actor of the infinitive clause

Question

Identifying whether the infinitive clause is a purpose or a catenative complement helps me understand what the understood subject is. (I hope the interpretation below is correct)

He wrote the book to prove his point. (purpose adjunct)

In this sentence,the actor of the infinitive clause will be he.

He encourages the student to write a book. (catenative )

As for this sentence, the actor of the infinitive clause will be the student.

But when sentences get complicated, I can't tell what acts as the understood subject. For example:

Frictional unemployment: Temporary unemployment caused by the time required of workers to move from one job to another.

The infinitive tells the purpose(in order to move from...) , but the sentence structure is not as simple as the one above, so I am confused.

Is the understood subject workers or is it not mentioned?

He recruited new employees to solve this problem.

What is the understood subject of the infinitive clause to solve this problem?
Is it he or new employees?

Answer 1

There are different ways of looking at this. Where a to-infinitive clause is acting adverbially, then it could be argued to have an implied subject that matches the verb it modifies, if it has any implied subject at all. It can be helpful to mentally remove words to see what is modifying what.

On the other hand, you also have to think about the semantics - if there's an actual action involved, someone must be doing it. Often, there is more than one possible interpretation that might be resolved by the context - or might not be.

Most of the time, native speakers don't really think about the implied subject of a non-finite verb. The meaning is usually clear without bothering to think about it. Hopefully, that will be the case for learners as well, with enough practice.

Temporary unemployment caused by the time required of workers to move from one job to another.
... unemployment caused by the time required ... to move from one job to another.
... the time required to move from one job to another

The to-clause is acting as an adverb on required, not on a verb. It is a parameter saying what the time is required for. It has no subject. However, we can also think about who is doing the moving from one job to another. Obviously, it's the employees. So, from one angle is there is no subject; from another, it's the unspecified, general employees.

He recruited new employees to solve this problem.
He recruited ... to solve this problem.

Here, the to-clause is acting as an adverb on recruited, so grammatically it would appear to have the implied subject he. However, we want to think about who is doing the solving. Thus, it could be the new employees, or it could be the person recruiting them. Either could work; it he could have a problem with staffing levels in his restaurant, and recruiting new employees is the solution, or he could be running a software company and none of the current employees can work out how to do something - so he hired more people so the new people could solve that. You would have to work it out from context.

Answer 2

He wrote the book to prove his point. (purpose adjunct) In this sentence,the actor of the infinitive clause will be he.

Yes.

He encourages the student to write a book. (catenative )

As for this sentence, the actor of the infinitive clause will be the student.

Yes, “the student” is the syntactic object of “encourage” and the semantic (understood) subject of the subordinate clause.

But when sentences get complicated, I can't tell what acts as the understood subject. For example:

Frictional unemployment: Temporary unemployment caused by the time required of workers to move from one job to another.

The infinitive tells the purpose(in order to move from...) , but the sentence structure is not as simple as the one above, so I am confused. Is the understood subject workers or is it not mentioned?

Yes, it’s “workers”

He recruited new employees to solve this problem.

What is the understood subject of the infinitive clause to solve this problem? Is it he or new employees?

Strictly speaking it’s ambiguous. It could be a purpose adjunct in which case the subject is “he”. On the other hand, the subordinate clause could be an infinitival relative clause modifying “employees”, where it has a modal meaning comparable to that expressed by "can" or "should": He recruited new employees who could solve this problem.