Hudson on "determiners"

In a 2004 paper, Dick Hudson casts doubt on the very idea of determiners. But like so many others, he appears to confound the idea of a category and a function.

Take, for instance, the following claims:

We all agree that the English determiners include words like the, a, this, some, any, and my, and we agree that these have two things in common which justify a cover term‘determiner’:
(2) A singular countable common noun normally needs a determiner in order to be grammatical, e.g. I heard *(the) dog.
(3) Only one determiner is possible per common noun, e.g. I heard *the my dog.
These two characteristics are what distinguish determiners from adjectives, and make the traditional classification in terms of ‘demonstrative adjectives’, ‘possessive adjectives’ and so on completely inappropriate.
The resulting word class is quite heterogeneous semantically. (pp. 8 & 9)

At times, here, he's clearly talking about a category of words:

1. proposing a list of words (by the way, we don't all agree that my is in the same class with those other words; it's a pronoun)
2. contrasting with adjectives
3. mentioning "word class"

But, he also seems to be talking about a grammatical function. A function is the relationship between two words, so when he says that a singular common noun needs x to be grammatical, x must be a function, not a category. You don't say that a verb needs a noun to be grammatical but rather that it needs a subject, direct object, indirect object, complement, or whatever.

Similarly, if you claim a limit on a common noun of one x, again x must be a function. If you say, for instance, that a head noun can't have other nouns (a category), it's entirely unclear what you mean. If you say it can't have any nouns functioning as complements, then you're probably right. If you say that it can't have any nouns functioning as modifiers, then you're almost certainly wrong. It's not the category of noun that makes the difference but its function.

If you you're confused about whether x is a category or a function, then trying to argue that x doesn't exist won't really make much sense.

References

Hudson, R. A. (2004). Are determiners heads? Functions of Language, 11(1), 7–42. doi:10.1075/fol.11.1.03hud