiddle" and "wiggle" are rather squarely in the category of verbs.

Then of course you have your logical operators, (and binary operators are binary operators, right?) So A∧B is read as "A and B", and "and" is canonically a conjunction. Same goes for "implies"/→, "or"/∨, etc.

So, while nebulawindphone opened up with some great caveats (educated linguists may disagree on where "plus" should go), I think it's pretty clear that there is no way in hell that we would want to put all operators in the same single part of speech category. So far we have preposition, verb, and conjunction fairly safely established.
posted by SaltySalticid at 2:46 PM on November 17, 2017 [1 favorite]

(Yeah, my point was specifically about "plus." I agree that "implies" is unambiguously a verb; and I think "box" and "integral" and "union" are preeeeetty unambiguously nouns.)
posted by nebulawindphone at 4:39 PM on November 17, 2017

I would say, just as something to ponder, and as a further iteration of what nebulawindphone said, that in the context in which your colleague is using them - actually doing calculations - they are not parts of speech, since they're not performing any communicative function at all. They are incantations. He's not talking; his mouth is helping his brain do math. It is significant that he can't do it in English... it only works in his native tongue, Spanish.
posted by lefty lucky cat at 6:19 PM on November 17, 2017

Thanks, y'all. I guess, like nebulawindphone says, ask five linguists and get five answers!
My own closer examination comes up with some thoughts on specific operators:
-"Two plus three" is equivalent to "Two and three", and adding is, on a meta level, conjoining.
-"Five minus four" and "four minus five" are not the same thing, so minus is more like a verb with subject and object.
-The only parallel structure for division is something like "twelve over four", which is unambiguously a preposition.
posted by notsnot at 7:21 PM on November 17, 2017

I pretty much agree with nebulawindphone (and got there by having a similarly inconclusive conversation about which part-of-speech bucket "yes" goes in), but I'm going to share some thoughts on the subject anyway.

What part of speech are numbers? "Four" can be an adjective ("there are four lights"), a plural pronoun ("four were arrested"), or a noun ("the four of spades"). I'm a mathematician and a math teacher, and my view is that mathematical abstraction begins with the ability to think of four as a noun rather than an adjective or pronoun. That is, math is the realm where four is a thing in itself which can be operated on without reference to a thing that there are four of.

Now imagine being incapable of that leap. You'd never say "two times two is four", right? You'd say "two times two [things] are four". And in fact, people do say that, or did, and it used to be the predominant usage. (I remember first encountering that phrasing in Marmaduke Multiply, an old book of rhymes to teach children their multiplication tables.) I don't think this usage necessarily reflected lower mathematical competence, but it's interesting that its decline coincides with the universalization of abstract math education.

The word "times" itself sits uneasily as an operator in the modern usage. Remember, it's the same word as in the phrase "three times a lady" (where it's what, a postposition??), but turning it into a conjunction or even a quasi-verb (my students say things like "times it by two") disconnects it grammatically from those origins. But that's just how language evolves, and I would argue that math operators in general, when acting on numbers-as-abstract-nouns, are best thought of as their own special category, like a conjunction that doesn't just join two nouns in a sentence but crunches them up and replaces them with one noun. That's roughly how an operation is defined in a math textbook.

P. S. to SaltySalticid: No way is "twiddle" a verb in "A twiddle B". It's purely the name of the character.
posted by aws17576 at 7:38 PM on November 17, 2017 [1 favorite]

I am a mathematician, and I've studied a bit of linguistics. I'd say the best conventional part of speech they could easily map onto is "prepositions". If the number "three" (not counting anything, but the number itself, in a sort of Platonic ideal of threeness or what-have-you) is a noun, then "plus four" is a modifier to that noun, and the most straightforward way to modify a noun with that structure of (some word + other noun) would be a prepositional phrase.

Yes, addition is semantically conjoining, as you say, but so is "with", and "with" is unmistakably a preposition, not a conjunction.
posted by jackbishop at 12:49 PM on November 18, 2017

Great question. My feeling is: traditional grammar just breaks down with math. Mathematical expresions have their own syntax (largely defined by how we write them down), and their behavior is not like other parts of English.

You could try to shoehorn some of the simpler expressions in. E.g. "Two and two are four" is a normal sentence: numeral, conjunction, numeral, verb, numeral.

But I think it'd be pretty silly to attempt to use ordinary syntactic categories with, say, "x equals minus b plus or minus square root of b squared minus four a c over two a." It all came from ordinary language in some way, but it's just how we read out a standard mathematical formula.

In syntax, as I was taught it, you have to have syntactic tests for any proposed syntactic category. Preferably multiple tests, because some things don't neatly fit. Anyway, the point is: if you try to use the shoehorned categories for a mathematical expression, the tests just won't work. That's because they follow mathematical syntax, not English syntax.

An example: you can often (not always) tell a preposition by the fact that it can be modified with "right": I hit him right on the nose. He fell right in the water. Is plus a preposition? Let's try it: two right plus two is four. Doesn't work. Or maybe it's a conjunction? But conjunctions usually require both conjoints, while "plus four" is perfectly valid math.

So if you really wanted to properly handle math expressions, you'd probably end up defining an extra set of categories and behaviors. But it's simpler to just define how math formulas work and give the rules for reading them out loud.
posted by zompist at 12:41 AM on November 19, 2017 [1 favorite]

What part of speech are numbers? "Four" can be an adjective ("there are four lights"), a plural pronoun ("four were arrested"), or a noun ("the four of spades")

I think you could argue that four is functioning as an adjective in each of those; it's simply the descriptor. "Persons" is the implicit modified noun in your second example, and four simply denotes which spade--the one with rank "four"--in the third.

As others have stated, in most common English operands function as prepositions, in that they express a relationship among words/elements of speech. But that breaks down quickly, to the point you might just consider operands a distinct linguistic category, as zompist says. There are things you can do with--or to, or by, or with relation to--numbers, which usually seem to take on the characteristics of verbs ("divide," "iterate").

But these can usually be expressed in other ways: the product of/difference between x and y, for example.

So to my mind the FPP example isn't one of linguistic difference so much as having learned by rote a different way to conceive of and express a basic arithmetical concept; "three more than four is seven" is a perfectly cromulent phrase in English, but if you've not learned it that way, it might be confusing. See also "twice twelve is twenty-four."
posted by aspersioncast at 2:16 PM on November 19, 2017

nebulawindphone's answer is probably the most objective, but:

Vodka with tomato juice, Tabasco and Worcester sauce is a Bloody Mary. < = > Two plus two is four.

A Bloody Mary without vodka is a Virgin Mary. < = > Four minus one is three.

I think it's fulfilling the role of a preposition. Otherwise you could chuck it in the adverb basket, but it's getting full.

Also telling, we explicitly prepositionify division: "A divided by B" becomes "A over B". So we switch to using a word which is normally a preposition in English. Indeed, although I don't do it in my maths idiolect, people use "by" for multiplication.

I could speculate that oral descriptions of mathematical operations are really visually describing what the written form looks like, rather than providing instructions on what to do. But I guess you'd need to do proper research and determine whether "close bracket" is a noun or verb phrase when people use it.
posted by Wrinkled Stumpskin at 3:18 AM on November 20, 2017

zompist has posted some more thoughts on the subject over at his blog; they are well worth reading.
posted by Johnny Assay at 5:15 AM on November 23, 2017 [2 favorites]

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