Direct object and indirect object in the sentence "Bill promised Mary to fix her car."

In the following sentence

Bill promised Mary to fix her car.

Maybe I can write this sentence like this:

Bill promised Mary (for Bill) to fix her car.

Bill is the subject of the verb fix, and also the verb promised. So, promised will have two objects: Mary and the clause (for Bill) to fix her car, one is the direct object and the other is the indirect object.

Which is the direct object and Which is the indirect object? Why? (By the way, I don't know if it is right to analyse this sentence in this way.)

Solution 1:

Promise is a very troublesome verb, syntactically speaking.

Most bitransitive communicational verbs, like tell, order, or ask, take infinitive complements with B-Equi from the Indirect Object, thus:

• Su told/ordered/asked IO [(for IO) to VP], as in
  They told him to prune the peaches.
  She ordered him to leave immediately.
  I asked her to stop by after church.

These cases are prototype examples of B-Equi, which means that the Indirect Object of the main clause is also understood to be the Subject of the infinitive clause.
They did the telling to him, while he did the pruning. Etc.

With promise, however, the pattern breaks:

• Su promised IO [(for Su) to VP], as in
  She promised me to leave right after she talked to Bill.
  I promised her to take out the garbage.

Here, She did the promising, and she was to do the leaving. In other words, it's the Subject of promise that is understood to be the subject of its infinitive, and not its Indirect Object, as in the prototype cases. This is the pattern for A-Equi, where there is no Indirect Object, as in

• She promised to be home before 11.
• She wanted to be home before 11.
• She tried to be home before 11.
• She managed to be home before 11.

In these A-Equi cases, She is the subject of both the main clause and the infinitive.

It feels like promise is less bitransitive than performative. Performative verbs require an audience, and promise, in particular, requires someone (even if only oneself) to attend to the promise. But that's taken for granted, just like the audiences for say, or swear, or claim, or any other performative verb. The identity of the audience of performative verbs normally need not be expressed in the sentence; this allows promise to be more comfortable with A-Equi and without an indirect object.

Promise also feels more comfortable with a that-complement, when an indirect object is present:

• I promised her that I would trim the magnolias after school tomorrow.
• I promised her to trim the magnolias after school tomorrow.

In a tensed clause, of course, subjects are required and aren't deleted, so no reference problem arises.

Solution 2:

A dictionary actually helps here. This is part of the OED's definition for promise:

1. trans. To make a promise of (something), to give verbal assurance of; to undertake or commit oneself to do or refrain from (a specified thing or act) or to give or bestow (a specified thing). Freq. with indirect object or with to and a noun phrase, indicating the person to whom the promise is made.

a. With infinitive, expressing the act promised.

1997 J. Hawes Rancid Aluminium (1998) xx. 242, I had promised Sarah to take 1000mg of VitC+Zinc every night if I went drinking.

b. With simple direct object, expressing the thing or act promised.

2001 Time 30 Oct. 59/1 A cruel blow to parents who had promised Junior one of the first units.

Thus the indirect object is the person to whom the promise is made [Mary], and the direct object is what is actually promised [fixing her car].

In that respect, it's very similar to a simple verb like give. The direct object is what is given; the indirect object is to whom it is given.