This is a follow-up question of an earlier question titled:

In X bar theory, is the first auxiliary the head of an interrogative clause and the remainder the complement?

In that question, I had this example:

Will she have finished it by tomorrow?

And I'd like to ask a more general question about this example:

Do all frameworks of syntax view the string following an inverted auxiliary verb in English as the complement of the auxiliary?

  • @AlexB. Do you happen to know of such a theory?
    – JK2
    Sep 4, 2021 at 16:25
  • If I understand Anderson 2006 correctly, in the Radical Construction Grammar, proposed by William Croft (e.g. Croft 2001), the lexical verb is the head, and not the auxiliary Croft 2001: 259). Let me re-read it.
    – Alex B.
    Sep 4, 2021 at 18:58

1 Answer 1


Most modern phrase structure grammars will assume that the string immediately after an inverted auxiliary is the complement of the auxiliary, as the question implies. This fact is largely due to the assumption among these grammars that all syntactic branching is binary. If indeed all branching is binary, one has no other option but to view that string as a constituent and hence as the complement of the auxiliary.

If one is willing to acknowledge ternary branching, though, then one can easily position the subject and the non-finite verb phrase as sibling dependents of the auxiliary, as shown next:

enter image description here

This analysis views the entirety as an auxiliary phrase, which means that the auxiliary verb is construed as the head. The subject he and the verb phrase leaving soon are, then, sibling dependents of the auxiliary. Such analyses were likely to occur back in the 1970s before the desire for strict binarity of branching in all cases led the mainstream syntax community astray.

In the type of grammar I prefer, which is a dependency grammar (DG), the sentence structures are flatter (in part because one assumes dependency rather than phrase structure as the underlying principle of syntactic organization). The dependency analysis of (1) that I prefer is along the following lines:

enter image description here

If one is used to phrase structure trees, which most linguists and students of linguistics are, then this dependency analysis might seem strange – in part because its so simple, just four nodes in the structure. It is, though, in a sense isomorphic with the phrase structure analysis in (1), for it can be automatically translated directly to (1) -- and similarly, the phrase structure analysis in (1) can be automatically translated to the dependency analysis in (2). The key insight in both cases is that the subject nominal and non-finite VP are sibling dependents of the auxiliary, which means they together do not form a constituent. For discussion of subject-auxiliary inversion (and inversion more generally) from a DG perspective, see pages of 216-220 in my book on DG: https://www.jbe-platform.com/content/books/9789027262288. I can connect you up with an electronic copy of the book if you contact me via email: [email protected].

There is an observation that strongly supports the flat analysis. This observation is that nothing ever intervenes between the auxiliary and the subject in such cases. For instance, it is impossible to separate the two with an adverb, e.g. * Is really he leaving soon?. The adverb can, though, appear immediately after the subject and before the non-finite verb, e.g. Is he really leaving soon?, which indicates that the subject nominal and non-finite VP do indeed NOT form a constituent, meaning that the flat analysis is well-motivated.

The example sentence in the question receives the following DG analysis:

enter image description here

Alex B commented that Croft’s Radical Construction Grammar likely does not view the string immediately after the auxiliary as the complement of the auxiliary. Alex is probably right. Be aware, though, that Croft rejects most syntactic tree analyses outright. He views constituent structure analyses as dubious from the start. His approach is hence rather nihilistic in this regard and is therefore indeed “radical”.

  • So it's clear from your two answers that, X-bar or not, modern English grammarians would always treat the first auxiliary verb in a finite clause as the head of the clause, except for some radical theories like Croft's. But traditional grammar (a.k.a. school grammar) ,based on the rudimentary analysis in the late 19th - early 20th century, originally coined the term 'auxiliary' to mean that auxiliaries are merely "helping" lexical verbs (head). If modern grammars almost universally treat auxiliaries as heads, why keep using what seems to be the wrong term "auxiliaries"?
    – JK2
    Sep 5, 2021 at 4:27
  • 1
    Yes, most modern theories of syntax view the auxiliary as the head in one way or another. But the term one chooses as the label is a secondary matter. Call it an "auxiliary" (Aux) or a "helping verb" (Hv) or a "function verb" (Fv), etc. Concerning school grammar, I would be careful in that area. There is another approach, which I have not yet mentioned, that would view the auxiliary and the content verb forming a constituent. School grammar might opt for such an approach. Sep 5, 2021 at 6:47
  • Interestingly, the matter of whether function words should be construed as heads over, or dependents under, content words is currently quite debated. Martin Haspelmath is arguing for content word as heads. Have a look and a read here: academia.edu/s/0a30d240fc?source=created_email. Sep 5, 2021 at 7:32
  • Thanks for the paper. I remember P.H. Matthews arguing that auxiliaries depend on lexical verb in Syntax (1981), and I found the argument quite convincing. So I was wondering what happened to treating auxiliaries as dependents.
    – JK2
    Sep 5, 2021 at 12:33
  • Yes, Matthews (1981) does do that. But among DG people (and PSG people), many more choose to subordinate the content verb to auxiliary verb. I myself have argued extensively for doing so. I can connect you to some literature that addresses the issue directly, if you are interested. This literature can answer your question. If you want a quick answer, peruse through the comments in Haspelmath's paper. You will find one comment where I address the matter directly, providing examples. Sep 5, 2021 at 13:36

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