Indirect complement or postmodifier in NP

In the sentence

[1] He is the most talented artist (that) I know

what is (that) I know in terms of function – an indirect complement, licensed by most, or simply a common postmodifier? Why?

Similarly, what is in the world in

[2] the most talented artist in the world

and why?

Addition to the original post: Having read the answer and the comments that I've received for this question, along with answers to other questions about licensing and the modifier/complement distinction, I have to give this another go:

According to the comments below, we are dealing with modifiers rather than (indirect) complements in both the above examples. Now, I'm not doubting the validity of these comments – I just still don't understand. This is why:

As far as I've been able to understand, licensing is all about setting up "slots" for specific kinds of structure. For instance, a verb such as give sets up a slot for something being given, and a slot for a recipient; consequently it licenses two object complements (direct and indirect object). Part of the deal is also that the slots set up are specific to a subset of "licensers"; in this case: not all verbs license two objects.

Now, to me it seems that this 'setting up slots that are specific to a certain subgroup' is exactly what superlatives do, something that, I think, is supported by John Lawler's answer below:

Most is a superlative marker and takes a superlative construction. One of the things required for the construction is a range for comparison

Looking again at [1] and [2], it seems to me that both the relative clause in [1] and the PP in [2] elaborate on the "range-for-comparison-slot" set up by most; hence, they should both be licensed by most, no?

Now, if these dependents are indeed licensed, they should be complements – shouldn't they? Only, since they aren't licensed by the head noun, but rather by another constituent within the NP, they'd be indirect complements.

This is my take on all this – could someone please explain to me where I go wrong, and how I should think instead?

Thank you

Solution 1:

Both of these are simply the Superlative construction.

Most is a superlative marker and takes a superlative construction. One of the things required for the construction is a range for comparison, which can be expressed as a relative clause modifying the superlative NP:

• He is the tallest boy who is in the class.

Of course, such relative clauses are often trimmed down to prepositional phrases by Whiz Deletion:

• He is the tallest boy in the class.

In your terms, yes, it's a post-modifier and it's licensed by most (or by -est).
If you called it an indirect complement I'd be puzzled, but that's nothing new.
I don't know what you'd call a reduced relative clause.
It may be a heretical notion, though it's not a new one.

Solution 2:

I think I may have figured out the answer to my own question!

[1] He is the most talented artist (that) I know

[2] He is the most talented artist in the world

I think the reason that the relative clause and the PP here seem like complements is that although they are modifiers, they are modifiers not of the head noun artist, but rather of the head of the NP complementing an ellipted PP – where the ellipted PP in turn functions as a complement licensed by most:

[1a] He is the most talented artist of all the artists that I know

[2a] He is the most talented artist of all the artists in the world

What do you think?