The book takes the principled position that a noun phrase following a preposition is a Complement of that preposition, not an Object or other Complement of the verb. For that reason, the elephant is not an Object of any sort in the examples below:
- I looked at the elephant.
- I gave a book to the elephant.
And thus, in turn, looked in the first example above cannot be transitive as it has no Object. The verb gave in the second example cannot be ditransitive, because it doesn't have two Objects. Notice that whether a verb is transitive or intransitive depends on how it is used in a particular clause, as described by the Original Poster. (Another way of viewing this is that it is clauses and not verbs which are transitive or intransitive.)
To recap the basic descriptive principle:
- Intransitive = no object
- Transitive = (at least) one object
- Ditransitive = two objects
Many ditransitive verbs, as noted by John Lawler, are verbs of transfer (sometimes called benefactive verbs). They thus involve a thing being given and a recipient of that thing. In English, when such verbs have two objects, the recipient usually comes first and the thing being given comes second:
- Bob sent Mary a letter.
Now, in some languages, like Latin for example, nouns have different inflections (i.e. they appear with different endings) in different environments. These inflections depend on the grammatical relations that the larger noun phrase has within the sentence. One common type of inflection, which is used to mark the recipient noun phrase (amongst other things), is called the dative:
- Bob Jacobo librum dedit. ['Bob Jacob book gave']
In (6) above the noun Jacobo is in the dative case. If we wanted to translate this example into English we would have a choice. We could use either (7) or (8) below:
- Bob gave Jacob a book.
- Bob gave a book to Jacob.
Notice that in both sentences the verb give takes two Complements. However, in (7) these are both noun phrases but in (8) the first is a noun phrase and the second is a preposition phrase (henceforth NPs and PPs). Now, for those who enjoy the spurious pastime of pretending that English is a version of Latin, we can pretend that the noun Jacob has the same grammatical relations in the two sentences. However, it very clearly does not, even though the two sentences are each excellent translations of the Latin sentence in (6). And one thing is certain, the NP Jacob is not dative in either example. English common nouns do not have case. They have no inflections like the Latin -o in Jacobo, which tell us what their grammatical relation are.
At this point we need to be absolutely clear about a little problem that we introduced early on in this post. Grammatical relations (aka syntactic functions) such as Subject, Object, Indirect Object, Predicative Complement, Determiner and so forth are about how a sentence is structured, they tell us about the job that a particular word or phrase is doing in a larger phrase or sentence. They are expressly not about meaning. To help a schoolkid identify a Subject, it is a fast and dirty heuristic to tell them that the Subject is the person or thing doing the action. However, this is not an illusion we should allow to fester for more than a morning or two. Many verbs do not denote actions, and the entities denoted by Subjects are often not doing anything at all. Consider:
- Bob survived the accident.
- Bob received a blow to the chin.
And, of course, the Subjects of passive clauses characteristically do not carry out actions:
- Bob was fired.
And some NP Subjects are meaningless dummies, existing merely to fill the Subject position (an obligatory slot in tensed clauses in English):
- It was raining
- It is good to talk.
- There is a problem.
We can clearly see that any attempt to define grammatical relations primarily in terms of meaning is doomed. Let us never do this again!
This applies to all grammatical relations, not just Subjects, but Objects and Indirect Objects and so forth as well. Consider the sentences below:
- Bob eyeballed [the book].
- Bob stared [at the book].
Now semantically, the entity denoted by the noun phrase the book stands in the same relation to Bob in each of these sentences. However, in (15) the book is a Direct Object of the verb eyeball and in (16) it is not. In (16) the book is a Complement of the preposition at. The two clauses are structured very differently. The two verbs in (15)—(16) take different types of Complement, one takes a noun phrase and the second a preposition phrase. We can use the NP Complement as a Subject in a passive version of the sentence, but not the PP one:
- The book was eyeballed by Bob.
- *At the book was stared by Bob. [ungrammatical]
For these types of reason, we need to distinguish between clauses like (15), which are transitive, and those such as (16), which are not. The verb in (16) has no Direct Object.
