I am just a little curious about the construction of syntactic trees when they involve infinitives in English. Basically, I want to know what role does the the "to" play? I don't think it is like a prepositional, as it normally would be. An example would be "He asked to go to the store."
This answer is based on chapter 2 (section 8: "Infinitival to) of Minimalist Syntax: Exploring the structure of English by Andrew Radford (2004), and "Auxiliaries: To's company" (2012) by Robert Levine in Journal of Linguistics.
Infinitival to is an auxiliary. It is the same category as the other auxiliaries, but it is considered "defective" in a single respect; it does not have inflected forms. It's as simple as that. All the properties you can come up with in which to seems to differ from finite auxiliaries, it shares with non-finite auxiliaries.
What are some reasons to believe to is an auxiliary? The most intuitive one is the structural parallel. Like other auxiliaries, to takes as a complement a verb phrase headed by a bare verb or non-finite auxiliary.
- John expects Mary to [like Bill]
- John expects Mary will [like Bill]
- John expects Mary will [have liked Bill]
- John expects Mary to [have liked Bill]
Perhaps the most widespread argument for the analysis of to as an auxiliary is that it is capable of elliptical stranding, a property characteristic of auxiliaries. Notice that both finite and non-finite auxiliaries have this property.
- They said that John would have gone to the store...
- and he has ___.
- and he should ___.
- and he should have ___.
- and he expects to ___.
Additionally, in Verb Phrase (VP) topicalization, auxiliaries are not fronted with the VP but left behind. This is true of both finite and non-finite auxiliaries. Sentences with fronted auxiliaries are ungrammatical, even when they are non-finite.
- They said that John would go to the store...
- and [VP go to the store] he should have ___.
- *and [VP have gone to the store] he should ___.
And to has the same distribution.
- I now have the evidence to challenge all those involved...
- and [VP challenge them] I intend to ___.
- *and [VP to challenge them] I intend ___.
To also patterns along with non-finite auxiliaries in its acceptance of stress. Non-finite auxiliaries resist contrastive stress (indicated below by an acute accent) before a gap created by VP-deletion. This property is shared by infinitival to.
- They wanted John to meet Mary...
- and he shóuld have ___.
- *and he should háve ___.
- and he wánted to ___.
- *and he wanted tó ___.
An answer above points out that to cannot precede clausal negation. It would not be unreasonable at first glance to see this as a problem for the analysis of to as an auxiliary. However, in reality, the fact that to cannot precede clausal negation follows straightforwardly from to's status as a non-finite auxiliary. Notice that the same distribution is shared by non-finite auxiliaries. In the following, the interpretation of not as clausal negation is unacceptable. Only the interpretation of not as VP negation obtains, making the relevant predicates "not joke" and "not like."
- John may be not joking.
- John may have not liked Mary.
- John expects Mary to not like Bill.
Elliptical stranding makes the restriction more evident, as in the following.
- *They said that John might not be joking, and he may be not ___.
- *They said that John wouldn't like Mary, and he may have not ___.
- *They said that John expected Ann to like Bill, but he expected Mary to not ___.
The fact that to follows negation is therefore not an argument against its status as an auxiliary; it should actually be considered evidence that it is.
Another property which comes as a consequence of to's being a non-finite auxiliary is that it cannot undergo inversion, which is what a previous answer seems to be getting at with the claim that to must follow "complementizers, foci, [and] subjects." Tensed auxiliaries undergo inversion in English, for instance in questions and stylistic inversion, but non-finite auxiliaries do not; as a non-finite auxiliary, to is completely unexceptionable in this respect.
Here is a summary of the above evidence that to is a non-finite auxiliary:
- To is distributionally and selectionally parallel to other auxiliaries
- To licenses elliptical stranding
- To is left behind in VP-topicalization
- To resists stress
- To follows clausal negation
Now, in conclusion, let's reconsider the idea that to is "defective." The allegedly "defective" property of to is that it does not have inflected forms; how defective is that property, really? Notice that modal auxiliaries in fact lack uninflected forms. Are they defective as well? We might well say that to is defective, but we can only say so in the same capacity that we're willing to say modals are defective as well for their lacking uninflected forms.
