Diagram "Two plus two equals four"?

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eldin raigmore
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Diagram "Two plus two equals four"?

Post by eldin raigmore » 01 May 2017 01:06

Since the fifth grade I've wondered what part-of-speech "plus" is in the sentence "two plus two equals four".
Since the tenth grade I've wondered how to draw a Reed-Kellog diagram of that sentence.
Several teachers gave me several answers to the question "What part of speech is 'plus'?", but none gave me a convincing explanation why that was the correct answer.
As to "How do I diagram 'two plus two equals four'?" I think the only answer I remember ever receiving was "However you do it, if you do it in your homework, I'm going to mark it wrong.".

So, now I really want to know:

1. Is "plus" a preposition in "two plus two equals four"?
2. If so, why? If not, why not?
3. What parts-of-speech are all the other words in that sentence? (Also, what PoS is "plus", in case that's not part of your answers to questions 1 and/or 2.)
4. And why are those the right answers?
5. Can anyone draw a Reed-Kellogg diagram of that sentence?
6. If so, how do you know that is the correct answer?
6'. If no-one can, can you explain why it's impossible to diagram?

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Re: Diagram "Two plus two equals four"?

Post by Sumelic » 01 May 2017 01:37

I'll start with the part that seems easiest to me: I don't see how "equals" in that sentence could be anything but a verb. It plays the semantic role of a verb, it has verb morphology (the third-person singular present-tense suffix -s) and it can be converted to "does... equal" in a question ("What does two plus two equal?").

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Re: Diagram "Two plus two equals four"?

Post by qwed117 » 01 May 2017 02:10

eldin raigmore wrote:Since the fifth grade I've wondered what part-of-speech "plus" is in the sentence "two plus two equals four".
Since the tenth grade I've wondered how to draw a Reed-Kellog diagram of that sentence.
Several teachers gave me several answers to the question "What part of speech is 'plus'?", but none gave me a convincing explanation why that was the correct answer.
As to "How do I diagram 'two plus two equals four'?" I think the only answer I remember ever receiving was "However you do it, if you do it in your homework, I'm going to mark it wrong.".

So, now I really want to know:

1. Is "plus" a preposition in "two plus two equals four"?
2. If so, why? If not, why not?
3. What parts-of-speech are all the other words in that sentence? (Also, what PoS is "plus", in case that's not part of your answers to questions 1 and/or 2.)
4. And why are those the right answers?
5. Can anyone draw a Reed-Kellogg diagram of that sentence?
6. If so, how do you know that is the correct answer?
6'. If no-one can, can you explain why it's impossible to diagram?

----------
Thanks! You'll be helping me to "scratch" a 50-to-55-year-long "itch"!
two with two, two of two, two up by two, make four
but then
two and two, two more two, two squared, make four.


It's a noun complement of some sort. Reed-Kellogg diagrams are notoriously underequipped to go past adjectives and such.
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Re: Diagram "Two plus two equals four"?

Post by Axiem » 01 May 2017 06:41

I've always considered most math terminology, when talking out a set of symbols, to be its own special "grammar" without necessarily much bearing on the grammar of the host language. But that's also probably a result of only learning anything math-wise in English; the most I've really encountered in any other language is counting, and maybe saying "two and two are four".
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Re: Diagram "Two plus two equals four"?

Post by Rosenkohl » 01 May 2017 11:01

1. I wouldn't call it that.

2. Seems more like a conjunction to me. I don't see why it's so different from "and". Surely someone could point out how, in some languages, comitative case markers/prepositions develop from/into additive conjunctions, and there does seem to be some overlap. I tend to think it's more elegant to see "plus" as a coordinating conjunction, in such a way that there's no separate prepositional phrase. It also ties in nicely with other uses of "plus"; cf. "they gave me my money back plus £10 in credit for my trouble"; "my husband got us tickets to Hawaii; plus they're first class tickets, too!"

3. noun conjunction noun verb noun.

4. I prefer labelling the numbers there as nouns rather than numerals because they aren't quite quantifying anything, but you are rather referring to the numbers themselves (cf. "blue and yellow make(s) green", where it's even acceptable to have singular morphology for the verb element as well).

5. <flame>Reed-Kellog diagrams are silly.</flame> What the syntax tree will look like will depend mostly on your approach to syntactic coordination, there are several ways to represent it.

6. I don't. I haven't thought about this very long.

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Re: Diagram "Two plus two equals four"?

