First of all, the sentence
is an example of a Construction. That is, there is a special model for this clause, with its own unique sets of meanings, uses, restrictions and affordances. So one shouldn't expect it to be a normal short sentence.
And it isn't. In a sentence with only 5 words, there are 2 verbs and two noun phrases, so the question of the function of my hair is a normal one.
There are two "have +
Noun Phrase +
Past Participle" constructions in English.
One is adversative, the other, like the example sentence, is causative.
- I had my tires slashed.
- I had my tires fixed.
(1) is a non-volitional adversative; it means that something bad happened to me: someone indefinite slashed my tires. I did not arrange for that, or cause it.
(2) is a volitional causative; it means that something has happened because I arranged for it to happen. Presumably this was something beneficial, because I arranged for it; but that's just an inference in (2), not a given like the bad outcome of (1).
There are other causative constructions with have, using different verb forms besides
- I had them fix the clutch while the engine was out. (fix is an
- I had them rolling in the aisles. (rolling is a
In all of these constructions, the noun phrase in the middle is the subject of the following verb, whatever it is, and whatever form it's in. If that verb is a past participle, it's passive; so my hair is the subject of (be) cut, which is the right meaning.
In the other examples, my tires is the subject of both passives (be) slashed and (be) fixed, and them is the subject of fix the clutch and (be) rolling in the aisles, all of which are the right meanings too.
So if it's the subject of the second verb, why is it where the object ought to be? The answer is Subject Raising, a syntactic rule that applies to subjects of infinitive complements of certain verbs. Raised subjects may become direct objects of the clauses they follow, under certain conditions, even though they didn't start out that way.
For instance, in
- She expects Bill to select the committee.
Bill is the subject of the infinitive to select. If we passivize the infinitive clause, producing
- She expects the committee to be selected by Bill.
the committee is now the subject. Either one may be considered the direct object of expects, as shown by the fact that they can undergo Passive, too:
- He is expected (by her) to select the committee.
- The committee is expected (by her) to be selected by Bill.
These examples are not special constructions, though; they're more or less normal. In a construction the ordinary contexts and rules don't always apply, and when they do, they often have odd restrictions; these are syntactic idioms, like let alone, and idioms are odd.
So, essentially you can consider my hair a derived direct object, just like you can consider my hair a derived subject of passive was cut, even though it is the object of active cut.