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He arrived at 10 p.m.

At in this sentence is clearly a preposition because it can be replaced with another preposition.

He laughed at me.

How can we prove that at in the above sentence is a preposition?

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Laugh at is a phrasal verb. Some linguists call at a "particle" rather than a "preposition". It doesn't matter what it's called. How it functions and what it means is what's important. – user21497 Jan 5 '13 at 13:13
This rule doesn't always work. You can "think through a plan" and *"think about a plan", but here "think through" is a phrasal verb, so "through" is a particle and not a preposition. You can tell in this case because you can also "think a plan through". (You can also "think up a plan" and "think over a plan"; neither of these are prepositions, either.) – Peter Shor Jan 5 '13 at 14:18
@BillFranke I think in this case the linguists would call the at in laugh at a preposition rather than a particle because it must appear before the object: laugh at him rather than *laugh him at. – StoneyB Jan 5 '13 at 14:18
Different linguists would call it different things for different purposes, often several different things in the same discourse. As Bill and Peter point out, it's the construction that matters; [names are just convenient labels](); terminology is sposta be a help, not a yoke. – John Lawler Jan 5 '13 at 14:32
Oh, and you can't ever prove anything in syntax. Or in any science; only in mathematics, which has no data. The best you can do in science is to argue convincingly for one position or another. By presenting evidence. Lots of evidence. – John Lawler Jan 5 '13 at 14:33

Laugh at, as Bill Franke tells us, is a “phrasal verb” — that is, a construction of the form V + P (Verb + Preposition) which must be treated as a single term with a meaning distinct from the use of the two components in merely accidental juxtaposition.

For example:

In I laughed at sunrise, laugh is the ordinary intransitive verb meaning “to express mirth”, and at sunrise is an ordinary prepositional phrase telling when I laughed.
In I laughed at the sunrise, laugh at is a transitive phrasal verb meaning “to mock”, and the sunrise is its object.

There are two sorts of phrasal verb. In the first sort, the P-component must appear before the object of the verb, so it looks exactly a preposition heading a prepositional phrase. Laugh at is phrasal verb of this type; we say

John laughed at Bill’s stupid mistake. ... but we do not say
*John laughed Bill’s stupid mistake at.

Linguists tend (but usage varies) to call the P-component here a preposition.

In the second sort of phrasal verb the P-component may appear (but is not required to) after the object. For example, we may say either

John ran over the pedestrian. ... OR
John ran the pedestrian over.

In this case, linguists tend to call the P-component a particle.

Where the particle is placed in these phrasal verbs tends to depend on the “weight” of the object: the longer the NP which acts as the object of the verb, the more likely it is that the particle will be placed before it:

John ran over the pedestrian in his path is more likely than
?John ran the pedestrian in his path over.

Accordingly, the best “test” for whether the P-component in a phrasal verb is a particle or a preposition is to offer a Native Informant a sentence with the “lightest” possible object — a simple pronoun — preceding the P-component and ask whether that sentence is idiomatic:

?I laughed him at.

However, there’s still one tricky bit here: some phrasal verbs have two meanings, distinguished by particular or prepositional use. For instance, run over may mean either “knock down and tread upon in running” or “examine from beginning to end”:

John ran over the pedestrian in his path ... or
John ran over the list of alternatives line by line.

So when you perform your test you must make sure you provide a context:

John failed to see the pedestrian in his path and ran him over. ... acceptable
*John took up the list of candidates and ran it over line by line. ... not acceptable

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A preposition doesn't have to be replaceable by other prepositions to qualify as a preposition itself. At is only a preposition, and in many cases it is the only preposition that can be used in particular constructions to express a specific meaning.

Still, in your sentence, at is not the only possibility.

He laughed with me.

He laughed for me.

He laughed near me.

He laughed by me.

And so on would all work, though they would mean different things.

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QED? That proves that? – Kris Jan 9 '13 at 5:11

Laugh at is a prepositional verb, and at is a preposition. Unlike transitive phrasal verbs, prepositional verbs do not allow particle movement (the particle in a prepositional verb being a preposition). The preposition ‘always comes before the noun phrase that is the object (‘Longman Student Grammar of Spoken and Written English’). We can’t say *He laughed me at.

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+1 If only this answer appeared sooner, much hair-splitting could have been avoided on this page. – Kris Jan 9 '13 at 5:16
"the particle in a prepositional verb being a preposition" nails it. – Kris Jan 9 '13 at 5:17

I don't think I can endorse the answers analyzing "laugh at" as a phrasal verb, but they have raised some interesting points.

You have identified one diagnostic for telling whether something is a preposition:

A preposition may be replaced by another preposition without altering the grammaticality of a sentence.

The reason this test fails to show that at is a preposition is that the prepositional phrase (i.e., a preposition followed by a noun phrase which acts as a unit) in the test sentence has a special function, meaning roughly "project something in X's general direction, not very accurately." The prepositional phrase is called a conative argument in traditional usage. Some examples of sentences with conative arguments:

  • Thomas shot at Carmen.
  • Thomas threw stones at Carmen.
  • Thomas spat at Carmen.
  • Thomas hurled insults at Carmen.
  • Thomas fired at Carmen.

The test mentioned at the start of this answer fails because conative arguments are only formed with at. You are not likely to get a grammatical sentence if you interchange conative at with another preposition.

