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I am struggling to understand the syntactic relevance of the distinction between complement and modifier in theories such as the one presented in the Cambridge Grammar of the English Language by Huddleston and Pullum (henceforth CaGel).

Specifically, I'd like to know

(i) Is there a concise, precise definition of each of these functions, saying exactly what it means to be a modifier and a complement respectively (according to the theory presented in CaGel)? There are obviously lots of examples with extensive discussion, but no matter how much I've searched, I haven't been able to find actual, concise definitions.

(ii) What is the syntactic relevance of the distinction between complement and modifier? That is, what general syntactic phenomenon or phenomena does this distinction explain?

(iii) Are there any reliable syntactic tests for making the distinction, and, if so: what are they? I know of two tests:

  • the substitution test, which involves substituting the head of a phrase containing a dependent with a head that unequivocally doesn't license complements, to see if the dependent still "works" – in which case it would be a modifier
  • the omission test, which involves omitting a dependent to see if the result is still grammatical – which may imply that the dependent in question is a modifier.

However, neither of these tests seem reliable to me – the substitution test seems unreliable for reasons discussed here, and the omission test is unreliable because complements can sometimes be omitted without rendering the result ungrammatical – as in e.g. She stayed in her room/She stayed) – which means that it only works in cases where omission renders the result ungrammatical.

Finally, I'm asking you please not to mark this as a duplicate of this question, because it's not. In that other question I'm asking specific questions about the substitution test; here I'm asking whether there are any other tests to distinguish between complements and modifiers, and this is furthermore just one of the questions I pose here.

Thank you!

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Here is an extract from another post of mine, slightly modified:

1.0 Complements versus Modifiers

1.1 Complements

OK, so let´s have a look at what Modifiers and Complements actually are. Well, roughly speaking, a Complement is a phrase which fills a special slot set up by another word or phrase in the sentence. So for example, the verb TEACH sets up a slot for the thing being taught, the Direct Object, and the people being taught, the so-called Indirect Object. These terms such as Direct Object, Indirect Object, Locative Complement and so forth are just more specific names for Complements of a verb. Prepositions take Complements too, often noun phrases which we can also sometimes describe as Predicative Complements or Objects. Adverbs can often take Complements either directly or indirectly as well. So for example, the infinitival clause to eat in one go fills a special slot set up by the adverb too in It was too big to eat in one go. Adjectives can take their own various sorts of Complements too; consider on chess in keen on chess or to leave in keen to leave.

So, all sort of words and phrases can set up these slots, and all sorts of words and phrases can fill them too. Sometimes Complements are obligatory and sometimes they aren't. Of course, it's nice and handy when Complements are obligatory, because it's easy to identify them. It is also, in such cases, easy to demonstrate how that word or phrase has a special relationship with the Head of the phrase. So, unfortunately, Complements are often construed as obligatory essential accompaniments to other words or phrases when we first start to learn about them. This isn't always the case. Let's revisit the verb TEACH:

  • I teach.
  • I teach English.
  • I teach students.
  • I teach students English.
  • I teach English to students.

Here we see this verb taking no Complements, taking one Object, taking two Objects and taking an Object and a preposition phrase Complement. These different Complements are Complements because this verb sets up a special slot for them, not because they are obligatory.

Complements, of course, have other features. For example, they are usually selected by the word they are the Complements of. These Heads will allow certain types of Complements but not others. So for example, the adjective keen will select preposition phrases headed by the preposition on, but not ones headed by the preposition of:

  • keen on spiders
  • *keen of spiders (ungrammatical)

The verb inquire can take interrogative clauses as Complements, but not declarative ones:

  • I inquired whether the elephants had left.
  • *I inquired that the elephants had left. (ungrammatical)

Complements are thought of as being more tightly integrated into the phrases they occur in than Modifiers are. Whereas Complements are often required to be adjacent to the words that license them, Modifiers can often be moved further away from the phrases they modify or appear on either side of them. So if we see both Complements and Modifiers in the same phrase, as a rule of thumb, all other things being equal, we expect the Complements to be closer to the Head word than the Modifiers:

  • Put it on the shop floor on Thursday.
  • *Put it on Thursday on the shop floor. (awkward if not ungrammatical)

A sentence or phrase will often sound marked, awkward or ungrammatical if this does not occur. In the sentence above the Complement on the shop floor will ideally come closer to the verb put than the Modifier on Thursday.

Because Complements are more tightly integrated into the phrases they occur in than Modifiers, they are often obligatorily replaced when we use a proform, whereas Modifiers may be repeated or addended to such phrases:

  • *I put my beer in the fridge and Bob did so in the cupboard. (ungrammatical)
  • I drank my beer in the kitchen but Bob did so in the living room.

  • *I am counting on their help, but I don't want you to do so on their help. (ungrammatical)

  • I am counting on their help, but I don't want you to do so.

In the first sentence in the fridge is a Locative Complement. As the anaphoric proform do so includes the Locative Complement in the second clause in that example, we cannot then add a second Locative Complement, in the cupboard. In the second sentence, where in the kitchen is a Locative Adjunct (a Modifier), we can freely add another Locative Adjunct in the second clause, in the living room. In the last pair we see that the sentence is grammatical if we omit the Complement on their help after do so, and ungrammatical if we repeat it.

Lastly, semantically, Complements usually have a close relationship with the words that license them. Words inherently describe semantic relations between different things. So the verb PUT brings to mind a putter, a thing being put, and a location. It doesn't inherently involve any idea of time. So in Put it in the fridge tonight, we would not expect tonight to be a Complement of the verb put, but we would expect both it and in the fridge to be Complements, which as we have seen above, they are. The thing being put and the destination of that thing are suggested by the very use of the verb PUT. Similarly the noun collector also inherently implies that there are things which are collected and someone who collects them. The noun resignation implies a resigner. So in a collector of antique books, we would expect of antique books to be a Complement, and we would expect of the President to be a Complement in the resignation of the President. But we would not expect in the corner to be a Complement in the collector in the corner, because the noun collector does not inherently imply a location.