This same kind of principle applies to verbs that take two complements. Consider these examples again (renumbered here for convenience):
- Bob gave Jacob a book.
- Bob gave a book to Jacob.
In (19) Jacob is the (Indirect) Object of the verb gave, but in (20) it is the Complement of the preposition to. The verb give in (19) has two Complements, both NPs. In (20), in contrast, the verb give has an NP Complement and a PP Complement. The NP Complement, Jacob in (19) can become the Subject of a passive version of the sentence. The same is not true of the PP complement to Jacob in (20):
- Jacob was given a book by Bob.
- *To Jacob was given a book by Bob. [ungrammatical]
For the same kind of reasons that we don't regard the book a Direct Object of the verb in Bob stared at the book, we don't regard Jacob as an Indirect Object in Bob gave a book to Jacob. And again, for the same reason that Bob eyeballed the book is a transitive clause and Bob stared at the book is not, (19) is a ditransitive clause, but (20) is not. It is neither here nor there that Jacob is the recipient of the book in both clauses. This kind of semantic consideration does not tell us how the sentence is structured. And terms like Subject and Object and so forth are all structural terms.
The Original Poster's question
To try and define Direct Objects, Indirect Objects, Subjects and so forth by their meanings is a lost cause. It will never work and will always result in confusion and serious problems. It is not our fault that this is how we were taught grammar in school. It is how our teachers had been taught themselves. It was not their fault either.
Some grammarians nowadays still like to talk about Jacob in Bob gave a book to Jacob as an Indirect Object because Jacobo would be an Indirect Object in the Latin version of the sentence. While it might be useful to understand that while Latin used the dative case to mark out the recipients of verbs of transfer and that a similar kind of job is being done by the preposition to in such English sentences, there is no getting round the fact that the structure of the English sentence is different. And since grammatical relations terms are about structure and not about meaning, this difference in structure is important. The word Jacob in Bob gave the book to Jacob does not have the same structural job as it does in either I gave Jacob the book or Jacobo does in Bob Jacobo librum dedit.
In short where a noun phrase is a Complement of a preposition, it is not a Complement of the verb! And for that reason we cannot consider Ken an Object of the verb in:
- Tim kicked the ball [to Ken].
The structure of that sentence is Subject, Predicator (read 'verb'), Direct Object, Locative Complement. Within the Locative Complement, Ken is the Complement of the preposition to. This is not a ditransitive use of the verb kick.
- Passion replaced desperation.
- The problems led to desperation.
Desperation is an Object of the verb in (23), but not in (24), where it is the Complement of a preposition. We can use desperation as the Subject of a passivised version of (23), but we cannot do this with to desperation in (24):
- Desperation was replaced by passion.
- *To desperation was led by the problems. (ungrammatical)
Sometimes we can create a prepositional passive and take the object of a preposition in an active clause and turn it into the subject of a passive clause:
- *Desperation was led to by the problems. (ungrammatical)
The fact that even this is not available shows that desperation doesn't even have a vaguely Object-like semantics in (24). The structure of (24) is Subject, Predicator, Locative Complement. The verb led is used intransitively within this clause.
Note on terminology
It is a free world. You are perfectly free to call the Complements of Prepositions the Indirect Objects of the verb higher up in the syntax tree if you so desire. Heck, you can call Subjects 'Indirect Objects' if you want. Who am I to complain?
However, if you really want to do this, you must face, square and head on, the problems that you are going to create for your readers. First of all, are you using Indirect Object as a semantic term or a syntactic one—because nobody else will be able to tell now that you've skewed the line between the two. Secondly, how can a word or phrase be a constituent of two different phrases/clauses at the same time. Is an Indirect Object a constituent of the verb phrase it occurs in? Note that it can't be if the Indirect Object of a verb is the complement inside a preposition phrase. And having an Indirect Object which isn't a constituent of the verb phrase it occurs in is very confusing and utterly weird. Nonetheless, it's a free world!