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The word “any” is a determiner that’s used to refer to one or some of a thing or number of things, no matter how much or how many. It therefore normally denotes a single entity, not membership or belongingness to a group; as such, it’s of the type of determiner known as a quantifier, not of the type known as a distributive.
Whether used in a negative or positive sense in a sentence, “any” can’t be considered a distributive when the existence of a group to which it belongs—the noun it modifies—is not established. In the negative statement “She doesn’t have any admirer in class,” in particular, it’s clear that there is no group of admirers to belong to or to be a member of; there is therefore no way that “any” can function as a distributive in that situation. Similarly, in the positive statement “Any policeman can direct you,” the existence of a group of policemen is not established and can’t just be presumed from a semantic standpoint; indeed, what we have here is a simple declarative statement that a policeman—simply by virtue of being such and not because he or she is part of a group of policemen—can do the job of giving directions to one who asks.
However, the situation will be different if the negative sentence we took up above were, say, in this form: “She can’t identify any of my six admirers in class.” Here, the premodifying phrase “any of my six” clearly establishes a group of admirers in the class; in this case, the whole premodifying phrase “any of my six” functions as a distributive, but that grammatical function is obviously not performed by “any” as a stand-alone determiner but by the whole modifying phrase instead.
The situation will likewise be different if the positive statement we took up above were, say, in this form: “Any of the ten policemen under my command can direct you.” Here, the premodifying phrase “any of the ten” and the postmodifying phrase “under my command” clearly establishes a specific group of policemen. Together, the premodifying phrase and postmodifying phrase obviously function as a distributive; that function is definitely not performed by “any” as a stand-alone determiner but by the entire set of modifying phrases.
One conclusion we can make from this analysis is that when used in combination, determiners and predeterminers can transcend their stand-alone functions and collectively perform different modifying functions from those they normally do by themselves. Indeed, this is why it’s sometimes difficult and baffling to classify particular determiners and predeterminers by function when they are working as composite modifiers in a sentence.