1. There is no infinitive in either phrase, though it is true that "writing" is a non-finite form. As you note, it is a gerund.
2. While you are correct to say that a gerund is a noun, you're wrong to say that it isn't a verb. You can clearly see that it retains the complements of the verb. A gerund is a verb cast into the syntactic form of a noun just as a participle is a verb cast into the syntactic form of an adjective.
3. A transitive verb is one that takes a direct object. An intransitive verb is any other verb.
4. "Them" is a direct object of "write" in "writing them", but an indirect object, marked by the preposition to, in "writing to them".
5. Just to be really clear, it is only possible to supply a direct object to the gerund "writing" because it is a verb that (in British usage) takes a direct object. There is no such concept as the object of a noun.
> 2. While you are correct to say that a gerund is a noun, you're wrong to say that it isn't a verb. You can clearly see that it retains the complements of the verb. A gerund is a verb cast into the syntactic form of a noun just as a participle is a verb cast into the syntactic form of an adjective.
Conceded also. This is going terribly. Have I been hustled? Are you a ringer?
> 3. A transitive verb is one that takes a direct object. An intransitive verb is any other verb.
> 4. "Them" is a direct object of "write" in "writing them", but an indirect object, marked by the preposition to, in "writing to them".
Sure, though I didn't say otherwise. I admit I wouldn't have said #3 part B so absolutely; I wonder if there are edge cases.
> I admit I wouldn't have said #3 part B so absolutely; I wonder if there are edge cases.
Sort of. There isn't a semantic difference between direct and indirect objects (there are some tendencies). Latin verbs with a prefix very commonly take indirect objects where you would expect a direct one. It's pretty normal (for us) to just think of that situation as the verb taking its object in a weird case; I have no idea how the Romans thought about it.†
As a matter of technical terminology, those are just the definitions of transitive and intransitive verbs. How you apply the concept of "direct object" may vary from language to language. In English a direct object is one that is an otherwise unmarked object of a verb (assuming we're happy with our ability to identify those) and an indirect object is one marked by a preposition. In Latin a direct object is one that appears in the accusative case, and an indirect object is one in the dative case. In Mandarin Chinese direct objects are unmarked and most typically appear after the verb, while indirect objects are marked with a preposition and appear before the verb... but if you want to rearrange the elements of a sentence, there is a preposition of this kind that serves no other purpose than to allow a direct object to be positioned before the verb.
† This is a hazier situation than occurs with deponent verbs, where the evidence is very strong that the verbs "really are" active in Latin despite requiring grammatically passive forms.
Thanks. If you like, share how you know grammar and syntax so well (I was joking about the GPT and of course nobody is required to disclose anything). I know a good bit; I am unused to being outgunned; and I'd like to learn more.
I have some undergraduate training in linguistics, though I wouldn't attribute much grammar knowledge to that. It does come in when you see me complaining that there's no semantic distinction between direct and indirect objects.
I've always been interested in language, so I am likely to pick things up and remember them.
You get fun facts about Latin and Mandarin because those are the languages I have studied. If you want to have examples available of how different languages work and how different categories might or might not be realized in different languages, there's not really a substitute for learning different languages.†
Studying Latin in particular is likely to familiarize you with a lot of English grammatical terminology, much of which was developed for the purpose of discussing Latin grammar. Latin's grammatical structures can be very explicit compared to English or Chinese (where the grammatical structure is of course still present, but it's more difficult to point at something concrete in the sentence and say "_this_ element of the sentence reflects _this_ grammatical feature!")
† Another example of what you might consider edge cases in the space of transitive/intransitive verbs or direct/indirect objects: in Latin, dono is a "ditransitive" verb, which is to say that it may take two direct objects, defined appropriately for Latin as objects which appear in the accusative case. This is pretty unusual. The two direct objects of dono (source of the English verb donate) are a gift and a recipient.
Latin has a much more common giving-related verb, do, which means "give". It is obviously possible to supply a gift and a recipient to do, but for this verb the gift is a direct object and the recipient is an indirect object. (In fact, this verb is the source of the dative case's name!)
So far these are just fun facts about Latin. But if you draw analogies to English, you find something interesting: once we define English direct objects as unmarked and indirect objects as marked by a preposition, we find that most English verbs accepting an indirect object may be regularly transformed into ditransitive verbs. "He bought a dress for his wife" and "he bought his wife a dress" are exactly equivalent statements. Here, some additional structure is provided by the ironclad English requirement that the first object in "ditransitive form" must correspond to the indirect object in "transitive form", and it's common to just call the first of the ditransitive objects an indirect object.
This might lead us to think that "ditransitive" doesn't really make sense as a separate class of verbs in English, but that's not quite true either; there are certain verbs, like bet, which can accept multiple direct objects none of which may appear as indirect objects instead. ("Bet [you] [four dollars] they won't.")
I believe that either object of an English verb in ditransitive form may be promoted to the subject of a passive form of the verb. That would be good evidence that it is really a direct object, except that in English the prepositionally-marked indirect objects of verbs may also be promoted to the subject of a passive form of the verb ("The baby wants to be sung to").
Does the infinitive [edit: ^H^H^H^H^H^H^H^H^H] made it intransitive? Also, 'writing' is a noun (a gerund), not a verb.