Is the "Actor" a Proper Element of an Infinitive Phrase?

[THIRD EDIT]:

A well-written question from two years ago hits on essentially the same point as my question, but from a different direction. Unfortunately, the one or two responses to that question and the comments, here, lead to the conclusion that the diagramming of these sorts of sentences can (A) vary dramatically depending upon seemingly minor differences, and (B) require arbitrary decisions on indeterminate matters.

Consider the following sentence:

Tell him to make a sandwich.

This article at the Purdue Writing Lab teaches that the word him should be analyzed as being an "actor" of the infinitive phrase to make a sandwich. The actor is described as being akin to the subject of an independent clause. The cited article explains that him, as the actor, is part of the infinitive phrase.

I question the validity of the actor concept. It seems to me that the pronoun, him, is the indirect object of the verb, tell. Certainly, in the following sentence, him is an indirect object.

Tell him a story.

I find it odd to think that the role of him in the sentence would morph if the direct object, a story, is replaced with the infinitive phrase, to make a sandwich. Following the logic of the cited article, him would cease to be an indirect object, and would become part of the infinitive phrase.

I have not seen the actor concept taught elsewhere. Is the actor a proper element of an infinitive phrase?

[EDIT: I ask this question from the viewpoint of a user who has learned a traditional, schoolbook grammar, not as an academic studying the subject. As @Shoe implies, perhaps the author of the article is writing from a theoretic point of view.]

[SECOND EDIT:]

I, here, add a confounding contra example. One can rewrite the second sentence to replace the indirect object with an adverbial prepositional phrase.

Tell a story to him.

However, the first sentence cannot be rewritten in that fashion.

Tell to make a sandwich to him. [nonsense]

That contrast implies, perhaps, the nature of the word him is altered by the presence of the infinitive phrase.

How would one analyze him in the first two sentences (using traditional grammar)? I believe the answer is that it is an indirect object in both cases, but I'm starting to doubt that conclusion.

The verb "to tell" takes a direct object and an indirect object. You tell somebody something / You tell something to somebody.

2 The indirect object, when preceded by "to" or "for" becomes an adverbial prepositional phrase as a complement (APP-C) and transfers to the end of the sentence. - You tell something to somebody.

3 The direct object is always a communication - often an example of speech of some sort.

4 Either or both objects may be stated or implied:

A: I heard a secret yesterday.

B(i): Do tell! - implied: it and [to] me

B(ii): Tell the secret (direct object)! - implied: me (indirect object) or to me (APP-C)

B(iii): Tell me (indirect object) the secret (direct object)! - implied: nil

B(iv): Tell the secret (direct object) to me (APP-C)! - implied: nil

B(v): Tell me (indirect object)! - implied: it.

Compare "Tell him this" to "Tell this to him." and * Tell this him

Tell.........him.............a story.

V...indirect object... direct object

Tell.........a story.....................................to him.

V.......direct object...adverbial prepositional phrase as a complement

This phenomenon is know as "the dative shift". In Old English there were grammatical cases, one of which was the dative. The dative implied "to" or "for" noun. Syntax in Old English was quite loose and word order depended more on emphasis. When the grammatical case inflections were lost following the introduction of Norman French, syntax became paramount and the implied "to and for" had to be stated if the syntax did not follow S,V,IO,DO ([S] Tell him the story) - there are exceptions to this but these need not bother us now.

Your next problem is the infinite phrase, which is a noun phrase:

"To make a sandwich is simple"

This must not be confused with

"To make a sandwich, you need bread." in which "to make a sandwich = in order to make a sandwich** which is an adverbial phrase

To make a sandwich, in the context given, is an infinite noun phrase. It approximates to a content clause

1.Tell........him ...............to make a sandwich. = Tell him {that he should make a sandwich}.

....V...indirect object... NP (noun phrase) object.=....................content clause

The problem is that an infinite noun phrase cannot act as a direct or indirect object if there is no other object.

Tell to make a sandwich - wrong

Tell......... to make a sandwich.........................to him. - wrong

..V........NP (infinite noun phrase)...............adverbial phrase

You will note that there is no direct object.

Before commenting on the 'actor' concept employed by the Purdue Writing Lab, let me first refute that the pronoun him is the indirect object of the verb tell in Tell him to make a sandwich.

Firstly, the same verb tell has a different meaning in the above sentence and in Tell him a story. In the latter, the verb means 'express something' whereas in the former it means 'order somebody to do something'. So you're comparing apples and oranges.

Secondly, an indirect object test reveals that him is not an indirect object in the former sentence. Instead of the imperatives, which is impossible to apply the indirect object test to, let's use these:

(1) He's the one who(m) I told to make a sandwich.

(2) ?He's the one who(m) I told a story.

An indirect object is resistant to fronting in relativization, so (2) understandably sounds awkward at best. But (1) sounds perfectly natural, which refutes that him in Tell him to make a sandwich is an indirect object. Therefore, him in Tell him to make a sandwich is not an indirect object but a direct object.

The 'actor' concept proposed by the Purdue Writing Lab is very problematic. The "actor" is explained in the Lab as follows:

Actors: In these last two examples the actor of the infinitive phrase could be roughly characterized as the "subject" of the action or state expressed in the infinitive. It is somewhat misleading to use the word subject, however, since an infinitive phrase is not a full clause with a subject and a finite verb. Also notice that when it is a pronoun, the actor appears in the objective case (me, not I, in the fourth example).

So the Lab uses the term "actor" to replace "subject" simply because to-infinitival clauses (e.g., to make a sandwich) are not full clauses (i.e., finite clauses).

The problem with this approach is that the Lab is conflating and even confusing a syntactic concept such as "subject" with a semantic concept such as "actor" (or more aptly "agent"). The verb tell takes only people, which can easily be actors, as direct object, but there are other verbs that can take something that cannot be actors as direct object, as in:

(3) I want there to be a sandwich.

Here, there cannot possibly be an "actor" or "agent".

More importantly, him is not even the subject of to make a sandwich in Tell him to make a sandwich. At least not syntactically. So the reasoning behind calling it an "actor" cannot hold water.