In this context I think it's impossible to say that number is the head of the Subject noun phrase a number of boys.
I don't have CGEL, but in Huddleston's precis (A Short Overview of English Syntax) he
- distinguishes a determinative (a class of word or phrase) from a
Determiner (a syntactic function) (3), and
- defines the Head of a noun phrase as a noun (7.1.b)
It would be consistent with these to say that number is the Head of the noun phrase a number of which acts as the Determiner of the Subject noun phrase a number of boys, thus:
[SUBJECT NOUN PHRASE [DETERMINER NOUN PHRASE Determiner a Head number ?? of] HEAD boys]
REVISED September 2015:
But it may be just a slip, or an improper revision of a passage which was originally something beginning "The number of boys", or any number of things.
I now have CGEL and find that it treats constructions of this sort at section 3.3 (pp. 349-50) under the heading Non-count quantificational nouns. In these expressions, where the "quantificational noun" (number in your example) is complemented by a preposition phrase of + "what we shall call the oblique" (boys in your example)
... the number of the whole NP depends on the oblique; we will say that [number] is number-transparent in that it allows the number of the oblique to percolate up to determine the number of the whole NP. [...] [I]t has been bleached of its original meaning and is a non-count noun [...] The of complement can be omitted in ellipsis, but it remains understood and continues to determine the number of the NP [...]
On pp. 351-2, under the heading "Syntactic structure of NPs like a number of protesters", CGEL contrasts the analysis I have given above with one which understands the quantificational noun as head of the NP:
[NP [Det a] [Head:Nom [Head:N number] [Comp:PP [Head:Prep of] [Comp:NP boys]]]]
CGEL gives fairly compelling syntactic reasons for preferring this analysis to mine.
I think there is something more to be said, but frankly I don't know what that something is. For the time being I think we have to take number as a head to which the construction imputes plurality.
2http://www.lel.ed.ac.uk/~gpullum/grammar/detv_sli.pdf – snailplane – 2013-07-17T09:28:09.507
1Can someone explain why they think this is a "What's your favorite _____?" question? There are four POB close votes, but as far as I can tell, this question asks about a fact ("Why does CGEL call number the head of a number of boys?"). If someone gives their opinion, they've probably given the wrong answer. – snailplane – 2013-07-17T16:18:17.490
2OP doesn't ask which we analysis consider correct, Downing or CGEL (which would indeed be a matter of opinion); she asks for the reasoning behind CGEL's analysis. Reopen. – StoneyB on hiatus – 2013-07-24T22:40:54.030
I'm probably misunderstanding, but "what is the possible reason" (or, more simply, "why is it") certainly sounds opinion-based, hence my vote. Without the input of the CGEL's writers, it can't really be answered. (Apologies if I've been so blind as to overlook their presense on ELL.) There's some old discussion on MSO about the subject. I'm happy to be wrong or to have misunderstood; more good questions are a good thing for the site.
– Jonathan Garber – 2013-07-26T21:02:12.123