I'll quote the last couple few of "Auxiliaries: To's company" because I think it's appropriate (the paper argues in favor of an argument originally made by Geoffrey Pullum in 1982 that to is an auxiliary).
"Certainly there is room for argument – very few questions in the descriptive analysis of even as well-studied a language as English can be said to have been answered definitively – but I believe the preceding discussion vindicates Pullum’s (1982) original conclusions."
In Old English, the "to" of "He asked to go to the store" would, indeed, have been a preposition governing a noun (in this case a 'noun of action' in the dative case). Since then, however, the "to" of infinitives has lost its capacity to assign dative case to its complement, its complement no longer behaves as a noun, and "to" has been 'reanalysed' as a 'function word' that governs/selects a VP complement with zero inflection (a 'bare VP').
Its precise syntactic category, however, has proven more difficult to establish. Since "to" can precede auxiliary "have" and "be", it has been considered similar to modal verbs, which also select bare VPs and precede such auxiliaries, and since it licenses VP ellipsis just as modal verbs do (cf. "They asked me to give a talk, but this time I prefer not to [give a talk]"), it has actually been occasionally argued to be a 'modal verb', but, of course, its being uninflectable makes that 'verbal' hypothesis improbable, and the fact that when the infinitival clause is negative negation must precede "to" definitely discards that analysis as untenable.
Pace Lawlor above, however, "to" cannot be a 'complementizer' ('Comp', 'C'), either, since a) it must follow the complementizer "for" and the accusative-Case subject that must nowadays accompany it (cf. "It was a mistake for him to tell his wife he had lost his job"), and b) it must also follow interrogative "wh"-phrases in focus that must, in their turn, follow complementizers (cf. "I don't know what to do" vs. "*I don't know to what do").
Thus, Modern English "to" is surely some kind of function word (a 'functional category', in Chomskian jargon) that a) precedes aspectual auxiliaries (which, as stated, makes it similar to modal auxiliaries), but b) cannot be inflected and must follow complementizers, foci, subjects, and negation (which precludes its being treated as a modal verb, or, in general, as an auxiliary, after all). What kind of 'function word' is it, then?
Since it seems to be in paradigmatic opposition to Tense/Finiteness (called 'Infl' in Chomsky's GB and P&P theories of the early 1980's), Chomskian syntacticians have long classified it as an 'Infl [-Tense]'. However, it cannot literally occupy the same slot [+Tense] does above all auxiliaries because tensed auxiliaries must precede clausal negation (negative 'Polarity') (cf. "He should not have accepted" vs."*He not should have accepted"), whereas, as stated, "to" must follow clausal negation. [N.B.: when it seems not to, as in "To not go to your mother's wedding would be unacceptable" (usually: "Not to go to your mother's wedding..."), it is because "not" is not really clausal negation, but VP-internal negation, as it clearly is in "You cannot [not go to your mother's wedding]"; note that in that context "can" rejects a clausal complement, cf. "*You cannot not to go to your mother's wedding"; correspondingly, a bare (non-clausal) negative VP is not allowed in subject position, where only infinitival clauses are possible, cf. "*Not go to your mother's wedding would be unacceptable"].
In sum, a) "to" is a 'functional category', b) selects bare infinitives, c) is non-finite, so [-Tense], but d) does not alternate with [+Tense] in the highest T/Infl position. In early Chomskian GB/P&P analyses, that was a problem; in later 'minimalist' ones, however, any clause containing n verbs (i.e., a 'main' verb plus n-1 auxiliaries) also necessarily contains n 'Infl' heads, and, under such assumptions, there is no problem in categorizing "to" as an 'Infl[-Tense]' provided it is clear that it must be lower in the tree than the Infl[+Tense] that contains the tense and agreement features that characterize finite clauses.
Whether you choose to label it 'I/Infl[-Tense]', or 'Inf'(initival), or anything similar does not really matter, but you should certainly not label it either 'Aux [Verb]' or 'Complementizer'.