Is there a syntactic term for finite verb + infinitive constructions such as “wants to paint”?

Question

In the sentence "Pete wants to paint," "wants" is of course the finite verb, and "to paint" is of course the infinitive. But is there are syntactic term for a construction such as "wants to paint"?

Here's a bonus question: In English, constructions such as the one just described can consist of three or more verbs, e.g. "wants to begin to change," and "needs to want to begin to change." These constructions each consist of one finite verb plus X number of infinitives.

Are there any languages in which equivalents to such constructions would consist of X number of finite verbs followed by one infinitive, as in this nonce English example: "needs wants begins to change"?

Answer 1

If we see those constructions just as finite + infinitive, I wouldn't know other term different from complex verb phrase. However, your example includes the verb want, which has some particular features. In the sentence Pete wants to paint, the matrix verb want is followed by the nonfinite clause to paint. In English, these clauses do not have an overt subject, so they are said to have a nonfinite null subject called PRO. Thus, the sentence structure is something like Pete wants [PRO to paint]. We think that this null subject PRO is controlled by the subject of the sentence, in this case Pete. You can see the subject as an antecedent of the null pronoun PRO. The sentence would mean something like Peter wantshimselfto paint. Verbs such as want or like, which admit this kind of infinitive complements, are called control verbs, and the clause with a null PRO subject is a control clause. The complete phrase would be then known as control predicate or control structure. This explains what happens in English, but languages vary in terms of the kind of clauses that allow null subjects.