Why don't we use "do" in an interrogative object clause?

A friend of mine, an English learner (reasonably advanced), asked me to proofread the sentence "Could you tell me how many people you do have?" I told her to leave out the "do", but she was curious about the reason why, and after thinking about it for a while I'm not sure. I'm guessing it probably has something to do with using a clause as an object, since "How many people do you have?" is an entirely different issue, but that doesn't really give me much to go on.

Can someone here fill in the answer?

I've looked at a few related questions (1) (2) (3), but none of them seem to address the particular case of an auxiliary verb in an interrogative object clause. In fact the answer typically given elsewhere, that a question does require an auxiliary verb, clearly doesn't apply here.

Short answer

Only the matrix clause in a sentence requires subject-auxiliary inversion to make it interrogative (and not if the wh-word is part of a Subject phrase). In other words, all other things being equal, we use subject-auxiliary inversion to mark sentences, not subordinate clauses as interrogative.

We only use the auxiliary DO, when some grammatical operation or construction requires an auxiliary and we do not already have one in the canonical version of the sentence.

Full answer:

Making questions

• Her elephant can dance.

In the sentence above the Subject is the noun phrase her elephant. The word can is an auxiliary verb taking the verb dance as a Complement. If we want to turn this sentence into a canonical interrogative sentence to make a question, then we need to do a very simple operation on it. We need to invert the Subject and the auxiliary verb:

• Can her elephant dance?

If we want to make the sentence emphatic, we stress the auxiliary verb:

• Her elephant can dance.

Let's look at a different type of sentence:

• My elephant ate five donuts.

This sentence is different because it has no auxiliary verb. It has the verb ate as the Head of the Predicate. Also it contains a Direct Object, five donuts. This Object consists of a noun phrase. It has the noun donuts as its Head and the numeral five in Determiner function. Now suppose we want to make this sentence emphatic. To do this we need to stress the auxiliary verb. This is problematic because there is no auxiliary verb. In situations like this we insert the dummy auxiliary DO to give us an auxiliary to stress:

• My elephant did eat five donuts.

Ok, so now let's assume that we want to change the sentence into a question. We want the undetermined part of the question to refer to the numeral:

• My elephant ate [how many] donuts?

To turn this into a canonical question, we need to move the interrogative word to the front of the question. Because the question word appears within a noun phrase, the whole noun phrase must move to the front of the sentence:

• *How many donuts my elephant ate? (ungrammatical)

However, this is not enough. We still need to invert the Subject and the auxiliary verb. We have the same problem we had when we wanted to make the sentence emphatic. There's no auxiliary to invert. Again we will need to insert DO:

• How many donuts did my elephant eat?

Embedded interrogatives

We can embed interrogative clauses as the complements of other verbs:

• She will ask [how many donuts my elephant ate].
• Will she ask [how many donuts my elephants ate]?

Notice that the bracketed subordinate interrogative clauses here do not exhibit subject auxiliary inversion. They are like our ungrammatical question how many donuts my elephant ate?. There is an important difference between the two sentences above. The first sentence is a declarative sentence used as a statement. The second is an interrogative sentence used as a question. Notice that we only need to use subject-auxiliary inversion in the main (technically the matrix) clause. In other words subject-auxiliary inversion is only required to turn the whole sentence into an interrogative clause. We don't need to use subject-auxiliary inversion in subordinate interrogative clauses. In the sentences above, because we do not need subject-auxiliary inversion in the subordinate clause, we do not need to insert the dummy auxiliary DO.

However, we might still want to make the subordinate clause emphatic. For example, we might want to contrast it with an incorrect idea that has been previously mentioned:

A: You incorrectly stated that my elephant ate five donuts.

B: Could you tell me how many donuts your elephant did eat?

Here we have inserted the dummy auxiliary DO to make the subordinate clause emphatic. Notice that the word do is coming after the Subject here, not before it. The do insertion is for emphasis, not because this subordinate clause is interrogative.

The Original Poster's example

1. Could you tell me how many people you have?
2. Could you tell me how many people you do have?

The first example above is the normal way to phrase this sentence. The subordinate interrogative clause "how many people you have" does not require subject-auxiliary inversion and therefore we do not need to use the auxiliary DO to make the clause interrogative.

The second example, however, is also grammatical. It makes the subordinate clause emphatic. Notice that this has nothing to do with the clause being interrogative. The do is being inserted to give us an auxiliary to stress. Notice as well that the auxiliary do comes after the Subject, not before it.

In English, you used to be able to form questions by inverting the verb and the subject. So Shakespeare could say

where go you with bats and clubs?

We no longer do this: If the main verb has an auxiliary verb (is, do, can, will, etc.) we invert the subject and the auxiliary verb. But if there's no auxiliary verb, then unless the main verb is a form of to have or to be, we now must insert some form of the auxiliary verb do before we invert.

So we now say

where do you go with bats and clubs?

On the other hand, if you formed the question without using inversion, you don't need to add do, and you should only add do for emphasis. For example if you have the question

who gave you the bats and clubs?

you don't need to insert do because there's no inversion.

In this case, you only insert do for emphasis. For example, if somebody said "the senate didn't give us the bats and clubs", you might ask:

who did give you the bats and clubs?

A possible historical reason for this:

Why do we do this? I don't know whether this is historically the correct reason, but in some cases it's necessary. We no longer decline nouns for case in English, and haven't for centuries, and without do-insertion it is impossible to distinguish the subject and the object. If we didn't add do, for example, you couldn't tell whether

How many people killed Caesar?

meant

How many people did Caesar kill?

or

How many people did it take to kill Caesar?

If we declined nouns, these would be easy to distinguish:

How many people killed he?
How many people killed him?

Unless it is emphasized or separated from the main verb, the tense of a clause is expressed as a suffix on the main verb. Your example sentence is grammatical if do is emphasized. In the analysis Chomsky gave in Syntactic Structures, this is handled by treating emphasis as a separate morpheme Emph, which works like a verbal auxiliary and to which do can be attached.