grammaticality - One noun but two determiners?

In this earlier thread titled 'Can I precede a noun with more than one determiner?', the most-voted answer by Barrie England says:

Yes, more than one determiner can precede a noun, but they do so in a particular order. All, both and half come before articles, so your example would have to read I saw two cats this morning. Both the cats were very young (but in this case the can be omitted).

At first blush, this answer may seem to have already addressed my question, but that is not so, because it failed to distinguish the difference between a determiner (function) and a determinative (category), in part because it wasn't clear whether the question itself was about the former or the latter.

For this distinction, please see this earlier question 'Determiner vs. Determinative' and its answer.

According to this distinction, I think that, when coming before articles, all, both and half are not determiners but predeterminers, and that both in both cats were very young is a determiner.

Against this backdrop, I'd like to ask basically the same question with this determiner/determinative distinction in mind. And I'm not asking about 'determinative' (lexical category), I'm asking about 'determiner' (grammatical function).

With regard to the 'both the' example of the earlier question, I will say that you have only one determiner (function) and that is 'the', with 'both' being a predeterminer.

Does this mean that there can be only one determiner (function) that precedes a noun, in general?

How about this example?

another three days

Are both 'another' and 'three' determiners (function)? Or is only one of them a determiner (function)? If so, which one is the determiner?

Answer

^{[Note: Here, as elsewhere on EL&U, I try to use capitalised words for grammatical relations/syntactic functions and small case only for terms indicating word categories and phrasal categories.]}

---

Preamble

Traditional grammars, as well as modern grammars such as Oxford Modern English Grammar (Aarts 2011) or The Cambridge Grammar of the English Language (Huddleston & Pullum 2002), recognise that English noun phrases usually have two main parts. So with regard to the phrase those pink elephants, the phrase comes in two chunks. The first is the word those and the second is the string pink elephants. This second chunk is of course itself a phrase, not a single word. In order to distinguish phrases like pink elephant from the larger noun phrases they occur in, they are referred to here as nominals.

---

The Original Poster's Question

According to frameworks like the one used in The Cambridge Grammar of the English Language (Huddleston and Pullum, 2002), there is only one Determiner per noun phrase. Within CamGEL, the term Determiner is short for the more explicit label Central Determiner. This is necessary because such grammars also recognise a separate function Predeterminer. So in the phrase:

• All the elephants

the word all is in Predeterminer function and the word the is in Determiner function. Notice that in terms of word category, both the and all are determinatives. The word all, like all other determinatives can also occur in Determiner function, as in the phrase:

• All elephants

The fact that we can only have one Central Determiner per noun phrase is born out by the ungrammaticality of phrases such as :

• *the my friend


• *some the people


• *any his words


• *no those friends

Cardinal numbers, which CamGEL regard as determinatives, can occur within this framework both as Determiners, or as Modifiers within nominals:

1. Three elephants


2. The three elephants

In example (2), the word three is occurring in Determiner function and the nominal, the Head of the noun phrase, is the item elephants. In example (3), however, the Determiner is the word the and the nominal is the phrase three elephants. Within this nominal the word three is a Modifier and the word elephants is the Head.

In the original Poster's example:

3. Another three days

The determinative three is occurring as a Modifier within the nominal three days. The determinative another is occurring in Determiner function within the larger noun phrase another three days—according to the CamGEL analysis.