Post by Creyeditor » 01 May 2017 12:20

I agree with Rosenkohl, 'plus' looks like a conjunction, that coordinates two nouns. Conjunctions are definitely difficult in diagrams. Most often the difficulty is based on the symetry of conjunction, which is difficult to show in sentence diagrams. I read up a bit on Reed-Kellog diagrams. This page has a solution. I will try to diagram your sentence here:
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Image
A minor option might be, that the verb 'equal' has some copula-like properties, so you might want to seperate 'equal' and 'four' by a '\' instead of a '|'.

Interestingly, I would guess that 'minus' on the other hand, acts more like a preposition. Maybe the line between internominal conjunction and prepositions is not that clear, as Rosenkohl pointed out.
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Re: Diagram "Two plus two equals four"?

Post by Salmoneus » 01 May 2017 13:22

Seems like, in general, a non-meaningful issue. Do you call it a 'conjunction' or a 'preposition'? Depends how you define 'conjunction' and 'preposition'. I suspect, given that they pretty much the same, it will depend on the precise textbook you're following or the conventions of a specific language.

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Re: Diagram "Two plus two equals four"?

Post by Sumelic » 01 May 2017 17:23

I'm sure there are already better arguments about this, but I haven't read them, so here is a short argument I thought of in favor of it being a preposition (when followed by an NP complement; my understanding is that traditional grammar would require it to be analyzed as a conjunction):

- It can be coordinated with a phrase starting with "minus": "It has a capacity of ten liters, plus or minus 2 percent." "Minus" is certainly not a symmetrical coordinating conjunction; the fact that it is coordinated here with "plus" indicates that it belongs to the same part of speech; hence "plus" is likely not a symmetrical coordinating conjunction either.

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Re: Diagram "Two plus two equals four"?

Post by Salmoneus » 01 May 2017 20:08

Sumelic wrote:I'm sure there are already better arguments about this, but I haven't read them, so here is a short argument I thought of in favor of it being a preposition (when followed by an NP complement; my understanding is that traditional grammar would require it to be analyzed as a conjunction):

- It can be coordinated with a phrase starting with "minus": "It has a capacity of ten liters, plus or minus 2 percent." "Minus" is certainly not a symmetrical coordinating conjunction; the fact that it is coordinated here with "plus" indicates that it belongs to the same part of speech; hence "plus" is likely not a symmetrical coordinating conjunction either.
This seems to beg the question. OK, so "plus" might be the same POS as "minus". But why can't "minus" be a conjunction too? I don't find the word "symmetrical" convincing here. "If", for instance, is not semantically symmetrical ("dangerous if eaten" does not mean the same as "eaten if dangerous"). Nor are any subordinating conjunctions, obviously. "But" and "yet" aren't symmetrical either: "I do eat fish but not salmon" means something different from "I do eat salmon, but not fish" (for a start, the former is a reasonable declaration while the latter is delusional!); indeed, even where they are truth-functionally symmetrical, their are not truely semantically symmetrical - "old men forget, yet all shall be forgot" has a different connotation entirely from "all shall be forgot, yet old men forget"!. And then there's things like "I ate ferrets for a week - but enough of that." We can hardly have "enough of that - but I ate ferrets for a week".

So if you make 'symmetry' the defining feature of conjunctions, it would seem that you:
- reduce 'conjunctions' just purely down to 'and' and 'or', and i'm not 100% about 'or';
- raise the question of why you're separating out those two words from all the others that look to be of their class purely because of 'symmetry'

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Re: Diagram "Two plus two equals four"?

Post by Creyeditor » 01 May 2017 20:10

Just a reminder that 'conjunction' has two definitions, one is 'coordinating conjunction' (with the antonym disjunction), the other is 'conjunction in general' or 'word that is used to join two words or phrases together'.
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Re: Diagram "Two plus two equals four"?

Post by Axiem » 02 May 2017 05:24

Consider also "divided by": "Ten divided by five is two".

And then "Two to the third power is eight"

And then "For all ex, there exists a wye such that the integral of sine theta dee theta from ex to wye is zero"
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Re: Diagram "Two plus two equals four"?

Post by Rosenkohl » 02 May 2017 10:54

Maybe that's extrapolating a bit (since OP was asking about English), but the distinction between prepositions and conjunctions can be quite clear-cut. Take, for example, languages with case marking (cf. "I ate two-ACC apples-ACC plus three-ACC bananas-ACC" vs. "I ate two-ACC apples-ACC plus three-SOME_OBLIQUE_CASE bananas-SOME_OBLIQUE_CASE").

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Re: Diagram "Two plus two equals four"?

