verb agreement - A Question About Quantifier Shift for "each of you" to "you each"

I understand from reading similar posts on this topic that if I want to write a sentence using "each of you," I should follow this with a singular verb. So, for example, "Each of you has given your all this year" is correct, and "Each of you have given your all this year" is incorrect.

If I'm right on this point, could someone explain how the quantifier shift would work if I wanted to rewrite the sentence beginning "You each"?

To my ear, "You each have given your all this year" sounds correct, and "You each has given your all this year" sounds horrible and wrong.

But is it wrong? If so, why is it wrong?

Answer

The fact that you can't always tell whether the subject of a sentence is singular or plural isn't your fault. It's English itself that doesn't make this clear. In a noun phrase of the form "each of [NP Noun ... ]", you could count either the "each" as the head of the entire noun phrase, or you could consider "each" to be a quantifier/determiner/article element and take the noun after the "of" to be the head.

If "each" is quantifier, then the grammatical number of the following head noun, which will be plural when there is an "of", will determine the number of the entire subject, and we'll get "Each of you have left". But if "each" is taken to be the head noun or pronoun of the subject noun phrase, since it appears to be singular, the entire subject will be considered singular. Then we'll get "Each of you has left".

The fact that "each" is subject to a transformation called Quantifier Float, which gives "You have each left", is sometimes taken as evidence that it should be "Each of you have left", the reasoning being that if "each" is a quantifier, it can't also be a noun or pronoun, so the plural "you" must be the real head noun. But that's not very good reasoning. Just because when "each" was converted into an adverb, the "you" graduated to become subject, that doesn't mean "you" was subject before the "each" was moved. It doesn't follow.

So there is no real answer to the question of how the verb should agree except to appeal to people's opinions. Take a vote, consult an authority, toss a coin. Whatever.

Above, I said 'the "you" graduated to become subject' in "You have each left". So it must be the head, because it's the only noun there in the subject. In "You each have left", I think we can also conclude that "you" is head of the subject, either because the "each" is an adverb and not within the subject, or if it is, it would have to be an adjective modifying "you" (English does not permit NP containing just two Ns). So, assuming that the verb will agree in number with the head of its subject noun phrase, we would expect the verb to agree with logically plural "you" when "each" has been floated.