Possessive-gerund/ sentence structure

Here's an alternative/clearer version of my original question:

Consider the following sentence:

Instead of his being stationed on a plank, I want him on a pedestal.

This shows the possessive gerund. However, the "I want him..." being juxtaposed with "his being..." seems awkward (as was pointed out in the ensuing comment section).

It is the stationing that I want to discuss. So, to make it less awkward, instead of using "him" for the subject, since we are using "being stationed" as a noun in the first part, can we use a pronoun for it in the second part?

In other words, can I make the sentence

Instead of his being stationed on a plank, I want [his being stationed] on a pedestal.

where the [text] is replaced by a pronoun (and appropriate grammatical changes).

Is an alternative path better (and what)?

ORIGINAL:

I was writing a question in a different Stack Exchange site and had a doubt about my sentence structure. This is what I typed:

instead of its being defined on an interval [maths], its definition is on an interval [maths]

The first part of the sentence shows the possessive-gerund. I was wondering if I could restructure this sentence as

instead of its being defined on an interval [maths], I want it on an interval [maths]/it is on an interval [maths]

where it refers to the "being-defined"-ness? The reason behind my asking this question is that the reason we use the possessive form is because we are discussing the particular characteristic ("being-defined"-ness) of the subject under scrutiny, so in the next part of the sentence, can we use it to refer to the characteristic without ambiguity? Or can it be confused for the subject? Or does using it make sense only when it is referring to the subject (which makes the most sense to me).

To be honest, using "its definition" in the sentence I originally typed also sounds a little weird to me (I was going to put in "I want it to be defined on..." instead), but I do think that it grammatically agrees with "its being defined".

Ultimately, what I am asking is if "being defined" may be used exactly as a noun might. Because the second sentence certainly makes perfect sense if I had used "definition" instead of "being defined" (with the necessary grammatical changes).

Solution 1:

A sentence can sometimes be made to stand in the position of a noun phrase (NP) by nominalizing it. There are two nominalized sentences in your example:

Instead of his being stationed on a plank, I want him on a pedestal.

"his being stationed on a plank" is a POSS-ing nominalization of "He is stationed on a plank", and the nominalization is object of the preposition "instead of". "him on a pedestal" is probably a FOR-TO nominalization of "he is on a pedestal" (a more regular form would be ?"for him to be on a pedestal"), and the nominalization is object of the verb "want".

The English nominalization system is quite disorderly. A general feature of it is that the particular form of nominalization used depends on the function of the nominalization in the larger construction. In the example, if we were to use a POSS-ing nominalization after "want", we'd get the ungrammatical *"I want his being on a pedestal". Why? It's just an idiosyncrasy of "want" that it does not allow a following POSS-ing nominalization. Compare the verb "like" which tolerates both kinds of nominalization:

I like him on a pedestal.  
I like his being on a pedestal.  

Classifying the -ing form of the verb in POSS-ing nominalizations as a gerund is not at all helpful in analyzing them, since this verb form has verbal properties and no nominal properties whatsoever within the sentence that has been nominalized.