Post by OTʜᴇB » 02 May 2017 11:42

I'd say it was some form of compound of nouns. "two plus two" here is behaving as a single noun, with the verb and object afterwards. The "plus" might be a grammatical form of "added to" that is used in such numerical compounding.
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Re: Diagram "Two plus two equals four"?

Post by Lambuzhao » 03 May 2017 23:17

"plus" originally is :lat: many<COMPAR.N.SG>, used adverbially.
One could easily use /et/ in :lat:.
:esp: uses /mas/ ADV or /y/ CNJ.

Incidentally, the :grc: word for 'minus' is

λείψει
[le:.pse:]
lack.FUT.3SG
it will lack ; it will release

kind of like :eng: 'take away'

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Re: Diagram "Two plus two equals four"?

Post by Lambuzhao » 03 May 2017 23:27

We had/have a 'Math' thread, where I think this was (sort of) explored.

That was where I explained :con: Rozwi's use of grammatical cases for the operations of addition, subtraction, multiplication and division. :wat:

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Re: Diagram "Two plus two equals four"?

Post by clawgrip » 05 May 2017 14:45

Math phrases in Japanese are spoken according to the actual equation written down which breaks the grammar:

2 + 2 is ni tasu ni, where tasu is the verb "add", but of course it comes in the middle which is not normal for a SOV language. Same goes for the other three "minus" hiku, "times" kakeru, and "divided by" waru. These are all verbs, but they come in the middle rather than at the end.

However, when adding the answer, you can say ni tasu ni ikōru yon, but it is more common to replace ikōru "equal" with the nominative particle ga, i.e. ni tasu ni ga yon.

So Japanese, anyway, totally breaks its own grammar for math expressions.

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Re: Diagram "Two plus two equals four"?

Post by Salmoneus » 05 May 2017 18:28

clawgrip wrote:Math phrases in Japanese are spoken according to the actual equation written down which breaks the grammar:

2 + 2 is ni tasu ni, where tasu is the verb "add", but of course it comes in the middle which is not normal for a SOV language. Same goes for the other three "minus" hiku, "times" kakeru, and "divided by" waru. These are all verbs, but they come in the middle rather than at the end.

However, when adding the answer, you can say ni tasu ni ikōru yon, but it is more common to replace ikōru "equal" with the nominative particle ga, i.e. ni tasu ni ga yon.

So Japanese, anyway, totally breaks its own grammar for math expressions.
It's possible - both in Japanese and in English - that many spoken equations are actually just quotations (or names), rather than grammatical speech. That is, "plus" in an equation might not have any part of speech, it might just be the middle part of "two plus two", another way of writing "2+2" - quoting the writen sum, or naming it.

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Re: Diagram "Two plus two equals four"?

Post by Lambuzhao » 05 May 2017 21:17

clawgrip wrote:Math phrases in Japanese are spoken according to the actual equation written down which breaks the grammar:

2 + 2 is ni tasu ni, where tasu is the verb "add", but of course it comes in the middle which is not normal for a SOV language. Same goes for the other three "minus" hiku, "times" kakeru, and "divided by" waru. These are all verbs, but they come in the middle rather than at the end.

However, when adding the answer, you can say ni tasu ni ikōru yon, but it is more common to replace ikōru "equal" with the nominative particle ga, i.e. ni tasu ni ga yon.

So Japanese, anyway, totally breaks its own grammar for math expressions.

One might ask "How long back does this tendency stretch in Japanese?

Do you think that the agrammaticality of Japanese math-speak was influenced in any way by Western numerical mathematical notation?

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Re: Diagram "Two plus two equals four"?

Post by lsd » 06 May 2017 09:41

And what about the traditional Japanese method (before western sciences domination)...

In ezakholulwimilizwe, a priori language, there is no difference between linguistic and mathematical notation ...
As a consequence, mathematics is a little removed from the Western standart...
For instance addition (seen as coordination) has some precedence over multiplication (seen as verb) and equals (a topics mark) need multiplication (verb) and is generally on the result placed before...
so 2+2=4 is written 4=1x2+2...
and 18=3×4+2...

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Re: Diagram "Two plus two equals four"?

Post by Ear of the Sphinx » 07 May 2017 01:55

I'd say that “two plus two equals four” is a transcription of a methematical formula “2+2=4” and, as such, this type of diagrams isn't designed to deal with that.

“plus” looks like a conjunction because infix operators tend to look like conjunctions. (In general, they have a similar role.)

But then, the mathematical notation doesn't always work like a natural language. There are, for instance, formulas like “ee equals em cee squared” (E=mc²), with multiplication by juxtaposition (“null” infix operator), which doesn't have a counterpart in the natural language (“null conjunction”?).
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