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I gave Alice the book. -Alice is the indirect object

I gave the book to Alice. -Is Alice still a indirect object? if not why?

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hi123I gave Alice the book.
Alice is the indirect object.

Right.

hi123I gave the book to Alice.
Is Alice still the indirect object? if not, why?

No, not at all. It functions as complement of the preposition 'to'.

The PP 'to Alice' functions as complement of the verb 'gave'.

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''The PP 'to Alice' functions as complement of the verb 'gave''.when people use this term: complement I don't understand, since to me a complement is D.O or I.O , one user said it's a complement clause which I dont't understand a thing,can you explain it to me?

In simple terms, a complement is a necessary constituent of a sentence. It may be a word, phrase, or a clause.

e.g., He is a teacher.

If we remove the underlined NP (noun phrase), the sentence will become *incomplete—

*He is

So, in this example, the PC (predicative complement) 'a teacher' is a noun phrase (as its part of speech) and functions as complement of the verb 'is'.

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e.g., He is handsome.

In this one, the PC 'handsome' is 'an adjective' and functions as complement of the linking verb 'is'.

Note that linking verbs don't license objects, but complements.

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I bought a book.

Here, the underlined noun phrase is an object (a kind of complement); again the sentence would become *incomplete without it—

*I bought

An important key to realize weather what comes after a predicator (main verb of a clause) is an object or not is that objects always take the form of a noun phrase.

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I bought him a book. (Indirect object, Direct object)

As you see, both 'him' and 'a book' are noun phrases, and 'buy' is not a linking verb because it doesn't license *adjective phrases—

*I bought beautiful.

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I bought a book for him.

Here we have a noun phrases and a preposition phrase.

With the caveat given earlier, objects are always noun phrase.

In the PP 'for him', the noun phrase 'him' is the object of the preposition 'for', and the PP itself is complement of the predicator 'bought'.

The NP 'a book' is the object of the predicator 'bought'. In this case, we don't use the term 'direct object' because there is no indirect object.

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I told him to buy a book.

In this case, 'to buy a book' is an infinitival clause that functions as complement of the predicator 'told'.

The NP 'him' is an object.

In the clause 'to buy a book', the NP 'a book' is object of the predicator 'buy'.

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I hope the given explanation helps you gain a better insight into the matter. I think your problem is mostly with determining different phrases and their parts of speech. Half of the the battle is won if you try to recognize phrases and their heads correctly.

Thanks a lot!

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