Because of semantic factors above we also expect Heads to impose semantic, as well as syntactic, selectional restrictions on their Complements. We can annoy elephants but not tables, unless we ascribe some sort of animacy to our tables for some reason. We don't expect such tight restrictions with Modifiers. One can do almost anything on Wednesday and almost anything pointlessly. And whereas the number of possible Complements is specified by the Head both semantically and syntactically, the number of Modifiers is not.

1.2 Modifiers

Modifiers are never obligatory. We can characterise them as syntactically extra elements. They are usually semantically extra too, in the sense that they are not automatically implied by the words or phrases that they modify. Unlike Complements, Modifiers are usually only loosely integrated into the larger phrases they occur in. Their position is often only loosely determined:

  • I play foot ball [in the park][on Fridays][with my friends]
  • I play football [with my friends][on Fridays][in the park]
  • I play football [on Fridays][in the park][with my friends]
  • [On Fridays] I play football [with my friends] [in the park]

As shown further above unlike Complements, modifiers are not obligatorily relaced when we use proforms to refer back to a larger phrase.

We can use various forms of cycle as an analogy for phrases here: unicycles, bicycles, tricycles, tandems and so forth. If we regard the frame of the cycle as the Head of a phrase or clause, then the Complements are all the things that fit into the different slots in the frame. So the frame dictates the size and number of wheels, saddles, handlebars and so forth (some of which may be optional, for example in the case of tandems) that the frame can take. These things are all Complements. You can't put the wrong Complements on the wrong frames. For example, a unicycle frame won't usually allow handlebars in the same way that an intransitive verb won't allow a Direct Object. Also you can't fit the wrong size parts into the wrong slots. So the stem of your handlebars must fit into the frame, for example. It cannot be too big or too small. So the frame puts restrictions on what can be slotted into it. In contrast, any lights, bells, mudguards, panniers, stickers and so forth are always optional extras. They are, to extend the metaphor, Modifiers. You can't ride your unicycle without a wheel, but a light is definitely an optional extra. Notice as well, that the bicylce frame puts very few selectional restrictions on the Modifiers available. You can stick lights, bells or horns on any cycle you want to, and any number of each as well—although admittedly things might get awkward if you do decide to use very many.

  • In, "Put it on the shop floor on Thursday," it's not clear why the "when" PP has a different status from the "where" PP. As a matter of usage we usually say place before time, unless we put time before the verb ("On Thursday, put it on the floor.") But it's hard to see a syntactical difference. Both are, in logical terms, arguments of the verb "put." – remarkl Feb 24 at 18:51
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    @remarkl I don't think I agree. Let the it here be a shop dummy: I put the dummy on the shop floor is perfectly fine, but I put the dummy on Thusday is definitely wonky and doesn't make sense (unless Thursday is a place or person). So the when PP is not an argument of the verb. – Araucaria Feb 24 at 19:00
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    @remarkl Yes, repetitions etc always skew the water with elipses contrastive meanings and so forth. For a clearer understanding imagine saying it to someoneas the first utterance in a conversation. Your ate example is indeed very different from put. The verb eat does not take a locative complement whereas put and place usually do. Other tests here: You asked me to put the dummy on the shop floor on Thursday and I did it on Thursday versus You asked me to put the dummy on the shop floor and I did it on the shop floor-which is wonky. – Araucaria Feb 24 at 19:17
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    I agree, but if relocating "On the floor" doesn't make it a modifier, then how can moving "on Thursday" prove it's a modifier? What about put and place? (I also think you may be playing fast and loose with the word "it," which is awfully malleable.) But, all that said, you may well be right. I just wanted to get some more thoughts out there to help Hannah see why a simple test is not likely to appear. – remarkl Feb 24 at 19:28
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    Holy cow... this is an absolutely awesome answer!!! Thank you so, so much, Araucaria! :) And thanks @remarkl for playing devil's advocate for me :) – Hannah Feb 24 at 21:39
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When X is appended to Y to make a constituent of category Y, X is a modifier; otherwise it isn't.

Notice that it follows (in a CF language) that modifiers are always optional, and that if one modifier is permitted, then any number of them are also permitted.

(This might not always work.)

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    Hm... I'm afraid I understand absolutely nothing of this... – Hannah Feb 24 at 21:41
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    @GregLee Just devil´s advocating for a sec. How about Read slowly, where the addition of slowly seems to transform a verb into a verb phrase? (I´m assuming that Read is a verb inside a 1-word verb phrase?) – Araucaria Feb 25 at 11:47
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    @Araucaria, you seem to have solved the puzzle yourself. The adverb "slowly" is a VP modifier. As such, it can be appended to the VP "read" to form the VP "read slowly". It is an accident of the example that "read" has no object in its VP. Compare "[[read the book] slowly]", where "the book" is not a modifier, because it transforms the verb "read" into the VP "read the book". – Greg Lee Feb 25 at 15:55
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    @Araucaria, Perhaps I should also point out that the Lakoff-Ross criterion gives us an independent witness to which constituents are VPs rather than verbs. A VP following a like antecedent can be replaced by "do so", but a verb cannot. "He asked her to read the book, and she did so slowly." But not **He asked her to read the book, but she did so the magazine instead." And "He asked her to read, and she did so." – Greg Lee Feb 25 at 18:16
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    @GregLee Yes, I'm with you all the way! That was really more for OP's and other readers' benefit. (I used LR type data in my post & comments, I think). – Araucaria Feb 25 at 18:57

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