Here is an extract from another post of mine on another SE site, slightly modified:
1.0 Complements versus Modifiers
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. (However, see the linked-to paper at the end of this post, where it is argued that there is no meaningful syntactic distinction between the Modifiers and Complements of nouns.)
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.
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.
2.0 The rat at the corner of the room
Here, most would agree that the noun phrase the rat is fully formed as it is. The noun rat certainly does not suggest a location, and the locative preposition phrase at the corner of the room is not filling any special slot set up by the noun rat, and must therefore be considered a Modifier. Some might argue that, in contrast, the noun corner does set up a slot for a following preposition phrase. A corner, it might be argued, inherently implies the existence of something that it is the corner of. We might be minded in this case to do some syntactic tests to see whether of the room was a Complement here. However, recent work by linguists, such as Payne, Pullum, Scholz & Berlage 2013, §3.5, have cast doubt on whether nouns ever actually take PP complements, in part by showing that the tests commonly used for establishing the Complementhood of nouns are flawed.