There are various other properties of prepositions that can be used in addition to the replacement test, however. One that will be useful here is the pied-piping alternation, roughly as follows:

In a relative clause or a content question, a prepositional phrase can be fronted in toto, with both the preposition and noun phrase moving to the front of the clause (pied-piping), or only the noun phrase can be fronted, with the preposition itself remaining in its original position (stranding).

Here are some examples of this kind of alternation (prepositions in square brackets, object noun phrases in round brackes).

Thomas laughed [at] (the man). (original sentence)
The man [at] (whom) Thomas laughed... (pied-piping)
The man (who) Thomas laughed [at]... (stranding)
[At] (whom) did Thomas laugh? (pied-piping)
(Who) did Thomas laugh [at]? (stranding)

This type of alternation, involving prepositional phrases, does not affect the meaning of the sentences. Similar alternations are not available for other word classes, so at is a preposition.

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You don't have to endorse answers that analyze "laugh at" as a phrasal verb. If you don't like that classification, you can take it up with Collins COBUILD. Argue with the lexicographers who wrote their dictionary of phrasal verbs. Don't insist that you're any more of an expert on this topic than they are. You're still an amateur & will be for a few more years. What's the point? Do you think that a label explains anything? If so, you haven't been paying attention to the real world. – user21497 Jan 5 '13 at 16:21
I'd like to offer my hearty applause to @BillFranke for his spirited and thoughtful defense of the phrasal verb analysis. as ever, the community can only rejoice when a diversity of viewpoints on important issues in English grammar abound. – jlovegren Jan 5 '13 at 16:37
The trouble with constituency tests: (1) A word of caution is warranted when employing these tests, since they often deliver contradictory results. (Wikipedia). (2) Reasonably accomplished linguists often cite a particular test which supports their pet analysis. Here, the degrees of 'binding' between the verb-and-prepositiony-thingy and between the -thingy-and-completer are important. In he arrived at 10pm, at 10pm is surely the more strongly-bound. In he took off Tommy Cooper, took and off are more strongly-bound. In he laughed at me / adversity, we have intermediate cases. – Edwin Ashworth Jan 5 '13 at 17:34
Conative is a new term to me, so I may be misunderstanding it; but it appears to me that it is used not of directed action tout simple but of attempted directed action distinguished from accomplished directed action, eg He kicked at the ball distinguished from He kicked the ball. This is not the case with laughed at. ... But your answer raises fascinating issues which I don't think can be addressed in Comments, and which are not really relevant to OP's question; I intend to raise a separate Question when I can get my thoughts together. – StoneyB Jan 5 '13 at 18:44
@EdwinAshworth +1 for what turns out to be skepticism about labels and functions. Whatever it is, it's still 'at'. – Mitch Jan 5 '13 at 21:00

Prove it by consulting a dictionary:

at1 preposition:
5. expressing the object of a look, thought, action, or plan

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Yes, a dictionary can provide what I would call evidence rather than proof that at is a preposition. Were it only a preposition, however, the string *"I don't like to be looked" would be meaningful rather than incomplete. To be complete, the string must be "I don't like to be looked at", which means that it's part of the verb and, contrary to its name, not a pre-position but a post-position or, as some linguists maintain, a "particle" attached to a phrasal verb rather than a preposition that expresses the object of a look. Again, terminology fails to explain anything. – user21497 Jan 5 '13 at 14:22
@Bill: You can say "windows are for looking out of, and not climbing out of". Does that mean that in "climb out of" and "look out of" are phrasal verb? – Peter Shor Jan 5 '13 at 19:22
@P: That's a good question. But it's one that has great value only to a few categories of people: professional linguists, lexicographers, taxonomists, & dogmatists. Does knowing whether they are phrasal verbs it help anyone understand how to use the language? If yes, it's worth knowing the answer to. If no, then it isn't. But, as I've said in another comment on this page, you can take issue with the lexicographers at Collins COBUILD: They & not I put it in their dictionary of phrasal verbs. Does it matter whether guns kill, bullets kill, or people who use guns & bullets kill? Not to the dead. – user21497 Jan 5 '13 at 23:56
One authority does not make a tablet-of-stone ruling (except in the original case). – Edwin Ashworth Jan 6 '13 at 9:14

After reading a lot of the above answers and comments, I feel that people are coming at this problem from different and entrenched viewpoints.

First, let me say that I feel it is counter-productive to view multi-word verbs (eg take in = deceive, turn down = reject, show up = embarrass or appear on the scene) as anything other than the equivalents of single-word verbs – even if they are separable (eg She looked up a friend. / She looked a friend up.)

Second, however, though there are obvious MWVs (eg the plane took off) and obvious V + PP constructions (eg he ran to the man), there are many isomorphic constructions in English that are difficult to determine as being in one camp or the other. To quote Phil Hunt (who uses the term 'phrasal verb' in the way ESL teachers do but which term I avoid) (and also plumps for 'preposition' in his example) in this article at Wordwizard:

This [distinction] becomes even further blurred when using verb combinations such as 'look for'. Is it a phrasal verb or a verb+preposition[?] The basic element of the verb, that of sight, has not changed, but the meaning of 'search' has been added by the addition of the preposition [-or-is-it]. One of the problems that I see many teachers struggling with is how to classify these 'phrasal' verbs which seem to have a foot in both camps. Perhaps this is one reason H&P have decided to update the definitions. ...

I'd say that laugh at someone is another hard-to-classify case – the basic meaning of the verb laugh is retained, but an element of ridicule / put down is (or may be) added. Which would make it not the same usage as in laughed for sheer joy at the glorious sight of the canyon walls lit by the setting sun.

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